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luda_lava [24]
3 years ago
11

12x⁴y²divided by 3x³y to the 5 th power....Please help me out....

Mathematics
1 answer:
ki77a [65]3 years ago
5 0
To divide the expression we proceed as follows:
12x⁴y²÷3x³y⁵
=12x⁴y²/3x³y⁵
=(12÷3)×(x⁴÷x³)×(y²÷y⁵)
when you divide number with the same base, you subtract the numerators:
=4×(x⁴⁻³)×(y²⁻⁵)
simplifying this we get
=4xy⁻³
Answer: 4xy⁻³

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Mike runs for the president of the student government and is interested to know whether the proportion of the student body in fa
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Answer:

We conclude that the proportion of student body in favor of him is significantly less than or equal to 50%.

Step-by-step explanation:

We are given that Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent.

A random sample of 100 students was taken. Fifty-five of them favored Mike.

<em>Let p = </em><u><em>proportion of the students who are in favor of Mike.</em></u>

So, Null Hypothesis, H_0 : p \leq 50%      {means that the proportion of student body in favor of him is significantly less than or equal to 50%}

Alternate Hypothesis, H_A : p > 50%      {means that the proportion of student body in favor of him is significantly more than 50%}

The test statistics that would be used here <u>One-sample z proportion</u> <u>statistics</u>;

                        T.S. =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of students body in favor of Mike = \frac{55}{100} = 0.55

           n = sample of students taken = 100

So, <em><u>test statistics</u></em>  =   \frac{0.55-0.50}{\sqrt{\frac{0.55(1-0.55)}{100} } }

                               =  1.01

The value of z test statistics is 1.01.

<em>Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.</em>

<em>Since our test statistic is less than the critical value of z as 1.01 < 1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><u><em>we fail to reject our null hypothesis</em></u><em>.</em>

Therefore, we conclude that the proportion of student body in favor of him is significantly less than or equal to 50% or proportion of the students in favor of Mike is not significantly greater than 50 percent.

4 0
3 years ago
Use the net to find the surface area of the rectangular prism.
Komok [63]

Answer:

220

Step-by-step explanation:

The surface area is  given by

SA = 2 ( lw+wh+lh)  where  l is length h is height and w is width

SA = 2(3*4 + 3*14+ 4*14)

     = 2(12+42+56)

    = 2(110)

    = 220

3 0
3 years ago
What is the simplified form of 0.2 to the fifth power?
Tanya [424]

Answer:

0.32

Step-by-step explanation:

0.2 to the fifth power is 0.00032, so that simplified is 0.32.

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2 years ago
Read 2 more answers
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You start at (-1, 2). You move right 5 units and down 6 units. Where do you end?
Irina-Kira [14]

Answer:

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Step-by-step explanation:

Just plot it or like I did it like this

Since moving right or left is X axis, just add 5 to -1 becuase its ont he X axis

Then for the bottom and up, thats Y so subtract  that to the Y axis so 2-6=-4

4,-4

5 0
3 years ago
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