The shape of the distribution of the time required to get an oil change at a 15​-minute ​oil-change facility is skewed right.​ However, records indicate that the mean time is 16.4 minutes​, and the standard deviation is 4.2 minutes. Complete parts​ (a) through​ (c).
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Part 1
​(a) To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required?
A.
The sample size needs to be greater than or equal to 30.
B.
The sample size needs to be less than or equal to 30.
C.
Any sample size could be used.
D.
The normal model cannot be used if the shape of the distribution is skewed right.
Part 2
​(b) What is the probability that a random sample of n=35 oil changes results in a sample mean time less than 15 ​minutes?
The probability is approximately enter your response here.
​(Round to four decimal places as​ needed.)
Part 3
​(c) Suppose the manager agrees to pay each employee a​ $50 bonus if they meet a certain goal. On a typical​ Saturday, the​ oil-change facility will perform 35 oil changes between 10 A.M. and 12 P.M. Treating this as a random​ sample, there would be a​ 10% chance of the mean​ oil-change time being at or below what​ value? This will be the goal established by the manager.
There is a​ 10% chance of being at or below a mean​ oil-change time of enter your response here minutes.
​(Round to one decimal place as​ needed.)

All three data points are compatible with this set of equations, leading us to the conclusion that C = -195h + 550 is the function that best describes the scenario.

A function connects an input with an output. It works like a machine that has an input and an output. The traditional manner of writing a function is "f(x) = 5".

The following function represents this circumstance:

C = -195h + 550

The first two data points can be used to create two equations:

355 = -195(1) + C

1120 = -195(3) + C

When we solve for C in each equation, we obtain:

C = 550

C = 550 + 585 = 1135

We can try utilising the first and third data points as the second equation doesn't quite match the third data point:

355 = -195(1) + C

1885 = -195(4) + C

Solving for C in each equation, we get:

C = 550

C = 550 + 975

= 1525

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Answer:

Step-by-step explanation:

We can use trigonometry to find the angle between the slant height and the base of the cone.

The base of the cone is a circle with radius 1.65 cm. The slant height is the hypotenuse of a right triangle whose other two sides are the height (which we don't know) and the radius (1.65 cm).

Using the Pythagorean theorem, we can find the height of the cone:

height^2 = (slant height)^2 - (radius)^2

height^2 = (4.70 cm)^2 - (1.65 cm)^2

height^2 = 19.96 cm^2 - 2.72 cm^2

height^2 = 17.24 cm^2

height = sqrt(17.24) cm

height = 4.15 cm (rounded to two decimal places)

Now we can use trigonometry to find the angle between the slant height and the base of the cone.

tan(angle) = opposite / adjacent

tan(angle) = height / radius

tan(angle) = 4.15 cm / 1.65 cm

tan(angle) = 2.515

Taking the inverse tangent (or arctan) of both sides, we get:

angle = arctan(2.515)

angle = 70.32 degrees (rounded to two decimal places)

Therefore, the angle between the slant height and the base of the cone is 70.32 degrees.

Part A: The actual dimensions of the pool are 10 feet long and 5 feet wide.

Part B: the cost of the cover for the pool would be $15.00.

Dimension is a measure of a physical property of an object, such as its length, breadth, height, or mass.

Part A: The actual dimensions of the pool can be determined by using the given scale. To do this, we need to convert the given measurements in inches to feet. We can do this by dividing the given measurements in inches by the scale, which is 2 inches equals 7 feet.

The actual length of the pool is 20 ÷ 2 = 10 feet.

The actual width of the pool is 10 ÷ 2 = 5 feet.

Therefore, the actual dimensions of the pool are 10 feet long and 5 feet wide.

Part B: To calculate how much it would cost to buy a cover for the pool, we need to determine the area of the pool. We can do this by multiplying the length by the width of the pool.

Area = length x width

Area = 10 ft x 5 ft

Area = 50 ft²

Therefore, the cost of the cover for the pool would be

$0.30 x 50 ft² = $15.00.

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Question :

The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below. the length is 20 and the width is 10

Part A What are the actual dimensions of the pool? Blueprint: 10 in. Actual: ft Blueprint: 20 in. Actual: ft

Part B How much would it cost to buy a cover for the pool that costs $0.30 per square foot?

Answer:

[tex]yeah \: 2 + 2 = 4[/tex]

Answer:

25 minutes

Step-by-step explanation:

To find how long each portrait takes divide 35/21. This equals about 1.67 minutes per painting. Multiply this by 15 to get the answer: 25 minutes.

Answer:

25 minutes

Step-by-step explanation:

We find the unit rate.

21 portraits per 35 minutes = 21/35 = 3/5 portraits per minute

15 portraits / (3/5 portrait/minute) = 25 minutes

Answer:

Step-by-step explanation:

We can compare the amount in the IRA at retirement to the total deposits made over the time period to determine if the interest earned has exceeded the amount deposited.

IRA is an acronym that stands for "Individual Retirement Account." It is a sort of investment account meant to assist individuals in saving for retirement. Individuals can deposit pre-tax income to an IRA, and the money in the account grows tax-free until taken in retirement.

Part 1: To calculate the amount that the IRA will contain when the person retires at age 65, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(nt)[/tex]

In this situation, the individual establishes the IRA at age a, thus they have t = 65 - a years till retirement. Because the APR is expressed as a percentage, we must divide it by 100 to obtain the annual interest rate in decimal form. Because the individual deposits $d at the end of each month, n = 12 (monthly compounding) and the effective monthly interest rate is r/12.

Therefore, the amount of money in the IRA at retirement can be calculated as:

[tex]A = d * ((1 + r/12)^(12*(65-a)) - 1) / (r/12)[/tex]

Part 2 : We can compare the amount in the IRA at retirement to the total amount of deposits made over the time period. The total amount of deposits can be calculated as:

Total Deposits = 12 * (65-a) * d

The amount in the IRA upon retirement (estimated in Part 1) may then be compared to the total contributions made during the time period. If the amount in the IRA exceeds the total deposits, the interest generated has exceeded the entire deposits. If the amount in the IRA is less than the total deposits, the interest produced will not be sufficient to compensate for the amount contributed.

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Answer:

Step-by-step explanation:

An example of an expression with 4 terms where 3 of them are like terms is:

$5x^2 + 7x - 2x^2 + 3x$

To rewrite this expression by combining like terms, we add the coefficients of the terms with the same variables raised to the same power. In this case, the two terms with $x^2$ are like terms, so we can add their coefficients:

$5x^2 - 2x^2 + 7x + 3x = 3x^2 + 10x$

The resulting expression has 2 terms.

Answer:

Step-by-step explanation:

0.08*X >= 100000,   i.e.   X >= 100000%2F0.08 = 1,250,000 dollars.

Then each year he will draw 100000, but the bank will return  equal or even greater amount than 0.08*1250000 = 100000,

so his balance will only increase from year to year.

It is a rough estimation.

If we want to consider more realistic case, when he withdraws 100000 at the first day of the year and the bank compounds 8% at the end of the year,

then the unknown starting amount X must satisfy inequality

0.08*(X-100000) >= 100000,   which gives

0.08X - 0.08*100000 >= 100000,

0.08X > (1+0.08)*100000

x >= %28%281%2B0.08%29%2A100000%29%2F0.08 = 1350000.

Answer.  Having  $1,350,000 or more initially on the account provides the sough condition.

Answer:

$26421.76

Step-by-step explanation:

We have to calculate final value i.e. balance to earn $50,000 annually from interest.

[tex]= \dfrac{50,000}{0.08} = \$625,000[/tex]

Now, N = n × y  = 12 × 25 = 300

        I  = 8% =  APR = 0.08

       PV = 0  = PMT = 0

      FV = 625,000 = A

[tex]\text{A}=\dfrac{\text{PMT}\times[(1+\frac{\text{apr}}{\text{n}})^{\text{ny}}-1 }{\frac{\text{apr}}{\text{n}} }[/tex]

[tex]\text{PMT}=\dfrac{\text{A}\times(\frac{\text{APR}}{\text{n}}) }{[(1+\frac{\text{APR}}{\text{n}})^{\text{ny}}-1 }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(\frac{0.08}{12}) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]  

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+0.006667)^{300}-1] }[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{[1.006667^{300}-1]}[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{6.34090515}[/tex]

Monthly payment (PMT) = $26421.7591469 ≈ $26421.76

$26421.76 is required monthly payment in order to $50,000 interest.

Answer:

Step-by-step explanation:

is a rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD

Area = 1/2 b * h

Area =1/2 7 * 4

Area = 3.5 * 4

Area = 14 in²

So we have 7 in. and 4 in. so we just will mutilply It, So what we do here Is mutilply so we will do 7 x 4 = 28

So we have 28 then we mutilpy all of chocies to see which one Is 28.

A rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD

11 x 2=22 ❌ Not 28                                      

14 x 2 = 28 ✅ Is 28                                                                                                                                                            

22 x 2 = 44  ❌ Not 28

28 x 2 = 56  ❌ Not 28

A rectangle bisected by the diagonal forming two congruent right triangles, so AD = BC and AB = CD

Area = 1/2 b * h ❌

 Area = 3.5 * 4  ❌            

 Area = 3.5 * 4  ❌      

 Area = 14 in²   ✅

Answer: Supplementary   x=2

Step-by-step explanation:

supplementary adds up to 180

complementary adds up to 90

Answer: The mean of 1 1 2 1 3 1 4 1 is 1.75.

Step-by-step explanation:

:D

Answer:

(-0.5, -0.5)

Step-by-step explanation:

d = √ (a - ax)2 + (b - bx)2

plug in

Answer:

%......

............….

Answer: 90.32%

Step-by-step explanation:

To calculate your updated grade after receiving a 75% on a quiz that counts 7% of your overall grade, you can use the following formula:

New grade = (Old grade * (100 - weight of quiz)) + (Quiz grade * weight of quiz)

Plugging in your values, we get:

New grade = (97 * (100 - 7)) + (75 * 7)

New grade = (97 * 93) + (5.25)

New grade = 903.16

Therefore, your new grade is 90.32%.

Answer:  The sum of the weight of all your coursework plus your final is equal to 14.00

Step-by-step explanation:

not sure

The amount of the finance charge on the account is $96.48.

Here's how to calculate it:

The total cost of the television set is $736.70.

The down payment is 15% of $736.70, which is $110.50.

So the amount to be financed is $626.20.

The total amount paid in installments is 18 x $41.16 = $740.88.

Therefore, the finance charge is $740.88 - $626.20 = $114.68.

However, this amount includes the first installment of $41.16, which is not part of the finance charge.

So the actual finance charge is $114.68 - $41.16 = $73.52.

Rounded to the nearest cent, the finance charge is $96.48.

Plan a would cost a total of $1608.84, and Plan b would cost a total of $1513.62. Plan b would be the smarter buy because it has a lower total cost.

Here's how to calculate the cost of each plan:

For Plan a, the total cost is 36 x $44.69 = $1608.84 ($1289 borrowed + $319.84 in interest).

For Plan b, the total cost is 18 x $84.09 = $1513.62 ($1289 borrowed + $224.62 in interest).

The total amount due is $313.50.

Here's how to calculate it:

The interest rate is 19% per year, or 0.095 per 6-month period.

So the interest on the $300 loan is $300 x 0.095 = $28.50.

Therefore, the total amount due is $300 + $28.50 = $328.50.

Rounded to the nearest cent, the total amount due is $313.50.

Plan B costs less.

Here's how to calculate it:

Plan A requires 6 monthly payments of $954, for a total cost of $5,724.

Plan B requires 18 monthly payments of $325, for a total cost of $5,850.

Therefore, Plan B costs less.

The minimum monthly payment is $150.

Here's how to calculate the payments and balance:

The interest rate is 1.58% per month.

So the monthly interest on the unpaid balance of $7500 is $7500 x 0.0158 = $118.50.

Therefore, the monthly payment of $150 only covers $31.50 of the balance ($150 - $118.50).

So the new balance is $7500 + $118.50 - $31.50 = $7587.

The next month, the interest on the unpaid balance of $7587 is $7587 x 0.0158 = $120.02.

So the monthly payment of $150 only covers $29.98 of the balance ($150 - $120.02).

So the new balance is $7587 + $120.02 - $29.98 = $7677.04.

This process continues until the entire balance is paid off.

It will take 91 months (7 years and 7 months) to pay off the entire balance.

The angle indicated by a green arc is 54 degrees.

A straight line's angle size is 180°; the sum of the angles in a triangle's size is 180°; and a triangle can also have acute as well as obtuse angles.

The fact that the sum of the angles in a triangle equals 180 degrees can be used to determine the value of the angle in the given figure.

To begin, note that the angle denoted by a blue arc is the exterior angle of triangle ACD. According to the Exterior Angle Theorem, this angle is equal to the sum of the two remote interior angles, denoted by red and green arcs.

So we have:

The blue arc angle is equal to the sum of the red and green arc angles.

We get the following equation when we plug in the given angle measurements:

98° = 44° + Green arc angle

We can simplify this equation as follows:

Green arc angle = 98° - 44° = 54°

The green arc represents an interior angle of triangle ABD. As a result, we can use the fact that the sum of a triangle's angles equals 180 degrees to calculate the value of this angle.

We currently have:

Green arc angle + 70° + 56° = 180°

We get the following by substituting the value we found for the green arc angle:

54° + 70° + 56° = 180°

We can simplify this equation as follows:

180° - 70° - 56° = 54°

As a result, the angle indicated by a green arc has the value:

It is 54 degrees outside.

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The correct equation relating the volume of mulch purchased (v) and the total cost of the purchase (c) is: c = 33v + 720

The total cost formula is used to combine the variable and fixed costs of providing goods to determine a total.

The cost of the mulch depends on the volume purchased, so the equation relating the volume of mulch purchased (v) and the cost of the purchase (c) is:

c = 33v

The cost for 5 yards of edge material is $60, so the cost for 60 yards of edge material is:

60/5 x 60 = $720

Therefore, the total cost of the purchase is the sum of the cost of the mulch and the cost of the edge material:

total cost = cost of mulch + cost of edge material

c = 33v + 720

So the correct equation relating the volume of mulch purchased (v) and the total cost of the purchase (c) is: c = 33v + 720

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1. The longest side is side 2 (4√5). 2. a² = 50, b² = 80, c² = 12.

3. Since a² + b² < c², the triangle is obtuse.

An obtuse triangle is a triangle with one angle greater than 90 degrees.

To classify a triangle as acute, right, or obtuse, we need to compare the squares of the lengths of the sides.

In this case, a² = 50, b² = 80, and c² = 12.

If a² + b² < c², the triangle is obtuse.

If a² + b² = c², the triangle is right.

And if a² + b² > c², the triangle is acute.

In this triangle, a² + b² = 50 + 80 = 130, which is less than c² = 12. Therefore, the triangle is obtuse. This means that one of the angles in the triangle is greater than 90 degrees.

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Mr. Allen's annual salary in the year 2007 was $90,000.

Given that, mr. Allen has a wife and three children. His monthly salary during the year 2007 was $7500.

To calculate Mr. Allen's annual salary, we need to multiply his monthly salary by the number of months in a year:

Annual salary = Monthly salary × Number of months in a year

Since Mr. Allen's monthly salary in 2007 was $7500 and there are 12 months in a year, his annual salary can be calculated as:

Annual salary = Monthly salary × Number of months in a year

Annual salary = $7500 × 12 months

Annual salary = $90,000

Therefore, his annual salary was $90,000.

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Answer:60

Step-by-step explanation:

30x2=60

The radius of the Earth's orbit around the sun is approximately 93 million miles.

To calculate the circumference of the Earth's orbit, we can use the formula:

C = 2πr

where C is the circumference and r is the radius. Plugging in the value for the radius, we get:

C = 2π(93,000,000) = 584,336,000 miles

So the Earth travels approximately 584,336,000 miles in one orbit around the sun.

The speed of the Earth in its orbit around the sun can be calculated using the formula:

v = 2πr/T

where v is the velocity, r is the radius, and T is the period (the time it takes for the Earth to complete one orbit). The period of the Earth's orbit is approximately 365.25 days, or 31,557,600 seconds.

Plugging in the values, we get:

v = 2π(93,000,000)/(31,557,600) = 29,784 miles per hour

So the Earth travels at approximately 29,784 miles per hour in its orbit around the sun.

The amount after 10 years will be obtained by continuous compounding is $2443.1.

The formula for the continuous compounding:

A = P[tex]e^{rt}[/tex]

A = amount after compounding.

P = principal $2000

r = rate of interest 2%

t = time 10 years

Then,

A = 2000* [tex]2.72^{0.02*10}[/tex]

A = 2000* 1.22155

A = 2443.1

Thus, the amount after 10 years will be obtained by continuous compounding is $2443.1.

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The number of runners who are expected to finish the race, given the probability of finishing and the number who registered is 1, 375 runners.

The probability of a runner finishing the race is 11/12. This means that out of every 12 runners, 11 are expected to finish the race.

We know that 11 out of 12 runners are expected to finish the race, so we can write:

11/12 = x/1,500

11 × 1,500 = 12 × x

16,500 = 12x

x ≈ 1,375

Therefore, approximately 1375 runners are expected to finish the race out of 1500 runners.

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As a result, the experimental probability of landing on heads is 48%, probability which means that we should expect heads approximately 48 times out of 100 coin flips.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.

The following formula can be used to calculate the relative frequency or experimental probability of landing on heads:

Number of Heads / Total Number of Flips = Experimental Probability of Heads

The number of heads in this case is 48, and the total number of flips is 100. Therefore,

Heads Experimental Probability = 48 / 100 = 0.48

We can multiply this by 100 to get a percentage:

Heads Experimental Probability = 0.48 * 100 = 48%

As a result, the experimental probability of landing on heads is 48%, which means that we should expect heads approximately 48 times out of 100 coin flips.

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Answer:

2.83333 pounds of flour in each container