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stiv31 [10]
3 years ago
11

How do you do an exponent in parentheses to another exponent outside of it

Mathematics
2 answers:
guajiro [1.7K]3 years ago
6 0
To multiply exponential<span> terms with the same base, </span>add<span> the </span>exponents<span>. An </span>exponent<span>applies only to the value to its immediate left. When a quantity in </span>parentheses<span> is raised to a power, the </span>exponent<span> applies to everything inside the </span>parentheses<span>. Simplify the expression, keeping the answer in </span>exponential<span> notation.</span>
Anestetic [448]3 years ago
5 0
If the exponent is like this (x^2)^2 then you multiply the exponents. If it's like this (x^2) (x^2) then just add the exponents
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The diameters of bearings used in an aircraft landing gear assembly have a standard deviation of ???? = 0.0020 cm. A random samp
vovikov84 [41]

Answer:

(a) We conclude after testing that mean diameter is 8.2500 cm.

(b) P-value of test = 2 x 0.0005% = 1 x 10^{-5} .

(c) 95% confidence interval on the mean diameter = [8.2525 , 8.2545]

Step-by-step explanation:

We are given with the population standard deviation, \sigma = 0.0020 cm

Sample Mean, Xbar = 8.2535 cm   and Sample size, n = 15

(a) Let Null Hypothesis, H_0 : Mean Diameter, \mu = 8.2500 cm

 Alternate Hypothesis, H_1 : Mean Diameter,\mu \neq 8.2500 cm{Given two sided}

So, Test Statistics for testing this hypothesis is given by;

                           \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } follows Standard Normal distribution

After putting each value, Test Statistics = \frac{8.2535-8.2500}{\frac{0.0020}{\sqrt{15} } } = 6.778

Now we are given with the level of significance of 5% and at this level of significance our z score has a value of 1.96 as it is two sided alternative.

<em>Since our test statistics does not lie in the rejection region{value smaller than 1.96} as 6.778>1.96 so we have sufficient evidence to accept null hypothesis and conclude that the mean diameter is 8.2500 cm.</em>

(b) P-value is the exact % where test statistics lie.

For calculating P-value , our test statistics has a value of 6.778

So, P(Z > 6.778) = Since in the Z table the highest value for test statistics is given as 4.4172  and our test statistics has value higher than this so we conclude that P - value is smaller than 2 x 0.0005% { Here 2 is multiplied with the % value of 4.4172 because of two sided alternative hypothesis}

Hence P-value of test = 2 x 0.0005% = 1 x 10^{-5} .

(c) For constructing Two-sided confidence interval we know that:

    Probability(-1.96 < N(0,1) < 1.96) = 0.95 { This indicates that at 5% level of significance our Z score will lie between area of -1.96 to 1.96.

P(-1.96 <  \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P(-1.96\frac{\sigma}{\sqrt{n} } < Xbar - \mu < 1.96\frac{\sigma}{\sqrt{n} } ) = 0.95

P(-Xbar-1.96\frac{\sigma}{\sqrt{n} } < -\mu < 1.96\frac{\sigma}{\sqrt{n} }-Xbar ) = 0.95

P(Xbar-1.96\frac{\sigma}{\sqrt{n} } < \mu < Xbar+1.96\frac{\sigma}{\sqrt{n} }) = 0.95

So, 95% confidence interval for \mu = [Xbar-1.96\frac{\sigma}{\sqrt{n} } , Xbar+1.96\frac{\sigma}{\sqrt{n} }]

                                                        = [8.2535-1.96\frac{0.0020}{\sqrt{15} } , 8.2535+1.96\frac{0.0020}{\sqrt{15} }]

                                                        = [8.2525 , 8.2545]

Here \mu = mean diameter.

Therefore, 95% two-sided confidence interval on the mean diameter

           =  [8.2525 , 8.2545] .

6 0
3 years ago
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X + 10 = 20 ?????????????????????????????????????
Phoenix [80]
X  = 20 - 10
x = 10 

Easy)
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I need help with this question please and thank you
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Answer:

y = -1x + 3 or f(x) = -1x + 3

Step-by-step explanation:

Rise/run = 3/-3 =<em> <u>-1</u></em>

Crosses the y-axis at <em><u>3</u></em>

y = <em><u>-1</u></em>x + <em><u>3</u></em> or f(x) = <em><u>-1</u></em>x + <em><u>3</u></em>

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Find the common difference of the sequence shown.
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Answer:

1/6

Step-by-step explanation:

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1) Ms. Roth has 2 black skirts and 3 gray skirts. She chooses a skirt at random on Monday, wears it, puts
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I think the answer would be ⅖

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