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3 years ago

Why do whole numbers raised to an exponent get bigger while fractions raised to an exponent get smaller

Mathematics

1 answer:

Brilliant_brown [7]3 years ago

5 0

Answer:

when you multiply a whole number by itself it will obviously get bigger.

4 to the 2nd power equals 16 because 4x4 = 16

if you were to multiply a smaller number though, it wouldn't get as big.

Each number you put to the same exponent will not get bigger at the same rate since each number isnt being multiplied by the same thing.

ex. 4 and 6 are raised to the second power both dont get multiplied by the same number 4 is multiplied by 4, and 6 by 6, therefore the bigger the number the bigger it grows.

Fractions get smaller for this reason when you have the fraction 2/3 raised to the second, both numbers must be raised. 2 to the second equals 4 while 3 to the second is 9.

1/2 to the second would then equal 1/4 since 1 to the second equals 1 and 2 to the second equals 4.

Step-by-step explanation:

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The parent function of the function g(x) = (x – h)2 + k is f(x) = x2. The vertex of the function g(x) is located

Katen [24]

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Answer:

(h, k) = (9, -8)

Step-by-step explanation:

The function g(x) is "vertex form" for a quadratic whose vertex is (h, k). We are told the vertex is (9, -8), so we have ...

(h, k) = (9, -8) . . . . the values of h and k

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3 years ago

An automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry ou

Katyanochek1 [597]

Answer:

$t=\frac{29.35-30}{\frac{1.365}{\sqrt{6}}}=-1.17$

$p_v =P(t_{(5)}$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We can say that at 5% of significance the true mean is not significantly less than 30 so then the claim that true average fuel efficiency is (at least) 30 mpg makes sense

Step-by-step explanation:

Data given and notation

The mean and sample deviation can be calculated from the following formulas:

$\bar X =\frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)}{n-1}}$

$\bar X=29.35$ represent the sample mean

$s=1.365$ represent the sample standard deviation

$n=6$ sample size

$\mu_o =30$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is lower than 30 or no, the system of hypothesis are :

Null hypothesis: $\mu \geq 30$

Alternative hypothesis: $\mu < 30$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{29.35-30}{\frac{1.365}{\sqrt{6}}}=-1.17$

P-value

We need to calculate the degrees of freedom first given by:

$df=n-1=6-1=5$

Since is a one-side left tailed test the p value would given by:

$p_v =P(t_{(5)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We can say that at 5% of significance the true mean is not significantly less than 30 so then the claim that true average fuel efficiency is (at least) 30 mpg makes sense

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3 years ago

What's the digit in the tenths place

Darya [45]

Tenths is the digit in the tenths place. Like 0.1 being 1 tenth.

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3 years ago

How many edgès does the figure have?

lbvjy [14]

Depending on the shape