Margaret said the exact product of 602 and 341 is 205,282. Is she correct? Use paper and the standard algorithm to support your reasoning.

Answers

Answer 1

Answer:

Answer:

Yes, she is. The exact product of 602 and 341 is 205,282.

Step-by-step explanation:

To determine the exact product of 602 and 341, both numbers must be multiplied, obtaining the result. To do this, said number can be decomposed, to facilitate the operation and to be able to corroborate the accuracy of the result.

So, we can multiply 602 by 300, plus 602 by 40 and 602 by 1, and add the results.

Therefore, since 602 times 300 is equal to 180,600 (602 x 300 = 180,600); that 602 times 40 is equal to 24,080 (602 x 40 = 24,080); and since 602 times 1 is equal to 602, all those values must be added.

So 180,600 plus 24,080 equals 204,680. And in turn, 204,680 plus 602 equals 205,282. Therefore, the proposed result is correct.

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"The municipal transportation authority determined that 58% of all drivers were speeding along a busy street. In an attempt to reduce this percentage, the city put up electronic speed monitors so that drivers would be warned if they were driving over the speed limit. A follow-up study is now planned to see if the speed monitors were effective. The null and alternative hypotheses of the test are H0 : π = 0.58 versus Ha : π < 0.58. It is planned to use a sample of 150 drivers taken at random times of the week and the test will be conducted at the 5% significance level. (a) What is the most number of drivers in the sample that can be speeding and still have them conclude that the alternative hypothesis is true? (b) Suppose the true value of π is 0.52. What is the power of the test? (c) How could the researchers modify the test in order to increase its power without increasing the probability of a Type I Error?"

Answers

Answer:

a) X=77 drivers

b) Power of the test = 0.404

c) Increasing the sample size.

Step-by-step explanation:

This is a hypothesis test of proportions. As the claim is that the speed monitors were effective in reducing the speeding, this is a left-tail test.

For a left-tail test at a 5% significance level, we have a critical value of z that is zc=-1.645. This value is the limit of the rejection region. That means that if the test statistic z is smaller than zc=-1.645, the null hypothesis is rejected.

The proportion that would have a test statistic equal to this critical value can be expressed as:

$p_c=\pi+z_c\cdot\sigma_p$

The standard error of the proportion is:

$\sigma_p=\sqrt{(\pi(1-\pi))/(n)}=\sqrt{(0.58*0.42)/(150)}\n\n\n \sigma_p=√(0.001624)=0.04$

Then, the proportion is:

$p_c=\pi+z_c\cdot\sigma_p=0.58-1.645*0.04=0.58-0.0658=0.5142$

This proportion, with a sample size of n=150, correspond to

$x=n\cdot p=150\cdot0.5142=77.13\approx 77$

The power of the test is the probability of correctly rejecting the null hypothesis.

The true proportion is 0.52, but we don't know at the time of the test, so the critical value to make a decision about rejecting the null hypothesis is still zc=-1.645 corresponding to a critical proportion of 0.51.

Then, we can say that the probability of rejecting the null hypothesis is still the probability of getting a sample of size n=150 with a proportion of 0.51 or smaller, but within a population with a proportion of 0.52.

The standard error has to be re-calculated for the new true proportion:

$\sigma_p=\sqrt{(\pi(1-\pi))/(n)}=\sqrt{(0.52*0.48)/(150)}\n\n\n \sigma_p=√(0.001664)=0.041$

Then, we calculate the z-value for this proportion with the true proportion:

$z=(p-\pi')/(\sigma_p)=(0.51-0.52)/(0.041)=(-0.01)/(0.041)=-0.244$

The probability of getting a sample of size n=150 with a proportion of 0.51 or lower is:

$P(p<0.51)=P(z<-0.244)=0.404$

Then, the power of the test is β=0.404.

The only variable left to change in the test in order to increase the power of the test is the sample size, as the significance level can not be changed (it is related to the probability of a Type I error).

It the sample size is increased, the standard error of the proprotion decreases. As the standard error tends to zero, the critical proportion tend to 0.58, as we can see in its equation:

$\lim_(\sigma_p \to 0) p_c=\pi+ \lim_(\sigma_p \to 0)(z_c\cdot\sigma_p)=\pi=0.58$

Then, if the critical proportion increases, the z-score increases, and also the probability of rejecting the null hypothesis.

(2 - (- 2)²)² +5 · ( -4)

Answers

Answer:

-164

Step-by-step explanation:

(2 - (- 2)²)² +5 · ( -4)

(2 + 2²) ² +5 · ( -4)

(2 + 2 + 2)² +5 · ( -4)

6² +5 · ( -4)

6 · 6 + 5 · -4

36 + 5 · -4

41 · -4

-164

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths. Base 1 1/2 feet, altitude 6 inches. Area = sq. ft. ...?

Answers

area of a parallelogram = A =base*height

so in this case is just (1½)(6).

first off let's convert the mixed fraction to "improper",

$\bf \stackrel{mixed}{1(1)/(2)}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}} \n\n\n \cfrac{3}{2}\cdot 6\implies \cfrac{18}{2}\implies 9$

Answer:

3/4 sq. ft.

Step-by-step explanation:

The question is using feet and inches. So, you'd have to convert the 6 inches to feet. How many inches in one foot? 6. So 6=1/2 feet so you do 1 1/2*1/2=3/4

PLEASE HELP I DONT UNDERSTAND

Answers

Answer:

y=20x+25, this equation is linear, the rate of change is constant

Step-by-step explanation:

She starts with 25$, that doesn't change so its our constant. Let x represent each week. Each week she ears 20$

So, let y represent the total amount of money she has

y=20x+25, this equation is linear, the rate of change is constant

the answer is y=20x+25

I do have a time limit. I appreciate any helpIf YB = ZA find the value of X and the length of YB

Answers

Since ZA and YB are equal in length and the two lines are parallel to each other.

Also, we can see that YZ and AB are perpendicular to both ZA and YB, thus

YZ = AB

16x - 4 = 4 - 4x

16x + 4x = 4 + 4

20x = 8

x= 8/20 = 2/5

YB = ZA = 20x - 5 = 20(2/5) - 5 = 3

Thus, the value of x is 2/5 and length of YB is 3 units.

So, the correct answer is option A

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Answers

Answer:

Step-by-step explanation:

Hope it helps

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