the area of corresponding faces of two similar triangular prisms are 49cm^2 and 25cm^2. what is the ratio of the corresponding side lengths of the perimeters of the corresponding faces? of the volumes?

The solution of 5x² + 20x -7 =0 is ±√(27+5) - 2.

What is an equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical declaration that illustrates the equality of two mathematical expressions.

The given equation is

5x² + 20x -7 =0

Take 5 common from the first two terms:

5(x² + 4x) -7 =0

Add 7 on both sides:

5(x² + 4x) -7+7 =0 + 7

5(x² + 4x) = 7

Add and subtract 4:

5(x² + 4x + 4 - 4) = 7

5(x² + 4x + 4) - 5×4 = 7

Apply the formula (a+b)² = a² + 2ab +b²

5(x +2)²  = 7 + 20

5(x +2)² = 27

Divide both sides by 5:

(x +2)² = 27/5

Take square root on both sides:

x+2 = ±√(27+5)

Subtract 2 from both sides:

x = ±√(27+5) - 2

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The required number is n = 10.

Given, f(x) = eˣ²

Differentiating wrt x

f'(x) = 2xeˣ²

Differentiating wrt x

f''(x) = 2xeˣ² (2x) + 2eˣ²

= 4x² eˣ² +2eˣ²

f''(x) = (4x² + 2)eˣ²

Differentiating wrt x

f'''(x) = (4x² +2)(2x)eˣ² + 8xeˣ²

= (8x³ +4x + 8x)eˣ²

f'''(x) = (8x³ +12x)eˣ²

Differentiating wrt x

f''''(x) = (8x³ + 12x)(2x)eˣ²+(24x² + 12)eˣ²

= (16x⁴ + 24x² +24x² +12)eˣ²

= (16x⁴ + 48x² + 12)eˣ²

Since, f''''(x) is an increasing function for x>0

SO, |f''''(x)| = (16x⁴ + 48x² + 12)eˣ² ≤ (16 + 48 + 12)e

|f''''(x)| ≤ 76e                     for 0≤x≤1

We take k = 76, a = 0, b= 1

For getting error 0.0001 in Simpson's rule

We should choose n such that

k(b-a)⁵/180n⁴ < 0.0001

76e/180n⁴ < 0.0001

n⁴ = 76e/0.018

n = 10.35

Rounding to integer

n = 10

Therefore, the required number is n = 10.

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The "general-solution" of differential-equation, "x(dy/dx) + 6y = x³ - x" is y(x) = (x³/9) - (x/7) + c/x⁶.

The differential-equation is given as : x(dy/dx) + 6y = x³ - x,

We first divide the whole "differential-equation" by variable "x",

So, we get,

dy/dx + (6/x)y = x² - 1,

The next-step, we integrate, it can be written as :

y×\(e^{\int{\frac{6}{x} } \, dx }\) = ∫\(e^{\int{\frac{6}{x} } \, dx }\).(x² - 1),

y.x⁶ = ∫(x⁸ - x⁶).dx

y.x⁶ = x⁹/9 - x⁷/7 + c,

Dividing both the sides by x⁶, we get

y = (x⁹/9)/x⁶ - (x⁷/7)/x⁶ + c/x⁶,

So, y(x) = (x³/9) - (x/7) + c/x⁶,

Therefore, the required general-solution is y(x) = (x³/9) - (x/7) + c/x⁶.

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The given question is incomplete, the complete question is

Find the general solution of the given differential equation. x(dy/dx) + 6y = x³ - x.

To maximize the number of interviews, 12 undergraduate students, 4 graduate students, and 4 faculty members should be hired. The maximum number of interviews that can be conducted is 684.

Let x, y, and z be the number of undergraduate students, graduate students, and faculty members hired, respectively. The objective is to maximize the number of interviews, which is given by the function

N = 18x + 25y + 30z.

The total cost of hiring interviewers is given by the function

C = 100x + 150y + 200z.

The constraints are x + y + z ≤ 20 (due to transportation limitations), and C ≤ 3200 (the budget constraint). Using linear programming techniques, we can solve for the optimal values of x, y, and z, which are 12, 4, and 4, respectively.

The maximum number of interviews is 18(12) + 25(4) + 30(4) = 684.

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Answer:tttaergfzgsfbvzfsbzfzbfs

The amount of interest that you earn after a year will be $7.875.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

\(\rm A = P \left (1 + \dfrac{r}{n} \right ) ^{nt}\)

Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.

You have $350 in your savings account, which has a 2.25% interest rate.

Then the amount of interest that you earn after a year will be given as,

I = A - P

I = $350(1 + 0.0225) - $350

I = $350 (1.0225) - $350

I = $357.875 - $350

I = $7.875

The amount of interest that you earn after a year will be $7.875.

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Answer:   A  C and D

Step-by-step explanation:

The experimenter was most likely conducting a randomized controlled trial, also known as a randomized experiment.

In this type of experiment, participants are randomly assigned to different groups, such as an experimental group or a control group, to ensure that any observed effects can be attributed to the intervention being tested rather than other factors.

In this case, the experimenter is using a random number to assign Chris to a group with nineteen other students, which suggests that there may be multiple groups involved in the experiment. This type of design is often used in scientific research to test the effectiveness of a new treatment, intervention, or program.

Randomized controlled trials are considered the gold standard in research design because they provide strong evidence for causal relationships between variables. By randomly assigning participants to different groups, researchers can control for confounding variables and ensure that any observed differences between groups are due to the intervention being tested.

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Answer:

4

Step-by-step explanation:

i know this is late but on the diagram all the angles across from each other count as a vertical angle and i took the assignment and got it rigth

4 pairs of vertical angles are there in the diagram.

Two lines intersects each other, then the angles formed is opposite to each other are called vertical angles.

4 lines intersect to form 14 angles.

The diagram is attached below for reference.

Angles 14 and 12, 11 and 13, 10 and 8, and 7 and 9 are vertical angles.

There are 4 pairs of vertical angles are here.

Hence, 4 pairs of vertical angles are there in the diagram.

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Answer:

its 90 bc the angle has a square (tbh I'm just guessing

On the tenth day, the fraction of the original pie he ate that day is 1/1024

To solve the how much of the pie he ate on the tenth day, use the exponential decay formula.

Exponential growth and decay functions are written in standard form as

A = A₀•b^kt

where A = final amount

A₀ = initial amount = 1

b = growth factor = 1/2

k = growth rate = 1/day

t = time = 10 days

Plug in the values to the equation and solve for the final amount, A.

A = A₀•b^kt

A = 1•(1/2)^(1/day)(10 days)

A = 1•(1/2)^(10)

A = 1•(1/1024)

A = 1/1024

Divide the amount he ate on the tenth day(A = 1/1024) by the initial amount(A₀ = 1).

fraction = A / A₀ = 1/1024 / 1 = 1/1024

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The upper bound of 206.264 to 3 decimal places would be 206.265.

What is upper bound?

In mathematics, an upper bound is a value that is greater than or equal to all of the values in a set. For example, if we have a set of numbers {1, 2, 3}, then 3 is an upper bound of this set because it is greater than or equal to all the numbers in the set.

An upper bound can be either a member of the set or not. If the upper bound is a member of the set, then it is called a maximum element of the set. If the upper bound is not a member of the set, then it is called a strict upper bound of the set.

In the context of rounding, the upper bound refers to the next highest value that a number could be rounded to. For example, if we are rounding a number to the nearest integer, the upper bound would be the next integer greater than the original number.

The upper bound of 206.264 to 3 decimal places would be 206.265.

This is because the third decimal place of the original number is 4, and any number greater than or equal to 5 in the next decimal place would round the number up to the next value. Therefore, rounding 206.264 to 3 decimal places gives 206.265.

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Answer:

40

Step-by-step explanation:

Answer: 62

Step-by-step explanation: In the red empty spot, the #5 would go there and in the blue spot the #6 would go there. 8x2=16 and 16+16= 32: t=This is for the to rectangle shapes on both sides. Now for the square in the middle, since the red spot is 5 and the blue is 6, 5x6= 30. So, 30+32=62.

a) The null hypothesis (H0): The population mean completion time under new management is equal to or greater than 14.4 minutes. The alternative hypothesis (Ha): The population mean completion time under new management is less than 14.4 minutes. b) The type of test statistic to use is a one-sample z-test, since the sample size is small and the population standard deviation is known. c) The calculated test statistic is approximately -1.632. d) The p-value is slightly greater than 0.05. e) Based on the p-value being greater than the significance level (0.05), we fail to reject the null hypothesis.

a) The null hypothesis (H0): The population mean completion time under new management is equal to or greater than 14.4 minutes.

The alternative hypothesis (Ha): The population mean completion time under new management is less than 14.4 minutes.

b) Since the sample size is small (n = 12) and the population standard deviation is known, we will use a one-sample z-test.

c) The test statistic for a one-sample z-test is calculated using the formula:

z = (\(\bar x\) - μ) / (σ / √n), where \(\bar x\) is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values from the problem:

z = (13.8 - 14.4) / (1.8 / √12) ≈ -1.632

d) To find the p-value, we will compare the test statistic to the critical value from the standard normal distribution. At a significance level of 0.05 (α = 0.05), for a one-tailed test, the critical value is -1.645 (approximate).

The p-value is the probability of obtaining a test statistic more extreme than the observed test statistic (-1.632) under the null hypothesis. Since the test statistic is slightly larger than the critical value but still within the critical region, the p-value will be slightly greater than 0.05.

e) Since the p-value (probability) is greater than the significance level (0.05), we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that the population mean completion time under new management is less than 14.4 minutes at the 0.05 level of significance.

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False , the variance and standard deviation are not measures of central location

Given data ,

The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset

Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset

The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.

In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.

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Answer:

Molecules in both the metal and the surrounding air will start moving at lower speeds?

Step-by-step explanation:

I'm not sure this is the right answer, because i thought that the air and the metal would be in equilibrium.

So sorry if this is wrong, chemistry isn't my strongest subject.

Answer:

The air molecules that are surrounding the metal will speed up, and the molecules in the metal will slow down.

Step-by-step explanation:

Answer: I believe the answer is 6.3 I will research more and get a definite answer just dam me for the answer!

Step-by-step explanation:

:)

Answer:

24 is 44% of 54.55

Step-by-step explanation:

24 ÷ 44% = y ÷ 100%

Solve for y - To do so, we will use cross multiplication.

44y = 24 × 100

44y = 2400

y = 2400 ÷ 100

y = 54.55

Answer:

k = 5

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 20 when x = 4, then

20 = 4k ( divide both sides by 4 )

5 = k

Answer:

The value of k = 5

Step-by-step explanation:

We know when  y varies directly as x, we get the equation

y ∝ x

y = kx

Here 'k' is the 'constant' of proportionality

Given

so substituting y = 20, x = 4 in the equation y = kx

y = kx

20 = k(4)

k = 20 / 4

k = 5

Therefore, the value of k = 5

The quantity of purple marbles that Leslie has would be = 32 purple marbles.

The number of bags of marbles that Leslie has = 6 bags.

The quantity of marbles that is found in each bag = 16 marbles.

Therefore the total number of marbles = 6× 16 =96 marbles.

The fraction of purple marbles that Leslie has = 1/3 of 96

Therefore the total number of purple marbles the Leslie have = 1/3× 96 = 32

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Complete question:

Leslie has 6 bags of marbles. Each bag has 16 marbles. If ⅓ of the marbles are purple, how many purple marbles does Leslie have?

Answer:

Explanation:

Here, we want to rewrite the given expression

What we have to do is to start by opening up the bracket

To do this, we have to multiply the term on the left with each term inside the bracket

Then we collect the like terms and perform the necessary arithmetic operation

We have this as follows:

Answer:

68y-42

Step-by-step explanation:

7(9y+2y-6)-9y

Find the expression in simplest terms

Combine like terms

7(11y-6)-9y

Distribute

77y -42-9y

Combine like terms

68y-42

Answer:

There is no photo here so sorry.

Step-by-step explanation:

A student states that the exterior angle of a triangle can never be a right angle. The statement is incorrect.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

A student states that the exterior angle of a triangle can never be a right angle.

The given statement is incorrect because, in the right-angle triangle, the interior and exterior angles are equal that is right angle.

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We can conclude that there is a positive association between educational achievement and home ownership.

To understand the relationship between educational achievement and home ownership based on the given information,

we can analyze the overlapping groups within the random sample.

Let's define the following terms:

- A = Number of people who are homeowners

- B = Number of people who are high school graduates

According to the information provided:

- A = 340 (number of homeowners)

- B = 310 (number of high school graduates)

- A ∩ B = 221 (number of people who are both homeowners and high school graduates)

Based on this, we can analyze the relationships as follows:

1. Proportion of homeowners who are high school graduates:

To find this proportion, we divide the number of homeowners who are high school graduates (A ∩ B) by the total number of homeowners (A):

Proportion = (A ∩ B) / A = 221 / 340

2. Proportion of high school graduates who are homeowners:

To find this proportion, we divide the number of high school graduates who are homeowners (A ∩ B) by the total number of high school graduates (B):

Proportion = (A ∩ B) / B = 221 / 310

3. Proportion of high school graduates who are not homeowners:

To find this proportion, we subtract the number of high school graduates who are homeowners (A ∩ B) from the total number of high school graduates (B):

Proportion = B - (A ∩ B) = 310 - 221

Based on the information provided, we can calculate the proportions and make conclusions about the relationship between educational achievement and home ownership. However, without specific values for the proportions, we cannot determine the exact nature of the relationship.

The relationship between educational achievement and home ownership can be analyzed based on the given information. In the random sample of 500 people from the 2000 census, 340 were homeowners, 310 were high school graduates, and 221 were both homeowners and high school graduates.

From this data, we can conclude that there is a positive association between educational achievement and home ownership. This means that being a high school graduate increases the likelihood of being a homeowner. However, it is important to note that this relationship does not imply causation.

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Answer:

The answer is D

Step-by-step explanation:

50,000 x 0.15 = 7500 and then you add the car cost (7500) it will add up to 15,000$

This means the Probability of drawing a star is now 4/8 or 1/2, which is equal to the probability of drawing a card without a star. Thus, the game is now fair.

To make the game fair, we need to ensure that the probability of drawing a card with a star is the same as the probability of drawing a card without a star.

Currently, there are 4 cards with stars and 6 cards without stars, which means the probability of drawing a star is 4/10 or 2/5, while the probability of drawing a card without a star is 6/10 or 3/5.

To make the game fair, we need to adjust the number of cards with stars and without stars so that the probabilities are equal.

Option A is not correct because the game is not currently fair.

Option B is not correct because adding 2 cards with stars will increase the probability of drawing a star to 6/12 or 1/2, which is not equal to the probability of drawing a card without a star.

Option C is also not correct because adding a star to 1 of the blank cards will still result in a probability of drawing a star that is not equal to the probability of drawing a card without a star.

Therefore, the correct answer is option D: take away 2 blank cards. If we remove 2 blank cards, we are left with 4 cards with stars and 4 cards without stars. This means the probability of drawing a star is now 4/8 or 1/2, which is equal to the probability of drawing a card without a star. Thus, the game is now fair.

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Answer:

-20

Step-by-step explanation:

The critical points are (2,1) and (0,0). Given, z = 3x² - xy + 2y² - 4x - 7y + 12.1. Find the critical points at which the function may be optimized.

To find the critical points, we need to solve the following system of equations: ∂z/∂x = 0, ∂z/∂y = 0∂z/∂x = 6x - y - 4 = 0∂z/∂y = -x + 4y - 7 = 0By solving these equations, we get two critical points: (2,1) and (0,0).2. Determine whether at the computed points, the function takes on its maximum or minimum value.

To determine whether each critical point is a maximum, minimum, or saddle point, we need to compute the second partial derivatives of z: ∂²z/∂x² = 6, ∂²z/∂y² = 4, ∂²z/∂x∂y = -1At the point (2,1), the second partial derivatives satisfy the condition (∂²z/∂x²)(∂²z/∂y²) - (∂²z/∂x∂y)² = (6)(4) - (-1)² = 25 > 0 and ∂²z/∂x² > 0, so z has a minimum value at this point.At the point (0,0), the second partial derivatives satisfy the condition (∂²z/∂x²)(∂²z/∂y²) - (∂²z/∂x∂y)² = (6)(4) - (-1)² = 25 > 0 and ∂²z/∂x² > 0, so z has a minimum value at this point.Therefore, the function z = 3x² - xy + 2y² - 4x - 7y + 12 is optimized at (2,1), where the minimum value is z = 3(2)² - (2)(1) + 2(1)² - 4(2) - 7(1) + 12 = -10.

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Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

x + y = 420; y = 6x

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.

The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.

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Answer:

5n is equal to 5 x n.

Step-by-step explanation:

If n = 6 , then 5n would equal 5 x 6 , or 30.

Answer:

5n means 5 × a number

Step-by-step explanation:

say if your problem is 5n=20

20 ÷ 5=4

n=4

5 × 4= 20

hope this helps!