Math

Problem 2601

experstimn. 48116\frac{4}{8} \frac{1}{16}
2. 8x+438 x+\frac{4}{3}
8. 34+14\frac{3}{4}+\frac{1}{4} 5828258^{2} \frac{8}{2} (a) 23+164\frac{2}{3}+\frac{16}{4}

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Problem 2602

2. TRANSLATE into an equation. The word "of" here means multiplication. Translate the problem from words to an equation by completing the table below

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Problem 2603

7. Find the points of inflection on the curves: (i) y=x46x2+8x1y=x^{4}-6 x^{2}+8 x-1 (iii) y=x39x2+7x6y=x^{3}-9 x^{2}+7 x-6. (iii) y=(xa)(xb)(xc)y=(x-a)(x-b)(x-c). (iy) a2y2=x2(a2x2)a^{2} y^{2}=x^{2}\left(a^{2}-x^{2}\right). (v) y=x46x3+12x2+5x+2y=x^{4}-6 x^{3}+12 x^{2}+5 x+2. (vi) y=x33x29x+9y=x^{3}-3 x^{2}-9 x+9 (vii) x=(y1)(y2)(y3)x=(y-1)(y-2)(y-3). (viii) 54y=(x+5)2(x310)54 y=(x+5)^{2}\left(x^{3}-10\right)

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Problem 2604

x+5x=4,x0x+\frac{5}{x}=4, x \neq 0

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Problem 2605

Solve the following formula for t . C=J(1+t)C=J(1+\mathrm{t})
The solution is t=\mathrm{t}= \square (Simplify your answer.)

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Problem 2606

limx0xcotx\lim _{x \rightarrow 0} x \cot x

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Problem 2607

i) The following data shows weights of toffee boxes in gms. Determine the mean weight of a box. \begin{tabular}{|l|c|c|c|c|c|c|c|} \hline Classes/group & 090-9 & 101910-19 & 202920-29 & 303930-39 & 404940-49 & 505950-59 & 606960-69 \\ \hline Frequency & 2 & 10 & 5 & 9 & 6 & 7 & 2 \\ \hline \end{tabular}

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Problem 2608

4. If the pp-value is 0.023 and the significance level is 0.001 , then the decision is: A. Accept both H0\mathrm{H}_{0} and Ha\mathrm{H}_{a} B. Accept H0\mathrm{H}_{0} C. Reject H0\mathrm{H}_{0} D. Cannot be detemine
5. If the test statistic of two tailed test is 2.25 , then the pp-value is A. 0.025 B. 0.0244 C. 0.0122 D. 0.9756
6. if the p -value of given test is 0.0635 and based on a significance level 0.05 The decision will be : A. Accept the alternative hypothesis B. Accept the null hypothesis C. Reject the null hypothesis D. Accept both hypothesis

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Problem 2609

Let XX be a random variable with the following probability distribution \begin{tabular}{|c|c|} \hline Value xx of XX & P(X=x)P(X=x) \\ \hline 30 & 0.05 \\ \hline 40 & 0.05 \\ \hline 50 & 0.15 \\ \hline 60 & 0.15 \\ \hline 70 & 0.35 \\ \hline 80 & 0.25 \\ \hline \end{tabular}
Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E(X)E(X) of XX. E(X)=E(X)= \square

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Problem 2610

1-If a preferred stock pays 4 percent on its par, or stated, value of $100\$ 100, and your required rate of return is 7 percent, what is the stock worth to you?
2. What features of preferred stock are different from bonds?

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Problem 2611

Activity 5 Express the following to a perfect square trinomials and write as square of binomials.
1. x2+2x+x^{2}+2 x+ \qquad
6. x2+11x+x^{2}+11 x+ \qquad
2. t2+20t+t^{2}+20 t+ \qquad
7. x215x+x^{2}-15 x+ \qquad
3. r216r+r^{2}-16 r+ \qquad
8. w2+21w+w^{2}+21 w+ \qquad
4. r2+24r+r^{2}+24 r+ \qquad
9. s2+23s+s^{2}+\frac{2}{3} s+ \qquad
5. x230x+x^{2}-30 x+ \qquad
10. h234h+h^{2}-\frac{3}{4} h+ \qquad

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Problem 2612

Resolva essas funções encontre as raízes da função do estudo da concavidade e o vértice da parábola 10:49 letra C) 2x2+5x3=0Δ=b24ac2 x^{2}+5 x-3=0 \quad \Delta=b^{2}-4 a c 13:31

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Problem 2613

The straight line y=3x6y=3 x-6 intersect the yy-axis at the point (6,0)(6,0).
ص \bigcirc خ \bigcirc

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Problem 2614

5x+14x+3=05 x+14 x+3=0

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Problem 2615

Titulo de la tarea: Presupuesto de ventas y de producción.
Resultados de aprendizaje: Aplica el proceso contable relacionado a empresas industriales sobre sus actividades diarias. Calcula los costos de producción.
1. Presupuesto de ventas.
2. Presupuesto de producción (unidades).
3. Presupuesto de materia prima.
4. Presupuesto de compra de materiales.
5. Presupuesto de mano de obra.
6. Presupuesto de Gastos Indirectos de Fabricación.
7. Presupuesto de Costos de producción total.
8. Presupuesto Costo de producción unitario.
9. Presupuesto del Costo de Venta.
10. Presupuesto del Estado de Resultados Integral. TALLER DE PRESUPUESTO dE PRODUCCIÓN La fábrica de llantas LA RUEDA S.A. se dedica a la elaboración de tres modelos de llantas con aros de magnesio de 15,1715^{\prime \prime}, 17^{\prime \prime} y 1818^{\prime \prime} y ha presentado dificultades en la generación de ingresos y utilidad, asi como el exceso de costos y gastos; esto ha retrasado el cumplimiento de obligaciones adquiridos por la falta de interés; la empresa también presume que su precio de venta no es muy competitivo y es porque para cubrir el margen de utilidad solicitado por los promotores se ha tenido que elevar el PVP, por lo tanto existe un riesgo inminente de perder clientes. En vista de todos los problemas presentados en el inciso anterior, usted tiene la responsabilidad en esta situación de alto riesgo de desarrollar un presupuesto operativo que permite conocer la realidad de la empresa y permita ajustar los valores tomando decisiones en función de optimizar los costos, minimizar los gastos y aumentar las ventas. Inventario inicial de productos terminados: - Aros de magnesio 1515^{\prime \prime} de 3.100 unidades. - Aros de magnesio 17" de 3.500 unidades. - Aros de magnesio 1818^{\prime \prime} de 3.200 unidades. Así también se espera finalizar con un inventario Final estimado de productos terminados para afrontar variaciones de la demanda por ser temporada alta; - Aros de magnesio 1515^{\prime \prime} de 2,000 unidades. - Aros de magnesio 1717^{\prime \prime} de 2,450 unidades. - Aros de magnesio 1818^{\prime \prime} de 1,240 unidades El departamento de venta pronostica vender para el presente año 80,000 llantas de 15"; 75,000 llantas de 1717^{\prime \prime}; y 70,000 llantas de 1818^{\prime \prime} a un precio de $125,$165\$ 125, \$ 165 y $190\$ 190 respectivamente; siendo estos precios revisados al final para ver si son competitivos. El departamento de compras previo a reunión informa que cuenta con dos tipos de materia prima que son: - "materia prima A=\mathrm{A}= caucho" cuya unidad de medida es Kg . y el precio de compra es $9.50\$ 9.50 cada kg. - y la "materia prima B = magnesio para aros" cuya unidad de medida es kg. Y el precio de compra es $15\$ 15 cada kg. El jefe de bodega confirma que la materia prima A tiene un inventario inicial de 25,000 kg y por politica de inventario se debe mantener un inventario final de 7,500 kg7,500 \mathrm{~kg}; en cambio, la materia prima B tiene un inventario inicial de 26,800 piezas y por politica se debe mantener 10,000 piezas como inventario final. El departamento de producción menciona que para fabricar una unidad de 1515^{\prime \prime} se necesitan 4 kg de materia prima A y 4 kg de materia prima de B, para fabricar cada unidad de 1717^{\prime \prime} se necesitan 5 kg de materia prima A y 5 kg de materia prima de B y para fabricar cada unidad de 1818^{\prime \prime} se necesitan 6 kg de materia prima A y 6 kg de materia prima de B . Para el presupuesto de Mano de obra el jefe de producción y el jefe de talento humano indican que una unidad de 1515^{\prime \prime} se tarda 2 horas su fabricación y se paga $5.00\$ 5.00 la hora al personal asignado; mientras que para cada unidad de 17* se necesitan 3 horas y se pagan $6.00\$ 6.00 la hora, finalmente cada unidad de 1818^{\prime \prime} necesita 4 horas y se pagan $7\$ 7 la hora. Finalmente, el departamento de Contabilidad estima que el total de los ClF "Costos indirectos de fabricación" serán de $803,000\$ 803,000; Asi también los gastos administrativos son de $1,245,000\$ 1,245,000, los gastos de publicidad son de $500,000\$ 500,000. Se espera después de haber realizado el levantamiento de la información en los diferentes departamentos dentro de la empresa, usted realice el presupuesto y a partir de aquello asesore a los administradores y promotores de la empresa para mejorar el escenario financiero de la organización.

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Problem 2616

Series 1 b) Define Histogram. Draw a histogram for the following frequency distribution: \begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline X & 32 & 37 & 42 & 47 & 52 & 57 & 62 & 67 \\ \hline f & 3 & 17 & 28 & 47 & 54 & 31 & 14 & 4 \\ \hline \end{tabular}
Answer:

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Problem 2617

surse ilctvo.arg/content/enforced/23228188-MCV4U-EN-02-03-ON-(I-D-0323)/course_content/assets/locker_docs/mcv4u_01.04.04.html?ou=23228188 ACA's Paralegal Dro.
3. Explain the difference between a secant line and a tangent line. How do they relate to the rate of change of a function? Include a sketch of each type of line in your solution. [ 6 marks]

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Problem 2618

4. The path of a baseball relative to the ground can be modelled by the function d(t)=t2+8t+1d(t)=-t^{2}+8 t+1 where d(t)d(t) represents the height of the ball in metres after tt seconds. a. Find the average rate of change of the ball between 1 and 3 seconds. [4 marks] b. Using the secant method, find the instantaneous rate of change at 2 seconds. [5 marks]

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Problem 2619

Use Partial fraction technique to the following integrals (1) (6) x1(3x+1)(x+1)dx\int \frac{x-1}{(3 x+1)(x+1)} d x (2) x+5(x+3)2dx\int \frac{x+5}{(x+3)^{2}} d x x1x2(x+1)dx\int \frac{x-1}{x^{2}(x+1)} d x (3) (8) 231x21dx3x(2x+1)(x+4)dx\int_{2}^{3} \frac{1}{x^{2}-1} d x \quad \int \frac{3 x}{(2 x+1)(x+4)} d x (4) (9) 2114x2dxx2(2x+1)(x29)dx\int_{2}^{1} \frac{1}{4-x^{2}} d x \quad \int \frac{x^{2}}{(2 x+1)\left(x^{2}-9\right)} d x (5) (10) 1x2(5x1)dx\int \frac{1}{x^{2}(5 x-1)} d x

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Problem 2620

Line ss is the perpendicular bisector of JKundefined\widetilde{J K}. If line s intersects JK\overline{J K} at point L , which of the following statements must be true?
Check all that apply. A. Point L is the midpoint of JK B. Line s intersects JK\overline{\mathrm{JK}} at a 180180^{\circ} angle C. JLKLJ L K L D. Line s is parallel to JK E. Line s is perpendicular to JK\overline{J K}

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Problem 2621

Rates of Change Assignment
1. Determine the average rate of change of yy in the function y=2x3+7x2+2x3y=2 x^{3}+7 x^{2}+2 x-3 over the interval [3, 5]. [5 marks]

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Problem 2622

Which of these expressions is equivalent to 15÷0.915 \div 0.9 ? 1.5÷91.5 \div 9 15÷915 \div 9 150÷9150 \div 9 1,500÷91,500 \div 9

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Problem 2623

Use the "Completing Square Method" to express the following quadratic equations in the form of: (x+p)2+q(x+p)^{2}+q and a(x+p)2+qa(x+p)^{2}+q respectively.  b): 5x230x+47=0\text { b): } 5 x^{2}-30 x+47=0

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Problem 2624

\begin{tabular}{|l|} \hline Titulo de la tarea: \\ Presupuesto de ventas y \\ de producción. \\ \hline Resultados de \\ \hline aprendizaje: \\ \hline Aplica el proceso contable \\ relacionado a empresas \\ industriales \\ \hline sobre sus \\ actividades \\ \hline diarias. \\ \hline Calcula los \\ costos de \\ producción. \\ \hline \end{tabular}
1. Presupuesto de ventas.
2. Presupuesto de producción (unidades).
3. Presupuesto de materia prima.
4. Presupuesto de compra de materiales.
5. Presupuesto de mano de obra.
6. Presupuesto de Gastos Indirectos de Fabricación.
7. Presupuesto de Costos de producción total.
8. Presupuesto Costo de producción unitario.
9. Presupuesto del Costo de Venta.
10. Presupuesto del Estado de Resultados Integral. TALLER DE PRESUPUESTO DE PRODUCCIÓN La fábrica de llantas LA RUEDA S.A. se dedica a la elaboración de tres modelos de llantas con aros de magnesio de 15,1715^{\prime \prime}, 17^{\prime \prime} y 1818^{\prime \prime} y ha presentado dificultades en la generación de ingresos y utilidad, asi como el exceso de costos y gastos; esto ha retrasado el cumplimiento de obligaciones adquiridos por la falta de interés; la empresa también presume que su precio de venta no es muy competitivo y es porque para cubrir el margen de utilidad solicitado por los promotores se ha tenido que elevar el PVP, por lo tanto existe un riesgo inminente de perder clientes. En vista de todos los problemas presentados en el inciso anterior, usted tiene la responsabilidad en esta situación de alto riesgo de desarrollar un presupuesto operativo que permite conocer la realidad de la empresa y permita ajustar los valores tomando decisiones en función de optimizar los costos, minimizar los gastos y aumentar las ventas. Inventario inicial de productos terminados: - Aros de magnesio 1515^{\prime \prime} de 3.100 unidades. - Aros de magnesio 1717^{\prime \prime} de 3.500 unidades. - Aros de magnesio 1818^{\prime \prime} de 3.200 unidades. Asi también se espera finalizar con un inventario Final estimado de productos terminados para afrontar variaciones de la demanda por ser temporada alta; - Aros de magnesio 1515^{\prime \prime} de 2,000 unidades. - Aros de magnesio 17" de 2,450 unidades. - Aros de magnesio 1818^{\prime \prime} de 1,240 unidades El departamento de venta pronostica vender para el presente año 80,000 llantas de 15"; 75,000 llantas de 1717^{\prime \prime}; y 70,000 llantas de 1818^{\prime \prime} a un precio de $125,$165\$ 125, \$ 165 y $190\$ 190 respectivamente; siendo estos precios revisados al final para ver si son competitivos.

El departamento de compras previo a reunión informa que cuenta con dos tipos de materia prima que son: - "materia prima A=\mathrm{A}= caucho" cuya unidad de medida es Kg . y el precio de compra es $9.50\$ 9.50 cada kg . - y la "materia prima B = magnesio para aros" cuya unidad de medida es kg. Y el precio de compra es $15\$ 15 cada kg . El jefe de bodega confirma que la materia prima A tiene un inventario inicial de 25,000 kg y por politica de inventario se debe mantener un inventario final de 7,500 kg7,500 \mathrm{~kg}; en cambio, la materia prima B tiene un inventario inicial de 26,800 piezas y por politica se debe mantener 10,000 piezas como inventario final. El departamento de producción menciona que para fabricar una unidad de 1515^{\prime \prime} se necesitan 4 kg de materia prima A y 4 kg de materia prima de B, para fabricar cada unidad de 1717^{\prime \prime} se necesitan 5 kg de materia prima A y 5 kg de materia prima de B y para fabricar cada unidad de 1818^{\prime \prime} se necesitan 6 kg de materia prima A y 6 kg de materia prima de B . Para el presupuesto de Mano de obra el jefe de producción y el jefe de talento humano indican que una unidad de 1515^{\prime \prime} se tarda 2 horas su fabricación y se paga $5.00\$ 5.00 la hora al personal asignado; mientras que para cada unidad de 1717^{\prime \prime} se necesitan 3 horas y se pagan $6.00\$ 6.00 la hora, finalmente cada unidad de 1818^{*} necesita 4 horas y se pagan $7\$ 7 la hora. Finalmente, el departamento de Contabilidad estima que el total de los CIF "Costos indirectos de fabricación" serán de $803,000\$ 803,000; Asi también los gastos administrativos son de $1,245,000\$ 1,245,000, los gastos de publicidad son de $500,000\$ 500,000. Se espera después de haber realizado el levantamiento de la información en los diferentes departamentos dentro de la empresa, usted realice el presupuesto y a partir de aquello asesore a los administradores y promotores de la empresa para mejorar el escenario financiero de la organización.

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Problem 2625

2. Given the function f(x)=2x2+3x+1f(x)=2 x^{2}+3 x+1, a. Find the instantaneous rate of change when x=1x=1 using the secant method. [4 marks] b. Find the value of the derivative at x=1x=1 using first principles. [4 marks]

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Problem 2626

Rates of Change Assignment
1. Determine the average rate of change of yy in the function y=2x3+7x2+2x3y=2 x^{3}+7 x^{2}+2 x-3 over the interval [3, 5]. [5 marks]

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Problem 2627

Sin2αCos2βCos2αSin2β=Sin2αSin2β\operatorname{Sin}^{2} \alpha \operatorname{Cos}^{2} \beta-\operatorname{Cos}^{2} \alpha \operatorname{Sin}^{2} \beta=\operatorname{Sin}^{2} \alpha-\operatorname{Sin}^{2} \beta

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Problem 2628

1. Evaluate the following functions at x=2x=-2. (a) f(x)=x3f(x)=x-3 (b) g(x)=x32x+5g(x)=x^{3}-2 x+5 (c) h(x)=x2+x+33h(x)=\sqrt[3]{x^{2}+x+3} (d) p(x)=x2+1x4p(x)=\frac{x^{2}+1}{x-4} (e) q(x)=x3q(x)=|x-3|, where x3|x-3| means the absolute value of x3x-3

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Problem 2629

In this activity, you will be asked to performl operations on functions as provided at the right sperate at the left to its cor are matching functions you are provided inside the box for your refer Activity 4. MATCH II! Functions are prot of matching! choose Me... Let f(x)=3x22x1g(x)=x21f(x)=3 x^{2}-2 x-1 \quad g(x)=x^{2}-1 o. 3x22x13 x^{2}-2 x-1
Operate Me...
1. (fg(x)(f-g(x) - x+13x+1\frac{x+1}{3 x+1}
2. (f+h)(x)(f+h)(x) - 2x22x2 x^{2}-2 x
3. g(x)h(x)\frac{g(x)}{h(x)}
4. (hg)(x)(\mathrm{h}-\mathrm{g})(\mathrm{x}) o. 2x22x22 x^{2}-2 x-2
5. (1)g(2)H(0)\int(-1) \cdot g(2) \cdot H(0) - 24 - 7x24x37 x^{2}-4 x-3 o. -24

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Problem 2630

6 a) Write the sequence got by adding 2 to the successive multiples of 3 . b) What is its algebra? c) Can the difference between any two terms be a multiple of 2 ?

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Problem 2631

Letf(x)=3x22x\operatorname{Let}_{f(x)}=3 x^{2}-2 x  o 3x22x1\text { o } 3 x^{2}-2 x-1
Operate Me...
1. (fg)(x)(f-g)(x)
2. (f+h)(x)(f+h)(x) - 2x22x2 x^{2}-2 x
3. g(x)h(x)\frac{g(x)}{h(x)} - x3x\frac{x}{3 x}
4. (hg)(x)(h-g)(x) - 2x22x22 x^{2}-2 x-2
5. f(1)g(2)h(0)f(-1) \cdot g(2) \cdot h(0) - 24 - 7x24x37 x^{2}-4 x-3 00240_{0}-24

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Problem 2632

Sin2αCos2βCos2αSin2β=Sin2αSin2β\operatorname{Sin}^{2} \alpha \operatorname{Cos}^{2} \beta-\operatorname{Cos}^{2} \alpha \operatorname{Sin}^{2} \beta=\operatorname{Sin}^{2} \alpha-\operatorname{Sin}^{2} \beta

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Problem 2633

(a) f(2)f(2) (b) f(12.5)f(12.5) (c) f(3)f(-3) (d) f(5)f(5) (e) f(1.5)f(1.5)

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Problem 2634

presented earlier in the right sid provided at the righ to operate the box for your are the h(x)=4x22x2h(x)=4 x^{2}-2 x-2 functions Functions are provided ins g(x)=x2+xg(x)=x^{2}+x
Choose Me... Let f(x)=3x22x1f(x)=3 x^{2}-2 x-1 o. 3x22x13 x^{2}-2 x-1
Operate Me...
1. (fg)(x)(f-g)(x) - x+13x+1\frac{x+1}{3 x+1}
2. (f+h)(x)(f+h)(x) 02x22x02 x^{2}-2 x 0
3. g(x)h(x)\frac{g(x)}{h(x)}
4. (bg)(x)(b-g)(x) o. 2x22x22 x^{2}-2 x-2
5. (f(1)g(2)h(0)(f(-1) \cdot g(2) \cdot h(0) o 24 - 7x24x37 x^{2}-4 x-3 o. 24

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Problem 2635

Phetoho sells soccer balls. 37\frac{3}{7} of the soccer balls in Phetoho's shop are red. 14\frac{1}{4} of the remainder are blue. The rest of the soccer balls are green. 1.
If the total number of soccer balls in the shop is bb, determine simplified expressions for each of the following in terms of bb :
1. The number of red soccer balls.
2. The number of blue soccer balls.

Answer:
1. Red soccer balls: 47b\frac{4}{7} b 14b\frac{1}{4} b 37b\frac{3}{7} b 37\frac{3}{7}
2. Blue soccer balls:

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Problem 2636

In this activity, you will be asked to performl operations on functions as provided at the right sperate at the left to its cor are matching functions you are provided inside the box for your refer Activity 4. MATCH II! Functions are prot of matching! choose Me... Let f(x)=3x22x1g(x)=x21f(x)=3 x^{2}-2 x-1 \quad g(x)=x^{2}-1 o. 3x22x13 x^{2}-2 x-1
Operate Me...
1. (fg(x)(f-g(x) - x+13x+1\frac{x+1}{3 x+1}
2. (f+h)(x)(f+h)(x) - 2x22x2 x^{2}-2 x
3. g(x)h(x)\frac{g(x)}{h(x)}
4. (hg)(x)(\mathrm{h}-\mathrm{g})(\mathrm{x}) o. 2x22x22 x^{2}-2 x-2
5. (1)g(2)H(0)\int(-1) \cdot g(2) \cdot H(0) - 24 - 7x24x37 x^{2}-4 x-3 o. -24

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Problem 2637

QUESTIION 4  (2 + 2 = 4 Marks \text { (2 + } 2 \text { = } 4 \text { Marks }
Solve each of the following quadratic equations for xx using "Quadratic Formula". Leave your answer in surd (exact) form. (a). 3(x2)2+4x2=5\frac{3}{(x-2)^{2}}+\frac{4}{x-2}=5

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Problem 2638

uscles.
6. The magnifying power of terrestrial teles cope is 16 . when it is in normal adjustment and thelengthof the tclescope is 118 cm . If the focal length of the reccting lens is 5 cm , the focal lengths of the objective and the eye-piecer dre?

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Problem 2639

3. f(y)=log2(y+1)log2(y+3)f(y)=\log _{2}(y+1)-\log _{2}(y+3)
Find the domain of t(y1t\left(y_{1}\right. Find the volue of yy if f(y)=1f(y)=1

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Problem 2640

I. Word Problems. Solve the following problems and show your solutions.
1. A cone has a radius of 4 cm and a height of 9 cm . Find the volume of the cone.
2. A cone has a slant height of 10 cm and a base radius of 6 cm . Calculate the surface area of the cone.
3. The volume of a cone is 150 cm3150 \mathrm{~cm}^{3} and its base radius is 5 cm . Determine the height of the cone.
4. A cone has a total surface area of 150 cm2150 \mathrm{~cm}^{2} and a slant height of 12 cm . Find the radius of the base.
5. A cone has a volume of 200 cm3200 \mathrm{~cm}^{3} and a base radius of 5 cm . Find the slant height of the cone.
6. A square pyramid has a base edge of 8 cm and a height of 15 cm . Calculate the volume.
7. A triangular pyramid has a base area of 20 cm220 \mathrm{~cm}^{2} and a slant height of 10 cm . If each triangular face has an area of 25 cm225 \mathrm{~cm}^{2}, find the total surface area.
8. The volume of a rectangular pyramid is 240 cm3240 \mathrm{~cm}^{3} and the base dimensions are 6 cm by 4 cm . Find the height of the pyramid.
9. A pyramid has a volume of 500 cm3500 \mathrm{~cm}^{3} and a height of 10 cm . If the base is a regular hexagon, find the area of the base.
10. A pyramid has a base side of 9 cm and a total surface area of 648 cm2648 \mathrm{~cm}^{2}. Calculate the slant height if the height of the pyramid is 12 cm .
11. A frustum of a cone has a lower base radius of 7 cm , an upper base radius of 4 cm , and a height of 10 cm . Find the volume.
12. Find the surface area of a frustum with a lower base radius of 6 cm , an upper base radius of 3 cm , and a slant height of 8 cm .
13. A frustum of a cone has a volume of 400 cm3400 \mathrm{~cm}^{3}, a height of 12 cm , and radii of 5 cm and 3 cm for the lower and upper bases. Find the slant height.
14. The frustum of a cone has a total surface area of 300 cm2300 \mathrm{~cm}^{2}, lower base radius of 5 cm , and an upper base radius of 3 cm . Find the height of the frustum if the slant height is 7 cm .
15. A frustum with a height of 8 cm has a volume of 320 cm3320 \mathrm{~cm}^{3}. The radius of the lower base is 6 cm and the radius of the upper base is unknown. Find the radius of the upper base.

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Problem 2641

Activity 1: The Secret of Carl What is 1+2+3++50+51++98+99+100?1+2+3+\ldots+50+51+\ldots+98+99+100 ?
It age of 7 , fie surgrised fit teacfier fy aiffing mamfees ; to soo afmoot instanily by quickly figuring so gairs of numbors fry taking the int nimiver i and Gist numine roo, then werond number 2 and seomif Cut nimmler 99 and s0s 0 on, with each nair nomming lo lor as it is shewn befow 1undefined101+2+2++98undefined101+99+100\underbrace{1}_{101}+\underbrace{2+2+\ldots+98}_{101}+99+100

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Problem 2642

Suppose mm and nn are roots of the quadratic equation 3x27x5=03 x^{2}-7 x-5=0 Find the value of mmn+nm-m n+n.

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Problem 2643

4. If 201×61=12261201 \times 61=12261, what is 2.01×6.12.01 \times 6.1 equal to? A. 1226.1 B. 122.61 C. 12.261
5. If a meter of cloth cost P88.50, how much would 5.5 mcos5.5 \mathrm{~m} \cos ? A. P575. 25 D. 1.2281 B. P486 75 C. P398.25
6. What is the area of a rectangular garden with a length of 3.25 m and a vidh of 115 m ? D. P309 75 A. 4.4 m24.4 \mathrm{~m}^{2} B. 3.7375 m23.7375 \mathrm{~m}^{2} C. 27275 m227275 \mathrm{~m}^{2} D. 2.1 m22.1 \mathrm{~m}^{2}
7. Carlo bought a dozen of ballpen at P6 75 each. How much did he pay? A. P6.75 B. P47.25 C. P6 50 D. P81.00

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Problem 2644

In Singapore, if we borrow books from a public library and are late in returning the Direct Proportion books, we will be fined 15 cents per day for each overdue book. Table 1.1 shows the fines for an overdue book. \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|} \hline Number of days (x)(x) & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Fine (y(y cents )) & 15 & 30 & 45 & 60 & 75 & 90 & 105 & 120 & 135 & 150 \\ \hline \end{tabular}
Table 1.1
1. If the number of days a book is overdue increases, will the fine increase or decrease?
2. If the number of days a book is overdue is doubled, how will the fine change? Hint: Compare the fines when a book is overdue for 3 days and for 6 days.
3. If the number of days a book is overdue is tripled, what will happen to the fine?
4. If the number of days a book is overdue is halved, how will the fine change? Hint: Compare the fines when a book is overdue for 10 days and for 5 days.
5. If the number of days a book is overdue is reduced to 13\frac{1}{3} of the original number, what will happen to the fine?

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Problem 2645

Write 133\frac{13}{3} as a decimal.

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Problem 2646

Refer to the information below to answer Question 14 and 15. Two forces of 3 N and 4 N are acting at a point such that the angle between them 6060^{\circ}. (2 marks)
14. Draw the diagram. R2=32+42(3)(4)cos(120)R=32+422(3)(4)cos(120)2=34 N\begin{array}{l} R^{2}=3^{2}+4-2(3)(4) \cos (120) \\ R=\sqrt{3^{2}+4^{2}-2(3)(4) \cos (120)} \\ 2=\sqrt{34} \mathrm{~N} \end{array} (5 marks)
15. Find the resultant force.

Working out: , R2=FF+FF2+2F1F2cos( theta ), where F1=3N,F2=4NR^{\wedge} 2=F F^{\wedge}+F F^{\wedge} 2+2^{*} F_{1}^{*} F 2^{*} \cos (\text { theta }) \text {, where } F_{1}=3 N, F 2=4 N

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Problem 2647

Let F(s)F(s) be the Laplace Transform of f(t)f(t). If you know that limt0f(t)=limssF(s)\lim _{t \rightarrow 0} f(t)=\lim _{s \rightarrow \infty} s F(s), then the Laplace Transform of f(t)=0tsin(x)xdxf(t)=\int_{0}^{t} \frac{\sin (x)}{x} d x is

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Problem 2648

9. There is a hexagon MNOPQR of each side 5 cm and symmetric about NQ. Suresh and Rushika divided it into different ways. Find the area of this hexagon using both ways. Fig. (i)
Suresh's Method Rushika's Method Fig. (ii)

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Problem 2649

8. The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m2\mathrm{m}^{2} is Rs. 4 .

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Problem 2650

8.2. AA and BB are two events. The probability the event AA will occur is 0,4 and the probability that event B will occur is 0,3. The probability that either event AA or BB will occur is 0,58 8.2 .1 - Are events AA and BB mutually socclusive. 8.2.2. Are event. AA and BB independent? Justity your answer with appropriate calculations.

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Problem 2651

In C++\mathrm{C}++
Group 7
7. Searching * Function: Describe a function to search for a specific element in the linked list. * Implementation: Provide the code for the function, including how it compares the data of each node with the target value. 19:41

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Problem 2652

cos2θsin2θdθ\int \sqrt{\cos 2 \theta} \sin 2 \theta d \theta

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Problem 2653

Q : All of the statements below are true except? A. Coprime numbers are numbers whose GCF is 1 B. A perfect number is a positive integer equal to the sum of its properties C. A complex number is a combination of a real number and an imaginary number D. All whole numbers are positive integers

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Problem 2654

Find the value of the unknown ' xx ' in the following triangles. X PP\mathrm{P}_{\mathrm{P}} \qquad (i) (ii)

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Problem 2655

12.) For every natural number ' nn ', (n+1)2n2(n+1)^{2}-n^{2} equals. (a) n(n+1)n-(n+1) (b) (n+1)n(n+1)-n (c) (n1)+n(n-1)+n (d) (n+1)+n(n+1)+n

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Problem 2656

Find the direction cosines of 4i3j+5k4 i-3 j+5 k

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Problem 2657

952×π180\frac{95}{2} \times \frac{\pi}{180}

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Problem 2658

Determine the independent and dependent variables of the study described below. A math instructor announces a study session to be held the night before a test. The instructor lists the students who attended the session and compares their scores to the grades of the students who did not attend. \square Whether the student attended the study session
1. Independent \square Test grade
2. Dependent

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Problem 2659

tan(19π3)-\tan \left(\frac{19 \pi}{3}\right)

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Problem 2660

Determine whether the statement below is an example of descriptive or inferential statistics.
Based on a study of 5000 students, a study has concluded that the average credit card debt of college graduates increased from the year 2009 to 2010.. -- Select an Option --
Previous Page Next Page Page 5 of 14 Submit Quiz

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Problem 2661

g) x2y=9,2x+y=2x-2 y=-9,2 x+y=2 i) 3x+2y=4,2xy=53 x+2 y=4,2 x-y=5

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Problem 2662

What is the dividend yield on Stock AA that sells at $20/\$ 20 / share, when Company A pays a quarterly dividend of $0.15\$ 0.15 per share?

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Problem 2663

What is the dividend yield on Stock AA that sells at $25/\$ 25 / share, when Company A pays a quarterly dividend of $0.15\$ 0.15 per share?

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Problem 2664

What is the dividend yield on Stock AA that sells at $30\$ 30 /share, when Company A pays a quarterly dividend of $0.20\$ 0.20 per share?

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Problem 2665

Classify the following as a random, systematic, stratified, or cluster sampling. A company has 1000 employees, of whom 800 are full-time and 200 are part-time. Twenty employees are randomly selected from each group and asked to complete a survey about their opinions regarding benefits. -- Select an Option --

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Problem 2666

5. The mean age of five children is 11 years, If the age of four children are, reapectively, 9,13,109,13,10, then years, find the age of the fifth child.
6. The mean of five numbers is 38 . It was found later that number 21 was wrongly written as 12 . Find the correct mean. .) Mamz'38, \Rightarrow tal Surt a 38 d S=190S=190 a. 16,2,0,1,6,13,8,12,1116,2,0,1,6,13,8,12,11 b. 25,48,20,32,43,4725,48,20,32,43,47
8. The runs scored by a cricketer in a cricket match in 11 overs are as follows: 5,0,11,8,13,6,9,4,17,20,145,0,11,8,13,6,9,4,17,20,14 Find the median score.
9. Solve the following: a. Find the mode of the following data: 2,5,2,1,6,8,1,7,2,1,9,1,1,62,5,2,1,6,8,1,7,2,1,9,1,1,6 b. Find the mean of the first 15 odd natural numbers. c. Compare the mean, median, and mode of the following data: 8,15,15,178,15,15,17, and 20 ,
10. The median of observations 4,5,8,11,x+2,x+4,19,26,29,324,5,8,11, x+2, x+4,19,26,29,32 is 13 . Find the value of xx if the values already written in ascending order:
11. The weight (in kg ) of 20 students of a class are as follows: 36,42,45,36,40,45,38,41,36,39,49,43,44,34,50,48,52,41,51,3636,42,45,36,40,45,38,41,36,39,49,43,44,34,50,48,52,41,51,36

Find the mean, median and mode of the given data,
12. A dice was rolled 30 times and the following scores were obtained: 1,6,5,2,6,3,5,1,6,5,3,5,1,3,3,2,6,4,4,4,5,3,4,6,6,2,1,3,5,31,6,5,2,6,3,5,1,6,5,3,5,1,3,3,2,6,4,4,4,5,3,4,6,6,2,1,3,5,3

Find the mode of the given data.
13. Find the mean of the following data: \begin{tabular}{|l|c|c|c|c|c|c|} \hline Age & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline No. of students & 23 & 19 & 35 & 18 & 32 & 46 \\ \hline \end{tabular} 260

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Problem 2667

An investor purchased 70 shares of stock in a company for \3,010,withan$8commission.Later,allofthestockwassoldat3,010, with an \$8 commission. Later, all of the stock was sold at \40 40 per share. What was the gain or loss on this investment?

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Problem 2668

What is the yield on a corporate bond with a $1000\$ 1000 face value purchased at a discount price of $925\$ 925, if it pays 5%5 \% fixed interest for the duration of the bond?

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Problem 2669

From the information given, find the quadrant in which the terminal point determined by tt lies. Input I, II, III, or IV. (a) sin(t)<0\sin (t)<0 and cos(t)<0\cos (t)<0, quadrant \square (b) sin(t)>0\sin (t)>0 and cos(t)<0\cos (t)<0, quadrant \square ; (c) sin(t)>0\sin (t)>0 and cos(t)>0\cos (t)>0, quadrant \square ; (d) sin(t)<0\sin (t)<0 and cos(t)>0\cos (t)>0, quadrant \square

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Problem 2670

What is the yield on a corporate bond with a $1000\$ 1000 face value purchased at a discount price of $850\$ 850, if it pays 8%8 \% fixed interest for the duration of the bond?

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Problem 2671

Attempt ALL Questions Brief Answer Questions (10×2=20)(10 \times 2=20)
1. Write any two features of cost accounting.
2. Explain the importance of BEP.
3. Define 'Theory of Constraints'.
4. What is opportunity cost?
5. Define the meaning of static budget.
6. Assume that six monthly observations of indirect manufacturing costs Y and machine hours X are to be used as a basis for developing the cost volume formula Y=a+bX\mathrm{Y}^{\prime}=\mathrm{a}+\mathrm{b} \mathrm{X}. The sums are available as

Required: Determine the fixed cost and the variable rate using the Least Squares Method
7. The company produces 10,000 units of output incurring cost Rs. 1,000,000 which includes fixed cost Rs.200,000.

Required: Budgets for 8,000 and 11,000 units.
8. The following information are provided:  Fixed manufacturing cost = Rs. 50,000 Profit from Absorption Costing Statement = Rs. 130,000 Closing stock =2,000 units  Opening stock =1,000 units  Normal output =10,000 units \begin{array}{ll} \text { Fixed manufacturing cost } & =\text { Rs. } 50,000 \\ \text { Profit from Absorption Costing Statement } & =\text { Rs. } 130,000 \\ \text { Closing stock } & =2,000 \text { units } \\ \text { Opening stock } & =1,000 \text { units } \\ \text { Normal output } & =10,000 \text { units } \end{array}

Required: Profit of Variable Costing Statement
9. A company is considering the purchase of a machinery costing Rs. 50,000 having expected life of 5 years. The cost of capital is 10%10 \%. Net cash flow during the expected life of the machinery is given below. \begin{tabular}{|l|c|c|c|c|c|} \hline Years & 1 & 2 & 3 & 4 & 5 \\ \hline CFAT & 16,000 & 14,000 & 15,000 & 12,000 & 10,000 \\ \hline \end{tabular}

Required: Discounted Pay Back period
10. The standard material for one unit of output is 5 Kg . the actual output for 100 units is 480 Kg . The actual price for 480 Kg material is Rs. 1,440 and standard price per Kg of material is Rs. 2. ΣX=570ΣY= Rs. 3,785ΣXY= Rs. 364,000ΣX2=55,000ΣY2= Rs .2,413,925\begin{array}{l} \Sigma X=570 \\ \Sigma \mathrm{Y}=\text { Rs. } 3,785 \\ \Sigma X Y=\text { Rs. } 364,000 \\ \Sigma X^{2}=55,000 \\ \Sigma \mathrm{Y}^{2}=\text { Rs } .2,413,925 \end{array}

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Problem 2672

Solve this pair of simultaneous equation graphically, y=x2+4x5y=x^{2}+4 x-5 and y=2x2y=2 x-2. And also shade the region defined simultaneously by the inequalities; yx2+4x5y \geq x^{2}+4 x-5 and y2x2y \leq 2 x-2 on the same graph.

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Problem 2673

Solve tt nis pair of simultancous equation graphically, y=x2+4x5y=x^{2}+4 x-5 and y=2x2y=2 x-2. And also shade the region defined simultaneously by the inequalities yx2+4x5y \geq x^{2}+4 x-5 and y2x2y \leq 2 x-2 on the same graph.
Unit 11.2 Graphs \& Functions ... Topici: Quadratic Equations \& Quadratic Gri

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Problem 2674

Attempt ALL Questions Brief Answer Questions (10×2=20)(10 \times 2=20)
1. Write any two features of cost accounting.
2. Explain the importance of BEP.
3. Define 'Theory of Constraints'.
4. What is opportunity cost?
5. Define the meaning of static budget.
6. Assume that six monthly observations of indirect manufacturing costs Y and machine hours X are to be used as a basis for developing the cost volume formula Y=a+bX\mathrm{Y}^{\prime}=\mathrm{a}+\mathrm{b} \mathrm{X}. The sums are available as ΣX=570ΣY= Rs. 3,785ΣXY= Rs. 364,000ΣX2=55,000ΣY2= Rs. 2,413,925\begin{array}{l} \Sigma X=570 \quad \Sigma Y=\text { Rs. } 3,785 \quad \Sigma X Y=\text { Rs. } 364,000 \quad \Sigma X^{2}=55,000 \\ \Sigma Y^{2}=\text { Rs. } 2,413,925 \end{array}

Required: Determine the fixed cost and the variable rate using the Least Squares Method
7. The company produces 10,000 units of output incurring cost Rs. 1,000,000 which includes fixed cost Rs.200,000.

Required: Budgets for 8,000 and 11,000 units.
8. The following information are provided: \begin{tabular}{ll} Fixed manufacturing cost & == Rs. 50,000 \\ Profit from Absorption Costing Statement & == Rs. 130,000 \\ Closing stock & =2,000=2,000 units \\ Opening stock & =1,000=1,000 units \\ Normal output & =10,000=10,000 units \end{tabular}

Required: Profit of Variable Costing Statement
9. A company is considering the purchase of a machinery costing Rs. 50,000 having expected life of 5 years. The cost of capital is 10%10 \%. Net cash flow during the expected life of the machinery is given below. \begin{tabular}{|l|c|c|c|c|c|} \hline Years & 1 & 2 & 3 & 4 & 5 \\ \hline CFAT & 16,000 & 14,000 & 15,000 & 12,000 & 10,000 \\ \hline \end{tabular}

Required: Discounted Pay Back period
10. The standard material for one unit of output is 5 Kg . the actual output for 100 units is 480 Kg . The actual price for 480 Kg material is Rs. 1,440 and standard price per Kg of material is Rs. 2.

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Problem 2675

0.25 km=0.25 \mathrm{~km}= \qquad dmd m

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Problem 2676

QUESTION 5 A rectangle has a perimeter of 40 cm and a length of x cmx \mathrm{~cm}. Show that its area is given by A=20xx2A=20 x-x^{2} and find the length when the area is 96 cm296 \mathrm{~cm}^{2}.

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Problem 2677

5 kg=5 \mathrm{~kg}= \qquad dag

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Problem 2678

Find the circumference of a circle with a diameter of 16 cm . Use 3.14 for π\pi and include the correct units in your answer.

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Problem 2679

Write in expanded fo ab6a b^{6}

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Problem 2680

لتكن f وg دالتين معرفتين ومستمرتين على المجال[ [0;1] بييث f(1)=g(0)=1,f(0)=g(1)=0f(1)=g(0)=1, f(0)=g(1)=0
بين انه يوجد على الاقل عدد حقيقيه من المجال] 1 ; 10 بحيث : f(α)=2022g(α)f(\alpha)=2022 g(\alpha)

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Problem 2681

Unit 1: Geometry Assignments 1.1 Name: \qquad ALGEBRA REVIEW Solve each equation for the indicated variable. The correct solution to each problem should show up once in the solution bank.  1. x+3=5\text { 1. } x+3=5
2. x4=11x-4=11
3. 13x=6\frac{1}{3} x=6
4. 2x=122 x=12
5. 2x11=1052 x-11=105
6. 34x11=22\frac{3}{4} x-11=22
7. 3x+2=113 x+2=11
8. 3x+8+2x5=233 x+8+2 x-5=23
9. 3x+8=2x+133 x+8=2 x+13

Solution Bank: 5215581846443\begin{array}{lllllllll}5 & 2 & 15 & 58 & 18 & 4 & 6 & 44 & 3\end{array}
Solving Equations with Variables on Both Sides and Fractions
10. 5+12x=31-5+12 x=31
11. 9x+18+3x=909 x+18+3 x=90
12. 4y+110=34 y+1-10=3
13. 3x+5x=243 x+5 x=24
14. 10x+1=18010 x+1=180
15. x+13=2x+2x+13=2 x+2

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Problem 2682

```latex \documentclass{article} \usepackage[utf8]{inputenc} \begin{document}
Usando el ejemplo de la camioneta, supongamos que la camioneta de William tiene un filtro de aire sucio, lo que causa que el consumo de gasolina sea de entre 16 y 18 millas por galón. ¿Cuántas horas puede William conducir con un tanque lleno según esta información?
\end{document} ```

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Problem 2683

For 9-11, solve for x\mathbf{x}.
9. 2x3+x+10=522 x-3+x+10=52
10. 5x2=785 x-2=78
11. 5x22=2x+355 x-22=2 x+35 12.) Sketch the diagram. Then use the given information to solve for xx and the indicated lengths and mm

Given: MM is between NN and LL. PR\overline{P R} and NL\overline{N L} intersect at MM. M is the midpoint of PR\overline{P R}. PM=40\mathrm{PM}=40 PR=3x+8\mathrm{PR}=3 x+8 Find: x=x= MR=\mathrm{MR}= PR=\mathrm{PR}=

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Problem 2684

SKETCHING FIGURES Sketch the lines segments and rays.
21. Sketch and label 3 collinear points A, B, and C. 22. Sketch and label MNundefined\overleftrightarrow{M N} intersecting PQundefined\overleftrightarrow{P Q} at R.
23. Draw four points J,K,LJ, K, L, and MM, no three of which are collinear. Then sketch JKundefined,KL,LMundefined\overrightarrow{J K}, \overline{K L}, \overleftrightarrow{L M}, and MJundefined\overrightarrow{M J}.
24. Evaluate: 8(4)35+528(4)-35+5^{2} A. 28 B. 22 C. 2 D. 92
25. Use x=5x=5, to evaluate the expression 4x+84 x+8 A. 17 B. 28 C. 9 D. 33
26. What is the simplified form of the expression 5(x2)5(3+x)5(x-2)-5(3+x) ? A. -5 B. 5 C. 10x2510 x-25 D. -25

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Problem 2685

(3) lnxlnx+1=2\ln x-\ln x+1=2

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Problem 2686

Problema 2. En la elaboración de una bebida se desea garantizar que el porcentaje de CO (gas) por envase esté entre 2.5 y 3.0. Los siguientes datos son obtenidos del monitoreo del proceso: 2.612 .622 .652 .562 .682 .512 .562 .622 .632 .572 .602 .532 .692 .53 2.672.662.632.522.612.602.522.622.672.582.612.642.492.582.612.532.672 .662 .63 \quad 2.52 \quad 2.612 .602 .522 .622 .672 .582 .612 .642 .492 .582 .612 .53 2.532.572.662.512.572.552.572.562.522.582.642.592.572.582.522.612.532 .572 .662 .51 \quad 2.572 .552 .572 .562 .522 .582 .642 .592 .572 .582 .522 .61 2.552.552.732.512.612.712.642.592.602.642.562.602.52.482.602.612.55 \quad 2.55 \quad 2.732 .51 \quad 2.61 \quad 2.712 .642 .592 .60 \quad 2.642 .562 .602 .5 才 \quad 2.482 .602 .61 2.552 .662 .692 .562 .642 .67 2.73

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Problem 2687

10. x+4+2x=14x+-4+2 x=14
11. 4(y+1)=84(y+1)=-8

See Solution

Problem 2688

Classify the numbers as rational or irrational. 6 19\sqrt{19} 6+196+\sqrt{19} 6196 \cdot \sqrt{19} rational irrational

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Problem 2689

Find the EAR in each of the following cases. (Use 365 days a year. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

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Problem 2690

See your tevels
Helen just started training for her first triathlon. She worked out twice a day for 10 days. For her morning workouts, she biked mm minutes and ran 20 minutes. For her afternoon workouts, she biked mm minutes and ran 30 minutes.
Pick all the expressions that represent how long Helen trained. 20m+50020 m+500 10(m+20)+10(m+30)10(m+20)+10(m+30) 10m+50m10 m+50 m 10m+200+10m+30010 m+200+10 m+300

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Problem 2691

First National Bank charges 14.1 percent compounded monthly on its business loans. First United Bank charges 14.4 percent compounded semiannually. Calculate the EAR for First National Bank and First United Bank (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) \begin{tabular}{|l|l|l|} \hline First National & & %\% \\ \hline First United & & %\% \\ \hline \end{tabular}
As a potential borrower, to which bank would you go for a new loan? First National Bank First United Bank

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Problem 2692

Bella wants to buy 71/271 / 2 cups of almonds. There are 11/211 / 2 cups of almonds in each package. How many packages of almonds should Bella buy?
Write your answer as a fraction or as a whole or mixed number. \square packages

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Problem 2693

b) x37x6=0x^{3}-7 x-6=0

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Problem 2694

An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays $170\$ 170 annually if the next payment occurs one year from today? The market rate is 4.4 percent. (Round your answer to 2 decimal places, e.g., 32.16.)
Present value

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Problem 2695

Given: r=32 centimeters r = 32 \text{ centimeters} θ=π4 radians \theta = \frac{\pi}{4} \text{ radians}
Find the length in cm.

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Problem 2696

The elephants at the zoo eat 2 buckets of bananas each day. The zookeeper bought 41/441 / 4 buckets of bananas. How many days will the bananas last?
Write your answer as a fraction or as a whole or mixed number. \square days

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Problem 2697

Solve the problem below. Merry is five years younger than Lyn. In three years, the product of her age and Lyn's age year ago will be 22 years. Find their age three years from now.
Activity:
1. Make table of values.
2. Form an equation to solve the problem.
3. Show your complete solutions and encircle your final answer.

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Problem 2698

Investment XX offers to pay you $5,400\$ 5,400 per year for nine years, whereas Investment YY offers to pay you $7,700\$ 7,700 per year for five years. a. Calculate the present value for Investments XX and YY if the discount rate is 6 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) b. Calculate the present value for Investments XX and YY if the discount rate is 16 percent. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 3216.) \begin{tabular}{|c|c|c|} \hline a. Investment XX & \ & 36,728.98 \\ \hline a. Investment Y & \$ & 32,434.23 \\ \hline b. Investment X & \$ & 25,179.82 \\ \hline b. Investment Y$ & \$ & 25,211.49 \\ \hline \end{tabular}

See Solution

Problem 2699

6. Evaluate the following limits. a. limx4x216x4\lim _{x \rightarrow 4} \frac{x^{2}-16}{x-4} [3 marks] b. limx8x35x2+176x3+2x24x\lim _{x \rightarrow \infty} \frac{8 x^{3}-5 x^{2}+17}{6 x^{3}+2 x^{2}-4 x} [3 marks] c. limh049+h7h\lim _{h \rightarrow 0} \frac{\sqrt{49+h}-7}{h} [4 marks] d. limy2y382y27y+12\lim _{y \rightarrow-2} \frac{y^{3}-8}{2 y^{2}-7 y+12} [3 marks] e. limh042+h2h[3\lim _{h \rightarrow 0} \frac{\frac{4}{2+h}-2}{h}[3 marks ]]

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Problem 2700

Multiply. 4w2(5w3)4 w^{2}\left(-5 w^{3}\right)
Simplify your answer as much as possible.

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