The slant height if the cone is 13 cm. What is the volume of a cone having a radius of 5 cm and a slant height of 13 cm.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - (-3)~~)^2 + (~~0 - (-6)~~)^2} \implies d=\sqrt{(5 +3)^2 + (0 +6)^2} \\\\\\ d=\sqrt{( 8 )^2 + ( 6 )^2} \implies d=\sqrt{ 64 + 36 } \implies d=\sqrt{ 100 }\implies d=10[/tex]

Answer:

48.91

Step-by-step explanation:

r=cos^-1(.92)

r=23.07

cos(23.07)=45/y

y=45/cos(23.07)

48.91

Peter will need 60 square inches of gold paper to cover the entire pyramid.

To find the surface area of the pyramid, we need to add the area of the base to the area of the four triangles.

Area of the base = 20 square inches

Area of each triangle = 10 square inches

Total area of the four triangles = 4 x 10 = 40 square inches

Total surface area = Area of base + Total area of four triangles

                                = 20 + 40

                                = 60 square inches

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A linear function would be the  best fit for the data.

A function that would be the best for this data is: D. y = -4/25(x) + 10

The amount of snow that would be on the ground when the temperature reaches 55° is 1.2 inches.

In this scenario, the temperature would be plotted on the x-axis (x-coordinate) of the scatter plot while the snow (inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the temperature and the snow (inches), an equation for the line of best fit is given by:

y = -0.16x + 10

y = -4/25(x) + 10

When x = 55, the amount of snow is given by;

y = -4/25(55) + 10

y = 1.2 inches.

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The function represents exponential decay with a percentage rate of decrease of 9.8%.

The given exponential function y = 660(0.902) represents decay because the base of the exponent is less than one.

This means that the output value of the function will decrease as the input value increases.

To determine the percentage rate of decrease, we need to find the value of the base of the exponent subtracted from one and then multiply it by 100.

The base of the exponent is 0.902, so we subtract it from one to get 0.098.

Multiplying by 100 gives us a percentage rate of decrease of 9.8%.

This means that for every unit increase in the input value, the output value of the function will decrease by approximately 9.8%.

For example, if the input value increases from 1 to 2, the output value will decrease by 9.8%, and if the input value increases from 2 to 3, the output value will again decrease by 9.8%.

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Value of p is approximately 0.987.

To find the p-value for the given claim that the mean body temperature at 12 AM is μ > 98.6°F with a sample size of n=8 and a test statistic of t=-2.687, follow these steps:

1. Identify the degrees of freedom: Since the sample size is n=8, the degrees of freedom (df) are calculated as n-1, which is 8-1=7.

2. Determine the tail of the test: The claim states that the mean body temperature is greater than 98.6°F (μ > 98.6), which indicates a right-tailed test.

3. Find the p-value using the t-distribution table or a calculator: With a test statistic of t=-2.687 and df=7, you can look up the corresponding p-value using a t-distribution table or an online calculator. Since it's a right-tailed test, the p-value will be the area to the right of the test statistic in the t-distribution.

After completing these steps, the p-value is found to be approximately 0.987.

Therefore, your answer is: The p-value for the claim that the mean body temperature at 12 AM is μ > 98.6°F, given a sample size of n=8 and a test statistic of t=-2.687, is approximately 0.987.

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The value of s is, 27 yards

:: Volume of cube with side s, is equal to s³

So, as the given volume is 19,683 cubic yards.

Therefore, it can related as,

s³ = 19,683 (yards)³

So,

s = ∛(19,683) yards

s = 27 yards

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The expression that can be used to find the third number in Mark's pattern is 3[3(5) - 1]. The correct option is C.

In Mark's pattern, the rule is to subtract 1 from the previous number and then multiply the result by 3.

Starting with 5 as the first number, we can apply this rule step by step to find the subsequent numbers.

First step: Subtract 1 from 5, giving us 4.

Second step: Multiply 4 by 3, which equals 12.

So, the second number in Mark's pattern is 12.

Now, to find the third number, we apply the same rule.

First step: Subtract 1 from 12, giving us 11.

Second step: Multiply 11 by 3, which equals 33.

Therefore, the third number in Mark's pattern is 33.

Option C, 3[3(5) - 1], correctly represents this calculation, where 5 is subtracted by 1, multiplied by 3, and then multiplied by 3 again.

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To compute Bu(1.-3) - 88 - (1, -3), we need to substitute the values of u and v into the expression for w.

First, we need to find the values of u and v. Since u = 1.-3 and v = (1, -3), we have:

u = 1.-3 = 1 - 0.3 = 0.7
v = (1, -3)

Next, we can substitute these values into the expression for w:

w = 2xy + y^2 - 4x^2
 = 2(1)(-3) + (-3)^2 - 4(1)^2  (substituting x = 1 and y = -3)
 = -6 + 9 - 4
 = -1

Finally, we can compute Bu(1.-3) - 88 - (1, -3) by multiplying the gradient of w by the vector (1, -3) and subtracting 88:

Bu(1.-3) - 88 - (1, -3) = (-8x + 2y, 2x + 2y)  (1, -3) - 88
                        = (-8(1) + 2(-3), 2(1) + 2(-3))  (1, -3) - 88
                        = (-14, -4)  (1, -3) - 88
                        = (-14)(1) + (-4)(-3) - 88
                        = -14 + 12 - 88
                        = -90

Therefore, Bu(1.-3) - 88 - (1, -3) = -90.

Since the question seems to have some typos or missing information, I'll assume you want to find the partial derivatives of w with respect to x and y, and evaluate them at the point (1, -3).

Given w = 2xy + y² - 4x², let's compute the partial derivatives:

∂w/∂x = 2y - 8x
∂w/∂y = 2x + 2y

Now, let's evaluate these partial derivatives at the point (1, -3):

∂w/∂x(1, -3) = 2(-3) - 8(1) = -6 - 8 = -14
∂w/∂y(1, -3) = 2(1) + 2(-3) = 2 - 6 = -4

Thus, the evaluated partial derivatives are ∂w/∂x(1, -3) = -14 and ∂w/∂y(1, -3) = -4.

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The mode of the number of push-ups is 40.

A stem-and-leaf plot is a way of organizing data where the stems (the tens digit) and leaves (the ones digit) are separated. Each row represents a stem and the leaves represent the values that belong to that stem.

Here's the stem-and-leaf plot for the number of push-ups:

3 | 5 6 8

4 | 0 0 1 2 2 3 5 6 8 9

5 | 0 1 3 4 5 5 7 8 9

6 | 0 1 2 2 3 4 5 7 8 9

7 | 0 2 5 8

8 | 1 2 4

9 | 0

To find the mode, we look for the value that appears most frequently. In this case, the number 40 appears three times, which is more than any other value. Therefore, the mode of the number of push-ups is 40.

Note that the stem-and-leaf plot makes it easy to see the distribution of the data. For example, we can see that there are a lot of values between 40 and 49, and relatively few values above 60.

We can also see that there are no values between 90 and 99.

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There are 3 ordered pairs (x, y) that satisfy the equation y=(x-5)^2-1.

To find the ordered pairs (x, y) for 3 < x < 7 that satisfy the equation y=(x-5)^2-1, follow these steps:

Step 1: Set the range of x values: 3 < x < 7

Step 2: Plug in each whole number value of x within the given range (4, 5, and 6) into the equation and calculate the corresponding y values.

For x = 4:
y = (4 - 5)^2 - 1
y = (-1)^2 - 1
y = 0

For x = 5:
y = (5 - 5)^2 - 1
y = (0)^2 - 1
y = -1

For x = 6:
y = (6 - 5)^2 - 1
y = (1)^2 - 1
y = 0

Step 3: Write the ordered pairs (x, y) based on the calculated y values.

For x = 4, the ordered pair is (4, 0)
For x = 5, the ordered pair is (5, -1)
For x = 6, the ordered pair is (6, 0)

In the given range, there are 3 ordered pairs (x, y) that satisfy the equation y=(x-5)^2-1.

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Out of the 150 new couples, we can expect about:

45 * (150/240) = 28.125 couples where the husband prefers action but the wife does not.

30 * (150/240) = 18.75 couples where the wife prefers action but the husband does not.

What is probability?

Probability is a measure of the likelihood of an event occurring.

Based on the given data from the survey of 225 couples, we can construct a contingency table as follows:

                      Husband   Wife   Total

Action                45          30        75

Comedy            30          45        75

Drama               45          45        90

Total                 120        120       240

From the contingency table, we can see that:

Out of 240 respondents, 75 (45 from husbands and 30 from wives) preferred action movies.

Out of 240 respondents, 60 (30 from husbands and 30 from wives) preferred comedy movies.

Out of 240 respondents, 90 (45 from husbands and 45 from wives) preferred drama movies.

To answer the question of how many of the 150 couples will have exactly one spouse who prefers action movie, we can use the information that:

Out of 240 respondents, 45 husbands preferred action movies but their wives did not.

Out of 240 respondents, 30 wives preferred action movies but their husbands did not.

Therefore, out of the 150 new couples, we can expect about:

45 * (150/240) = 28.125 couples where the husband prefers action but the wife does not.

30 * (150/240) = 18.75 couples where the wife prefers action but the husband does not.

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Answer:

1) a = 14

2) -4 (x - 2)² - 5

Step-by-step explanation:

To obtain a vertex, you take h and k in a equation.

So a(x-h)²+k = a(x-2)² -5

For the point (1, - 9),

a[(1)-2]² - 5 = - 9

a(1) = -9+5

a = -4

so the final equation is

-4(x-2)² - 5

I'm not 100% sure about this but I tried. Let me know if it makes sense

If Chris bought 5 tacos and 2 burritos for $13. 25 and  Brett bought 3 tacos and 2 burritos for $10. 75, the price of one taco is $1.25, and the price of one burrito is $3.50.

Let the price of one taco be T and the price of one burrito be B. We have the following equations:

5T + 2B = $13.25
3T + 2B = $10.75

To find the prices of the taco and the burrito, we can use the system of equations. First, subtract the second equation from the first equation:

(5T + 2B) - (3T + 2B) = $13.25 - $10.75
2T = $2.50

Now, divide by 2 to find the price of one taco:

T = $1.25

Next, plug the value of T back into one of the equations (let's use the second equation):

3($1.25) + 2B = $10.75
$3.75 + 2B = $10.75

Now, subtract $3.75 from both sides:

2B = $7.00

Finally, divide by 2 to find the price of one burrito:

B = $3.50

So, the price of one taco is $1.25, and the price of one burrito is $3.50.

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The probability that the mean cost of the 9 weddings is more than the mean cost of the 6 showers is approximately 0.0207 or 2.07%.

The probability that the mean cost of the 9 weddings is more than the mean cost of the 6 showers can be found using the Z-score and the difference between the means of two normally distributed variables.

1: Calculate the difference in means and standard deviations.
Δμ = μ_weddings - μ_showers = $82.30 - $65 = $17.30
Δσ = sqrt((σ_weddings²/n_weddings) + (σ_showers²/n_showers)) = sqrt((18.20²/9) + (17.73²/6)) = $8.47

2: Calculate the Z-score.
Z = (Δμ - 0) / Δσ = (17.30 - 0) / 8.47 ≈ 2.04

3: Determine the probability using a Z-table.
P(Z > 2.04) ≈ 0.0207

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Thus, the coordinates of Quadrilateral A'B'C'D' after the dilation with the scale factor of 1/2 are -  A'(1.5, 2), B'(0.5, 5), C'(6, 7), D'(4.5, 1.4).

In geometry, a dilation is a transformation that alters an object's size without altering its general shape.

Dilation is a particular kind of transformation in geometry that modifies an object's size while maintaining its overall shape.

Given:

scale factor = 1/2

coordinates of Quadrilateral ABCD

A(3,4) , B(1,10) ,C(12,14), D(9,3)

Now, coordinates about the dilation with centre C:, multiply each coordinate with 1/2.

A'(3*1/2,4*1/2)   --> A'(1.5, 2)

B'(1*1/2,10*1/2)    ---> B'(0.5, 5)

C'(12*1/2,14*1/2), --> C'(6, 7)

D'(9*1/2,3*1/2) ---> D'(4.5, 1.4)

Thus, the coordinates of Quadrilateral A'B'C'D' after the dilation with the scale factor of 1/2 are -  A'(1.5, 2), B'(0.5, 5), C'(6, 7), D'(4.5, 1.4).

Graph is attached.

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The combination of side lengths that would not form a triangle is C.XY = 11 mm, YZ = 14 mm, XZ = 21 mm.

We shall use the triangle inequality theorem to determine if a set of side lengths can form a triangle.

The triangle inequality theorem says that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

We shall calculate each of the options:

For option A:

XY + YZ = 7 mm + 14 mm = 21 mm which is < XZ = 25 mm.

Therefore, option A does form a triangle.

For option B:

XY + YZ = 11 mm + 18 mm = 29 mm, which is > XZ = 21 mm.

YZ + XZ = 18 mm + 21 mm = 39 mm, which is > XY = 11 mm.

XY + XZ = 11 mm + 21 mm = 32 mm, which is > YZ = 18 mm.

Therefore, option B does form a triangle.

For option C:

XY + YZ = 11 mm + 14 mm = 25 mm, and is > XZ = 21 mm.

Therefore, option C does not form a triangle.

For option D:

XY + YZ = 7 mm + 14 mm = 21 mm, which is > XZ = 17 mm.

YZ + XZ = 14 mm + 17 mm = 31 mm, which is > XY = 7 mm.

XY + XZ = 7 mm + 17 mm = 24 mm, which is > YZ = 14 mm.

Therefore, option D does form a triangle.

Therefore, the combination of side lengths that would not form a triangle is XY = 11 mm, YZ = 14 mm, XZ = 21 mm.

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The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of the data. From the box-and-whisker plot given, the IQR is 12.

The box-and-whisker plot provides us with the following information:

Therefore, the range of the data is the difference between the maximum and minimum values:

Range = maximum value - minimum value = 13 - 1 = 12

So, the range of the data is 12.

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Full Question: The box-and-whisker plot shows the number of pigeons spotted by visitors at the park during the last weekend. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 What is the interquartile range of the data? Provide your answer below:

Image attached

Answer: B, C, E

Step-by-step explanation: Other dude posted wrong answer.

For the g(x) functions provided, here are their key features:

g(x) = (x + 2)(x − 1)(x − 2)

End behavior: As x approaches negative or positive infinity, g(x) approaches positive infinity.

Y-intercept: g(0) = -4

Zeros: x = -2, 1, 2

Ray and Kelsey could both be accurate, all depending on the stated third-degree polynomial function.

It is conceivable for a third-degree polynomial to present up to three zeros, thus corroborating Kelsey's point that the function can have up to three intersection points with the x-axis maximum. Moreover, it can even occur that this function possesses a repeatable zero, causing a fourth interception.

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(i) A Venn-diagram of this information is shown below.

(ii) The number of students who like picnic = 34

(iii) The number of students who like hiking only = 51

(iv) The percentage of students who like picnic only. = 45.33%

Let us assume that A represents the set of students who like picnic.

B represents the set of students who like the hiking.

The total number of students in a  class are: n(A U B) = 75

Out of 75 students, 10 like both the activities.

n(A ∩ B) = 10

The ratio of the number of students who like picnic to those who like hiking is 2 : 3

Let number of students like tea n(A) = 2x

and the number of students like coffee n(B) = 3x

n(A U B) = n(A) + n(B) - n(A ∩ B)

75 = 2x + 3x - 10

75 + 10 = 5x

85/5= x

x = 17

The number of students like picnic = 2x

                                                          = 2 × 17

                                                          = 34

The number of students like hiking = 3x

                                                           = 3 × 17

                                                           = 51

This informtaion in Venn diagram is shown below.

The percentage of students who like picnic only would be,

(34/75) × 100 = 45.33%

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Answer: ln|y/8| + C
Explanation:

First, we need to recognize that the derivative of arctan(x) is 1/(1+x^2). Therefore, the derivative of arctan(y/8) is 8/(64+y^2).

Now, using the substitution u = y/8, we can rewrite the integral as:

∫(1/u)(64+64u^2)(8/(64+64u^2))du

Simplifying, we get:

∫(1/u)du = ln|u| = ln|y/8|

Therefore, the final answer is:

ln|y/8| + C

where C is the constant of integration.

The technician will bill a total of 150 hours to the job. To find the total hours, we need to determine how many hours the technician will work during the first three weeks and the last three weeks, and then add them together.

1. First three weeks:

The technician will be 25% billable during these weeks. They work 40 hours per week, so we need to calculate 25% of 40 hours for each week:

25% of 40 hours = 0.25 * 40 = 10 hours per week

Since there are three weeks, we'll multiply these hours by 3:
10 hours/week * 3 weeks = 30 hours

2. Last three weeks:

The technician will be 100% billable during these weeks. They work 40 hours per week, so they'll bill 40 hours for each of these weeks:
40 hours/week * 3 weeks = 120 hours

3. Finally,

we need to add the hours from the first and last three weeks together to find the total hours the technician will bill to the job:
30 hours (first three weeks) + 120 hours (last three weeks) = 150 hours

The technician will bill a total of 150 hours to the job.

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194 children, 58 students, and 97 adults attended the movie.

Let's use algebra to solve this problem.

Let's assume the number of children who attended the movie is C, the number of students is S, and the number of adults is A.

From the problem, we know that:

The seating capacity of the theater is 349:

C + S + A = 349

The theater charges $5 for children, $7 for students, and $12 for adults:

5C + 7S + 12A = $2540

There are half as many adults as there are children:

A = 1/2C

Now we can substitute A = 1/2C from the third equation into the first and second equations:

C + S + 1/2C = 349

3/2C + S = 349

5C + 7S + 12(1/2C) = $2540

5C + 7S + 6C = $2540

11C + 7S = $2540

Now we have two equations with two variables, C and S.

We can solve for S in the first equation:

3/2C + S = 349

S = 349 - 3/2C

Now we can substitute S = 349 - 3/2C into the second equation:

11C + 7S = $2540

11C + 7(349 - 3/2C) = $2540

11C + 2443 - 10.5C = $2540

0.5C = 97

C = 194

Therefore, 194 children attended the movie of total sales.

We can use A = 1/2C from the third equation to find the number of adults:

A = 1/2C

A = 1/2(194)

A = 97

Therefore, 97 adults attended the movie.

We can use C + S + A = 349 to find the number of students:

C + S + A = 349

194 + S + 97 = 349

S = 58

Therefore, 58 students attended the movie.

In summary, 194 children, 58 students, and 97 adults attended the movie.

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The solution of the quadratic equation is y = (x + 3)(x - 3).

The solution of the quadratic equation is calculated by applying difference of two squares as shown below;

y = x² - 9

y = x² - 3²

the difference of two square of x² - 3² = (x + 3)(x - 3)

The solution of the quadratic equation is calculated as;

y = (x + 3)(x - 3)

Thus, solution of the quadratic equation has been determined using  square root method.

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Both situations can be represented by the number line as they both involve values either greater than or less than 75.

The number line the teacher drew can represent both Brooke's and Eileen's situations.

In Brooke's situation, the number line can represent the amount of money Christopher needs to earn to buy a new bicycle. If he needs to earn more than $75, any point on the number line greater than 75 would represent the amount of money he has earned that is sufficient for purchasing the bicycle.

In Eileen's situation, the number line can represent the time left in Paul's flight. If Paul has less than 75 minutes left, any point on the number line less than 75 would represent the time remaining in his flight.

Both situations can be represented by the number line as they both involve values either greater than or less than 75.

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The greatest of the three interior angles in the triangle is approximately 71.2 degrees.

To find out which of the three interior angles in the triangle is the greatest, we can use the fact that the largest angle is opposite the longest side. So, in this case, the longest side is 22, which means that the angle opposite it must be the greatest. We can use the Law of Cosines to find the measure of this angle:

c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides. Plugging in the values we know, we get:

22^2 = 12^2 + 17^2 - 2*12*17*cos(C)

484 = 144 + 289 - 408*cos(C)

51 = 408*cos(C)

cos(C) = 51/408

C = cos^-1(51/408)

C ≈ 71.2 degrees

So the greatest of the three interior angles in the triangle is approximately 71.2 degrees.

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