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rosijanka [135]

3 years ago

13

Find x

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1 answer:

MArishka [77]3 years ago

5 0

I will assume the question is log (8x) = 4/3

This means, "The exponent we put on 10 to get 8x is 4/3"

10^(4/3) = 8x

x = [10^(4/3)]/8

x = 2.69

log (8*2.69) = 4/3 ?
log (21.52) = 4/3
1.33 = 4/3
1.33 = 1.33

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A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of

notsponge [240]

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.98}{2} = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.01 = 0.99$ , so Z = 2.327.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031$

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.0001 = 2.327\frac{0.0003}{\sqrt{n}}$

$0.0001\sqrt{n} = 2.327*0.0003$

$\sqrt{n} = \frac{2.327*0.0003}{0.0001}$

$(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2$

$n = 48.73$

Rounding up

49 measurements are needed.

7 0

2 years ago

Which of the following is a rational number?

scoray [572]

Examples of rational numbers are: -2 = -2/1, -5 = -5/1, -14 = -14/1, 1/2, 2/3, 5/8, 3/4, 17/5, . 6 = 6/10 = 3/5, . 25 = 1/4, . 33 = 33/100, 2¾ = 11/4, 3⅓ = 10/3, .

5 0

3 years ago

What is the median of 74,83,79,62,65,73

Allisa [31]

Answer:

Step-by-step explanation:

Median: 73.5

4 0

3 years ago

Can someone help me? I'm trying to find the slope form of 4x + 2y = 4.

Neporo4naja [7]

Here, Equation: 4x + 2y = 4
Divide the equation by 2,
2x + y = 2
y = -2x + 2

Now, compare the equation with y = mx + c
Here, slope (m) = -2

In short, Your Answer would be -2

Hope this helps!

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=2%28x%20-%208%29%20%2B%204x%20%3D%206%28x%20-%202%29%20-%204" id="TexFormula1" title="2(x - 8)

Flauer [41]

In this question, you're solving for x.

Solve for x:

2(x - 8) + 4x = 6(x - 2) - 4

Distribute the 2 to the variables inside the parenthesis.

2x - 16 + 4x = 6(x - 2) - 4

Distribute the 6 to the variables inside the parenthesis.

2x - 16 + 4x = 6x - 12 - 4

6x - 16 = 6x - 12 - 4

6x - 16 = 6x - 16

Subtract 6x from both sides

-16 = -16

Add 16 to both sides

0 = 0

Answer:

All real numbers and solutions

8 0

3 years ago

Read 2 more answers