How to get my answer

ANTONII [103]

C, Reflection across Y = X

7 0

3 years ago

Dave drives to work each morning at about the same time. His commute time is normally distributed with a mean of 35 minutes and

IgorLugansk [536]

Answer:

The percentage of time that his commute time is less than 44 minutes is equal to the area under the standard normal curve that lies to the left of 1.8.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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, or the area of the normal curve to the left of Z. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, or the area of the normal curve to the right of Z.

In this problem, we have that:

$\mu = 35, \sigma = 5$

Less than 44 minutes.

Area to the left of Z when X = 44. So

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

$Z = \frac{44 - 35}{5}$

$Z = 1.8$

So the answer is:

The percentage of time that his commute time is less than 44 minutes is equal to the area under the standard normal curve that lies to the left of 1.8.

7 0

2 years ago

(-4)^2=

Lunna [17]

Answer:

16

Step-by-step explanation:

raise -4 to the power of 2

=16

6 0

2 years ago

Read 2 more answers

F(x)=-3x • G(x) = x +7

kirill [66]

Answer:

-3x^2 - 21x

Step-by-step explanation:

This question is representing multiplying two functions :

We are finding f(x) * g(x)

We know that f(x) is -3x and g(x) is x + 7, therefore :

(-3x)(x + 7)

Follow FOIL :

First :

(-3x)(x)

-3x^2

Outer :

(-3x)(7)

-21x

Therefore the answer is :

-3x^2 - 21x

7 0

3 years ago

A deck of cards with four suits; hearts, diamonds, spades, and clubs. you pick one card, put it back and thennpick another card.

Llana [10]

1. First, let us find the probability that the first card is a diamond.

Now, since we are given that there are four suits and there are, assumably, an equal number of cards in each suit, we can say that the probability of choosing a diamond card is 1/4. We can also write this out as such, where D = Diamond:

Pr(D) = no. of diamond cards / total number of cards

There are 52 cards in a deck, and 13 cards of each suit, thus:

Pr(D) = 13/52 = 1/4

2. Now we need to calculate the probability of not choosing a diamond as the second card.

In many cases, when given a problem that requires you to find the probability of something not happening, it may be easier to set it out as such:

Pr(A') = 1 - Pr(A)

ie. Pr(A not happening, or not A) = 1 - Pr(A happening, or A)

This works because the total probability is always 1 (100%), and it makes sense that to find the probability of A not happening, we take the total probability and subtract the probability of A actually happening.

Thus, given that we have already calculated that the probability of choosing a Diamond is 1/4, we can now set this out as such:

Pr(D') = 1 - Pr(D)

Pr(D') = 1 - 1/4

Pr(D') = 3/4

3. Now we come to the final step. To find the probability of something and then something else happening, we must multiply the two probabilities together. Thus, given that Pr(D) = 1/4 and Pr(D') = 3/4, we get:

Pr(D)*Pr(D') = (1/4)*(3/4)

= 3/16

Thus, the probability of choosing a diamond as the first card and then not choosing a diamond as the second card is 3/16.

7 0

3 years ago