20) If the area of a rectangular playground is
p^2 -6p - 7 square feet, what is the perimeter of the
playground?

Answer:

y = 7.25 + 0.65x

Step-by-step explanation:

y = total cost

x = each mile

it starts at 7.25

any mile after that is an extra $0.65

y = 7.25 + 0.65x

The proportion of variability in gross revenue that can be explained by the estimated multiple regression equation is 0.910. Adjusting for the number of independent variables, the proportion of variability that can be explained is 0.858.

R-squared (R2) measures the proportion of variability in the dependent variable that can be explained by the independent variables in the regression model. In this case, R2 is calculated by dividing SSR (sum of squares regression) by SST (total sum of squares): R2 = SSR/SST. Therefore, R2 = 23.395/25.8 = 0.910, which means that 91% of the variability in gross revenue can be explained by the two independent variables (television and newspaper advertising) in the model.

However, as the number of independent variables in the model increases, R2 tends to overestimate the proportion of variability that can be explained by the model. Therefore, an adjusted R2 (Ra2) is used to account for the number of independent variables in the model. Ra2 is calculated by subtracting the residual mean square (MSE) from 1 and multiplying by (n-1)/(n-k-1), where n is the sample size and k is the number of independent variables in the model. Therefore, Ra2 = (1 - MSE/SST) x (n-1)/(n-k-1) = (1 - 1.436/25.8) x (8-1)/(8-2-1) = 0.858, which means that after adjusting for the number of independent variables, 86% of the variability in gross revenue can be explained by the two independent variables in the model.

Therefore, the estimated multiple regression equation is a good fit for the data and can explain a large proportion of the variability in gross revenue, even after adjusting for the number of independent variables in the model

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Solving problems involving normal proportions requires careful attention to detail, as well as a good understanding of statistical concepts such as standardization and probability.

When solving a problem where you want to find normal proportions, you can follow the following steps:

Define the problem: Clearly define the problem you are trying to solve, including any relevant details such as the population, sample size, and the variable of interest.

Check assumptions: Check if the conditions for using normal distributions are met. The data should be continuous, the sample size should be large enough, and the distribution should be approximately normal.

Calculate the sample mean and standard deviation: If you are working with a sample, calculate the sample mean and standard deviation.

Standardize the data: Convert the data into standard normal distribution, by subtracting the mean from each observation and dividing by the standard deviation.

Determine the probability: Once the data has been standardized, you can use a standard normal distribution table or a calculator to determine the probability of the variable falling within a certain range or above/below a certain value.

Interpret the results: After determining the probability, interpret the results in the context of the problem. For example, you might conclude that there is a 95% chance that a randomly selected observation falls within a certain range, or that the variable of interest is higher than a certain value in 5% of cases.

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Step-by-step explanation:

The sample space for rolling a six-sided die is: {1, 2, 3, 4, 5, 6}

The probability of each outcome in the sample space is: 1/6 or approximately 0.1667

The best prediction for the number of times Lina will roll a 5 in 24 rolls is:

Number of rolls * Probability of rolling a 5

= 24 * 1/6

= 4

Therefore, the best prediction for the number of times Lina will roll a 5 in 24 rolls is 4 times.

Therefore, after answering the given query, we can state that With simple interest  a 5% rise per year, Beth's income in 14 years will be $69,394.38.

By dividing the base by the interest income, the time between payments, and many other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula for use in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating payment is as a portion of the principle amount. For example, if he takes $100 from a buddy and undertakes to pay back the loan at 5% interest, he only will pay his share of the 100% curiosity. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must collect interest when you give it. Typically, interest is determined as an indicator of the overall of the loan total. The loan's interest is the name given to this percentage.

The following is the compound interest formula:

A is equal to P(1 + r/n)(n*t), where A is the total sum.

P is equal to the starting principal.

the annual compound interest rate at the annual compound interest rate at the annual compound interest rate at the rate at the rate (as a decimal)

n represents how many times the interest is compounded annually.

t = the duration in years

The beginning wage (P) in this scenario is $37,000, the interest rate (r) is 5%, the number of times compounded (n) is 1 (since we're assuming the raise occurs once a year), and the number of years (t) is 14. This allows us to enter these values into the formula:

A =\($37,000(1 + 0.05/1)^(1*14)\)

A = $37,000(1.05)^14*A =  $69,394.38

With a 5% rise per year, Beth's income in 14 years will be $69,394.38.

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Answer: 9

Step-by-step explanation:

Can you provide a picture?

Hey there :)

Please check the attached image for answer with explanation.

\(Benjemin360 :)\)

Integrate by parts to find some useful recurrences relating Iₙ and Jₙ.

\(\displaystyle I_n = \int_{-\pi}^\pi x^n \cos(x) \, dx = uv \bigg|_{x=-\pi}^{x=\pi} - \int_{-\pi}^\pi v\, du \\\\ \implies I_n = -n \int_{-\pi}^\pi x^{n-1} \sin(x) \, dx \\\\ \implies I_n = -n J_{n-1}\)

where u = xⁿ and dv = cos(x) dx.

\(\displaystyle J_n = \int_{-\pi}^\pi x^n \sin(x) \, dx = uv \bigg|_{x=-\pi}^{x=\pi} + \int_{-\pi}^\pi v\, du \\\\ \implies J_n = \pi^n - (-\pi)^n + n \int_{-\pi}^\pi x^{n-1} \cos(x) \, dx \\\\ \implies J_n = \pi^n - (-\pi)^n + n I_{n-1}\)

The integrals for n = 0 are trivial:

\(\displaystyle I_0 = \int_{-\pi}^\pi \cos(x) \, dx = \sin(\pi) - \sin(-\pi) = 0\)

\(\displaystyle J_0 = \int_{-\pi}^\pi \sin(x) \, dx = -\cos(\pi) - (-\cos(-\pi)) = 0\)

Now, the integral we're interested in is

\(\displaystyle \int_{-\pi}^\pi x^n f(x) \cos(x) \, dx\)

but we know f(x) is quadratic, and we want to find its coefficients a, b, and c such that

\(\displaystyle \int_{-\pi}^\pi x^n (ax^2+bx+c) \cos(x) \, dx\)

But this is simply

\(\displaystyle \int_{-\pi}^\pi (ax^{n+2}+bx^{n+1}+cx^n) \cos(x) \, dx = aI_{n+2} + bI_{n+1} + cI_n\)

Using the recurrences above and the initial values we've computed, we find

• I₁ = -J₀ = 0

• J₁ = π - (-π) + I₀ = 2π

• I₂ = -2 J₁ = -4π

• J₂ = π² - (-π)² + 2 I₁ = 0

• I₃ = -3 J₂ = 0

• J₃ = π³ - (-π)³ + 3 I₂ = 2π³ - 12π

• I₄ = -4 J₃ = -8π³ + 48π

When n = 0, the integral we care about is

\(aI_2 + bI_1 + cI_0 = -4\pi a + 0 + 0 = 4\pi \implies a = -1\)

When n = 1,

\(aI_3 + bI_2 + cI_1 = 0 - 4\pi b + 0 = 4\pi \implies b = -1\)

When n = 2,

\(aI_4 + bI_3 + cI_2 = (48\pi - 8\pi^3)a + 0 - 4\pi c = 4\pi \implies c = 2\pi^2 - 13\)

so that

\(f(x) = \boxed{-x^2 - x + 2\pi^2 - 13}\)

Answer:

B. Since \(\triangle ABC \cong \triangle DEF\) by SSS and \(\triangle DEF \cong \triangle GHJ\) by SAS, \(\triangle ABC \cong \triangle GHJ\) by the Transitive Property of Congruence.

The congruent statement and the reason why the triangles are congruent is (b) Since AC ≅ GJ and CB ≅ JH, AB must be congruent to GH. So, ABC ≅ GHJ by SSS

From the question, we have the following parameters that can be used in our computation:

Triangles = ABC, DEF and GHJ

There are several theorems that make any two triangles to be congruent

One of these theorems is the SSS congruent theorem

The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent

From the question, we can see that the following corresponding sides on the triangles ABC and GHJ have the same mark

AC and GJ

CB and JH

This implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following angles must also be congruent

AB must be congruent to GH

Hence, the congruent statement on the congruency of the triangles is (d)

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Answer:

big bodie built

Step-by-step explanation:

i used to be dusty

Based on the calculations, the value of the given prefix expression is equal to 2205.

The preorder traversal of a tree (T) are typically used in discrete mathematics to determine the value of a prefix expression on a specific expression tree.

For the preorder traversal of this tree (T), we would start from the right most expression:

Prefix expression = * + 3 + 3 ↑ 3 + 3 3 3

Prefix expression = * + 3 + 3 ↑ 3 6 3

Prefix expression = * + 3 + 3  3⁶  3

Prefix expression = * + 3 3 729 3

Prefix expression = * + 3 732 3

Prefix expression = * 735 3   ⇒ 735 × 3

Value = 2205.

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Complete Question:

Given the following prefix expression:

* + 3 + 3 ↑ 3 + 3 3 3

What is the value of the prefix expression?

The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level.

not significantly more than 3 minutes.

The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.

1. The null hypothesis is that the population mean is equal to 3 minutes.

2. A sample of 100 customers was taken, with an average length of calling time of 3.1 minutes and a sample standard deviation of 0.5 minutes.

3. The p-value from the sample data is 0.28, which is higher than the 0.05 significance level.

4. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.

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Jorge is a recent college graduate who is eagerly seeking new job opportunities after completing his degree.

Currently, he is working part-time to cover his expenses, but his true ambition lies in finding a job that aligns with his long-term career plans. In order to achieve this, Jorge has been actively applying to various positions that match his professional aspirations and utilize the knowledge and skills he acquired during his college education.

Jorge's qualifications can be measured by various factors such as his college degree, GPA, relevant coursework, internships, and any additional certifications he may have obtained. These factors contribute to his overall level of qualification, denoted as x.

Mathematically, we can express this as:

C(x) ≥ D(x)

This inequality indicates that Jorge's qualifications need to meet or surpass the demands of the job market for him to be considered a strong candidate for the career opportunities he desires.

In summary, Jorge's current situation involves a pursuit of a fulfilling career that matches his aspirations.

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Answer:

If the model is 3 inches tall, the model bookcase should be 2 inches wide.

Step-by-step explanation:

When using similar figures, set up a proportion of the model measurements to the actual measurements:

\(\frac{3}{48}=\frac{x}{32}\)

Then cross multiply and solve for x:

\(48x=96\\x=\frac{96}{48}\\x=2\)

If this helped, a brainliest would be greatly appreciated!

Answer:

(0,-5)

Step-by-step explanation:

Terminal minus initial. (3-3, -7+2) = (0,-5)

Answer:

speak English

Step-by-step explanation:

Answer:

Open dot to the left. Dot on zero.

Step-by-step explanation:

Answer:

I hope this helps!

To set up an integral for the area of the resulting surface when the given curve is rotated about the x-axis, we can use the disk or washer method. The disk or washer method allows us to calculate the volume of a 3-dimensional figure by integrating a 2-dimensional figure around a central axis.

For part (a), we integrate with respect to x from 1 to e:

A = ∫1e 2πx(x2 - ey) dx

For part (b), we integrate with respect to y from 0 to 2:

A = ∫02 2π(x2 - ey) dy

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In a case whereby concrete sidewalk is being put around a square park. If the diagonal line across the center of a square park is 24 feet, the exact length of each side is 12 feet.

Based on the given condition from the question, We know that A diagonal is a line segment that joins two opposing polygonal vertices (or corners). In other terms, a diagonal is a line segment that joins two polygonal vertices that are not next to one another. One type of straight line is the diagonal. There is no straight up, down, or across in a diagonal line. It is a line that joins two shape's corners.

Then we can formulate as 24/2

= 12 feet.

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Answer:

42%

Step-by-step explanation:

\(\frac{84}{200}(100)=8400/200= 42\)

Hope this helps

Answer:

c is the answer ....

mark me brainliest

The inflection points of the given function are at x = 0 only. The answer is D.

To find the inflection points of the given function, we need to find the second derivative of the function and set it equal to zero.

y = 5x^4 - x^5

y' = 20x^3 - 5x^4

y'' = 60x^2 - 20x^3

Setting y'' = 0, we get:

60x^2 - 20x^3 = 0

20x^2(3 - x) = 0

x = 0 or x = 3

Now, we need to determine whether these values of x correspond to inflection points. To do this, we can examine the sign of the second derivative in the intervals around each value of x.

For x < 0, y'' is positive (since both terms are positive), so there is a local minimum at x = -3.

For 0 < x < 3, y'' is negative (since 60x^2 < 20x^3), so there is a point of inflection at x = 0.

For x > 3, y'' is positive (since both terms are positive), so there is a local minimum at x = 3.

Therefore, the inflection points of the given function are at x = 0 only. The answer is D.

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Standard deviation affects the skewness more.

In data sets containing outliers or skewed distributions, the interquartile range is the most accurate indicator of variability.   It's unlikely to be impacted by outliers because it's based on numbers that come from the center half of the distribution.

A measure of dispersion that demonstrates how closely a set of data's values resemble the mean is called standard deviation.

Outliers in a data set or a skewed data distribution might have an impact on the standard deviation.

Interquartile Range (IQR) is a spread indicator that depicts the variation between a data set's first and third quartiles.

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Answer:

1:30

Step-by-step explanation:

45 times 4

1 times 2

30 times 4

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

Answer:

Ax + By = C

5x + 4y = -20

a is 5, b is 4

Step-by-step explanation:

Find slope:

  m = (y₂ - y₁) / (x₂ - x₁)

      = (0 - (-5)) / (-4 - 0)

     = 5 / -4

  m = -5/4

Use m above and anyone point to find y-intercept, let's use (-4, 0):

  y = mx + b

  0 = -5/4(-4) + b

  0 = 5 + b

  b = -5

Slope intercept form using m and b from above:

  y = mx + b

  y = -5/4x - 5

Standard form Ax + By = C:

  y = -5/4x - 5

  5/4x + y = -5

  5x + 4y = -20

Answer:

AS a fraction: 1\(\frac{11}{20}\)

AS a decimal: 1.55

Step-by-step explanation:

4/5 + 3/4

least common multiple of 5 and 4 is 20. Conver \(\frac{4}{5}\) and \(\frac{3}{4}\) to fractions with denominator 20.

16/20 + 15/20

since \(\frac{16}{20} and \frac{15}{20}\)  have the same denominator, add them by adding their numerators.

\(\frac{16 + 15}{20}\)

Add 16 and 15 to get 31.

\(\frac{31}{20}\)

\(\frac{31}{2^{2}x5 } = 1\frac{11}{20}\)

Hope that helps and have a great day! =) ~sunshine~

The solutions to the quadratic  equation 3x² + 8x - 50x = 42 correct to 2 decimal places are approximately x = 12.07 and x = 1.93.

What exactly are quadratic equations?

A quadratic equation in algebra is a second-degree polynomial equation of the form: ax² + bx + c = 0, where a, b, and c are constants and x is the variable. For the equation to be quadratic, the coefficient a must not be equal to zero.

Now,

To solve the equation 3x² + 8x - 50x = 42 algebraically, we can follow these steps:

3x² - 42x = 42

Move all the terms to one side of the equation, so that the equation equals 0:

3x² - 42x - 42 = 0

Divide both sides of the equation by the common factor of 3 to simplify it:

x² - 14x - 14 = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = -14, and c = -14, so we can substitute these values into the formula:

x = (-(-14) ± √((-14)² - 4(1)(-14))) / 2(1)

= (14 ± √(232)) / 2

≈ 12.07 or 1.93

Therefore, the solutions to the equation 3x² + 8x - 50x = 42 correct to 2 decimal places are approximately x = 12.07 and x = 1.93.

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Right question:-

Solve this equation algebraically. Give your solutions correct to 2 decimal places. 3x² + 8x - 50 x = 42.

The question is incomplete. Here is the complete question

Matrices C and D are shown below:

\(C=\left[\begin{array}{ccc}2&1&0\\0&3&4\\0&2&1\end{array}\right]\)     \(D=\left[\begin{array}{ccc}a&b&-0.4\\0&-0.2&0.8\\0&0.4&-0.6\end{array}\right]\)

What values of a and b will make the equation CD = I true?

(i) a = 0.5

  b = 0.1

(ii) a = 0.1

    b = 0.5

(iii) a = -0.5

    b = -0.1

Answer: (i) a = 0.5

                  b = 0.1

Step-by-step explanation: Identity Matrix (I) is a n x n square matrix with the number 1 on the main diagonal and 0 everywhere else.

The question asks for multiplication of matrices, i.e.:

\(\left[\begin{array}{ccc}2&1&0\\0&3&4\\0&2&1\end{array}\right]\)  .   \(\left[\begin{array}{ccc}a&b&-0.4\\0&-0.2&0.8\\0&0.4&-0.6\end{array}\right]\) = \(\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\)

To multiply matrices, the number of columns of the 1st matrix must be the same as the number of rows of the 2nd.

Matrix C is a 3x3 square matrix and so is matrix D, so, values of a and b:

\(2a=1\)                           \(2b-0.2=0\)

\(a=\frac{1}{2}\)                            \(2b=0.2\)

a = 0.5                          \(b=0.1\)

For the equation CD=I be true, a and b has to be 0.5 and 0.1, respectively.

Answer:

They spent 2hrs and 30min

Step-by-step explanation:

If you cut 5 in half you get 2.5

60 cut in half equals 30

In other words... 2.5 = 2hrs and 30min

The length of the longest side is 50 units based on the stated length of sides and perimeter.

As per the relation between sides of triangle and it's perimeter, the formula is -

Side + side + side = perimeter

Keeping the values in formula to find the value of x

6x + 8x + 2 + 10x = 122

Performing addition on Left Hand Side of the equation

24x + 2 = 122

Rearranging the equation

24x = 122 - 2

Subtract the values

24x = 120

x = 120/24

Performing division on Right Hand Side

x = 5

Length of each side = 6×5 + ((8×5)+2), 10×5

Length = 30, 42, 50

Hence, the length of the longest side is 50.

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