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2 years ago

Solve the following system of equations 3x+4y=16 and -4x-3y = -19

1 answer:

4 0

3x + 4y = 16
-4x - 3y = -19

4( 3x + 4y = 16)
3( -4x - 3y = -19)
Distribute
12x + 16y = 64
-12x - 9y = -57
Now subtract both equations
7y = 7
/7 on both sides
y = 1

Substitute y = 1 in one of the equations.
3x + 4y = 16
3x + 4(1) = 16
-4 on both sides
3x = 12
/3 on both sides
x = 4

Answer:
x = 4
y = 1

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2. Graph x < 8 and x > -1.

dimulka [17.4K]

Answer:

I'll try my best in explaining the steps.

Considering both signs are greater than and less than sign, its an open circle.

For the first equation, you would have an open circle, basically one that isn't colored in, on 8 on the number line. The arrow would be pointing to the left because the equation is telling us numbers that are less than 8.

For the second equation, you would have an open circle, basically one that isn't colored in, on -1 on the number line. The arrow would be pointing to the right because the equation is telling us numbers that are greater than -1.

Step-by-step explanation:

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2 years ago

Two random samples are taken, with each group asked if they support a particular candidate. A summary of the sample sizes and pr

Minchanka [31]

Answer:

And we got $\alpha/2 =0.01$ so then the value for $\alpha=0.02$ and then the confidence level is given by: $Conf=1-0.02=0.98[/tex[ or 98%Step-by-step explanation:A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval". The margin of error is the range of values below and above the sample statistic in a confidence interval. Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean". [tex]p_1$ represent the real population proportion for 1

$\hat p_1 =0.768$ represent the estimated proportion for 1

$n_1=92$ is the sample size required for 1

$p_2$ represent the real population proportion for 2

$\hat p_2 =0.646$ represent the estimated proportion for 2

$n_2=95$ is the sample size required for 2

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

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

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}$

For this case we have the confidence interval given by: (-0.0313,0.2753). From this we can find the margin of erro on this way:

$ME= \frac{0.2753-(-0.0313)}{2}=0.1533$

And we know that the margin of erro is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}$

We have all the values except the value for $z_{\alpha/2}$

So we can find it like this:

$0.1533=z_{\alpha/2} \sqrt{\frac{0.768(1-0.768)}{92} +\frac{0.646 (1-0.646)}{95}}$

And solving for $z_{\alpha/2}$ we got:

$z_{\alpha/2}=2.326$

And we can find the value for $\alpha/2$ with the following excel code:

"=1-NORM.DIST(2.326,0,1,TRUE)"

And we got $\alpha/2 =0.01$ so then the value for $\alpha=0.02$ and then the confidence level is given by: $Conf=1-0.02=0.98$ or 98%

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2 years ago

Ms. Salta buys buffalo wings for a party. If there are 3 servings per buffalo pound, exactly how many servings does she have for

gtnhenbr [62]

Answer:

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Missing

Step-by-step explanation:

i think

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2 years ago

Need emergency help!!

Dafna1 [17]

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3 years ago

Solve: 6x + 10 = 4x -8. Determine how many solutions? (exactly one, infinitely many, no solution)

Vesnalui [34]

Answer:

x = - 9

Step-by-step explanation:

6x + 10 = 4x - 8

6x - 4x = - 10 - 8

2x = - 18

x = - 18 : 2

x = - 9

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2 years ago