>>> The equation T^2 = A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is k times the mean distance from the sun as planet X, by what factor is the orbital period increased? <<

Answers

Answer 1

Answer: If planet Y is k times the mean distance from the sun than planet X, the right side of the equation becomes (kA)^3. which is k^3 times the left side, T^2. To equate both sides of the equation, multiply T by k^3/2 so that the left side becomes ((k^3/2) x T)^2 which simplifies into (k^3) x (T^2). Therefore, the answer is k^3/2.

Answer 2

Answer:

Answer:

Given the equation:

$T^2 =A^3$

shows the relationship between a planet's orbital period T and the planet's mean distance from the sun, A in Astronomical units

then:

For planet X:

Orbital period is:

$T_(X) = (A)^{(3)/(2)}$ .....[1]

As per the statement:

If planet Y is k times the mean distance from the sun as planet X.

⇒ A planet Y= kA mean distance from the sun as planet X.

then orbital period of Planet Y is:

$T_(Y) = (kA)^{(3)/(2)}=k^{(3)/(2)}\cdot (A)^{(3)/(2)}$ ....[2]

Divide equation [2] by [1] we have;

$(T_(Y))/(T_(X)) = \frac{k^{(3)/(2)}\cdot (A)^{(3)/(2)}}{A^{(3)/(2)}}$

Simplify:

$(T_(Y))/(T_(X)) =k^{(3)/(2)}$

$T_(Y) =k^(3)/(2) T_X$

Therefore, the orbital period is increased by factor $k^(3)/(2)$

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If 6y-8=28, what is the value of y

Answers

The answer would be y = 6

6y-8=28
add 8 to both sides
6y=36
divide both sides by 6
y=6

4. You have a deck of 40 number cards: five of each number 2 to 9. You shuffle the deck, pick a card, look at it, return it to the deck, and then repeat for a second card. Determine each theoretical probability. a) sum is 12 b) difference is less than 5 c) product is odd

Answers

To determine the theoretical probabilities, we'll analyze the different possible outcomes for each case.

Total number of cards = 40 (5 cards for each number from 2 to 9)

a) Sum is 12:

There are several combinations of cards that can result in a sum of 12:

3 and 9
4 and 8
5 and 7
7 and 5
8 and 4
9 and 3

Total favorable outcomes = 6 (since there are 6 possible combinations)

Total possible outcomes (since you're drawing two cards) = 40 * 40 = 1600

Probability (sum is 12) = (Number of favorable outcomes) / (Total possible outcomes)

Probability (sum is 12) = 6 / 1600 = 0.00375

b) Difference is less than 5:

There are several combinations of cards that can result in a difference less than 5:

2 and 3
3 and 2
3 and 4
4 and 3
4 and 5
5 and 4
5 and 6
6 and 5
6 and 7
7 and 6
7 and 8
8 and 7
8 and 9
9 and 8

Total favorable outcomes = 14

Total possible outcomes = 1600

Probability (difference is less than 5) = 14 / 1600 = 0.00875

c) Product is odd:

For the product to be odd, one or both of the numbers drawn must be odd. Since there are five odd numbers (3, 5, 7, 7, 9), and each number has five cards, the total number of favorable outcomes is 5 + 5 + 5 + 5 + 5 = 25.

Total possible outcomes = 1600

Probability (product is odd) = 25 / 1600 = 0.015625

To summarize:

a) Probability (sum is 12) ≈ 0.00375
b) Probability (difference is less than 5) ≈ 0.00875
c) Probability (product is odd) ≈ 0.015625

In Juneau, Alaska, the 30-year annual snowfall average is 86.7 inches with a standard deviation of 40.4 inches. The last four years saw an average annual snowfall of 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Hia performs a hypothesis test on this data to determine if the next 30-year norm will have a different average if the trend from the last four years continues. She uses a significance level of 5%. Which of the following is a conclusion that she may make?a) The z-statistic is 1.44, so the null hypothesis cannot be rejected.
b) he z-statistic is 1.68, so the null hypothesis cannot be rejected.
c) The z-statistic is 1.85, so the null hypothesis should be rejected.
d) The z-statistic is 4.6, so the null hypothesis should be rejected.

Answers

The expected value of the amount of average snowfall for over 30 years is 86.7 inches with a standard deviation of 40.4 inches. To verify if this particular trend continues, we must check the significance value of the amount snowfall for the past four years. Given that the snowfall for past years are as follows: 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Thus the mean of the sample would be: (115.7 + 62.9 + 168.5 + 135.7)/4 = 120.7 inches. To compute for the z-score, we have z-score = (x – μ) / (σ / √n) where x is the computed/measured value, μ is the expected mean, σ is the standard deviation, and n is the number of samples. Using the information we have, z-score (z) = (120.7 - 86.7) / (40.4/ √4) = 1.68 In order to reject the null hyptohesis our probability value must be less than the significance level of 5%. For our case, since z = 1.68, P-value = 0.093 > 0.05. Therefore, the answer is B.

Answer:

its B

Step-by-step explanation:

If a car travels 340 miles on 20 gallons of gas how far can it travel on 25 gallons of gas

Answers

First, divide 340 miles by 20 gallons of gas, to see how many miles you have per gallon. 340 divided by 20 = 17 mpg. Next you multiply 17 mpg by 25 gallons of gas to see how many miles you can go.
17 times 25 = 425 miles. Your answer is 425 miles.

Lisa invests $4,000 in two types of bonds, bond A and bond B. Bond A offers a 10% return, and bond B offers a 6% return. Lisa invests $x in bond A and $y in bond B. Her total return on the investment is $340. The system of linear equations defining the situation is x+y=4,000 and .1x=.06y=340. The amount Lisa invested at the rate of 10% is ___ , and the amount she invested at the rate of 6% is ___ .

Answers

Lisa invests $4,000 in two types of bonds, bond A and bond B. A + B = 4000 Bond A offers a 10% return, and bond B offers a 6% return. .10 A + .06 B = 340 Her total return on the investment is $340. since the relationship A+B=4000 must satisfy the setup for all values A and B we can state that A = 2000 + n, and B = 2000 -n afterall: 2000 +n + 2000 - n = 4000 for all n .10(2000+n) + .06(2000-n) = 340, once we know n we know A and B

Which angle measures approximately 152°?

Answers

Answer:

The answer is YZC, so the third option

Step-by-step explanation:

The explanation for this one is fairly simple, as the lines are already drawn out for you!

The line labeled C lines up with 152 on the protractor, and after connecting that to the base point Z in the middle and then the base line of Y, you get YZC

Hopefully I helped you!

Answer:

yzc

Step-by-step explanation:

i took the test and got it right

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