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3 years ago

According to astronomers, what is a "light year" answer key

1 answer:

3 0

A light-year is defined as the distance the light can cover in one year.

The light travels at speed of $c=3 \cdot 10^8 m/s$ , and one year converted into seconds is
$1 y = 365 \frac{d}{y} \cdot 24 \frac{h}{d} \cdot 60 \frac{m}{h} \cdot 60 \frac{s}{m}=3.15 \cdot 10^7 s$

So the distance covered by the light in one year is
$S=vt =(3 \cdot 10^8 m/s)(3.15 \cdot 10^7 s)=9.45 \cdot 10^{15} m$
And this is the distance that corresponds to one light-year.

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There are 7 pens in a bag. Four of the pens are blue and the other 3 are red. What's the probability of pulling out a red

GarryVolchara [31]

Answer:

3/7

Step-by-step explanation:

P(red) = number of red pens / total number of pens

= 3/7

6 0

2 years ago

Read 2 more answers

Your dad is designing a new garden for your backyard. He has 20 feet of fencing to go around the garden. He wants the length of

Komok [63]

Answer:

Length = 6.25 feet

Step-by-step explanation:

Your dad is designing a new garden for your backyard. He has 20 feet of fencing to go around the garden.

Let the width is x.

Length is 2 1/2 feet longer than the width i.e. (x+2 1/2) = (x+2.5) feet

Perimeter = 20 feet

2(l+b) = 20

(l+b) = 10

(x+2.5+x) = 10

2x+2.5 = 10

2x = 7.5

x = 3.75 feet

Length = (x+2.5)

= (3.75+2.5)

= 6.25 feet

So, the length of the garden is 6.25 feet.

3 0

2 years ago

In a sample of 70 stores of a certain company, 62 violated a scanner accuracy standard. It has been demonstrated that the condi

uysha [10]

Answer:

We need at least 243 stores.

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 of the interval is:

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

For this problem, we have that:

$n = 70, p = \frac{62}{70} = 0.886$

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 $Z = 1.96$ .

Determine the number of stores that must be sampled in order to estimate the true proportion to within 0.04 with 95% confidence using the large-sample method.

We need at least n stores.

n is found when M = 0.04. So

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

$0.04 = 1.96\sqrt{\frac{0.886*0.114}}{n}}$