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3 years ago

you have $120 to donate equally to several charities. Does this situaton represent direct or inverse variation? Explain.

1 answer:

8 0

This situation represents inverse variation.

The difference between direct and inverse variation is in direct variation, as one variable goes up the other does too, while in inverse, as one variable goes up the other falls.

In this case, as you donate to more charities, the amount you donate to each charity falls, because you donate an equal amount. This means it's inverse variation.

Hope this helps!

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Solve the system of equations below.

Ostrovityanka [42]

C - no solution
you take the second solution and times the entire equation by -1
then simply
and you get 0x + 0y = 20

5 0

3 years ago

Read 2 more answers

Nonstandard dice can produce interesting distributions of outcomes. you have two balanced, six-sided dice. one is a standard die

Artyom0805 [142]

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

One die can show the values 1-6, while the other die can only show 0 or 6. So the possible totals are 1 through 6 plus 0 and 1 through 6 plus 6. Written out, one-by-one, this gives: 1+0 = 1 2+0 = 2 3+0 = 3 4+0 = 4 5+0 = 5 6+0 = 6 1+6 = 7 2+6 = 8 3+6 = 9 4+6 = 10 5+6 = 11 6+6 = 12

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3 years ago

The volume of the triangluar block is 4 cubic inches. What is the approximate length of y?

Artist 52 [7]

The volume of the triangluar block is 4 cubic inches. What is the approximate length of y? -- 2.8 inches

3 0

3 years ago

2 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.

vaieri [72.5K]

Answer:

Dimension of box:-

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

$500=x^2y$

Therefore, $y=\dfrac{500}{x^2}$

It is open box. The surface area of box, S .

$S=x^2+4xy$

Put $y=\dfrac{500}{x^2}$

$S(x)=x^2+\dfrac{2000}{x}$

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

$S'(x)=2x-\dfrac{2000}{x^2}$

For critical point, S'(x)=0

$2x-\dfrac{2000}{x^2}=0$

$x^3=1000$

$x=10$

Put x = 10 into $y=\dfrac{500}{x^2}$

y = 5

Double derivative of S(x)

$S''(x)=2+\dfrac{4000}{x^3}$ at x = 10

$S''(10) > 0$

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

7 0

3 years ago

In the Salk vaccine field trial, 400,000 children were part of a randomized controlled double-blind experiment. Just about half

EastWind [94]

Answer:

Step-by-step explanation:

From the given information:

The number of children that were randomly allocated to each vaccination group; n₁ = 200,000

No of polio cases X₁ = 57

Now, in the vaccine group:

the proportion of polio cases is:

$\hat p_1 = \dfrac{57}{200000}$

= 0.000285

The number of children that were randomly allocated to the placebo group, n₂ = 200,000

No of polio cases X₂ = 142

In the placebo group

the proportion of polio cases is:

$\hat p_2 = \dfrac{142}{200000}$

Null and alternative hypothesis is computed as follows:

H₀: There is no difference in the proportions of polio cases between both groups.

H₁: There is a difference in the proportions of polio cases between both groups.

Let assume that the level of significance ∝ = 0.05

The test statistic can be computed as:

$Z = \dfrac{\hat p_1-\hat p_2}{\sqrt{\dfrac{\hat p_1 \hat q_1}{n_1}+ \dfrac{\hat p_2 \hat q_2}{n_2}}}$

$Z = \dfrac{0.000285-0.000710}{\sqrt{\dfrac{0.000285(1-0.000285)}{200000}+ \dfrac{0.000710(1-0.000710)}{200000}}}$

$Z = \dfrac{-4.25\times 10^{-4}}{\sqrt{\dfrac{0.000285(0.999715)}{200000}+ \dfrac{0.000710(0.99929)}{200000}}}$

Z = - 6.03

P-value = 2P(Z < -6.03)

From the Z - tables

P-value = 2 × 0.0000

= 0.000

We reject the H₀ provided that P-value is very less.

Therefore, we may conclude that there is a difference in the proportions of polio cases between the vaccine group and placebo group not due to chance.

7 0

3 years ago