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tiny-mole [99]
3 years ago
9

Find the standard form of the circle x2 + y2 – 6x + 10y + 24 = 0 by completing the square.

Mathematics
1 answer:
hichkok12 [17]3 years ago
6 0

Answer:

(x-3)^2+ (y+5)^2=10

Step-by-step explanation:

Given the equation of the circle: x^2 + y^2 - 6x + 10y + 24 = 0

We wish to express it in a Standard form:

We begin by re-arranging:

x^2 - 6x + y^2  + 10y  = - 24

Next, divide the coefficient of x by 2, square it and add it to both sides.

Do the same for y.

x^2 - 6x +(-3)^2+ y^2  + 10y+5^2  = - 24+(-3)^2+5^2

Next, we factorize

(x-3)^2+ (y+5)^2  = - 24+9+25\\(x-3)^2+ (y+5)^2=10

This is the standard form.

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Because of safety considerations, in May 2003 the Federal Aviation Administration (FAA) changed its guidelines for how small com
Rasek [7]

Answer:

a) The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

b)

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c) They are respected, as the upper bound of both intervals is below the new FAA recommendations.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve these questions.

Question a:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 100 - 1 = 99

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 99 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 1.9842

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.9842\frac{20}{\sqrt{100}} = 4

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 183 - 4 = 179 pounds.

The upper end of the interval is the sample mean added to M. So it is 183 + 4 = 187 pounds.

The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

Question b:

Critical value is the same(same sample size and confidence level).

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.9842\frac{23}{\sqrt{100}} = 4.6

The lower end of the interval is the sample mean subtracted by M. So it is 190 - 4.6 = 185.4 pounds.

The upper end of the interval is the sample mean added to M. So it is 190 + 4.6 = 194.6 pounds.

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c. The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the confidence interval estimates from Parts (a) and (b).

They are respected, as the upper bound of both intervals is below the new FAA recommendations.

7 0
3 years ago
Solve the equation 4 1/5+b= 9 3/5
victus00 [196]
4 1/5 + b = 9 3/5

4 1/5 - 4 1/5 + b = 9 3/5 - 4 1/5
(taking the same amount from each side to keep it balanced)

0 + b = 5 2/5
(subtracting 4 1/5 from each side)

b = 5 2/5
8 0
2 years ago
Read 2 more answers
3<br> Select the correct answer.<br> What are the solutions to this equation?<br> 16x² + 9 = 25
Charra [1.4K]

Answer:

Step-by-step explanation:

16x^2 + 9 = 25

16x^2 = 16

x^2 = 1

x = 1, -1

4 0
3 years ago
We have three coins: one with heads on both faces, the second with tails on both faces, and the third a regular one. We choose o
Finger [1]

Answer:

Probability: \frac{1}{2} = 0.5 = 50%

Step-by-step explanation:

Based on the question one coin is chosen at random and tossed. That coin then lands and is heads. Since the coin landed on heads we can <u>eliminate the possibility</u> of the coin that was chosen being the coin with double tails.

The following possibilities are that the coin has double heads or is a regular coin with both tails and heads. Seeing as the coin landed on heads, there are only two possible out comes for the other side of the coin

The other side is either Heads or Tails. That gives us a 50% chance of the other side being tails.

\frac{1}{2} = 0.5 = 50%

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

4 0
3 years ago
The sum of 5x and 2x is a least 70
diamong [38]

Answer:

7x ≥ 70

Step-by-step explanation:

5x + 2x ≥ 70

7x ≥ 70

x ≥ 10

Hope this helps!

-sruthi123

5 0
3 years ago
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