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3 years ago

Why is everything 1 when raised to the 0th power?

Mathematics

2 answers:

Nitella [24]3 years ago

5 0

Answer:

Step-by-step explanation:

Use the laws of exponents, specifically the law for division.

When dividing, the exponents are subtracted.

For example, $\frac{x^{8} }{x^{2} }=x^{8-2} =x^{6}$

Now let's do an example where the exponent will equal zero.

$\frac{5^{2} }{5^{2} } = 5^{2-2}=5^0=1$

Now let's see why this equals 1. If you actually solve $5^2$ it equals 25. So, let's solve the numerator and denominator and simplify.

$\frac{5^{2} }{5^{2} } = \frac{25}{25} =1$

As you can see, an exponent of 0 represents having the same number in the numerator and denominator, which when solved it equals 1.

olga_2 [115]3 years ago

3 0

Yeah dang i have no idea. great question tho

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The area of miguels rectangular garden is 450 square feet. The garden is 9 feet wide. How many feet of fencing will Miguel need

sattari [20]

Answer: 118 feet

Step-by-step explanation:

For a rectangular shape: Area = W × L

450 = 9 × L

450 ÷ 9

L = 50

Perimeter of a rectangular shape = 2L + 2W

Perimeter = (2 × 50) + (2 × 9)

= 100 + 18 = 118 feet

4 0

3 years ago

Thirty-seven percent of all Americans drink bottled water more than once a week (Natural resources Defense Council, December 4,

lesantik [10]

Answer:

a) The sampling distribution for n=540 has a mean sample proportion of p=0.37 and a standard deviation of σs=0.0208.

b) probability = 0.99998

d) probability = 0.99874

e) You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

Step-by-step explanation:

a) We have a known population proportion π=0.37 and we have to describe the sampling distribution when the sample size is n=540.

The mean sample proportion is expected to be the same as the population proportion:

$\bar p = \pi = 0.37$

The standard deviation of the sampling will be the population standard deviation divided by the square root of the sample size:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{540}}=\sqrt{0.000431667}=0.0208$

Then, we can say that the sampling distribution will have a p=0.37 and a standard deviation σs=0.0208.

b) We have to calculate the probability that the sample proportion will be within 0.09 of the population proportion.

We can calculate the z-value as:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0208}=4.3269\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0208}=-4.3269$

As the distribution is symmetrical, we can calculate the probabilty that he sample proportion will be within 0.09 of the population proportion as:

$P(|p-\bar p|$

probability = 0.99998

d. Now the sample is smaller (n=300), so the standard deviation of the samping distribution:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{300}}=\sqrt{0.000777}=0.0279$

We have to recalculate the z-scores:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0279}=3.2258\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0279}=-3.2258$

And the probability is:

$P(|p-\bar p|$

probability = 0.99874

e. The increase in sample size is 80%

$\Delta n\%=\dfrac{n_1}{n_2}-1=\dfrac{540}{300}-1=1.8-1=0.8=80\%$

and the increase in probability is 0.12%

$\Delta P\%=\dfrac{P_1}{P_2}-1=\dfrac{0.99998}{0.99874}-1=1.0012-1=0.0012=0.12\%$

You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

7 0

3 years ago

1) What percent of 153.9 is 150?

BaLLatris [955]

Answer:

It would be 1.026

Step-by-step explanation:

When you are doing percents, you usually divide. So 153.9 divded by 150 would give you 1.026.

5 0

3 years ago

Read 2 more answers

I need a word problem that has a negative - positive

AleksandrR [38]

Answer:

Here it is

Step-by-step explanation:

You are 58 dollars in debt, and your friend pays you 73 dollars. How much money do you have? Does that work for you?

8 0

3 years ago

3 tomatoes cost $1.29<br><br> How much will 5 tomatoes<br> cost?

wolverine [178]

Answer:

$2.15

Step-by-step explanation:

Since 3 Tomatoes cost $1.29

Then let's first find how much is 1 Tomatoes.

To do that we have to divide Cost by # of Tomatoes

3/1.29 = 0.43

Thus, 1 Tomatoes Cost 0.43

Now, the question is: How much will 5 tomatoes cost?

Therefore, 0.43 * 5 =2.15

Hence, 5 Tomatoes cost $2.15

[RevyBreeze]

6 0

3 years ago