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3 years ago

State whether -4^-2 and (-4)^-2 represent the same quantity

Mathematics

1 answer:

timofeeve [1]3 years ago

3 0

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, "x^-2" just means "x2, but underneath, as in 1/x^2.

-4^-2 means the power -2 is only applied to 4 and not the negative sign. -4^-2 = -(4^-2), which is equal to -1/16.

Whereas, (-4)^-2 means the power -2 affects on both negative sign and 4. For example, (-4)^2 is equal to (-4 * -4) which is just 16. Moving on, with (-4)^-2 equals to 1/(-4*-4) = 1/16.

//Hope this helps.

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If a hose is filling a swimming pool at a rate of 20 liters per minute, how long will it take to fill the 3,600-gallon pool?

Cloud [144]

Answer: the correct answer is 11 hours, 21 seconds and 3738 fractions of a second.

Step-by-step explanation:

An American gallon has 3.78541 liters.

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We will need 681.3738 minutes to fill the pool since 13,627.46 liters divided by 20 liters per minute = 681.3738 minutes

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3 years ago

How to find the slope and y intercept from two coordinate pairs

aivan3 [116]

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2 years ago

Read 2 more answers

Use the table at the right.<br> a. What is the approximate volume of the small truck?

irina [24]

Volume of the small truck = 554.54 cubic ft

Solution:

Given data:

Length of the small truck = $11\frac{1}{13}$ ft

Width of the small truck = $7\frac{5}{12}$ ft

Height of the small truck = $6\frac{3}{4}$ ft

Volume of the small truck = length × width × height

$$=11\frac{1}{13}\times7\frac{5}{12}\times 6\frac{3}{4}$

Let us change the mixed fraction into improper fraction.

$$=\frac{11\times 13 + 1}{13}\times\frac{7 \times 12 + 5}{12}\times \frac{6 \times 4 + 3}{4}$

$$=\frac{144}{13}\times\frac{89}{12}\times \frac{27}{4}$

$$=\frac{7209}{13}$

= 554. 54 cubic ft

Volume of the small truck = 554.54 cubic ft

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3 years ago

2. A marketing firm is trying to estimate the proportion of potential car buyers that would consider

Maurinko [17]

Answer:

a. The number of people that should be in the pilot study are 600 people

b. The point estimate is 0.62 $\overline 6$

c. At 95% confidence level the true population proportion of potential car buyers of hybrid vehicle is between the confidence interval (0.588, 0.6654)

d. Two ways to reduce the margin of error are;

1) Reduce the confidence interval

2) Use a larger sample size

Step-by-step explanation:

a. The given parameters for the estimation of sample size is given as follows;

The margin of error for the confidence interval, E = 4% = 0.04

The confidence level = 95%

The sample size formula for a proportion as obtained from an online source is given as follows;

$n = \dfrac{Z^2 \times P \times (1 - P)}{E^2}$

Where, P is the estimated proportions of the desired statistic, therefore, we have for a new study, P = 0.5;

Z = The level of confidence at 95% = 1.96

n + The sample size

Therefore, we have;

$n = \dfrac{1.96^2 \times 0.5 \times (1 - 0.5)}{0.04^2} = 600.25$

Therefore, the number of people that should be in the pilot study in order to meet this goal at 95% confidence level is n = 600 people

b. The point estimate for the population proportion is the sample proportion given as follows;

$\hat p = \dfrac{x}{n}$

Where;

x = The number of the statistic in the sample

n = The sample size

From the question, we have;

The number of potential car buyers, n = 600

The number of respondent in the sample that indicated that they would consider purchasing a hybrid, x = 376

Therefore, the point estimate, for the proportion of potential car buyers that would consider buying a hybrid vehicle, $\hat p$ = 376/600 = 0.62 $\overline 6$