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The height of the second square base prism is 50 cm.

The volume of the first square base prism is represented as follows:

v = ha²

where

Therefore, the height of the prism is 10 cm.

v = 10a²

Hence, the volume of the initial prism is 5 times the volume. Therefore,

v = 5(10a²)

v = 50a²

Therefore,

50a² = ha²

divide both sides by a²

50a² / a² = ha² / a²

50 = h

h = 50  cm

Therefore, the height of the second square base prism is 50 cm.

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Answer:

32.7 min

Step-by-step explanation:

60 x 300 = 18000 /  550 = 32.7

The team at Prime Video is developing a method to divide movies into groups based on the number of awards they have won. This method involves the following steps:

1. Collecting data: The team will gather information about movies, including the number of awards they have won. This data can be obtained from reliable sources such as award shows, film festivals, and reputable databases.

2. Grouping movies: Based on the number of awards won, the team will divide movies into different groups. For example, movies with more than 100 awards can be placed in one group, while movies with fewer awards can be placed in another group.

3. Defining criteria: The team will establish specific criteria for each group. These criteria may include the minimum and maximum number of awards required for a movie to be included in a particular group.

By developing this method, the team at Prime Video aims to categorize movies based on their award achievements. This will allow viewers to easily discover and explore movies that have received significant recognition in the industry.

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Answer:

7.3593

-3

I took the test on edge and made a 100

The coefficient of the product is 7.35932 and the exponent is -3

The number is written in the form  \(a \times 10^b\) where we have \(1 \leq a < 10\)

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

When we multiply numbers in scientific notation, then

1.466 x 5.02 =7.56932

Then we add the exponents on the powers of 10 as;

10^(-8+5) = 10^(-3)

The result is 7.56932 x 10^-3

Using a calculator, we get 0.00735932, this is not in scientific notation.  

0.00735932 changed to scientific notation

Now Move the decimal until a nonzero digit is to the left of the decimal

7.35932

Which that means our exponent is -3

7.35932 x 10^-3

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Answer:

A

Step-by-step explanation:

For test A, the unit rate is 30 words per minute divided by 4 minutes, or 7.5 words per minute.

Unit rate = 78 words/15 minutes = 5.2 words per minute for test B.

The unit rate for test C is 99 words/22 minutes, or 4.5 words per minute.

Answer:

Square= 12 units

Triangle long sides= 19 units

Triamgle short side= 10 units

Step-by-step explanation:

It is a square, so all sides are the same.  That means 3x+3 equals 4x.  What number can be subsituted into x to equal 4?  If x is 3, then 3x+3 would be 3(3)+3.  It equals 12.  4 times 3 is also 12.  It works!  That also means the square's side is 12 units.

Square= 12 units

So, x=3

The triangle's longer sides are 7x-2.  Subsitute x in, which is 3, and you get 7(3)-2.  It equals 19.  The two longer sides of the triangle are the same length, so both are 19 units.

Triangle long sides= 19 units

The triangles shorter side is 2x+4.  Subsitute 3 in for x and you get 2(3)+4.  It equals 10, so the shorter side is 10 units.

Triangle short side= 10 units

Answer:

Square: 12 unites

triangle shorter side: 10 units

triangle longer sides: 19 units, 19 units

Step-by-step explanation:

Hello!

First, we make the equations to find the perimeters of each shape by adding all the sides

Square: 4x + 4x + (3x+ 3) + (3x + 3)

Triangle: (7x - 2) + (7x - 2) + (2x + 4)

Since the perimeters are equal we can show that

4x + 4x + (3x+ 3) + (3x + 3) = (7x - 2) + (7x - 2) + (2x + 4)

Now we can solve for x.

Combine like terms

14x + 6 = 16x

Subtract 14x from both sides

6 = 2x

Divide both sides by 2

3 = x

Now we know what x is we can put that into the sides of the shapes

Square

4(x)

Put in x

4(3) = 12

The Square is 12 units

Triangle Short Side

2x + 4

Put in x

2(3) + 4

6 + 4

10

The shorter side of the triangle is 10 units

Triangle Longer Side

7x - 2

Put in x

7(3) - 2

21 - 2

19

The longer sides are 19 units

Hope This Helps!

Answer:

The "!" represents a factorial

Step-by-step explanation:

In math, a factorial when there is an ! followed by a number.

For example, 5! = 5 factorial.

To solve factorials, multiply every integer below the number before the factorial, including the number.

5! = 5 x 4 x 3 x 2 x 1 = 120.

Answer: 1: -8x+6

Step-by-step explanation:

Answer:

Step-by-step explanation:

To compute the magnitude of the cross product |u x v|, we need to know the values of u and v. However, you mentioned that u and v are unit vectors, which means their magnitudes are both equal to 1.

The magnitude of the cross product between two vectors u and v is given by |u x v| = |u| * |v| * sin(theta), where theta is the angle between the two vectors.

In this case, since u and v are unit vectors, their magnitudes are both equal to 1. Additionally, you mentioned that the angle between u and v is π/4.

Therefore, |u x v| = 1 * 1 * sin(π/4) = 1 * 1 * (√2/2) = √2/2.

Hence, the magnitude of the cross product |u x v| is equal to √2/2.

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(a) The number 72% is a D. statistic.

(b) The unknown true percentage of American citizens who like ''real TV'' is a C. parameter.

It is related to statistics and parameters.

(a) The number 72% is a statistic because it represents a summary measure of the sample of individuals who participated in the phone-in poll.

A statistic is a numerical value calculated from a sample of data, and it is used to make inferences about the population from which the sample was drawn.

(b) The unknown true percentage of American citizens who like ''real TV'' is a parameter.

A parameter is a numerical characteristic of a population, such as a mean, proportion, or standard deviation, and it is typically unknown and estimated from sample data.

In this case, the percentage of all American citizens who like ''real TV'' is unknown and cannot be directly observed, so it is considered a parameter.

The phone-in poll only represents a sample of individuals who called in to the newspaper and cannot be used to estimate the parameter for the entire population.

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a. dy/dx exists for all t in the interval (0, π), and there is no discontinuity. b. there are no inflection points on the curve. c. the length of the curve on the interval [0, π/2] is 2.

Part A. Determining where dy/dx does not exist and the type of discontinuity:

To find where dy/dx does not exist, we need to calculate the derivative of y with respect to x, which involves differentiating both x(t) and y(t) with respect to t.

x(t) = 2cos²(t)

y(t) = 2sin²(t)

Differentiating x(t) with respect to t:

dx/dt = -4cos(t)sin(t)

Differentiating y(t) with respect to t:

dy/dt = 4sin(t)cos(t)

To find dy/dx, we divide dy/dt by dx/dt:

dy/dx = (4sin(t)cos(t)) / (-4cos(t)sin(t))

Simplifying the expression, we get:

dy/dx = -1

The derivative dy/dx is a constant value of -1, indicating that it is defined for all values of t. Therefore, dy/dx exists for all t in the interval (0, π), and there is no discontinuity.

Part B. Finding the inflection point(s) of the curve on the interval [0, π]:

To find the inflection point(s), we need to determine where the curvature changes sign. The curvature of a curve is given by the second derivative of y with respect to x.

Differentiating dy/dx with respect to t:

d²y/dx² = d/dt(dy/dx)

= d/dt(-1)

= 0

Since the second derivative is 0, we need to find where the first derivative dy/dx is either increasing or decreasing. In this case, dy/dx is a constant value of -1, so it does not change.

Therefore, there are no inflection points on the curve.

Part C. Finding the length of the curve on the interval [0, π/2]:

To find the length of the curve, we can use the arc length formula:

L = ∫[a,b] √(dx/dt)² + (dy/dt)² dt

In this case, we have:

x(t) = 2cos²(t)

y(t) = 2sin²(t)

Differentiating x(t) and y(t) with respect to t:

dx/dt = -4cos(t)sin(t)

dy/dt = 4sin(t)cos(t)

Substituting these derivatives into the arc length formula:

L = ∫[0, π/2] √((-4cos(t)sin(t))² + (4sin(t)cos(t))²) dt

= ∫[0, π/2] √(16(cos²(t)sin²(t) + sin²(t)cos²(t))) dt

= ∫[0, π/2] √(16sin²(t)cos²(t) + 16sin²(t)cos²(t)) dt

= ∫[0, π/2] √(32sin²(t)cos²(t)) dt

= ∫[0, π/2] √(8sin(2t)) dt

= ∫[0, π/2] 2√2 sin(t) dt

= 2√2 ∫[0, π/2] sin(t) dt

= 2√2 (-cos(t)) [0, π/2]

= 2√2 (-cos(π/2) + cos(0))

= 2√2 (0 + 1)

= 2

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Answer: t= 7

Step-by-step explanation:

Take 56 divided by 8 and you get the remainder of 7. So t must equal 7.

Answer:

The answer is 114.1.

Step-by-step explanation:

You have to substitute the s and t value into the expression :

\(9.1s + 8.5t\)

\(let \: s = 6\)

\(let \: t = 7\)

\(9.1(6) + 8.5(7)\)

\( = 54.6 + 59.5\)

\( = 114.1\)

Answer:

From (0,0) and go down 1 and put a dot then down 4 and over to the right 1 and draw a line.

Step-by-step explanation:

Hope this helps have a nice day!

Answer:

Step-by-step explanation:

√69 is 8.30 and √72 is 8.48.

The one after N should be 8.50.

So really it should be N, not M, im sorry. Because M is 8.20

So its N

In order to test the given hypothesis, we need to compare the test statistic (Z) with the critical value (Z alpha), where alpha is the level of significance. Since the alternative hypothesis states that mu1 - mu2 is greater than 0, we are interested in the right-tailed test.

This means that we need to find the critical value for the upper tail area under the standard normal distribution, which corresponds to the level of significance.

The null hypothesis will be rejected if the test statistic (Z) is greater than the critical value (Z alpha). Therefore, the correct option is (b) > = z alpha. This means that if the calculated value of Z is greater than or equal to the critical value of Z alpha, we can reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.

It's important to note that the value of sigma is known in this case, which means that we can use the standard normal distribution to calculate the critical value and the test statistic. In summary, we reject the null hypothesis if Z is greater than or equal to the critical value Z alpha, which corresponds to the level of significance alpha for a right-tailed test.

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The demand per hour for gasoline at a local station follows a normal distribution with a mean of 850 gallons and a standard deviation of 55, allowing for the calculation of probabilities for different demand levels.

To find the probability distribution for the demand per hour for gasoline at a local station, we can use the normal distribution. Given that the demand is normally distributed with a mean of 850 gallons and a standard deviation of 55, we can calculate the probability of certain demand levels.

To find the probability of the demand being less than a certain value, we calculate the cumulative distribution function (CDF). For example, to find the probability that the demand is less than 900 gallons, we calculate P(X < 900) using the standard normal distribution table or statistical software.To find the probability of the demand being within a range, we subtract the CDF of the lower bound from the CDF of the upper bound. For example, to find the probability that the demand is between 800 and 900 gallons, we calculate P(800 < X < 900) = P(X < 900) - P(X < 800).

By using these calculations, we can determine the likelihood of different demand levels at the local station, aiding in inventory management and operational decision-making.Therefore, The demand per hour for gasoline at a local station follows a normal distribution with a mean of 850 gallons and a standard deviation of 55, allowing for the calculation of probabilities for different demand levels.

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The exact probability that the absolute value of the difference between the sample sum of the labels and -581.4 exceeds 31.54 is approximately 0.1128 or 11.28%.

To find the exact probability, we will use the properties of the normal distribution.

Let X be the random variable representing the sum of the labels on the tickets. We know that the mean of X (μ) is -581.4 and the standard deviation of X (σ) is √(17) × 4.5.

We want to find the probability that the absolute value of the difference between X and -581.4 exceeds 31.54. In other words, we want to find P(|X - (-581.4)| > 31.54).

Convert the inequality into a standard normal distribution form.

The standard normal distribution has a mean of 0 and a standard deviation of 1. To convert X to a standard normal random variable Z, we use the formula:

Z = (X - μ) / σ

In our case:

Z = (X - (-581.4)) / (√(17) * 4.5)

Calculate the Z-score.

Z = (31.54) / (√(17) * 4.5) ≈ 1.591

Find the probability using a standard normal distribution table or a calculator.

P(Z > 1.591) ≈ 0.0564 (rounded to four decimal places)

Account for both tails of the distribution.

Since we are interested in the absolute difference, we need to consider both tails of the normal distribution. Therefore, the total probability of the absolute difference exceeding 31.54 is:

P(|X - (-581.4)| > 31.54) = 2 P(Z > 1.591) ≈ 2 × 0.0564 ≈ 0.1128

So, the exact probability that the absolute value of the difference between the sample sum of the labels and -581.4 exceeds 31.54 is approximately 0.1128 or 11.28%.

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For this equation: a=5, b=-13, c=6

5x^2−13x+6=0

Use the quadratic formula with a=5, b=-13, c=6.

x= [−(−13)± √(−13)2 −4(5)(6)] / 2(5)

x= (13±√49)/10

x=2 or x= 3/5

Answer:

50

Step-by-step explanation:

The perimeter of triangle is 66.24 units.

What is triangle?

In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane

Main body:

according to question :

c = 28

let the vertices be A,B,C

∠A= 30°

by using trigonometric ratios,

BC/ AB = sin30°

AB = C = 28

BC/28 = sin30°

BC = 28*sin30°

BC= 28*(1/2)

BC = 14

similarly

AB /CA = cos 30°

28/CA = √3/2

CA = 28*√3/2

CA = 14/√3

CA = 24.24

Hence , perimeter = AB +BC +CA = 28+14+24.24

                              =66.24 units

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Answer:

Finding the 6th term is really easy, we can simply double two more times to get 5, 10, 20, 40, 80, 160.

Step-by-step explanation:

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

Answer:

proved in attachment thanks if you like my answer mark me brilliantest

Answer:

x = 4

y = 4√3

Step-by-step explanation:

Reference angle = 30°

Hypotenuse = 8

Adjacent = y

Opposite = x

Recall: SOHCAHTOA

✔️To find x, apply SOH:

Sin 30 = Opp/Hyp

Sin 30 = x/8

x = 8 × sin 30

x = 8 × ½ (sin 30 = ½)

x = 4

✔️To find y, apply CAH:

cos 30 = Adj/Hyp

Cos 30 = y/8

y = 8 × Cos 30

y = 8 × √3/2 (cos 30 = √3/2)

y = 4 × √3

y = 4√3

Answer:

a=2/5

Step-by-step explanation:

1.7((2)/(5))+0.3((2)/(5)) = 0.8=80/100=4/5

Answer:

the answer is a=2/5

Step-by-step explanation:

combine like terms 1.7+0.3=2

get the varliable alone 2/4/5

answer 2/5

Answer:

A.  the number of textbooks in a classroom

Step-by-step explanation:

quantitative data  is information about quantities; that is, information that can be measured and written down with numbers.