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3 years ago

The sum of three consecutive even numbers is 96. What is the smallest of the three numbers

1 answer:

8 0

The answer is 30.

First off, the numbers are consecutive even numbers. So, the difference between every consecutive number is 2 (numbers go from even to odd to even to odd...). Since the sum of their numbers is 96, I divided that by 3 to get 32. This gives me the median of the three numbers. To find the smallest number, I simply subtracted 2 from the 32.

This may help:

96/3=32

32 + 32 + 32 = 96
(32-2)+(32+0)+(32+2)=96
30+32+34=93

You might be interested in

Evaluate to 212 base 3 - 121 base 3 + 222 base 3

aksik [14]

Answer:

212 bp^3 (base pairs cubed) - 121 bp^3 (base pairs cubed) + 222 bp^3 (base pairs cubed) = 313 bp^3 (base pairs cubed

Step-by-step explanation:

5 0

3 years ago

a math teacher claims that she has developed a review course that increases the score of students on the math portion of a colle

madam [21]

Answer:

$H_0: \mu\leq514\\\\H_1: \mu>514$

B. Z=2.255. P=0.01207.

C. Although it is not big difference, it is an improvement that has evidence. The scores are expected to be higher in average than without the review course.

D. P(z>0.94)=0.1736

Step-by-step explanation:

<em>A. state the null and alternative hypotheses.</em>

The null hypothesis states that the review course has no effect, so the scores are still the same. The alternative hypothesis states that the review course increase the score.

$H_0: \mu\leq514\\\\H_1: \mu>514$

B. test the hypothesis at the a=.10 level of confidence. is a mean math score of 520 significantly higher than 514? find the test statistic, find P-value. is the sample statistic significantly higher?

The test statistic Z can be calculated as

$Z=\frac{M-\mu}{s/\sqrt{N}} =\frac{520-514}{119/\sqrt{2000}}=\frac{6}{2.661}=2.255$

The P-value of z=2.255 is P=0.01207.

The P-value is smaller than the significance level, so the effect is significant. The null hypothesis is rejected.

Then we can conclude that the score of 520 is significantly higher than 514, in this case, specially because the big sample size.

C. do you think that a mean math score of 520 vs 514 will affect the decision of a school admissions adminstrator? in other words does the increase in the score have any practical significance?

Although it is not big difference, it is an improvement that has evidence. The scores are expected to be higher in average than without the review course.

D. test the hypothesis at the a=.10 level of confidence with n=350 students. assume that the sample mean is still 520 and the sample standard deviation is still 119. is a sample mean of 520 significantly more than 514? find test statistic, find p value, is the sample mean statisically significantly higher? what do you conclude about the impact of large samples on the p-value?

In this case, the z-value is

$Z=\frac{520-514}{s/\sqrt{n}} =\frac{6}{119/\sqrt{350}} =\frac{6}{6.36} =0.94\\\\P(z>0.94)=0.1736>\alpha$

In this case, the P-value is greater than the significance level, so there is no evidence that the review course is increasing the scores.

The sample size gives robustness to the results of the sample. A large sample is more representative of the population than a smaller sample. A little difference, as 520 from 514, but in a big sample leads to a more strong evidence of a change in the mean score.

Large samples give more extreme values of z, so P-values that are smaller and therefore tend to be smaller than the significance level.

8 0

2 years ago

Please help me with this<br><br> 10x(3xy)

sineoko [7]

Answer:

Step-by-step explanation:

10x(3xy)

10*3*x*x*y

30x²y

6 0

3 years ago

Three times x less than y is five times y plus two times x in a verbal sentence please help

tankabanditka [31]

SOLUTION:

As an equation it is:

y - 3x = 5y + 2x

If you are asking for it as a sentence ( I will do it as a written sentence as I unfortunately can't show you the sentence verbally as you had asked ), then it is as you had written in your question so:

Three times x less than y is five times y plus two times x

Or you could write is as:

y subtracted by three times x is equivalent to the sum of five times y and two times x.

Essentially, even with the small alterations that you can make to the phrasing and sentence structure, the concepts are the same so you can use one of the above answers or alter it as you please.

Hope this helps! :)

6 0

3 years ago

Using the distributive property to find the product (y – 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay – 4y

Crank

Answer:

The answer to your question is a = 16

Step-by-step explanation:

Polynomial

(y - 4) (y² + 4y + 16)

Process

1.- Multiply y by each term of the polynomial

y(y² + 4y + 16) = y³ + 4y² + 16y

2.- Multiply -4 by each term of the polynomial

-4(y² + 4y + 16) = -4y² - 16y - 64

3.- Write both results

y³ + 4y² + 16y - 4y² - 16y - 64

In bold we notice that a = 16

8 0

3 years ago