Evaluate: 8x6 + (12-4) divided by 2

Answers

Answer 1

Answer: It’s is 28 I will explain how to do it first times 8x6 then subtract 12 and 4 and the two numbers u get add them and then divide it by 2

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The daily high temperature in Chicago for the month of August is approximately normal with mean 78 degrees F, and standard deviation 9 degrees F. a. What is the probability that a randomly selected day in August will have a high temperature greater than the mean daily high temperature of 78 degrees F?
b. What is the percentile for a day in August with a high temperature of 75 degrees F?
c. What is the 75th percentile for the daily high temperature for the month of August?
d. What is the interquartile range for the daily high temperature for the month of August?

Answers

Answer:

a) $P(X>78) = P(Z> (78-78)/(9)) = P(Z>0)= 0.5$

b) $P(X<75)= P(Z< (75-78)/(9)) = P(Z<-0.333) = 0.370$

So then 75 F correspond to approximately the 37 percentile

c) $z=0.674<(a-78)/(9)$

And if we solve for a we got

$a=78 +0.674*9=84.07$

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

d) $IQR = 84.07-71.93= 12.14$

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:

$X \sim N(78,9)$

Where $\mu=78$ and $\sigma=9$

We are interested on this probability

$P(X>78)$

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

$z=(x-\mu)/(\sigma)$

Using the z score we got:

$P(X>78) = P(Z> (78-78)/(9)) = P(Z>0)= 0.5$

Part b

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

$P(X<75)$

If we use the z score formula we got:

$P(X<75)= P(Z< (75-78)/(9)) = P(Z<-0.333) = 0.370$

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:

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

$P(X<a)=0.75$ (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:

$P(X<a)=P((X-\mu)/(\sigma)<(a-\mu)/(\sigma))=0.75$

$P(z<(a-\mu)/(\sigma))=0.75$

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

$z=0.674<(a-78)/(9)$

And if we solve for a we got

$a=78 +0.674*9=84.07$

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 $IQR = Q_3 - Q_1 = P_(75)-P_(25)$

So then we just need to find the percentile 25.

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

$P(X<a)=0.75$ (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:

$P(X<a)=P((X-\mu)/(\sigma)<(a-\mu)/(\sigma))=0.25$

$P(z<(a-\mu)/(\sigma))=0.25$

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

$z=-0.674<(a-78)/(9)$

And if we solve for a we got

$a=78 -0.674*9=71.93$

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:

$IQR = 84.07-71.93= 12.14$

Write the ratio in fractional notation in lowest terms. 28 inches to 42 inches

Answers

28 to 42 means 28/42

We now reduce 28/42 to lowest terms.

28 ÷ 7 = 4

42 ÷ 7 = 6

We now have 4/6.

We now reduce 4/6.

4 ÷ 2 = 2

6 ÷ 2 = 3

Final answer: 2/3

The quadratic function f(x) has a vertex at (9, 8) and opens upward. If g(x) = 4(x − 8)2 + 9, which statement is true?A.
The maximum value of f(x) is greater than the maximum value of g(x).
B.
The maximum value of g(x) is greater than the maximum value of f(x).
C.
The minimum value of f(x) is greater than the minimum value of g(x).
D.
The minimum value of g(x) is greater than the minimum value of f(x).

Answers

ANSWER

D.
The minimum value of g(x) is greater than the minimum value of f(x).

EXPLANATION

It was given that;

$f(x)$
has a vertex at

$(9,8)$

and opens upwards.

This means that f(x) is a minimum graph and hence have a minimum value of 8.

Also ,

$g(x) = 4 {(x - 8)}^(2) + 9$

When we compare this function to

$y = a {(x - h)}^(2) + k$

We can see that,a=4, h=8 and y=9.

The vertex is

$(8,9)$

Since a>0, the graph opens upwards.

The graph has a minimum point which is (8,9) and hence the minimum value is 9.

We can see that, the minimum value of g(x) is greater than the minimum value of f(x).

Therefore the correct answer is D.

On Wednesday, a local hamburger shop sold a combined total of 360 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Wednesday?

Answers

Answer:

120

Step-by-step explanation:

360 combined, 2/3 is cheese, so 1/3 is hamburger, 1/3 of 360 is 120.

What is the solution of the system of equations: -2x+8y=-8 and 5x-8y=20 using elimination

Answers

Answer:

x = 4 and y = 0

Step-by-step explanation:

Given expression:

-2x + 8y = -8

5x - 8y = 20

Now, to solve this problem by elimination, follow this procedure:

-2x + 8y = -8 --- i

5x - 8y = 20 --- ii

Coefficient of y in both expression have similar values;

Now, add equation i and ii;

(-2x + 5x) + (8y -8y ) = -8 + 20

3x = 12

Divide both sides by 3;

x = $(12)/(3)$ = 4

Now, to find y; put x = 4 into equation i,

-2(4) + 8y = -8

-8 + 8y = -8

Add +8 to both sides of the expression;

-8 + 8 + 8y = -8 + 8

8y = 0

y = 0

A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =