Here is question 3 of 6. Thank you for the help

If three squares are placed to form a right triangle as shown. The statement that must be true is: C .The difference of the areas of the smaller squares is always equal to the area of the largest square.

Let's use the letters a, b, and c to denote the side lengths of the squares, with c standing for the hypotenuse of the right triangle. Assuming that an is the shortest side length to preserve generality a2 is the area of the smallest square. The largest square has a surface area of c2 whereas the medium square has a surface area of b2.

The Pythagorean theorem demonstrates that a + b equals c. If we rewrite this equation, we obtain:

c^2 - b^2 = a^2

c^2 - a^2 = b^2

This means that the size of the largest square is equal to the difference between the areas of the two smaller squares, which is either a2 or b2.

Therefore the correct option is C.

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The base area of the cylinder is 78.54 ft².

The height of the cylinder is 2 ft.

The cylinder has a volume of 157.08 ft cube and the radius of the cylinder is 5 ft.

Therefore, the area of the base of the cylinder can be found as follows:

base area of the cylinder = πr²

base area of the cylinder = 3.1416 × 5²

base area of the cylinder = 3.1416 × 25

base area of the cylinder = 78.54 ft²

Therefore, let's find the height of the cylinder.

volume of the cylinder = πr²h

where

157.08 = 78.54 h

divide both sides by 78.54

h = 157.08 / 78.54

h = 2 ft

Therefore,

height of the cylinder = 2 ft

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Answer: 525 jumping jacks

Step-by-step explanation:

she does 25 x 3 = 75 jumping jacks per day.

so in a week, (7 days) she will do 7 x 75 = 525 jumping jacks

a) The probability that the student was female is 43/76

b) The probability that the student was female AND got a "C" is 9/38

c) The probability that the student was female OR got a "C" is 45/76

We have,

             A   B   C  

Male     16  15  2  33

Female 14  11  18  43

Total     30 26 20 76

a) The probability that the student was female

= 43/76

b) The probability that the student was female AND got a "C"

= 18/76

= 9/38

c) The probability that the student was female OR got a "C"

= 43 /76 + 20/76 - 18/76

= 45/76

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Answer:21y -78

Step-by-step explanation: Distribute the 7 to 3y and -10 to get 21y and -70.

Then combine like terms so the equation would be 21y -78

Step-by-step explanation:

-8+7(3y-10)

-8+21y-70

21y-70+8

21y-78

Last step because there is no more like terms to combine

Hope this helps

Expression for -16x squared +36 in factored form is [tex]-4(2x - 3)(2x + 3).[/tex]

The given equation is [tex]-16x^{2} +36[/tex]

simplifying the equation,

[tex]-16x^2 + 36 = 4(-4x^2 + 9)[/tex]

[tex]=-4x^2 + 9\\ = -(2x)^2 + 3^2 \\= -(2x - 3)(2x + 3)[/tex]

when compared together,

[tex]-16x^2 + 36 = 4(-4x^2 + 9) = 4(-(2x - 3)(2x + 3)) = -4(2x - 3)(2x + 3)[/tex]

The expression for the equation in factored form is -4(2x - 3)(2x + 3).

The question is incomplete. complete question will be "which of these expression is equivalent to [tex]-16x^{2} +36[/tex] in factored form?

options- 4(x+2)(3-2x) , -4(2x - 3)(2x + 3) or (4x+2x)(9x-2x)"

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Answer:

A) [tex]x = \dfrac{\log_6(46) + 6}{4}[/tex]

B) [tex]x = \dfrac{\ln(11)}{2}[/tex]

C) [tex]x = \dfrac{11}{5}[/tex]

Step-by-step explanation:

A) We can solve for x by taking log base 6 of both sides.

[tex]\log_6(6^{4x-6}) = \log_6(46)[/tex]

[tex]4x - 6 = \log_6(46)[/tex]

[tex]4x = \log_6(46) + 6[/tex]

[tex]\boxed{x = \dfrac{\log_6(46) + 6}{4}}[/tex]

B) First, we have to divide both sides by 2.

[tex]2e^{2x} / 2= 22 / 2[/tex]

[tex]e^{2x} = 11[/tex]

Then, we can solve for x by taking the natural log (log base e) of both sides.

[tex]\ln(e^{2x})= \ln(11)[/tex]

[tex]2x= \ln(11)[/tex]

[tex]\boxed{x = \dfrac{\ln(11)}{2}}[/tex]

C) We can solve for x by raising 2 to the power of each side.

[tex]2^{\log_2(5x + 5)} = 2^4[/tex]

This cancels the log base 2 on the left.

[tex]5x + 5 = 16[/tex]

[tex]5x = 11[/tex]

[tex]\boxed{x = \dfrac{11}{5}}[/tex]

The probability that a day in Dayton will include rain or snow is 38%.

Let's assume that there are 365 days in a year (not considering leap years), and we are aware that Dayton typically experiences 25 days of snow per year, in addition to 110 days of rain. We can add the total number of rainy and snowy days in Dayton and then divide that total by the number of days in a year to determine the likelihood that a given day will be either one of those things:

probability of rain or snow = [tex]\frac{110+25}{365}[/tex]

                                             =0.38

The probability that a day in Dayton will have rain or snow is 0.38 or 38%.

The question is incomplete, complete question is " Dayton is a small town in Ohio, which receives  110 days of rain and 25 days of snow per year. Ignoring leap years, Find the probability that a day in Dayton will include rain or snow."

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Answer: B: cone with a height of 4 units and a radius of 3 units

Step-by-step explanation:

Surface Area: 9pi + 15pi = 24pi square units

Volume: 9pi x 4 x 1/3 = 12pi cubic units

The time taken to reach a population of 500 is gotten from  500=50e^0.55t

Exponential growth is a process that increases quantity over time as in the bacterial culture here.

We know that from the question, we have;

P(t)=Poe^rt

P(t) = population at time t

Po= Initial population

r = growth rate

t = time taken

Then we have that;

150 = 50e^2r

3=e^2r

ln3 = 2r

r = ln3/2

r = 0.55

If the rate of growth is 0.55, then to reach a population  of 500;

500=50e^0.55t

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The True statement is An equilateral triangle is always an isosceles triangle.

An equilateral triangle is always an isosceles triangle is True because isosceles triangle have two sides equal and equilateral have three sides equal.

A right triangle is never an isosceles triangle is False statement.

An obtuse triangle is sometimes an acute triangle is False statement.

An isosceles triangle is always a scalene triangle is False statement.

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Answer:Assuming that the number on the end of the number line is a 1 (I cant read it too clearly), this number line goes to 7/7ths so that means A would be 1/7th and B would be 4/7th

Step-by-step explanation: thats how Number lines work

"Data are collected about a population," is not a characteristic of both experiments and surveys. Option A

A survey is a technique for gathering data about a study variable from the respondents of the population. An experiment is a technique used in science to isolate the problem being examined and test a theory.

Options B, C, and D are characteristics obtained in the case of the  experiments and surveys. In both types of research, subjects may be randomly selected (option B), the data collected may be studied for patterns (option C).

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The order will be $50.4 with the price increase

From the question, we have the following parameters that can be used in our computation:

Order = $45

Percentage increase = 12%

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

New order = Order * (1 + Percentage increase)

Substitute the known values in the above equation, so, we have the following representation

New order = 45* (1 + 12%)

Evaluate

New order = 50.4

Hence, the new order is $50.4

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The estimated population of the city after 3 years would be 8,537 people.

To find the population of the city after 3 years, we can use the formula for compound interest;

A = P ×[tex](1+r)^{t}[/tex]

where;

A = the final amount (population after 3 years)

P = the initial amount (initial population of the city) = 5,741

r = the annual growth rate (as a decimal) = 14% = 0.14

t = the number of years = 3

Plugging in the values, we get

A = 5,741 × (1 + 0.14)³

Simplifying the expression inside the parentheses first;

A = 5,741 × (1.14)³

Then, raising 1.14 to the power of 3;

A = 5,741 × 1.485136

A ≈ 8,536.98

So, the estimated population of the city after 3 years would be approximately 8,536.98 people. Since population cannot be in decimal numbers, we can round it to the nearest whole number;

A ≈ 8,537

Therefore, the estimated population of the city after 3 years would be 8,537 people.

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Since r is a positive rational number, an inequality must also be true include the following: A.) q < 0.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the square root of 11.

Next, we would solve the given inequality in order to determine all of the solutions that satisfies the variable q. This ultimately implies that, we would simplify the inequality by cancelling out the variable r as follows;

r × q/r < 0 (r is a positive rational number).

q < 0

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Complete Question:

An inequality is given, where r is a positive rational number.

r • q/r < 0

Which inequality must also be true?

A.) q < 0

B.) q > 0

C.) q < - r

D.) q/r < - r

A system of linear equations that describes this situation include the following;

x = 5y

x + y = 24

In order to write a linear equation or function to describe this situation, we would assign variables to the length of the longer piece and the length of the shorter piece in feet respectively, and then translate the word problem into a linear equation as follows:

Since one piece is five times as long as than the other and the length of the longer piece plus the length of the shorter piece equals 24 feet, a system of linear equations or function to describe this situation can be written as follows;

x = 5y

x + y = 24

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We will conduct a one-sample t-test to determine if the mean length of the particular size of dress is significantly different from 29 inches.

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We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

What is the null hypothesis?

The null hypothesis is the assertion that there is no association between the two sets of data or variables being investigated in a scientific study. The term "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal relationship exists.

Here, we have

Given: A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of the dress is designed to be 29 inches. The most recent simple random sample of 22 dresses had a mean length of 31.53 inches with a standard deviation of 8.24 inches.

We will conduct a one-sample t-test to determine if the mean length of the particular size of the dress is significantly different from 29 inches.

In the null hypothesis, the mean length of the particular size of the dress is equal to 29 inches.

In the alternative hypothesis, the mean length of the particular size of the dress is significantly longer or shorter than 29 inches.

We will use a 0.005 level of significance, which corresponds to a critical value of ±2.807 for a two-tailed test with 21 degrees of freedom.

Our test statistic is: t = (31.53 - 29) / (8.24 / sqrt(22)) = 1.774

Since our test statistic (1.774) is not greater than the critical value (2.807) or less than the negative of the critical value (-2.807), we fail to reject the null hypothesis.

Hence, We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

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The y-intercept of the line of best fit is: y = 20

The formula for equation of a line of best fit is:

y = mx + c

where:

m is slope

c is y-intercept

Now, the y-intercept is simply defined as the point where the line crosses the y-axis.

In this case, the line crosses the y-axis at y = 20.

Thus, we can conclude that it is the y-intercept

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If the Lions in their "seventh-game" scored 14 runs, then the true statement is (b) The mean increases and the median remains the same.

To determine how the additional 14 runs affect the mean and median, we need to calculate the original mean and median.

The mean is the sum of all the runs divided by the number of games:

So, Mean = (5 + 8 + 1 + 5 + 2 + 7)/6 = 28/6 = 4.67,

The median is defined as "middle-value" when data is arranged in order. In this case, the data in order is : 1, 2, 5, 5, 7, 8

So, the median is 5.

If the Lions scored 14 runs in their seventh game, the total number of runs for seven games is:

⇒ 5 + 8 + 1 + 5 + 2 + 7 + 14 = 42,

The new mean is the sum of all the runs for seven games divided by the number of games:

⇒ Mean = 42/7 = 6,

The new data in order is : 1, 2, 5, 5, 7, 8, 14,

So, the new median is also 5.

Comparing the original mean and median to the new mean and median, we can see that:

⇒ The median remains the same.

⇒ The mean increases from 4.67 to 6.

Therefore, the correct option is (b).

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Answer:

THE ANSWER OF 7×4=28 !!!!!!!

Answer: 16* 2

Step-by-step explanation:

The value of the composite function t(s (2)) is 8

From the question, we have the following parameters that can be used in our computation:

s(x) = -x + 5

t(x) = 2x + 2

The composite function t(s(x)) is calculated as

t(s(x)) = 2s(x) + 2

Substitute the known values in the above equation, so, we have the following representation

t(s(x)) = 2(-x + 5) + 2

Again, substitute the known values in the above equation, so, we have the following representation

t(s(2)) = 2(-2 + 5) + 2

Evaluate

t(s(2)) = 8

Hence, the value of t(s(2)) is 8

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Answer:

x = -31 maybe

Step-by-step explanation:

The requried line of reflection is the x-axis.

To determine the line of reflection, we need to find the line that maps each vertex of the first polygon to the corresponding vertex of the second polygon.

We can start by reflecting the first polygon across the x-axis. This will map V to V', W to W', X to X', Y to Y', and Z to Z', as shown below:

First Polygon (VWXYZ) Second Polygon (V'W'X'Y'Z')

(3, 2) V (3, -10) V'

(3, 0) W (3, -8) W'

(6, -7) X (6, -1) X'

(9, 0) Y (9, -8) Y'

(9, 2) Z (9, -10) Z'

Next, we can compare the coordinates of each vertex in the first and second polygons to determine the line of reflection. We notice that reflecting the first polygon across the x-axis negates the y-coordinates of all vertices. Therefore, the line of reflection must be the x-axis.

Therefore, the line of reflection is the x-axis.

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The critical values of the function are x = 0 and x = 4.

The critical values of a function f(x) are the values of x for which f'(x) = 0.

In this problem, the function is:

f(x) = [tex]\frac{x^4}{5(x-2)^2}[/tex]

The derivative is found as follows, applying the quotient rule:

f'(x) = [tex]\frac{2x^3(x-4)}{5(x-2)^3}[/tex]

The zeros of the function are the zeros of the numerator, thus:

2x³(x-4) = 0

∴ x = 0, 4

Hence, the critical values of the function are x = 0 and x = 4.

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