At a park, 80 out of the 200 people there are men. The rest are women. What percent of the people are women?

How to remember nagative exponents how to solve nagative exponents

marishachu [46]

To solve the negative exponents , we have to apply the negative exponent rule or the fractional exponent rule.

<h3>How are negative exponent calculated?</h3>

To calculate the negative exponent we need to remember about the negative exponent that the base is on the opposite side of the fraction. Here , We need to flip the fraction so that the base will be on the other side.

Negative exponent Rule :-

$a^{-n} = \frac{1}{a^{n} }$

Now , we will solve a fraction with negative exponent

For example ; Simplify the fraction $\frac{3^{-2} }{9^{-2} }$

Solution : $\frac{3^{-2} }{9^{-2} } = \frac{9^{2} }{3^{2} }= \frac{81}{9}$

= 9

Here, 9 is the answer of the above example.

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7 0

2 years ago

One 8.3 ounce can of Red Bull contains energy in two forms: 27 grams of sugar and 80 milligrams of caffeine. One 23.5 ounce can

bulgar [2K]

Answer:

41) 2 Red Bull and 1 Jolt Cola

42) 1 Red Bull and 3 Jolt Cola

43) 2 Red Bull and 2 Jolt Cola

44) 3 Red Bull and 4 Jolt Cola

Determine the number of cans of each drink that when combined will contain 403 grams sugar and 1200 milligrams caffeine: 1 Red Bull and 4 Jolt Cola

Step-by-step explanation:

Let X be the cans of Red Bull.

Let Y be the cans of Jolt Cola.

41)

One can of Red Bull has 27g of sugar. One can of Jolt cola has 94g of sugar. So we have the equation:

X(27)+Y(94)=148...(1)

One can of Red Bull has 80mg of caffeine. One can of Jolt cola has 280mg of caffeine. So we have the equation:

X(80)+Y(280)=440...(2)

We find the answear by solving the system of equations:

27X+94Y=148...(1)

80X+280Y=440...(2)

Solving the system:

27X+94Y=148...(1)

27X=148-94Y

X=148/27 -(94/27)Y

Substituting X in (2)

80X+280Y=440...(2)

80[148/27 -(94/27)Y]+280Y=440

(11840/27)-(7520/27)Y+280Y=440

(11840/27)+(40/27)Y=440

(40/27)Y=440-(11840/27)

(40/27)Y=40/27

Y=1

Substituting Y in (1)

27X+94Y=148...(1)

27X+94(1)=148

27X+94=148

27X=148-94

X=54/27

X=2

So we need 2 cans of Red Bull and 1 of Jolt Cola to get 148g of sugar and 440mg of caffeine.

42) Following the same steps we have:

27X+94Y=309...(1)

80X+280Y=920...(2)

Solving the system:

27X+94Y=309...(1)

27X=309-94Y

X=309/27 -(94/27)Y

Substituting X in (2)

80X+280Y=920...(2)

80[309/27 -(94/27)Y]+280Y=920

(24720/27)-(7520/27)Y+280Y=920

(24720/27)+(40/27)Y=920

(40/27)Y=920-(24720/27)

(40/27)Y=40/9

Y=3

Substituting Y in (1)

27X+94Y=309...(1)

27X+94(3)=309

27X+282=309

27X=27

X=1

So we need 1 can of Red Bull and 3 of Jolt Cola to get 309g of sugar and 920mg of caffeine.

43) Following the same steps we have:

27X+94Y=242...(1)

80X+280Y=720...(2)

Solving the system:

27X+94Y=242...(1)

27X=242-94Y

X=242/27 -(94/27)Y

Substituting X in (2)

80X+280Y=720...(2)

80[242/27 -(94/27)Y]+280Y=720

(19360/27)-(7520/27)Y+280Y=720

(19360/27)+(40/27)Y=720

(40/27)Y=720-(19360/27)

(40/27)Y=80/27

Y=2

Substituting Y in (1)

27X+94(2)=242...(1)

27X+188=242

27X=54

X=2

So we need 2 can of Red Bull and 2 of Jolt Cola to get 242g of sugar and 720mg of caffeine.

43) Following the same steps we have:

27X+94Y=457...(1)

80X+280Y=1360...(2)

Solving the system:

27X+94Y=457...(1)

27X=457-94Y

X=457/27 -(94/27)Y

Substituting X in (2)

80X+280Y=1360...(2)

80[457/27 -(94/27)Y]+280Y=1360

(36560/27)-(7520/27)Y+280Y=1360

(36560/27)+(40/27)Y=1360

(40/27)Y=1360-36560/27

(40/27)Y=160/27

Y=4

Substituting Y in (1)

27X+94Y=457...(1)

27X+94(4)=457

27X+376=457

X=3

So we need 3 cans of Red Bull and 4 of Jolt Cola to get 457g of sugar and 1360mg of caffeine.

Determine the number of cans of each drink that when combined will contain 403 grams sugar and 1200 milligrams caffeine

Following the same steps we have:

27X+94Y=403...(1)

80X+280Y=1200...(2)

Solving the system:

27X+94Y=403...(1)

27X=403-94Y

X=403/27 -(94/27)Y

Substituting X in (2)

80X+280Y=1200...(2)

80[403/27 -(94/27)Y]+280Y=1200

(32240/27)-(7520/27)Y+280Y=1200

(32240/27)+(40/27)Y=1200

(40/27)Y=1200-(32240/27)

(40/27)Y=160/27

Y=4

Substituting Y in (1)

27X+94Y=403...(1)

27X+94(4)=403

27X=-94(4)+403

X=1

So we need 1 can of Red Bull and 4 of Jolt Cola to get 403g of sugar and 1200mg of caffeine.

4 0

3 years ago

Factor the following expression.

Marysya12 [62]

10x^5 + 5x^3 - 14x^2 - 7

= 5x^3(2x^2 + 1) - 7(2x^2 + 1)

= (5x^3 - 7)(2x^2 + 1)

Answer is D

(5x^3 - 7)(2x^2 + 1)

4 0

3 years ago

Read 2 more answers

The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth-grade students. Scores on the test

katovenus [111]

Answer:

1) The standard deviation of the sampling distribution is:

√ V(X[bar])= 0.3033

2) 95% of the values on the normal distribution are between μ ± 0.6066

3) The formula for the confidence interval is:

[284.5; 285.5]

Step-by-step explanation:

Hello!

Your study variable is

X: "score obtained on the test by an eighth-grader"

This variable has normal distribution:

X~N(μ;σ²)

Now the since the sample mean, X[bar], is obtained from n samples of the study variable, it is also a variable and has the same distribution as the original variable with the difference that is conditioned by the number of n samples from which it was calculated. So its distribution is:

X[bar]~N(μ;σ²/n)

Where E(X[bar])=μ and V(X[bar])= σ²/n

The sample information is:

n= 170100

X[bar]= 285

And the population standard deviation is known to be σ= 125.1

1) The standard deviation of the sampling distribution is:

√ V(X[bar]) = √(σ²/n) = σ/√n = 125.1/√170100 = 0.3033

2) 95% of the values on the normal distribution are between μ ± 2σ

This is μ ± 2*0.3033 = μ ± 0.6066

3) The formula for the confidence interval is:

X[bar] ± $Z_{1-\alpha /2}$ *σ/√n