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Iteru [2.4K]
3 years ago
12

Factor: 462 - 12b + 9

Mathematics
1 answer:
IrinaVladis [17]3 years ago
6 0

Answer:3(154-4b+3)

Step-by-step explanation:462/3=154.  -12b/3=-4b.   9/3=3

3(154-4b=3)

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Simplify (6x^-2)^2 (0.5x)^4 Show your work<br> PLEASE HELP THANK YOU!
goldenfox [79]

Use Multiplication Distribute Property: (xy)^a = x^ay^a

6^2(x^-2)^2(0.5x)^4

Simplify 6^2 to 36

36(x^-2)^2(0.5x)^4

Use this rule: (x^a)^b = x^ab

36x^-4(0.5x)^4

Use the Negative Power Rule: x^-a = 1/x^a

36 × 1/x^4(0.5x)^4

Use the Multiplication Distributive Property: (xy)^a = x^ay^a

36 × 1/x^4 × 0.5^4x^4

Simplify 0.5^4 to 0.0625

36 × 1/x^4 × 0.0625x^4

Simplify

2.25x^4/x^4

Cancel x^4

<u>2.25</u>

6 0
3 years ago
A local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle. In o
Mandarinka [93]

Answer:

(a) Null Hypothesis, H_0 : \mu = 22 ounces  

    Alternate Hypothesis, H_A : \mu\neq 22 ounces

(b) The value of the test statistic is -2.687.

(c) The critical values are -1.96 and 1.96.

(d) We conclude that Reject H_0 since the value of the test statistic is less than the negative critical value.

Step-by-step explanation:

We are given that a local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle.

He takes a random sample of 65 bottles. The mean weight of the passion fruit juice in the sample is 21.54 ounces. Assume that the population standard deviation is 1.38 ounce.

<em>Let </em>\mu<em> = average ounces of passion fruit juice used to fill each bottle.</em>

(a) So, Null Hypothesis, H_0 : \mu = 22 ounces     {means that the average of 22 ounces of passion fruit juice is used to fill each bottle}

Alternate Hypothesis, H_A : \mu\neq 22 ounces     {means that the average different from 22 ounces of passion fruit juice is used to fill each bottle}

The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;

                        T.S. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean weight of the passion fruit juice = 21.54 ounces

            \sigma = population standard deviation = 1.38 ounce

            n = sample of bottles = 65

So, <u><em>test statistics</em></u>  =  \frac{21.54-22}{\frac{1.38}{\sqrt{65} } }  

                               =  -2.687

(b) The value of z test statistics is -2.687.

(c) Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

<em>Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><u><em>we reject our null hypothesis</em></u><em>.</em>

Therefore, we conclude that Reject H_0 since the value of the test statistic is less than the negative critical value which means that the average different from 22 ounces of passion fruit juice is used to fill each bottle.

6 0
3 years ago
the city of brice is planning to build a skate park. An architect designed the area shown at the right. in the plan, the perimet
Amiraneli [1.4K]

The actual skate park's perimeter is 130 inches.

Explanation:

Step 1; Assume the initial garden has a width of y inches. It is given that the length is 25 inches. The perimeter of any given rectangle is twice the sum of the length and the width of the same rectangle. The initial perimeter is given as 80 inches.

Perimeter = 2 × (length of the rectange + width of the rectangle).

80 = 2 × (25 + y), 40 = 25 + y, y = 40 - 25 = 15

So the initial park has a width of 15 inches.

Step 2; Now we calculate the actual skate park's perimeter. The length is given as 50 inches and the width was found to be 15 inches.

Perimeter = 2 × (length of the rectange + width of the rectangle).

Perimeter = 2 × (50 + 15) = 2 × 65 = 130 inches.

5 0
3 years ago
Can someone answer this question please I need it right now
Lady bird [3.3K]

Answer: Choice B) -5.2 degrees

=====================

Work Shown:

Add up the given temperatures

-42 + (-17) + 14 + (-4) + 23 = -26

Then divide by 5 since there are 5 values we're given

-26/5 = -5.2

6 0
3 years ago
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scZoUnD [109]
<h3>Answer: B) 30</h3>

Any amount of rotation will not change the angle between the two spokes. This is because each piece of the wheel moves in unison as the rotation is applied. Nothing changes about the wheel. Imagine instead of rotating the wheel, we instead rotated the camera that is capturing the wheel (or the person looking at the wheel rotates their head). This is a good way to see how the wheel itself isn't changing at all, but instead rather just the look of it is changing.

5 0
2 years ago
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