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3 years ago

The sum of two numbers is 8, and the sum of their squares is 34. what is the larger number

Mathematics

1 answer:

bija089 [108]3 years ago

6 0

Answer:

The larger number is 5.

Step-by-step explanation:

Let the numbers be represented by x and y. Then:

x + y = 8 is their sum, and

x² + y² = 34 is the sum of their squares.

Let's solve this system of equations using substitution. Since x + y = 8,

x = 8 - y. Subbing this 8 - y for x into the second equation, we get:

(8 - y)² + y² = 34, or

64 - 16 y + y² + y² = 34

Simplifying, we get first: 30 - 16y + 2y² = 0, and then:

2y² - 16y + 30 = 0, and after reducing, y² - 8y + 15 = 0.

This factors into (y - 3)(y - 5) = 0, and so y = 3 and y = 5.

The larger number is 5.

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3 years ago

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2 years ago

Assume that the helium porosity of coal samples taken from any particular seam is Normally distributed with true standard deviat

riadik2000 [5.3K]

Answer:

a) $4.85-2.33\frac{0.75}{\sqrt{20}}=4.46$

$4.85+2.33\frac{0.75}{\sqrt{20}}=5.24$

b) $4.56-2.33\frac{0.75}{\sqrt{16}}=4.12$

$4.56+2.33\frac{0.75}{\sqrt{16}}=4.99$

c) $n=(\frac{1.960(0.75)}{0.2})^2 =54.02 \approx 55$

Step-by-step explanation:

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.33$

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

$4.85-2.33\frac{0.75}{\sqrt{20}}=4.46$

$4.85+2.33\frac{0.75}{\sqrt{20}}=5.24$

Part b

$4.56-2.33\frac{0.75}{\sqrt{16}}=4.12$

$4.56+2.33\frac{0.75}{\sqrt{16}}=4.99$

Part c

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.4/2 =0.2 we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got:

$n=(\frac{1.960(0.75)}{0.2})^2 =54.02 \approx 55$

5 0

3 years ago

I NEED TO KNOW NOW IT'S DUE!!

umka2103 [35]

x = # of days Maria worked

x + 5 = # of days Fred worded

$16(x + 5) + $18x = $1780

Let's distribute the $16

$16x + $80 + $18x = $1780

Combine like terms

$34x + $80 = $1780

Subtract $80 from both sides.

$34x = $1700

Divide both sides by $34

x = 50 days

Maria worked 50 days

3 0

3 years ago