What are the value too F(-3)= F(-1)= F(3)=

John has four more apples than Kim. Kim has three times as many apples than Rob. Altogether, they have 46 apples. How many apple

Anika [276]

Answer:

Step-by-step explanation:

j=k+4

k=3r

j=3r+4

j+k+r=46

3r+4+3r+r=46

7r+4=46

7r=42

r=6, since k=3r

k=18, since j=k+4

j=22

j,k,r=22,18,6

5 0

3 years ago

Joann is looking at a map. The map shows that two towns are 13.5 inches apart. If the scale factor for the map is 1.25 inch = 10

k0ka [10]

Answer:

biotbhuvb2tupbpu2

Step-by-step explanation:

6 0

3 years ago

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.9 minutes and a standard deviation of 2.9

Eva8 [605]

Answer:

a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes

c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

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 $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

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

Mean of 8.9 minutes and a standard deviation of 2.9 minutes.

This means that $\mu = 8.9, \sigma = 2.9$

Sample of 37:

This means that $n = 37, s = \frac{2.9}{\sqrt{37}}$

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?

320/37 = 8.64865

Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}$

$Z = -0.53$

$Z = -0.53$ has a p-value of 0.2981

0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?

275/37 = 7.4324

Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}$

$Z = -3.08$

$Z = -3.08$ has a p-value of 0.001

1 - 0.001 = 0.999

0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?

Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So

0.2981 - 0.0010 = 0.2971

0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

7 0

3 years ago

Hey plsss help meeeeee

nalin [4]

Answer:

The first, third, and fourth answer choices represent a function.

Step-by-step explanation:

A relation is a relationship between sets of values. The two quantities that are being related to each other are the input (x-variable) and the output (y-variable). But relations in general aren't always a good way to relate between x and y.

Say that I have situation where I want to give x dollars to the cashier so he can change them to y quarters. Here is a "example" of the relation:

Dollars (x) | Quarters (y)

----------------------------------

0 | 0

1 | 4

2 | 8

2 | 12

Do you see something wrong here? Yes! We all know that you can't exchange 2 dollars for 12 quarters. You can only exchange 2 dollars for 8 quarters and only 8 quarters. This is a general reason why we don't rely on general relations for real-life situations. One x-variable does not exactly map to one and only one y-variable.

However, a relation that can map one x-variable to one and only one y-variable is known as a function. Let's make the above example an actual function to prove a point:

Dollars (x) | Quarters (y)

----------------------------------

0 | 0

1 | 4

2 | 8

3 | 12

Now, the 3 dollars make 12 quarters as it should. This is how a function should look like.

There are two ways to check if a relation is a function. On a relation, table, or a set of ordered pairs, you have to make sure there is no "x-variable" that repeats. All x-values of a relation have to be unique in order to be a function. On a graph, you can also perform the Vertical Line Test. If you draw vertical lines over a relation and if the lines cross only once, then it is a function. If not, it fails the Vertical Line Test.

So to answer you're question, the first, third, and fourth choices are functions because they all have unique x-variables. The second choice is not a function because it fails the Vertical Line Test.

7 0

3 years ago

A square has an area of 49 cm^2

crimeas [40]

To find area you need to multiply
length x width

Since 49 can be square rooted it equals seven

L x W = Area
Area = 7 x 7
Area = 49

Meaning since it’s a square the perimeter is
7 by 7 by 7 by 7 in other words 7 + 7 + 7 + 7 OR 7 x 4(equal sides)

4 0

3 years ago