Write the equation of each line in slope-intercept form.
(If possible please show work)

Answer:

a)

b)

So then 75 F correspond to approximately the 37 percentile

c)

And if we solve for a we got

So the value of height that separates the bottom 75% of data from the top 25% is 84.07 F.  

d)

See explanation below.

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".  

Part a

Let X the random variable that represent the daily high temperature in Chicago for the month of August of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

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

Using the z score we got:

Part b

For this case we can find the percentile with the following probability:

If we use the z score formula we got:

So then 75 F correspond to approximately the 37 percentile

Part c

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

  (a)

  (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:

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

And if we solve for a we got

So the value of height that separates the bottom 75% of data from the top 25% is 84.07 F.  

Part d

For this case we know that

So then we just need to find the percentile 25.

  (a)

  (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 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

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

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

And if we solve for a we got

So the value of height that separates the bottom 25% of data from the top 75% is 71.93 F.  

So then the interquartile range would be:

Answer:

P(X≥11) = 0.1648

Step-by-step explanation:

Given

Mean, μ = 7.3

Potholes, n = 11

The interpretation of the question is to calculate P(X ≥ 11)

It is known that

P(X) = P(1) + P(2) +.......+P(infinite)

We can say that

P(X) = P(X≤10) + P(X>10)

Make P(X>10) the subject of formula

P(X>10) = P(X) - P(X≤10)

P(X>10) is equivalent to P(X≥11) and P(X) = 1.

By substituton, we have

P(X≥11) = 1 - P(X≤10)

So, we'll solve P(X≤10) using the following steps using n as 10.

To solve the above question using Microsoft Office Excel, follow the highlighted steps below

1. First goto FORMULAS tan

2. Select INSERT FUNCTION.

3. Select the POISSON.DIST function.

4. Enter the values for the number of events and the mean of occurrences per interval. In this case, enter 10 and 7.8, in that order and 1 for Cumulative since this is a cumulative probability.

5. Press OK.

Excel would display the probability.

In this case, it is 0.83523

Remember that

P(X≥11) = 1 - P(X≤10)

By substituton

P(X≥11) = 1 - 0.83523

P(X≥11) = 0.16477

Approximately,

P(X≥11) = 0.1648

(See attachment)

Answer:

421906

is 421910 to the nearest hundred thousand

Answer:

D. (2, -3/4)

Step-by-step explanation:

Using the substitution method:

-5x+4(1/8x-1)=-13

-5x+0.5x-4=-13

-4.5x/4.5=-9/4.5

-x=-2

x=2

You are supposed to replace 2 in the first equation now but as there is no other option with x value of 2 D is the answer.

If continued:

-5(2)+4y=-13

-10+4y=-13

4y=-3

y=-3/4

Answer:

The first graph , y=x³ is a cubic function graph and that of the second graph, y = 3(x – 4)3 + 7 is a linear graph.

Step-by-step explanation:

The graph of y=x³ is a cubic function graph where the x term has the highest power of x as 3. As attached in the first graph.

The second graph for y = 3(x – 4)3 + 7. is a linear graph that can be written as;

y=(3x-12)3 +7

y=9x-36 + 7

y=9x - 29

which is a linear graph with a slope of 9 and cuts the y-axis at -29 as shown in the second attached graph.

Final answer:

The student correctly solved the equations given for x. Note that an equation with an unknown variable squared might have two solutions. The way to solve for x alters according to what the equation requires, whether it is adding, subtracting, or dividing.

Explanation:

It seems like the student is trying to solve equations for x. The equations given were all solved correctly. Keep in mind that when an equation contains an unknown variable squared, there could be two solutions, and one or both could be reasonable depending on the problem. For example, consider the equation x² +0.0211x -0.0211 = 0. This could be rearranged to solve for x. Other variables are known unless additional calculations needed if they are not.

Remember that the principle of altering the equation to solve for x is employed, whether we add, subtract or divide by certain values. Like mentioned in the information provided, when dividing by powers of 10, you would move the decimal to the left, corresponding to the number of zeros in the power of ten.

Learn more about Solving for x here:

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