The length of a rectangle is 9 inches more than twice the width, w, of the rectangle. The quadratic function, A(w) represents the area A, in square inches, of the rectangle for a given value of w.

If Morris wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be 9.

The t-test would be an inferential statistic that is used to assess whether or not there is a significant variation between the averages for two groups & how they are related.

Some key features of t-test statistics are-

Now, according to the question;

The degrees of freedom of first sample t-test are df=n-1

where n is the sample size.

So, n=10, then df = n-1 = 10-1 = 9.

Therefore, the degree of freedom for the t-test is 9.

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Answer:

Step-by-step explanation:

To find the total area of the track, we need to calculate the area of each section and then add them together.

Area of a semi-circle with radius 31m:

A = (1/2)πr^2

A = (1/2)π(31m)^2

A = 4795.4m^2

Area of a rectangle with length 92.7m and width 31m (the straight parts):

A = lw

A = (92.7m)(31m)

A = 2873.7m^2

To find the total area, we need to add the areas of the two semi-circular ends and the two straight sections:

Total area = 2(Area of semi-circle) + 2(Area of rectangle)

Total area = 2(4795.4m^2) + 2(2873.7m^2)

Total area = 19181.6m^2

Rounding this to 1 decimal place, we get:

Total area ≈ 19181.6 m^2

Therefore, the total area of the track is approximately 19181.6 square meters.

Given that the triangles are equal then the ratio of similar sides are equal

(x + 3)/15 = x/(15 - 6)

(x + 3)/15 = x/9

Cross multiply

15x = 9(x + 3)

Expand

15x = 9x + 27

Collect like terms

15x - 9x = 27

6x = 27

Divide both sides by 6

x = 27/6

= 9/2

= 4.5

Answer:

T = $12

S =$18

Step-by-step explanation:

This question would be solved using simultaneous equation

Let t = cost of t-shirt

s = price of sweatshirt

two equations can be derived from this question

12s + 8t = 312   eqn 1

8s + 13t = 300   eqn 2

Multiply eqn 1 by 8 and eqn 2 by 12 :

96s + 64t = 2496 eqn 3

96s + 156t = 3600 eqn 4

subtract eqn 3 from 4

92t =1104

t = 12

Substitute for t in eqn 1

12s + 8(12) = 312

12s + 96 = 312

12s = 216

s = 18

Answer:

7.33333333333

Step-by-step explanation:

3x - 7 = 15

3x = 15 + 7

3x = 22 (divide both sides by 3 to get x)

3x/3 = 22/3

x = 7.33333333333

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

:)

Answer:

Step-by-step explanation:

\(3x+7=15\\\\\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}\\\\3x+7-7=15-7\\\\Simplify\\\\3x=8\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3x}{3}=\frac{8}{3}\\\mathrm{Simplify}\\\\x=\frac{8}{3}\)

Answer:

The answer is A.

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

slope(m)=3/2

Step-by-step explanation:

It is not possible to describe the standard deviations of salary, hourly rate, years worked, education, and age without having the data.

Standard deviation is a measure of the spread or dispersion of a set of data. It is calculated as the square root of the variance and is used to give an idea of how far the individual values in a data set are from the mean or average.

In order to describe the standard deviations of salary, hourly rate, years worked, education, and age, we would need to have the actual data for those variables. Without the data, it is not possible to calculate the standard deviations and describe what they tell us about the variables.

It is important to note that the standard deviation can give us information about the distribution of the data and the variability of the values. For example, if the standard deviation is small, this means that the majority of the values are close to the mean, while a larger standard deviation indicates that the values are more spread out. This information can be useful in making inferences about the variables and in making predictions about future values.

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The equivalent equation to f(x) = 7(x - 60) - 28 is f(x) = 7x - 448 and the y-intercept is -448

Given that

f(x) = 7(x - 60) - 28

To produce an equivalent equation that reveals the y-intercept of the function f(x) = 7(x-60) - 28, we need to simplify the expression by evaluating it when x = 0, since this will give us the y-intercept.

When the brackets are expanded, we have the following

f(x) = 7x - 420 - 28

Evaluate the like terms

So, we have

f(x) = 7x - 448

So, substituting x = 0 into f(x) gives:

f(0) = 7(0) - 448

Evaluate the expression

f(0) = -448

Therefore, the y-intercept is -448.

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Answer:

m∠1 = 51°

m∠2 = 16°        

Step-by-step explanation:

First ,check the attached photo.

=================

In the right triangle ABC :

m∠1 = 90 - 39

       = 51°

……………………

In the right triangle ABD :

m∠2 = 90 - 74

       = 16°

Answer:

• ∠ 1 = 51°

• ∠ 2 = 16°

Step-by-step explanation:

•  ∠ 1, the 39° angle, and the right angle marked in red are angles of a triangle.

∴  ∠ 1 + 90° + 39° = 180°             [Angles in a triangle add up to 180°]

⇒ ∠ 1 = 180° - 90° - 39°

⇒ ∠ 1 = 51°

• The small triangle on the top-left of the image consists of ∠ 2, a right-angle (marked in red) and a 74° angle.

∴  ∠ 2 + 90° + 74° = 180°            [Angles in a triangle add up to 180°]

⇒ ∠ 2 = 180° - 90° - 74°

⇒ ∠ 2 = 16°

\(\bold{\huge{\purple{\underline{ Solution }}}}\)

We know that,

For nth term of an AP

\(\bold{\red{ an = a1 + (n - 1)d }}\)

We have ,

\(\sf{ a3 = 4x - 2y ...eq(1)}\)

\(\sf{ a9 = 10x - 8y ...eq(2)}\)

But, From above formula :-

\(\sf{ a3 = a1 + (3 - 1)d}\)

\(\sf{ a3 = a1 + 2d...eq(3)}\)

And

\(\sf{ a9 = a1 + (9 - 1)d}\)

\(\sf{ a9 = a1 + 8d...eq(4)}\)

From eq(1) and eq( 3) :-

\(\sf{ a1 + 2d = 4x - 2y }\)

\(\sf{ a1 = 4x - 2y - 2d ...eq(5)}\)

From eq(2) and eq( 4) :-

\(\sf{ a1 + 8d = 10x - 8y }\)

\(\sf{ a1 = 10x - 8y - 8d ...eq(6)}\)

From eq( 5) and eq(6) :-

\(\sf{ 4x - 2y - 2d = 10x - 8y - 8d }\)

\(\sf{ -2d + 8d = 10x - 4x - 8y + 2y }\)

\(\sf{ 6d = 6x - 6y }\)

\(\sf{ 6d = 6(x - y) }\)

\(\sf{ d = }{\sf{\dfrac{ 6(x - y) }{6}}}\)

\(\bold{\blue{ d = x - y }}\)

Hence, The common difference of the given AP is x - y.

The common difference of the given arithmetic progression is; d = x - y

Formula for the nth term of an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

n is position of term in the sequence

d is common difference

Thus;

a₃ = 4x - 2y

a₉ = 10x - 8y

Using the general formula, we know that;

a₃ = a + (3 - 1)d

a₃ = a + 2d   ----(eq 1)

a₉ = a + 8d   -----(eq 2)

Subtract eq 1 from eq 2 to get;

a₉ - a₃ = 6d

Put the given values of a₃ and a₉  to get;

10x - 8y - (4x - 2y) = 6d

6x - 6y = 6d

divide through by 6 to get;

d = x - y

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Answer:

I think it is C. Number cube

Let 1,2 = pop

Let 3,4 = jazz

Let 5, 6 = rock

Roll cube two times. Repeat.

Step-by-step explanation:

Answer: 76774

Step-by-step explanation: (34 x 2256) + (35 x 2) = 76774.

Answer:

76,774

Step-by-step explanation:

Break the question down, and you will get the same answer :)

Answer: True

Step-by-step explanation:

Answer: oooo those seem like a good deal

Step-by-step explanation:

The relative frequency of heads is reasonably close to 40%.Mr. Clark's claim about the theoretical probability is likely to be false. This means that the theoretical probability of tails is most likely 0.60.

The relative frequency is the ratio of the number of times an event occurred to the total number of trials. In this case, the relative frequency of heads is 0.38 and tails is 0.62.The theoretical probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.

Here, Mr. Clark claims that the coin is weighted so that the probability of heads is 40%. Therefore, the theoretical probability of heads is 0.40.However, the relative frequency of heads after 200 trials is only 0.38, which is reasonably close to 0.40. Hence, the relative frequency of heads is reasonably close to 40%.

Mr. Clark's claim about the theoretical probability of heads is likely to be false because the relative frequency of heads is less than the theoretical probability of heads (0.38 < 0.40).Therefore, the theoretical probability of tails is 1 - 0.40 = 0.60 because the coin is fair, so the probabilities of heads and tails should add up to 1. Thus, the theoretical probability of tails is most likely 0.60.

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The last year's salary was Rs 8250 and he is drawing this year Rs 9075.

What is the percentage of a number?

The percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'  known as percentage symbol.

The monthly salary of Mr. Maharjan was Rs 7500 before last year and it was increased by 10% last year.

So, The last year's Salary was 7500 +750 = 8250

Again, it increased by 20% this year.

Then, Drawings of current year = 7500 + 20% of 7500

7500 + 1500 = 9000

8250 + 10% of 8250 = 9075

Drawings of current year = 9075.

Hence, the last year's salary was Rs 8250 and he is drawing this year Rs 9075.

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Answer:

C edge 23'

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

To find the system of equations that is satisfied by the solution shown on the graph, we will simply need to find the equations of our two lines.

So, we will begin by finding the slope of each line and then proceed to find the entire equation.

Red Line:

To find the slope, we will first pick any two points from the red line.

Two sample points include (-5, 5) and (-4, 6).

The slope formula is given by:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Lett (-5, 5) be (x₁, y₁) and (-4, 6) be (x₂, y₂). Substitute:

\(\displaystyle m=\frac{6-5}{-4-(-5)}=\frac{1}{1}=1\)

Hence, the slope of the red line is 1.

Now, we can find the entire equation. We will use the slope-intercept form:

\(y=mx+b\)

Where m is the slope and b is the y-intercept.

We know that the slope m is 1. Hence:

\(y=x+b\)

We need to find our y-intercept b. For the red line, we know that when x is -5, y is 5. Hence:

\((5)=(-5)+b\)

Solving for b yields:

\(b=10\)

Therefore, our entire equation is:

\(y=x+10\)

Blue Line:

Again, we will find the slope first.

Picking two points, we get (0, 6) and (1, 5).

Using the slope formula by letting (0, 6) be (x₁, y₁) and (1, 5) be (x₂, y₂), we acquire:

\(\displaystyle m=\frac{5-6}{1-0}=\frac{-1}{1}=-1\)

Hence, the slope of the blue line is -1.

Again, we can use the slope-intercept form:

\(y=mx+b\)

Fortunately, we already know the y-intercept in this case. Since we have the point (0, 6), the y-intercept b is 6.

Therefore, our equation is:

\(y=-x+6\)

So, our two equations are:

\(y=x+10\text{ and } y=-x+6\)

Our answers are in standard form, so we will convert the two equations to standard form. Standard form is given by:

\(Ax+By=C\)

Where A, B, and C are integers and A is positive.

For the first equation, we can subtract x from both sides to get:

\(-x+y=10\)

Since A should be positive, we multiply both sides to get:

\(x-y=-10\)

For the second equation, we can add x to both sides:

\(x+y=6\)

Hence, our two equations in standard form is:

\(x+y=6\text{ and } x-y=-10\)

Therefore, our final answer is D.

Answer: D x + y = 6 and x − y = -10

Step-by-step explanation:

Malaki will have approximately $296.16 in his Savings account after 7 years.

To calculate the amount Malaki will have in his savings account after 7 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount in the account,

P is the principal amount (initial deposit),

r is the annual interest rate (expressed as a decimal),

n is the number of times interest is compounded per year, and

t is the number of years.

Given:

P = $250 (initial deposit),

r = 2.5% = 0.025 (interest rate expressed as a decimal),

n = 1 (interest compounded annually),

t = 7 (number of years).

Plugging these values into the formula, we have:

A = $250(1 + 0.025/1)^(1*7)

A = $250(1 + 0.025)^7

A = $250(1.025)^7

A = $250(1.184654712)

A ≈ $296.16

Therefore, Malaki will have approximately $296.16 in his savings account after 7 years.

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Answer: Parallel

Step-by-step explanation:

We can find their slopes to determine if the lines are parallel or perpendicular.

\(m_a=\frac{10-6}{2-9}=-\frac{4}{7}\\\\m_b=\frac{11-7}{2-9}=-\frac{4}{7}\)

Since the equations of the lines are not the same but the slopes of the lines are equal, they are parallel.

Case 2

The quadratic equation x² - 14 · x + 48 = 0 have the following roots: x₁ = 6 and x₂ = 8. (Correct choice: B)

Case 3

We need to add + 64 to both sides. (Correct choice: B)

Case 4

We need to add + 16 to both sides. (Correct choice: C)

In this problem we find three cases of quadratic equation that are not perfect square trinomials, these equations can be rewritten partially in that form by algebra properties. Completing the square offers a quick method to determine the roots of quadratic equations with integer coefficients. Now we proceed to determine the solutions corresponding to each case:

Case 2

x² - 14 · x + 48 = 0

x² - 14 · x + 49 = 1

(x - 7)² = 1

x - 7 = ± 1

x = 7 ± 1

The roots of the quadratic equation x² - 14 · x + 48 = 0 are x₁ = 6 and x₂ = 8, respectively.

Case 3

x² - 16 · x = - 21

x² - 16 · x + 64 = 64 - 21

(x + 8)² = 43

The first step consists in adding both sides by + 64.

Case 4

x² - 8 · x = 0

x² - 8 · x + 16 = 16

(x - 4)² = 16

The first step consists in adding both sides by + 16.

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The function y(t) reaches maximum when t = 0.

Given differential equation is y'' + 4y' + 4y = 0.

Solution: The given differential equation is

y'' + 4y' + 4y = 0

Characteristics equation: m² + 4m + 4 = 0

⇒ (m + 2)² = 0

Roots of the characteristic equation: m₁ = m₂

= -2

The general solution is given by:

y = (c₁ + c₂t)e⁻²t

Also,

y(0) = c₁ - 1 ...(i)

y'(0) = c₂ - 2c₁ ...(ii)

Putting the value of c₁ from equation (i) in equation (ii), we get:

c₂ = y'(0) + 2y(0)

= -1 + 2

= 1

So, the particular solution is given by

y = (c₁ + c₂t)e⁻²t

Putting the values of c₁ and c₂, we get

y = (1 - t)e⁻²t

Now,

y' = -2te⁻²t

The function y(t) reaches maximum when y'(t) = 0 and y''(t) < 0.

Therefore, -2te⁻²t = 0

⇒ t = 0

Thus, at t = 0 the function y(t) reaches maximum. 

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The equations Verdita could use to represent the data sets include the following:

A. Data Set A: y = 4x-2

Data Set B: y = x +4

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of data set A;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 + 6)/(1 + 1)

Slope (m) = 8/2

Slope (m) = 4

At data point (1, 2) and a slope of 4, a linear equation for data set A can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 4(x - 1)

y = 4x - 2

At data point (0, 4) and a slope of 1, a linear equation for data set B can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = 1(x - 0)

y = x + 4

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

the radius of convergence (R) is ∞, and the interval of convergence (I) is (-∞, ∞).

To find the radius of convergence (R) and the interval of convergence (I) of the series given by:

∑ 7(-1)^(n-1) n^n x^n

We can apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L as n approaches infinity, then the series converges absolutely if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

Let's apply the ratio test to the given series:

L = lim(n→∞) |(7(-1)^(n-1) (n+1)^(n+1) x^(n+1)) / (7(-1)^(n) n^n x^n)|

Simplifying and canceling out common factors:

L = lim(n→∞) |(7(n+1) x) / (n^n)|

Taking the absolute value:

L = lim(n→∞) |7(n+1) x / n^n|

Now, let's evaluate the limit:

L = |7x| lim(n→∞) (n+1) / n^n

The limit can be further simplified by applying the ratio test for the sequence:

lim(n→∞) (n+1) / n^n = 0

Therefore, the limit L simplifies to:

L = |7x| * 0 = 0

Since L = 0, which is less than 1, the ratio test indicates that the series converges absolutely for all values of x. Thus, the series converges for all x.

For a series that converges for all x, the radius of convergence (R) is infinite (∞), and the interval of convergence (I) is the entire real number line (-∞, ∞).

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Answer:

B. $35.50/hr and \$6,079.38 in total income

Step-by-step explanation:

Given the following :

Total regular pay earning for the year = $73,840

Let basic salary = b

Overtime = 1.5b

Regular earning per week :

Regular year earning / number of weeks per year

$73840 / 52 = $1420

Regular hours = 40

Regular earning per week = $1420

Regular earning per hour = $1420 / 40

Regular earning per hour = $35.50

Number of overtime hours :

4 hours + 3.5hours = 7.5hours

Overtime pay per hour = 1.5 * regular earning

Overtime pay per hour = 1.5 * 35.5 = $53.25

Total overtime pay = Overtime pay per hour * Number of overtime hours

Total overtime pay = $53.25 * 7.5

Total overtime pay = 399.375

Total pay for the month :

160 regular hours + 7.5 overtime hours

(160 * 35.5) + $399.375

$5,680 + 399.375 = $6,079.375

= $6,079.38

Answer:

The system of equations y=14-2x and 6x+3y=42.

Step-by-step explanation:

Please see attachment to see the answer as a graph.

Hope this helps!