The graph of the function f(x) = sin(x) is shown. What is the domain of the function?

Payton leaves to go on an 85 minute bike ride at 3:27 p.m. Payton's family eat dinner 5:45 p.m.

r-ruslan [8.4K]

Answer:

2 hours and 18 minutes

Step-by-step explanation:

3 0

3 years ago

The triangles below are similar. Find x.

Anni [7]

Answer: 105

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so

$\frac{x}{14}=\frac{97.5}{13}\\\\=\frac{x}{14}=7.5\\\\x=\boxed{105}$

8 0

2 years ago

I don't know how to do this?

miskamm [114]

Do you know foil? FOIL= First,Outside,Inside, and Last

7 0

3 years ago

Read 2 more answers

The article "Monte Carlo Simulation—Tool for Better Understanding of LRFD" (J. Structural Engr., 1993: 1586–1599) suggests that

Sedaia [141]

Answer:

a) $P(X$

And we can find this probability using the normal standard distribution or excel and we got:

$P(z$

b) $P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)$

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

$P(z>3.78)=1-P(Z$

c) $z=0.674$

And if we solve for a we got

$a=43 +0.674*4.5=46.033$

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(43,4.5)$

Where $\mu=43$ and $\sigma=4.5$

Part a

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard distribution or excel and we got:

$P(z$

Part b

$P(X>40)=P(\frac{X-\mu}{\sigma}>\frac{60-\mu}{\sigma})=P(Z>\frac{60-43}{4.5})=P(z>3.78)$

And we can find this probability using the complement rule and normal standard distribution or excel and we got:

$P(z>3.78)=1-P(Z$

Part c

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674$

And if we solve for a we got

$a=43 +0.674*4.5=46.033$

So the value of height that separates the bottom 75% of data from the top 25% is 46.033.

8 0

3 years ago

Can someone help. “At the market you can buy 5 bags of apples for $23.60. At the orchard you can get 7 bags of apples for $32.76

labwork [276]

Answer:

7 for $32.76

Step-by-step explanation:

23.60/5 is $4.72

32.76/7 is $4.68

6 0

3 years ago

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