rectangular swimming pool is 6 ft deep. One side of the pool is 4.5 times longer than the other. The amount of water needed to fill the swimming pool is 2700 cubic feet. Find the dimensions of the pool.

Answer:

-3x-2(5x-7)=-12

-3x-10x+14=-12

-13x+14=-12

-13x=-16

x=2

Answer:

2.5 inch i think because 1 inch equals 100 miles and .5 i think it is 50 miles

Answer:

D

Step-by-step explanation:

Professional Degree

A person with a Bachelor's Degree is expected to earn an average of $52,200 each year. Thus, option c is correct.

The average is defined as the sum of all observation to the total number of observation.

Given that:

Professional Degree: $109,600

Doctoral Degree: $89,400

Master's Degree: $62,300

Bachelor's Degree: $52,200

Associate's Degree: $38,200

Some College: $36,800

High School Diploma: $30,400

Some High School: $23,400

The best answer from the choices is Bachelor's Degree. Thus, option c is correct.

Learn more about average here:

https://brainly.com/question/8501033

#SPJ7

Answer:

x = 0.37686455

Step-by-step explanation:

Answer: x≈0.37686455

Step-by-step explanation:

Correlation coefficients greater than 0.50 rarely occur in the social sciences due to the complexity of human behavior and the limitations of research methods.

Human behavior is influenced by numerous interacting variables, including biological, psychological, sociocultural, and environmental factors. These variables collectively contribute to the observed behavior, making it challenging to find strong correlations with a single variable. Human behavior is a multifaceted phenomenon that cannot be adequately captured by a single measure or variable. Constructing measures of behavior, such as depression or compassion, is inherently difficult. These constructs involve subjective experiences and emotions, which are challenging to quantify accurately. Different aspects and dimensions of behavior may not be fully captured by available measures, leading to a restricted range of variation and lower correlation coefficients.

Moreover, social scientists face constraints in experimental design, as ethical considerations may limit their ability to manipulate certain variables or conduct controlled experiments. This lack of control over variables reduces the likelihood of establishing strong and causal relationships. While social scientists continuously explore and identify variables that predict human behavior, the complex nature of behavior and the inherent limitations in research methods make it rare to observe correlation coefficients greater than 0.50 in the social sciences. Understanding human behavior requires a comprehensive and multifaceted approach that considers the interactions among various factors rather than relying solely on single variables.

Learn more about Correlation here: brainly.com/question/32248645

#SPJ11

The length of the vector function F(t) over the interval -6 ≤ t ≤ 8 is  D) L = 14√56.

The length of the vector function F(t) = <3 - 4t, 6t, -(9 + 2t)> from -6 ≤ t ≤ 8, we need to calculate the integral of the magnitude of the derivative of F(t) with respect to t over the given interval.

The magnitude of a vector v = <x, y, z> is given by ||v|| = √(x² + y² + z²).

First, let's find the derivative of F(t):

F'(t) = <-4, 6, -2>

Next, let's find the magnitude of F'(t):

||F'(t)|| = √((-4)² + 6² + (-2)²)

= √(16 + 36 + 4)

= √56

Now, we can calculate the length of F(t) over the interval -6 ≤ t ≤ 8 by integrating ||F'(t)|| with respect to t:

L = ∫(√56) dt

= √56 ∫dt

= √56 × t + C

Evaluating the integral over the given interval:

L = √56 × t + C| (-6)⁸

= √56 × (8 - (-6))

= √56 × 14

= 14√56

Therefore, the length of the vector function F(t) over the interval -6 ≤ t ≤ 8 is 14√56.

To know more about vector function click here :

https://brainly.com/question/31396553

#SPJ4

For the given matrix A, the minors M13, M23, M33 are 8, -4, and 10 respectively. The cofactors C13, C23, C33 are 8, 4, and 10 respectively. The determinant det(A) is 68.

To find the minors of a matrix, we need to find the determinants of the submatrices obtained by removing the row and column corresponding to the element of interest. In this case, the minors M13, M23, and M33 correspond to the determinants of the 2x2 submatrices obtained by removing the first row and the third column, second row and third column, and third row and third column, respectively.

To find the cofactors, we multiply each minor by a positive or negative sign based on its position in the matrix. The signs alternate starting with a positive sign for the top left element. In this case, the cofactors C13, C23, and C33 correspond to the minors M13, M23, and M33 respectively.

Finally, the determinant of a 3x3 matrix can be found by using the formula det(A) = a11C11 + a12C12 + a13C13, where a11, a12, and a13 are the elements of the first row of the matrix and C11, C12, and C13 are their corresponding cofactors. In this case, the determinant det(A) is 68.

Therefore, the minors M13, M23, M33 are 8, -4, and 10 respectively. The cofactors C13, C23, C33 are 8, 4, and 10 respectively. And the determinant det(A) is 68.

Learn more about submatrices here:

https://brainly.com/question/31669133

#SPJ11

Answer:

Length is 32. 6 cm and width is 5.9 cm

Step-by-step explanation:

width(w)=w

perimeter(p)=78 cm

length(L) = 4w+9

p=2L+2w

78=2(4w+9)+2w

78=8w + 19 + 2w

10w=59

w=5.9 cm

L=4w+9

L=4(5.9)+9

L=32.6 cm

Therefore length is 32.6 cm and width is 5.9 cm

The area of the sidewalk in square feet is 56 square ft if the sidewalk that is 2 feet wide surrounds a rectangle that is 4 feet by 6 feet.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that:

A sidewalk that is 2 feet wide surrounds a rectangle that is 4 feet by 6 feet.

As we know,

The area of the rectangle = length x width

First, the area of the rectangle = 4x6 = 24ft²

If you draw it out, you get that the area = (4 + 2 + 2)(6 + 2 + 2)

= 8x10

= 80 square ft

The sidewalk area:

= 80 - 24 = 56 square ft

Thus, the area of the sidewalk in square feet is 56 square ft if the sidewalk that is 2 feet wide surrounds a rectangle that is 4 feet by 6 feet.

Learn more about the rectangle here:

https://brainly.com/question/15019502

#SPJ2

Answer:

x=−1

Step-by-step explanation:

Let's solve your equation step-by-step.

−5x−16+3x=−23−9x

Step 1: Simplify both sides of the equation.

−5x−16+3x=−23−9x

−5x+−16+3x=−23+−9x

(−5x+3x)+(−16)=−9x−23(Combine Like Terms)

−2x+−16=−9x−23

−2x−16=−9x−23

Step 2: Add 9x to both sides.

−2x−16+9x=−9x−23+9x

7x−16=−23

Step 3: Add 16 to both sides.

7x−16+16=−23+16

7x=−7

Step 4: Divide both sides by 7.

7x

7

=

−7

7

x=−1

Answer:

x=−1

Answer: x= -1

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be False.

In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.

Here,

False.

The order of operations we use to solve two-step equations is the same order we use to solve every other mathematical statement,

which is commonly recalled by the acronym PEMDAS. (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

The fundamental distinction is that we are carrying out the operations against the equation's representation. For instance, consider the following equation:

=> 2x + 5 = 11

To get the following result, we would first subtract 5 from both sides, then divide by 2.

=> x = 3

In order to "undo" the operations that were carried out on the variable in the original equation, we are utilising the same series of operations as usual, but in reverse order.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The statement that an example of Instructional Task Learning is the Count on Sesame Street counting to 10, is True.

Instructional task learning refers to a type of education where students gain expertise in a particular skill or concept by completing multiple tasks that have been specifically devised to aid them in mastering the subject matter.

On Sesame Street, the students are acquiring the knowledge of numerically counting up to 10 via the character of Count. The Count offers several activities aimed at imparting the same skill to learners, including object counting, singing songs that involve counting, and engaging in counting games. Through the completion of these assignments, students can proficiently acquire the ability to accurately count up to 10.

Find out more on learning at https://brainly.com/question/30181805

#SPJ1

Answer:

Yes it is a function ...

Domain = {-7,1,4,5,8}

Range = {3,8,-7,-9,-2}

mark me as brainliest ❤️

Step-by-step explanation:

yes, it is a function. why ?

because every used x value has one unique y value assigned. that is the definition of a function. if any x value could lead to 2 or more different results (y values), it is not a function.

the domain is the interval/set of valid x (input) values to the function.

the range is the interval/set of produced and valid y (functional result) values.

so, the domain is the set of all the x values of the ordered pairs

{-7, 1, 4, 5, 8}

the range is the set of y values corresponding to the used x values

{-9, -7, -2, 3, 8}

Let G be a finite group and p a prime. To prove that P is an element of Syl p(H) and to prove that P is an element of Syl p(H), the following method is followed.

(i)If P is an element of Syl p(G) and H is a subgroup of G containing P, then prove that P is an element of Syl p(H).
We know that, p-subgroup of G, which is of the largest order, is known as a Sylow p-subgroup of G. Also, the set of all Sylow p-subgroups of G is written as Sylp(G).By the third Sylow theorem, all the Sylow p-subgroups are conjugate to each other. That is, if P and Q are two Sylow p-subgroups of G, then there is a g ∈ G such that P = gQg⁻¹. Let P be an element of Sylp(G) and H be a subgroup of G containing P. Now we will prove that P is an element of Syl p(H).Now, the order of P in G is pⁿ, where n is the largest positive integer such that pⁿ divides the order of G. Similarly, the order of P in H is p^m, where m is the largest positive integer such that p^m divides the order of H. We know that, the order of H is a divisor of the order of G. Since P is a Sylow p-subgroup of G, n is the largest integer such that pⁿ divides the order of G. Thus pⁿ does not divide the order of H. That is, m < n. Thus the order of P in H is strictly less than the order of P in G. So P cannot be a Sylow p-subgroup of H. Hence, P is not a Sylow p-subgroup of H. Therefore, P is an element of Sylp(H).

(ii)To prove this we have assumed that H is a subgroup of G and P is a Sylow p-subgroup of G containing H. Therefore, we need to show that P is a Sylow p-subgroup of H. The order of P in G is pⁿ, where n is the largest positive integer such that pⁿ divides the order of G. Similarly, the order of P in H is p^m, where m is the largest positive integer such that p^m divides the order of H. We need to prove that P is the unique Sylow p-subgroup of H. For that, we need to show that if Q is any other Sylow p-subgroup of H, then there exists h ∈ H such that P = hQh⁻¹. Now, the order of Q in H is p^m, and since Q is a Sylow p-subgroup of H, m is the largest integer such that p^m divides the order of H. Since P is a Sylow p-subgroup of G, n is the largest integer such that pⁿ divides the order of G. We know that, the order of H is a divisor of the order of G. Therefore, m ≤ n. But P is a Sylow p-subgroup of G containing H, so P is a subgroup of G containing Q. Therefore, by the second Sylow theorem, there exists a g ∈ G such that Q = gPg⁻¹. Now, g is not necessarily in H, but we can consider the element hgh⁻¹, which is in H, since H is a subgroup of G. Also, hgh⁻¹P(hgh⁻¹)⁻¹ = hgPg⁻¹h⁻¹ = Q. Hence, P and Q are conjugate in H, and therefore, Q is also a Sylow p-subgroup of G. But P is a Sylow p-subgroup of G containing H. Hence, Q = P. Therefore, P is the unique Sylow p-subgroup of H.

Hence, we can conclude that if P is an element of Syl p(G) and H is a subgroup of G containing P, then P is an element of Syl p(H).Also, we can conclude that if H is a subgroup of G and Q is an element of Syl p(H), then gQg^-1 is an element of Syl p(gHg^-1).

Learn more about finite group here:

brainly.com/question/31942729

#SPJ11

Below, you will learn how to solve the problem.

(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)

m = 12/4

m = 3

Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6

b = -1

So the linear relationship between x = year and y = profit is:

y = 3x - 1

(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1

y = 8

So the company's profit at the end of 3 years is $8 million.

(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:

y = 3(8) - 1 = 23

So the company's profit at the end of 8 years is predicted to be $23 million.

For more information about equation, visit:

https://brainly.com/question/22688504

#SPJ11

See attachment for math work and answer.

The equation that represents s, the total number of seventh-grade students at the middle school is given by: Option A: \(18 = 0.1s\)

Suppose that the whole thing is of value V.

Then its one-nth part is symbolically written as: \(V \times \dfrac{1}{n}\) (V is divided in n equal part, and each part is called one-nth part of V).

For the considered case, we've got the figures as:

Every seventh grade student at considered school takes one language class. It means, if s = Total number of seventh grade student, then:

\(\dfrac{s}{7}\)  is the number of students taking language class.

Now, it is said that: One-tenth of the seventh grade students like French, and that they are total 18 in counts.

Writing it symbolically gives:

\(\dfrac{s}{10} = 18\)

Since we know that \(\dfrac{a}{b} = a \times \dfrac{1}{b}\)

Thus,

\(\dfrac{s}{10} = s \times \dfrac{1}{10} = s \times 0.1= 18\\\\0.1 s = 18\\18 = 0.1s\)

(sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)

Thus, the equation that represents s, the total number of seventh-grade students at the middle school is given by: Option A: \(18 = 0.1s\)

Learn more about forming equations here:

https://brainly.com/question/11938672

Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

Answer:

3rd

Step-by-step explanation:

x & y are both negative in 3rd

Answer:

\(B' = (16,14)\)

\(C' = (24,18)\)

\(D' =(6,20)\)

Step-by-step explanation:

Given

\(B = (8,7)\)

\(C = (12,9)\)

\(D = (3,10)\)

\(r = 2\) --- the scale factor

Required

The new coordinate of each point

To do this, we will interpret dilation as stretching.

So, the new point is calculated as:

\(New = Old * Scale\ factor\)

\(New = Old * r\)

So, we have:

\(B = (8,7)\)

\(B' = (8,7) * 2\)

\(B' = (16,14)\)

\(C = (12,9)\)

\(C' = (12,9) * 2\)

\(C' = (24,18)\)

\(D = (3,10)\)

\(D' =(3,10) * 2\)

\(D' =(6,20)\)

Hence, the new points are:

\(B' = (16,14)\)

\(C' = (24,18)\)

\(D' =(6,20)\)

Answer:

68%

Step-by-step explanation:

In normal distribution, the empirical rule (aka 68-95-99.7 rule) describes the approximate proportion of data that falls within certain distances from the mean of a normal distribution. Specifically, the rule states that:

Is the relation a function:

To determine if the relation is a function, we need to check if there is exactly one output for each input.

Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).

This means that there are two outputs for the same input, so the relation is not a function.

Therefore, the correct answer is: "No, because for each input there is not exactly one output."

Learn more about graphs at

https://brainly.com/question/19040584

#SPJ1

Answer:

76,650

Step-by-step explanation:

Answer: 187, 565

Step-by-step explanation:can i have brainliest?

A - Growth (25%)

B- Growth (75%)

C - Growth

D - Growth (100%)

E - Growth (99%)

An rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

Learn more about exponential:https://brainly.com/question/28596571

#SPJ1

Given:

Matthew's dad hired him to paint 6 wooden patio chairs for $125.

Time taken by him to paint all of the chairs = 9 hours.

It takes the same amount of time to paint each chair.

To find:

The fraction of an hour does it take Matthew to paint one chair

Solution:

Total time = 9 hours

Total number of chairs = 6

Now, time taken by Matthew to paint one chair is

\(\dfrac{\text{Total time}}{\text{Total number of chairs}}=\dfrac{9}{6}\)

\(\dfrac{\text{Total time}}{\text{Total number of chairs}}=\dfrac{3}{2}\)

Therefore, Mattew takes \(\dfrac{3}{2}\) of an hour to paint one chair.

Thinking with a model: On dividing the total time by total number of chairs we get time taken by Mattew (in hours) to paint one chair. So, the result represents the fraction of an hour taken by Matthew to paint one chair.

Answer:

  8.5 years

Step-by-step explanation:

You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.

The depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...

  value = (initial value) × (1 - (depreciation rate))^t

where the rate is "per year" and t is in years.

  value = 18500·(1 -0.08)^t

  9100 = 18500·0.92^t . . . . fill in the value of interest

  9100/18500 = 0.92^t . . . . divide by 18500

  log(91/185) = t·log(0.92) . . . . take logarithms

  t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509

It will be about 8.5 years until the value is $9100.

__

Additional comment

The graph shows the solution to ...

  18500·0.92^t -9100 = 0

We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.

$5 for 1 shirt

y = cost

x = number be shirts

10y = 2x

5y = x