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4 years ago

Can anyone help? Give the answer in four significant figures.

Mathematics

1 answer:

Llana [10]4 years ago

5 0

X + 0.5y = 3
x^2 - y = 15

from the first equation:-
0.5y = 3 - x
y = 6 - 2x

Substitute for y in second equation:-
x^2 - (6 - 2x) = 15
x^2 + 2x - 21 = 0
x = [-2 +/- sqrt((4 - 4*-21)] / 2
= 3.6904 , -5.6904

Plugging in these into first equation we get

3.6904 + 0.5y = 3 so y = 2(3-3.6904) = -1.3808
-5.6904 + 0.5y = 3 so y = 2(3 + 5.6904) = 17.3808

Solution is x = 3.690, y = -1.381 ; x = -5.690, y = 17.38 ( to 4 s.f's)

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F(x) = 2x2 − 30, find f(4).

Leviafan [203]

Answer:

F(4)= 2

Step-by-step explanation:

F(x) = 2x^2 − 30, find f(4).

F(4)= (2)(4)^2 - 30

F(4)= (2)(16) - 30

F(4)= 32 - 30

F(4)= 2

6 0

3 years ago

A magazine conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale,

Lyrx [107]

Answer:

a) The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =85.82-81.90=3.92$

b) $SE=\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=0.975$

And the Margin of error is given by:

$Me= z_{\alpha/2} * SE=1.96*0.975=1.910$

c) The 95% confidence interval would be given by $2.009 \leq \mu_1 -\mu_2 \leq 5.83$ .

Step-by-step explanation:

Notation and previous concepts

$n_1 =35$ represent the sample of ships that carry fewer than 500 passengers

$n_2 =44$ represent the sample of ships that carry 500 or more passengers

$\bar x_1 =85.82$ represent the mean sample of of ships that carry fewer than 500 passengers

$\bar x_2 =81.90$ represent the mean sample of of ships that carry 500 or more passengers

$\sigma_1 =4.55$ represent the population deviation of ships that carry fewer than 500 passengers

$\sigma_2 =3.97$ represent the sample deviation of ships that carry 500 or more passengers

$\alpha=0.05$ represent the significance level

Confidence =95% or 0.95

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{(\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2})}$ (1)

Part a

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =85.82-81.90=3.92$

Part b: At 95% confidence, what is the margin of error?

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

The standard error is given by the following formula:

$SE=\sqrt{(\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2})}$

And replacing we have:

$SE=\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=0.975$

And the Margin of error is given by:

$Me= z_{\alpha/2} * SE=1.96*0.975=1.910$

Part c: What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships?

Confidence interval

Now we have everything in order to replace into formula (1):

$3.92-1.96\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=2.009$

$3.92+1.96\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=5.830$

So on this case the 95% confidence interval would be given by $2.009 \leq \mu_1 -\mu_2 \leq 5.83$ .

7 0

3 years ago

39)

Semmy [17]

let

brenda: b

will: 3b

b + 3b = 240

4b = 240

b = 60 lbs (BRENDA)

3b = will

3 (60) = will

180 = WILL

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3 years ago

The perimeter of a square Is 176 centimeters. If the square is dilated by a scale factor of 0.75, what is the length of each sid

seropon [69]

Answer: The answer is a decimal.

Step-by-step explanation:

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3 years ago

HELP ASAP WILL REWARD BRAINLIEST

Marina CMI [18]

Answer:

3. B. 128

4. B. 50.24

Step-by-step explanation:

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The numbers of the problem make it quite easy.

We can easily figure out how many books will be stacked in each dimension of the trunk.

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So, we can saw the trunk is 4 books long, by 4 books wide by 8 books thick... so, the number of books you can fit in that trunk is:

B = 4 * 4 * 8 = 128

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First, we have to find the volume of that big can...

Since it's a cylinder, its volume is calculated by:

V = π * r² * h and we have everything we need:

V = 3.14 * 4² * 12 = 192 * 3.14 = 602.88 cu in

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5 0

4 years ago