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andrew11 [14]
3 years ago
6

In a random sample of 1,000 exams, the average score was 500 points with a standard deviation of 80 points.

Mathematics
1 answer:
bagirrra123 [75]3 years ago
5 0
90% c.I. is given by







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Both the heads and tails will have a probability of 0.5 with a fair coin. ... TO find probability that foe the 7th toss head appears exactly 4 times.
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A linear equation in two variables has infinitely many solution the set of all solutions to a linear equation in two variables f
Greeley [361]
<span>1, During a 1-hr television program, there were 22 commercials, Some commercials were 15 sec and some were 30 sec long. Find the number of 15- sec commercials and the number of 30 sec commercial if the total playing time for commercial was 9.5 minutes.

</span>a) <span>show how to formulate your system of equations for your problem,

Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language

b) state the two equations:

- translate the word statement into algebraic equations:

</span><span>* there were 22 commercials => x + y = 22
* the total playing time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 </span><span>

Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y =  570

c) state which method you will use to solve either addition or substitution

Answer:
adition: multiply the first equation times - 15 and add the two equations.

d) solve your system showing and explaining each step of the process

Answer:
- muliply eq (1) times - 15

-15x - 15y = - 330

- add that to the eq (2):

-15x + 15x - 15y + 30y = -330 + 570

- add like terms: 15y = 240

- divide both members by 15: 15y/15 = 240 / 15 => y = 16

- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6

Solution: x = 6, y = 16

e) Be sure to check your solution!

x + y = 22
6 + 16 = 22
22 = 22 --> check

15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check

f) Once a solution is found explain what this solution means in the context of the problem, write the answer to the word problem in words</span><span>

The solution means that d</span><span>uring a 1-hr television program, there were</span><span> 6 commercials of 15 sec and 16 commercials of 30 sec.

2, How many quarts of water should be mixed with a 30% vinegar solution to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).</span>

a) variables:

- state the variables
x: number of quarters of water
y: number of quarters of vinegar

- translate the words into mathematical language

12 qt 25% vinegar solution

=> total number of quarts = 12 = x + y

balance in vinegar:

vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution

0 + 0.3y = 0.25 (x + y)

c) Equations

Eq (1) x + y = 12

Eq (2): 0.3y = 0.25x + 0.25y

=> 0.25x - 0.05y = 0

d) solve

- multiply eq (1) times 0.05 and add to eq (2)

0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
------------------------
0.30x = 0.6

x = 0.6 / 0.3 = 2

x + y = 12 => y = 12 - y = 12 - 2 = 10

Solution: x = 2, y = 10

e) check:

x + y = 12
2 qt + 10qt = 12 qt
12 qt = 12 qt ---> check

vinegar:

10*0.3 = 12*0.25
3 = 3 -> check

f) Explanation of the solution

The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.

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3 years ago
Gerald has a bag of 10 colored balls: 3 green, 3 red, and the rest yellow. He randomly draws two balls, one at a time without re
butalik [34]

Answer:

2/3

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome.

Given that there are 10 balls of which 3 green, 3 red, and the rest yellow

Number of yellow balls = 10 - 3 - 3 = 4

Probability of picking a;

Green ball  = 3/10

Red ball = 3/10

Yellow ball = 4/10

If two balls are picked without replacement, the probability that one is at least yellow will be

YR RY YG GY YY

= 4/10*3/9 + 3/10*4/9 + 4/10*3/9 + 3/10*4/9 + 4/10*3/9

=12/90 *5

= 2/3

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It might be the last one but I don't know
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3 years ago
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Oduvanchick [21]
A=7,500×(1+0.04)^(2)
A=8,112
7 0
3 years ago
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