find the volume of this composite object!
(use 3 for pi)

The volume of sphere A is 256π/3 cm³.

The volume of sphere B is  288π cm³.

The volume of sphere C is   2048π/3 cm³.

The volume of each sphere is calculated as follows;

V = ⁴/₃ πr³

where;

Volume of sphere A;

V = ⁴/₃ πr³

V = ⁴/₃ π(4³) = 256π/3 cm³

Volume of sphere B;

V = ⁴/₃ πr³

V = ⁴/₃ π(6³) = 288π cm³

Volume of sphere C;

V = ⁴/₃ πr³

V = ⁴/₃ π(8³) = 2048π/3 cm³

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If the area of a square of side (4x-1) is equal to 49, the perimeter of the square is 12 units.

We can start by using the formula for the area of a square, which is side squared, to solve for the side of the square. In this case, we know that the area of the square is 49, so we can set up the equation as follows:

(4x-1)² = 49

Expanding the left side of the equation, we get:

16x² - 8x + 1 = 49

Subtracting 49 from both sides, we get:

16x² - 8x - 48 = 0

Dividing both sides by 8, we get:

2x² - x - 3 = 0

We can solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values of a, b, and c from our equation, we get:

x = (-(-1) ± √((-1)² - 4(2)(-3))) / 2(2)

x = (1 ± √(25)) / 4

x = (1 ± 5) / 4

x = 1 or x = -3/2

Since the side of a square cannot be negative, we can only use the solution x = 1.

Therefore, the side of the square is 4x-1 = 4(1)-1 = 3.

To determine the perimeter of the square, we can use the formula for the perimeter of a square, which is 4 times the length of one side. In this case, the length of one side is 3, so the perimeter of the square is:

4 x 3 = 12

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The scenario that represents the expression is Making three payments of $20 each to total paying. Option A

3(-20) denotes three times negative twenty, which is simplified to -60.

This can illustrate the scenario of making three $20 payments to total $60, as each payment of $20 leads in a $60 drop in total. The proper scenario is Option A.

Option B entails paying 20 $3 payments for a total payment of $60, but the phrase 3(-20) does not describe this circumstance.

Option C entails getting money from three pals, which has nothing to do with the payment phrase 3(-20).

Option D entails paying $3 for each of 20 arcade games, for a total payment of $60, although this situation is unrelated to the payment phrase 3(-20).

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The claim that the population mean is less than 125 (Option E) would

the interval tends to refute.

The 90% confidence interval for the population mean is 135 to 160. This means that if we were to repeat the process of taking samples from the same population and constructing a 90% confidence interval, we would expect 90% of the intervals to contain the true population mean.

With this in mind, let's consider each claim:

A. The interval does not rule out the possibility that the population mean is more than 110, as 110 is less than the lower bound of the interval.

B. The interval does not rule out the possibility that the population mean is less than 150, as 150 is greater than the upper bound of the interval.

C. The interval does not rule out the possibility that the population mean is between 140 and 150, as both of these values fall within the interval.

D. The interval does not rule out the possibility that the population mean is more than 140, as 140 is less than the upper bound of the interval.

E. The interval refutes the claim that the population mean is less than 125, as 125 is less than the lower bound of the interval.

Therefore, the answer is (E) The population mean is less than than 125.

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The measure of the angle ∠6 as 57 degrees.

Same-side interior angles are pairs of angles that are on the same side of the transversal and between the two parallel lines. When two parallel lines are intersected by a transversal, the same-side interior angles are supplementary, which means that they add up to 180 degrees. This is known as the Same-Side Interior Angles Theorem.

Now, let's apply this theorem to the given problem. We are given that ∠4 is 123 degrees and we need to find the measure of ∠6. Since ∠4 and ∠6 are same-side interior angles, we know that they add up to 180 degrees. We can use this information to set up an equation:

∠4 + ∠6 = 180

Substituting the value of ∠4 as 123 degrees, we get:

123 + ∠6 = 180

To solve for ∠6, we can subtract 123 from both sides of the equation:

∠6 = 180 - 123

Simplifying the right-hand side of the equation, we get:

∠6 = 57

Therefore, the measure of ∠6 is 57 degrees.

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Complete Question:

Same-side interior angles always add up to 180°. If ∠4 and ∠6 are same-side interior angles, what is the measure of ∠6 where the value of ∠4 is 123 degrees?

The required volume and total surface area of the pentagonal pyramid are 15√3

Using the Pythagorean theorem, we can find s:

s² = (3√2)² + (s/2)²

s²2 = 18 + (s²/4)

3s²/4 = 18

s² = 24

s = 2√6

Now, we can find the area of each triangle:

Area of triangle = (1/2) * apothem * side

Area of triangle = (1/2) * 3√2 * 2√6

Area of triangle = 3√3

The total area of the base pentagon is 5 times the area of each triangle:

Area of base = 5 * 3√3

Area of base = 15√3

Now, we can find the volume of the pentagonal pyramid:

V = (1/3) * Base Area * Height

V = (1/3) * 15√3 * 3

V = 15√3

To find the surface area of the pentagonal pyramid,
Area of triangular face = (1/2) * side * slant height
The slant height is the distance from the midpoint of one of the sides of the pentagon to the apex of the pyramid.
slant height² = height² + (s/2²
slant height² = 9 + 6
slant height = √15

Now, we can find the area of each triangular face:
Area of triangular face = (1/2) * 2√6 * √15
Area of triangular face = 3√10

There are five triangular faces, so the total area of the triangular faces is:

Total area of triangular faces = 5 * 3√10
The total area of triangular faces = 15√10

Adding the area of the pentagonal base, we get the total surface area:

Total surface area = 15√3 + 15√10

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Equation to find b is 0.05b = 5.10.

Let's use the variable b to represent the cost of the haircut.

According to the problem, the tip was 5% of the cost of the haircut, which can be written as:

0.05b = 5.10

To solve for b, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.05:

b = 5.10 ÷ 0.05

b = 102

So the cost of the haircut was $102. We can check this by calculating 5% of $102, which gives us a tip of $5.10, as stated in the problem.

Therefore, the equation to find b, the cost of the haircut, is:

0.05b = 5.10

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From the given scatter plot we can conclude that No, Fabricio should draw the line with all of the data points above it.

Hence the correct option is (A).

The given graph is a scatter plot of a data set.

The line should fit the scatter points that is the line must passes through most of the points which shows a common trends or which depicts the characteristics of the data set.

Here in the given scatter plot we can see that the points chronically goes in downward direction.

So the fit line should be a straight line in downward direction that is a decreasing straight line.

But Fabricio drew a increasing line.

So the correct choice is (A).

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The question us incomplete. The complete question will be -

4√5+2√5

4+2(√5)

6√5

option C

To find the point P on the line y=3x that is closest to the point (50,0), we need to use the formula for the distance between a point and a line. This formula is:

distance = |Ax + By + C| / sqrt(A^2 + B^2)

Where A, B, and C are the coefficients of the equation of the line in the form Ax + By + C = 0.

In this case, the equation of the line y=3x can be written as -3x + y = 0. So we have:

A = -3, B = 1, C = 0

Now we can plug in the values of (50,0) and solve for x and y to find the point P that is closest to it:

distance = |-3x + y| / sqrt((-3)^2 + 1^2)
distance = |-3x| / sqrt(10)

To minimize the distance, we need to minimize |-3x|. This occurs when x = 0. So the point P that is closest to (50,0) is the point (0,0).
To find the point P on the line y = 3x that is closest to the point (50, 0), we need to minimize the distance between P and (50, 0).

Let P(x, y) be a point on the line y = 3x. The distance between P and (50, 0) is given by the distance formula:

D = sqrt((x - 50)^2 + (y - 0)^2)

Since y = 3x, we can rewrite the distance formula as:

D = sqrt((x - 50)^2 + (3x)^2)

To minimize the distance, we can minimize the square of the distance (D^2), as it avoids dealing with the square root:

D^2 = (x - 50)^2 + (3x)^2

Now, we can find the derivative of D^2 with respect to x and set it to 0 to find the critical points:

d(D^2)/dx = 2(x - 50) + 2(3x)^2 * 6x = 0

Solve this equation to find the x-coordinate of the point P. Then, use y = 3x to find the corresponding y-coordinate. Finally, you'll have the coordinates of the point P that is closest to (50, 0).

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Answer:

3

Step-by-step explanation:

1/2x3x2

1.5x2

3

Hope this helps :)

[tex]\textit{Pythagorean Identities} \\\\ \sin^2(\theta)+\cos^2(\theta)=1\implies \cos^2(\theta )=1-\sin^2(\theta ) \\\\ 1+\cot^2(\theta)=\csc^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{1-\sin^2(\theta )}{1+\cot^2(\theta )}~~ = ~~\sin^2(\theta )\cos^2(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1-\sin^2(\theta )}{1+\cot^2(\theta )}\implies \cfrac{\cos^2(\theta )}{\csc^2(\theta )}\implies \cfrac{\cos^2(\theta )}{ ~~ \frac{1}{\sin^2(\theta )} ~~ }\implies \cos^2(\theta )\sin^2(\theta )[/tex]

The alternative hypothesis μ ≠ 0 would indicate a two-tailed test.

Option  C is the correct answer.

We have,

A two-tailed test is a statistical test where the alternative hypothesis is that the population parameter is not equal to a specific value.

In this case,

The alternative hypothesis of μ ≠ 0 indicates that the population mean can be either greater than or less than zero, leading to two possible outcomes

in the test. It means that the test will check if the population mean is significantly different from zero in either direction.

This is in contrast to a one-tailed test, where the alternative hypothesis is directional and indicates that the population parameter is either greater than or less than a specific value.

Thus,

The alternative hypothesis μ ≠ 0 would indicate a two-tailed test.

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The complete question.

Which of the following alternative hypotheses would indicate a two-tailed test?

μ  > 0

μ < 0

μ ≠ 0

μ = 0

The total number of arrangements, we can simply add up the results from each case:

C(21,8) + C(5,1) C(21,7) 8 + C(5,2) C(21,6) 2

Now, We can solve this problem, we can break it down into three cases, based on the number of vowels included in the arrangement.

Hence, Here are the three cases:

Case 1: No vowels included: In this case, we need to select 8 letters from the 21 consonants in the alphabet.

This can be done with C(21,8) ways.

Case 2: One vowel included:

Here, we need to select one of the five vowels and then select 7 letters from the 21 consonants.

The vowel can be placed in any of the 8 positions, but once it is placed, the other vowels must be placed in alphabetical order.

Therefore, the number of arrangements in this case is, C(5,1) C(21,7) 8.

Case 3: Two vowels included: In this case, we need to select two of the five vowels, and then select 6 letters from the 21 consonants.

Again, the vowels must be placed in alphabetical order once they are selected.

However, we have two possible orders to place the vowels - either at the start or in the middle of the 8-letter arrangement.

Therefore, the number of arrangements in this case is C(5,2) C(21,6) 2.

So, The total number of arrangements, we can simply add up the results from each case:

C(21,8) + C(5,1) C(21,7) 8 + C(5,2) C(21,6) 2

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Answer:

C

D

Step-by-step explanation:

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ r=13 \end{cases}\implies A=\cfrac{(42)\pi (13)^2}{360} \\\\\\ A=\cfrac{1183\pi }{60}\implies \implies A\approx 61.94[/tex]

Answer:

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2.

Step-by-step explanation:

The range is the simplest measure of variability and is the difference between the largest and smallest values. In this case, the largest value is 20 and the smallest value is 2, so the range is:

Range = 20 - 2 = 18

However, since there are some extreme values (2 and 20), it may be better to use a measure of variability that is less affected by outliers. The interquartile range (IQR) is a good measure of variability that is less affected by extreme values.

To find the IQR, we need to find the median of the data set. The median is the middle value when the data is arranged in order. In this case, the data set has an even number of values, so the median is the average of the two middle values:

Median = (10 + 12) / 2 = 11

Next, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set. In this case, the lower half of the data set is {2, 10, 10} and the upper half of the data set is {12, 12, 20}.

Q1 = Median of lower half = 10

Q3 = Median of upper half = 12

So, the IQR is:

IQR = Q3 - Q1 = 12 - 10 = 2

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2.

There is a 25% chance that a flight between New York City and Chicago will take between 97 and 98 minutes.

Since the time to fly between New York City and Chicago is uniformly distributed between 96 and 100 minutes, the probability of a flight being between any two times is proportional to the length of the time interval between those two times.

To find the probability that a flight is between 97 and 98 minutes, we need to calculate the length of the time interval between those two times, which is 1 minute.

Then, we divide the length of the interval by the length of the entire time range (100-96 = 4 minutes) to obtain the probability of a flight being between 97 and 98 minutes: Probability = 1 minute / 4 minutes = 0.25 or 25%.

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To find the limit, we can begin by multiplying the numerator and denominator by the conjugate of the numerator, which is (√1 + 8x + √1 - 10x):

lim (√1 + 8x - √1 - 10x)/x

= lim [(√1 + 8x - √1 - 10x)/(√1 + 8x + √1 - 10x)] * [(√1 + 8x + √1 - 10x)/x]

= lim [(8x - 10x)/ (x(√1 + 8x + √1 - 10x))] * [(√1 + 8x + √1 - 10x)/x]

= lim [(8 - 10)/ (√1 + 8x + √1 - 10x)]

= lim [-2/ (2√1)]

= -1/√1

= -1

Therefore, the limit of the given expression as x approaches 0 is -1. We didn't need to use l'Hospital's Rule for this problem, as it was possible to simplify the expression before applying the limit.

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Answer:

Yes, you need to find the GCF (greatest common factor) to solve this word problem.

The greatest common factor of 35 and 42 is 7. So you can create 7 teams with equal number of boys and girls on each team without leaving anyone out

Step-by-step explanation:

Answer:jessica

Step-by-step explanation:

do distance divided by time for all of them except noah and find the greatest

The student's parents will pay half of the first-year cost, which is $12,000.

The academic scholarship will pay an additional $500, leaving the student with a remaining cost of $24,000 - $12,000 - $500 = $11,500 for the first year.

If the student wants to pay off the remaining $11,500 by the end of 12 months, they will need to save an average of $958.33 per month.

Therefore, the minimum amount that the student will need to save every month is approximately $958.33.

The function f(x) is a logarithmic function with a vertical asymptote at x = -8. The range of the function is from negative infinite to positive infinity, and it is increasing on it's entire domain. The end behavior of the function on the left side is that as x -> -8^+, y -> -∞, and to the right side, is that as x -> +∞, y -> +∞.

The function starts being defined at x = -8, hence the vertical asymptote of the function is given as follows:

x = -8.

The range of the function is the set containing all values assumed by y on the graph, hence it is in fact from negative infinity to positive infinity, and the function is increasing on it's entire domain.

The end behavior is the values on the extreme left and extreme right of the graph.

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Answer:

84.5 square units.

Step-by-step explanation:

The formula to calculate the area of a trapezoid is:

Area = (base 1 + base 2) * height / 2

Using the measurements you provided, we can calculate the area of the trapezoid as follows:

Area = (12 + 14) * 6.5 / 2

Area = 26 * 6.5 / 2

Area = 169/2

Area = 84.5

Therefore, the area of the trapezoid is 84.5 square units.

Answer: Each piece of poster board with be 0.78 cents each.

Step-by-step explanation: In order to find x, you need to figure out why 35 pieces of poster boards came up to a total of $27.30.

You will divide in this situation. If you divide $27.30 by 35 poster boards, you should get 0.78 as the result, representing the cost of each poster board.

By using completing the square method, the solution to this quadratic equation is x = √13 ± 2.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 4x - 9 = 0

x² - 4x = 9

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 4x + (4/2)² = 9 + (4/2)²

x² - 4x + 4 = 9 + 4

x² - 4x + 4 = 13

By simplifying, we have;

(x - 2)² = 13

x = √13 ± 2

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well, hmmm keeping in mind that complex roots never come all by their lonesome, their sister always comes along, namely their conjugate, so if we have the complex roots of "i" or namely "0 + i", we also have her sister "0 - i", and if we have "1 - 2i", she also came with "1 + 2i", and we also have the root of 5, and that'd give us the fifth degree polynomial, so

[tex]\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = 1-2i &\implies x -1+2i=0\\ x = 1+2i &\implies x -1-2i=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -1+2i )( x -1-2i )( x -5 ) = \stackrel{0}{y}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2-i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill[/tex]

[tex]( x -1+2i )( x -1-2i )\implies \stackrel{ \textit{difference of squares} }{( [x -1]+2i )( [x -1]-2i )} \\\\\\ (x-1)^2 -(2i)^2\implies (x^2-2x+1)-4i^2\implies (x^2-2x+1)-4(-1) \\\\\\ x^2-2x+1+4\implies x^2-2x+5 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{so we can say}}{a(x^2+1)(x^2-2x+5)(x-5)=y}\hspace{5em}\textit{we also know that } \begin{cases} x=0\\ y=-75 \end{cases} \\\\\\ a(0^2+1)(0^2-2(0)+5)(0-5)=-75\implies -25a=-75 \\\\\\ a=\cfrac{-75}{-25}\implies a=3 \\\\[-0.35em] ~\dotfill[/tex]

[tex]3(x^2+1)(x^2-2x+5)(x-5)=y\implies 3(x^3-5x^2+x-5)(x^2-2x+5)=y \\\\\\ 3(x^5-7x^4+16x^3-32x^2+15x-25)=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} 3x^5-21x^4+48x^3-96x^2+45x-75=y \end{array}}~\hfill[/tex]

Check the picture below.

Approximately 5% of students spent their day off playing outside.

To find the percentage of students who spent their day off playing outside, we first need to determine the total number of students. We can do this by adding the number of votes for each activity:

Sleeping: 24

Playing Games 56

Playing Outside: 8

Shopping: 45

Fun Projects: 17

Total Votes (Students) = 24 + 56 + 8 + 45 + 17 = 150

Now we can calculate the percentage of students who spent their day off playing outside:

Percentage = (Number of students who played outside / Total number of students) * 100

Percentage = (8 / 150) * 100 = 0.0533 * 100 = 5.33%

Now, we'll round to the nearest percent:

Percentage ≈ 5%

So, approximately 5% of students spent their day off playing outside.

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