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2 years ago

Complete the chart of congruence proofs and reasons

Mathematics

1 answer:

babymother [125]2 years ago

4 0

Answer:

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Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a

rusak2 [61]

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

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

$\alpha = \frac{1 - 0.95}{2} = 0.025$

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 $1 - 0.025 = 0.975$ , so Z = 1.96.

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.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that $\sigma = 2$

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when $M = 0.5$ . So

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

$0.5 = 1.96\frac{2}{\sqrt{n}}$

$0.5\sqrt{n} = 2*1.96$

Dividing both sides by 0.5

$\sqrt{n} = 4*1.96$

$(\sqrt{n})^2 = (4*1.96)^2$

$n = 61.5$

Rounding up

We would have to take a sample of 62 to achieve this result.

8 0

2 years ago

What is 45=m(25)+b solving for m

STatiana [176]

Answer:

$\frac{45-b}{25}$

Step-by-step explanation:

given

45 = 25m + b ( isolate the term in m by subtracting b from both sides )

45 - b = 25m ← divide both sides by 25

$\frac{45-b}{25}$ = m

7 0

2 years ago

Which set of graphs can be used to find the solution set to 3e* > >-x?

kobusy [5.1K]

The attached graph represents the solution set of $3e^x > \frac 12^x$

<h3>How to determine the graph?</h3>

The complete options are not given.

So, I would plot the graph that represents the solution set

The inequality is given as:

$3e^x > \frac 12^x$

Start by splitting the inequalities as follows:

$f(x) > 3e^x$

$g(x) > \frac 12^x$

The above means that we plot the graphs of f(x) and g(x) to represent the solution set

See attachment

Read more about inequalities at:

brainly.com/question/25275758

#SPJ1

7 0

1 year ago

Find the number of ways you can arrange (a) all of the letters and (b) two of the letters in the word TRY. a. The number of ways

Phantasy [73]

Answer:

a) 6 ways

b) 6 ways

Step-by-step explanation:

a) for all of the letters

for the first letter, we have 3 options

for the second, we have 2 options

for the third, we have 1 option

So the number of options will be;

3 * 2 * 1 = 6

b) for the first, we have 3 options, for the second, we have 2 options

so the number of options will be 3 * 2 = 6 options

8 0

2 years ago

-34 + 91 = -3 (4x + 1) + 6x

ra1l [238]

$-34 + 91 = -3(4x+1) + 6x\\57 = -12x - 3 + 6x\\6x = -60\\x= -10\\$

Thus x = -10.

Hope that helps!

3 0

2 years ago

Read 2 more answers