A gas station stores its gasoline in a tank underground. The tank is a cylinder lying horizontally on its side. The radius is 5 ft, the length is 15 ft, and the top of the tank is 10 feet under the ground. Assume the tank is full and all of the gasoline will be pumped to the surface of the ground. The density of gasoline is 42 lb/ ft3. Consider a slice of gasoline that is delta y ft thick and located y ft above the center of the cylinder. Use delta or the CalcPad for delta . Leave pi in your answer. Volume of slice : ft3 Displacement of slice : ft Find the endpoints of the integral needed to find the exact work required to pump all the gasoline to the surface of the ground. Lower endpoint = Upper endpoint =

Answer:

D. The standard deviation is known and n > 30.

Step-by-step explanation:

A two-population z test should be used when the standard deviation is known and the sample size is greater than 30.

The circumstances under which you should use a two-population z test are:

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Answer:

457 sand dollars

Step-by-step explanation:

Let the number=x

The number she has collected is greater than 400 and less than 460

400<x<460

The number in hundreds place is one less than the number in the tens place.

The number in the Hundreds place is 4. Since it is one less, our number for now will be of the form 45* where * is the ones digit.

Also, the number in the ones place is two more than the number in the tens place.

The number in the tens place is 5. If it is two more than 5, the number in the ones place is 7.

Therefore Chelsea has collected 457 sand dollars

Answer:

22.5

Step-by-step explanation:

All of the angles inside the triangle equals 180. Therefore, the equation is x+2x+5x=180. Then, you solve for x. The final equation should look like 8x=180 And that is how we get 22.5

Answer:

22.5

Step-by-step explanation:

The sum of the interior angles in a triangle is 180 degrees, so we have the equation $x+2x+5x=180$, so $x=\boxed{22.5}$.

Answer:

yp = -x/8

Step-by-step explanation:

Given the differential equation: y′′−8y′=7x+1,

The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)

First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;

y′′−8y′=0

The auxiliary equation will give us;

m²-8m = 0

m(m-8) = 0

m = 0 and m-8 = 0

m1 = 0 and m2 = 8

Since the value of the roots are real and different, the complementary solution (yc) will give us

yc = Ae^m1x + Be^m2x

yc = Ae^0+Be^8x

yc = A+Be^8x

To get yp we will differentiate yc twice and substitute the answers into the original DE

yp = Ax+B (using the method of undetermined coefficients

y'p = A

y"p = 0

Substituting the differentials into the general DE to get the constants we have;

0-8A = 7x+1

Comparing coefficients

-8A = 1

A = -1/8

B = 0

yp = -1/8x+0

yp = -x/8 (particular integral)

y = yc+yp

y = A+Be^8x-x/8

Answer:

Cumulative frequency distribution

Step-by-step explanation:

Cumulative frequency distribution is a form of a frequency distribution that represents the sum of a class and all classes below it. Remember that frequency distribution is an overview of all distinct values (or classes of values) and their respective number of occurrences.

Final answer:

Placing in the 99th percentile means a student did better than 99% of test takers, akin to scoring beyond the second standard deviation, a high achievement.

Explanation:

If a student places in the 99th percentile on an exam, this indicates that her performance was better than 99% of all students who completed the exam. Her achievement is akin to being beyond the second standard deviation in the context of a normal distribution, showing an exceptional score. In the given context, this means she likely scored higher than what is considered the range for the majority of her peers.

Being in the 90th percentile would indicate that 90 percent of test scores were at or below that mark, a clear demonstration of high achievement compared to peers. In educational measurement, the choice between absolute rating and relative ranking can greatly affect the evaluation of student performance. With relative ranking, a student's performance is compared against that of their peers, such as being in the top 10% as opposed to achieving a specific score percentage, which would be an absolute rating.

When x is greater than or equal to 0 use the equation x +2

The x value is given as 3 in f(3)

Now replace x with 3 in the equation and solve:

F(3) = 3 + 2 = 5.

The answer is 5

Answer:

53 by the fact NFL players use a for wheeler u Dan je e eka a f wjd r

Answer:

The range of the data = 99 -22 = 77min

The mean of the dataset is given as

The IQR  = 92 - 77 = 15 min

SIQR = IQR / 2 = 15 / 2 = 7.5 min

variance = 55.05 min

Step-by-step explanation:

First we need to arrange the data in ascending or descending order

22 ,58, 77, 84, 87, 87,91, 92, 99, 99 in ascending order

The range of the data is calculated by substracting the numbers at the extreme that is the lowest number subtracted from the highest number

range = 99 - 22 =  77min

The IQR stands for Inter-quartile range Q3 - Q1 where

Q1  is the middle value in the first half of the data set. i.e

Q1 is the middle of 22 ,58, 77, 84, 87 which is  77

Q1 = 77 min

Q3  is the middle value in the second half of the data set. i.e

Q3 is the middle of 87,91, 92, 99, 99 which is  92

Q1 = 92 min

Therefore IQR = Q3 - Q1 = 92min - 77min = 15 min

The SIQR stands for the semi-interquartile range. it is calculated by IQR / 2

SIQR = 15 / 2 = 7.5 min

To calculate the population variance we need to get the mean say X

The mean is the data point at the center. Since the dataset is even, there are two of them. which is 87 and 87

Therefore the mean is X = (87 + 87)/ 2 = 87

The variance = ∑[tex](X-x)^{2} /n[/tex]

where X is the mean = 87

x is a datapoint on the given dataset

n is the datasize = 10

variance =  [tex]((22-87)^{2} + (58-87)^{2} + (77-87)^{2} + (84-87)^{2} + (87-87)^{2} + (87-87)^{2} + (91-87)^{2} + (92-87)^{2} + (99-87)^{2} + (99-87)^{2} ) /10[/tex]

variance = [tex]((-65)^{2} + (-29)^{2} + (-10)^{2} + (-3)^{2} + (0)^{2} + (0)^{2} + (4)^{2} + (5)^{2} + (12)^{2} + (12)^{2} ) /10[/tex]

variance = [tex]((4225) + (841) + (100) + (9) + (0) + (0) + (16) + (25) + (144) + (144) ) /10[/tex]

variance = 5505/10

variance = 550.5 min

Answer:

Range =77

IQR=15

SIQR=7.5

Variance=550.5

Step-by-step explanation:

Range:

First find the lowest and the highest number in the data and then subtract high with the low to find the range. 99-22=77.

IQR:

Ascend the data from low to high like this:

22 58 77 84 87 87 91 92 99 99

Then break into two half

22 58 77 84 87 | 87 91 92 99 99

Find the median of all the two half

77 is rhe median in the first half and 92 is the median in the second half.

Then subtract them: 92-77=15 IQR

SIQR:

Divide the IQR/2

Hence 15/2=7.5.

Variance:

Find the mean of the data first i.e. 79.6

variance = 5505/10

variance = 550.5

Answer:

2(7-i)

Step-by-step explanation:

(8 +5i) + (6 - 7i)

Opening each bracket

8 +5i +6 -7I

8 +6 +5i-7i

14-2i

2(7-i)

Answer:

14 - 2 i

Step-by-step explanation:(8 + (5 * i)) + (6 - (7 * i)) =

Answer:

The answer to your question is Jay will receive $1.07 and Kay will receive $0.93.

Step-by-step explanation:

Data

Jay brought 2 gallons

Kay brought 1.75 gallons

Money = $2

Process

1.- Calculate the total amount of water

Water = 2 + 1.75

          = 3.75 gallons

2.- Calculate the money Jay will receive using proportions

               3.75 gallons ---------------- $2.00

               2      gallons  ---------------  x

               x = (2 x 2) / 3.75

               x = 4/3.75

               x = $1.07

3.- Calculate the money Kay will receive using proportions

               3.75 gallons ----------------$2.00

               1.75 gallons   --------------- x

               x = (1.75 x 2.00) / 3.75

               x = 3.5/3.75

               x = $0.93

Option C: [tex]5 x(4 x+7)(3 x+2)[/tex] is the possible expressions for length, width and height of the prism.

Explanation:

The volume of the rectangular prism is [tex]60 x^{3}+145 x^{2}+70 x[/tex]

To determine the length, width and height of the rectangular prism, let us factor the expression.

Thus, factoring 5x from the expression, we have,

[tex]5 x\left(12 x^{2}+29 x+14\right)[/tex]

Let us break the expression [tex]12 x^{2}+29 x+14[/tex] into two groups, we get,

[tex]5x[\left(12 x^{2}+8 x\right)+(21 x+14)][/tex]

Factoring 4x from the term [tex]12 x^{2}+8 x[/tex] , we get,

[tex]5x[4 x(3 x+2)+(21x+14)][/tex]

Similarly, factoring 7x from the term [tex]21 x+14[/tex] , we get,

[tex]5x[4 x(3 x+2)+7(3x+2)][/tex]

Now, let us factor out [tex]3x+2[/tex], we get,

[tex]5 x(4 x+7)(3 x+2)[/tex]

Hence, the possible expressions for length, width and height of the prism is [tex]5 x(4 x+7)(3 x+2)[/tex]

Therefore, Option C is the correct answer.

Answer:

E(X) = 0.64

Sd(X) = 0.933

Step-by-step explanation:

3(0.07) + 2(0.11) + 1(0.21)

E(X²) = 3²(0.07) + 2²(0.11) + 1²(0.21)

= 1.28

Var(X) = 1.28 - 0.64² = 0.8704

Sd = 0.933

Answer:

Step-by-step explanation:

Let x represent the length of fence parallel to the house. Then the length perpendicular is ...

  y = (120 -x)/2

The area of the yard is the product of these dimensions, so is ...

  A = xy = x(120-x)/2

This is the equation of a parabola that opens downward and has zeros at x=0 and x=120. The maximum (vertex) is on the line of symmetry, halfway between these zeros, at x=60.

The fence parallel to the house is 60 feet.

The fence perpendicular to the house is (120-60)/2 = 30 feet.

The area of the yard is (60 ft)(30 ft) = 1800 ft^2.

Answer:

She will earn $442.89 in one week after the changes.

And this is more than her previous weekly earnings.

Step-by-step explanation:

Given:

Alondra received a 14% hourly raise, but the number of hours worked decreased by 7.5%. If her wage was $10.50 an hour and she worked 40 hours per week before the changes.

Now, to find money she will earn in one week after the changes.

Her wage was = $10.50.

She worked per week = 40 hours.

So, her salary before changes:

[tex]10.50\times 40\\\\=\$420.[/tex]

Thus, the salary per week before changes is $420.

Now, to get her salary after 14% hourly raise:

[tex]10.50+14\%\ of\ 10.50\\\\=10.50+\frac{14}{100} \times 10.50\\\\=10.50+1.47\\\\=11.97[/tex]

Salary after hourly raise = $11.97 per hour.

Then, to get the number of hours worked decreased by 7.5%:

[tex]40-7.5\%\ of\ 40\\\\=40-\frac{7.5}{100} \times 40\\\\=40-3\\\\=37.[/tex]

Number of hours per week after hours of worked decreased  = 37 hours.

Now, to get the salary after changes:

Salary after hourly raise × number of hours per week after hours of worked decreased

[tex]=11.97\times 37[/tex]

[tex]=\$442.89.[/tex]

Salary after changes in one week = $442.89.

As, the previous salary was $420 in one week.

And after changes this salary is $442.89 in one week which is more than previous.

Therefore, she will earn $442.89 in one week after the changes.

And this is more than her previous weekly earnings.

Answer:

2

Step-by-step explanation:

Answer: 2.)a1 =-3, d = 7, an = 7n - 10

Step-by-step explanation:

In an arithmetic sequence, consecutive terms differ by a common difference.

The formula for determining the nth term of an arithmetic sequence is expressed as

an = a1 + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a1 = - 3

d = 4 - - 3 = 11 - 4 = 18 - 11 = 25 - 18 = 7

Therefore, the Explicit Rule for this arithmetic sequence is

an = - 3 + 7(n - 1)

an = - 3 + 7n - 7

an = 7n - 7 - 3

an = 7n - 10

Answer: the number of hpurs that Fran can watch this week is lesser than 12

Step-by-step explanation:

Let x represent the number of hours of television that Fran can watch in a week.

Fran is limited to watching television less than 12.6 hours per week. She has already watched 4.2 hours, and each show is 0.7 of an hour long. The inequality representing the situation is expressed as

0.7x + 4.2 < 12.6

0.7x + 4.2 < 12.6 - 4.2

0.7x < 8.4

x < 8.4/0.7

x < 12

Answer:

12

Step-by-step explanation:

Fran has wached 4.2 hours of tv out of 12.6, if the equasion is curect that means that she has wached 6 shows already.

From here there is two ways to do his one is to look at how meny shows she can watch in 12.6 hours and subtract how meny shows she has wached from it  and then convert back to desimals.

The other way to do this( the better way) is to do 12.6-4.2=8.4 then do 8.4 / .7 and you would get 12

Answer:

Vera used the wrong number in her inequality.

Step-by-step explanation:

Inequalities are graphed to present a clearer picture of their behavior

To graph an inequality, the following are required steps

(1) Locate the indicated number on the other side of the  inequality sign variable x in the inequality equation (in this case we have 78.9999 ≥ x)

(2) Draw a number line and place an open or shaded circle around around the number specified in the inequality equation depending on whether the variable is also equal to the number

(3) Shade the possible numbers of the variable

In this case Vera used 78.999 in the equation and 79 on the graph

Answer:

Vera used the wrong number in her inequality.

Step-by-step explanation:

Vera graphed the inequality -78.9999 ≥ x. However, she plotted the point at -79, not -78.9999. Thus, we can tell the answer is Vera used the wrong number in her inequality.

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Answer:

The conditional probability that I get four heads given I pulled out the weighted coin = 0.2401

Step-by-step explanation:

Probability of getting 4 heads from 4 trials for a fair coin = 0.5⁴

But given that it is the weighted coin that is pulled out,

The probability of getting 4 heads from 4 trials = 0.7⁴ = 0 2401

Answer: 15

Step-by-step explanation:

Answer:

he have to kep cutting them until he find out he answer

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Given that in a sample of n = 6 scores, the smallest score is X = 3, the largest score is X = 10

Mean = 6

Since mean = 6 we get sum of all the 6 scores = [tex]6(6) = 36[/tex]

Now  II part says 10 is changed to 20

i.e. original sum = 36

Changed value  = 10

Adjusted value =26

Add: new value  =22

New sum            =48

So we have sum = 48

New mean= [tex]\frac{48}{6} =8[/tex]

(This can also be done using the formula

old mean + positive change in one score/6)

Final Answer:

The new mean after changing the largest score from 10 to 22 is 8.

Explanation:

To solve this problem, we will follow these steps:
1. Calculate the total sum of all scores using the original mean.
2. Subtract the original largest score from the total sum.
3. Add the new largest score to the total sum to get the new total sum.
4. Calculate the new mean by dividing the new total sum by the sample size.

Let's go through these steps one by one:
Step 1: Calculate the original total sum of scores.
Given that the mean (M) is 6 for a sample size (n) of 6:
Total sum of scores (original) = Mean × Sample size = M × n = 6 × 6 = 36

Step 2: Subtract the original largest score from the total sum.
Original total sum = 36 (from Step 1)
Original largest score = 10
Total sum after removing the original largest score = 36 - 10 = 26

Step 3: Add the new largest score to the total sum to get the new total sum.
Total sum after removing the original largest score = 26 (from Step 2)
New largest score = 22
New total sum of scores = 26 + 22 = 48

Step 4: Calculate the new mean.
New total sum of scores = 48 (from Step 3)
Sample size (n) = 6
New mean = New total sum of scores ÷ Sample size = 48 ÷ 6 = 8

Therefore, the new mean after changing the largest score from 10 to 22 is 8.

Answer:

The p-value of the test is 0.1416.

The null hypothesis was not rejected concluding that μ = 100.

Step-by-step explanation:

The hypothesis is defined as:

H₀: μ = 100 vs. Hₐ: μ ≠ 100

The test is a two-tailed test.

The test statistic value is z = 1.47.

The significance level of the test is α = 0.10.

The p-value is computed as follows:

[tex]p-value=2\times P(Z<-1.47)=2\times0.0708=0.1416[/tex]

Decision rule:

If the p-value of the test is less than the significance level 0.10, then the null hypothesis is rejected and vice-versa.

The p-value = 0.1416 > α = 0.10.

The p-value is more than the significance level.

The null hypothesis was not rejected.

Conclusion:

The mean value is not different than 100.

To find the p-value for the test, calculate the area under the standard normal curve more extreme than the observed test statistic. The p-value is 0.1416, and we fail to reject the null hypothesis at α = 0.10.

To find the p-value for the test, we need to calculate the area under the standard normal curve that is more extreme than the observed test statistic. In this case, the test statistic is z = 1.47. Since it is a two-tailed test, we need to find the probability in both tails.

First, we find the area to the right of 1.47 by subtracting the cumulative probability from the mean to 1.47 from 1: P(Z > 1.47) = 1 - P(Z < 1.47) = 1 - 0.9292 = 0.0708.

Next, we double this probability to get the total p-value for both tails: p-value = 2 * 0.0708 = 0.1416. Since the p-value (0.1416) is greater than the significance level (α = 0.10), we fail to reject the null hypothesis. This means we do not have enough evidence to conclude that the population mean is not equal to 100.

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Answer:

$327.25

Step-by-step explanation:

$435 - $50 = 385

15% = 15/100 = 0.15

$385 * 0.15 = 57.75

$385 - $57.75 = $327.25

The price, in dollars, of a $435 dollar refrigerator after both discounts is $327.25.

= $435 - $50

= 385

Since there is 15% discount

So here we have to do 15% discount of $385

i.e.

= $385 - 15% of $385

= $385 - $57.75

= $327.25

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Option A: [tex]-2500[/tex] is the value of [tex]S_{25[/tex]

Explanation:

It is given that the first term is [tex]a_1=20[/tex]

The common difference is [tex]d=-10[/tex]

We need to determine the sum of 25 terms.

The sum of  terms of an arithmetic series can be determined using the formula, [tex]S_n=\frac{n[2a_1+(n-1)d]}{2}[/tex]

Substituting [tex]n=25[/tex] , [tex]a_1=20[/tex] and [tex]d=-10[/tex]

Thus, we have,

[tex]S_{25}=\frac{25[2(20)+(25-1)(-10)]}{2}[/tex]

Simplifying the values, we get,

[tex]S_{25}=\frac{25[40+(24)(-10)]}{2}[/tex]

[tex]S_{25}=\frac{25[40-240]}{2}[/tex]

Subtracting the terms within the bracket, we get,

[tex]S_{25}=\frac{25[-200]}{2}[/tex]

Multiplying the terms in the numerator, we have,

[tex]S_{25}=\frac{-5000}{2}[/tex]

Dividing, we get,

[tex]S_{25}=-2500[/tex]

Thus, the sum of the 25 terms is [tex]-2500[/tex]

Therefore, Option A is the correct answer.

Answer:

-2500 answer

Step-by-step explanation:

Using the principles of Pythagorean theorem, we can figure out that the radius of the circle inscribed by the given isosceles triangle is 5 units.

To solve this problem, we need to apply the principles of the Pythagorean theorem and radius calculation in a circle inscribed by a triangle.

To recall, the Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, if you have a right triangle, you can calculate the hypotenuse c with the formula: c = √a² + b².

In this case, the altitude to the base forms two right-angled triangles within the isosceles triangle. These triangles both have legs of 5 (altitude) and half the base.

We first need to calculate this half base. The half base can be calculated by using Pythagorean theorem where one leg of the right triangle is the altitude (5) and the other leg is half the base, and the hypotenuse is one side of the isosceles triangle (13). Solving this yields a half base of 12.

Now, with the whole base equal to twice this value, or 24, we have a right triangle where the hypotenuse of the triangle (the diameter of the circle) is also the side of the isosceles triangle (13) and one leg is the whole base of the isosceles triangle (24), and the other leg is the altitude from the center of the base to the top of the isosceles triangle which is also the radius of the circle we are looking for.

Applying the Pythagorean theorem here yields a radius of √(13² - 12²) which simplifies to 5. Therefore, the radius of the circle is 5 units.

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Answer:

a) 1.92

b) 3.25

c) 1.5

d) -5.23

Step-by-step explanation:

We are given the following in the question:

4, 7, -1, 1, 0, 5, -2, 2, -1, 6, 5, -3

a) mean of score change

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{23}{12} = 1.92[/tex]

b) standard deviation for this population

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

Sum of squares of differences = 126.92

[tex]\sigma = \sqrt{\frac{126.92}{12}} = 3.25[/tex]

c) median change score

[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]

Sorted data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7

Median =

[tex]\dfrac{6^{th} + 7^{th}}{2} = \dfrac{1+2}{2} = 1.5[/tex]

d) change score that is 2.2 standard deviations below the mean.

[tex]x = \mu - 2.2(\sigma)\\x = 1.92-2.2(3.25)\\x = -5.23[/tex]

Answer:

61 divided by 10 and that should even out how many hours they worked

Step-by-step explanation:

Answer: the equation that can be used to solve for the hourly labor rate is

2x + 10 = 61

Step-by-step explanation:

Let x represent the amount charged by the landscaping company per hour of labour.

The landscaping company charges a $10 fee to make a house call plus an hourly rate for labor. This means that the total charge for y hours is

xy + 10

If the total bill for a job that takes two hours comes to $61.00, the equation that can be used to solve for the hourly labor rate would be

2x + 10 = 61

Answer:

non sampling error

Step-by-step explanation:

Sampling error in a statistical analysis arising from the unrepresentativeness of the  sample taken.

Non Sampling error is a term used in statistics that refers to an error that occurs during data collection, causing the data to differ from the true values.

Answer:

sampling error

Step-by-step explanation:

Answer:

g(f(x)) = [tex]\sqrt{f(x)} +2=\sqrt{x+1} +2[/tex]

Domain = [-1,∞)

Step-by-step explanation:

Given f(x) = x+1 and g(x) = √x + 2

g(f(x)) is a composite function.

g(f(x)) = [tex]\sqrt{f(x)} +2=\sqrt{x+1} +2[/tex]

To find the domain of composite function we must get both domains right (the composed function and the first function used).

The domain of f(x) is all the real numbers.

The domain of g(f(x)) is the values of x provide that the square root is greater than or equal zero

So, x+1 ≥ 0

∴ x ≥ -1

So, the domain = [-1,∞)

The domain of the composite function g(f(x)) is x ≥ -2.

The domain of a function is the set of all possible input values for which the function is defined. To determine the domain of the composite function g(f(x)), we need to consider two things:

In this case, the domain of f(x) is all real numbers because there are no restrictions on the input values for f(x) = x + 1.

However, the domain of g(x) = √(x + 2) is limited by the requirement that the radicand (the expression inside the square root) must be greater than or equal to zero. So, x + 2 ≥ 0.

Solving this inequality, we get x ≥ -2.

Therefore, the domain of g(f(x)) is x ≥ -2, which can be written in interval notation as (-∞, -2] or [-2, ∞).

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Area of the largest circle fit in the fire pit is 4069.44 square inches.

Solution:

Length of the rectangular pit = 7 feet

Width of the rectangular pit = 6 feet

The diameter of a largest circle inscribed in a rectangle is equal to the smaller side of the rectangle.

Diameter of the largest circle = 6 feet

Radius of the largest circle = 3 feet

Area of the circle = πr²

                             = 3.14 × 3²

Area of the circle = 28.26 square feet

Let us convert square feet into square inches.

1 square feet = 144 square inches

28.26 square feet = 28.26 × 144

                              = 4069.44 square inches

Area of the largest circle fit in the fire pit is 4069.44 square inches.

Answer:

Probability = 0.241

Step-by-step explanation:

We can find the probability that a given class period runs through the given time recognizing that a uniform probability distribution is mostly a rectangle with an area equal to 1.

Therefore,

Probability = 51.7551 - 50.550/53.053 - 48.0480 = 1.2057/5.005

= 0.241

Answer:

The probability of selecting a class that runs between 50.550.5 and 51.7551.75 minutes is 0.24

Step-by-step explanation:

A uniform distribution is a flat distribution that has the same probability density for every number. The area under the graph of the distribution must be 1. Since this distribution runs from 48.048.0 to 53.053.0  minutes,

it has a range of 5.005 (53.053.0 - 48.048.0).

The density must be 1/5.005 ≅ 0.2, so that 5.005*0.2 ≅ 1.0.

To find the probability of being between two numbers multiply the range between the numbers by the probability density.

range:51.7551.75 - 50.550.5 ≅ 1.2

1.2*0.2 = 0.24

P(50.550.5 < x < 51.7551.75) = 0.24

The probability of selecting a class that runs between 50.550.5 and 51.7551.75 minutes is 0.24