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3 years ago

Which table shows y as DIRECTLY PROPORTIONAL to x?

Mathematics

1 answer:

klemol [59]3 years ago

7 0

Answer:

Option B gives the directly proportional relation.

Step-by-step explanation:

If a function can be written as in the form y = kx ........... (1), where x is the independent variable, y is the dependent variable and k is the proportionality constant.

Now, from the given four tables in options, the table in option B only satisfies this relation between x and y.

The ordered pairs in the option B are (1,0.5), (2,1), (3,1.5) and (4,2).

Now, take any two pairs of coordinates and find the equation of the function that satisfies all four points.

Taking (1,0.5) and (2,1) points, the equation of the straight line will be

$\frac{y - 1}{1 - 0.5} = \frac{x - 2}{2 - 1}$

⇒ 2(y - 1) = x - 2

⇒ 2y = x

⇒ $y = \frac{1}{2} x$ ............. (2)

Therefore, this equation (2) is similar to equation (1) and hence this table is directly proportional relationship. (Answer)

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A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

4 0

2 years ago

Convert y+7=4(x-3) standard form

True [87]

Answer:

-4x+y = -5

Step-by-step explanation:

Y+7=4(x-3)

Y+7=4x-12

+7. +7

Y=4x-5

-4x+y=-5

7 0

3 years ago

Which graph represents a function?

Temka [501]

Answer:

The last one

Step-by-step explanation:

x can only have one value whereas y can be constants like in last graph

6 0

2 years ago

Read 2 more answers

If you borrow 421$ for nine years at an interest rate of 4% how much will you pay

satela [25.4K]

Interest = (Principal X rate X time)/100
Interest =421*9*4/100
Interest = 151.56 dollars

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3 years ago

Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped with side lengths of 9 inches, and t

MatroZZZ [7]

To solve this problem, you must follow the proccedure below:

1. The block was cube-shaped with side lengths of 9 inches and to calculate its volume (V1), you must apply the following formula:

V1=s³

s is the side of the cube (s=9)

2. Therefore, you have:

V1=s³
V1=(9 inches)³
V1=729 inches³

3. The lengths of the sides of the hole is 3 inches. Therefore, you must calculate its volume (V2) by applying the formula for calculate the volume of a rectangular prism:

V2=LxWxH

L is the length (L=3 inches).
W is the width (W=3 inches).
H is the heigth (H=9 inches).

4. Therefore, you have:

V2=(3 inches)(3 inches)(9 inches)
V2=81 inches

5. The amount of wood that was left after the hole was cut out, is:

Vt=V1-V2
Vt=648 inches³

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2 years ago