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Sladkaya [172]
3 years ago
15

Solve the following system of equations by graphing and select the correct answer below:

Mathematics
2 answers:
Rudiy273 years ago
6 0

Answer:

Option A is correct.

x =4 , y = 2

Explanation:

Given the system of equation:

2x+6y = 20                   ......[1]

3x-2y = 8                       .....[2]

Multiply equation [2] by 3 both sides we get;

3 \cdot (3x-2y) = 3 \cdot 8

Using distributive property: a\cdot (b+c) = a\cdot b+ a\cdot c

9x - 6y = 24                     .....[3]

Add equation [1] and [3], to get eliminate y we get;

2x+6y+9x-6y= 20+24

Combine like terms we have;

11x = 44

Divide both sides by 11 we get;

x = 4

Substitute the value of x =4 in [1] we get;

2(4) + 6y = 20

8 + 6y = 20

Subtract 8 from both sides we have;

6y = 12

Divide both sides by 6 we have;

y = 2

Therefore, the values of x and y are; 4 and 2.


LUCKY_DIMON [66]3 years ago
5 0
The only answer is x = 4, y = 2, 
2(4) + 6(2) = 20
3(4) _ 2(2) = 8
the graph is so easy, please try!!
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The mean of a normal probability distribution is 500 and the standard deviation is 10. about 95 percent of the observations lie
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Answer:

So about 95 percent of the observations lie between 480 and 520.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

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99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

The mean is 500 and the standard deviation is 10.

About 95 percent of the observations lie between what two values?

From the Empirical Rule, this is from 500 - 2*10 = 480 to 500 + 2*10 = 520.

So about 95 percent of the observations lie between 480 and 520.

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3 years ago
How many possible outfit combinations come from 10 shirts, two slacks, and five ties? A.  17B.  25C.  100D.  20 
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3 years ago
Read 2 more answers
When people make estimates, they are influenced by anchors to their estimates. A study was conducted in which students were aske
12345 [234]

Answer:

The null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0

where μ1: mean calorie estimation for the cheesecake group and μ2: mean calorie estimation for the organic salad group.

There is enough evidence to support the claim that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first (P-value=0.0000002).

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>"Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first.</em>

<em>At the 0.01 level of significance, is there evidence that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first?"</em>

<em />

This is a hypothesis test for the difference between populations means.

The claim is that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first.

Then, the null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0

The significance level is 0.01.

The sample 1 (cheese cake), of size n1=20 has a mean of 780 and a standard deviation of 128.

The sample 2 (organic salad), of size n2=20 has a mean of 1041 and a standard deviation of 140.

The difference between sample means is Md=-261.

M_d=M_1-M_2=780-1041=-261

The estimated standard error of the difference between means is computed using the formula:

s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{128^2}{20}+\dfrac{140^2}{20}}\\\\\\s_{M_d}=\sqrt{819.2+980}=\sqrt{1799.2}=42.417

Then, we can calculate the t-statistic as:

t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-261-0}{42.417}=\dfrac{-261}{42.417}=-6.153

The degrees of freedom for this test are:

df=n_1+n_2-1=20+20-2=38

This test is a left-tailed test, with 38 degrees of freedom and t=-6.153, so the P-value for this test is calculated as (using a t-table):

P-value=P(t

As the P-value (0.0000002) is smaller than the significance level (0.01), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first.

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Solve the system using elimination
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2x + 3y = 9
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----------------
2x + 3y = 9
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solution is (3,1)
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