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2 years ago

Question 9 of 10

Mathematics

1 answer:

WARRIOR [948]2 years ago

3 0

Answer:

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

y = (x + 7)² - 9 ← is in vertex form

with h = - 7 and k = - 9

vertex = (- 7, - 9 )

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Which are the center and radius of the circle with equation (x + 5)2 + (y - 4)2 = 9?

alina1380 [7]

Answer:

Center (-5,4) radius 3

Step-by-step explanation:

The standard equation of a circle is

(x-h)^2+(y-k)^2=r^2

where the center is (h,k) and r is the radius

so h=-5 in this case and k is 4

r^2=9 so r=3

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3 years ago

A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a

laila [671]

Complete Question

A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a margin of error of ±5% with 90% confidence, and we do not have any prior knowledge about the proportion who might support the law. How many people need to be included in the sample?

Round your answer up to the nearest integer.

sample size = _____

Answer:

The sample size is $n = 271$

Step-by-step explanation:

From the question we are told that

The margin of error is E = 5% = 0.05

Generally given that there was no prior knowledge about the proportion of who might support the law, we will assume the sample proportion to be

$\^ p = 0.5$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )$

=> $n = [\frac{1.645 }{0.05} ]^2 * 0.5 (1 - 0.5 )$

=> $n = 271$

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3 years ago

1. Mr. Green works as the art teacher at Hamburg Summer Day Camp. Six hundred

NeTakaya

The amount of percentaile of 600 to 6 is 1%

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3 years ago

To increase an amount by 40% what single multiplier would you use

Veronika [31]

You would use the number 1.4 and multiply it by the number you are trying to increase.

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3 years ago

University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some studen

ira [324]

Answer:

A. 0.1

B. 0.8

C. 0.5

Step-by-step explanation:

Given:

P(Science) = 0.3

P(Arts) = 0.6

P(none) = 0.2

From the above, it is understood that the events are independently events; meaning that the probability that a students gets a Bachelor of Science degree does not affect the probability of the same student getting a Bachelor of Arts degree.

A. The probability that a student gets a Bachelor of Science and Bachelor of Arts degree

Let P(Arts and Science) = the probability that a student gets a Bachelor of Arts degree and Bachelor of Science degree

For independent events,

P(A) + P(B) - P(A and B) + P(none)= 1

If we translate the above formula to suit our needs, we have something like this

P(Science) + P(Arts) - P(Arts and Science) + P(none) = 1

P(Arts) + P(Science) - P(Arts and Science) + P(none) = 1

From this, we have

0.3 + 0.6 - P(Arts and Science) + 0.2 = 1

1.1 - P(Arts and Science) = 1

-P(Arts and Science) = 1 - 1.1

-P(Arts and Science) = -0.1

P(Arts and Science) = 0.1

B. The probability that a student gets a Bachelor of Science or Bachelor of Arts degree

For independent events

P(A or B) = P(A) + P(B) - P(A and B)

So, P(Arts or Science) = P(Arts) + P(Science) - P(Arts and Science)

P(Arts or Science) = 0.3 + 0.6 - 0.1

P(Arts or Science) = 0.8

C. The probability that a student gets only Bachelor of Arts

P(A only) = P(A) - P(A and B)

P(Arts) = P(Arts) - P(Arts and Science)

P(Arts) = 0.6 - 0.1

P(Arts) = 0.5

6 0

3 years ago