14 The roof of a house has a slope of 5/12
What is the width of the house if the
height of the roof is 8 ft?

Liberal arts colleges have a higher median SAT score and a lower acceptance rate compared to research universities, while research universities have a higher expenditure per student and a higher percentage of top 10% high school graduates.

Descriptive statistics were calculated for liberal arts colleges and research universities based on the data given in the Excel file. The summary of descriptive statistics for each variable by school type is as  shown in the table.

Based on the results, it appears that liberal arts colleges have higher median SAT scores, lower acceptance rates, and lower expenditures per student than research universities. On the other hand, research universities have higher mean expenditures per student and higher median percentages of top 10% high school graduates than liberal arts colleges. Overall, there are differences in the characteristics of these two types of colleges.

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--The complete question is, Compute descriptive statistics for liberal arts colleges and research universities in the Excel file Colleges and Universities. Compare the two types of colleges. What can you conclude?

Colleges and Universities

School Type Med SAT Accept Rate Exp./Student Top 10% HS Grad %

Amherst Lib Arts 1315 22% $26,636 85 93

Barnard Lib Arts 1220 53% $17,653 69 80

Bates Lib Arts 1240 36% $17,554 58 88

Berkeley Univ 1176 37% $23,665 95 68

Bowdoin Lib Arts 1300 24% $25,703 78 90

Brown Univ 1281 24% $24,201 80 90

Bryn MawrLib Arts1255 56% $18,847 70 84

Cal Tech Univ 1400 31% $102,262 98 75

Carleton Lib Arts 1300 40% $15,904 75 80

Carnegie University1225 64% $33,607 52 77

Claremont Lib Arts1260 36% $20,377 68 74

Colby Lib Arts 1200 46% $18,872 52 84

Colgate Lib Arts 1258 38% $17,520 61 85

ColumbiaUniversity1268 29% $45,879 78 90

Cornell University1280 30% $37,137 85 83

DavisdsonLib Arts 1230 36% $17,721 77 89

Duke University 1310 25% $39,504 91 91

GeorgetownUniv 1278 24% $23,115 79 89

Grinnell Lib Arts 1244 67% $22,301 65 73

HamiltonLib Arts 1215 38% $20,722 51 85

Harvard Univ 1370 18% $46,918 90 90

HaverfordLib Arts 1285 35% $19,418 71 87

Johns Hop. Univ 1290 48% $45,460 69 86

MiddleburyLib Arts 1255 25% $24,718 65 92

MIT University 1357 30% $56,766 95 86

Mount Lib Arts 1200 61% $23,358 47 83

NWrn University 1230 47% $28,851 77 82

Oberlin Lib Arts 1247 54% $23,591 64 77

Occidental Lib Arts 1170 49% $20,192 54 72

Pomona Lib Arts 1320 33% $26,668 79 80

Princeton University 1340 17% $48,123 89 93

Rice University 1327 24% $26,730 85 88

Smith Lib Arts 1195 57% $25,271 65 87

Stanford University 1370 18% $61,921 92 88

Swarthnore Lib Arts 1310 24% $27,487 78 88

U of MI University 1195 60% $21,853 71 77

U of Chi University 1300 45% $38,937 74 73

U of Roc University 1155 56% $38,597 52 73

U PA University 1280 41% $30,882 87 86

U Va University 1218 37% $19,365 77 88

UCLA University 1142 43% $26,859 96 61

UNC University 1109 32% $19,684 82 73

Vassar Lib Arts 1287 43% $20,179 53 84

Wash U University 1225 54% $39,883 71 76

Wash & Lee Lib Arts 1234 29% $17,998 61 78

Wellesley Lib Arts 1250 49% $27,879 76 86

Wesleyan Lib Arts 1290 35% $19,948 73 91

Williams Lib Arts 1336 28% $23,772 86 93

Yale University 1350 19% $52,468 90 93--

Answer:

[tex]y - ( - 20) = 9(x - ( - 2))[/tex]

[tex]y + 20 = 9(x + 2)[/tex]

Step-by-step explanation:

[tex]m = \frac{79 - ( - 20)}{9 - ( - 2)} = \frac{99}{11} = 9[/tex]

[tex]y - ( - 20) = 9(x - ( - 2))[/tex]

[tex]y + 20 = 9(x + 2)[/tex]

Answer: 3.71

Step-by-step explanation:

Answer:

Let's call the number of nuts "n", the number of bolts "b", and the number of screws "s".

From the problem, we know:

s = 3n (Since there are 3 times as many screws as nuts)

b = n + 32 (Since there are 32 more bolts than nuts)

n + s + b = 782 (Since the total number of nuts, screws, and bolts is 782)

Now we can use substitution to solve for one of the variables in terms of the others. Let's solve for "n":

n + 3n + (n + 32) = 782

5n + 32 = 782

5n = 750

n = 150

Now we know there are 150 nuts. We can use this information to find the number of bolts:

b = n + 32

b = 150 + 32

b = 182

Finally, we can use the information we have about the screws to find their number:

s = 3n

s = 3(150)

s = 450

Therefore, there are 450 screws in the box.

The solution to the system of equations is p = 4 and q = 2

The substitution method is a way to solve a system of linear equations. In this method, we solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. This produces a new equation with one variable, which we can then solve for its value. Once we know the value of one variable, we can substitute it back into one of the original equations to find the value of the other variable.

To solve the system of equations using the method of substitution, we need to solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. We can start by solving the second equation for p:

p + 2q = 8

p = 8 - 2q

Now we can substitute this expression for p in the first equation:

2p - 3q = 2

2(8 - 2q) - 3q = 2

16 - 4q - 3q = 2

16 - 7q = 2

-7q = -14

q = 2

We can now substitute q = 2 into the expression we found for p:

p = 8 - 2q

p = 8 - 2(2)

p = 4

Therefore, the solution to the system of equations is p = 4 and q = 2.

correct question  Solve the equations 2p – 3q = 2 and p + 2q = 8, using the method of substitution.

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Answer:15

You multiply 6 and 5. That equals 30 then divide the 30 by 2 and that equals 15

Answer:

0.375 × a² × b³ × c⁵ ÷ x⁴ ÷ y³ ÷ z

Step-by-step explanation:

First, we can represent 3/8 in decimal form:

0.375

Next, we can show the numerator using multiplication:

0.375 × a² × b³ × c⁵

Then, we can individually divide by each factor in the denominator using the principle:

[tex]\dfrac{A}{B \times C} = A \div (B \times C) = A \div B \div C[/tex]

0.375 × a² × b³ × c⁵ ÷ x⁴ ÷ y³ ÷ z

Answer:

1) 24

2) 25

Step-by-step explanation:

Given:

2a + 3b = 8

4x + 10y = 50

.

1)

[tex] \frac{6a + 9b}{2a + 3b} = \frac{3(2a + 3b)}{2a + 3b} = 3[/tex]

Since the second expression is 3 times greater then the previous one, the product will also be 3 times greater:

6a + 9b = 3 × 8 = 24

.

2)

[tex] \frac{2x + 5y}{4x + 10y} = \frac{2x + 5y}{2(2x + 5y)} = \frac{1}{2} = 0.5[/tex]

The second expression's value is two times smaller than the first one's, so the product will also be two times smaller:

2x + 5y = 0,5 × 50 = 25

Answer:

First, we can simplify the coefficients:

(24/50) * (30/8) = (6/25) * (15/2) = 9/5

Then we can simplify the variables:

x^3 / x^2 = x^(3-2) = x

Therefore, the simplified expression is:

9/5 * x

So answer will be as follows:

(24x^(3))/(50x)*(30)/(8x^(2)) = 9/5 * x

Assuming the black and red squares are equally likely and there is no bias in the coin, the probability that it will land heads up on a black square is 1/2, or 50%.

Probability is a branch of mathematics that studies the likelihood of a random event occurring. When a coin is tossed into the air, for example, the possible outcomes are Head and Tail.

We will have a probability of 50%; this is because there are two equally likely outcomes when flipping a coin - heads or tails - and each square on the checkerboard has an equal chance of being landed on.

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The probability of selecting a football card and then a basketball card is 0.16 or 16%. The probability of selecting a football card and then a basketball card can be calculated by multiplying the probability of selecting a football card on the first draw and the probability of selecting a basketball card on the second draw.

Since the first card is replaced before the second draw, the probability of selecting a football card or a basketball card remains the same on both draws.

The probability of selecting a football card on the first draw is 2/10, or 0.2, since there are 2 football cards in a total of 10 cards in the bag. The probability of selecting a basketball card on the second draw is 8/10, or 0.8, since there are 8 basketball cards left after the first draw.

Therefore, the probability of selecting a football card and then a basketball card can be calculated as follows:

P(Football and Basketball) = P(Football on 1st draw) x P(Basketball on 2nd draw)

= (2/10) x (8/10)

= 0.16

So, the probability of selecting a football card and then a basketball card is 0.16 or 16%.

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The lines r and s  (A) are parallel because the given angles are (F) supplementary angles and they (H) do not have equal angle measures.

When two straight lines or beams intersect at a single endpoint, an angle is created.

The vertex of an arc is the location where two points come together. The Latin term "angulus," which means "corner," is where the word "angle" originates.

There are, however, a few fundamental perspectives.

Your camera options expand tremendously when combined with various shots.

This angle, which entails shooting a scene from directly overhead, is the most perplexing of the five.

So, according to the given situation:

= r║s

= Pair of angles are supplementary angles

Therefore, the lines r and s  (A) are parallel because the given angles are (F) supplementary angles and they (H) do not have equal angle measures.

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Correct questions:

in the given figure, can you conclude r ∥ s? Use the drop-down menus to explain your answer.

The lines-------------parallel because the given angles are----------angles and they -----------have equal angle measures.

(A) first line: (A) are (B) are not

second line: (C) same side interior (D) corresponding (E) alternate (F) supplemental

third line: (G) do (H) do not

Answer:

after 80 years, approximately 2.15 grams of the initial 16 grams of cesium-137 would remain. This means that about 13.4 grams would have decayed during this time period.

Answer: 9 and 1/3

Step-by-step explanation:

First of all, you have to find the unit rate. So 28 divided by 2 = 14.

The bird flies at a unit rate of 14 miles in 1 hour.

Next, we need to find out what fraction of an hour is 40 minutes.

How many minutes in an hour? 60... so 40 would be 40/60 of an hour or 4/6 or 2/3 of an hour.

Next, remember the formula D=rt which is distance= rate multiplied by time

We can use this formula here: 14 times 2/3 = 9 and 1/3

After answering the presented question, we can conclude that it contains  inequality the extremes of Terri's data, which may not be representative of her typical time spent at the fitness club.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many simple inequalities can be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

The interquartile range is the most acceptable measure of variability for Terri's data (IQR).

The IQR is an acceptable measure of variability in this example because it focuses on the middle 50% of the data, which is where Terri spends the majority of her time at the fitness club. The mean and median are measures of central tendency rather than variability, and the range would be less useful in this situation because it contains the extremes of Terri's data, which may not be representative of her typical time spent at the fitness club.

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Answer:

522/9=58

11-9=2

58*2=116

522+116=638

Step-by-step explanation:

Answer:

638

Step-by-step explanation:

180º-110º = 70º

m∠7 = 70°

the measures of the angles of the triangle are A = 26.29 degrees, B = 131.45 degrees, and C = 22.29 degrees.

How to solve angles?

To solve for the angles of a triangle, we need to use the fact that the sum of the angles of a triangle is equal to 180 degrees. We can use this fact to set up equations based on the given information.

Let's start by assigning variables to the angles of the triangle. Let A be the measure of angle A, B be the measure of angle B, and C be the measure of angle C.

We are given that angle B is 5 times angle A, which we can express as B = 5A. We are also given that angle C is 4 times less than angle A, which we can express as C = A - 4.

Using the fact that the sum of the angles of a triangle is 180 degrees, we can write the following equation:

A + B + C = 180

Substituting the expressions we found for B and C, we get:

A + 5A + (A-4) = 180

Simplifying the equation, we get:

7A - 4 = 180

Adding 4 to both sides of the equation, we get:

7A = 184

Dividing both sides by 7, we get:

A = 26.29

Now that we know the measure of angle A, we can use the expressions we found for B and C to find their measures:

B = 5A = 131.45

C = A - 4 = 22.29

Therefore, the measures of the angles of the triangle are A = 26.29 degrees, B = 131.45 degrees, and C = 22.29 degrees.

In summary, we used the fact that the sum of the angles of a triangle is 180 degrees and the given information about the relationship between the angles to set up an equation and solve for the measure of angle A. We then used the expressions we found for angles B and C to find their measures.

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The amοunt οf prize mοney each winner received can be represented by the expressiοn: $480 / x

A linear equatiοn is a mathematical equatiοn that represents a straight line when graphed, and is in the fοrm οf y = mx + b, where m represents the slοpe οf the line and b represents the y-intercept.

The amοunt οf prize mοney each winner received can be represented by the expressiοn:

$480 / x

This is because the prize mοney οf $480 was split equally amοng x winners, sο dividing the tοtal prize mοney by the number οf winners (x) gives the amοunt each winner received. This expressiοn calculates the quοtient οf $480 divided by the number οf winners (x), resulting in the amοunt οf prize mοney each winner received.

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The given measure of ∠ DEC = 80 degrees

We have the following details

m ∠BAC = 46 degrees

m ∠ CBA = 54 degrees

We are to find the measure of angle DEC

This is a question that shows us two similar triangles

We have ∠BAC = DCE

∠ CBA = ∠ EDC

then ∠ DEC  = ∠ BCA

The measure of the angles that are in a triangle is given as 180 degrees

we have ∠BAC + ∠ CBA + ∠ BCA = 180

46 + 54 + ∠ BCA = 180 degrees

∠ BCA = 180 - 100

∠ BCA = 80 degrees

We know that corresponding angles are equal when we have parallel lines

since ∠ DEC  = ∠ BCA

∠ DEC = 80 degrees

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Answer: 9 - i

Step-by-step explanation:

The sum of numbers 12 - 5i and - 3 + 4i is, (9 - i)

We have to give that,

The sum of numbers 12 - 5i and - 3 + 4i.

Now, we can find the sum of complex numbers as,

(12 - 5i) + (- 3 + 4i)

12 - 5i - 3 + 4i

Combine like terms,

12 - 3 - 5i + 4i

9 - i

Therefore, The sum of numbers 12 - 5i and - 3 + 4i is, (9 - i)

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As a result, we have demonstrated: 1 / (cos(x) - cot(x)) = cos (x) + cot(x) as the right side of the equation .

Trig ratios are ratios between the sides and angles of a right triangle. The sine, cosine, and tangent are the three main trigonometric ratios (tan). These are their definitions: The ratio of a right triangle's hypotenuse's length to the height of the opposite end is known as the sine (sin) of an angle. The ratio of a right triangle's neighbouring side to hypotenuse length is known as the cosine (cos) of an angle. The ratio of a right triangle's adjacent side's length to its opposite side's length is the angle's tangent (tan).

given

cot + csc(x) (x)

= cos(x)/sin(x) 1/sin(x) (x) [using the csc(x) and cot(x) definitions]

= (cos(x) + 1) / sin (x) [combining the phrases by reducing them to a single value]

The right side of the equation will then be made simpler:

(csc(x) - cot(x)) = 1

= 1 / (1/cos(x)/sin(x) - sin(x)) [using the csc(x) and cot(x) definitions]

= Sin(x) / Cos(x) [using the reciprocal and a denominator that is simpler]

We shall now demonstrate that the left and right sides are equal:

Sine (1 + cos(x)) (x)

= [(1 + cos(x))] / [(1 + sin(x)] *[1 - cos(x)] / (1 - cos(x)] [by adding 1 - cos(x) to the numerator and denominator]

= sin(x) * (1 - cos(x) / (1 - cos2(x)) [reduce the numerator]

= sin2(x)/sin(x)*(1 - cos(x)) [by applying the formula sin2(x) = 1 - cos2(x)]

= Sin(x) / Cos(x) [removing the common sin(x) factor]

As a result, we have demonstrated: 1 / (csc(x) - cot(x)) = csc(x) + cot(x) as the right side of the equation .

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Here is the graph of the point (-4, -6) with a slope of 7/3.

To create the graph, start at the point (-4,-6) and plot it on the coordinate axis. From there, use the slope of 7/3 to find another point on the same line. To do this, you can move 7 units up and 3 units to the right from the point (-4,-6) to get to the point ( -1, -1). Plot this point on the graph as well. Finally, draw a straight line passing through both points to get the line representing the equation of the given point and slope.

Answer:

for the firsts ones :

1. 12 x 2 x 5

2. 4 x 11 x 2,25

3. 6.5 x 22.6 x 10

Step-by-step explanation:

Step-by-step explanation:

38%  X  78 894.24

  = .38 X 78 894.24 =  $ 29,979.81  tax

So, 100000+1X2 + 222+222+22222222222x111111111111111111111+222222222222222222 = 24,691,458,024,691,358,024,691,826

What does an expression mean?

It is preferable to use moving integer variables, which can be rising, decreasing, or blocking, rather than estimates that are generated at random. They could only assist one another by exchanging resources, knowledge, or answers to problems. A declaration of truth equation may include the justifications, components, and mathematical comments for strategies like extra disapproval, production, and mixture.

Let's solve this equation step by step:

100000+1X2

This is a simple expression which involves addition and multiplication.

100000+1X2 = 100000 + 2 (since 1X2 equals 2)

Therefore, 100000+1X2 = 100002

222+222+22222222222x111111111111111111111

This expression involves addition and multiplication as well.

We need to multiply 22222222222 by 111111111111111111111 first, and then add 222+222 to the result.

22222222222 x 111111111111111111111 = 24,691,358,024,691,358,024,691,358

222+222 = 444

So, 222+222+22222222222x111111111111111111111 = 24,691,358,024,691,358,024,691,802

222222222222222222

This is a simple number.

So, 100000+1X2 + 222+222+22222222222x111111111111111111111+222222222222222222 = 24,691,458,024,691,358,024,691,826

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The condition that must be satisfied to use a chi-square goodness-of-fit test is D. The expected count for each category is at least 5.

A chi-square goodness-of-fit test is a statistical test used to determine whether the observed frequencies of categorical data match the expected frequencies. This test is often used to analyze categorical data, such as determining if the distribution of colors in a bag of candies matches the expected proportions.

The reason behind this condition is that the chi-square test is based on the assumption that the data follow a specific distribution. When the expected count for each category is less than 5, the test might not accurately represent the true distribution, and the results may be misleading. By having an expected count of at least 5 in each category, the test can better approximate the true distribution and provide more reliable results. Therefore, option D is correct.

The Question was Incomplete, Find the full content below :

which of the following is a condition that must be satisfied to use a chi-square goodness-of-fit test?

A. The sample size is greater than 30.

B. The number of categories is less than 10% of the number of observations.

C. The expected count is the same for each category. the population distribution is approximately normal.

D. The expected count for each category is at least 5.

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[tex]\begin{bmatrix} 5&2\\ 3&x \end{bmatrix}~~ = ~~x^2\implies \stackrel{ \textit{determinant of a }2\times 2 ~matrix}{(5)(x)~~ - ~~(3)(2)}~~ = ~~x^2\implies 5x-6=x^2 \\\\\\ 0=x^2-5x+6\implies 0=(x-3)(x-2)\implies x= \begin{cases} 3\\ 2 \end{cases}[/tex]

Answer: B

Step-by-step explanation:

The answer is 9x^2 + 14xy -19y^2