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4 years ago

Evaluate the exponent: 4^-3

1 answer:

3 0

An negative exponent or power, means that the number elevated to that negative power is one divided by that number raised to the positive same power, that is:

x^-n = 1/x^n
n being a positive number. So in this case we have:
4^-3 = 1/4^3
= 1/(4*4*4)
= 1/64

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ladessa [460]

Answer: 15?

Step-by-step explanation:

6 0

3 years ago

Use the zero product property to find the solutions to the equation x^2 + x -30=12

Alla [95]

Answer:

The solutions are x = -7, 6.

Step-by-step explanation:

To find the solutions, move everything to one side of the equation so the equation is equal to 0. Then factor. Set the factors equal to 0 and solve for x.

$x^2 + x - 30 = 12\\x^2 + x -42=0\\(x+7)(x-6) = 0$

x+7 = 0

x = -7

and

x-6 = 0

x = 6

The solutions are x = -7, 6.

6 0

3 years ago

Read 2 more answers

Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining wh

Molodets [167]

Answer:

(A) The mean for the differences is 2.0.

(B) The test statistic is 1.617.

(C) At 90% confidence the null hypothesis should not be rejected.

Step-by-step explanation:

We are given that a random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.

The following data (in miles per gallon) show the results of the test;

Driver Manufacturer A Manufacturer B

1 32 28

2 27 22

3 26 27

4 26 24

5 25 24

6 29 25

7 31 28

8 25 27

Let $\mu_1$ = mean MPG for the fuel efficiency of Manufacturer A brand

$\mu_2$ = mean MPG for the fuel efficiency of Manufacturer B brand

SO, Null Hypothesis, $H_0$ : $\mu_1-\mu_2=0$ or $\mu_1= \mu_2$ {means that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles}

Alternate Hypothesis, $H_A$ : $\mu_1-\mu_2\neq 0$ or $\mu_1\neq \mu_2$ {means that there is a significant difference in the mean MPG (miles per gallon) for the fuel efficiency of these two brands of automobiles}

The test statistics that will be used here is Two-sample t test statistics as we don't know about the population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t__n__1+_n__2-2$

where, $\bar X_1$ = sample mean MPG for manufacturer A = $\frac{\sum X_A}{n_A}$ = 27.625

$\bar X_2$ = sample mean MPG for manufacturer B = $\frac{\sum X_B}{n_B}$ = 25.625

$s_1$ = sample standard deviation for manufacturer A = $\sqrt{\frac{\sum (X_A-\bar X_A)^{2} }{n_A-1} }$ = 2.72

$s_2$ = sample standard deviation manufacturer B = $\sqrt{\frac{\sum (X_B-\bar X_B)^{2} }{n_B-1} }$ = 2.20

$n_1$ = sample of cars selected from manufacturer A = 8

$n_2$ = sample of cars selected from manufacturer B = 8

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(8-1)\times 2.72^{2}+(8-1)\times 2.20^{2} }{8+8-2} }$ = 2.474

(A) The mean for the differences is = 27.625 - 25.625 = 2

(B) The test statistics = $\frac{(27.625-25.625)-(0)}{2.474 \times \sqrt{\frac{1}{8}+\frac{1}{8} } }$ ~ $t_1_4$

= 1.617

(C) Now at 10% significance level, the t table gives critical values between -1.761 and 1.761 at 14 degree of freedom for two-tailed test. Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.

5 0

4 years ago

If your friend Doug is on a balcony and asks you to throw him a donut, how many stories up can he be and you would still feel co

Katena32 [7]

The building that I would imagine would be 40 stories, about 404 feet tall perhaps. If he were to throw the donut from that distance until the ground, catching it would be impossible. So no, I am not confident in catching the donut all the way there.

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3 years ago

B=1/4af solve for a if u could answer this as fast as possible that would be great

liq [111]

Answer:

b/(1/4)(f)=a

Step-by-step explanation:

b=1/4af

b/(1/4)(f)=a

6 0

3 years ago

Read 2 more answers