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Answer:

the answer is 41

Step-by-step explanation:

C. 41

Step-by-step explanation:

The dimensions that will maximize the area of the garden are 112.5 feet and 112.5 feet and the largest possible area is 12656.25 unit².

From the information given, the perimeter of the rectangle will be:

x + x + y + (y - 50)

= 2x + 2y - 50

The perimeter of given as 400. This will be:

2x + 2y - 50 = 400

Collect like terms

2x + 2y = 450

Divide through by 2.

x + y = 225

y = 225 - x

The area will be:

Area = Length × Width

Area = x × y

Area = x(225 - x)

Area = 225x - x²

But differentiating with respect to x, x = 112.5

y will be: = 225 - x = 225 - 112.5 = 112.5

Therefore, the maximum area will be:

= 112.5 × 11.25

= 12656.25 unit²

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c. Linear regression could be appropriate if a scatter plot shows a linear relationship between exam scores and hours studied.

The best response in this scenario is option c. Linear regression is a statistical method used to model and predict relationships between variables. In this case, the correlation coefficient of 0.62 suggests a moderate positive linear relationship between exam scores and hours studied. However, it is important to visually inspect the scatter plot of the data to confirm if a linear relationship is present. If the scatter plot shows a clear linear pattern, then linear regression can be an appropriate method to predict the score of a student who has studied 10 hours for the final exam.

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The correlation coefficient ρ for X and Y is ρ = -0.6675 in the given function.

The correlation coefficient is a statistical concept that aids in establishing a relationship between expected and actual values obtained through statistical experimentation. The calculated correlation coefficient's value explains why the difference between the predicted and actual values is so exact.

Correlation Coefficient value is always in the range of -1 to +1. A similar and identical relationship exists between the two variables if the correlation coefficient value is positive. Otherwise, it reveals how differently the two variables behave.

Pearson's correlation coefficient is calculated by taking the covariance of two variables and dividing it by the sum of their standard deviations. is typically used to represent it (rho).

The correlation coefficient is computed as,

\($ \rho & =\frac{{Cov}(X, Y)}{\sqrt{V(X)} \times \sqrt{V(Y)}}\)

\($=\frac{-0.0267}{\sqrt{0.04} \times \sqrt{0.04}}\)

= -0.6675

Thus, the correlation coefficient ρ for X and Y is ρ = -0.6675.

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Answer:

R and Z

Step-by-step explanation:

A point that "touches" the circle once.

Step-by-step explanation:

-9x+15=3(2-x)

6-6x

2. collect like terms

-9x+15= 6-6x

15-6 = 6x+9x

11= 15x

3. divide both sides by the coefficient of X which is 15

x= 11/15

The exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.

The exterior angle adjacent to the largest interior angle in a triangle is equal to the sum of the other two interior angles.

Let's call the measures of the angles in the triangle x, x, and 2x. Then,

x + x + 2x = 180 degrees,

so 4x = 180 degrees, and

x = 45 degrees.

The largest interior angle is 2x, or 90 degrees. The exterior angle that is adjacent to this angle is equal to 180 degrees minus the interior angle, which is 180 - 90 = 90 degrees.

So the exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.

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Answer:

6⁹

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

\(\displaystyle \frac{6^6}{6^{-3}}\)

Step 2: Simplify

The running rate is 5 miles per hour.Let's denote the running rate as "r" and the driving rate as "9r" (since the driving rate is nine times the running rate).

To find the running rate, we need to determine the time spent driving and running separately and then add them together to equal 3 hours.

The time spent running can be calculated as the distance divided by the running rate:

Time running = Distance / Running rate = 5 / r

The time spent driving can be calculated similarly:

Time driving = Distance / Driving rate = 90 / (9r) = 10 / r

The total time spent driving and running is given as 3 hours:

Time running + Time driving = 3

5 / r + 10 / r = 3

To solve this equation, we can combine the fractions on the left side:

(5 + 10) / r = 3

15 / r = 3

Next, we can cross-multiply to isolate the variable:

15 = 3r

Dividing both sides by 3, we find:

r = 5

Therefore, the running rate is 5 miles per hour.

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Answer:

Step-by-step explanation:

\(7x=4x^{2} -1\)

\(7x - (4x^{2} -1)= 0\)

\(7x - 4x^{2} +1 = 0\)

\(-4x^{2} +7x+1=0\)

\(4x^{2} -7x-1=0\)

use the quadratic formula: \(x = \frac{ -b \frac{+}{-} \sqrt{b^{2} -4ac }}{2a}\)

a = 4  b = -7  c = -1

·\(x = \frac{-(-7)\frac{+}{-} \sqrt{(-7)^{2}-4 times 4(-1)} }{2 times 4}\)

\(x = \frac{7\frac{+}{-} \sqrt{49-16} }{8}\)

\(x = \frac{7\frac{+}{-} \sqrt{65} }{8}\)

hope this helped!

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Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

The options that have equivalent expression(s) are:

The expressions that are equivalent be determined by checking the given options one after the other to determine the ones that will have the same value if properly expressed.

The second option is (4)^3x^2 , and it can as well be expressed as 1/4^3x2 because 1/4 is the same expression as 4^-1

The third option (1/4)3x^2  is equivalent with the expression we got at the first option.

Therefore, the expression that is equivalent to each other from the given expression are the second option and the third option.

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Answer:

its c and d

Step-by-step explanation:

The statements that are true for Trapezoid WXYZ are:

We are told that;

Shape is a trapezoid WXYZ.

Now, In a trapezoid, one pair of opposite sides are parallel and parallel lines have the same slope.

Lastly, the slope of line parallel to x axis is 0 and so If the line starts at the bottom left and goes towards the top right it has negative slope. Thus, all the statements that are true for Trapezoid WXYZ are:

Complete question is;

Four lines are drawn on a coordinate plane to form trapezoid WXYZ. Which statements are true about the lines? Select all that apply.

Line WZ has the same slope as line XY.

Line YX has a greater slope than line ZY.

Line XW has a lesser slope than line YZ.

Line ZW has the same y-intercept as line WZ.

Line XY has a greater y-intercept than line XW

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Answer:

y = 4 (x + 1)² - 16

Step-by-step explanation:

Step 1: Equation at the end of step 1

(2²x²+8x)-12

Step 2:

Step 3: Pulling out like terms

Pull out like factors :

4x² + 8x - 12  =   4 • (x² + 2x - 3)

Trying to factor by splitting the middle term

Factoring  x²+ 2x - 3

The first term is,  x²

its coefficient is  1 .

The middle term is,  +2x  its coefficient is  2 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   2 .

   -3    +    1    =    -2  

     -1    +    3    =    2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  3

x² - 1x + 3x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-1)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-1)

Step-5 : Add up the four terms of step 4 :

                   (x+3)  •  (x-1)

            Which is the desired factorization

Final result :

Final result :

 4 • (x + 3) • (x - 1)

Now convert to vertex form:

y = 4 (x + 1)² - 16

A) Where the calibration of the graph represents a unit each, the approximate coordinates of the points  of intersection of the two graphs is (4.5, 3)

This means that after after a given number of days, the area covered by both types of mold were the same.

b) given the function, the number days it takes for the mold to cover 1000 square millimeters is 46 days.

A) this is observed by exploring the graph.

b) Let A(d) = 1000
⇒ 1000 = 100 x \(e^{0.05d}\)

If we divide both sides by 100 to simplify, we will get

\(e^{0.05d}\) = 10

To solve for d we need to compute the natural log of both sides, so we get

ln \(e^{0.05d}\) = ln (10)

Recall that ln (eˣ) = x so

ln \(e^{0.05d}\) = ln (10)

⇒ 0.05d = ln (10)

Divide both sides by 0.05

d = ln10/0.05

d = 2.30258509299/0.05

d = 46.0517018599

d ≈ 46 days.

thus,

it will take about 46 days for the mold to cover 1000 millimeters.

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A good residual plot should have the points randomly scattered around the horizontal line with no discernible pattern.

This indicates that the model is well fit to the data. The residuals should also be equally distributed on either side of the horizontal line. This can be seen as the sum of the residuals being equal to 0, or mathematically expressed as the sum of the residuals (e) being equal to 0, where \(e = y - ŷ\), where y is the observed value and ŷ is the predicted value. The equation can be expressed as Σe=0.

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Answer:

Keep it simple c da answer

Step-by-step explanation:

Answer:c

Step-by-step explanation:

Answer:

x=71

Step-by-step explanation:

409+x=480

x=480-409

x=71

Answer:

x=263

Step-by-step explanation:

261+148=409

409+x=672

x=672-409

x263

The spring is compressed to 95.5 cm to the right if 129 N of force are used.

In this question, we have been given the spring constant k = 283 N/m

if 129 N of force are used then we need to find distance  that the spring compressed to the right.

Let the spring stretch from the equilibrium position x.

An equation for the spring's potential energy is,

PE = 1/2 ​kx^2

129 = 1/2 * 283 * x^2

2 * 129 = 283 * x^2

258/283 = x^2

x^2 = 0.9117

x = 0.9548 m

x = 95.5 cm

Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.

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Tax prep software can be used for federal taxes but not always for state taxes, which may require separate forms.

While documenting your government and state charges, you have a couple of choices for how to plan and submit them. One choice is to involve charge planning programming for government charges, which can simplify the cycle and more smoothed out.

In any case, you for the most part can't involve a similar programming for state charges, as each state has its own expense code and necessities.

All things being equal, you might have to set up your state burdens independently, either by finishing up paper structures or utilizing separate duty readiness programming planned explicitly for your state.

A few states bring concurrences with specific expense programming suppliers to the table free or limited programming to occupants, so it merits checking with your state's duty position to see what choices are accessible to you.

It's critical to take note of that while government and state burdens frequently require comparative data, they might require various structures and estimations, so giving close consideration to the particular prerequisites for each kind of tax is significant.

Furthermore, on the off chance that you live in an express that doesn't have a personal expense, you may just have to record a government expense form.

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Answer:

The correct option is;

(0, -3), (-1, 0) and (3, 0)

Step-by-step explanation:

From the given graph of the function we have the following observations;

There are two x-intercepts which are;

1) To the left of the vertical y-axis having coordinates (-1, 0)

2) To the the right of the y-axis having coordinates (3, 0)

There is only one y-intercept  having coordinates, (0, -3)

Therefore, all the intercepts of the function are, (0, -3), (-1, 0) and (3, 0).

Answer:

(0, -3), (-1, 0) and (3, 0)

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

There are ten balls numbered 1 through 10.

Five of those balls are not even numbers (odd numbers): 1, 3, 5, 7, 9

Of those five, none are divisible by 2.

Therefore, the probability is 0/10 = 0.

Answer:

A. B. D. C.

Step-by-step explanation:

Individuals who eat citrus fruit are significantly more likely to develop cold sores.

Given,

Relative risk = 1.89

p value = 0.047

Here,

This p-value is less than the alpha value or level of significance of 0.05 or 5%, so we reject the null hypothesis and concludes that relative risk is statistically significant.

\(H_{0} \\\) : Null hypothesis is rejected.

This means, in context of given example, Individuals who eat citrus fruit are significantly more likely to develop cold sores.

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Answer:

b

Step-by-step explanation:

There are 2 sequences with a₁ = 47, b and d

The common difference of both is

(b)

d = a₂ - a1 = 29 - 47 = - 18

(d)

d = a₂ - a₁ = 65 - 47 = 18

The the sequence with first term 45 and common difference - 18 is b

The required sequence which has a first term equal to 47 and a common difference of -18 is {47, 29, 11, -7, …}. Option B is correct.

Arithmetic progression is the series of numbers that have common differences between adjacent values

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
An arithmetic sequence has a first term equal to 47 and a common difference of -18,
a = 47
d = -18

The sequence formed given as,
⇒ a, a + d, a + 2d, a + 3d
⇒ 47, 47 - 18, 47 + 2(-18), 47 + 3(-18)
⇒ 47 , 29, 11, -7 . . . . .

Thus, the above sequence matches the sequence given in option b.

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The truck takes 0.04 hours (or 2.4 minutes) to travel 18 miles.

The equation given, d = 451, represents the distance traveled by the truck in miles after a certain number of hours. However, since the equation does not involve any variables or factors related to time, it indicates that the truck is traveling at a constant speed. In other words, the truck covers the same distance regardless of the time elapsed.

To determine how long it takes the truck to travel a specific distance, such as 18 miles, we can substitute the value of d into the equation and solve for the time. Plugging in d = 18 into the equation d = 451, we get:

18 = 451.

This equation is not true since 18 is not equal to 451. Therefore, there is no solution to the equation, and it implies that the truck does not cover a distance of 18 miles. This result suggests that the information provided is inconsistent or incomplete.

Without additional information about the truck's speed or rate of travel, we cannot accurately determine how long it takes for the truck to travel 18 miles.

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Answer:

y = 2.2x

Yes, it represents a linear function

Step-by-step explanation:

Given that :

Stopper applied at t = 0

At t = 5 minutes ; water in tub = 11 gallons

At t = 10 minutes ; water in tub = 22 gallons

General form of a linear function :

y = mx + c

Where c = intercept ; m = Slope ; y and x are dependent and independent variables respectively

The intercept = gallon of water at t = 0 ; this is not given and will be taken as 0

Slope = change in y / charge in x

Slope = (22 - 11) / (10 - 5)

Slope = 11 / 5

Slope = 2.2

Hence ;

y = 2.2x + 0

y = 2.2x

Yes, it represents a linear function

The probability that the sum of the numbers rolled is even or greater than 9 is 25/36.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, two number cubes at the same time. Each cube has sides numbered 1 through 6.

There are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Probability of getting sum as even number:

Number of favourable out comes = 18

Total number of outcomes = 36

Now, probability = 18/36

Probability of getting sum as greater than 9:

Number of favourable out comes = 7

Total number of outcomes = 36

Now, probability = 7/36

So, the probability of event is 18/36 + 7/36

= 25/36

Therefore, the probability that the sum of the numbers rolled is even or greater than 9 is 25/36.

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