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Lerok [7]
3 years ago
7

Question Which of these strategies would eliminate a variable in the system of equations? 2x - y = 11 5x + 3y = -11 How many pos

sible solutions will this system have?
Mathematics
1 answer:
kenny6666 [7]3 years ago
3 0

Answer:

Elimination (multiplication and subtraction)

There is 1 solution

Step-by-step explanation:

The only way to solve this system of equations is by elimination (multiplication). Let's say that we want to cancel out the x. You multiply the first equation by 5 and you multiply the second equation by 2.

Your equations now are:

10x-5y=55 and 10x+6y=-22

You can subtract these equations to get -11y = 77.

Now that we know that y = -7, we can substitute y in to solve x.

10x-5(-7) = 55

10x=20

x=2

Final answer (2,-7)

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After the translation, where is A located?
vovikov84 [41]

Answer:

(-3, 13)

Step-by-step explanation:

The transformation that moves a point 4 left and 8 up is ...

 (x, y) ⇒ (x -4, y +8)

The transformation that reflects a point across the y-axis is ...

 (x, y) ⇒ (-x, y)

Applied after the translation, the transformation of ∆ABC becomes ...

 (x, y) ⇒ (-(x -4), y +8) = (4 -x, y +8)

Then point A gets moved to ...

 A(7, 5) ⇒ A'(4 -7, 5 +8) = (-3, 13)

7 0
2 years ago
Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on pa
Debora [2.8K]

Answer:

a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

b) 0.4129 = 41.29% probability that the mean return will be less than 8%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean 8.7% and standard deviation 20.2%.

This means that \mu = 8.7, \sigma = 20.2

40 years:

This means that n = 40, s = \frac{20.2}{\sqrt{40}}

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?

This is 1 subtracted by the pvalue of Z when X = 13. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{13 - 8.7}{\frac{20.2}{\sqrt{40}}}

Z = 1.35

Z = 1.35 has a pvalue of 0.9115

1 - 0.9115 = 0.0885

0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

(b) What is the probability that the mean return will be less than 8%?

This is the pvalue of Z when X = 8. So

Z = \frac{X - \mu}{s}

Z = \frac{8 - 8.7}{\frac{20.2}{\sqrt{40}}}

Z = -0.22

Z = -0.22 has a pvalue of 0.4129

0.4129 = 41.29% probability that the mean return will be less than 8%

8 0
2 years ago
Need help <br> Please<br> Thank u
Volgvan

Answer:

i think its b

Step-by-step explanation:

4 0
3 years ago
Hello can anyone please help me with this assignment it’s due tomorrow please and thanks !
snow_lady [41]

Answer:

PART 2,4,6 are not solvable since they do not have any number

Part 1

1 = 61

2 = 119

3 = 61

4 = 119

5 = 61

6 = 119

7 = 61

8 = 119

Part 3

1 = 128

2 = 52

3 = 128

4= 52

5 = 128

6 =52

7 = 128

8 =52

Part 5

1 = 135

2 = 45

3 = 135

4 = 45

5= 135

6= 45

7=135

8= 45

8 0
3 years ago
the container overflowed because the kids tried to pour in 3 and 3/5 times the amount it would hold. if they tried to pour in 28
ANEK [815]

Answer: 80 Gallons

Explanation:

3 \frac{3}{5} =  3\frac{6}{10}   = 3.6 \\  \frac{288}{3.6}  = 80

8 0
3 years ago
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