Supposed that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in the tank. When carrying 14 gallons of fuel the airplane weighs 2177 pounds when carrying 42 gallons of fuel it weighs 2331 pounds. How much does the airplane weigh if it is carrying 48 gallons of fuel?

Answer:

a) The mean is 18 and the standard deviation is 1.79.

b) The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.

c) 0.2005 = 20.05% probability that a sample of 20 students has a mean score of 19.5 or more.

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 estabilishes 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.

Mean of 18 and a standard deviation of 8.

This means that [tex]\mu = 18, \sigma = 8[/tex]

Sample of 20:

This means that [tex]n = 20, s = \frac{8}{\sqrt{20}} = 1.79[/tex]

(a) Calculate the mean and standard deviation of the sampling distribution of x¯.

By the Central Limit Theorem, the mean is 18 and the standard deviation is 1.79.

(b) Interpret the standard deviation from part (a).

The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.

(c) Find the probability that a sample of 20 students has a mean score of 19.5 or more.

This is 1 subtracted by the pvalue of Z when X = 19.5. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{19.5 - 18}{1.79}[/tex]

[tex]Z = 0.84[/tex]

[tex]Z = 0.84[/tex] has a pvalue of 0.7995

1 - 0.7995 = 0.2005

0.2005 = 20.05% probability that a sample of 20 students has a mean score of 19.5 or more.

Answer:

Step-by-step explanation:

use pythagoras theorem

a squared +b squared =c squared

4.12 squared +8 squared =x squared

16.9744+64=x squared

take the square root of 80.9744

x=9

Answer:

C

Step-by-step explanation:

y=2x-1 your welcome I need to put more characters so skdjdnnn

Answer:

Y=2x-1

Step-by-step explanation:

the three data sets all work for y=2x-1

-7=-6-1

-7=-7

or

-1=0-1

-1=-1

or

3=4-1

3=3

Answer:

I believe it would be 4 seconds

Step-by-step explanation:

PLATO/Edmentum

The time it takes for the friend in the left seat to move upward, downward, and then back to the initial position is 4 seconds.

A function assigns the value of each element of one set to the other specific element of another set.

Two friends are sitting on a seesaw at the park. The height, h(t), of the left seat, in inches above the ground, is modeled by a sine function.

Let t represent the time, in seconds, since the friends started seesawing.

The friends start seesawing with the plank in a level position. The initial position at 0 of them is at 24.

The group has to come back to this position after moving upward and downward. The time it takes to reach upward is,

[tex]f(48)=t_{up}\\f(48)=1[/tex]

The time it takes to reach downward after going upward is,

[tex]f(0)=t_{down}\\f(0)=3[/tex]

Coming back to initial potion,

[tex]f(24)=t_{i}\\f(24)=4[/tex]

Thus, the time it takes for the friend in the left seat to move upward, downward, and then back to the initial position is 4 seconds.

Learn more about Function here:

https://brainly.com/question/5245372

#SPJ2

9514 1404 393

Answer:

  11.1

Step-by-step explanation:

The tangent makes a right angle with the diameter at the point of tangency. So, the triangle is a right triangle, and the Pythagorean theorem can be used to find the length of x. The radius is shown as 7.1, so the diameter will be 14.2.

  x^2 + 14.2^2 = 18^2

  x^2 = 122.36

  x = √122.36 ≈ 11.1

The length of the tangent is about 11.1 units.

Answer:

c = 9.2m is the answer.

Step-by-step explanation:

a = 6m

b = 7m

c = ?

According to the Pythagoras theorem,

a² + b² = c²

6² + 7² = c²

36 + 49 = c²

c² = 85

c = 9.2m

∴ the distance between the school and the candy store is 9.2m

Answer:

C. 4x + x < 150

Step-by-step explanation:

x = Joey's points

4x = Liz's Points

together they have fewer than 150 points means the inequality is < 150

So the answer is:  4x + x < 150

Answer:

This may help you I think so

Answer:

the answer is 1.5 x 10-2 that's what I got

Answer:

Step-by-step explanation:

Sin(35) =  opposite / hypotenuse

Sin(35) = 4 / hypotenuse                  Multiply both sides by the hypotenuse

hypotenuse * sin(35) = 4                  Divide by Sin(35)

hypotenuse = 4/Sin(35)

Sin(35) = 0.5736

hypotenuse = 4/0.5736

hypotenuse = 6.9737

Rounded answer 6.97

Answer:

4035 grams

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Well its a incomplete Question but i am solving a realted type Question .

• Find the slope of the line -3x - 4y = 12 :-

Ans ) The given equation can be converted into Slope intercept form , which is y = mx + c , where ,

⇒ -3x -4y = 12

⇒ -4y = 12 +3x

⇒ y = 3x + 12 /4

⇒ y = 3/4x + 12/3

⇒ y = ¾x + 4

⇒ m = ¾

⇒ c = 4

Answer:

Option (3)

Step-by-step explanation:

Given sequence is,

8, -8, 8,...........

Ratio of the 2nd and 1st term = [tex]\frac{-8}{8}[/tex]

                                                = -1

Ratio of 3rd and 2nd term = [tex]\frac{8}{-8}[/tex]

                                           = -1

Therefore, there is a common ratio 'r' = (-1)

And the sequence is a geometric sequence.

Explicit formula for the nth term of a geometric sequence is given by,

[tex]T_n=a(r)^{n-1}[/tex]

Here, 'a' = First term of the sequence

r = Common ratio

n = nth term

For the given sequence xth term of the sequence will be,

[tex]T_x=8(-1)^{x-1}[/tex]

Option (3) will be the answer.

Answer: are cylinders similar to what its not asking so id.kkk

Step-by-step explanation:

Answer:

t = 22[tex]\frac{2}{3}[/tex]

2t = 45[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

3t = 68

t = 68/3

Answer:

6 inches

Step-by-step explanation:

If 3 blocks equals 2 inches, then we must first find out how many times 3 can fit into 9. We do this by dividing 9 by 3 to get 3. To get your final answer just multiply 2 by 3 and you will get 6 inchs. I hope this helped :0

Answer:

I think C

Step-by-step explanation:

sorry if I'm wrong

D i answered this one on khan.

Answer:

The 2 rays the form ACB ARE AC and CB

Answer:

The absolute value is 5 1/6

Step-by-step explanation:

The absolute value is how far away an answer is to zero so we just take away the negative for this question.

Answer:

All terms separated by 6 so #20 = 4 + 6 * 19 = 118

(if the first term were 6 instead of 4 the 20th would be 120)

Also, #10 = 58 and #11 = 64   (you can use the same reasoning)

The 1st and 20th term add to 4 + 118 = 122

The 2nd and 19th add to 10 + 112 = 122

Likewise 10th and 11th add to 58 + 64 = 122

So 10 * 122 = 1220

Answer:

D- The blackcaps will begin nesting at their wintering sites in Spain or the United Kingdom, resulting in a larger blackcap population migrating back to Germany after the breeding season has ended.

Step-by-step explanation:

By the inhabitants of Spain and the United Kingdom placing feeders out for the blackcaps, the birds in their nesting sites during the winter will have food to eat, meaning a bigger population of the Blackcaps when they return to their main home in Germany.

This best predicts the effect on the blackcap population if humans in the United Kingdom continue to place food in feeders during the winter.

Answer:

Step-by-step explanation:

The slope of the line is 4/3.

The value of y when x = 0 is -7.

Equation of line:

y = (4/3)x - 7

Answer:

B

Step-by-step explanation:

By using the fraction strip, if you think about it:

Pretend to color in 5/6 on the yellow side, and do the same to the 1/12 part, instead pretend to shade in 5/12. If you see how much remaining you have, you get 5/12.

H⁣⁣⁣⁣ere's l⁣⁣⁣ink t⁣⁣⁣o t⁣⁣⁣he a⁣⁣⁣nswer:

bit.[tex]^{}[/tex]ly/3a8Nt8n

Answer:

12) F.0

13) 3/2

Step-by-step explanation:

12)

(5, 0) and (10, 0)

Slope:

m=(y2-y1)/(x2-x1)

m=(0-0)/(10-5)

m = 0

13)

(3, 2) and (-1, -4)

Slope:

m=(y2-y1)/(x2-x1)

m=(-4-2)/(-1-3)

m=(-6)/(-4)

m= 3/2

Polygon: "a plane figure with at least three straight sides and angles, and typically five or more."

1. P

2. NP

3. P

4. NP

5. P

"A planar polygon is convex if it contains all the line segments connecting any pair of its points."

1. C

2. NC

3. NC

4. C

5. NC