The volume of a right cone is 168
π
π units
3
3
. If its diameter measures 12 units, find its height.

Answer:

angle EDC = 64 degrees

Answer:

To find out how many giant parade balloons could be filled with 6.2 billion cubic feet of helium, we can divide the total volume of helium by the volume of one balloon:

Number of balloons = Total volume of helium / Volume of one balloon

First, we need to convert 6.2 billion cubic feet to cubic feet:

6.2 billion = 6,200,000,000

Now we can calculate the number of balloons:

Number of balloons = 6,200,000,000 / 700,000

Number of balloons = 8,857.14

So, approximately 8,857 giant parade balloons could be filled with 6.2 billion cubic feet of helium.

Answer:

The probability of taking either one job or the other job can be calculated by adding the probabilities of taking the first job and taking the second job, and then subtracting the probability of taking both jobs (since we cannot take both).

Let A be the event of taking the first job, and B be the event of taking the second job. Then, the probability of taking the first job is P(A) = 0.5, and the probability of taking the second job is P(B) = 0.4. The probability of taking both jobs is zero, since we cannot take both.

Therefore, the probability of taking either one job or the other job is:

P(A or B) = P(A) + P(B) - P(A and B)

= 0.5 + 0.4 - 0

= 0.9

So the probability of taking either one job or the other job is 0.9 or 90%

Answer:

9 inches

Step-by-step explanation:

A foot is 12 inches long. To find a fourth of a foot, divide 12 by four to get 3. This means that Julio has already dug a hole one foot and three inches deep. To make his hole two feet deep, he will need to dig the other 3/4 of the foot. To find 3/4 of a foot, take 1/4 of a foot (3 inches) and multiply by 3 (9 inches).
Julio will have to dig 9 more inches.

The line of reflection is reflection across x = −4

Explain the term line

A line is an infinitely long and infinitely thin one-dimensional object that extends in opposite directions. It has no endpoints and is often represented by a straight line with two arrowheads. Lines are a fundamental concept in mathematics and are used to define other objects such as planes, angles, and shapes.

According to the given information

Let's use points A(-3, 3) and A'(-5, 3). The midpoint of the line segment connecting A and A' is ((-3 + (-5))/2, (3 + 3)/2) = (-4, 3). The slope of the line segment connecting A and A' is (3 - 3)/(-5 - (-3)) = 0. Since the line of reflection is perpendicular to this line segment, its slope is the negative reciprocal of 0, which is undefined. This means that the line of reflection is a vertical line.

Since the midpoint of the line segment connecting A and A' lies on the line of reflection and has an x-coordinate of -4, we can conclude that the line of reflection is x = -4.

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Answer:

Step-by-step explanation:

One way for Paul to display his data is by using a scatter plot. A scatter plot is a graph that uses ordered pairs to represent data points. In this case, each data point would represent a friend's score and the number of minutes they spent studying science over the weekend.

To create a scatter plot, Paul would plot each data point as an ordered pair on a coordinate plane. The x-coordinate would represent the number of minutes spent studying, and the y-coordinate would represent the friend's score on the science test. Paul could then use a title and labels for the x and y axes to make the graph clear and informative.

A scatter plot is a good choice for this data because it allows Paul to easily see any relationship between the amount of time spent studying and the scores on the science test. He can also use the graph to identify any outliers or patterns in the data.

The probability that the appliance will work at least six years without requiring repairs is 0.2231 or 22.31%.

To find the probability that the appliance will work at least six years without requiring repairs, we need to consider the exponential distribution and the given average repair time. Given that the appliance requires repairs once every four years on average, the rate parameter (λ) for the exponential distribution is 1/4, or 0.25.

Here we want to find the probability that the appliance will work at least six years without requiring repairs, which can be represented as [tex]P(X ≥ 6)[/tex], where X is the time between repairs. Using the complementary probability, we can rewrite this as [tex]P(X ≥ 6) = 1 - P(X < 6)[/tex]

The cumulative distribution function (CDF) of the exponential distribution is given by

[tex]F(x) = 1 - e^{(-λx)}[/tex]

Now, we can plug in the values:

[tex]P(X ≥ 6) = 1 - F(6) \\ P(X ≥ 6) = 1 - (1 - e^{(-0.25 \times 6)}) \\ P(X ≥ 6) = 1 - (1 - e^{(-1.5)}) \\ P(X ≥ 6) = e^{(-1.5)}[/tex]

Therefore, the probability that the appliance will work at least six years without requiring repairs is approximately 0.2231 or 22.31%.

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The inverse of the graphs are added as an attachment

To plot the inverse of a graph, you can follow these steps:

See attachment for the graphs

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There are 14,400 paths from $a$ to $b$ consisting of exactly six line segments (vertical, horizontal or inclined).

Assuming that the distance between adjacent lattice points is equal to 1 unit, we can find the number of paths from [tex]a$ to $b$[/tex] consisting of exactly six line segments by using the concept of permutations and combinations.

To reach [tex]b$ from $a$[/tex] using exactly 6 line segments, we need to make 3 horizontal and 3 vertical moves, with each move covering a distance of 1 unit. The order in which we make these moves is important.

Out of the 6 moves, we can choose 3 moves to be horizontal and the remaining 3 to be vertical. The number of ways of doing this is given by the combination formula:

[tex]$C(6,3) = \frac{6!}{3!3!} = 20$[/tex]

Once we have selected the 3 horizontal moves and 3 vertical moves, we can arrange them in any order. The number of ways of doing this is given by the permutation formula:

[tex]$P(6,6) = 6! = 720$[/tex]

Therefore, the total number of paths from[tex]$a$ to $b$[/tex]consisting of exactly six line segments (vertical, horizontal or inclined) is given by the product of the number of ways of choosing 3 horizontal moves out of 6, and the number of ways of arranging the 6 moves:

[tex]$20 \times 720 = 14,400$[/tex]

Hence, there are 14,400 paths from $a$ to $b$ consisting of exactly six line segments (vertical, horizontal or inclined).

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There are 4096 paths from point a to point b that consist of exactly six line segments (vertical, horizontal, or inclined).

We can use the concept of permutations and combinations.

First, we need to consider the possible directions for each line segment:

vertical, horizontal, and inclined (assume inclined in both the top-right and bottom-right directions).

So there are 4 possible directions for each segment.

Since we have 6 line segments, we need to find the total number of paths that can be formed by arranging the 4

directions for the 6 segments.

We can use the formula for permutations with repetition, which is [tex]n^r[/tex], where n is the number of possible directions (4)

and r is the number of segments (6).

Plug in the values into the formula:

[tex]4^6[/tex] = 4096.

So, there are 4096 paths from point a to point b that consist of exactly six line segments (vertical, horizontal, or

inclined).

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A rhombus is a quadrilateral with all four sides of equal length. When AB¯¯¯¯¯¯ || CD¯¯¯¯¯¯ and AB¯¯¯¯¯¯ ≅ CD¯¯¯¯¯¯, we know that ABCD is a parallelogram with opposite sides parallel and equal in length. The correct Answer is B.

To show that it is a rhombus, we need to prove that all four sides are equal.

Since the diagonals of a parallelogram bisect each other, we know that AP = CP and BP = DP.

If we can show that BC = AD, we can conclude that ABCD is a rhombus.

Using the fact that AB¯¯¯¯¯¯ || CD¯¯¯¯¯¯, we can show that ΔABP ≅ ΔCDP

Therefore, we have: BP/DP = AB/CD

Hence, the correct answer is B.

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The values of x and y using trigonometric ratios are: 12) x = 8, y = 4√3 and 14) y = 11√2, x = 11√2

Some of the common trigonometric ratios are:

Using the above as a guide, we have the following:

12) Let us solve for x and y using trigonometric ratios to get:

4/x = sin 30

4/0.5 = x

x = 8

Similarly:

4/y = tan 30

y = 4/tan 30

y = 4√3

Using the above as a guide, we have the following:

14) Let us solve for x and y using trigonometric ratios to get:

y/22 = sin 45

y = 11√2

Similarly:

x/22 = cos 45

x = 11√2

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The values of x and y using trigonometric ratios are:

12) x = 8, y = 4√3

14) x = 11√2, y = 11√2

The three most common trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = adjacent/hypotenuse

12) We can find x and y using trigonometric ratios as follows:

4/x = sin 30

x = 4/sin 30

x =4/0.5

x = 8

We can solve for y as:

4/y = tan 30

y = 4/tan 30

y = 4(1/√3)

y = 4√3

14) We can find x and y using trigonometric ratios as follows:

y/22 = sin 45

y = 22 * 1/√2

Rationalizing the denominator gives:

y = 11√2

We can find x as:

x/22 = cos 45

x = 22 * 1/√2

Rationalizing the denominator gives:

x = 11√2

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An equation in slope-intercept form for the line shown in the given graph is equal to y = -5x + 5.

What is the slope-intercept form?

The line with m as the slope, m, and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

Here, we have

Given graph and we have to find the equation for the line shown in the given graph.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 20)/(0 + 3)

Slope (m) = -15/3

Slope (m) = -5.

At data point (0, 5) and a slope of -5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -5(x - 0)

y - 5 = -5x

y = -5x + 5

Hence, an equation in slope-intercept form for the line shown in the given graph is equal to y = -5x + 5.

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Answer: 26 degrees

Step-by-step explanation:

12/24 = 1/2

Answer: 136

Step-by-step explanation: it's the only big number

Answer:

Step-by-step explanation:

To find the point that is a certain fraction of the way between two given points, we can use the midpoint formula and the scalar multiplication of vectors.

Let's first find the vector that points from point A to point B:

�

�

⃗

=

(

4

−

3

)

−

(

−

3

−

2

)

=

(

7

−

1

)

AB

=(

4

−3

​

)−(

−3

−2

​

)=(

7

−1

​

)

The scalar multiplication of a vector with a scalar value scales the length of the vector. To find the point that is 3/4 of the way from point A to point B, we can multiply the vector $\vec{AB}$ by 3/4:

3

4

�

�

⃗

=

3

4

(

7

−

1

)

=

(

21

4

−

3

4

)

4

3

​

AB

=

4

3

​

(

7

−1

​

)=(

4

21

​

−

4

3

​

​

)

Finally, we can add this vector to point A to get the point that is 3/4 of the way from point A to point B:

(

−

3

−

2

)

+

(

21

4

−

3

4

)

=

(

3

4

,

−

11

4

)

(

−3

−2

​

)+(

4

21

​

−

4

3

​

​

)=

(

4

3

​

,−

4

11

​

)

​

0.3895 Answer

Step-by-step explanation:

I thought you meant it on paper.

Answer:

0.3895

Step-by-step explanation:

Write out the division problem: 389.5 ÷ 1000.

Since we're dividing a decimal number by 1000, we can simply move the decimal point three places to the left to convert 1000 to 1.000: 389.5 ÷ 1.000.

Moving the decimal point three places to the left also means we need to add three trailing zeroes to the dividend: 389.5 becomes 389.500.

Now we can perform the long division: divide 3 by 1, write the quotient 3 above the 8, and subtract 3 from 8 to get 5 as the new remainder. Bring down the next digit 8 to get 58.

Divide 58 by 1, write the quotient 58 above the 9, and subtract 58 from 89 to get 31 as the new remainder. Bring down the next digit 5 to get 315.

Divide 315 by 1, write the quotient 315 above the decimal point, and subtract 315 from 389 to get 74 as the new remainder.

Since there are no more digits to bring down, we've reached the end of the long division. The final quotient is 0.3895.

Don't forget to include the decimal point in the answer, since we moved it three places to the left in step 2. The final answer is 0.3895.

So, 389.5 ÷ 1000 = 0.3895.

The notation "||v||" typically refers to the Euclidean norm (also known as the magnitude or length) of a vector v in a Euclidean space. The Euclidean norm of a vector v in n-dimensional space is defined as the square root of the sum of the squares of its components:

||v|| = sqrt(v1^2 + v2^2 + ... + vn^2)

Given that ||v|| = 8, we can find the Euclidean norm of -7v as follows:

||-7v|| = 7 * ||-v|| = 7 * sqrt((-v1)^2 + (-v2)^2 + ... + (-vn)^2)

Since -v has the same magnitude as v but points in the opposite direction, we can replace each vi in the above expression with -vi:

||-7v|| = 7 * sqrt((-v1)^2 + (-v2)^2 + ... + (-vn)^2) = 7 * sqrt(v1^2 + v2^2 + ... + vn^2)

But we know that ||v|| = sqrt(v1^2 + v2^2 + ... + vn^2) = 8, so we can substitute:

||-7v|| = 7 * ||v|| = 7 * 8 = 56

Therefore, ||-7v|| is 56.

Answer:

Step-by-step explanation:

The area of the regular pentagon is 6.88 unit².

The area of a regular pentagon can be found if one side is known. The formula used for finding the area of a regular pentagon is:

A = 1/4 * [√5(5+ 2√5)] * s²

where s is the length of one side of the regular pentagon.

In this case, s = 2:

A = 1/4 * [√5(5+ 2√5)] * s²

A = 1/4 * [√5(5+ 2√5)] * 2²

A = 1/4 * [√5(5+ 2√5)] * 4

A = 6.88 unit²

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The length of the second shelf is 98 centimeters.

Let's denote the length of the first shelf as x centimeters. According to the problem, we have the following equations for the lengths of the other shelves:

Second shelf: 2x + 18 cm

Third shelf: x - 12 cm

Fourth shelf: x + 4 cm

Robert must use the entire 2.5-meter board for the shelves, so the sum of the lengths of the four shelves should be equal to 2.5 meters, or 250 centimeters. Thus, we can write an equation:

x + (2x + 18) + (x - 12) + (x + 4) = 250

Simplify the equation:

x + 2x + 18 + x - 12 + x + 4 = 250

Combine like terms:

6x + 10 = 250

Subtract 10 from both sides:

6x = 240

Now, divide by 6:

x = 40

Now that we have the length of the first shelf (x = 40 cm), we can find the length of the second shelf:

Second shelf = 2x + 18 = 2(40) + 18 = 80 + 18 = 98 cm

So, the length of the second shelf is 98 centimeters.

Answer:

114 cm

Step-by-step explanation:

Let's start by finding the shortest shelf.

The second shelf is 18 centimeters longer than twice the length of the first shelf. The first shelf is smaller than the second shelf.

The third shelf is 12 centimeters shorter than the first shelf. The third shelf is shorter than the first shelf, so, the third shelf is the shortest shelf.

Let's call the length of the third shelf s.

We know that the third shelf is 12 centimeters shorter than the first shelf. In other words, s is 12 centimeters shorter than the first shelf. So, we can write the length of the first shelf as:

[tex]s+12[/tex]

We also know that the second shelf is 18 cm longer than twice the length of the first shelf.

Start by multiplying the length of the first shelf by 2.

[tex]2(s+12)=2s+24[/tex]

Now, let's add 18.

[tex]2s+24+18=2s+42[/tex]

So, the length of the second shelf is 2s+42.

The remaining shelf is 4 centimeters longer than the first shelf. Remember that the first shelf is s+12. Let's add 4.

[tex]s+12+4=s+16[/tex]

So, the first shelf is s+12, the second shelf is 2s+42, the third shelf is s, and the remaining shelf is s+16.

When you add them all together, you will get the 2.5 meter board.

2.5 meters is equal to 250 cm.

So, the first shelf plus the second shelf plus the third shelf plus the remaining shelf is equal to the entire board, or 250 cm.

Let's rewrite that in terms of s:

[tex](s+12)+(2s+42)+s+(s+16)=250=\\5s+70=250=\\5s=180=\\s=36[/tex]

We now know that s=36 cm.

The problem asks how long the second shelf is. Recall that the second shelf is 2s+42.

Let's plug in 36 to this expression:

[tex]2s+42=\\2(36)+42=\\72+42=\\114[/tex]

So, the second shelf is equal to 114 cm.

The requried length of measure of GH and CH in triangle GCH is 16 and 12 respectively.

Here,
AC is the perpendicular bisector of side GH, But this bisector also bisects the triangle in two equal halves.
So,
GH =2GB
FH = 2 * 8 = 16

CH = CG
CH = 12

Thus, the requried length of measure of GH and CH in triangle GCH is 16 and 12 respectively.

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Jamar would need to invest approximately $12,115.77, rounded to the nearest ten dollars, for the value of the account to reach $18,000 in 7 years using compound interest.

We can use the formula for compound interest to solve for the initial investment amount, which is:

A = P(1 + r/n)^(nt)

where A is the future value, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we want to find P, and we know that A = $18,000, r = 0.047, n = 4 (quarterly compounding), and t = 7. Substituting these values, we get:

$18,000 = P(1 + 0.047/4)^(4*7)

$18,000 = P(1.01175)^28

P = $12,115.77

Therefore, Jamar would need to invest approximately $12,115.77, rounded to the nearest ten dollars, for the value of the account to reach $18,000 in 7 years.

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In 2016, the total number of cars produced in the world was 72 million (rounded to the nearest whole number) by forming linear equation.

In 2011, the total number of cars produced in the world was 59.9 million.

In 2016, the total number of cars produced in the world was 21% greater than the total number produced in 2011.

Let us say in 2016 the total number of cars produced in the world was N million.

Therefore, by expressing the given problem in a linear equation we get,

Total number produced in 2016, N = 59.9 + (21% of 59.9 )     in millions

⇒ N = 59.9 + [tex][ \frac{21}{100} ] 59.9[/tex]     ( in millions )

= 59.9 + 12.579    ( in millions )

= 72.479  ( in millions )

= 72 millions ( rounded to the nearest whole number)

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The length of ZW is 45 inches.

A parallelogram is a member of quadrilateral which has a pair of opposite sides to be equal, and a pair of slant opposite sides.

In the given information, we have;

WX = YZ (a pair of opposite side of a parallelogram are equal)

2x + 15 = 4x - 21

collect like terms,

21 + 15 = 4x - 2x

36 = 2x

x = 36/2

x = 18

So that;

WX = 2x + 15

      = 2(18) + 15

WX = 36 + 15

      = 51

XY = x + 27

     = 18 + 27

     = 45

Therefore,

ZW = XY  (a pair of opposite sides are equal)

ZW = 45

The length of ZW is 45 inches.

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The area of the circle in the graph is 113 square units.

Remember that for a circle of radius R, the area is given by the simple formula you can see below.

A = pi*R²

Where pi = 3.14, so we can use this formula to find the area of the circle.

On the diagram we can see that the radius of the circle is:

R = 6 units

Replacing that in the area formula we will get.

A = 3.14*(6 units)²

A = 113.04 units ²

The correct option is the third one.

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The mean and range of the same population can differ if there is a significant difference between the sampled respondents.

Between Jayden and Carter, Carter's calculation will provide a better understanding of the population.

The reason is that he sampled more people with a wider time range.

The mean is the average number of minutes it took for the respondents to dress up. The goal of any survey work is to capture a significant size of the population whose opinions can give a true picture of the situation being examined.

In the case of Carter, we see that he took a more sizable amount of the population having randomly selected 7 samples of 10 students. A greater number of respondents will give a truer picture of the factor being surveyed.

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By following these steps, we can easily find the slope of a normal line based on the equation of a tangent line.

To find the slope of a normal line based on the equation of a tangent line.

Identify the slope of the tangent line:

Look at the equation of the tangent line, which will usually be in the form y = mx + b, where m is the slope of the tangent line and b is the y-intercept.

Extract the value of m from the equation.
Calculate the negative reciprocal:

To find the slope of the normal line, we'll need to calculate the negative reciprocal of the tangent line's slope.

The negative reciprocal of a number is found by flipping the fraction and changing the sign (from positive to negative, or from negative to positive).

For example, if the slope of the tangent line (m) is 3, the negative reciprocal will be -1/3.

If the slope of the tangent line is -2/3, the negative reciprocal will be 3/2.
The slope of the normal line:

The negative reciprocal calculated in step 2 is the slope of the normal line.

This slope will be perpendicular to the tangent line, meaning that the angle between the normal and tangent lines is 90 degrees.

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Answer:

Jessica has 400 cm^3 of material. She uses 35cm^3 to make a right triangular prism. She wants to make a second prism that is a dilation of the first prism with a scale factor of 2.5.

The volume of the first prism is 35 cm^3. Since the second prism is a dilation of the first prism with a scale factor of 2.5, its volume will be (2.5)^3 = 15.625 times greater than that of the first prism. Therefore, the volume of the second prism will be 35 x 15.625 = 546.875 cm^3.

To make the second prism, Jessica needs an additional material of 546.875 - 35 = 511.875 cm^3.

So Jessica needs an additional material of 511.875 cm^3 to make the second prism.

Step-by-step explanation:

The statement that is true is:

The probability that a randomly selected player on Team C is 10 years old is 5/16.

Option A is the correct answer.

We have,

The probability that a randomly selected player on Team C is 10 years old.

= Number of 10 years old players in Team C / Total players in Team C

= 5./16

The probability that a randomly selected player on Team A is 8 years old.

= Number of 8 years old players in Team A / Total players in Team A

= 4/15

The probability that a randomly selected 8-year-old player is on Team C.

= Number of 8 years old players in Team C / Total  8 years old players

= 8/21

The probability that a randomly selected 10-year-old player is on Team B.

= Number of 10 years old players in Team C / Total 10 years old players

= 5/14

Thus,

The probability that a randomly selected player on Team C is 10 years old is 5/16.

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