Bob Nale is the owner of Nale's Gas Station. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. He assumes a population standard deviation of 2.30 gallons. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold is 8.60. What is the z-statistic for a 99% confidence interval for the population mean.

Answers:

x = 7*sqrt(3)

y = 7

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Explanation:

We have a 30-60-90 triangle here since the missing acute angle is 90-60 = 30 degrees. Or you could note how 30+60+90 = 180.

The side length y is the shorter leg as it's opposite the smallest angle. It's equal to half of the hypotenuse. So y = 14/2 = 7.

The longer leg x is equal to y*sqrt(3). We multiply the shorter leg by sqrt(3) to get the longer leg. This means

x = y*sqrt(3) = 7*sqrt(3)

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You could also use the pythagorean theorem if you knew that y = 7 and you had the hypotenuse value as well. You could solve like so

a^2 + b^2 = c^2

7^2 + b^2 = 14^2

b^2 = 14^2 - 7^2

b^2 = 147

b = sqrt(147)

b = sqrt(49*3)

b = sqrt(49)*sqrt(3)

b = 7*sqrt(3)

Which matches up with the value of x we found earlier.

Answer:

15

Step-by-step explanation:

ΔRST ≈ ΔRDE

[tex]\frac{RS}{RT} =\frac{RD}{RE} \\\\\frac{35}{56} =\frac{x}{24} \\\\56x=840\\x=15[/tex]

RD = 15

Answer:

[tex]20[/tex]

Step-by-step explanation:

[tex]12[/tex]²[tex]+16[/tex]²[tex]=400.[/tex]

[tex]\sqrt{400}[/tex][tex]=20[/tex]

Answer: More than 26.5 inches

Step-by-step explanation:

Solve this equation :

[tex]\frac{32+24+x}{3} \geq 27.5[/tex]

x>26.5

Answer:

Step-by-step explanation:

1. Not a function

2. Not a Function

3. Function

Answer:

15: Yes, no, yes, yes, no; 16A: C = ($0.29)X + ($1.45)Y + ($2.50)Z; 16B: Yes

Step-by-step explanation:

For question 15: We need to multiply the widths and lengths given to see if they equal the area we are trying to achieve. Therefore, some of them work, and some do not.

For question 16:

Part A: We'll set a variable for the number of each supply she can buy. Pencils will be represented by X, pens by Y and Notebooks by Z, and we'll represent total cost by C. The total cost will therefore be represented by C = ($0.29)X + ($1.45)Y + ($2.50)Z.

Part B: We'll plug the numbers of items she wants to buy into our formula and see if it comes out to less than $20. So in this case C = ($0.29)(3) + ($1.45)(4) + ($2.50)(2). Therefore, C = $11.67, which is less than $20, so she can afford her school supplies.

Answer:

Step-by-step explanation:

first use tan Ф = opp /adj      to find x         tan(30) = √3 / 3

then use sin Ф = opp / hyp   to find y         sin(30) = 1/2

       tan(30) = (√3) / 3  =  x / 48

                           x = (48√3) / 3

                          x = 16√3

        sin(30) = 1/2  = x / y

                        y  =  x / (1/2)

                        y  =  2x        x = 16√3

                        y  =  2[16√3]

                        y  =  32√3

check  using      a² + b²  = c²

             x² + 48² = y²

            (16√3)² + 48² = (32√3)²

           256 · 3  + 2304  =  1024 · 3

           768   +  2304   =   3072

                         3072  =  3072

Answer:

it seems you have made a typo

Step-by-step explanation:

Answer:

a) The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.

b) 0.05 = 5% probability that he has four goals and two assists in one game

Step-by-step explanation:

In hockey, a point is counted for each goal or assist of the player.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval. The standard deviation is the square root of the mean.

(a) Find the mean and standard deviation for the total revenue he earns per game.

60% of six are goals, which means that 60% of the time he earned 3K.

40% of six are goals, which means that 40% of the time he earned 1K.

The mean is:

[tex]\mu = 6*0.6*3 + 6*0.4*1 = 13.2[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{\mu} = \sqrt{13.2} = 3.63[/tex]

The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.

(b) What is the probability that he has four goals and two assists in one game

Goals and assists are independent of each other, which means that we find the probability P(A) of scoring four goals, the probability P(B) of getting two assists, and multiply them.

Probability of four goals:

60% of 6 are goals, which means that:

[tex]\mu = 6*0.6 = 3.6[/tex]

The probability of scoring four goals is:

[tex]P(A) = P(X = 4) = \frac{e^{-3.6}*(3.6)^{4}}{(4)!} = 0.19122[/tex]

Probability of two assists:

40% of 2 are assists, which means that:

[tex]\mu = 6*0.4 = 2.4[/tex]

The probability of getting two assists is:

[tex]P(B) = P(X = 2) = \frac{e^{-2.4}*(2.4)^{2}}{(2)!} = 0.26127[/tex]

Probability of four goals and two assists:

[tex]P(A \cap B) = P(A)*P(B) = 0.19122*0.26127 = 0.05[/tex]

0.05 = 5% probability that he has four goals and two assists in one game

Answer:

H

Step-by-step explanation:

(5x-3) x (2x+7)

10x^2 + 35x - 6x - 21

10x^2 + 29x - 21

Answer:

B : 177

Step-by-step explanation:

hello :

put x=3.5 in the equation you have : y = 50(3.5)+2 =175+2=177

Answer: The answer is C

Step-by-step explanation:

Answer:

Step-by-step explanation:

tan(G) = 28.2/45.8

G = arctan(28.2/45.8) = 31.6°

Answer:

A

Step-by-step explanation:

B, C, D are all symmetrical

Answer:

a

Step-by-step explanation:

since B, C, D are all symmetrical it should be a

Answer:

10

Step-by-step explanation:

Answer:

where's the question???

Step-by-step explanation:

Step-by-step explanation:

Volume of cylinder=πr²h

Answer:

bro its 10

Step-by-step explanation:

5 kilometers in 30mins and if he stayed at the same rate for an hour he would have ran 10 kilometers cause 5 x 2 = 10

Answer:

the answer is 55m^2 I think

Answer:

55 is the Area

Step-by-step explanation:

4 x 10 = 40

5 x 3 = 15

15 ÷ 2 = 7.5

5 x 3 = 15

15 ÷ 2 = 7.5

7.5 + 7.5 = 15

40 + 15 = 55

Give Me Brainllest

Answer:

0.0814 = 8.14% probability that at least one of the women has a Chlamydia infection

Step-by-step explanation:

For each women, there are only two possible outcomes. Either they have a Chlamydia infection, or they do not. The probability of a woman having the infection is independent of any other women. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among U.S. women ages 20 to 24 is 2791.5 per 100,000.

This means that:

[tex]p = \frac{2791.5}{100000} = 0.027915[/tex]

Take a random sample of three U.S. women in this age group.

This means that [tex]n = 3[/tex]

What is the probability that at least one of the women has a Chlamydia infection?

This is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.027915)^{0}.(1-0.027915)^{3} = 0.9186[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9186 = 0.0814[/tex]

0.0814 = 8.14% probability that at least one of the women has a Chlamydia infection

1247.5

Hope this helps :T

Answer:

r(t)= -3/t+6

r(t)= -3/6t=6

Answer: the answer is D

Step-by-step explanation:

Just did the assignment rn

Answer:

3

Step-by-step explanation:

[tex]72[/tex]÷[tex]24=3[/tex]

Answer:

w < 9

Step-by-step explanation:

w + 9 < 18

To solve this inequality, we MUST get the w by itself

Subtraction Property of Equality  w + 9 - 9 < 18 - 9

Answer w < 9

Answer:

531 m²

Step-by-step explanation:

9x9x5=405 (5 sides that are 9x9, including the bottom)

1/2x9x7x4=126 (4 triangles on top)

405+126=531

Answer:

X = 2 If the exponent 2 in the 2 does not have the x

Step-by-step explanation: