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evablogger [386]
3 years ago
7

A box has 14 camera of which 6 are refurbished and 8 are new. If four of these 14 cameras are selected at random without replace

ment, what is the probability that (i) one new camera will be selected? (ii) at most one new camera will be selected?
Mathematics
1 answer:
lutik1710 [3]3 years ago
4 0

Answer:

160/1001, 175/1001

Step-by-step explanation:

i) There are:

₈C₁ ways to choose 1 new camera from 8 new cameras

₆C₃ ways to choose 3 refurbished cameras from 8 refurbished cameras

₁₄C₄ ways to choose 4 cameras from 14 cameras

The probability is:

P = ₈C₁ ₆C₃ / ₁₄C₄

P = 8×20 / 1001

P = 160 / 1001

P ≈ 0.160

ii) At most one new camera means either one new camera or no new cameras.  We already found the probability of one new camera.  The probability of no new cameras is the same as the probability of choosing 4 refurbished cameras:

P = ₆C₄ / ₁₄C₄

P = 15 / 1001

So the total probability is:

P = 160/1001 + 15/1001

P = 175/1001

P ≈ 0.175

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Although the Line is included in the region, I will say the your answer is B and D

Step-by-step explanation:

The region shaded is below the Line graph, son we have a < sign, now, I can see the region including the Line graph, so I will say that the inequality should have the = sign, nevertheless no options include the =sign, so, if it is nothing missing, your answer should be:

y<x

3 0
3 years ago
What is the slope of the line that passes through the points (4, -9)(4,−9) and (8, -3) ?(8,−3)? Write your answer in simplest fo
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Answer:

\frac{3}{2}

Step-by-step explanation:

I am assuming that you mean (4,−9) and (8, -3).

m=\frac{rise}{run}=\frac{-3+9}{8-4}=\frac{6}{4}=\boxed{\frac{3}{2}}

Hope this helps.

6 0
2 years ago
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What is 43% of 600 gallons of water
Leokris [45]
43% of 600 gallons of water is 258

Convert your percentage into a decimal:
\frac{43}{100} = 0.43

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0.43 \times 600 = 258
3 0
3 years ago
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The National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time requir
Paha777 [63]

Answer:

95​% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Step-by-step explanation:

We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                              P.Q. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean time = 5.15 years

            \sigma = sample standard deviation = 1.68 years

            n = sample of college graduates = 4400

            \mu = population mean time

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.</em>

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5%

                                               level of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ]

                                              = [ 5.15-1.96 \times {\frac{1.68}{\sqrt{4400} } } , 5.15+1.96 \times {\frac{1.68}{\sqrt{4400} } } ]

                                             = [5.10 , 5.20]

Therefore, 95​% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

8 0
3 years ago
Please help
ratelena [41]

Answer:

rom the relation for linear regression formula, Y = b·X + a, we have ;

For car 1

ΣXY = 102780

(ΣX)² = 36

ΣX = 6

ΣY = 52390

ΣX² = 14

N = 3

b = -1000

a = 19463

Y = -1000×X + 19463

For Car 2

ΣXY = 102539.8

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a = 19602

Y = -1076.7×X + 19602

Step-by-step explanation:

part B ^

8 0
2 years ago
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