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3 years ago

Solve the linear system of equations using the linear combination method.

1 answer:

6 0

Hello!

4x - 9y = 20
2x - 6y = 16

You first need one of the variables have the same coefficient

We can do this by multiplying the second equation by 2

4x - 12y = 32

Subtract the equations to get rid of x

4x - 9y = 20
4x - 12y = 32

3y = -12

Divide both sides by 3

y = -4

Put y into one of the original equations

2x - 6(-4) = 16

Multiply

2x - -24 = 16

We you subtract a negative it is the same as addding

2x + 24 = 16

Subtract 24 from both sides

2x = -8

Divide both sides by 2

x = -4

The answers are x = -4 and y = -4

Hope this helps!

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Lyrx [107]

X+96+5x=180
6x=84
X=14 which is B.

Check: 14+96+5(14)=110+70=180

7 0

4 years ago

$100 gift card to purchase 48.40 worth of 40 movies and songs

Alexus [3.1K]

40s+48.40=100

Each song costed 1.29.

Hope this helps!

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4 years ago

A middle school took all of its 6th grade students on a field trip to see a symphony. The students filled 576 seats, which was 3

Novosadov [1.4K]

Step-by-step explanation:

since 36% is 576 seats, 100% would be 576/36 x 100 = 1600seats

Topic: Percentage

If you like to venture further, feel free to check out my insta (learntionary). It would be best if you could give it a follow. I'll be constantly posting math tips and notes! Thanks!

3 0

3 years ago

a sports statistician claim that the mean winning times for boston marathon women's open division champions is at least 2.68 hou

GenaCL600 [577]

Answer:

We conclude that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.

Step-by-step explanation:

We are given that a sports statistician claim that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.

The mean winning time of a sample of 30 randomly selected Boston marathon women's open division champions is 2.60 hours. assume the population standard deviation is 0.32 hours.

Let $\mu$ = mean winning times for Boston marathon women's open division champions.

So, Null Hypothesis, $H_0$ : $\mu\geq$ 2.68 hours {means that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours}

Alternate Hypothesis, $H_A$ : p < 2.68 hours {means that the mean winning times for Boston marathon women's open division champions is less than 2.68 hours}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean winning time = 2.60 hours

$\sigma$ = population standard deviation = 0.32 hours

n = sample of women's open division champions = 30

So, test statistics = $\frac{2.60-2.68}{\frac{0.32}{\sqrt{30} } }$

= -1.37

The value of z test statistics is -1.37.

Now, P-value of the test statistics is given by following formula;

P-value = P(Z < -1.37) = 1 - P(Z $\leq$ 1.37)

= 1 - 0.9147 = 0.0853

Since, P-value of the test statistics is more than the level of significance as 0.0853 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean winning times for Boston marathon women's open division champions is at least 2.68 hours.

6 0

3 years ago

What is the probability of rolling a 2 or a 4 on a 6 section spinner?

sergey [27]

Rolling an even number (2, 4 or 6) is an event, and rolling an odd number (1, 3 or 5) is also an event. In Experiment 1 the probability of each outcome is always the same. The probability of landing on each color of the spinner is always one fourth.

3 0

3 years ago