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3 years ago

A=3b what is solution for b

Mathematics

2 answers:

nalin [4]3 years ago

8 0

A = 3b Divide both sides by 3
$\frac{A}{3}$ = b Switch the sides so it's easier to read

b = $\frac{A}{3}$

victus00 [196]3 years ago

8 0

A/3 because you have to divide by 3 to get b alone

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Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:

Vikentia [17]

Answer:

$\= x = 18.5$ , $\sigma = 5.15$

$15.505 < \mu < 21.495$

$14.93 < \mu < 22.069$

Step-by-step explanation:

From the question we are are told that

The sample data is 21, 14, 13, 24, 17, 22, 25, 12

The sample size is n = 8

Generally the ample mean is evaluated as

$\= x = \frac{\sum x }{n}$

$\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}$

$\= x = 18.5$

Generally the standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}$

$\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}$

$\sigma = 5.15$

considering part b

Given that the confidence level is 90% then the significance level is evaluated as

$\alpha = 100-90$

$\alpha = 10\%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.645$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.645 * \frac{5.15 }{\sqrt{8} }$

=> $E = 2.995$

The 90% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 2.995 < \mu < 18.5 + 2.995$

$15.505 < \mu < 21.495$

considering part c

Given that the confidence level is 95% then the significance level is evaluated as

$\alpha = 100-95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.96 * \frac{5.15 }{\sqrt{8} }$

=> $E = 3.569$

The 95% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 3.569 < \mu < 18.5 + 3.569$

$14.93 < \mu < 22.069$

8 0

3 years ago

You buy five books that are equal in

Georgia [21]

Answer:

5x+8=26.50

Step-by-step explanation:

Because the books are equal in price, we can use x to represent the price of the books and 5 to represent the amount, so it would be written as 5x. Then we add 8 because that's the price of the one DVD. It tells the total is 26.50, so the full equation written would be <u>5x+8=26.50</u>

4 0

2 years ago

Read 2 more answers

The width of a rectangle is three more than twice the length. The perimeter is 96 inches. Find the length and the width.

ExtremeBDS [4]

Answer:

The length of the rectangle is 15 inches and the width is 33 inches

Step-by-step explanation:

The dimensions for the rectangle are as follows:

L=L and W=2L+3

The equation for perimeter of a rectangle is:

P=2l+2w

To Solve:

1. Plug values into perimeter equation

96=2(L)+2(2L+3)

2. Simplify the equation above.

96=2L+4L+6

3. Combine like terms:

96=6L+6

4. Solve for L by subtracting 6 from both sides:

90=6L

5. Solve for L by dividing both sides by 6:

15=L.

6. Plug 15 into the equation for the width:

2(15)+3=w

30+3=w.

7 0

3 years ago

Data collected over time on the utilization of a computer core (as a proportion of the total capacity) were found to possess a r

Marianna [84]

Answer:

The probability that the proportion of the core being used at any particular time will be less than 0.10 is 0.08146

Step-by-step explanation:

$\mu =\frac{\alpha }{\alpha +\beta } = \frac{1}{1 + \frac{\beta}{\alpha} }$ 1/3 0.33 = 33.33 %

The Probability of that the proportion of the core being used at any particular time will be less than 0.10 is given by

PDF = $\frac{x^{\alpha -1} (1-x)^{\beta -1} }{\int\limits^1_0 {u^{\alpha -1} (1-u)^{\beta -1}} \, du }$

where x = 0.1

α = 2 and β = 4

PDF = $\frac{0.0729 }{\int\limits^1_0 {u^{\alpha -1} (1-u)^{\beta -1}} \, du }$ = 1.458

CDF = $\frac{\int\limits^{0.1}_0 {t^{\alpha -1} (1-t)^{\beta -1}} \, du }{\int\limits^1_0 {u^{\alpha -1} (1-u)^{\beta -1}} \, du }$ = 0.08146

The probability that the proportion of the core being used at any particular time will be less than 0.10 = 0.08146.

3 0

3 years ago

What is the approximate side length of the square? 3.0 units 3.5 units 4.2 units 4.9 units

AVprozaik [17]

Answer:

(っ◔◡◔)っ ♥ the answer is C ♥

Step-by-step explanation:

4 0

1 year ago