The time it takes a customer service complaint to be settled at a small department store is normally distributed with a mean of 10 minutes and a standard deviation of 3 minutes. Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.

Answer:

a) Their average weight is of 187 pounds.

b) 0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c) 0.002 = 0.2% probability that the maximum safe weight will be exceeded

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?

8228/44 = 187

Their average weight is of 187 pounds.

b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For men, we have that [tex]\mu = 186, \sigma = 60[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{60}{\sqrt{44}}[/tex]

This probability is 1 subtracted by the p-value of Z when X = 187. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{187 - 186}{\frac{60}{\sqrt{44}}}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

1 - 0.5438 = 0.4562

0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For women, we have that [tex]\mu = 157, \sigma = 69[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{69}{\sqrt{44}}[/tex]

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{187 - 157}{\frac{69}{\sqrt{44}}}[/tex]

[tex]Z = 2.88[/tex]

[tex]Z = 2.88[/tex] has a p-value of 0.998.

1 - 0.998 = 0.002.

0.002 = 0.2% probability that the maximum safe weight will be exceeded

Answer:

The point-slope form is y - 2 = 1/2 (x - 3)

Step-by-step explanation:

The point-slope form is y - y1 = m (slope) (x - x1). All I did was plug the numbers in the correct locations to get my answer.

Answer:

20%

Step-by-step explanation:

The total number of students is: 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 (students)

The probability is: 6/30 = 1/5 = 0.2 = 20%

The probability that the student is a male given that he's a sophomore is approximately 60%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The probability that the student is a male given that it's a sophomore can be calculated using the formula:

P(male | sophomore) = P(male and sophomore) / P(sophomore)

The number of male sophomores is 6, and the total number of sophomores is 6+4=10.

So, the probability of selecting a sophomore is:

P(sophomore)

= (number of sophomores) / (total number of students)

= 10 / 23

The number of male sophomores is 6.

So,

The probability of selecting a male sophomore is:

P(male and sophomore) = 6 / 23

Therefore,

The probability that the student is a male given that it's a sophomore is:

P(male | sophomore)

= (6 / 23) / (10 / 23)

= 6 / 10

= 3 / 5

Rounding to the nearest whole percent, we get:

P(male | sophomore) ≈ 60%

Thus,

The probability that the student is a male given that he's a sophomore is approximately 60%.

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Answer:

x = 5

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

2(x + 8) = 26

Step 2: Solve for x

Answer:

first question is D

second question is D .875

Step-by-step explanation:

35*2.5= 87.5

7 divided by 8= .875

Answer:

D   87.5 miles

D  0.875 = 7/8 so it is a decimal that terminates after 3 dp.

Step-by-step explanation:

We write;

Scale Inch x Miles

2.5 x 35 = 87.5 miles

Why??

87.5 miles is found when we use the scale of 35 miles = 1inch

Answer = D 87.5 miles

The second one we can either multiply by 7/8 or divide by 1-7/8 = 1/8 to show that;

1/ 1/8 = 0.125

1-0.125 = 0.875  

Answer:

(11.847 ; 15.813)

Step-by-step explanation:

We are given 12 samples which are :

8, 20, 20, 11, 18, 12, 6, 5, 7, 22, 12, 25

We use a T-distribution to find the confidence interval since the sample size. is small, n < 30

Using a calculator :

The sample mean, xbar = 13.83

Sample standard deviation, s = 6.87

The confidence interval, C.I

C.I = xbar ± Tcritical * s/√n)

Tcritical at 95%, df = n - 1, 12 - 1 = 11

Tcritical(0.05, 11) = 2.20

Hence,

C.I = 13.83 ± 2.20(6.87/√12)

C.I = 13.83 ± 1.9831981

C. I = (13.83 - 1.983 ; 13.83 + 1.983)

C. I = (11.847 ; 15.813)

Answer:

Step-by-step explanation:

Part A

The x-intercept are the values of the variable "x" for which the value of the function, f(x) is zero (f(x) = 0)

The given parameters are;

The values of the function, f(x) = The company's profit

The values of the independent variable, "x" = The price of erasers

Therefore, at the x-intercept, where the values of the variable "x" are 0 and 8, the profit of the company, (f(x)) is 0 (the company does not make any profit)

2) The maximum value, which is the highest point of the graph with coordinate (4, 270), gives the company's maximum profit, f(x) = $270, and the price of the eraser, x-value, at which the company makes maximum profit which is at the price of an eraser, x = $4

3) The intervals where the function is increasing is 0 ≤ x ≤ 4

At the interval where the function is increasing, the sale price is increasing and the profits are increasing

The intervals where the function is decreasing is 4 ≤ x ≤ 8

At the interval where the function is decreasing, the sale price is increasing and the profits are decreasing

Part B

The appropriate average rate of change of the graph from x = 1 to x = 4 where f(x) = 120 and 270 respectively is given as follows

Rate of change of the graph from x = 1 to x = 4 is (270 -120)/(4 - 1) = 50

The average rate of change of the graph represents that the as the price of the eraser increases by $1.00 the profits increases by $50.00

THIS WAS NOT MY OWN ANSWER, PLEASE LET oeerivona TAKE THE POINTS!!

Answer:

Matthew travels 0.0161 meters per second.

Step-by-step explanation:

Given that Matthew travels 42/50 meters In 26/30 minutes, to find the speed of Mathew in meters per second the following calculation must be performed:

42/50 = 0.84

26/30 = 0.86

0.86 x 60 = 52

0.84 meters in 52 seconds

0.84 / 52 = 0.01615

Therefore, Matthew travels 0.0161 meters per second.

Answer:

Area = 72.62 m²

Step-by-step explanation:

Area of a triangle with the given three sides is given by,

Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Here, s = [tex]\frac{a+b+c}{2}[/tex]

And a, b, c are the sides of the triangle.

From the question,

a = 20 m, b = 10 m and c = 15 m

s = [tex]\frac{20+10+15}{2}[/tex]

s = 22.5

Substitute these values in the formula,

Area = [tex]\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)}[/tex]

        = [tex]\sqrt{22.5(2.5)(12.5)(7.5)}[/tex]

        = [tex]\sqrt{5273.4375}[/tex]

        = 72.62 m²

Answer:

(52.30 ; 52.62)

Step-by-step explanation:

Given :

Sample size, n = 20

Mean, xbar = 52.46

Standard deviation, s = 0.42

We assume a t - distribution

The 90% confidence interval

The confidence interval relation :

C.I = xbar ± Tcritical * s/√n

To obtain the Tcritical value :

Degree of freedom, df = n - 1 ; 20 - 1 = 19 ; α = (1 - 0.90) /2 = 0.1/2 = 0.05

Using the T-distribution table, Tcritical = 1.729

We now have :

C.I = 52.46 ± (1.729 * 0.42/√20)

C. I = 52.46 ± 0.1624

C.I = (52.30 ; 52.62)

9514 1404 393

Answer:

  x = 64°

  y = 26°

Step-by-step explanation:

Angle x and 26° together make a right angle, so ...

  x = 90° -26° = 64°

Angles x and y together make a right angle, so ...

  y = 90° -(90° -26°) = 26°

Answer:

The volume of water is 396 cubic meter.

Step-by-step explanation:

Area of water, A = 132000 square meter

Height, h = 3 mm = 0.003 m

The volume of water is given by

V = Area x height

V = 132000 x 0.003

V = 396 cubic meter.

Following are the responses to the given points:

For point a:

[tex]Diameter\ (d)= 16\ m\\\\[/tex]

Calculating the 3 rotations for every minute:

Calculating time for completing 1 rotation:

[tex]1\ rotation=\frac{60}{3}= 20\ second\\\\period=20 \ second\\\\[/tex]

The standard form of the equation of the sine and cosine function is:

[tex]y=A \sin \{ B(x-c)\} +D\\\\y=A \cos \{ B(x-c)\} +D\\\\[/tex]

Calculating the Amplitue:

[tex]A=\frac{max-min}{2}=\frac{17-1}{2}=\frac{16}{2}=8\\\\Period=\frac{2\pi}{B}\\\\20=\frac{2\pi}{B}\\\\B=\frac{2\pi}{20}\\\\B=\frac{\pi}{10}\\\\[/tex]

Calculating the phase shift:

for [tex]\sin[/tex] function: [tex]c=5[/tex]

for [tex]\cos[/tex] function: [tex]c=10[/tex]

Calculating the vertical shift:

[tex]\to D=\frac{max+ min }{2}=\frac{17+ 1}{2}=\frac{18}{2}=9\\\\y=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\y=8 \cos \{ \frac{\pi}{10}(t-10)\} +9\\\\[/tex]

For point b:

[tex]y> 12\ m\\\\12=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\12-9=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\3=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\\frac{3}{8}=\sin \{ \frac{\pi}{10}(t-5)\} \\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (0.38439677)=(t-5) \\\\1.22357+5=t \\\\t=6.22357\ second\\\\t=6.22\ second\\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (2.7571961)=(t-5) \\\\t=8.7764+5\\\\t=13.78\ second\\\\t_2-t_1=13.7764-6.22357= 7.55283\approx 7.55\ second \\\\[/tex]

Learn more:

Rotation: brainly.in/question/39626227

Look at one side of the triangle. It forms a right triangle with 45 degree angles.

A 45 degree triangle the base and height are the same, so the height would also be 26.

The hypotenuse(x) of a 45 degree right triangle is the side length time the sqrt(2)

The answer is: 26 sqrt(2)

Answer:

option B

Step-by-step explanation:

option B

gdyfudjfjghfhguftduc

Answer:

1)a

the problem asks"what PERCENT of 5 is 4?"

2)part

it gives both the percent and the whole, so your left with the part

3)Whole

4 is a part which is 80%

Step-by-step explanation:

Answer:

$11.22

Step-by-step explanation:

100% = 187

1% = 187/100 = $1.87

6% = 1%×6 = 1.87×6 = $11.22

Answer:

In this case, you need to calculate the 6% of the price, which is 187 $.

We only need to multiply the price (187) by the percentage (6%):

187 * 0.06 = 11.22

So the tax would be $11.22

Answer:

5x^2(2-3x)

(n+4)(x+y)

Step-by-step explanation:

Answer:

25 cheeseburger

Step-by-step explanation:

I checked and get that 4 times fries as many as salad means that fries = 4 times Salad.

Brainliest please~

25 cheeseburgers were sold.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

Let cheeseburger be x

Price of x = 6

Let French Fries be y

Price of y = 3

Let salads be z

Price of z=8

x+ y+ z =220

6x + 3y + 8z = 1070

4 y = z     4 times as many as

= 4 times  - Fries is more than Salad

Substitute 3 in 1

x + 4 z + z =220

x+5z =220

Substitute 3 in 2

6x + 12z +8z = 1070

6x + 20z = 1070

3x + 10z - 535

From 4: x=220-5z

Substitute into 3 (220-5z) +10z = 535

660 - 15z+10z=535

- 5z = - 125

z = 25

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9514 1404 393

Answer:

  (b)  112.2 ft

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

For the given geometry, this becomes ...

  tan(65°) = (height above eye level)/(50 ft)

Then we have ...

  (height above eye level) = (50 ft)tan(65°) = 107.2 ft

Adding the height of eye level will give us the height of the building.

  building height = (eye level height) + (height above eye level)

  building height = (5 ft) + (107.2 ft)

  building height = 112.2 ft

Answer:

answer is 3 and ratio of two different numbers

Answer:

= 14w + 6

Step-by-step explanation:

= 12w + 2w + 6

Add similar elements: 12w + 2w = 14w

= 14w + 6

Answer:

Hope this will help.

Answer:

a=12-6b

Step-by-step explanation:

move b and a to their respective sides, getting a = -6b+12

tada :)

As per linear equation, the value of 'a' in terms of 'b' will be

a = 12 - 6b.

A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.

Given, (3a + 4b) = (a - 8b + 24)

⇒ 3a - a = - 8b + 24 - 4b

⇒ 2a = - 12b + 24

⇒ a = (- 12b + 24)/2

⇒ a = - 6b + 12

⇒ a = 12 - 6b

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Any linear equation can be written as

y = mx+b

where m is the slope and b is the y intercept

m = 1/2 in this case. It represents the idea that the snow fell at a rate of 1/2 inch per hour. In other words, the snow level went up 1/2 an inch each time an hour passed by.

b = 8 is the y intercept. It's the starting amount of snow. We start off with 8 inches of snow already.

The info "snow fell for 9 hours" doesn't appear to be relevant here.

9514 1404 393

Answer:

Step-by-step explanation:

The place value of a digit to the right of the decimal point is 10 to the negative power of the digit count. The 1st digit right of the decimal point has a place value of 10^-1.

Here, the most significant digit of 0.000000016 is in the 8th place to the right of the decimal point, so its place value is 10^-8.

  0.000000016 = 1.6×10^-8

Another way to write the same number is 1.6E-8. (The "E" is a stand-in for ×10^.)

_____

Your (graphing or scientific) calculator or a spreadsheet can display this in scientific notation for you.

__

That many nanoseconds, as this problem states, would be 1.6×10^-17 seconds. "Nano" is an SI prefix meaning 10^-9.

Answer:

The critical value for the 90% confidence interval is [tex]Z_c = 1.645[/tex].

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The critical value for the 90% confidence interval is [tex]Z_c = 1.645[/tex].

Answer:

4 cm by 5 cm (4 x 5)

Step-by-step explanation:

The area of a rectangle with length [tex]l[/tex] and width [tex]w[/tex] is given by [tex]A=lw[/tex]. Since the length of the rectangle is 7 less than 3 times its width, we can write the length as [tex]3w-7[/tex]. Therefore, substitute [tex]l=3w-7[/tex] into [tex]A=lw[/tex]:

[tex]A=lw,\\20=(3w-7)w[/tex]

Distribute:

[tex]20=3w^2-7w[/tex]

Subtract 20 from both sides:

[tex]3w^2-7w-20=0[/tex]

Factor:

[tex](w-4)(3w+5)=0,\\\begin{cases}w-4=0, w=\boxed{4},\\3w+5=0, 3w=-5, w=\boxed{-\frac{5}{3}}\end{cases}[/tex]

Since [tex]w=-\frac{5}{3}[/tex] is extraneous (our dimensions cannot be negative), our answer is [tex]w=4[/tex]. Thus, the length must be [tex]20=4l, l=\frac{20}{4}=\boxed{5}[/tex] and the dimension of the rectangle are 4 cm by 5 cm (4 x 5).

Answer: