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antoniya [11.8K]
3 years ago
14

Use the substitution method to solve the system of equations choose the correct ordered pair

Mathematics
1 answer:
Gekata [30.6K]3 years ago
4 0

Answer:

C. (4,28)

Step-by-step explanation:

The substitution method requires you to input a specified number in place of a variable. In this case, the variable 'x' should be replaced by the number 4. Using the order of operations, we know that multiplication should be applied before subtraction. When we replace 'x' with 4, we get the equation 'y=8(4)-4'. Multiplying 8 and 4 gives us 32. If we subtract 4 from 32, we get 28. The answer ends up being 'y=28'.

That is the first part of our solution. What we are actually looking for is an ordered pair. We know ordered pairs are written in the form (x, y). First, we need to find the 'x'. The 'x' has been given to us from the beginning, it is 4. Next is the 'y'. This is what we needed to find using substitution. We ultimately concluded that the 'y' is equivalent to 28. Therefore our ordered pair is (4, 28), the letter choice C.

I hope this helped you and that I clearly elaborated on the answer choice.

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<h3>What is a parallelogram?</h3>

A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

For a parallelogram, the pair of opposite sides are equal and parallel. Therefore,

1.)  For the first pair.

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2.) For the second pair

(x+2)=(2x-5)

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Since the measure of the pair of opposite sides is 15 units, the pair of the other two sides measure 9 units.

Hence, the correct option is A.

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Answer:

1) Randomization condition: We assume that we are selecting random samples so this condition is satisfied

2) 10% condition: We assume that the random sample selected is less than 10% of the population size

3) Success/ Failure condition:

For this case we need to satisfy this:

np \geq 10, n(1-p)\geq 10

So since the condition 1 and 2 are satisfied the correct option for this case would be:

a)np and nq must be respectively at least equal to 10

Step-by-step explanation:

Assuming the following options:

a)np and nq must be respectively at least equal to 10

b) as n increases, the distribution of sample proportions becomes less Normal

c) np and nq must be respectively less than 10

d) np plus nq must be at least 10.

For this case we need 3 basic conditions:

1) Randomization condition: We assume that we are selecting random samples so this condition is satisfied

2) 10% condition: We assume that the random sample selected is less than 10% of the population size

3) Success/ Failure condition:

For this case we need to satisfy this:

np \geq 10, n(1-p)\geq 10

So since the condition 1 and 2 are satisfied the correct option for this case would be:

a)np and nq must be respectively at least equal to 10

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3 years ago
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Answer:

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2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size

3) np = 500*0.66= 330 >10

n(1-p) = 500*(1-0.66) =170>10

So then we can use the normal approximation for the distribution of p, since the conditions are satisfied

The population proportion have the following distribution :

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And we have :

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Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).

Step-by-step explanation:

For this case we know that we have a sample of n = 500 students and we have a percentage of expected return for their sophomore years given 66% and on fraction would be 0.66 and we are interested on the distribution for the population proportion p.

We want to know if we can apply the normal approximation, so we need to check 3 conditions:

1) Randomization: We assume that we have a random sample of students

2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size

3) np = 500*0.66= 330 >10

n(1-p) = 500*(1-0.66) =170>10

So then we can use the normal approximation for the distribution of p, since the conditions are satisfied

The population proportion have the following distribution :

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})  

And we have :

\mu_p = 0.66

\sigma_{p}= \sqrt{\frac{0.66(1-0.66)}{500}}= 0.0212

And we can use the empirical rule to describe the distribution of percentages.

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).

8 0
3 years ago
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