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Olenka [21]
3 years ago
8

the brightness of the illumination of an object varies inversely as the square of the distance from the object to the source of

light. how far from the bulb does an object receive four times as much illumination as it does when it is 8 m from the bulb
Mathematics
1 answer:
Free_Kalibri [48]3 years ago
3 0
I=k/d^2

4=k/d^2 and 1=k/64  so if we divide the first by the second we get:

4/1=(k/d^2)/(k/64)

4=(k/d^2)*(64/k)

4=64/d^2

d^2=64/4

d^2=16

d=4 meters


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A team of 10 players is to be selected from a class of 6 girls and 7 boys. Match each scenario to its probability. You have to d
tankabanditka [31]
The selection of r objects out of n is done in

C(n, r)= \frac{n!}{r!(n-r)!} many ways.

The total number of selections 10 that we can make from 6+7=13 students is 

C(13,10)= \frac{13!}{3!(10)!}= \frac{13*12*11*10!}{3*2*1*10!}= \frac{13*12*11}{3*2}=  286
thus, the sample space of the experiment is 286

A. 
<span>"The probability that a randomly chosen team includes all 6 girls in the class."

total number of group of 10 which include all girls is C(7, 4), because the girls are fixed, and the remaining 4 is to be completed from the 7 boys, which can be done in C(7, 4) many ways.


</span>C(7, 4)= \frac{7!}{4!3!}= \frac{7*6*5*4!}{4!*3*2*1}= \frac{7*6*5}{3*2}=35
<span>
P(all 6 girls chosen)=35/286=0.12

B.
"</span>The probability that a randomly chosen team has 3 girls and 7 boys.<span>"

with the same logic as in A, the number of groups were all 7 boys are in, is 

</span>C(6, 3)= \frac{6!}{3!3!}= \frac{6*5*4*3!}{3!3!}= \frac{6*5*4}{3*2*1}=20
<span>
so the probability is 20/286=0.07

C.
"</span>The probability that a randomly chosen team has either 4 or 6 boys.<span>"

case 1: the team has 4 boys and 6 girls

this was already calculated in part A, it is </span>0.12.
<span>
case 2, the team has 6 boys and 4 girls.

there C(7, 6)*C(6, 4) ,many ways of doing this, because any selection of the boys which can be done in C(7, 6) ways, can be combined with any selection of the girls. 

</span>C(7, 6)*C(6, 4)= \frac{7!}{6!1}* \frac{6!}{4!2!} =7*15= 105
<span>
the probability is 105/286=0.367

since  case 1 and case 2 are disjoint, that is either one or the other happen, then we add the probabilities:

0.12+0.367=0.487 (approximately = 0.49)

D.
"</span><span>The probability that a randomly chosen team has 5 girls and 5 boys.</span><span>"

selecting 5 boys and 5 girls can be done in 

</span>C(7, 5)*C(6,5)= \frac{7!}{5!2} * \frac{6!}{5!1}=21*6=126

many ways,

so the probability is 126/286=0.44
6 0
3 years ago
Read 2 more answers
900x300+2.4000/3-2001
aliya0001 [1]
900x300=270,000 plus 2 would equal 270,002.4 devided by 3-2001 would equal 87,999.8
5 0
3 years ago
A polling organization asked a nation-wide random sample of 1600 new brides (those who got married in the past 2 years) the foll
iren [92.7K]

Answer:

It has millions of tickets. On each ticket is written a number a dollar amount. The exact average and SD are unknown but are estimated from the sample to be $20,000 and $5,000 respectively.

Step-by-step explanation:

Given that:

sample size n = 1600

sample mean \overline x = 20000

standard deviation = 5000

The objective is to choose from the given option about what most closely resembles the relevant box model.

The correct answer is:

It has millions of tickets. On each ticket is written a number a dollar amount. The exact average and SD are unknown but are estimated from the sample to be $20,000 and $5,000 respectively.

However, if draws are made without replacement, the best estimate of the average amount for the bride will be $20,000

Similarly, the standard error for the sample mean = \dfrac{s}{\sqrt{n}}

= \dfrac{5000}{\sqrt{1600}}

= \dfrac{5000}{40}}

the standard error for the sample mean = 125

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A guide wire for a palm tree makes a 32°angle with the ground and is staked 6 feet from the base of the tree. What is the length
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Answer:

b) 8.5 feet

Step-by-step explanation:


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Do the sides 9, 12 and 15 make a right triangle?
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Answer:

YES

Step-by-step explanation:

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