Julie has a jewelry box shaped like a cube. If the volume is
216 cm³, what is the edge length of Julie's jewelry box?
A 14.7 cm
B 108 cm
C 6 cm
D 72 cm

The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:

θ = 7π/6

We can start by manipulating the given equation to express cscθ in terms of cscx:

2 csc x = 3 csc θ − csc θ sin θ

2/cscθ = 3 - sinθ

cscθ/2 = 1/(3 - sinθ)

cscθ = 2/(3 - sinθ)

Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:

1/cosθ = 2/(3 - sinθ)

cosθ = (3 - sinθ)/2

Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:

sin²θ + cos²θ = 1

sin²θ + [(3 - sinθ)/2]² = 1

Multiplying both sides by 4, we get:

4sin²θ + (3 - sinθ)² = 4

Expanding and simplifying, we get:

8sin²θ - 6sinθ - 8 = 0

Dividing both sides by 2, we get:

4sin²θ - 3sinθ - 4 = 0

Using the quadratic formula with a = 4, b = -3, and c = -4, we get:

sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))

sinθ = [3 ± √49]/8

sinθ = (3 ± 7)/8

Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8

= -1/2 corresponds to an angle of 7π/6 in the third quadrant.

To find cosθ, we can use the identity sin²θ + cos²θ = 1:

cosθ = ±√(1 - sin²θ)

Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:

cosθ = -√(1 - (-1/2)²)

cosθ = -√(3/4)

cosθ = -√3/2

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Answer:

y=1/2+2

Step-by-step explanation:

go up 1 and right 2 thats how you get 1/2 also its 2 point above the orgin so its +2

remember y=x+b  1/2 is the x(slope) and 2 is b

Answer:

y = (1/2)x+2

Step-by-step explanation:

See attached image

Answer:

20

Step-by-step explanation:

5*4=20

5*5=25, but it is bigger than 24.

So the ans is 20

After adding (-7) to each value in the given data set, the mean is 38.25, the median is 38, the mode does not exist, the range is 24, and the standard deviation is approximately 8.85.

To find the mean of the data set, add all the values together (49, 30, 34, 43, 31, 37, 25, 47) and divide the sum by the total number of values (8). The mean is the average value of the data set.

To determine the median, arrange the values in ascending order (25, 30, 31, 34, 37, 43, 47, 49) and find the middle value. In this case, the median is the average of the two middle values (34 and 37).

The mode refers to the value(s) that appear most frequently in the data set. In this case, there is no mode since no value appears more than once.

The range is calculated by subtracting the smallest value (25) from the largest value (49). Thus, the range is 24.

To calculate the standard deviation, subtract the mean from each value, square the differences, calculate the mean of those squared differences, and finally take the square root of the resulting value. This provides a measure of the dispersion or spread of the data around the mean.

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The number of ways Patricia can choose 44 pizza toppings from a menu of 55 toppings, where each topping can only be chosen once, can be calculated using the concept of combinations.

In this case, the number of ways to choose 44 toppings from 55 can be calculated using the formula for combinations, which is denoted as "nCr" or "C(n, r)". The formula is given by:

C(n, r) = n! / (r!(n-r)!)

where "n" represents the total number of items available (in this case, 55 toppings), and "r" represents the number of items to be chosen (in this case, 44 toppings).

Using the formula, we can calculate:

C(55, 44) = 55! / (44!(55-44)!)

Simplifying the equation, we find that there are approximately 4,855,643,210 ways for Patricia to choose 44 pizza toppings from a menu of 55 toppings if each topping can only be chosen once.

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Answer:

201000

Step-by-step explanation:

Step-by-step explanation:

2.01 × 10^5. That's the answer

The graph of the parametric equations x = -2cos(t) and y = -sin(t) within the range 0 ≤ t < 2π is an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis.

To sketch the graph of the parametric equations x = -2cos(t) and y = -sin(t), where 0 ≤ t < 2π, we need to plot the coordinates (x, y) for each value of t within the given range.

1. Start by choosing values of t within the given range, such as t = 0, π/4, π/2, π, 3π/4, and 2π.

2. Substitute each value of t into the equations to find the corresponding values of x and y. For example, when t = 0, x = -2cos(0) = -2 and y = -sin(0) = 0.

3. Plot the obtained coordinates (x, y) on a graph, using a coordinate system with the x-axis and y-axis. Repeat this step for each value of t.

4. Connect the plotted points with a smooth curve to obtain the graph of the parametric equations.

The graph will be an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis. It will have a vertical compression and a horizontal stretch due to the coefficients -2 and -1 in the equations.

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The equation of a line passing through the given point and parallel to the given equation is y = -x + 2

The equation of a line in slope-intercept form is expressed as y = mx + b

where

m is the slope

b is the intercept

The equation in point-slope form is expressed as y - y1 =m(x - x1)

Given

Slope = -1

Point = (-2, 4)

Substitute

y - 4 =-1(x - (-2))

y - 4 = -(x+2)

y - 4 = -x - 2

y = -x - 2+ 4

y = -x + 2

Hence the equation of a line passing through the given point and parallel to the given equation is y = -x + 2

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In this case, the first two components are multiples \((4 = -2 * -2, 6 = -3 * -2)\), so if h is \(-16 (8 * -2),\) the vectors are scalar multiples, and thus linearly dependent. For all other values of h, the vectors are linearly independent.

To find the transpose of a matrix, interchange its rows and columns. The standard matrix of a linear transformation T, which rotates points through 3/4 pi radians counterclockwise, can be given as:

\([cos(3/4 pi) -sin(3/4 pi)][sin(3/4 pi)  cos(3/4 pi)]\)

To find the matrix product AB, first check if the dimensions are compatible. If not, AB is undefined.

To find the inverse of a matrix, check if it is invertible. If not, the matrix does not have an inverse.

To determine if columns of a matrix form a linearly independent set, analyze the solutions of Ax = 0. If it has only the trivial solution, the columns are linearly independent. If it has more than one solution, they are not linearly independent.

For the vectors [-2 -3 8] and [4 6 h] to be linearly independent, they must not be scalar multiples of each other.

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9514 1404 393

Answer:

Step-by-step explanation:

The graph shows C = 400 when p = 0 (at the left edge). This is the y-intercept value, and is the cost of production when no phones are produced. It is essentially the fixed cost of rent and equipment.

When p=1, the graph shows C = 500. That is, the cost goes up by 100 when p goes up by 1. This is the cost per phone. It shows up in the cost equation as the slope. So, the cost equation is ...

  C = 400 +100p

Answer:

he is at -3

Step-by-step explanation:

On a number chart, If he goes 3 left hes going 3 negative. So it would be -3

I hope this helps!

Answer:

-2

Step-by-step explanation:

You subtract 3 from one

First jump 0

Second jump -1

Third Jump -2

There is sufficient evidence to believe that the number of household pets leaving the shelter over the weekend is different from the proportion of wildlife animals leaving the shelter over the weekend.

To determine if there's sufficient evidence,

Let us define the null and alternative hypotheses for this test as follows:

Null hypothesis (H0): The proportion of household pets leaving the shelter over the weekend is the same as the proportion of wildlife animals leaving the shelter over the weekend.

Alternative hypothesis (Ha): The proportion of household pets leaving the shelter over the weekend is different from the proportion of wildlife animals leaving the shelter over the weekend.

The test statistic for two sample test is given by:

z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2))

where

p1 and p2 are the proportions of household pets and wildlife animals leaving the shelter over the weekend, respectively,

p is the pooled proportion,

n1 and n2 are the sample sizes for household pets and wildlife animals, respectively.

Pooled proportion is

p = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of household pets and wildlife animals leaving the shelter over the weekend, respectively.

Given

-n1 = 376, n2 = 52, x1 = 29, x2 = 10

p = (29 + 10) / (376 + 52) = 0.091

The observed proportions are:

p1 = x1 / n1 = 29 / 376 = 0.0771

p2 = x2 / n2 = 10 / 52 = 0.1923

The test statistic value

z = (0.0771 - 0.1923) / sqrt(0.091 * (1 - 0.091) * (1/376 + 1/52)) = -3.04

By using a standard normal distribution table,

The p-value is 0.00238.

Since the p-value (0.00238) is less than the level of significance (0.01), we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the number of animals leaving the shelter over the weekend for household pets and wildlife animals.

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Answer:

Tammy must run 5.5 miles more this week to reach her goal

Step-by-step explanation:

10 miles - 4.5 mies = 5.5 miles

the derivative Dx[log₁₀(arccos(2sinh(x)))] is given by the expression:\((1/(arccos(2sinh(x))log(10))) * (-2cosh(x))/\sqrt(1 - 4*sinh^2(x))\).

What is derivative?

The derivative of a function represents the rate at which the function changes with respect to its independent variable.

To find Dx[log₁₀(arccos(2*sinh(x)))], we can use the chain rule and the logarithmic differentiation technique. Let's break it down step by step.

Start with the given function: f(x) = log₁₀(arccos(2*sinh(x))).

Apply the chain rule to differentiate the composition of functions. The chain rule states that if we have g(h(x)), then the derivative is given by g'(h(x)) * h'(x).

Identify the innermost function: h(x) = arccos(2*sinh(x)).

Differentiate the innermost function h(x) with respect to x:

h'(x) = d/dx[arccos(2*sinh(x))].

Apply the chain rule to differentiate arccos(2sinh(x)). The derivative of \(arccos(x) is -1/\sqrt(1 - x^2)\). The derivative of sinh(x) is cosh(x).

\(h'(x) = (-1/\sqrt(1 - (2sinh(x))^2)) * (d/dx[2sinh(x)]).\\\\= (-1/\sqrt(1 - 4sinh^2(x))) * (2*cosh(x)).\)

Simplify h'(x):

\(h'(x) = (-2cosh(x))/\sqrt(1 - 4sinh^2(x)).\)

Now, differentiate the outer function g(x) = log₁₀(h(x)) using the logarithmic differentiation technique. The derivative of log₁₀(x) is 1/(x*log(10)).

g'(x) = (1/(h(x)*log(10))) * h'(x).

Substitute the expression for h'(x) into g'(x):

\(g'(x) = (1/(h(x)log(10))) * (-2cosh(x))/\sqrt(1 - 4*sinh^2(x)).\)

Finally, substitute h(x) back into g'(x) to get the derivative of the original function f(x):

\(f'(x) = g'(x) = (1/(arccos(2sinh(x))log(10))) * (-2cosh(x))/\sqrt(1 - 4sinh^2(x)).\)

Therefore, the derivative Dx[log₁₀(arccos(2sinh(x)))] is given by the expression:

\((1/(arccos(2sinh(x))log(10))) * (-2cosh(x))/\sqrt(1 - 4*sinh^2(x)).\)

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Function 1 has a greater slope than Function 2, and the answer is Function 1.

Function 1 is defined by the equation y = \(\frac{5}{4}r - 1\).

Function 2 is defined by line p, which is shown on the graph.

The problem asks which function has a greater slope.

The slope of a line is calculated by the ratio of the difference between the vertical axis values and the difference between the horizontal axis values.

This is shown in the formula:

slope = rise/run.

Here, rise refers to the vertical difference and run refers to the horizontal difference.

This means that the slope of a line measures how steeply the line is increasing or decreasing.

Function 1: y = \(\frac{5}{4}r - 1\)

Here, the equation of Function 1 is given as y = \(\frac{5}{4}\)r - 1.

From this equation, we can see that the slope of Function 1 is equal to \(\frac{5}{4}\).

Therefore, the slope of Function 1 is 1.25.Function 2: Line pNext, we need to determine the slope of line p, which represents Function 2.

To do this, we can use two points on the line.

From the graph, we can see that the line passes through the point (0, -2) and the point (4, 1).

The rise of this line is equal to 1 - (-2) = 3, while the run is equal to 4 - 0 = 4.

Thus, the slope of line p is equal to 3/4.

Therefore, the slope of Function 2 is 0.75.

Comparing the slopes, we can see that Function 1 has a greater slope than Function 2.

Specifically, the slope of Function 1 is 1.25, while the slope of Function 2 is 0.75.

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The slope - intercept form of equation is,

⇒ y = 2x + 1

We have to given that;

Equation of line is,

⇒ 8x - 4y = - 4

Now, We can change it into slope - intercept form as;

⇒ 8x - 4y = - 4

⇒ 8x + 4 = 4y

⇒ 4y = 8x + 4

⇒ y = 2x + 1

Hence, We get;

Slope = 2

y - intercept = 1

Thus, The slope - intercept form of equation is,

⇒ y = 2x + 1

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The the function to estimate the average age of employee of a company is A(s)=0.285s + 59  , then the average age of employee in 2003 is 65.27 and in 2009 is 66.98

To estimate the average age of an employee in 2003, we need to find the value of A(s) when s = 22  ;

because the number of years between 2003 and 1981 is = 22 years ;

So , A(22) = 0.285×22 + 59 = 65.27  ;

The average age of an employee in 2003 is approximately 65.27.

To estimate the average age of an employee in 2009,

we need to find the value of A(s) when s = 28

because the number of years between 2009 and 1981 is = 28 years ;

So , A(28) = 0.285×28 + 59 = 66.98  ;

The Average age of employee in 2009 is approximately 71.48.

The given question is incomplete , the complete question is

The function​ A(s) given by ​A(s)=0.285s + 59  can be used to estimate the average age of employee of a company in the year 1981 to 2009. Let​ A(s) be the average age of an​ employee, and "s" be the number of year since​ 1981; that​ is, s=0 for 1981 and s=9 for 1990. What is the average age of the employee in 2003 and in​ 2009 ?

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Answer:

166.72

Step-by-step explanation:

A= 2(wl+hl+hw)

A= 2(3.2×8.5+4.8×8.5+4.8×3.2)

A= 2(27.2+40.8+15.36)

A= 2(83.36)

A= 2×83.36

A= 166.72

Answer:

Step-by-step explanation:

A more complicated expression such as 64x3+27y3 64 x 3 + 27 y 3 is also a sum of cubes since 64x3=(4x)3 64 x 3 = ( 4 x ) 3 and 27y3=(3y)3 27 y 3 = ( 3 y ) 3 . Please note, that expressions such as 2x3 2 x 3 are not perfect cubes.

Answer:

C. 63

63 = 3 * 3 * 7

It is not a prime number or prime factor

Step-by-step explanation:

Answer:

The answer is A.8x+13

Step-by-step explanation:

If In a class of 29 students, 19 are female and 14 have an A in the class then 2 male students have an A in the class.

We can calculate the number of students who are male and have an A in the class by subtracting the given values from the total number of students.

Total students = 29

Female students = 19

Male students = Total students - Female students = 29 - 19 = 10

Students with an A = 14

Male students without an A = 8

To calculate the number of male students with an A, we subtract the number of male students without an A from the total number of male students.

Male students with an A = Male students - Male students without an A = 10 - 8 = 2

Therefore, there are 2 male students who have an A in the class.

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The distance of Miles' destination is 175 miles.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The map is a scale drawing of a larger town. The scale drawing is reduced by constant dimensions.

\(\sf Actual \ distance = \dfrac{(25 \times 7)}{1} = \bold{175 \ miles}\)

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The tangent line at x = 5 is vertical.The equation of the tangent line at x = 5 is x = 5, which represents a vertical line passing through the point (5, undefined).

To find the derivative of f(x) = 1/(-x - 5) using the limit definition, we'll follow these steps:

Step 1: Set up the limit definition of the derivative:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

Step 2: Plug in the function f(x):

f'(x) = lim(h->0) [1/(-(x + h) - 5) - 1/(-x - 5)] / h

Step 3: Simplify the expression:

To simplify the expression, we need to find the least common denominator (LCD) for the fractions.

The LCD is (-x - 5)(-(x + h) - 5), which simplifies to (x + 5)(x + h + 5).

Now, let's rewrite the expression with the LCD:

f'(x) = lim(h->0) [(x + 5)(x + h + 5)/(x + 5)(x + h + 5) - (-x - 5)(x + h + 5)/(x + 5)(x + h + 5)] / h

f'(x) = lim(h->0) [(x + 5)(x + h + 5) - (-x - 5)(x + h + 5)] / [h(x + 5)(x + h + 5)]

Step 4: Expand and simplify the numerator:

f'(x) = lim(h->0) [x^2 + xh + 5x + 5h + 5x + 5h + 25 - (-x^2 - xh - 5x - 5h - 5x - 5h - 25)] / [h(x + 5)(x + h + 5)]

f'(x) = lim(h->0) [2xh + 10h] / [h(x + 5)(x + h + 5)]

Step 5: Cancel out the common terms:

f'(x) = lim(h->0) [2x + 10] / [(x + 5)(x + h + 5)]

Step 6: Take the limit as h approaches 0:

f'(x) = (2x + 10) / [(x + 5)(x + 5)] = (2x + 10) / (x + 5)^2

Now we have the derivative of f(x) as f'(x) = (2x + 10) / (x + 5)^2.

To find the equation of the tangent line at x = 5, we need to find the slope and use the point-slope form of a line.

Slope at x = 5:

f'(5) = (2(5) + 10) / (5 + 5)^2 = 20 / 100 = 1/5

Using the point-slope form with the point (5, f(5)):

y - f(5) = m(x - 5)

Since f(x) = 1/(-x - 5), f(5) = 1/0 (which is undefined). Therefore, the tangent line at x = 5 is vertical.

The equation of the tangent line at x = 5 is x = 5, which represents a vertical line passing through the point (5, undefined).

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Answer:

A

Step-by-step explanation:

Subtract 1.6 from the height each hour and it shows that the answers match the height each hour.

36

Step-by-step explanation:

4 5/8*3 is 13.875

500 decided by 13.875 is a little over 36, so you can make 36 full ribbons

Answer:36

Step-by-step explanation:

4 5/8*3 is 13.875

The statement which correctly describes the number of possible positive zeros and the number of possible negative zeros is

\(f(x)=x^4+2x^3-11x^2-5x-6\)

there is only one sign change

So, there is a maximum of 1 positive zero

\(f(-x) = (-x)^4 + 2(-x)^3 - 11(-x)^2 - 5(-x) - 6\\\\f(-x) = x^6 - 2x^3 - 11x^2 + 5x - 6\)

Sign changes 3 times

So, number of negative zeros is either 3 or 1

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Answer:

20 ft by 12 ft

Step-by-step explanation:

(10 in x 24) / 12 ft = (240 in / 12 ft) = 20 ft

(6 in x 24) / 12 ft = (144 in / 12 ft) = 12 ft