write the equation for a line that passes through the points (5,5) and (7,-5)

The computed value of the test statistic is 2.94.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We have a sample size of n = 12, engine size (x) and emissions (y) are the two variables being correlated, and the sample correlation coefficient is r = 0.47.

The null hypothesis is that the population correlation is zero (H0: ρ = 0) and the alternative hypothesis is that the population correlation is positive (Ha: ρ > 0).

To compute the test statistic, we need to first calculate the degrees of freedom (df), which is (n-2) = 10 in this case.

We can then use the formula for the test statistic, which is:

t = (r√(df)) / √1 - r²

Substituting the values we have, we get:

t = (0.47 √10) / √(1 - 0.47²)

t = 2.94

Therefore, the computed value of the test statistic is 2.94.

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The regression equation computed by the researchers is Y=23.083+0.044X, where Y represents the ACT composite score and X represents household income (in $1000).

To determine whether household income predicts ACT scores, the researchers need to perform a hypothesis test. The null hypothesis for this test would be that the slope coefficient (β) is equal to 0, which means there is no relationship between household income and ACT scores. The alternative hypothesis would be that the slope coefficient is not equal to 0, indicating that there is a significant relationship between household income and ACT scores.
To determine whether the researchers have enough evidence to claim that household income predicts ACT scores, they would need to perform a significance test on the slope coefficient. They can calculate the t-value for the slope coefficient using the standard error of the slope, which can be obtained from the regression output. If the t-value is significant at the desired level of significance (typically 0.05), then the researchers can reject the null hypothesis and conclude that there is a significant relationship between household income and ACT scores.
However, based on the limited information provided in the question, it is not possible to determine whether the researchers have enough evidence to claim that household income predicts ACT scores. More information is needed on the sample size, the significance level, and the calculated t-value for the slope coefficient.

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Answer:

54 inches

Hope this helps! :)

Step-by-step explanation:

Answer:

C. $0.22 per box

Step-by-step explanation:

if it's two juice boxes and they cost $0.44 together. You divide by two, since there are two boxes. with that you get your answer, 44÷2=22. making the answer $0.22

Answer:5.25

Step-by-step explanation:

Answer:

10, 100, 1,000, 10,000, 100,000

If you are adding one zero in the end for every number, then 100,000 will be your next number

The correct option c. 20 cm, is the length of each sides of the regular pentagon.

A quadrilateral with five equal sides is known as a regular Pentagon.

Regular pentagon perimeter equals 5*side

Since we already know that a normal pentagon's perimeter is 100 cm.

Hence, 100 = 5*side

Side = 20 cm

Each side is 20 cm long.

As a result, the side of a regular pentagon is 20 cm long.

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Answer:

4 Hours.

Step-by-step explanation:

If the run 11 miles in a hour, then do 11 times as many hours.

11 x 4 = 44.

The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

Given that,

In a survey, it was discovered that 68% of women and 78% of men preferred computer-assisted education to lectures, respectively. Each sample contained 100 people that were chosen at random.

We have to calculate the 95% confidence range for the difference between the two proportions.

We know that,

The 95% confidence interval for difference between two population proportions is given as follows :

\(((\bar p_{1} -\bar p_{2})\)±\(Z_{0.05/2}\sqrt{\frac{PQ}{n_{1} } +\frac{PQ}{n_{2} }} })\)

Here,

p₁ is 0.78

p₂ is 0.68

n₁ is 100

n₂ is 100

Z is 1.96

P is 0.73

Q is 0.27

So,

((0.78-0.68)±\(1.96\sqrt{\frac{(0.73)(0.27)}{100 } +\frac{(0.73)(0.27)}{100 }} })\)

(0.10±0.122)

(0.10-0.122,0.10+0.122)

(-0.022,0.222)

Therefore, The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

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Answer:

4 quarters and 6 dimes

Step-by-step explanation:

4(0.25)+6(0.10)= 1.60

Using trigonometric identity, cos(A-B) is:

\(cos (A-B) = \frac{2\sqrt{8}\ + \sqrt{5}}{9}\)

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

If sin A = 1/3 and A terminates in Quadrant 1. All trigonometric functions in Quadrant 1  are positive

sin A = 1/3 (sine = opposite/hypotenuse)

adjacent = √(3² - 1²)

               = √8 units

cosine = adjacent/hypotenuse. Thus,

\(cos A = \frac{\sqrt{8} }{3}\)

If cos B = 2/3 and B terminates in Quadrant 4.

opposite = √(3² - 2²)

                = √5

In  Quadrant 4, sine is negative. Thus:

\(sin B = \frac{\sqrt{5} }{3}\)

We have:

cos(A-B) = cosA CosB + sinA sinB

\(cos (A-B) = \frac{\sqrt{8} }{3} * \frac{2}{3} + \left \frac{1}{3} * \frac{\sqrt{5} }{3}\)

\(cos (A-B) = \frac{2\sqrt{8} }{9} + \left\frac{\sqrt{5} }{9}\)

\(cos (A-B) = \frac{2\sqrt{8}\ + \sqrt{5}}{9}\)

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Answer:

A or 57 7/9ft3

Step-by-step explanation:

13/3x10/3x4/1 = 520/9=57 7/9

Answer:

The volume of the rectangle would be \(57\frac{7}{9}\) ft^3. (The first answer).

Step-by-step explanation:

To solve you have to multiply \(4\frac{1}{3},3\frac{1}{2}, and, 4\) to get an answer of \(57\frac{7}{9}\).
I hope this helps! :)

Answer: \(\Large\boxed{First~Choice.~-28}\)

Step-by-step explanation:

Given function expression

f(x) = -5x² - x + 20

Requirement of the question

Find the value of f(3)

Substitute the values into the function

f(x) = -5x² - x + 20

f(3) = -5(3)² - (3) + 20

Simplify the exponents

f(3) = -5(9) - 3 + 20

Simplify by multiplication

f(3) = -45 - 3 + 20

Simplify by subtraction and addition

f(3) = -48 + 20

\(\Large\boxed{f(3)=-28}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

(5,-3)

Step-by-step explanation:

Rewrite the equation in vertex form

y =-(x-5)^2 - 3

You take the value of -5 (that would be your x value) and change it to the opposite sign -> +5

Then you take -3 (that would be your y value) and take it as it is

therefore the answer is (5, -3)

Answer:

3 out of 13 chance of getting grey socks

Answer:

c = 3

Step-by-step explanation:

12 divided by 4 is 3

Answer:

C= 3

Step-by-step explanation:

A child of a parent with a mutation in collagen and displaying OI will have 50% probability of also having OI.

Osteogenesis imperfecta (OI) is an inherited or genetic bone disorder which is present at birth. It is also known as brittle bone disease. A child born with OI may have soft bones which fracture easily, bones which are not formed normally, and other problems. Signs and symptoms may range from mild to severe.

Life expectancy for OI babies vary greatly depending on OI type. Babies with Type II generally die soon after birth. Children with Type III may live longer, but mostly only until around age 10.

About 90% of OI cases are caused by autosomal dominant mutations in the type I collagen genes. Mutations in one or the other of these genes cause the body to make either abnormally formed collagen or too little collagen. Mutations in these genes cause OI Types I through IV.

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Answer:

h(75)+50 h is the number of hours worked

Step-by-step explanation:

Answer:

y = - 3

Step-by-step explanation:

Given

8(y - 3) = - 48 ( divide both sides by 8 )

y - 3 = - 6 ( add 3 to both sides )

y = - 3

Answer:  

Step-by-step explanation:

a)  Two lines are parallel and KN is transversal.

So, alternate interior angles are equal.

∠LNM =∠JKL

6x + 1 = 25

Subtract 1 from both sides.

6x + 1 - 1 = 25 -1

6x = 24

Divide both sides by 6

6x/6 = 24/6

x = 4°

b) ∠LMN = 3x +11

             = 3*4 + 11

              = 12 + 11

∠LMN = 23°

c)  ∠KJL = ∠LMN    {Alternate interior angles are equal, transversal JM}

∠KJL = 23°

In ΔKLJ,

∠JKL + ∠KLM + ∠LJK = 180°

25 + ∠KLM + 23 = 180

∠KLM + 48 = 180

∠KLM = 180 - 48

∠KLM = 132°

d) In ΔJKL & ΔLMN

∠J = ∠M

∠K=∠N

∠NLM = ∠KLJ     {Vertically opposite angles.

ΔKJL & ΔLMN  are similar triangles

Answer:

1/10

Step-by-step

Answer:

cos 75 = 16/x ---> x = 16/cos75 = 61.8 ft.

Answer:

Step-by-step explanation:

12y-19= 6y+1

12y-6y = 1 +19

6y = 20

y = 20/6

y= 10/3 or 3.33..

As per the double integral, the flux of the vector is 2√11(6z + 1) + 176

What is double integral small definition?

In math, Double integrals are used to find the flux of a vector field through a given surface S and find the normal to the given surface and equations of the surface to find the limits of integration.

And it is calculate by the formula as Flux= ∫∫F⋅ndS

Here we have given that S be the part of the plane 2x + 1y + z = 2 which lies in the first octant, oriented upward.

And we need to find the the flux of the vector field F = 1i + 1j + 3k across the surface S.

As per the formula of flux of vector, it can be written as,

=>Flux =  ∫∫(1i + 1j + 3k) . 2 dS

When we integrate this one the we get,

=> Flux = 2√11(6z + 1) + 176

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Answer:

19/40

Step-by-step explanation:

⅛ over 50

⅖ women

5 x 8 = 40

8 x 2 = 16

1 x 5 = 5

16 + 5 = 21

40 - 21 = 19

19/40

Answer:

19/40 are men under 50

Step-by-step explanation:

Given:

\(\begin{aligned}\textsf{Men under 50 yrs old} & = \textsf{total proportion of men} - \textsf{proportion of men over 50}\\\\& = \left(1-\dfrac{2}{5}\right)-\dfrac{1}{8}\\\\& = \dfrac{3}{5}-\dfrac{1}{8}\\\\& = \dfrac{3 \cdot 8}{5 \cdot 8}-\dfrac{1 \cdot 5}{8 \cdot 5}\\\\& = \dfrac{24}{40}-\dfrac{5}{40}\\\\& = \dfrac{19}{40}\end{aligned}\)

To check this, let's assign a number to the total number of players and use this to help us calculate the proportion of players who are men under 50 years old.

Let the total number of video game players be 400.

If 2/5 of all video game players are women, then the proportion of all video game players that are men is:  1 - 2/5 = 3/5

⇒ total number of men = 3/5 of 400 = 3/5 × 400 = 240

If 1/8 of all video game players are men over 50 years old then:

⇒ number of men over 50 yrs old = 1/8 × 400 = 50

Therefore:

⇒ number of men under 50 yrs old = 240 - 50 = 190

Finally, the fraction of men under 50 years old from all video game players is the number of men under 50 divided by the total number of men.

⇒ men under 50 years old = 190/400 = 19/40

Answer:

2. QR - TS and QT ║ RS

Step-by-step explanation:

Parallelogram is a rectangle with two pairs of parallel lines. The quadrilateral will be parallelogram if the two sides  pairs are parallel to each other. If QR and TS are parallel and QT and RS are parallel then the quadrilateral will be parallelogram.

The QR - TS and QT || RS ie. option (2) is correct in quadrilateral QRST.

It is given that the quadrilateral QRST, diagonals QS, and RT intersect at M.

It is required to find which statement would always prove quadrilateral QRST is a parallelogram.

It is defined as the four-sided polygon in geometry having four edges and four corners. It is a two-dimensional geometry.

We know the parallelogram is nothing but it is a rectangle geometry with two pairs of parallel sides, if, in the quadrilateral QRST, diagonals QS and RT intersect at M.

In the parallelogram, diagonals bisect each other which means that point M is a midpoint of the QS and RT.

Mathematically:

QM = SM and RM = TM

Also QT || RS.

Thus, the QR - TS and QT || RS ie. option (2) is correct in quadrilateral QRST.

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The most appropriate procedure from the given options that would improve the reliability and validity of grading short essay tests, thus addressing the complaint of sensitivity to bias and variability in grading, is: D) Using a scoring rubric.

A scoring rubric is a predefined set of criteria or guidelines that outlines the specific expectations and standards for evaluating student responses. By using a scoring rubric, the grading process becomes more objective, consistent, and transparent, thereby reducing bias and variability in grading.

A scoring rubric provides a structured framework that allows graders to assess and assign scores based on predetermined criteria, such as content knowledge, organization, clarity, coherence, and grammar. It ensures that all essays are evaluated using the same standards and eliminates subjective judgment as much as possible.

Administering more pretests (option A) may provide additional practice or feedback to students but does not directly address the issue of bias and variability in grading.

Grading on the curve (option B) adjusts grades based on the performance of other students in the class, which does not directly address bias or variability in grading. It can introduce its own set of issues and may not reflect the true quality of each individual student's work.

Implementing a contract system (option C) refers to a negotiated agreement between students and instructors regarding grading criteria, which may help clarify expectations but does not inherently address bias or variability.

Therefore, using a scoring rubric (option D) is the most appropriate procedure to improve the reliability and validity of grading short essay tests while minimizing sensitivity to bias and variability in grading.

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