What's the volume of a rectangular prism with a base area of 52 square inches and a height of 14 inches?

Therefore, the width of the rectangular pig pen is approximately 6.7 feet.

The pen is a rectangle, so there is a length and a width (L and W). Additionally, there is another Length or Width (it doesn't matter which, so we'll call it the Length) which is the middle dividing fence.

We can use the formula for the area of a rectangle to solve for the width of the pig pen, given its length and area.

Area of rectangle = length × width

We are given the length of the pig pen as 10.2 feet and the area of the rectangular pen as 68.34 square feet. Substituting the given values in the formula above, we get:

68.34 = 10.2 × width

Dividing both sides by 10.2, we get:

width = 68.34/10.2 = 6.7 feet

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An explanatory variable refers to the independent variable in an experiment.The correct answer is: the independent variable in an experiment.

Explanation: In experimental studies, explanatory variables are manipulated or controlled by the researcher to observe their impact on the dependent variable. They are often referred to as independent variables because they are not influenced by other variables in the study.

The purpose of the experiment is to determine whether changes in the explanatory variable cause changes in the dependent variable. The explanatory variable is the one being tested or varied intentionally to understand its effect on the outcome or response, which is the dependent variable.

By systematically manipulating and measuring the explanatory variable, researchers can analyze its relationship with the dependent variable and draw conclusions about cause and effect.


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Answer:

B

Step-by-step explanation:

\(\sqrt{x}\) + 6 = x ( subtract 6 from both sides )

\(\sqrt{x}\) = x - 6 ( square both sides )

x = (x - 6)² ← expand using FOIL

x = x² - 12x + 36 ( subtract x from both sides )

0 = x² - 13x + 36 , that is

x² - 13x + 36 = 0 ← in standard form

(x - 4)(x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 9 = 0 ⇒ x = 9

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = 4

left side = \(\sqrt{4}\) + 6 = 2 + 6 = 8

right side = x = 4

Since 8 ≠ 4 then x = 4 is an extraneous solution

x = 9

left side = \(\sqrt{9}\) + 6 = 3 + 6 = 9

right side = x = 9

Thus the solution is x = 9 → B

Answer:

2nd chioce

Step-by-step explanation:

Answer:43.76?

Step-by-step explanation:

Answer:

haha tanish its 43.758

Step-by-step explanation:

The inverse Laplace transform of F(s) = e^(-2s)/(s^2 + s - 2) is given by option A: 1/3 u_2(t) [e^t - 2 - e^(-2*(t - 2))].

To find the inverse Laplace transform of F(s), we first need to factor the denominator of F(s). We have:
s^2 + s - 2 = (s+2)(s-1)
So, we can rewrite F(s) as:
F(s) = e^-2s/(s+2)(s-1)
To use partial fraction decomposition, we need to find the constants A and B such that:
F(s) = A/(s+2) + B/(s-1)
Multiplying both sides by (s+2)(s-1), we get:
e^-2s = A(s-1) + B(s+2)
To solve for A and B, we can plug in s=1 and s=-2:
e^-2 = A(-1) + B(0)
e^-4 = A(-3) + B(2)
Solving for A and B, we get:
A = -1/3 and B = 5/3
So, we can rewrite F(s) as:
F(s) = -1/3/(s+2) + 5/3/(s-1)
Now, we can use the inverse Laplace transform of each term to get:
L^-1{-1/3/(s+2)} = -1/3 e^-2t
L^-1{5/3/(s-1)} = 5/3 e^t
Putting it all together, we get:
L^-1{F(s)} = -1/3 e^-2t + 5/3 e^t
None of the given choices match this answer exactly, but we can simplify it as:
L^-1{F(s)} = 5/3 (e^t - e^-2t)/2 - 5/2 e^t
This matches choice E:
1/2 = u_2(t) [e^t - 2 - e^-2(t-2)]
Multiplying both sides by 5/3 and adding -5/2 e^t, we get:
L^-1{F(s)} = 5/2 u_2(t) [-e^t - 2 + 2e^-2(t-2)]
So the correct answer is E.

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Answer:

1. C   Add/subtract the same quantity to/from both sides

2. A  Yes

Step-by-step explanation:

Start with Equation A.

3x - 1 = 7

Add 1 to both sides.

3x = 8

First question:

How can we get Equation B from Equation A?

Answer:

C   Add/subtract the same quantity to/from both sides

Second question:

Based on the previous answer, are the equations equivalent?

Since by doing a valid step (adding 1 to both sides) Equation A became Equation B, the two equations are equivalent.

Answer:

A  Yes

Answer:

The diameter is 91.

Step-by-step explanation:

The formula for circumference is 2*pi*radius(you can use circumference = diameter*pi too). Plug 285.74 into it. Divide both sides by 3.14, and you get 2*radius(aka the diameter) = 91

Answer:

91 yards

Step-by-step explanation:

The circumference of a circle can be found using the following formula:

c=π * d

We know that the circumference is 285.74 yards and we are using 3.14 for pi. Substitute 285.74 in for c and 3.14 for pi.

285.74= 3.14 *d

We want to find the diameter. Therefore, we need to get the variable d by itself. d is being multiplied by 3.14 The inverse of multiplication is division. Divide both sides of the equation by 3.14

285.74/3.14= 3.14*d/3.14

285.74/3.14=d

Divide

91=d

d= 91 yards

The diameter of the field is 91 yards.

Using the definition of divisibility, 2p is the greatest common factor.

In the given question we have to factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.

The given polynomial is 2p^3+6p.

Now taking 2p common from both terms

=2(p^2+3)

By the definition of divisibility, we get

2p | 2p^3 and 2p|6p, 2| 2p^3 and 2|6p also p|2p^3 and p|6p.

So, 2,p and 2p are common factors of 2p^3 and 6p.

Hence, 2p is the greatest common factor.

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The right answer is:

Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.

2p^3+6p

Answer:

parabola On a coordinate plane, a parabola opens up. It goes through (negative 5, 6), has a vertex of (0, 0), and goes through (5, 6). On a coordinate plane, a parabola opens up.

Step-by-step explanation:

Answer: C) the third graph

Step-by-step explanation: i got 100% on my quiz, hope this helps!!

Answer:

(1,3)

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form: \(y=mx+b\) where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis, or when x is equal to 0).

We're given that this line contains the point (0,1). This tells us that the y-intercept (b) of the line is 1.  We're also given that this line has a slope (m) of 2. Plug these values into \(y=mx+b\):

\(y=2x+1\)

Now, plug in all of the possible points to see which are solutions.

1) (1,3)

\(3=2(1)+1\\3=2+1\\3=3\)

Because the left side of the equation is equal to the right, (1,3) also lies on this line.

2) (3,1)

\(1=2(3)+1\\1=6+1\\1=7\)

Because the left side is not equal to the right, (3,1) does not lie on the line.

3) (2,2)

\(2=2(2)+1\\2=4+1\\2=5\)

Because the left side is not equal to the right, (2,2) does not lie on the line.

4) (2,3)

\(3=2(2)+1\\3=4+1\\3=5\)

Because the left side is not equal to the right, (2,3) does not lie on the line.

I hope this helps!

The equation of a line is 2x + 5y = 8.

The given equation is :

y = 5/2x + 4

Here we have to find the equation of a line perpendicular to the given line passing through the point (-1,2).

The slope of a line is 5/2.i.e., \(m_{1}\) = 5/2

To find the slope of a line perpendicular to the line we have a formula:

\(m_{1}\)×\(m_{2}\) = -1

\(m_{2}\) = -1 /\(m_{1}\)

\(m_{2}\)= -1 × 2/5

     =-2/5

The equation of a line is:

y = mx + c

The slope is -2/5 and the point is (-1,2)

c = y-intercept

So by putting the value we have:

2 = -2/5 × (-1) + c

c = 8/5

y   = -2/5x + 8/55

y = -2x + 82x + 5y = 8

Therefore the equation of a line is 2x + 5y = 8.

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For a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at \(\frac{x+1}{2}\)

Given,

The conditions

We know,

Median is the middle number of ordered data set.

Consider the number of observations as x

Then the median is located at \(\frac{x+1}{2}\)

Hence, for a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at \(\frac{x+1}{2}\)

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Answer:

70% increase

Step-by-step explanation:

the given series ∑k=1[infinity] 4 * 3^k is a divergent geometric series.

The given series is a geometric series with the common ratio (r) equal to 3k. To analyze this series, we'll complete parts a through d:

a) Determine the first term (a) of the series:

The first term of the series is obtained by substituting k = 1 into the series expression:

a = 4 * 3^1 = 12

b) Determine the common ratio (r) of the series:

The common ratio is obtained by evaluating the series expression for k = 2 and dividing it by the expression for k = 1:

r = (4 * 3^2) / (4 * 3^1) = 3^1 = 3

c) Determine the condition for convergence of the series:

For a geometric series, the series converges if and only if the absolute value of the common ratio (r) is less than 1:

|r| < 1

|3| < 1

3 < 1 (which is false)

Since the absolute value of the common ratio is greater than 1, the series diverges.

d) State the sum of the series (if it converges):

Since the series is divergent, there is no finite sum for the series.

In summary, the given series ∑k=1[infinity] 4 * 3^k is a divergent geometric series.

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Answer:

The Circumference of the circle = C = 24π mm

Hence, option C is true.

Step-by-step explanation:

Given

Radius  r = 12mm

To Determine

Circumference of circle C = ?

Using the formula to determine the Circumference of the circle

C = 2πr

substituting r = 12mm in the equation

C = 2π(12)

C = 24π mm

Therefore, the Circumference of the circle = C = 24π mm

Hence, option C is true.

Answer:

(50/12) + (2x) = L

Step-by-step explanation:

Let's assume the length of the wall is represented by "L" feet. Since we're given that the distance between the pictures and the distances from each picture to the end of the wall are the same, we can represent that distance as "x" feet.

To form the equation, we can consider the total length of the wall and the space occupied by the two pictures and the gaps between them.

The total length of the wall is "L" feet, and each picture is 25 inches across, which is equivalent to (25/12) feet. So, the combined width of the two pictures is (2 * 25/12) feet.

We have two gaps, one between the first picture and the end of the wall, and another between the second picture and the other end of the wall. Each gap has a length of "x" feet.

To set up the equation, we can add up the widths of the pictures and the gaps, and it should equal the total length of the wall:

(2 * 25/12) + (2 * x) = L

Step-by-step explanation:

The answer is (50/12)+(2x)=L

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{5}}}}}\)

Step-by-step explanation:

\( \sf{ - 4 - ( - 9)}\)

When there is a ( - ) in front of an expression in Parentheses, change the sign of each term

⇒\( \sf{ - 4 + 9}\)

Calculate

⇒\( \sf{5}\)

Hope I helped!

Best regards!!

Answer:

5

Step-by-step explanation:

- 4 - ( -9 )

Two negatives multiplied  = positive

Therefore,

-4 + 9 = 5

Answer: 25

Step-by-step explanation:

Answer:

3 and 1/3 of an hour

Step-by-step explanation:

Answer:

This dosen't make anysense to me

i am trying really hard

Step-by-step explanation:

Answer:

m=n

Step-by-step explanation:

i am not 100% sure what the answers would be but it would me m=n

1.62 is the volume (in cm3) of 2 troy ounces of pure gold .

What is full answer for density?

We determine the volume, V, corresponding to the given amount of gold. We do this by dividing the given mass, m, by the density, d, such that

               V = m/d

  m = 31.03 g

   d = 19.3 g/ml

We proceed with the solution

  V = m/d

     = 31.03/19.3

      ≈ 1.62 ml

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The binomial distribution applies to experiments where there are a fixed number of independent trials, each with only two possible outcomes, and a constant probability of success. The experiments that fit this description are: throwing a coin 50 times, drawing 5 marbles with replacement from a box containing 5 red and 2 yellow marbles, and drawing a sample of 20 bolts from a bin containing 5,000 bolts with a known 2% of them being faulty. So, the correct answer is A, B, C and E.

The binomial distribution applies to the following probability experiments

A coin is thrown 50 times, and the variable is the number of tails. This experiment satisfies the requirements for a binomial distribution because each trial has only two possible outcomes, the trials are independent, the probability of tails is constant, and there is a fixed number of trials. This satisfies the condition.

Fifty coins are each thrown once, and the variable is the number of tails. This experiment also satisfies the requirements for a binomial distribution because each trial has only two possible outcomes, the trials are independent, the probability of tails is constant, and there is a fixed number of trials. This satisfies the condition.

A box contains 5 red and 2 yellow marbles, and you draw out 5 marbles, replacing the marble each time. The variable is the number of yellow marbles drawn. This experiment does not satisfy the requirements for a binomial distribution because the trials are not independent since the marble is replaced each time. The probability of drawing a yellow marble changes from trial to trial, so the probability of success is not constant.  This satisfies the condition.

A box contains 5 red and 2 yellow marbles, and you draw out 5 marbles without replacement. The variable is the number of yellow marbles drawn. This experiment does not satisfy the requirements for a binomial distribution because the trials are not independent since the marbles are not replaced.

The probability of drawing a yellow marble changes from trial to trial, so the probability of success is not constant. This does not satisfies the condition.

A large bin contains 5,000 bolts, 2% of them are faulty, and you draw a sample of 20 bolts from the bin. The variable is the number of faulty bolts.

This experiment satisfies the requirements for a binomial distribution because each trial has only two possible outcomes, the trials are independent, the probability of drawing a faulty bolt is constant, and there is a fixed number of trials. This satisfies the condition.

So, the correct options that satisfies the condition of binomial distribution is A, B, C and E.

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Are 5,040 different possible settings for the suitcase lock if all four digits have to be different.

For the first dial, there are 10 possible digits (0 to 9) that can be set. For the second dial, there are 9 remaining digits to choose from (since we cannot repeat the digit from the first dial). For the third dial, there are 8 remaining digits to choose from (since we cannot repeat any of the digits from the first two dials). Finally, for the fourth dial, there are 7 remaining digits to choose from.

Therefore, the total number of possible settings for the suitcase lock with all four digits different is:

10 × 9 × 8 × 7 = 5,040

There are 5,040 different possible settings for the suitcase lock if all four digits have to be different.

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Answer:

This problem can be solved using the permutation formula, which is:

nPr = n! / (n - r)!

where n is the total number of items (cages in this case) and r is the number of items (animals in this case) that we want to select and arrange.

In this problem, we want to select and arrange 5 animals in 11 different cages, so we can use the permutation formula as follows:

11P5 = 11! / (11 - 5)!

     = 11! / 6!

     = 11 x 10 x 9 x 8 x 7

     = 55,440

Therefore, there are 55,440 ways to encage 5 animals in 11 cages if all of them should be in different cages.

The inequality that represents the constraint of the situation is x+y ≥ 400.

Inequality is defined as the mathematical expression in which both sides are not equal .

In inequalities the two vales are compared by "≤" , "≥" , "≠"  .

For Example : 2x+3y≥4 is an example of inequality .

In the given question

Part (a)

Given Kylie sell first oil painting in $x

and second oil painting in $y.

Kylie is trying to earn at least $400.

the term at least means she can earn $400 or greater than $400, so ≥ sign will  be used,

According to the question

we get , x+y ≥ 400    

So , x+y ≥ 400, is the inequality that represents the constraint of the situation.

Part (b)

The Graph of the inequality x+y ≥ 400 that represents the constraint on the sale is shown below .

Therefore , the inequality that represents the constraint of the situation is x+y ≥ 400.

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Depending on the accounting method used, the expense shown on the income and expense statement for the year would either be $150 or $500.

When purchasing a $500 stereo on an installment plan, the expense recorded on the income and expense statement for the year will depend on the accounting method used.

1. Cash Basis Accounting:

Under cash premise bookkeeping, costs are recorded when money is paid. In this case, since you made two payments of $75 each during the year, the expense recorded would be the total amount of cash paid, which is $75 x 2 = $150.

2. Accrual Basis Accounting:

Under accrual basis accounting, expenses are recorded when they are incurred, regardless of when the cash is paid. In this case, the expense recorded would be the total cost of the stereo, which is $500. The payments made during the year would be recorded as a reduction in the accounts payable liability associated with the stereo purchase.

Therefore, depending on the accounting method used, the expense shown on the income and expense statement for the year would either be $150 (cash basis accounting) or $500 (accrual basis accounting). It's important to note that the chosen accounting method should align with the accounting principles and regulations applicable to your situation.

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You are c) a structure. A structure is a collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.

A structure is a user-defined data type that allows you to group together related data. For example, you could create a structure to store the name, age, and address of a person. The structure would have three variables, each of a different type: a string variable for the name, an integer variable for the age, and a string variable for the address.

The advantage of using a structure is that it allows you to treat the related data as a single unit. This makes it easier to manipulate the data and to pass the data to functions.

The other answer choices are incorrect. A template is a blueprint for creating a generic class or function. An array is a collection of elements of the same type. Local variables are variables that are declared within a function and that are only accessible within the function.

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