Find the slope between the two points

The correlation is statistically significant, it is not a perfect relationship and there may be other factors at play that affect academic performance. Overall, the results suggest that studying for more hours per week may lead to better academic performance

Based on the given information, we can conclude that there is a positive correlation between the number of hours studied per week and academic performance of 25 UK University students. The correlation coefficient of 0.71 suggests a moderate to strong positive relationship between the two variables. This means that as the number of hours studied per week increases, the academic performance of the students also tends to increase. However, it is important to note that the "critical r" value of 0.87 with a significance level of p≤0.05 indicates that there is a chance of 5% that the observed correlation between the variables could be due to random chance. This means that while the correlation is statistically significant, it is not a perfect relationship and there may be other factors at play that affect academic performance. Overall, the results suggest that studying for more hours per week may lead to better academic performance, but it is not the only factor that contributes to success. Other variables such as natural ability, motivation, and study habits may also play a role in academic achievement.

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Answer:

H

Step-by-step explanation:

Its H because a square has 4 sides and 58 divided by 4 is 14.5

After simplifying the percentage, if 120% of a is equal to 80% of b, then a+b is 5.

In the given equation,

If 120% of a is equal to 80% of b, then we have to find the value of a+b.

We firstly express the statement in the algebraic equation.

It is given in the statement that 120% of a.

We write it as 120%×a.

From the statement, 80% of b.

We write its as 80%×b.

Both are equal to each other.

So the expression should be

120%×a=80%×b

Divide by 12% on both side

120%/120% ×a=80%/120% ×b

Simplifying

a=80%/120% ×b

As we know that % means 100 but both number 80 and 120 have % sign. So the % sign emitted.

So a=80/120 ×b

Divide by b on both side

a/b=80/120 ×b/b

a/b=80/120

Simplifying the ration

a/b=2/3

Hence, the value of a=2 and b=3.

Now finding the value of a+b.

a+b = 2+3

a+b = 5

Hence, if 120% of a is equal to 80% of b, then a+b is 5.

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The circumference of a circle is directly proportional to its radius. Given a circle with a radius of 6 in and a circumference of 37.68 in, we can find the circumference of the circle when the radius changes to 14 in. We will use the direct variation relationship between circumference and radius to solve for the new circumference.

Let's denote the circumference of the circle as C and the radius as r. We are given that C varies directly with r, which can be expressed as C = k * r, where k is the constant of variation. To find the value of k, we use the given information that when the radius is 6 in, the circumference is 37.68 in:

37.68 = k * 6

Solving for k, we divide both sides of the equation by 6:

k = 37.68 / 6

k ≈ 6.28

Now we can use the value of k to find the circumference when the radius is 14 in:

C = 6.28 * 14

C ≈ 87.92

Therefore, the circumference of the circle with a radius of 14 in is approximately 87.92 in. In summary, the circumference of a circle varies directly with its radius. By using the direct variation equation and the given information, we determined the constant of variation and used it to find the circumference when the radius changed to 14 in, which is approximately 87.92 in.

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Answer: True

Step-by-step explanation:

Cost = 15 + 3t

22.5 = 15 + 3(2.5)

22.5 = 15 + 7.5

22.5 = 22.5 <— true

Answer:

true

Step-by-step explanation:

2.50 x 3 = 7.50

15 + 7.50 = 22.50

22.50 = 22.50

In a negatively skewed distribution, the histogram with the longer tail on the left, the mean would be smaller than the median.

One of the histograms that has a mean smaller than the median is the one that is skewed to the left, also known as negatively skewed. In a negatively skewed distribution, the tail of the histogram is longer on the left side. This means that there are a few extremely low values that pull the mean towards the left, making it smaller than the median.

To understand this, imagine a histogram of people's incomes. If there are a few billionaires in the sample, their incomes would be extremely high, which would pull the mean towards the right. However, the median would not be affected much, as it is the value that splits the data into two equal halves. So, in this case, the mean would be larger than the median.

On the other hand, if the histogram represents a distribution of test scores and a few students perform extremely poorly, their scores would pull the mean towards the left. However, the median would still be in the center of the distribution. Hence, the mean would be smaller than the median.

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Answer:

\( \frac{9}{14} \)

Step-by-step explanation:

times top numbers and bottom numbers

6 × 3 = 18

7 × 4 = 28

18/28

*simplify*

9/14

The number of students in each bus is 21

Given data

Total number of students on the trip = 172

25 students traveled in cars

7 buses were filled

let the number students on each bus be x

number of students on the bus is gotten by

172 - 25 = 147

so 147 students travelled by bus and the total number of buses is 7.

to get the number of students in each bus we solve as follows

147 / 7 = 21

Hence each bus contains 21 students.

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Answer: r≈16.17

Step-by-step explanation: r=A

π=821

π≈16.16578

The inverse Fourier transform of F₂(jw) is given by f₂(t) = δ(t - 1/4) + δ(t + 1/4).

(a) To find the inverse Fourier transform of F₁(jw) = 1/(3+w) + 1/(4-jw), we can use the linearity property of the Fourier transform.

The inverse Fourier transform of F₁(jw) can be calculated by taking the inverse Fourier transforms of each term separately.

Let's denote the inverse Fourier transform of F₁(jw) as f₁(t).

Inverse Fourier transform of 1/(3+w):

Using the table of Fourier transforms,

F⁻¹{1/(3+w)} = e^(-3t) u(t)

Inverse Fourier transform of 1/(4-jw):

Using the table of Fourier transforms, we have:

F⁻¹{1/(4-jw)} = e^(4t) u(-t)

Now, applying the linearity property of the inverse Fourier transform, we get:

f₁(t) = F⁻¹{F₁(jw)}

      = F⁻¹{1/(3+w)} + F⁻¹{1/(4-jw)}

      = e^(-3t) u(t) + e^(4t) u(-t)

Therefore, the inverse Fourier transform of F₁(jw) is given by f₁(t) = e^(-3t) u(t) + e^(4t) u(-t).

(b) To find the inverse Fourier transform of F₂(jw) = cos(4w + π/3), we can use the table of Fourier transforms and properties of the Fourier transform.

Using the table of Fourier transforms, we know that the inverse Fourier transform of cos(aw) is given by δ(t - 1/a) + δ(t + 1/a).

In this case, a = 4, so we have:

F⁻¹{cos(4w + π/3)} = δ(t - 1/4) + δ(t + 1/4)

Therefore, the inverse Fourier transform of F₂(jw) is given by f₂(t) = δ(t - 1/4) + δ(t + 1/4).

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(A) N'(2) increasing: '-T'

(B) N'(2) decreasing: '-T'

(C) Average of inflection points: -1000

(D) Maximum rate of change of sales: 14100

To determine when the rate of change of sales, N'(2), is increasing or decreasing, we need to find the derivative of the sales function N(x) and evaluate it at x = 2.

Given: N(x) = -523 + 220x^2 - 3500x + 16000

Taking the derivative of N(x) with respect to x:

N'(x) = d/dx(-523) + d/dx(220x^2) - d/dx(3500x) + d/dx(16000)

N'(x) = 0 + 440x - 3500 + 0

N'(x) = 440x - 3500

To determine when N'(2) is increasing or decreasing, we evaluate N'(x) at x = 2:

N'(2) = 440(2) - 3500

N'(2) = 880 - 3500

N'(2) = -2620

(A) N'(2) is increasing: Since N'(2) is negative (-2620), it is decreasing rather than increasing. Therefore, there is no interval where N'(2) is increasing. We represent this using interval notation: N'(2) = '-T'.

(B) N'(2) is decreasing: As mentioned above, N'(2) is negative (-2620), indicating a decreasing rate. Therefore, N'(2) is always decreasing. We represent this using interval notation: N'(2) = '-T'.

To find the average of the x-values of all inflection points of N(x), we need to find the second derivative, N''(x), and solve for its roots:

N''(x) = d/dx(440x - 3500)

N''(x) = 440

Since N''(x) is a constant (440), it has no roots. Therefore, there are no inflection points. The average of the x-values of inflection points is -1000 (as instructed).

(C) Average of inflection points = -1000.

To find the maximum rate of change of sales, we look for critical points by setting N'(x) = 0 and checking the endpoints of the given interval (10 < x < 40):

N'(x) = 440x - 3500

440x - 3500 = 0

440x = 3500

x = 3500/440

x ≈ 7.95

We check the endpoints of the interval:

N'(10) = 440(10) - 3500

N'(10) = 4400 - 3500

N'(10) = 900

N'(40) = 440(40) - 3500

N'(40) = 17600 - 3500

N'(40) = 14100

The maximum rate of change of sales occurs at one of the endpoints since N'(x) is linear. The maximum rate is given by the larger value, N'(40).

(D) Maximum rate of change of sales = 14100.

The maximum rate of change of sales occurs at x = 40, which represents the endpoint of the interval. This means that the company estimates the highest rate of change in sales to be 14,100 units per thousand dollars spent on advertising when x (presumably representing some advertising-related factor) is at its maximum value within the given interval.

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Answer:

$4162.4

Step-by-step explanation:

As per the question statement,

The computer monitors are in cuboid structure.

Width of computer monitors = 22 inches

Length of computer monitors = 22 inches

Thickness of computer monitors = 2 inches

Average cost of production per cubic inch = $0.43

To find:

Cost to the company to make 10 monitors.

Solution:

Volume of a cuboid is given as following:

\(Volume = Length \times Width \times Height\)

Volume of one computer monitor as per the given dimensions = \(22\times 22 \times 2\) = 968 cubic inches

Volume of 10 such monitors = 968 \(\times\) 10 = 9680 cubic inches

Cost of manufacturing of 1 cubic inch = $0.43

Cost of manufacturing of 9680 cubic inch = $0.43 \(\times\) 9680 = $4162.4

Answer:

ok.

Step-by-step explanation:

hiiiiiiiiiiiiiiiiii

The image of the transformation of the ordered pair is (-2,-6)

The ordered pair is given as:

(1, -3)

The transformation is given as:

D₂ o Ry-axis

This means a dilation by a scale factor of 2 and then a reflection across the y-axis.

The image of the dilation is:

(x,y) = 2 * (1,-3)

(x,y) = (2,-6)

The rule of reflection across the y-axis is

(x,y) = (-x,y)

So, we have:

(x,y) = (-2,-6)

Hence, the image of the transformation is (-2,-6)

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Answer:

r=30

Step-by-step explanation:

r/30=-2+3

r/30=1

r=1×30

r=30

Answer:

Horizontal compression by a factor of 2 followed by a vertical shift by positive 3

Step-by-step explanation:

a*f(k(x-d))+c

k=2

c=3

Answer:

\(\frac{1}{120}\)

Step-by-step explanation:

To solve such a problem you need to simulate a situation in which this could happen in three picks and then make sure your equation takes into account that all three picks take place at the same time. One such situation could look like this:

1) At the start, the probability of picking one rotten apple with one pick is 2 out of 16 which 2/16.

2) After picking the first apple you have 15 apples left of which only 1 is rotten. So the chance to pick the second rotten apple is 1/15.

3) After you picked the second rotten apple you want the third one in the set to be good. As you are left with 14 apples of which all 14 are good, the probability of picking a good one is 14/14.

Now, because you are interested in ALL those 3 things happening at the same time, you need to multiply the probabilities. So this gives you the answer of:

\(\frac{2}{16} *\frac{1}{15} *\frac{14}{14} = \frac{1}{8} *\frac{1}{15} *1 = \frac{1}{120}\)

You can achieve the same result if your picks are in a slightly different order. The result won't change as long as the outcome is the same (set of 2 rotten apples and 1 good apple). So if you first pick a rotten apple (2/16), then you happen to pick a good apple (14 out of 15 left are good so 14/15) and then pick the second rotten apple last (1/14) you will see it's gives the same result because you also end up with 2 rotten and 1 good apples:

\(\frac{2}{16} * \frac{14}{15} * \frac{1}{14} = \frac{1}{8} * \frac{1}{15} = \frac{1}{120}\)

Answer: amount of wire needed is 5.84 feet.

Step-by-step explanation:

given data:

height of the first pole = 8 feet

height of the second pole = 10 feet

distance between both poles = 50 feet

SOLUTION:

L1 = \(\sqrt{x^{2} + 8^{2} } \\\)

= \(\sqrt{x^{2} + 64}\)

L2 = \(\sqrt{(50-x)^{2} +10^{2} }\)

= \(\sqrt{(50-x)^{2}+100 }\)

total length of wire

L = L1 + L2

L =  \(\sqrt{x^{2} + 64}+\sqrt{(50-x)^{2}+100 }\)

\(\frac{dL}{dx}=\frac{2x}{2\sqrt x^{2} +64} + \frac{2(50-x(-1)}{2\sqrt{(50-x)^{2} +100} } =0\)  

\(\frac{x}{\sqrt x^{2} +64} = \frac{50-x}{\sqrt{(50-x)+100} }\)

\(x\sqrt{(50-x} )^{2}+100 = (50-x)\sqrt{x^{2} +64}\)

\(x^{2} ((50-x)+100)=(15-x)^{2} (x^{2} +64)\)

\(x^{2} (50-x)^{2} +100x^{2} =x^{2} (50-x)^{2} +64(50-x)^{2} \\\\100x^{2} = 64(50-x)^{2} \\100x^{2} =64((50-x)(50-x))\\100x^{2} = 64(2500-100x+x^{2} )\\\\100^{2} =160000 -6400x+64x^{2} \\\\36x^{2} +6400x-160000=0\)

\(36x^{2} + 64x-1600=0\)

\(18x^{2} +32x+800=0\)

using quadratic equation

\(a=18\\b=32\\c=800\\\)

refer to the attached image

\(x=\frac{-8}{9} +\frac{4}{9} \sqrt{229} \\or \\x=x=\frac{-8}{9} +\frac{-4}{9} \sqrt{229}\)

\(x = 5.84\\or\\x= -7.61\)

An absolute value inequality that represents the acceptable amounts of sodium is; 35 ≤ A ≤ 45

We are told that a can of soda can have a minimum of 35 milligrams of sodium and a maximum of 45 milligrams of sodium.

Now, an absolute value inequality that represents this expression would be written as;

35 ≤ A ≤ 45

Thus, we conclude that an absolute value inequality that represents the acceptable amounts of sodium is; 35 ≤ A ≤ 45

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from the diagram, we can see that the height or line perpendicular to the parallel sides is 8.5.

likewise we can see that the parallel sides or "bases" are 24.3 and 9.7, so

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ h=8.5\\ a=24.3\\ b=9.7 \end{cases}\implies \begin{array}{llll} A=\cfrac{8.5(24.3+9.7)}{2}\\\\ A=\cfrac{8.5(34)}{2}\implies A=144.5~in^2 \end{array}\)

The area of the given trapezoid JKLM is 144.5 in². Hence, option C is the right choice.

The area is the two-dimensional space within the closed boundary of its surface.

The area of a trapezoid is found using the formula:

Area = (1/2)(sum of parallel sides)(the distance between the parallel sides).

In the question, we are asked to find the area of trapezoid JKLM.

We will determine the area of the trapezoid using the formula:

Area = (1/2)(sum of parallel sides)(the distance between the parallel sides).

In trapezoid JKLM, JK and ML are two parallel sides and the distance between them is given by the perpendicular from M to JK, which we take as MN.

Therefore, the area of the trapezoid JKLM = (1/2)(JK + ML)(MN),

or, the area of the trapezoid JKLM = (1/2)(24.3 + 9.7)(8.5) in²,

or, the area of the trapezoid JKLM = 0.5*34*8.5 in² = 144.5 in².

Hence, option C. 144.5 in² is the right choice.

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The winch needs to rotate approximately 10 times to roll in 5 feet of cable.

To find out how many times the winch needs to rotate, we first need to determine the length of cable that is being wound around the drum. We know that the diameter of the drum is 5 inches, so we can calculate the circumference of the drum:

Circumference = π × diameter = π × 5 inches = 15.71 inches

Next, we need to convert the 5 feet of cable into inches so that we can compare it to the circumference of the drum:

5 feet × 12 inches/foot = 60 inches

Now that we have both values in inches, we can divide the total length of the cable by the circumference of the drum to find out how many times the winch needs to rotate:

60 inches ÷ 15.71 inches = 3.83

Since the winch needs to rotate a full rotation each time the cable is wound around the drum, we will round up to the nearest whole number, which is 4.

So, the winch needs to rotate approximately 10 times to roll in 5 feet of cable.

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Answer:

It would be y = -5/3x + 50/3

Step-by-step explanation:

You would use the point slope formula y - y₁ = m ( x - x₁) and insert the point and slope.

Answer:

see below

Step-by-step explanation:

2*35-176+65/ 2

Following PEMDAS

Multiply and divide from left to right

2x35-176+65/ 2

70 -176+65/ 2

70-176+32.5

Then add and subtract from left to right

-106 +32.5

-73.5

or

(2*35-176+65)/ 2

Following PEMDAS

Parentheses first

Multiply and divide from left to right

(70 -176+65)/ 2

Then add and subtract in the parentheses

(-41)/2

-21

Step-by-step explanation:

2×35-176+65÷2

70-176+65÷2

70-176+32.5

70-176=-106

-106+32.5= -83.5

I hope this is correct.

Sorry if it isn't

=(

Answer:

my answer is A

Step-by-step explanation:

if you work out the equation where you know that at the x intercept y=0 you will find A to be true

Answer:

one fourth

Step-by-step explanation:

Answer:

Step-by-step explanation:

Number of 2's is 2

Total number is 8

Correct choice is B

If ∆PQR≅∆ XYZ

that means PQ≡XY;QR≡YZ;PR≡XZ

The car payment plan that has an APR of 1.9% is, on the short term, pocket

friendly.

The correct responses are;

Reasons:

The question parameters are;

Molly is comparing Auto Loans on Jeep website

Selling price of the Jeep, P = $25,495

The down payment Molly has = $2,500

The Cash Allowance = $500

Number of months of payment, n = 84 months

The Annual Percentage Rate, APR, r = 1.9%

First Part:

Loan needed = $25,495 - $2,500 - $500 = $22,495

The amount of loan Molly needs = $22,495

Second Part:

The monthly payment is given by the formula;

Therefore;

\(\displaystyle M = \dfrac{22,495 \times \left(\dfrac{0.019}{12} \right) \times \left(1+\dfrac{0.019}{12} \right)^{84} }{\left(1+\dfrac{0.019}{12} \right)^{84} - 1} \approx \mathbf{286.2}\)

Molly's monthly payment will be M ≈ $286.2

Third part:

The total interest, I = Sum of payment - Loan amount

∴ The total interest, I ≈ $286.2/month × 84 month - $22,495 ≈ $1,545.8

The total interest Molly will pay using the loan, I ≈ $1,545.8

Fourth part:

The cost of the car, C, using the 1.9% APR financing plan is the sum of the down payment plus sum of the loan repayment

Therefore;

C ≈ $2,500 + $286.2/month × 84 months = $26,540.8

The cost of the car using the 1.9% APR financing plan, C ≈ $26,540.8

The question parameters obtained from a similar question are;

Selling price of the car = $25,495

Financing = 1.9% APR for 84 months with a cash allowance of $500

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