Math Statement

Problem 23001

Find the limits of the function $g(x)$ defined as:
$g(x)=\begin{cases} 0 & \text{if } x \leq -6 \\ \sqrt{36-x^{2}} & \text{if } -6 < x < 6 \\ x & \text{if } x \geq 6 \end{cases}$
for $x \to -6^{-}, -6^{+}, 6^{-}, 6^{+}, 6$ .

See Solution

Problem 23002

Solve the initial value problem: $\frac{d y}{d t}=3 y\left(1-\frac{y}{12}\right)$ , $y(0)=2$ . Find $y(t)$ .

See Solution

Problem 23003

Calculate the work done by the force $F(x)=2 x^{-2}+4 x$ from $x=1$ to $x=2$ : evaluate $\int_{1}^{2}\left(2 x^{-2}+4 x\right) d x$ . Provide the answer to three decimal places.

See Solution

Problem 23004

Calculate the average of the numbers 5.34, 5.31, 5.30, 5.31, and 5.25. What is $\bar{X} = \frac{5.34+5.31+5.30+5.31+5.25}{5}$ ?

See Solution

Problem 23005

Find the value of $f(\pi)$ where $f(T)=\int_{0}^{x} x \cos (x) d x$ . Provide the answer to three decimal places.

See Solution

Problem 23006

Find the standard deviation from the variance $S^{2}=0.00107$ . Round your answer to five decimal places.

See Solution

Problem 23007

Find the value of $f(\pi)$ where $f(T)=\int_{0}^{T} x \cos (x) d x$ . Round to three decimal places.

See Solution

Problem 23008

Solve for $x$ in the equation $F(12) = 2x + 4$ .

See Solution

Problem 23009

Solve for $x$ in the equation $\ln _{2}(x+1)-\ln _{2}(x-1)=\ln _{2} 8$ .

See Solution

Problem 23010

Write an equation for how a neutral aluminum atom forms an aluminum ion, using $e^{-}$ for electrons.

See Solution

Problem 23011

Find the range (5.34 - 5.25) and the coefficient of variation: $CV = \left(\frac{0.0327}{5.302}\right) 100 \%$ . Round to four decimals.

See Solution

Problem 23012

Does the integral $\int_{0}^{3} \frac{1}{x} dx$ converge or diverge?

See Solution

Problem 23013

Determine if the integral $\int_{-1}^{4} \frac{1}{x^{2 / 3}} d x$ converges or diverges.

See Solution

Problem 23014

Find the mean of the five-year CDs: $\bar{X} = \frac{5.95 + 5.90 + 5.84 + 5.83 + 5.78}{5} = \square$ (Type an integer or decimal.)

See Solution

Problem 23015

Find the significant figures in the measurement $1036.48g$ .

See Solution

Problem 23016

Does the integral $\int_{-\infty}^{\infty} e^{-3 x} dx$ converge or diverge?

See Solution

Problem 23017

Find the decimal equivalents of these fractions: -31 86/100, -31 45/50, -23/20, 7/20, -60/22, 1/18.

See Solution

Problem 23018

Find the significant figures in the measurement $1036.48g$ .

See Solution

Problem 23019

Calculate the standard deviation from a variance of $0.00180$ . Round to four decimal places.

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Problem 23020

Find the limit: $\lim _{t \rightarrow 4^{+}} \frac{|7 t-28|}{t^{2}-16}$ .

See Solution

Problem 23021

Calculate $6 \times 6$ .

See Solution

Problem 23022

Find the area of an equilateral triangle as a function of its side length $s$ . Use the formula $A = \frac{\sqrt{3}}{4}s^2$ .

See Solution

Problem 23023

Find the maximum value of $f(x)=400 x-11 x^{2}-3$ graphically, rounded to four decimal places.

See Solution

Problem 23024

How many significant figures are in the measurement $5.0 \times 10^{-3}$ ?

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Problem 23025

Find the significant figures in these values: $5.0 \times 10^{-3}$ L, $20.8$ , $99.0$ , $13.70$ , $60,810,000$ g, $1036.48$ g.

See Solution

Problem 23026

Find the standard deviation given a variance of 0.00445. Round to four decimal places.

See Solution

Problem 23027

Find the value of $y(1)$ for the initial value problem $\frac{d y}{d x}=\frac{\ln (x)}{x}$ with $y(e)=3$ .

See Solution

Problem 23028

Convert 1 meter (m) to nanometers (nm): $1 \mathrm{m} = ? \mathrm{nm}$ .

See Solution

Problem 23029

1 km = ? m

See Solution

Problem 23030

Find the value of the integral $\int_{4}^{4} f(x) d x$ given that $f$ and $g$ are continuous functions.

See Solution

Problem 23031

Find the value of $\int_{2}^{5} f(x) d x$ given that $\int_{0}^{2} f(x) dx=-1$ and $\int_{0}^{5} f(x) dx=3$ .

See Solution

Problem 23032

Find the value of the integral $\int_{2}^{0} g(x) d x$ given $\int_{0}^{2} g(x) d x=8$ . Enter as a decimal or DNE.

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Problem 23033

Calculate the integral $\int_{0}^{2}(5 f(x)+g(x)) d x$ given that $\int_{0}^{2} f(x) d x=-1$ and $\int_{0}^{2} g(x) d x=8$ .

See Solution

Problem 23034

Determine if the function $g(x)=-4 x^{5}+5 x^{3}$ is even, odd, or neither.

See Solution

Problem 23035

Calculate the expression: $16 - 4 \div 1 / 4 + 2 =$

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Problem 23036

Find the constant $x$ in the equation $H=x \frac{v}{A}$ from $v=\frac{7}{4} A H$ .

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Problem 23037

Solve the equation: $4 + 4$ .

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Problem 23038

Calculate the product of 12 and 12: $12 \times 12 = ?$

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Problem 23039

If $x = 5$ , find the value of $6x$ , $5x$ , $30x$ , and $R^{30}$ .

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Problem 23040

Find the slope and y-intercept for each line: 39. $y=2x+1$ , 40. $y=3x+2$ , 41. $f(x)=-2x+1$ , 42. $f(x)=-3x+2$ , 43. $f(x)=\frac{3}{4}x-2$ , 44. $f(x)=\frac{3}{4}x-3$ , 45. $y=-\frac{3}{5}x+7$ , 46. $y=-\frac{2}{5}x+6$ , 47. $g(x)=-\frac{1}{2}x$ , 48. $g(x)=-\frac{1}{3}x$ . Graph each function.

See Solution

Problem 23041

Factor the expression $36 x^{3}+21 x^{2}+3 x$ as $a x(b x+1)(c x+1)$ with $b>c$ . Find the value of $c$ .

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Problem 23042

Find where the lines $y = x - 3$ and $y = 3x^2$ intersect.

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Problem 23043

Rewrite the equations in slope-intercept form, find the slope and y-intercept, and graph them. 59. $3x + y - 5 = 0$ 60. $4x + y - 6 = 0$ 61. $2x + 3y - 18 = 0$ 62. $4x + 6y + 12 = 0$

See Solution

Problem 23044

Find the values of $x \in \mathbb{R}$ for which $f(x)=\frac{x^{2}+1}{x-1}$ is defined and continuous (in interval notation).

See Solution

Problem 23045

Find the values of $x \in \mathbb{R}$ for which $f(x)=\ln (x+1)$ is defined and continuous (interval notation).

See Solution

Problem 23046

Convert $4.608 \mathrm{lb}$ to kilograms with four significant figures.

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Problem 23047

Find where the function $f(x)=\sqrt{4x+16}$ is continuous and express the $\mathrm{x}$ -values in interval notation.

See Solution

Problem 23048

Find the intersection of the curves $y=2x^2+3$ and $y=-x+6$ .

See Solution

Problem 23049

Find the value of $a$ so that the function $f(x)=\frac{30+x-x^{2}}{x-6}$ is continuous at $x=6$ .

See Solution

Problem 23050

Check if the function $f(x)=\left\{\begin{array}{ll} \frac{x^{2}-1}{x-1} & \text{if } x \neq 1 \\ 4 & \text{if } x=1 \end{array}\right.$ is continuous at $a=1$ .

See Solution

Problem 23051

Find the intersection points of the lines $y=3-x$ and $y=-x^{2}+2x+3$ .

See Solution

Problem 23052

Find the value of $a$ for which $f(x)$ is continuous at all $x$ :
$f(x)=\begin{cases} x^{2}-99, & x<11 \\ 2 a x, & x \geq 11 \end{cases}$
Options: A. $a=$ B. No solution.

See Solution

Problem 23053

Find the value of $x$ in $g = x \sqrt{p}$ if $p = \frac{2 g^{2}}{50}$ .

See Solution

Problem 23054

Model the fungus growth rate $R(t)$ as:
$R(t)=\left\{\begin{array}{ll} 2 e^{t} & \text { if } 0 \leq t \leq t_{c} \\ a & \text { if } t>t_{c} \end{array}\right.$
Find $a$ for continuity at $t=t_{c}$ . What is $a$ in terms of $e$ ?

See Solution

Problem 23055

Solve the equation $-0.0015 x^{2} + x + 2 = 0$ for $x$ .

See Solution

Problem 23056

Solve the equation $-0.0015 x^{2} + x + 2 = 0$ .

See Solution

Problem 23057

Divide 9.205 by 3.5.

See Solution

Problem 23058

Calculate the value of the expression: $\frac{3.5}{9.205}$ .

See Solution

Problem 23059

Model the fungus growth rate $R(t)$ as $R(t)=\{2 e^{t}, 0 \leq t \leq t_{c}; a, t>t_{c}\}$ . Find $a$ for continuity at $t=t_{c}$ .

See Solution

Problem 23060

Find values of the linear function $f(x)=x$ for $x = -2, -1, 0, 1, 2$ .

See Solution

Problem 23061

Express the set $-6<x \leq-1$ in interval notation.

See Solution

Problem 23062

Solve for x: -14 < -4x + 5 ≤ -13. Provide your answer in interval notation.

See Solution

Problem 23063

Solve for $x$ in the inequality $3 < -11(x+4) \leq -7$ . Answer in interval notation or type DNE if no solution exists.

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Problem 23064

Match each set builder expression with the correct interval:
1. $\{x \mid a<x\}$ : a. $[a, b]$
2. $\{x \mid x<b\}$ : b. $[a, b)$
3. $\{x \mid a<x \leq b\}$ : c. $(a, \infty)$
4. $\{x \mid a<x<b\}$ : d. $[a, \infty)$
5. $\{x \mid x \in \mathbb{R}\}$ : e. $(a, b]$
6. $\{x \mid a \leq x<b\}$ : f. $(-\infty, b)$
7. $\{x \mid a \leq x\}$ : g. $(-\infty, b]$
8. $\{x \mid x \leq b\}$ : h. $(-\infty, \infty)$
9. $\{x \mid a \leq x \leq b\}$ : i. $(a, b)$

See Solution

Problem 23065

Find the slope for points (0, a) & (b, 0) and (-a, 0) & (0, -b). State if the line rises, falls, horizontal, or vertical.

See Solution

Problem 23066

Solve the inequality: $-11-8x \leq 12+8x$ . Enter your answer as an interval, like $[a, oo)$ .

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Problem 23067

Solve the inequality: $\frac{9}{3}+b<\frac{35}{27}$ . Enter your answer as an interval using "oo" for $\infty$ .

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Problem 23068

Solve the inequality $|4x + 3| < 8$ and express your solution in interval notation.

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Problem 23069

Solve the inequality $\left|\frac{x+21}{7}\right|>1$ and express the solution as an interval.

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Problem 23070

Solve the inequality: $-4|x-1|-3 \leq-23$ . Provide the solution in interval notation.

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Problem 23071

Simplify the expression: $3n + 2(-2n - 1)$ . Choose the equivalent expression: (A) $-n + 2$ , (B) $n + 2$ , (C) $-n - 2$ , (D) $n - 2$ .

See Solution

Problem 23072

Simplify the expression: $-4(z+3)-4(5-4 z)$ . Choose the correct equivalent expression from the options.

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Problem 23073

Simplify the expression: $-3(2+4k)+7(2k-1)$ . Choose the correct equivalent expression: (A) $2k-13$ , (B) $8k-13$ , (C) $2k+13$ , (D) $2k-7$ .

See Solution

Problem 23074

Solve the inequality: $\frac{6}{2}+a \leq \frac{19}{12}$ . Provide your answer as an interval using "oo" for $\infty$ .

See Solution

Problem 23075

Solve the inequality: $\frac{6}{2}+a \leq \frac{19}{12}$ . Enter the answer as an interval using "oo" for $\infty$ .

See Solution

Problem 23076

Simplify the expression: $-r + 8(-5r - 2)$ . Choose the equivalent expression from the options provided.

See Solution

Problem 23077

Simplify the expression $\left[a^{4}-4 a^{2}+4\right]^{\frac{1}{2}}$ .

See Solution

Problem 23078

Solve the equation $x^{2}+4x-5=-x+1$ .

See Solution

Problem 23079

Find the domain of these sets and 'All Real Numbers': $\{-2,0,1,2,8\}$ , $\{-3,-2,0,1,2,3,4,5,8\}$ , $\{-3,3,4,5\}$ , and relate them to functions.

See Solution

Problem 23080

Solve the inequality -4|x+4|-2<-10 and express your solution in interval notation.

See Solution

Problem 23081

Solve the inequality: $-3|x+5|-5<-11$ . Provide the solution in interval notation.

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Problem 23082

Does the equation $x = y^{2} + 15$ define $y$ as a function of $x$ ? Choose A, B, C, or D.

See Solution

Problem 23083

Find the domain of the function $f(x) = 7x$ .

See Solution

Problem 23084

Solve the equation $2 x^{2}-x-1=2 x+1$ .

See Solution

Problem 23085

Calculate the value of $5^{3}$ . Options: 225, 15, 125.

See Solution

Problem 23086

Calculate the value of $\frac{36.56}{1.08}$ .

See Solution

Problem 23087

Calculate $0.00266 \times 5$ .

See Solution

Problem 23088

Calculate $\frac{(0.3250)(31)}{1.43}$ .

See Solution

Problem 23089

Does the function $f(x)=x^{3}-5 x^{2}+15 x-8$ have a zero in the interval $[0,1]$ ? Justify your answer.

See Solution

Problem 23090

Find the limit: $\lim _{x \rightarrow 4^{+}} \frac{3-x}{x^{2}-2 x-8}$ .

See Solution

Problem 23091

Find the derivatives of these functions: 1) $y=\sin 2x + (2x-5)^{2}$ 2) $y=\cot x + \sec^{2} x + 5$

See Solution

Problem 23092

Find the derivative of these functions:
1. $y=\cot ^{4} x$
2. $y=\sec ^{3} x$
3. $y=\cos x^{2}$
4. $y=\sqrt{\frac{\sec x+\tan x}{\sec x-\tan x}}$
5. $y=\sin 2 x+(2 x-5)^{2}$
6. $y=\cot x+\sec ^{2} x+5$
7. $y=\frac{\sec -1}{\sec x+1}$
8. $y=\operatorname{cosec} 3 x^{3}$
9. $y=\frac{\sin 3 x}{x+1}$
10. $y=\frac{\sin 2 x}{2 x+5}$
11. $y=\cot 2 x$
12. $y=\frac{(3 x+1) \cos 2 x}{e^{x}}$
13. $y=\sec x$

See Solution

Problem 23093

Write the linear equation $y=7 x-2$ in function notation.

See Solution

Problem 23094

Convert the equation $y=7 x-2$ into function notation.

See Solution

Problem 23095

Find the derivatives of these functions: 1. $y=\frac{\sin 3 x}{x+1}$ , 2. $y=\frac{\sin 2 x}{2 x+5}$ , 3. $y=\cot 2 x$ , 4. $y=\frac{(3 x+1) \cos 2 x}{e^{x}}$ , 5. $y=\sec x$ .

See Solution

Problem 23096

Find $c \in (3, 5)$ such that $\cos(c) = 7 - 2c$ using the Intermediate Value Theorem.

See Solution

Problem 23097

-6.59 as a fraction is: $-659 / 100$

See Solution

Problem 23098

Is the statement true or false? The derivative of $f(x)$ is the instantaneous rate of change of $y=f(x)$ with respect to $x$ . Choose A, B, C, or D.

See Solution

Problem 23099

Find the average velocity of a particle given $s(t)=t^{2}+4t-3$ over intervals [2,3] and [2,4].

See Solution

Problem 23100

Write the linear equation $y=2 x+5$ in function notation.

See Solution

1 ...228 229 230 231 232 233 234 ...269

Math Statement

Problem 23001

Problem 23002

Solve the initial value problem: dydt=3y(1−y12)\frac{d y}{d t}=3 y\left(1-\frac{y}{12}\right)dtdy​=3y(1−12y​), y(0)=2y(0)=2y(0)=2. Find y(t)y(t)y(t).

Problem 23003

Calculate the work done by the force F(x)=2x−2+4xF(x)=2 x^{-2}+4 xF(x)=2x−2+4x from x=1x=1x=1 to x=2x=2x=2: evaluate ∫12(2x−2+4x)dx\int_{1}^{2}\left(2 x^{-2}+4 x\right) d x∫12​(2x−2+4x)dx. Provide the answer to three decimal places.

Problem 23004

Calculate the average of the numbers 5.34, 5.31, 5.30, 5.31, and 5.25. What is Xˉ=5.34+5.31+5.30+5.31+5.255\bar{X} = \frac{5.34+5.31+5.30+5.31+5.25}{5}Xˉ=55.34+5.31+5.30+5.31+5.25​?

Problem 23005

Find the value of f(π)f(\pi)f(π) where f(T)=∫0xxcos⁡(x)dxf(T)=\int_{0}^{x} x \cos (x) d xf(T)=∫0x​xcos(x)dx. Provide the answer to three decimal places.

Problem 23006

Find the standard deviation from the variance S2=0.00107S^{2}=0.00107S2=0.00107. Round your answer to five decimal places.

Problem 23007

Find the value of f(π)f(\pi)f(π) where f(T)=∫0Txcos⁡(x)dxf(T)=\int_{0}^{T} x \cos (x) d xf(T)=∫0T​xcos(x)dx. Round to three decimal places.

Problem 23008

Solve for xxx in the equation F(12)=2x+4F(12) = 2x + 4F(12)=2x+4.

Problem 23009

Solve for xxx in the equation ln⁡2(x+1)−ln⁡2(x−1)=ln⁡28\ln _{2}(x+1)-\ln _{2}(x-1)=\ln _{2} 8ln2​(x+1)−ln2​(x−1)=ln2​8.

Problem 23010

Write an equation for how a neutral aluminum atom forms an aluminum ion, using e−e^{-}e− for electrons.

Problem 23011

Find the range (5.34 - 5.25) and the coefficient of variation: CV=(0.03275.302)100%CV = \left(\frac{0.0327}{5.302}\right) 100 \%CV=(5.3020.0327​)100%. Round to four decimals.

Problem 23012

Does the integral ∫031xdx\int_{0}^{3} \frac{1}{x} dx∫03​x1​dx converge or diverge?

Problem 23013

Determine if the integral ∫−141x2/3dx\int_{-1}^{4} \frac{1}{x^{2 / 3}} d x∫−14​x2/31​dx converges or diverges.

Problem 23014

Find the mean of the five-year CDs: Xˉ=5.95+5.90+5.84+5.83+5.785=□\bar{X} = \frac{5.95 + 5.90 + 5.84 + 5.83 + 5.78}{5} = \squareXˉ=55.95+5.90+5.84+5.83+5.78​=□ (Type an integer or decimal.)

Problem 23015

Find the significant figures in the measurement 1036.48g1036.48g1036.48g.

Problem 23016

Does the integral ∫−∞∞e−3xdx\int_{-\infty}^{\infty} e^{-3 x} dx∫−∞∞​e−3xdx converge or diverge?

Problem 23017

Find the decimal equivalents of these fractions: -31 86/100, -31 45/50, -23/20, 7/20, -60/22, 1/18.

Problem 23018

Find the significant figures in the measurement 1036.48g1036.48g1036.48g.

Problem 23019

Calculate the standard deviation from a variance of 0.001800.001800.00180. Round to four decimal places.

Problem 23020

Find the limit: lim⁡t→4+∣7t−28∣t2−16\lim _{t \rightarrow 4^{+}} \frac{|7 t-28|}{t^{2}-16}limt→4+​t2−16∣7t−28∣​.

Problem 23021

Calculate 6×66 \times 66×6.

Problem 23022

Find the area of an equilateral triangle as a function of its side length sss. Use the formula A=34s2A = \frac{\sqrt{3}}{4}s^2A=43​​s2.

Problem 23023

Find the maximum value of f(x)=400x−11x2−3f(x)=400 x-11 x^{2}-3f(x)=400x−11x2−3 graphically, rounded to four decimal places.

Problem 23024

How many significant figures are in the measurement 5.0×10−35.0 \times 10^{-3}5.0×10−3?

Problem 23025

Find the significant figures in these values: 5.0×10−35.0 \times 10^{-3}5.0×10−3 L, 20.820.820.8, 99.099.099.0, 13.7013.7013.70, 60,810,00060,810,00060,810,000 g, 1036.481036.481036.48 g.

Problem 23026

Find the standard deviation given a variance of 0.00445. Round to four decimal places.

Problem 23027

Find the value of y(1)y(1)y(1) for the initial value problem dydx=ln⁡(x)x\frac{d y}{d x}=\frac{\ln (x)}{x}dxdy​=xln(x)​ with y(e)=3y(e)=3y(e)=3.

Problem 23028

Convert 1 meter (m) to nanometers (nm): 1m=?nm1 \mathrm{m} = ? \mathrm{nm}1m=?nm.

Problem 23029

1 km = ? m

Problem 23030

Find the value of the integral ∫44f(x)dx\int_{4}^{4} f(x) d x∫44​f(x)dx given that fff and ggg are continuous functions.

Problem 23031

Find the value of ∫25f(x)dx\int_{2}^{5} f(x) d x∫25​f(x)dx given that ∫02f(x)dx=−1\int_{0}^{2} f(x) dx=-1∫02​f(x)dx=−1 and ∫05f(x)dx=3\int_{0}^{5} f(x) dx=3∫05​f(x)dx=3.

Problem 23032

Find the value of the integral ∫20g(x)dx\int_{2}^{0} g(x) d x∫20​g(x)dx given ∫02g(x)dx=8\int_{0}^{2} g(x) d x=8∫02​g(x)dx=8. Enter as a decimal or DNE.

Problem 23033

Calculate the integral ∫02(5f(x)+g(x))dx\int_{0}^{2}(5 f(x)+g(x)) d x∫02​(5f(x)+g(x))dx given that ∫02f(x)dx=−1\int_{0}^{2} f(x) d x=-1∫02​f(x)dx=−1 and ∫02g(x)dx=8\int_{0}^{2} g(x) d x=8∫02​g(x)dx=8.

Problem 23034

Determine if the function g(x)=−4x5+5x3g(x)=-4 x^{5}+5 x^{3}g(x)=−4x5+5x3 is even, odd, or neither.

Problem 23035

Calculate the expression: 16−4÷1/4+2=16 - 4 \div 1 / 4 + 2 = 16−4÷1/4+2=

Problem 23036

Find the constant xxx in the equation H=xvAH=x \frac{v}{A}H=xAv​ from v=74AHv=\frac{7}{4} A Hv=47​AH.

Problem 23037

Solve the equation: 4+44 + 44+4.

Problem 23038

Calculate the product of 12 and 12: 12×12=?12 \times 12 = ?12×12=?

Problem 23039

If x=5x = 5x=5, find the value of 6x6x6x, 5x5x5x, 30x30x30x, and R30R^{30}R30.

Problem 23040

Problem 23041

Solve the initial value problem: $\frac{d y}{d t}=3 y\left(1-\frac{y}{12}\right)$ , $y(0)=2$ . Find $y(t)$ .

Calculate the work done by the force $F(x)=2 x^{-2}+4 x$ from $x=1$ to $x=2$ : evaluate $\int_{1}^{2}\left(2 x^{-2}+4 x\right) d x$ . Provide the answer to three decimal places.

Calculate the average of the numbers 5.34, 5.31, 5.30, 5.31, and 5.25. What is $\bar{X} = \frac{5.34+5.31+5.30+5.31+5.25}{5}$ ?

Find the value of $f(\pi)$ where $f(T)=\int_{0}^{x} x \cos (x) d x$ . Provide the answer to three decimal places.

Find the standard deviation from the variance $S^{2}=0.00107$ . Round your answer to five decimal places.

Find the value of $f(\pi)$ where $f(T)=\int_{0}^{T} x \cos (x) d x$ . Round to three decimal places.

Solve for $x$ in the equation $F(12) = 2x + 4$ .

Solve for $x$ in the equation $\ln _{2}(x+1)-\ln _{2}(x-1)=\ln _{2} 8$ .

Write an equation for how a neutral aluminum atom forms an aluminum ion, using $e^{-}$ for electrons.

Find the range (5.34 - 5.25) and the coefficient of variation: $CV = \left(\frac{0.0327}{5.302}\right) 100 \%$ . Round to four decimals.

Does the integral $\int_{0}^{3} \frac{1}{x} dx$ converge or diverge?

Determine if the integral $\int_{-1}^{4} \frac{1}{x^{2 / 3}} d x$ converges or diverges.

Find the mean of the five-year CDs: $\bar{X} = \frac{5.95 + 5.90 + 5.84 + 5.83 + 5.78}{5} = \square$ (Type an integer or decimal.)

Find the significant figures in the measurement $1036.48g$ .

Does the integral $\int_{-\infty}^{\infty} e^{-3 x} dx$ converge or diverge?

Find the significant figures in the measurement $1036.48g$ .

Calculate the standard deviation from a variance of $0.00180$ . Round to four decimal places.

Find the limit: $\lim _{t \rightarrow 4^{+}} \frac{|7 t-28|}{t^{2}-16}$ .

Calculate $6 \times 6$ .

Find the area of an equilateral triangle as a function of its side length $s$ . Use the formula $A = \frac{\sqrt{3}}{4}s^2$ .

Find the maximum value of $f(x)=400 x-11 x^{2}-3$ graphically, rounded to four decimal places.

How many significant figures are in the measurement $5.0 \times 10^{-3}$ ?

Find the significant figures in these values: $5.0 \times 10^{-3}$ L, $20.8$ , $99.0$ , $13.70$ , $60,810,000$ g, $1036.48$ g.

Find the value of $y(1)$ for the initial value problem $\frac{d y}{d x}=\frac{\ln (x)}{x}$ with $y(e)=3$ .

Convert 1 meter (m) to nanometers (nm): $1 \mathrm{m} = ? \mathrm{nm}$ .

Find the value of the integral $\int_{4}^{4} f(x) d x$ given that $f$ and $g$ are continuous functions.

Find the value of $\int_{2}^{5} f(x) d x$ given that $\int_{0}^{2} f(x) dx=-1$ and $\int_{0}^{5} f(x) dx=3$ .

Find the value of the integral $\int_{2}^{0} g(x) d x$ given $\int_{0}^{2} g(x) d x=8$ . Enter as a decimal or DNE.

Calculate the integral $\int_{0}^{2}(5 f(x)+g(x)) d x$ given that $\int_{0}^{2} f(x) d x=-1$ and $\int_{0}^{2} g(x) d x=8$ .

Determine if the function $g(x)=-4 x^{5}+5 x^{3}$ is even, odd, or neither.

Calculate the expression: $16 - 4 \div 1 / 4 + 2 =$

Find the constant $x$ in the equation $H=x \frac{v}{A}$ from $v=\frac{7}{4} A H$ .

Solve the equation: $4 + 4$ .

Calculate the product of 12 and 12: $12 \times 12 = ?$

If $x = 5$ , find the value of $6x$ , $5x$ , $30x$ , and $R^{30}$ .

Factor the expression $36 x^{3}+21 x^{2}+3 x$ as $a x(b x+1)(c x+1)$ with $b>c$ . Find the value of $c$ .

Find where the lines $y = x - 3$ and $y = 3x^2$ intersect.

Rewrite the equations in slope-intercept form, find the slope and y-intercept, and graph them. 59. $3x + y - 5 = 0$ 60. $4x + y - 6 = 0$ 61. $2x + 3y - 18 = 0$ 62. $4x + 6y + 12 = 0$

Find the values of $x \in \mathbb{R}$ for which $f(x)=\frac{x^{2}+1}{x-1}$ is defined and continuous (in interval notation).

Find the values of $x \in \mathbb{R}$ for which $f(x)=\ln (x+1)$ is defined and continuous (interval notation).

Convert $4.608 \mathrm{lb}$ to kilograms with four significant figures.

Find where the function $f(x)=\sqrt{4x+16}$ is continuous and express the $\mathrm{x}$ -values in interval notation.

Find the intersection of the curves $y=2x^2+3$ and $y=-x+6$ .

Find the value of $a$ so that the function $f(x)=\frac{30+x-x^{2}}{x-6}$ is continuous at $x=6$ .

Check if the function $f(x)=\left\{\begin{array}{ll} \frac{x^{2}-1}{x-1} & \text{if } x \neq 1 \\ 4 & \text{if } x=1 \end{array}\right.$ is continuous at $a=1$ .

Find the intersection points of the lines $y=3-x$ and $y=-x^{2}+2x+3$ .

Find the value of $a$ for which $f(x)$ is continuous at all $x$ :
$f(x)=\begin{cases} x^{2}-99, & x<11 \\ 2 a x, & x \geq 11 \end{cases}$
Options: A. $a=$ B. No solution.

Find the value of $x$ in $g = x \sqrt{p}$ if $p = \frac{2 g^{2}}{50}$ .

Solve the equation $-0.0015 x^{2} + x + 2 = 0$ for $x$ .

Solve the equation $-0.0015 x^{2} + x + 2 = 0$ .

Calculate the value of the expression: $\frac{3.5}{9.205}$ .

Model the fungus growth rate $R(t)$ as $R(t)=\{2 e^{t}, 0 \leq t \leq t_{c}; a, t>t_{c}\}$ . Find $a$ for continuity at $t=t_{c}$ .

Find values of the linear function $f(x)=x$ for $x = -2, -1, 0, 1, 2$ .

Express the set $-6<x \leq-1$ in interval notation.

Solve for $x$ in the inequality $3 < -11(x+4) \leq -7$ . Answer in interval notation or type DNE if no solution exists.

Solve the inequality: $-11-8x \leq 12+8x$ . Enter your answer as an interval, like $[a, oo)$ .

Solve the inequality: $\frac{9}{3}+b<\frac{35}{27}$ . Enter your answer as an interval using "oo" for $\infty$ .

Solve the inequality $|4x + 3| < 8$ and express your solution in interval notation.

Solve the inequality $\left|\frac{x+21}{7}\right|>1$ and express the solution as an interval.

Solve the inequality: $-4|x-1|-3 \leq-23$ . Provide the solution in interval notation.

Simplify the expression: $3n + 2(-2n - 1)$ . Choose the equivalent expression: (A) $-n + 2$ , (B) $n + 2$ , (C) $-n - 2$ , (D) $n - 2$ .

Simplify the expression: $-4(z+3)-4(5-4 z)$ . Choose the correct equivalent expression from the options.

Simplify the expression: $-3(2+4k)+7(2k-1)$ . Choose the correct equivalent expression: (A) $2k-13$ , (B) $8k-13$ , (C) $2k+13$ , (D) $2k-7$ .

Solve the inequality: $\frac{6}{2}+a \leq \frac{19}{12}$ . Provide your answer as an interval using "oo" for $\infty$ .