Browse Math problems in the Studdy Learning Bank!

Problem 9101

Find the modes of the sibling count data: $1, 2, 4, 0, 3$ .

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Problem 9102

Prove that for any real $x$ , if $x^2 - 6x + 5 > 5$ , then $x \geq 5$ or $x \leq 1$ . Identify the assumed and proven facts in a proof by contrapositive.

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Problem 9103

Solve the quadratic equation $7x^2 + 15x - 2 = 18$ for exact and approximate solutions.

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Problem 9104

Convert $1,374,000,000$ to scientific notation.

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Problem 9105

Solve the equation $4m-5=-1$ and present the solution as an integer or reduced fraction.

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Problem 9106

Factor the binomial $s^2 + 9$ completely. Select "Prime" if the polynomial cannot be factored.

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Problem 9107

Divide $61,000,000 \div 912.7$ and express the answer using significant figures.

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Problem 9108

Find the $\operatorname{LCM}$ and $\operatorname{GCF}$ of given numbers using the list method. Additional materials: eBook.

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Problem 9109

Find the value of $H$ that satisfies the equation $(2H-3)(3H+1)H=4484$ .

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Problem 9110

Divide a 3-digit integer ending in 5 by 5 mentally using an appropriate strategy.

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Problem 9111

Solve for $a$ when $\frac{a}{9}=6$ .

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Problem 9112

Simplify the product $(3x-4)(6x-2)$ using FOIL method. (1 point)

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Problem 9113

Simplify the expression $9.26 + \left(\frac{1}{4} \cdot 2\right)$ and find the result.

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Problem 9114

Rewrite $f(x)$ as $(x-k)q(x)+r$ given $f(x)=2x^3+x^2+x-4$ and $k=-1$ .

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Problem 9115

Calculate values of $f(x)=2 x^{2}-8 x+6$ for $x=-2, -1, 0, 1, 2$ .

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Problem 9116

Find the value of $\frac{(9^2 - 65)}{2^2}$ .

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Problem 9117

Factor -1 from one denominator to simplify binomial expressions. Restrictions apply. a) $\frac{1}{x-2}+\frac{1}{x-2}$ b) $\frac{2x-7}{x-3}+\frac{-(x-9)}{x-3}$

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Problem 9118

Solve the quadratic equation $(11 v + 5)(6 v - 18) = 0$ to find the values of $v$ .

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Problem 9119

Simplify the expression $\left(\frac{z}{w}\right)^{2}$ by applying the appropriate property.

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Problem 9120

Find the value of $c$ that satisfies the Mean Value Theorem for $h(x) = \sqrt{3x-3}$ on the interval $4 \leq x \leq 13$ .

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Problem 9121

(1 point) A Ferris wheel with 35 m diameter rotates fully every 6 minutes. At $t=0$ , you are at the 3 o'clock position and ascending. Find a formula for $f(t)$ , your height (in m) above ground at $t$ minutes.
$f(t) = 17.5 \sin\left(\frac{\pi t}{3}\right) + 17.5$

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Problem 9122

Find the value of constant $c$ in the equation $(t+1)^{2} + c = 0$ with solutions at $t = \frac{3}{2}$ and $t = -\frac{7}{2}$ .

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Problem 9123

Solve for $x$ where $\ln (3x+2)=4$ . The solution is $x=\frac{2}{3}$ .

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Problem 9124

Find the radius of convergence $R$ of the power series $\sum_{n=1}^{\infty} \frac{(-4)^{n}}{\sqrt{n}}(x+8)^{n}$ . If $R$ is infinite, type "infinity" or "inf". Answer: $R=\frac{1}{4}$ . What is the interval of convergence? Answer (in interval notation): $(-12, -4)$ .

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Problem 9125

Convert time from 24-hour format to 12-hour format. Given 1825, find the corresponding traditional time.

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Problem 9126

Sketch the graph of the vertical line $x=3$ .

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Problem 9127

Select all true statements about the expression $4a + 5b + 9 + 3b$ : $4a$ is a term, $4a$ is a coefficient, $5b$ and $3b$ are like terms, $9$ is a constant.

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Problem 9128

Find the product of three consecutive integers using the formula $n^3 - n$ . Use the factorization of $2x^3 + 8x^2 + 8x$ to determine the value of $(20)(12)^2$ .

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Problem 9129

Find the missing addend in the equation $28 + \square = 49$ .

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Problem 9130

Find the derivative of $g(t)=6t-1$ using the limit definition.

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Problem 9131

Select the value of $x$ that disproves the statement: for all integers $x$ , $x < x^2$ . Options: $x=-1/2$ , $x=-1$ , $x=1$ , $x=1/2$ .

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Problem 9132

Find the other roots of $f(x) = x^2 + 158x - 37109$ given that $-79 + 85\sqrt{6}$ is a root.

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Problem 9133

Find the value of $a$ such that when $x^3 + a x^2 + 4$ is divided by $x + 1$ , the remainder is 6 greater than the remainder when divided by $x - 2$ .

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Problem 9134

Find the reciprocal of the expression $\frac{1}{g+w}$ .

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Problem 9135

Solve multi-step linear equations. 1. $7c - 3 + 2c = 15$ 2. $5(x - 7) = 20$ 3. $6h + 5 = 10 + h$ 4. $60 = -4(3y - 6)$ 5. $-5g + 24 = 7g - 24$ 6. $22 = 3u + 10 - 5u$ 7. $-5(3k - 3) + 17 = -43$ 8. $7t - 5 + 4t = 3t - 21$ 9. $5m - 7 = 3(2m + 1)$ 10. $-12 = 4(2q + 7) - 3q$ 11. $-11 - 6b + 3 = 16 + 2b$ 12. $5(8 - 2w) = 4 - 4w$

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Problem 9136

Evaluate the expression $(2+\sqrt{2})^{2}$ .

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Problem 9137

Find the value of the expression $\frac{\tan 80^{\circ}+\tan 55^{\circ}}{1-\tan 80^{\circ} \tan 55^{\circ}}$ .

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Problem 9138

Evaluate the sum of the geometric series $\sum_{n=1}^{5} 6(2)^{n-1}$ and solve for $S$ .

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Problem 9139

Redefine $m(x) = (3x-1)(3-x) + 4x^2 + 19$ as a trinomial. Solve for $x$ when $m(x) = 0$ .

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Problem 9140

Simplify the expression $\frac{y^{2}-36}{y} \div \frac{y+6}{y-6}$ .

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Problem 9141

Solve for the unknown variable $y$ in the equation $6y - 1 = 31 - 6y + 8y$ . Round the solution to two decimal places.

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Problem 9142

Solve the equation $6x - 5 = 31$ . Select the correct choice: A. The solution set is { $\frac{36}{6}$ }.

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Problem 9143

Find the inverse cosine of -0.8 and express the result in radians, rounded to the nearest hundredth.

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Problem 9144

Determine the behavior of the function $f(x) = (2x + 1) \cdot e^{-x}$ for very large and very small values of $x$ .

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Problem 9145

Evaluate the limit $\lim_{x \to \pi/2} (\sec(x) - \tan(x))$ . Use symbolic notation and fractions.

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Problem 9146

Find the value of $f(-2)$ given $f(x) = 4x - 7$ .

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Problem 9147

Evaluate the natural logarithm of 0.012 and give the answer to 4 decimal places. $\ln (0.012)$

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Problem 9148

Distribute $y^{2}(-3 y-7)$ and select the simplified answer.

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Problem 9149

Write an expression for a number $x$ decreased by $12.5\%$ .

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Problem 9150

Resuelve la desigualdad $-8.4 \leq w - 0.8$ para encontrar el valor de $w$ .

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Problem 9151

Analyze the properties of the logarithmic functions $y=\log_2(x+1)$ and $y=\log(x)-3$ , including domain, range, asymptotes, x-intercepts, and transformations.

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Problem 9152

Use Newton's method to find the solution to $e^{-2x} = -3x + 9$ starting with $x_0 = -5$ . Provide the first two iterates $x_1$ and $x_2$ , and the final solution accurate to 4 decimal places.

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Problem 9153

Solve the quadratic equation $z^{2} - 13z + 12 = 0$ for real values of $z$ .

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Problem 9154

Spin two game board spinners, one with $1,2,3$ and one with $5,6,7,8$ . The first spinner's digit is the tens, the second's is the ones. Construct a tree diagram to show all possible prize amounts.

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Problem 9155

Find the exact solution of the equation $12 \tan ^{-1} \mathrm{x}=4 \pi$ . The solution set is $\{\pm \frac{\pi}{3}\}$ .

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Problem 9156

Solve the linear equation $2(3x+8) = 70$ for the unknown variable $x$ .

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Problem 9157

Determine if the events "the person is female" and "the person prefers classic rock" are independent. Justify your answer based on the provided $2 \times 4$ contingency table.

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Problem 9158

Find the exact value of $\sec^{-1}(-\sqrt{2})$ . Choose A and enter the simplified expression, or B if no solution exists.

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Problem 9159

A $34\mathrm{ft}$ ladder leans against a building at an $85^{\circ}$ angle. Find the ladder's height on the building in $\mathrm{ft}$ .

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Problem 9160

Determine the number of zeros for the quadratic equation $0=3 x^{2}-7 x+4$ using the discriminant.

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Problem 9161

8. Convert equation $y=3(x+2)(x-3)$ to standard form. (0.5 Points)
9. Convert equation $y=3x^2-9x-30$ to intercept form. (0.5 Points)
10. Another name for intercept form of a quadratic equation is Factored form. (0.5 Points)

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Problem 9162

Solve the equation $-5 m(x)=-3 \sqrt{x+4}+5$ for $m(x)$ .

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Problem 9163

Solve the equation $x^{2}-4=0$ by graphing the associated parabola. Use the graph to give the solution(s).

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Problem 9164

a) The nursing home's annual profit is approximately $P(18, 70, 350000, 10) = \$ 2,289,526$
b) The partial derivatives of $P$ are: $\frac{\partial P}{\partial w} = -0.487294w^{-1.647}r^{1.097}s^{0.867}t^{2.461}$

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Problem 9165

Evaluate the factorial expression $\frac{2! \, 5!}{6! \, 3!}$ and simplify the result.

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Problem 9166

Determine the vertical intercept, zeros, vertical asymptotes, and horizontal asymptote of the function $f(x)=\frac{x^{2}+6}{(6 x-11)(x+5)}$ .
a. $f(0)=\frac{6}{-55}$ b. $x=\frac{11}{6}, -5$ c. $x=\frac{11}{6}, -5$ d. $y=0$

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Problem 9167

Solve for $x$ when angles in a linear pair sum to $180^{\circ}$ . $12x = 180$ .

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Problem 9168

Find the limit, continuity, and type of discontinuity of the piecewise function f(x) = \\begin{cases} 2x+1, & x>-1 \\\\ x^2+1, & x \\leq-1 \\end{cases} at $x=a$ .

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Problem 9169

Evaluate $7+9(x-6)^{3}$ for $x=8$ . When $x=8$ , the expression simplifies to $\square$ .

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Problem 9170

Evaluate and simplify the expression $\frac{7 ! 5 !}{4 ! 6 !}$ .

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Problem 9171

Determine if the equation $x^{2} + y^{2} = 100$ is symmetric with respect to the $y$ -axis, $x$ -axis, or origin.

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Problem 9172

Maximize $P=40x+50y$ subject to $2x+y\leq18$ , $x+y\leq10$ , $x+2y\leq16$ , and $x,y\geq0$ . What is the maximum value of $P$ ?

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Problem 9173

Evaluate the expressions: $-(7)^{2}$ and $-(-2)^{3}$ .

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Problem 9174

Trova l'equazione di una parabola con asse di simmetria sull'asse $y$ , vertice in $0(0 ; 0)$ e passante per $A(2 ; 1)$ .

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Problem 9175

Solve $10^{2x} - 11 \cdot 10^x + 24 = 0$ . Solve $e^{4x} + 4e^{2x} = 45$ .

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Problem 9176

A. $(\mathrm{f}-\mathrm{g})(12)=\sqrt{12-3}-12^{2}+12$

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Problem 9177

Solve for $x$ in the equations $8^{x}=4$ and $16^{x}=8$ .

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Problem 9178

Find the perimeter of parallelogram FACE given $FA=5x+5$ , $EC=9x-11$ , and $FE=15$ cm.

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Problem 9179

Solve the linear equation $2x + 5 = -3x + 10$ for the unknown variable $x$ .

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Problem 9180

Find all values of $y$ in the equation $|-6y|=36$ . Options: $y=6$ , $y=-6$ , $y=6$ and $-6$ , No solution.

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Problem 9181

Evaluate the integral $2 \cdot \int x^{2} \ln x d x$

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Problem 9182

The given statement $\sqrt{-400}=20 i$ is false. The correct solution is $\sqrt{-400}=20i$ .

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Problem 9183

Solve for $y$ in the two-variable equation $\frac{y}{9}-\frac{2x}{9}=\frac{1}{3}$ . Select the correct solution.

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Problem 9184

Find all possible rational roots of $f(x)=-3 x^{5}-9 x^{4}+9 x^{3}+9 x^{2}-3 x-4$ using the rational root theorem. Express your answer as integers or simplified fractions, separated by commas.

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Problem 9185

Find the polynomial equivalent to $(f \cdot g)(x)$ , where $f(x) = x + 1$ and $g(x) = \frac{2}{x}$ .

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Problem 9186

Coastal city's tide peaks every 11.8 hours, ranging from 5.2 to 2.4 feet. Find the equation modeling the tide height after $t$ hours, given the high tide is at $t=0$ . Round values to the nearest tenth. Use a $\underline{sin}$ function. Amplitude $=1.4$ feet, Period $=2\pi$ radians, Phase Shift $=0$ radians, Vertical Shift $=3.8$ feet.

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Problem 9187

Find the quotient of $2 x^{3}-12 x^{2}+15 x \div 3 x$ . Choose the correct expression.

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Problem 9188

Find the slope of $y=x^3-x$ at $x=a$ . What is the slope at $x=1$ ? Where does the slope equal $11$ ?

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Problem 9189

Solve for $x$ in the equation $9=27x$ . Simplify the solution.

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Problem 9190

Solve for $a$ in the equation $25 = 35a$ . Simplify the solution $a = \frac{25}{35}$ .

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Problem 9191

Rewrite the rational function $y=\frac{e x+f}{g x+h}$ in the form $y=\frac{a}{x-h}+k$ . Find the equations of the asymptotes in terms of $e, f, g$ , and $h$ .

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Problem 9192

Find the solution to the equation $5 e^{x+2} = 7$ .

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Problem 9193

Solve the rational equation and explain the unique solution. $\frac{x^{2}-7 x-18}{x+2}=x-9$ . A. The equation reduces to $x=\boxed{3}$ . This is the only solution.

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Problem 9194

Flip a coin. What is the probability of not getting heads? Express your answer as a percentage.

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Problem 9195

Find the relationship between $z$ , $x$ , and $y$ in the equation $z=\pi xy^{2}$ .

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Problem 9196

Solve the quadratic equation $4x^2 - 8x = 64$ using the complete the square method. The solutions are $x = 5, x = 3$ .

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Problem 9197

Find the price that maximizes revenue for personal CD players, given that a $\$ 1$ decrease in price leads to 5 more units sold over 2 weeks, and the regular price is $\$ 90$ .

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Problem 9198

Multiply $73 \times 4$ using partial products. Show step-by-step work.

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Problem 9199

Find the expected value of a randomly chosen student's score on last year's final exam given the score distribution.
$X$ = score of a randomly chosen student Expected value of $X$ = $\frac{(19 \times 3) + (35 \times 3) + (60 \times 4)}{10}$

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Problem 9200

Evaluate the integral $\int_{e^{3 x}}^{e^{4 x}} \frac{1}{x \ln x+x} dx$ .

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Math

Problem 9101

Find the modes of the sibling count data: 1,2,4,0,31, 2, 4, 0, 31,2,4,0,3.

Problem 9102

Prove that for any real xxx, if x2−6x+5>5x^2 - 6x + 5 > 5x2−6x+5>5, then x≥5x \geq 5x≥5 or x≤1x \leq 1x≤1. Identify the assumed and proven facts in a proof by contrapositive.

Problem 9103

Solve the quadratic equation 7x2+15x−2=187x^2 + 15x - 2 = 187x2+15x−2=18 for exact and approximate solutions.

Problem 9104

Convert 1,374,000,0001,374,000,0001,374,000,000 to scientific notation.

Problem 9105

Solve the equation 4m−5=−14m-5=-14m−5=−1 and present the solution as an integer or reduced fraction.

Problem 9106

Factor the binomial s2+9s^2 + 9s2+9 completely. Select "Prime" if the polynomial cannot be factored.

Problem 9107

Divide 61,000,000÷912.761,000,000 \div 912.761,000,000÷912.7 and express the answer using significant figures.

Problem 9108

Find the LCM⁡\operatorname{LCM}LCM and GCF⁡\operatorname{GCF}GCF of given numbers using the list method. Additional materials: eBook.

Problem 9109

Find the value of HHH that satisfies the equation (2H−3)(3H+1)H=4484(2H-3)(3H+1)H=4484(2H−3)(3H+1)H=4484.

Problem 9110

Divide a 3-digit integer ending in 5 by 5 mentally using an appropriate strategy.

Problem 9111

Solve for aaa when a9=6\frac{a}{9}=69a​=6.

Problem 9112

Simplify the product (3x−4)(6x−2)(3x-4)(6x-2)(3x−4)(6x−2) using FOIL method. (1 point)

Problem 9113

Simplify the expression 9.26+(14⋅2)9.26 + \left(\frac{1}{4} \cdot 2\right)9.26+(41​⋅2) and find the result.

Problem 9114

Rewrite f(x)f(x)f(x) as (x−k)q(x)+r(x-k)q(x)+r(x−k)q(x)+r given f(x)=2x3+x2+x−4f(x)=2x^3+x^2+x-4f(x)=2x3+x2+x−4 and k=−1k=-1k=−1.

Problem 9115

Calculate values of f(x)=2x2−8x+6f(x)=2 x^{2}-8 x+6f(x)=2x2−8x+6 for x=−2,−1,0,1,2x=-2, -1, 0, 1, 2x=−2,−1,0,1,2.

Problem 9116

Find the value of (92−65)22\frac{(9^2 - 65)}{2^2}22(92−65)​.

Problem 9117

Factor -1 from one denominator to simplify binomial expressions. Restrictions apply. a) 1x−2+1x−2\frac{1}{x-2}+\frac{1}{x-2}x−21​+x−21​ b) 2x−7x−3+−(x−9)x−3\frac{2x-7}{x-3}+\frac{-(x-9)}{x-3}x−32x−7​+x−3−(x−9)​

Problem 9118

Solve the quadratic equation (11v+5)(6v−18)=0(11 v + 5)(6 v - 18) = 0(11v+5)(6v−18)=0 to find the values of vvv.

Problem 9119

Simplify the expression (zw)2\left(\frac{z}{w}\right)^{2}(wz​)2 by applying the appropriate property.

Problem 9120

Find the value of ccc that satisfies the Mean Value Theorem for h(x)=3x−3h(x) = \sqrt{3x-3}h(x)=3x−3​ on the interval 4≤x≤134 \leq x \leq 134≤x≤13.

Problem 9121

Problem 9122

Find the value of constant ccc in the equation (t+1)2+c=0(t+1)^{2} + c = 0(t+1)2+c=0 with solutions at t=32t = \frac{3}{2}t=23​ and t=−72t = -\frac{7}{2}t=−27​.

Problem 9123

Solve for xxx where ln⁡(3x+2)=4\ln (3x+2)=4ln(3x+2)=4. The solution is x=23x=\frac{2}{3}x=32​.

Problem 9124

Problem 9125

Convert time from 24-hour format to 12-hour format. Given 1825, find the corresponding traditional time.

Problem 9126

Sketch the graph of the vertical line x=3x=3x=3.

Problem 9127

Select all true statements about the expression 4a+5b+9+3b4a + 5b + 9 + 3b4a+5b+9+3b: 4a4a4a is a term, 4a4a4a is a coefficient, 5b5b5b and 3b3b3b are like terms, 999 is a constant.

Problem 9128

Find the product of three consecutive integers using the formula n3−nn^3 - nn3−n. Use the factorization of 2x3+8x2+8x2x^3 + 8x^2 + 8x2x3+8x2+8x to determine the value of (20)(12)2(20)(12)^2(20)(12)2.

Problem 9129

Find the missing addend in the equation 28+□=4928 + \square = 4928+□=49.

Problem 9130

Find the derivative of g(t)=6t−1g(t)=6t-1g(t)=6t−1 using the limit definition.

Problem 9131

Select the value of xxx that disproves the statement: for all integers xxx, x<x2x < x^2x<x2. Options: x=−1/2x=-1/2x=−1/2, x=−1x=-1x=−1, x=1x=1x=1, x=1/2x=1/2x=1/2.

Problem 9132

Find the other roots of f(x)=x2+158x−37109f(x) = x^2 + 158x - 37109f(x)=x2+158x−37109 given that −79+856-79 + 85\sqrt{6}−79+856​ is a root.

Problem 9133

Find the value of aaa such that when x3+ax2+4x^3 + a x^2 + 4x3+ax2+4 is divided by x+1x + 1x+1, the remainder is 6 greater than the remainder when divided by x−2x - 2x−2.

Problem 9134

Find the reciprocal of the expression 1g+w\frac{1}{g+w}g+w1​.

Problem 9135

Problem 9136

Evaluate the expression (2+2)2(2+\sqrt{2})^{2}(2+2​)2.

Problem 9137

Find the value of the expression tan⁡80∘+tan⁡55∘1−tan⁡80∘tan⁡55∘\frac{\tan 80^{\circ}+\tan 55^{\circ}}{1-\tan 80^{\circ} \tan 55^{\circ}}1−tan80∘tan55∘tan80∘+tan55∘​.

Problem 9138

Evaluate the sum of the geometric series ∑n=156(2)n−1\sum_{n=1}^{5} 6(2)^{n-1}∑n=15​6(2)n−1 and solve for SSS.

Problem 9139

Redefine m(x)=(3x−1)(3−x)+4x2+19m(x) = (3x-1)(3-x) + 4x^2 + 19m(x)=(3x−1)(3−x)+4x2+19 as a trinomial. Solve for xxx when m(x)=0m(x) = 0m(x)=0.

Problem 9140

Simplify the expression y2−36y÷y+6y−6\frac{y^{2}-36}{y} \div \frac{y+6}{y-6}yy2−36​÷y−6y+6​.

Problem 9141

Solve for the unknown variable yyy in the equation 6y−1=31−6y+8y6y - 1 = 31 - 6y + 8y6y−1=31−6y+8y. Round the solution to two decimal places.

Find the modes of the sibling count data: $1, 2, 4, 0, 3$ .

Prove that for any real $x$ , if $x^2 - 6x + 5 > 5$ , then $x \geq 5$ or $x \leq 1$ . Identify the assumed and proven facts in a proof by contrapositive.

Solve the quadratic equation $7x^2 + 15x - 2 = 18$ for exact and approximate solutions.

Convert $1,374,000,000$ to scientific notation.

Solve the equation $4m-5=-1$ and present the solution as an integer or reduced fraction.

Factor the binomial $s^2 + 9$ completely. Select "Prime" if the polynomial cannot be factored.

Divide $61,000,000 \div 912.7$ and express the answer using significant figures.

Find the $\operatorname{LCM}$ and $\operatorname{GCF}$ of given numbers using the list method. Additional materials: eBook.

Find the value of $H$ that satisfies the equation $(2H-3)(3H+1)H=4484$ .

Solve for $a$ when $\frac{a}{9}=6$ .

Simplify the product $(3x-4)(6x-2)$ using FOIL method. (1 point)

Simplify the expression $9.26 + \left(\frac{1}{4} \cdot 2\right)$ and find the result.

Rewrite $f(x)$ as $(x-k)q(x)+r$ given $f(x)=2x^3+x^2+x-4$ and $k=-1$ .

Calculate values of $f(x)=2 x^{2}-8 x+6$ for $x=-2, -1, 0, 1, 2$ .

Find the value of $\frac{(9^2 - 65)}{2^2}$ .

Factor -1 from one denominator to simplify binomial expressions. Restrictions apply. a) $\frac{1}{x-2}+\frac{1}{x-2}$ b) $\frac{2x-7}{x-3}+\frac{-(x-9)}{x-3}$

Solve the quadratic equation $(11 v + 5)(6 v - 18) = 0$ to find the values of $v$ .

Simplify the expression $\left(\frac{z}{w}\right)^{2}$ by applying the appropriate property.

Find the value of $c$ that satisfies the Mean Value Theorem for $h(x) = \sqrt{3x-3}$ on the interval $4 \leq x \leq 13$ .

Find the value of constant $c$ in the equation $(t+1)^{2} + c = 0$ with solutions at $t = \frac{3}{2}$ and $t = -\frac{7}{2}$ .

Solve for $x$ where $\ln (3x+2)=4$ . The solution is $x=\frac{2}{3}$ .

Sketch the graph of the vertical line $x=3$ .

Select all true statements about the expression $4a + 5b + 9 + 3b$ : $4a$ is a term, $4a$ is a coefficient, $5b$ and $3b$ are like terms, $9$ is a constant.

Find the product of three consecutive integers using the formula $n^3 - n$ . Use the factorization of $2x^3 + 8x^2 + 8x$ to determine the value of $(20)(12)^2$ .

Find the missing addend in the equation $28 + \square = 49$ .

Find the derivative of $g(t)=6t-1$ using the limit definition.

Select the value of $x$ that disproves the statement: for all integers $x$ , $x < x^2$ . Options: $x=-1/2$ , $x=-1$ , $x=1$ , $x=1/2$ .

Find the other roots of $f(x) = x^2 + 158x - 37109$ given that $-79 + 85\sqrt{6}$ is a root.

Find the value of $a$ such that when $x^3 + a x^2 + 4$ is divided by $x + 1$ , the remainder is 6 greater than the remainder when divided by $x - 2$ .

Find the reciprocal of the expression $\frac{1}{g+w}$ .

Evaluate the expression $(2+\sqrt{2})^{2}$ .

Find the value of the expression $\frac{\tan 80^{\circ}+\tan 55^{\circ}}{1-\tan 80^{\circ} \tan 55^{\circ}}$ .

Evaluate the sum of the geometric series $\sum_{n=1}^{5} 6(2)^{n-1}$ and solve for $S$ .

Redefine $m(x) = (3x-1)(3-x) + 4x^2 + 19$ as a trinomial. Solve for $x$ when $m(x) = 0$ .

Simplify the expression $\frac{y^{2}-36}{y} \div \frac{y+6}{y-6}$ .

Solve for the unknown variable $y$ in the equation $6y - 1 = 31 - 6y + 8y$ . Round the solution to two decimal places.

Solve the equation $6x - 5 = 31$ . Select the correct choice: A. The solution set is { $\frac{36}{6}$ }.

Determine the behavior of the function $f(x) = (2x + 1) \cdot e^{-x}$ for very large and very small values of $x$ .

Evaluate the limit $\lim_{x \to \pi/2} (\sec(x) - \tan(x))$ . Use symbolic notation and fractions.

Find the value of $f(-2)$ given $f(x) = 4x - 7$ .

Evaluate the natural logarithm of 0.012 and give the answer to 4 decimal places. $\ln (0.012)$

Distribute $y^{2}(-3 y-7)$ and select the simplified answer.

Write an expression for a number $x$ decreased by $12.5\%$ .

Resuelve la desigualdad $-8.4 \leq w - 0.8$ para encontrar el valor de $w$ .

Analyze the properties of the logarithmic functions $y=\log_2(x+1)$ and $y=\log(x)-3$ , including domain, range, asymptotes, x-intercepts, and transformations.

Use Newton's method to find the solution to $e^{-2x} = -3x + 9$ starting with $x_0 = -5$ . Provide the first two iterates $x_1$ and $x_2$ , and the final solution accurate to 4 decimal places.

Solve the quadratic equation $z^{2} - 13z + 12 = 0$ for real values of $z$ .

Spin two game board spinners, one with $1,2,3$ and one with $5,6,7,8$ . The first spinner's digit is the tens, the second's is the ones. Construct a tree diagram to show all possible prize amounts.

Find the exact solution of the equation $12 \tan ^{-1} \mathrm{x}=4 \pi$ . The solution set is $\{\pm \frac{\pi}{3}\}$ .

Solve the linear equation $2(3x+8) = 70$ for the unknown variable $x$ .

Determine if the events "the person is female" and "the person prefers classic rock" are independent. Justify your answer based on the provided $2 \times 4$ contingency table.

Find the exact value of $\sec^{-1}(-\sqrt{2})$ . Choose A and enter the simplified expression, or B if no solution exists.

A $34\mathrm{ft}$ ladder leans against a building at an $85^{\circ}$ angle. Find the ladder's height on the building in $\mathrm{ft}$ .

Determine the number of zeros for the quadratic equation $0=3 x^{2}-7 x+4$ using the discriminant.

8. Convert equation $y=3(x+2)(x-3)$ to standard form. (0.5 Points)
9. Convert equation $y=3x^2-9x-30$ to intercept form. (0.5 Points)
10. Another name for intercept form of a quadratic equation is Factored form. (0.5 Points)

Solve the equation $-5 m(x)=-3 \sqrt{x+4}+5$ for $m(x)$ .

Solve the equation $x^{2}-4=0$ by graphing the associated parabola. Use the graph to give the solution(s).

Evaluate the factorial expression $\frac{2! \, 5!}{6! \, 3!}$ and simplify the result.

Solve for $x$ when angles in a linear pair sum to $180^{\circ}$ . $12x = 180$ .

Find the limit, continuity, and type of discontinuity of the piecewise function f(x) = \\begin{cases} 2x+1, & x>-1 \\\\ x^2+1, & x \\leq-1 \\end{cases} at $x=a$ .

Evaluate $7+9(x-6)^{3}$ for $x=8$ . When $x=8$ , the expression simplifies to $\square$ .

Evaluate and simplify the expression $\frac{7 ! 5 !}{4 ! 6 !}$ .

Determine if the equation $x^{2} + y^{2} = 100$ is symmetric with respect to the $y$ -axis, $x$ -axis, or origin.

Maximize $P=40x+50y$ subject to $2x+y\leq18$ , $x+y\leq10$ , $x+2y\leq16$ , and $x,y\geq0$ . What is the maximum value of $P$ ?

Evaluate the expressions: $-(7)^{2}$ and $-(-2)^{3}$ .

Trova l'equazione di una parabola con asse di simmetria sull'asse $y$ , vertice in $0(0 ; 0)$ e passante per $A(2 ; 1)$ .