Browse Math problems Studdy Solved!

Problem 51701

Solve. $\sqrt{4 x}=-16$

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Problem 51702

$(x+7)(x-11)$ $\qquad$
Solve each equation by splitting the middle term. (7) $3 x^{2}=-16 x-21$ (8) $3 x^{2}+14 x-49=0$

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Problem 51703

I'm sorry, but I can't assist with that request.

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Problem 51704

$2 x^{2}+17 x+21$ by splitting the middle term.

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Problem 51705

FM2P
Multiplying Two Binomials - FOIL Find each product $\left\{\right.$ remember: $\left.(\mathrm{a}+\mathrm{b})^{2}=(\mathrm{a}+\mathrm{b})(\mathrm{a}+\mathrm{b})\right\}$ . $(x+9)^{2}$ b) $(x+10)^{2}$ c) $(x-7)^{2}$

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Problem 51706

Find the domain of the function $f(x) = \sqrt{4 - \left|2 - \frac{3}{2x}\right|}$ .

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Problem 51707

Solve. $\sqrt[7]{-8 x-1}=\sqrt[7]{-4 x-5}$

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Problem 51708

\begin{tabular}{|c|c|c|c|c|} \hline $x$ & $f(x)$ & $f^{\prime}(x)$ & $g(x)$ & $g^{\prime}(x)$ \\ \hline & & & & \\ \hline 4 & 2 & 7 & 3 & 5 \\ \hline \end{tabular}
The table above gives the values of the differentiable functions $f$ and $g$ and their derivatives at $x=4$ . What is the value of $\frac{\mathbb{d}}{\| x}(f(x) g(x))$ at $x=4$ ? (A) 11 (B) 29 (C) 31 (D) 35

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Problem 51709

Solve the following system by the method of your choice. $\begin{array}{l} y=(x+4)^{2} \\ 5 x+2 y=-8 \end{array}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ (Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed. Simplify your answer.) B. There is no solution.

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Problem 51710

Work out the value of $x^{n}$ when $x=5$ and $n=3$

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Problem 51711

Verify that the function is a solution of the differential equation. \begin{tabular}{|c|c|} \hline Function & Differential Equation \\ \hline $y=(-\cos (x)) \ln (|\sec (x)+\tan (x)|)$ & $y^{\prime \prime}+y=\tan (x)$ \\ \hline \end{tabular}
Given the function $y=(-\cos (x)) \ln (|\sec (x)+\tan (x)|)$ , find the following. $\begin{array}{l} y^{\prime}=\square \\ y^{\prime \prime}=\square \end{array}$

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Problem 51712

If $f(x)=\frac{2 x^{2}-1}{5 x+3}$ , then $f^{\prime}(-1)=$ (A) $-\frac{3}{2}$ (B) $-\frac{4}{5}$ (C) $\frac{3}{4}$ (D) $\frac{13}{4}$

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Problem 51713

Express as a single logarithmic expression. You do NOT need to expand exponents. Assume all expressions represent positive numbers. $\log _{6}(x+1)-\log _{6}(x+5)=\log _{6}(\square)$
Question Help: Video Written Example Submit Question

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Problem 51714

Express the following equations in logarithmic form: (a) $4^{4}=256$ is equivalent to the logarithmic equation: $\square$ (b) $10^{-4}=0.0001$ is equivalent to the logarithmic equation: $\square$

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Problem 51715

Suppose that $f(x, y)=1 x^{4}+1 y^{4}-1 x y$ then the minimum is $\square$

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Problem 51716

Find the absolute maximum and minimum of $f(x, y)=5 x+4 y$ within the domain $x^{2}+y^{2} \leq 25$ . Please show your answers to at least 4 decimal places. Enter DNE if the value does not exist.
1. Absolute minimum of $f(x, y)$ is $\square$
2. Absolute maximum of $f(x, y)$ is $\square$

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Problem 51717

$\log _{2}(x-1)=3$

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Problem 51718

Find the following product, and write the product in rectangular form, $\begin{array}{l} {\left[2\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)\right]\left[5\left(\cos 195^{\circ}+i \sin 195^{\circ}\right)\right]} \\ {\left[2\left(\cos 30^{\circ}+i \sin . \quad\right)\left(\cos 195^{\circ}+i \sin 195^{\circ}\right)\right]=} \end{array}$ $\square$ (Type your answer in the form $a+b i$ )

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Problem 51719

Ine radius of a circle is 6 in . Answer the parts below. Make sure that you use the correct units in your answers. If necessary, refer to the list of geometry formulas. (a) Find the exact area of the circle. Write your answer in terms of $\pi$ .
Exact area: $\square$ (b) Using the ALEKS calculator, approximate the area of the circle.
To do the approximation, use the $\pi$ button on the calculator, and round your answer to the nearest hundredth.
Approximate area: $\square$

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Problem 51720

Adding and Subtracting Polynomials: $\begin{array}{c} \left(2 x^{2}+3\right)+\left(3 x^{2}+1\right) \\ 5 x+4 \end{array}$

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Problem 51721

4. Find the radius of convergence and the interval of convergence of the power series $\sum_{n=0}^{\infty} \frac{(-1)^{n+1}}{\sqrt[3]{n^{2}+n+1}} x^{n}$

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Problem 51722

Determine the domain of the function $f(x) = \frac{1}{e^x - 1}$ .

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Problem 51723

$2 a-3[2 a-(4+3 b)]+4(b+3 a)$
Select one: a. $8 a+13 b+12$ b. $-a+13 b+12$ C. $8 a-5 b+12$ d. $-a+7 b-4$ e. none of these f. I Don't Know

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Problem 51724

Simplify. $\sqrt{-2}$

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Problem 51725

8. Find the radius of convergence and the interval of convergence of the power series $\sum_{n=1}^{\infty}(-1)^{n-1}\left(\frac{2^{n}}{n+\ln n}\right)(3 x-5)^{n}$

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Problem 51726

Hasil dari $\int \cos 2 x(\sin 2 x+3)^{2} d x$ adalah

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Problem 51727

Find the midpoint of the points $(-3,5)$ and $(5,9)$ .
Select one: a. $(2,14)$ b. $(4,7)$ c. $(-4,-2)$ d. $(1,7)$ e. none of these f. I Don't Know

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Problem 51728

Exemple 3: Ėve fait voler un cerf-volant qui est fixé au bout d'une corde de 50 m . Le soleil se trouve directement au-dessus de sa tête et la corde crée un angle de $\pi / 6$ par rapport au sol. Le vent souffle plus fort et le cerfvolant s'élève jusqu'à ce que la corde forme un angle de $\pi / 3$ par rapport au sol. Détermine l'expression en valeur exacte qui définit la distance parcourue par l'ombre du cerf-volant entre les deux positions.

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Problem 51729

11. Find the radius of convergence and the interval of convergence of the power series $\sum_{n=1}^{\infty} \frac{x^{2 n}}{2^{n} n}$

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Problem 51730

Consider the function $f(x)=\frac{x^{2}-25}{x(x-5)}$ a. Evaluate $\lim _{x \rightarrow \infty} f(x)$ and $\lim _{x \rightarrow-\infty} f(x)$ , and then identify the horizontal asymptotes. b. Find the vertical asymptotes. For each vertical asymptote $x=a$ , evaluate $\lim f(x)$ and $\lim f(x)$ . $x \rightarrow a^{-} \quad x \rightarrow a^{+}$ a. Evaluate $\lim _{x \rightarrow \infty} f(x)$ . Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. $\lim _{x \rightarrow \infty} \frac{x^{2}-25}{x(x-5)}=\square$ (Simplify your answer.) B. The limit does not exist and is neither $-\infty$ nor $\infty$ .

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Problem 51731

13. Let $\left(a_{n}\right)_{n=0}^{\infty}=\left(a_{0}, a_{1}, a_{2}, \ldots\right)$ be a sequence of real numbers satisfying $a_{n}=4 a_{n-1}-9(n-2)$ for every positive integer $n$ . If $a_{0}=0$ , then prove by mathematical induction that $a_{n}=2 \cdot 4^{n}+3 n-2$ for every nonnegative integer $n$ . (Nonnegative integers are $0,1,2,3, \ldots$ .)

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Problem 51732

If a student scores $78 \%, 74 \%$ , and $75 \%$ on their first 3 exams, what would they need to score on their 4th exam in order to have an exam average of exactly 80\%?
Select one: a. $93 \%$ b. $97 \%$ c. $95 \%$ d. $90 \%$ e. none of these f. IDon't Know

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Problem 51733

Solve the system of linear equations by substitution. $\begin{array}{l} 6 x-9=y \\ y=-3 x \end{array}$
The solution is $\square$ $\square$

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Problem 51734

Question 1 (1 point) Write the equation to the line that has these features: Slope $=6$ $y$ -intercept = -2

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Problem 51735

$\int 6 x(x+2)^{5} d x$

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Problem 51736

Find the grade point average. Assume that the grade point values are 4.00 for an A, 3.00 for a B, and so on. \begin{tabular}{|c|c|} \hline Grades & \# of credit hours \\ B & 3 \\ B & 5 \\ B & 5 \\ C & 4 \\ \hline \end{tabular}
The grade point average is $\square$ (Round to the nearest hundredth as needed.)

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Problem 51737

Evaluate the following determinant. $\left|\begin{array}{ccc} 0 & -6 & 5 \\ -2 & 5 & -4 \\ 1 & 3 & -2 \end{array}\right|$

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Problem 51738

28. Let $\mathcal{A}=\{(0,1,0),(1,2,3),(5,7,1)\}, \mathcal{B}=\{(0,1),(1,1)\}, \mathcal{C}=\{(2,1),(1,0)\}$ and let $\varphi: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ denote the linear mapping given by the following condition: $M(\varphi)_{\mathcal{A}}^{\mathcal{B}}=\left[\begin{array}{lll}1 & 3 & 2 \\ 2 & 4 & 3\end{array}\right]$ , Let $\psi: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ be a linear mapping given by the formula $\psi\left(\left(y_{1}, y_{2}\right)\right)=\left(y_{1}-y_{2}, y_{1}+y_{2}\right)$ . Find $M(\psi \circ \varphi)_{\mathcal{A}}^{\mathcal{C}}$ . Find a formula expressing $\psi \circ \varphi$ .

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Problem 51739

c. $(2-5 \sqrt{6})(6+\sqrt{8})$ $3 \sqrt{3}+6 \sqrt{3}-5 \sqrt{3}-\sqrt[3]{3}$ $2 \sqrt{3}$ $\sqrt{3}$ .
23 $\qquad$
3. Determine the value of $k$ such that $f(x)=3 x^{2}-12 x+7+k$ , has only one zel [3]

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Problem 51740

4. Determine if the triangles are similar. If they are similar, complete the similarity statement, identify the theorem used and the scale factor of small triangle to the big triangle. $\qquad$ yes, they are similar: $\triangle \mathrm{PQT} \sim \Delta$ $\qquad$ by $\qquad$
Or Scale factor $=$ $\qquad$ $\qquad$ no, they are not similar

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Problem 51741

The solution to the equation $2|-5 x-3|=10 x+14$ is

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Problem 51742

Exercises:
1. A homeowner wants to fence off a rectangular garden plot next to the street. The fend along the street costs $\$ 14$ per meter. The fencing along the other three sides costs $\$ 10$ pe meter. The total amount of money available for fencing material is $\$ 240$ . Find the dime of the garden of maximum area.
2. A rancher plans to enclose a rectangular field next to a road (there will be no fence alo

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Problem 51743

16) Solve for the value of $x$ . $x=1 \frac{2}{5}$ or 1.4 $x=5 \frac{3}{5}$ or 5.6 $x=2 \frac{4}{5}$ or 2.8 $x=1$ $x=4 \frac{4}{5}$ or 4.8
17) Using the value of $x$ from question 16 , find the measure of $\angle A$ . $m \angle A=130^{d} e g$ $m \angle A=75^{d} \mathrm{eg}$ $m \angle A=65^{d} \mathrm{eg}$ $m \angle A=110^{\prime} \mathrm{eg}$ $\mathrm{m} \angle A=150^{\mathrm{d}} \mathrm{eg}$

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Problem 51744

$(E-500)(400)=927000$

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Problem 51745

Copy and complete the equation of line G below. $y=-x+-$

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Problem 51746

\begin{tabular}{|c|c|} \hline Caramel & 350 \\ \hline Peppermint & 200 \\ \hline Cinnamon & 150 \\ \hline Chocolate & 350 \\ \hline Butterscotch & 250 \\ \hline \end{tabular}
Complete parts (a) through (c) below. Assume that any candy mentioned comes from the box. (a) Write the following biconditional statement as a conditional statement and its converse.
Biconditional statement: A candy is caramel if and only if the candy has 350 calories.
Conditional statement: If (Choose one) $\square$ then $\square$ (Choose one)
Converse: If $\square$ (Choose one) then $\square$ (Choose one) (b) Use the table to determine the truth value of the conditional statement and its converse.
The conditional statement is $\square$ (Choose one)
The converse is (Choose one) $\mathbf{V}$ $\square$ (c) Determine the truth value of the biconditional statement.
The biconditional statement is (Choose one) V

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Problem 51747

A rectangular pool 24 meters by 16 meters is surrounded by a walkway.of width $x$ meters. At what value of $x$ will the area of the walkway equal the area of the pool? $\square$

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Problem 51748

$M=\left[\left(\frac{-2}{3}\right)^{6} \times\left(\frac{2}{-3}\right)^{4}\right] \div\left(\frac{2}{3}\right)^{8}$
1. Verify that $\mathrm{M}=\frac{4}{9}$ .

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Problem 51749

20) Classify the triangle by congruence. isosceles scalene adjacent equilateral vertical 21) Classify the triangle by angle measure. complementary right acute supplementary

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Problem 51750

$=\frac{1.33 \cdot 10^{24} \mathrm{ats}}{6.02 \cdot 10^{23}}$

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Problem 51751

Part 6 of 6 Points: $0 \%$ , 9 of 10 points Save
Color blindness is an inherited characteristic that is more common in males than in females. If M represents male and C represents red-green color blindness, using the relative frequencies of the incidences of males and red-green color blindness as probabilities results in the values below. Complete parts (a) through ( $f$ ) below. $P(C)=0.035, P(M \cap C)=0.033, P(M \cup C)=0.487$ (a) Find $P\left(C^{\prime}\right)$ . $P\left(C^{\prime}\right)=0.965$ (Type an integer or a decimal.) (b) Find $P(M)$ . $P(M)=0.485$ (Type an integer or a decimal.) (c) Find $P\left(M^{\prime}\right)$ . $P\left(M^{\prime}\right)=0.515$ (Type an integer or a decimal.) (d) Find $P\left(M^{\prime} \cap C^{\prime}\right)$ . $P\left(M^{\prime} \cap C^{\prime}\right)=0.513$ (Type an integer or a decimal.) (e) Find $P\left(C \cap M^{\prime}\right)$ . $P\left(C \cap M^{\prime}\right)=0.002$ (Type an integer or a decimal.) (f) Find $P\left(C \cup M^{\prime}\right)$ . $P\left(C \cup M^{\prime}\right)=\square_{4}$ (Type an integer or a decimal.)

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Problem 51752

Zoom a) What is the $y$ -intercept of this line? b) What is the gradient of this line?

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Problem 51753

$y=-x+3$ $b=3$
Use the given information to write the equation of each line in the form $y=m x+b$ . slope $=-3$ and $y$ -intercept $=4$ b.) $m=-5$ and $b=0$ $y=4-$ parallel to $y=6 x-1$ and $y$ -intercept $=-3$

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Problem 51754

Zoom a) What is the $y$ -intercept of this line? b) What is the gradient of this line?

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Problem 51755

Find the inverse of the function $f(x) = 4(2)^{3x} - 5$ .

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Problem 51756

Zoom a) What is the $y$ -intercept of this line? b) What is the gradient of this line?

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Problem 51757

Simplify the radical expression. $\sqrt{625 x^{15}}$
Write your answer in the form $\mathrm{A}, \sqrt{\mathrm{B}}$ , or $\mathrm{A} \sqrt{\mathrm{B}}$ , where A and B are constants or expressions in x . Use at most one radical in your answer, and at most one absolute value symbol in your expression for A . $\square$ Submit

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Problem 51758

A straight line is shown on the coordinate grid below.

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Problem 51759

A 14,000 N car starts from rest and rolls down a hill from a height of 10.0 m (see figure). It then moves across a level surface and collides with a light spring-loaded guardrail. (a) Neglecting any losses due to friction, and ignoring the rotational kinetic energy of the wheels, find the maximum distance the spring is compressed. Assume a spring constant of $1.4 \times 10^{6} \mathrm{~N} / \mathrm{m}$ . $\square$ m (b) Calculate the magnitude of the maximum acceleration of the car after contact with the spring, assuming no frictional losses. $\qquad$ $\mathrm{m} / \mathrm{s}^{2}$ (c) If the spring is compressed by only 0.30 m , find the change in the mechanical energy due to friction. $\square$ J

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Problem 51760

A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 281 vinyl gloves, $70 \%$ leaked viruses. Among 281 latex gloves, $6 \%$ leaked viruses. Using the accompanying display of the technology results, and using a 0.10 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1.
What are the null and alternative hypotheses? A. $H_{0}: P_{1}<P_{2}$ $H_{1}: p_{1}=p_{2}$ D. $H_{0}: p_{1}=p_{2}$ $H_{1}: p_{1} \neq p_{2}$ B. $H_{0}: p_{1}=p_{2}$ C. $H_{0}: p_{1}>p_{2}$ $H_{1}: p_{1}>p_{2}$ $H_{1}: p_{1}=p_{2}$ E. $H_{0}: p_{1}=p_{2}$ F. $H_{0}: p_{1} \neq p_{2}$ $H_{1}: p_{1}<p_{2}$
Identify the test statistic. 15.64 (Round to two decimal places as needed.) Identify the P -value. $\square$ (Round to three decimal places as needed.)

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Problem 51761

$P(\text{multiple of 4}) = \square$
Consider a spinner with sections numbered from 1 to 12. Calculate the probability that the spinner lands on a number that is a multiple of 4. Express your answer as a reduced fraction.

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Problem 51762

Simplify the expression: $\frac{2 x^{2} y^{4} \cdot 4 x^{2} y^{4} \cdot 3 x}{3 x^{-3} y^{2}}$

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Problem 51763

Questions 11-12 refer to the following: A company can sell all the units it can produce of either Product A or Product B. Product A has a unit contribution margin of $\$ 16$ and takes two machine hours to make and Product $B$ has a unit contribution margin of $\$ 30$ and takes three machine hours to make. Assume that there ar 1,200 machine hours available to manufacture a product.
11. Contribution margin will be A. $\$ 1,800$ more if only Product $A$ is made. B. $\$ 1,800$ more if only Product B is made.
34C. $\$ 2,400$ more if only Product $A$ is made (1.) $\$ 2,400$ more if only Product B is made. $\begin{array}{ll}\frac{A}{16} & \frac{B}{2} \\ \frac{2}{8} & \frac{3}{10}\end{array}$
12. If market demand is limited to 300 units on product $A$ and 200 on product then the optimal combination of $A \& B$ respectively is: A. 150 and 200 1200 B. 300 and 200 C. 300 and 100 $30 \times 1 \times 2=800$ D. none of these

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Problem 51764

2. Solve the following quadratic functions by factoring. If needed, write answers in fraction form, using the " $/ /$ key as the fraction bar. $3 x^{2}+11 x+10=0$
The smaller of the two answers is: $\qquad$
The larger of the two answers is: $\qquad$

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Problem 51765

Find $f^{-1}(x)$ for $f(x)=\frac{1}{x^{3}}$ and state whether or not it is a function. a. $f^{-1}(x)=\frac{1^{3}}{\sqrt{x}}$ ; function c. $f^{-1}(x)=\frac{1}{\sqrt[3]{x}} ;$ function b. $f^{-1}(x)=\frac{-1}{\sqrt[3]{x}}$ ; not a function d. $f^{-1}(x)=\frac{1}{\sqrt[3]{x}}$ ; not a function

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Problem 51766

$=\frac{3.22 \cdot 10^{24}}{6.02 \cdot 10^{23}}=$

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Problem 51767

Given $g(x)=\frac{3}{x^{2}+2 x}$ find $g^{-1}(x)$ . a. $g^{-1}(x)=-1 \pm \sqrt{\frac{3}{x}+1}$ c. $g^{-1}(x)=1 \pm \sqrt{\frac{3}{x}-1}$ b. $g^{-1}(x)=-1 \pm \sqrt{\frac{\pi}{3}+1}$ d $g^{-1}(x)=-1 \pm \sqrt{\frac{3}{x^{2}}+1}$

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Problem 51768

Find the measure of each marked angle. $(8 x-36)^{\circ}=$ $\square$ ${ }^{\circ}$ (Type integers or decimals.) $(6 x)^{\circ}=\square^{\circ}$

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Problem 51769

$f(x)=\frac{3 x}{1-2 x}, \quad f^{-1}(x)=?$

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Problem 51770

BI
Evaluate the following. $1.5^{2} \div 5+0.8(61.7)$

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Problem 51771

25. В прямоугольном треугольнике ABC гипотенуза $\mathrm{AB}=24$ , а площадь равна 72. Найди меньший острый угол этого треугольника. Ответ запиши в градусах.

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Problem 51772

According to TrueCar.com, the July 2016 market average price for a 2013 Honda Civic Coupe in Bellflower, CA was $\bar{x}=\$ 14,995$ . Suppose that the standard deviation for the price was $s=\$ 1,116$ , based on a sample of 144 cars. a. Construct and interpret a 90\% confidence interval for the market average price for all 2013 Honda Civic Coupes in Bellflower, CA. Use PMACC.

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Problem 51773

Use the sample data and confidence level given below to complete parts (a) through (d).
A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4571 patients treated with the drug, 112 developed the adverse reaction of nausea. Construct a $90 \%$ confidence interval for the proportion of adverse reactions. a) Find the best point estimate of the population proportion $p$ . $\square$ (Round to three decimal places as needed.) b) Identify the value of the margin of error E . $\mathrm{E}=\square$ (Round to three decimal places as needed.) c) Construct the confidence interval. $\square$ $\square$ $<p<$ (Round to three decimal places as needed.)

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Problem 51774

Question 5 of 12 (1 point) I Question Attempt: 1 of 3 $\checkmark 1$ $\times 2$ 3 4 5 6 7 8 9 10 11
A file that is 287 megabytes is being downloaded. If the download is $16.9 \%$ complete, how many megabytes have been downloaded? Round your answer to the nearest tenth. $\square$ megabytes

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Problem 51775

A study was conducted to determine the proportion of people who dream in black and white instead of color. Anong 324 people over the age of 55, 66 dream in black and white, and among 293 people under the age of 25,16 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 65 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test.
Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25 . What are the null and altemative hypotheses for the hypothesis test? A. $H_{0}: p_{1}=p_{2}$ B. $H_{0}: p_{1} \leq p_{2}$ C. $H_{0}: p_{1} \geq p_{2}$ $H_{1}: p_{1}<p_{2}$ $H_{1}: p_{1} \neq p_{2}$ $H_{1}: p_{1} \neq p_{2}$ D. $H_{0}: p_{1} \neq p_{2}$ E. $H_{0}: p_{1}=p_{2}$ F. $H_{0}: p_{1}=p_{2}$ $H_{1}: p_{1}=p_{2}$ $H_{1}: p_{1}>p_{2}$ $\begin{array}{l} H_{0}: p_{1}=p_{2} \\ H_{1}: p_{1} \neq p_{2} \end{array}$

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Problem 51776

Write the ritio as a fraction in lowest terms. 32 minutes to 4 hours
The ratio is $\square$ .

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Problem 51777

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 308 people over the age of 55, 66 dream in black and white, and among 286 people under the age of 25,20 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test.
Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25 . What are the null and alternative hypotheses for the hypothesis test? A. $H_{0}: p_{1}=p_{2}$ B. $H_{0}: p_{1} \leqslant p_{2}$ C. $H_{0}: p_{1}=p_{2}$ $H_{1}: p_{1}<p_{2}$ $H_{1}: p_{1} \neq p_{2}$ $H_{1}: p_{1}>p_{2}$
$\text { D. } \begin{array}{l} H_{0}: p_{1} \neq p_{2} \\ H_{1}: p_{1}=p_{2} \end{array}$ E. $H_{0}: p_{1}=p_{2}$ F. $H_{0}: p_{1} \geq p_{2}$ $H_{1}: p_{1} \neq p_{2}$ $H_{1}: p_{1} \neq p_{2}$
Identify the test statistic. $\mathrm{z}=\square$ (Round to two decimal places as needed.)

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Problem 51778

A supermarket was surveyed to find prices charged in various sizes. Find the best buy (based on the price per unit) for the item. \begin{tabular}{c|c} \multicolumn{2}{c}{ SALAD DRESSING } \\ Size & Price \\ \hline 16 oz & $\$ 1.57$ \\ \hline 32 oz & $\$ 3.87$ \\ \hline 48 oz & $\$ 7.15$ \\ \hline \end{tabular}
The best buy is the $\square$ -ounce size.

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Problem 51779

$\int \sin ^{3} x \cos ^{2} x d x=$

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Problem 51780

Solve the following problem. $35 \%$ of what number is 56 ?
35\% of $\square$ is 56. (Type an integer or a decimal.)

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Problem 51781

\begin{align} \text{We have the following data extracted from StatKey:} \\ \text{Original Sample:} \\ n &= 200, \\ \text{mean} &= 98.925, \\ \text{median} &= 96, \\ \text{stdev} &= 26.83. \\ \text{Randomization Sample:} \\ n &= 200, \\ \text{mean} &= 76.015, \\ \text{median} &= 73.075, \\ \text{stdev} &= 28.062. \\ \text{Null hypothesis: } \mu &= 72. \\ \text{Construct a 95\% confidence interval for the population mean.} \end{align}

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Problem 51782

Write the expression as a complex number in standard form: $(-2+5 i)(-1+4 i)$ $15-18 i$ $-18-13 i$ $-13-18 i$ $-18+13 i$

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Problem 51783

The cuboid below has two square faces with side length 4 cm .
Work out the volume of the cuboid. Give your answer in $\mathrm{cm}^{3}$ .

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Problem 51784

the ExpertTA.com Student: cristian.alvarez@ctstate.edu My Account Class Management I Help EXPERT Problem Status
HW7 Angular Motion Begin Date: 11/4/2024 12:01:00 AM Due Date: 11/22/2024 11:59:00 PM End Date: 12/13/2024 11:59:00 PM Problem 4: ( $25 \%$ of Assignment Value) A bowling ball of mass $m=2.4 \mathrm{~kg}$ drops from a height $h=14.4 \mathrm{~m}$ . A semi-circular tube of radius $r=6.2 \mathrm{~m}$ rests centered on a scale. Alvarez, Cristian - cristian.alvarez@ctstate.edu @theexpertta.com - tracking id: 8C84-EB-49-43-A913-26821. In accordance with Expert TA's Terms of Service, copying this information to any solutions sharing website is strictly forbidden. Doing so may result in termination of your Expert TA Account. Ctheexpertta.com
Part (a) Write an expression for the reading of the scale when the bowling ball is at its lowest point, in terms of the variables in the problem statement and $g$ . $W=$ $\square$ g 7 8 9 HOME 4 5 6 $\square$ 1 2 3 $\square$ 0 . END Grade Summary Deductions Potential Late Work \% Late Potential $10 \% \%$ $100 \%$ $78 \%$ $78 \%$ $\mathbf{7 8 \%}$ h m Submissions Attempt(s) Remaining: $5 \%$ Deduction per Attempt detailed view r - backspace DiE clear

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Problem 51785

lass Management I Help Student: cristian.alvarez@ctsta
W7 Angular Motion Begin Date: 11/4/2024 12:01:00 AM Due Date: 11/22/2024 11:59:00 PM End Date: 12/13/2024 11:59:00 PM roblem 1: (25\% of Assignment Value) At its lowest setting a centrifuge rotates with an angular speed of $\omega_{1}=250 \mathrm{rad} / \mathrm{s}$ . When it is switched to the next higher setting it takes $t=12.5 \mathrm{~s}$ to uniformly accelera 0 its final angular speed $\omega_{2}=650 \mathrm{rad} / \mathrm{s}$ . Alvarez, Cristian - cristian.alvarez@ctstate.edu @theex Irtta.com - tracking id: 8C84-EB-49-43-A913-26821. In accordance with Expert TA's Terms of Service. copying this information to any solutions sharing website is strictly forbidden. Doing so may result in termination of your Expert TA Account.
Part (a) Calculate the angular acceleration of the centrifuge $\alpha_{1}$ in $\mathrm{rad} / \mathrm{s}^{2}$ over the time interval $t$ . $\alpha_{1}=$ $\square$

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Problem 51786

\begin{tabular}{|l|l|} \hline \begin{tabular}{l} WIP, beginning inventory \\ (April 1) \end{tabular} & \begin{tabular}{l} 1,500 units \\ (100\% complete for DM, $80 \%$ for \\ conversion costs) \end{tabular} \\ \hline Started during April & 3,700 \\ \hline \begin{tabular}{l} Completed and TO during \\ April \end{tabular} & 3800 \\ \hline WIP, ending inventory & \begin{tabular}{l} 1,400 \\ \\ \end{tabular} \\ \hline \end{tabular}
Assume that the company uses FIFO method, what are the total equivalent units with respect to conversion costs? (DON"T USE THE DOLLAR SIGN OR COMMAS)
Answer. 3230

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Problem 51787

Luas daerah yang dibatasi oleh kurva $y=\sin 2 x$ dan sumbu $X$ pada selang $0 \leq x \leq \frac{\pi}{3}$ adalah . . . .

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Problem 51788

Solve the equation: $\sqrt{2}(3 x-2 \sqrt{ } 2)=4 x+\sqrt{2}$
Give your answer in the form $\mathrm{p} \sqrt{2}+\mathrm{q}$ , where p and q are simplified fractions.

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Problem 51789

A random sample of 11 employees produced the following data, where $x$ is the number of years of experience, and $y$ is the salary (in thousands of dollars). The data are presented below in the table of values. \begin{tabular}{cc} $x$ & $y$ \\ 12 & 38 \\ 15 & 30 \\ 17 & 39 \\ 19 & 35 \\ 20 & 36 \\ 23 & 58 \\ 25 & 42 \\ 27 & 62 \\ 29 & 65 \\ 30 & 63 \\ 32 & 51 \end{tabular}
What is the value of the intercept of the regression line, $b$ , rounded to one decimal place?
Provide your answer below:

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Problem 51790

Status Complete Partial
Complete @theexperta.com - tracking id: 8C84-EB-49-43-A913-26821. In accordance with Expert TA's Terms of Service. copying this information to any solutions sharing may result in termination of your Expert TA Account. - Part (a)
What is the period of rotation of the Earth in seconds? $t=8.640 \times 10^{4}$ $\checkmark$ Correct! Part (b) What is the angular velocity of the Earth in rad/s? $\omega=$ $\square$

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Problem 51791

$44 \%$ of a number is equal to $51 \%$ of 660.
What is the number? Give any decima answers to 1 d.p.

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Problem 51792

Use the function below to answer the following questions. $p(x)=4^{x-4}-2$ (a) Use transformations of the graph of $y=4^{x}$ to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.

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Problem 51793

5 a) Bestimmen Sie jeweils eine Parameterform der $x_{1} x_{2}$ -Ebene, der $x_{1} x_{3}$ -Ebene und der $x_{2} x_{3}$ -Ebene (Fig. 1). b) Geben Sie zu der $x_{1} x_{2}$ -Ebene, der $x_{1} x_{3}$ -Ebene und der $x_{2} x_{3}$ -Ebene jeweils eine weitere Parametergleichung an. c) Erläutern Sie, wie man an einer Parametergleichung erkennen kann, ob sie eine der drei Koordinatenebenen beschreibt. - Test

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Problem 51794

40 Trapezold EFGH will be reflected across the $y$ -axis. What will be the resulting coordinate of Point $H^{\prime}$ ? wucan earn 5 coins $(5,-4)$ $(-4,-3)$ $(-5,-2)$ $(5,-2)$

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Problem 51795

9) $\sqrt{175 x^{4} y^{2} z^{2}}$ A) $10 y z \sqrt{x z}$ B) $5 x^{2} y z \sqrt{7}$ C) $2 x z \sqrt{2 x y}$ D) $12 x y z \sqrt{2 z}$

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Problem 51796

4. Assuming that $\operatorname{gcd}(a, b)=1$ , prove the following: (b) $\operatorname{gcd}(2 a+b, a+2 b)=1$ or 3 .

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Problem 51797

Solve using the substitution method. Use a graphing calcu lator to check your answer. 17. $\begin{array}{l} \text { 17. } x+y=9 \\ 2 x-3 y=-2 \\ \text { 19. } x-2 y=7 \\ x=y+4 \end{array}$ 21. $\begin{array}{l} y=2 x-6 \\ 5 x-3 y=16 \end{array}$ 23. $\begin{array}{l} x+y=3 \\ y=4-x \end{array}$ 25. $\begin{array}{l} x-5 y=4 \\ y=7-2 x \end{array}$ 27. $\begin{aligned} x+2 y & =2 \\ 4 x+4 y & =5 \end{aligned}$ 29. $\begin{array}{l} 3 x-y=5 \\ 3 y=9 x-15 \end{array}$ 18. $\begin{array}{r} 3 x-y=5 \\ x+y=\frac{1}{2} \end{array}$ 20. $\begin{array}{l} x+4 y=6 \\ x=-3 y+3 \end{array}$ 22. $\begin{array}{l} 3 x+5 y=2 \\ 2 x-y=-3 \end{array}$ 24. $\begin{array}{l} x-2 y=3 \\ 2 x=4 y+6 \end{array}$ 26. $\begin{array}{c} 5 x+3 y=-1 \\ x+y=1 \end{array}$ 28. $\begin{array}{l} 2 x-y=2 \\ 4 x+y=3 \end{array}$ 30. $\begin{array}{l} 2 x-y=7 \\ y=2 x-5 \end{array}$

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Problem 51798

Graph the following piecewise functions. 1.) $f(x)=\left\{\begin{array}{c}x+2 \text { if } x \leq 0 \\ 2 x-3 \text { if } x>0\end{array}\right.$

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Problem 51799

Evaluate the polynomial function using Synthetic Division $\begin{array}{c} g(x)==-2 x^{4}-x^{3}+4 x-5 \\ \text { when } \mathrm{x}=-1 \end{array}$

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Problem 51800

Data on the weights (b) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. \begin{tabular}{|c|c|c|} \hline & Diet & Regular \\ \hline $\boldsymbol{\mu}$ & $\mu_{1}$ & $\mu_{2}$ \\ \hline $\mathbf{n}$ & 32 & 32 \\ \hline $\overline{\mathbf{x}}$ & 0.79654 lb & 0.81963 lb \\ \hline $\mathbf{s}$ & 0.00432 lb & 0.00754 lb \\ \hline \end{tabular}
The test statistic, t , is -15.03 . (Round to two decimal places as needed.) The P-value is 0.000 . (Round to three decimal places as needed.) State the conclusion for the test. A. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. B. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. C. Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda. D. Reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have - mean weights that are lower than the mean weight for the regular soda.

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Math

Problem 51701

Solve. 4x=−16\sqrt{4 x}=-164x​=−16

Problem 51702

(x+7)(x−11)(x+7)(x-11)(x+7)(x−11) \qquadSolve each equation by splitting the middle term. (7) 3x2=−16x−213 x^{2}=-16 x-213x2=−16x−21 (8) 3x2+14x−49=03 x^{2}+14 x-49=03x2+14x−49=0

Problem 51703

I'm sorry, but I can't assist with that request.

Problem 51704

2x2+17x+212 x^{2}+17 x+212x2+17x+21 by splitting the middle term.

Problem 51705

FM2PMultiplying Two Binomials - FOIL Find each product {\left\{\right.{ remember: (a+b)2=(a+b)(a+b)}\left.(\mathrm{a}+\mathrm{b})^{2}=(\mathrm{a}+\mathrm{b})(\mathrm{a}+\mathrm{b})\right\}(a+b)2=(a+b)(a+b)}. (x+9)2(x+9)^{2}(x+9)2 b) (x+10)2(x+10)^{2}(x+10)2 c) (x−7)2(x-7)^{2}(x−7)2

Problem 51706

Find the domain of the function f(x)=4−∣2−32x∣ f(x) = \sqrt{4 - \left|2 - \frac{3}{2x}\right|} f(x)=4−∣∣​2−2x3​∣∣​​.

Problem 51707

Solve. −8x−17=−4x−57\sqrt[7]{-8 x-1}=\sqrt[7]{-4 x-5}7−8x−1​=7−4x−5​

Problem 51708

Problem 51709

Problem 51710

Work out the value of xnx^{n}xn when x=5x=5x=5 and n=3n=3n=3

Problem 51711

Problem 51712

If f(x)=2x2−15x+3f(x)=\frac{2 x^{2}-1}{5 x+3}f(x)=5x+32x2−1​, then f′(−1)=f^{\prime}(-1)=f′(−1)= (A) −32-\frac{3}{2}−23​ (B) −45-\frac{4}{5}−54​ (C) 34\frac{3}{4}43​ (D) 134\frac{13}{4}413​

Problem 51713

Problem 51714

Express the following equations in logarithmic form: (a) 44=2564^{4}=25644=256 is equivalent to the logarithmic equation: □\square□ (b) 10−4=0.000110^{-4}=0.000110−4=0.0001 is equivalent to the logarithmic equation: □\square□

Problem 51715

Suppose that f(x,y)=1x4+1y4−1xyf(x, y)=1 x^{4}+1 y^{4}-1 x yf(x,y)=1x4+1y4−1xy then the minimum is □\square□

Problem 51716

Problem 51717

log⁡2(x−1)=3\log _{2}(x-1)=3log2​(x−1)=3

Problem 51718

Problem 51719

Problem 51720

Adding and Subtracting Polynomials: (2x2+3)+(3x2+1)5x+4\begin{array}{c} \left(2 x^{2}+3\right)+\left(3 x^{2}+1\right) \\ 5 x+4 \end{array}(2x2+3)+(3x2+1)5x+4​

Problem 51721

4. Find the radius of convergence and the interval of convergence of the power series ∑n=0∞(−1)n+1n2+n+13xn\sum_{n=0}^{\infty} \frac{(-1)^{n+1}}{\sqrt[3]{n^{2}+n+1}} x^{n}n=0∑∞​3n2+n+1​(−1)n+1​xn

Problem 51722

Determine the domain of the function f(x)=1ex−1 f(x) = \frac{1}{e^x - 1} f(x)=ex−11​.

Problem 51723

2a−3[2a−(4+3b)]+4(b+3a)2 a-3[2 a-(4+3 b)]+4(b+3 a)2a−3[2a−(4+3b)]+4(b+3a)Select one: a. 8a+13b+128 a+13 b+128a+13b+12 b. −a+13b+12-a+13 b+12−a+13b+12 C. 8a−5b+128 a-5 b+128a−5b+12 d. −a+7b−4-a+7 b-4−a+7b−4 e. none of these f. I Don't Know

Problem 51724

Simplify. −2\sqrt{-2}−2​

Problem 51725

8. Find the radius of convergence and the interval of convergence of the power series ∑n=1∞(−1)n−1(2nn+ln⁡n)(3x−5)n\sum_{n=1}^{\infty}(-1)^{n-1}\left(\frac{2^{n}}{n+\ln n}\right)(3 x-5)^{n}n=1∑∞​(−1)n−1(n+lnn2n​)(3x−5)n

Problem 51726

Hasil dari ∫cos⁡2x(sin⁡2x+3)2dx\int \cos 2 x(\sin 2 x+3)^{2} d x∫cos2x(sin2x+3)2dx adalah

Problem 51727

Find the midpoint of the points (−3,5)(-3,5)(−3,5) and (5,9)(5,9)(5,9).Select one: a. (2,14)(2,14)(2,14) b. (4,7)(4,7)(4,7) c. (−4,−2)(-4,-2)(−4,−2) d. (1,7)(1,7)(1,7) e. none of these f. I Don't Know

Problem 51728

Problem 51729

11. Find the radius of convergence and the interval of convergence of the power series ∑n=1∞x2n2nn\sum_{n=1}^{\infty} \frac{x^{2 n}}{2^{n} n}n=1∑∞​2nnx2n​

Problem 51730

Problem 51731

Problem 51732

If a student scores 78%,74%78 \%, 74 \%78%,74%, and 75%75 \%75% on their first 3 exams, what would they need to score on their 4th exam in order to have an exam average of exactly 80\%?Select one: a. 93%93 \%93% b. 97%97 \%97% c. 95%95 \%95% d. 90%90 \%90% e. none of these f. IDon't Know

Problem 51733

Solve the system of linear equations by substitution. 6x−9=yy=−3x\begin{array}{l} 6 x-9=y \\ y=-3 x \end{array}6x−9=yy=−3x​The solution is □\square□ □\square□

Problem 51734

Question 1 (1 point) Write the equation to the line that has these features: Slope =6=6=6 yyy-intercept = -2

Problem 51735

∫6x(x+2)5dx\int 6 x(x+2)^{5} d x∫6x(x+2)5dx

Problem 51736

Problem 51737

Evaluate the following determinant. ∣0−65−25−413−2∣\left|\begin{array}{ccc} 0 & -6 & 5 \\ -2 & 5 & -4 \\ 1 & 3 & -2 \end{array}\right|∣∣​0−21​−653​5−4−2​∣∣​

Problem 51738

Problem 51739

Problem 51740

Problem 51741

The solution to the equation 2∣−5x−3∣=10x+142|-5 x-3|=10 x+142∣−5x−3∣=10x+14 is

Problem 51742

Problem 51743

Problem 51744

(E−500)(400)=927000(E-500)(400)=927000(E−500)(400)=927000

Problem 51745

Copy and complete the equation of line G below. y=−x+−y=-x+-y=−x+−

Problem 51746

Problem 51747

A rectangular pool 24 meters by 16 meters is surrounded by a walkway.of width xxx meters. At what value of xxx will the area of the walkway equal the area of the pool? □\square□

Problem 51748

M=[(−23)6×(2−3)4]÷(23)8M=\left[\left(\frac{-2}{3}\right)^{6} \times\left(\frac{2}{-3}\right)^{4}\right] \div\left(\frac{2}{3}\right)^{8}M=[(3−2​)6×(−32​)4]÷(32​)81. Verify that M=49\mathrm{M}=\frac{4}{9}M=94​.

Solve. $\sqrt{4 x}=-16$

$(x+7)(x-11)$ $\qquad$
Solve each equation by splitting the middle term. (7) $3 x^{2}=-16 x-21$ (8) $3 x^{2}+14 x-49=0$

$2 x^{2}+17 x+21$ by splitting the middle term.

FM2P
Multiplying Two Binomials - FOIL Find each product $\left\{\right.$ remember: $\left.(\mathrm{a}+\mathrm{b})^{2}=(\mathrm{a}+\mathrm{b})(\mathrm{a}+\mathrm{b})\right\}$ . $(x+9)^{2}$ b) $(x+10)^{2}$ c) $(x-7)^{2}$

Find the domain of the function $f(x) = \sqrt{4 - \left|2 - \frac{3}{2x}\right|}$ .

Solve. $\sqrt[7]{-8 x-1}=\sqrt[7]{-4 x-5}$

Work out the value of $x^{n}$ when $x=5$ and $n=3$

If $f(x)=\frac{2 x^{2}-1}{5 x+3}$ , then $f^{\prime}(-1)=$ (A) $-\frac{3}{2}$ (B) $-\frac{4}{5}$ (C) $\frac{3}{4}$ (D) $\frac{13}{4}$

Express the following equations in logarithmic form: (a) $4^{4}=256$ is equivalent to the logarithmic equation: $\square$ (b) $10^{-4}=0.0001$ is equivalent to the logarithmic equation: $\square$

Suppose that $f(x, y)=1 x^{4}+1 y^{4}-1 x y$ then the minimum is $\square$

$\log _{2}(x-1)=3$

Adding and Subtracting Polynomials: $\begin{array}{c} \left(2 x^{2}+3\right)+\left(3 x^{2}+1\right) \\ 5 x+4 \end{array}$

4. Find the radius of convergence and the interval of convergence of the power series $\sum_{n=0}^{\infty} \frac{(-1)^{n+1}}{\sqrt[3]{n^{2}+n+1}} x^{n}$

Determine the domain of the function $f(x) = \frac{1}{e^x - 1}$ .

$2 a-3[2 a-(4+3 b)]+4(b+3 a)$
Select one: a. $8 a+13 b+12$ b. $-a+13 b+12$ C. $8 a-5 b+12$ d. $-a+7 b-4$ e. none of these f. I Don't Know

Simplify. $\sqrt{-2}$

8. Find the radius of convergence and the interval of convergence of the power series $\sum_{n=1}^{\infty}(-1)^{n-1}\left(\frac{2^{n}}{n+\ln n}\right)(3 x-5)^{n}$

Hasil dari $\int \cos 2 x(\sin 2 x+3)^{2} d x$ adalah

Find the midpoint of the points $(-3,5)$ and $(5,9)$ .
Select one: a. $(2,14)$ b. $(4,7)$ c. $(-4,-2)$ d. $(1,7)$ e. none of these f. I Don't Know

11. Find the radius of convergence and the interval of convergence of the power series $\sum_{n=1}^{\infty} \frac{x^{2 n}}{2^{n} n}$

If a student scores $78 \%, 74 \%$ , and $75 \%$ on their first 3 exams, what would they need to score on their 4th exam in order to have an exam average of exactly 80\%?
Select one: a. $93 \%$ b. $97 \%$ c. $95 \%$ d. $90 \%$ e. none of these f. IDon't Know

Solve the system of linear equations by substitution. $\begin{array}{l} 6 x-9=y \\ y=-3 x \end{array}$
The solution is $\square$ $\square$

Question 1 (1 point) Write the equation to the line that has these features: Slope $=6$ $y$ -intercept = -2

$\int 6 x(x+2)^{5} d x$

Evaluate the following determinant. $\left|\begin{array}{ccc} 0 & -6 & 5 \\ -2 & 5 & -4 \\ 1 & 3 & -2 \end{array}\right|$

The solution to the equation $2|-5 x-3|=10 x+14$ is

$(E-500)(400)=927000$

Copy and complete the equation of line G below. $y=-x+-$

A rectangular pool 24 meters by 16 meters is surrounded by a walkway.of width $x$ meters. At what value of $x$ will the area of the walkway equal the area of the pool? $\square$

$M=\left[\left(\frac{-2}{3}\right)^{6} \times\left(\frac{2}{-3}\right)^{4}\right] \div\left(\frac{2}{3}\right)^{8}$
1. Verify that $\mathrm{M}=\frac{4}{9}$ .

$=\frac{1.33 \cdot 10^{24} \mathrm{ats}}{6.02 \cdot 10^{23}}$

Zoom a) What is the $y$ -intercept of this line? b) What is the gradient of this line?

$y=-x+3$ $b=3$
Use the given information to write the equation of each line in the form $y=m x+b$ . slope $=-3$ and $y$ -intercept $=4$ b.) $m=-5$ and $b=0$ $y=4-$ parallel to $y=6 x-1$ and $y$ -intercept $=-3$

Zoom a) What is the $y$ -intercept of this line? b) What is the gradient of this line?

Find the inverse of the function $f(x) = 4(2)^{3x} - 5$ .

Zoom a) What is the $y$ -intercept of this line? b) What is the gradient of this line?

$P(\text{multiple of 4}) = \square$
Consider a spinner with sections numbered from 1 to 12. Calculate the probability that the spinner lands on a number that is a multiple of 4. Express your answer as a reduced fraction.

Simplify the expression: $\frac{2 x^{2} y^{4} \cdot 4 x^{2} y^{4} \cdot 3 x}{3 x^{-3} y^{2}}$

2. Solve the following quadratic functions by factoring. If needed, write answers in fraction form, using the " $/ /$ key as the fraction bar. $3 x^{2}+11 x+10=0$
The smaller of the two answers is: $\qquad$
The larger of the two answers is: $\qquad$

$=\frac{3.22 \cdot 10^{24}}{6.02 \cdot 10^{23}}=$

Find the measure of each marked angle. $(8 x-36)^{\circ}=$ $\square$ ${ }^{\circ}$ (Type integers or decimals.) $(6 x)^{\circ}=\square^{\circ}$

$f(x)=\frac{3 x}{1-2 x}, \quad f^{-1}(x)=?$

BI
Evaluate the following. $1.5^{2} \div 5+0.8(61.7)$

25. В прямоугольном треугольнике ABC гипотенуза $\mathrm{AB}=24$ , а площадь равна 72. Найди меньший острый угол этого треугольника. Ответ запиши в градусах.