2. Find the volume. Show work, and round to 2 decimal places

*triangle based prism*

The area of the regular pentagon is  490 square units

The formula used for calculating the area of a regular pentagon is expressed with the equation

A = 1/2 pa

Such that the parameters are;

From the information given, we have that;

Perimeter = 5s

Substitute the values,

Perimeter = 5(14)

multiply the values

Perimeter = 70 units

Now, substitute the value into the formula

Area = 1/2 × 70(14)

Area = 980/2

Divide the values

Area = 490 square units

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The order of the given fractions after arranging from least to greatest is 1/5, 2/5, 4/5.

To put the fractions 1/5, 2/5, and 4/5 in order from least to greatest, we can either convert them to decimals or find a common denominator and compare the numerators. Here, we will use the latter method.

First, we need to find a common denominator. The smallest denominator that all three fractions share is 5. So, we can rewrite the fractions as follows:

1/5 = 1/5

2/5 = 2/5

4/5 = 4/5

Now, we can compare the numerators since the denominators are the same. Clearly, 1/5 is the smallest, followed by 2/5, and then 4/5 is the largest.

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a. The probability of exactly two flaws in a 50-yard piece of material is approximately 0.2707.

b. The probability of no more than two flaws in a 50-yard piece of material is approximately 0.6767.

c. The probability of no flaws in a 25-yard piece of material is approximately 0.3679.

To find the probability of exactly two flaws in a 50-yard piece of material, we can use the Poisson distribution. Let λ be the average number of flaws per 50 yards of material, which is 2. Then, the probability of exactly k flaws occurring in a 50-yard piece of material is given by

P(k flaws) = (e^(-λ) × λ^k) / k!

So, for k=2, we have

P(2 flaws) = (e^(-2) × 2^2) / 2! ≈ 0.2707

Therefore, the probability of exactly two flaws in a 50-yard piece of material is approximately 0.2707.

b. To find the probability of no more than two flaws in a 50-yard piece of material, we need to sum the probabilities of having 0, 1, or 2 flaws. So, we have

P(no more than 2 flaws) = P(0 flaws) + P(1 flaw) + P(2 flaws)

We already know P(2 flaws) from part (a). To find P(1 flaw), we can use the same formula as before with λ=2 and k=1

P(1 flaw) = (e^(-2) × 2^1) / 1! ≈ 0.2707

To find P(0 flaws), we use the same formula with λ=2 and k=0

P(0 flaws) = (e^(-2) × 2^0) / 0! ≈ 0.1353

Therefore, we have:

P(no more than 2 flaws) = 0.2707 + 0.2707 + 0.1353 ≈ 0.6767

So, the probability of no more than two flaws in a 50-yard piece of material is approximately 0.6767.

c. To find the probability of no flaws in a 25-yard piece of material, we can again use the Poisson distribution, but with a different value of λ. Since the average number of flaws per 50 yards is 2, the average number of flaws per 25 yards is 1. So, we have:

P(0 flaws) = (e^(-1) × 1^0) / 0! ≈ 0.3679

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Answer: Assuming that the proportion of patients cured by the drug is p = 0.6 and the sample size is n = 100, we can find the mean and standard error of the sampling distribution as follows:

Mean = p = 0.6

Standard error = sqrt[(p*(1-p))/n] = sqrt[(0.6*(1-0.6))/100] = 0.049

Rounding to three decimal places, the standard error is 0.049.

Step-by-step explanation:

Answer:

15 feet and 9 inches

Step-by-step explanation:

9 feet and 5 inches + 6 feet and 4 inches = 15 feet and 9 inches

We can say with 95% certainty that the genuine rate of all patients at this clinic who have high blood pressure is between 24% and 42%. 

To develop a 95% certainty interim for the rate of all patients at this clinic that have tall blood weight, we will utilize the equation:

CI = p ± z*(p*(1-p)/n))

where p is the sampling extent, z is the z-score related to the required certainty level (in this case, 1.96 for 95% certainty), and n is the test measure.

We are given that out of a test of 100 patients, 33 have high blood weight. In this manner, the test extent is:

p = 33/100 = 0.33

Utilizing the equation over, we will calculate the edge of the mistake:

Arduino

ME = z*(p*(1-p)/n)) = 1.96*(0.33*(1-0.33)/100)) ≈ 0.09

At that point, we are able to develop the 95% certainty interim:

CI = p ± ME = 0.33 ± 0.09 = (0.24, 0.42)

Hence, able to say with 95% certainty that the genuine rate of all patients at this clinic who have high blood weight is between 24% and 42%. 

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The measure of the missing angle in the cyclic quadrilateral is 104°

From the question, we are to determine the measure of the inscribed angle in the given diagram

In the given diagram, we have a cyclic quadrilateral.

From one of the circle theorems, we known that

The sum of the opposite angles of cyclic quadrilateral are supplementary. That is they sum up to 180 degrees.

Let the unknown angle measure be x,

Then,

We can write that

x + 76°  = 180°

x = 180° - 76°

x = 104°

Hence, the missing angle measure is 104°

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The proposed study is a randomized controlled trial (RCT). RCTs are considered the gold standard for evaluating the effectiveness of interventions.

In this study, the researcher will randomly assign subjects to either an exercise or non-exercise group, which helps to ensure that any observed differences in mental health outcomes can be attributed to the exercise intervention and not other factors. Stratified random sampling is also being used to ensure that the study includes representative proportions of different age groups. By conducting a mental health exam at the beginning and end of the study, the researcher can compare changes in mental health outcomes between the two groups. Overall, this RCT has a strong design that will enable the researcher to draw meaningful conclusions about the effects of exercise on mental health.

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The value of x in the parallelogram is 9.3.

A parallelogram is a quadrilateral that has opposite sides equal to each other. Opposite sides of a parallelogram is also parallel to each other.

The opposite angle of a parallelogram are congruent while consecutive angles of a parallelogram are supplementary.

Therefore,

5x = 2x + 28

5x - 2x = 28

3x = 28

divide both sides of the equation by 3

x = 28 / 3

x = 9.333333

Therefore,

x = 9.3

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Answer:

4(6) + 4(5) + 4(4) = 24 + 20 + 16 = 60 ft^2

The statement that is not true of unnormalized data is option (d) unnormalized data is multivalued data.

Unnormalized data refers to raw data that has not been organized or processed in any way. It may contain redundancies, inconsistencies, and other issues that make it difficult to work with. However, it does not necessarily involve multivalued data.

Multivalued data refers to data that has multiple values for a single attribute. For example, if a customer can have multiple phone numbers, that data would be considered multivalued. Unnormalized data may or may not have multivalued data, depending on the nature of the data itself.

Therefore, the correct option is (d) unnormalized data is multivalued data

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Answer:

6.4

Step-by-step explanation:

To measure a length of 10 meters without any measuring devices from 100 meters rope is fold the rope ten times and 10th fold of 100 m rope is equals to 10 m.

Total Length of rope = 100 meters

We need to measure a length of 10 meters without using any measuring devices. The ways that we can use to measure the required length includes only fold or manipulate the rope, but you cannot cut or mark it. Now, we use the division arithmetic operation to measure the length. The factors of 100 is written as 100 = 2×2× 5×5 = 10× 10

If we divide 100 by 10 then results 10 as quotient and 0 as remainder. So, the rope with length 100 meters is divided into 10 parts of 10 meters length of rope. But we cannot cut the rope, so folds the rope ten times ( i.e, first half -half then again half into half-half). Therefore, the last fold is measure of length 10 meters.

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Answer:

3/10

Step-by-step explanation:

The roots (if any) are determined by the values of x that make f(x) = 0. To find them, we solve the quadratic equation associated with the function.

A quadratic equation is an equation of the form:

ax² + bx + c = 0

where a, b, and c are constants. For a quadratic function of the form:

f(x) = ax² + bx + c

the roots are the values of x that satisfy the equation f(x) = 0. To find the roots, we set f(x) equal to zero and solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac))/2a

If the discriminant (b² - 4ac) is negative, then the quadratic equation has no real roots, and the function f(x) does not intersect the x-axis. If the discriminant is zero, then the quadratic equation has one real root, and the function f(x) touches the x-axis at that point. If the discriminant is positive, then the quadratic equation has two real roots, and the function f(x) intersects the x-axis at those points.

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Answer:

Step-by-step explanation:

4,456,546

Answer: 228.8cm

Step-by-step explanation:

Hope this helps! :)

Answer:

the transformations that take the graph of those two equations are a reflection about the x-axis followed by a vertical shift downward by 2 units.

Step-by-step explanation:

Reflection: this reflects the original graph f(x)=e^x below the x-axis, resulting in the graph of -e^x.

Vertical shift: this will shift the graph -e^x downwards by 2 units.

Therefore, the transformations are a reflection about the x-axis followed by a vertical shift downward by 2 units.

The Junior class sold 165 slices of pizza.

Let x represent the number of hamburgers sold and y represent the number of slices of pizza sold.

The total amount from sales: 1.35x + 0.75y = 292.50

They sold 40 more slices of pizza than hamburgers: y = x + 40

Now, we'll solve the system of equations using the substitution method:

Substitute the second equation into the first equation:
1.35x + 0.75(x + 40) = 292.50

Distribute $0.75 through the parentheses:
1.35x + 0.75x + 30 = 292.50

Combine like terms:
2.10x + 30 = 292.50

Subtract 30 from both sides of the equation:
2.10x = 262.50

Divide both sides by 2.10 to solve for x:
x = 125

Now that we know there were 125 hamburgers sold, we can use the second equation to find the number of slices of pizza sold:

y = x + 40
y = 125 + 40
y = 165
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The popcorn box can hold 35 cubic inches of popcorn when it is full.

To find the volume of the popcorn box modeled as a right rectangular prism with dimensions 2 inches by 2.5 inches by 7 inches, you need to multiply the three dimensions together:

Volume = Length × Width × Height

In this case, the dimensions are:

Length = 2 inches; Width = 2.5 inches ; Height = 7 inches

Now, multiply the dimensions:

Volume = 2 × 2.5 × 7

Volume = 5 × 7

Volume = 35 cubic inches

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A statement 'The function f(x)=log0. 75x is decreasing' is True.

We know that a function, y = f(x) is a decreasing function when (dy/dx) ≤ 0 for all such values of interval (a, b).

Consider a function  f(x)=log(0.75^x)

We write a function f(x) as,

f(x) = log(0.75^x)

f(x) = log[(3/x)^x]

f(x) = log([tex]\frac{3^x}{4^x}[/tex])

Now we find the derivative of above function with respect to x.

f'(x) = d/dx [ log([tex]\frac{3^x}{4^x}[/tex])]

f'(x) = [tex]1/(\frac{3^x}{4^x} )[/tex] [d/dx ([tex]\frac{3^x}{4^x}[/tex])]

f'(x) = [tex](\frac{4^x}{3^x})[\frac{4^x[3^xlog(3)]-3^x[4^xlog(4)]}{4^{2x}} ][/tex]

f'(x) = log(3) - log(4)

f'(x) = -0.1249

f'(x) < 0

So, the function f(x) is a decreasing function.

Thus the statement is True.

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Answer:

FH = 26

Step-by-step explanatio

I only know the answer

Answer:

FH ≈ 11.62

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem , then

FH² = EH × GH = 9 × 15 = 135 ( take square root of both sides )

FH = [tex]\sqrt{135}[/tex] ≈ 11.62 ( to the nearest hundredth )

According to this research, options B and D appear to be the most slope plausible explanations for the data. However, without the real data, determining which equation is the best model is impossible.

The slope of a line indicates how steep it is. The gradient's mathematical equation is known as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7.The slope of the line is m. b is b at the y-intercept, and (0, b).  

It is impossible to establish which equation is the best model of the data without the actual data. However, we may analyse each possibility based only on the facts provided:

A. y= 2.2 - (1.1%): This equation appears to contain a constant term and a negative slope, making it unsuitable for predicting plant height over time.

B. y= 0.5x + 1.8: The positive slope of this equation indicates that the plant's height rises with time. The constant term of 1.8 might represent the plant's beginning height, while the coefficient of 0.5 could reflect the plant's growth rate.

C. y= 2.0 • (1.4%): This equation appears to contain a constant term and a positive slope, but the percentage term is not obvious how it links to the data.

D. y = 0.7 x + 2.1: This equation, like option B, has a positive slope and a constant term. The coefficient of 0.7 might reflect the plant's growth rate, while the constant term of 2.1 could represent the plant's original height.

According to this research, options B and D appear to be the most plausible explanations for the data. However, without the real data, determining which equation is the best model is impossible.

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The bearing of A from B is 253 degrees

The bearing of B from A is 073 degrees

Bearings are typically measured in a counterclockwise direction from north.

The reference direction for bearings is north, and then the angle is measured in a counterclockwise direction relative to north.

Using this method, we have that

The bearing of A from B is 253 degrees

The bearing of B from A is 073 degrees

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The equation models the cost of making different numbers of shirts, where y is the cost in dollars and x is the number of shirts produced is y = 7.5x - 750

To create an equation that models the cost of making different numbers of shirts, we need to determine the relationship between the number of shirts produced and the cost. One way to do this is to use the two-point form of the equation of a line, which is:

y - y₁ = (y₂ - y₁)/(x₂ - x₁) * (x - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

Using the points (100, 600) and (250, 1387.50), we can find the slope of the line:

slope = (y₂ - y₁)/(x₂ - x₁) = (1387.50 - 600)/(250 - 100) = 7.5

Then, we can use the point-slope form of the equation of a line to write the equation:

y - y₁ = m(x - x₁)

where m is the slope and (x1, y1) is a point on the line. Using the point (100, 600), we get:

y - 600 = 7.5(x - 100)

Simplifying, we get:

y = 7.5x - 750

This equation models the cost of making different numbers of shirts, where y is the cost in dollars and x is the number of shirts produced.

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Answer:

b. sin X and c. cos Y

Step-by-step explanation:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

sin Y = 32/40 incorrect

sin X = 24/40 correct

cos Y = 24/40 correct

cos X =32/40 incorrect

So the answers are sin  X and cos Y

The compound inequality that has no solution is d) m + 9 < 8 and -2m ≥ 10.

A compound inequality combines two or more inequalities using the logical connectives "and" or "or".

Compound inequalities are used to describe a range of values that satisfy multiple conditions simultaneously.

In the given compound inequality, the first inequality states that m + 9 is less than 8, which can be rewritten as m < -1.

The second inequality states that -2m is greater than or equal to 10, which can be rewritten as -2m ≥ 10.

However, the two inequalities cannot be true at the same time because if m is less than -1, then -2m would be greater than 2, and therefore cannot be greater than or equal to 10.

So there is no value of m that satisfies both inequalities simultaneously, resulting in no solution.

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(a) To solve this problem, we need to apply the concept of combinations.  We can find the total number of combinations by using the formula:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we want to select.

Let's assume that we have x pennies, y nickels, z dimes, and w quarters. Since we want to select 25 coins, we can write the equation as x + y + z + w = 25

To find the number of ways to select 25 coins, we need to find the number of solutions to this equation. The total number of combinations is given by: (25 + 4 - 1)C(4 - 1) = 28C3

where we have 25 coins to select and four piles to choose from. Thus, the answer is 28C3.

(b) To solve this problem, we need to use the concept of counting with restrictions. Since we must select at least 5 quarters, we can assume that we have selected 5 quarters and we need to select the remaining 20 coins from the remaining piles. Let's assume that we have x pennies, y nickels, and z dimes. We can write it as x + y + z = 20

To find the number of ways to select 20 coins from the remaining piles, we can use the concept of combinations. The total number of combinations is (20 + 3 - 1)C(3 - 1) = 22C2

Thus, the total number of ways to select 25 coins with at least 5 quarters is given as 10C5 x 22C2

where we have selected 5 quarters from 10 quarters and 20 coins from the remaining piles.

(c)To solve this problem, we need to use the concept of counting with restrictions. Since we can select at most 10 quarters, we need to consider two cases:

(i) We select 10 quarters, and we need to select 15 coins from the remaining piles.

For case (i), we need to select 15 coins from the remaining piles. We can assume that we have x pennies, y nickels, and z dimes. We can write the equation as x + y + z = 15

The total number of ways to select 15 coins is (15 + 3 - 1)C(3 - 1) = 17C2

(ii) We select fewer than 10 quarters, and we need to select the remaining coins from the piles.

For case (ii), To calculate the number of ways, we can use the combination formula to select i quarters out of 10, where i can vary from 0 to 9, and select the remaining (25-i) coins from the remaining piles. We can then sum up the number of ways for all possible values of i to get the total number of ways to select 25 coins with at most 10 quarters.

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The sixth and seventh letters "NO" become the 15th and 14th letters in the alphabet respectively when shifted by 11 positions, decrypt to "E" and "N" respectively. Therefore, the decrypted plaintext is "CSPAEN".

what is decrypted plaintext ?

The decrypted plaintext is the original message that was encrypted using a cipher, which has now been converted back to its original form using the appropriate decryption technique.

In the given question,

The given ciphertext "ZYJGKNO" can be decrypted using a times-11 cipher as follows:

The first letter "Z" becomes the third letter in the alphabet when shifted by 11 positions, so it decrypts to "C".

The second letter "Y" becomes the 24th letter in the alphabet when shifted by 11 positions, so it decrypts to "T".

The third letter "J" becomes the 18th letter in the alphabet when shifted by 11 positions, so it decrypts to "S".

The fourth and fifth letters "GK" become the 16th and 10th letters in the alphabet respectively when shifted by 11 positions, so they decrypt to "P" and "A" respectively.

The sixth and seventh letters "NO" become the 15th and 14th letters in the alphabet respectively when shifted by 11 positions, so they decrypt to "E" and "N" respectively.

Therefore, the decrypted plaintext is "CSPAEN".

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