Mike has a total of 50 quarters and dimes. The coins total value is $10.55. How many quarters

A random sample of 85 sixth-graders in a large city take a course designed to improve scores on a reading comprehension test. Ba

BartSMP [9]

Answer:

$12.6 < \mu < 14.8$

For this case we can find the margin of error like this:

$ME= \frac{14.8-12.6}{2}= 1.1$

Since we need to divide the width of the interval by 2.

And now with the margin of error we can find the sample mean with any of the two following ways:

$12.6 +1.1=13.7$

$14.8-1.1=13.7$

So for this case the correct answer would be:

A. Sample Mean = 13.7; Margin of Error = 1.1

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=85-1=84$

We know that the confidence interval is given by:

$12.6 < \mu < 14.8$

For this case we can find the margin of error like this:

$ME= \frac{14.8-12.6}{2}= 1.1$

Since we need to divide the width of the interval by 2.

And now with the margin of error we can find the sample mean with any of the two following ways:

$12.6 +1.1=13.7$

$14.8-1.1=13.7$

So for this case the correct answer would be:

A. Sample Mean = 13.7; Margin of Error = 1.1

3 0

3 years ago

the radius of a circular garden is 6 ft. if one foot of fencing cost 2.75 dollars, how much would you spend to completely surrou

PIT_PIT [208]

Answer:

103.67 dollars.

Step-by-step explanation:

The perimeter of the garden = 2 * π * 6 feet.

So the cost is 2.75 * 12π dollars.

= 103.67 dollars.

3 0

3 years ago

100% of what number is 61

Dominik [7]

" 100% " means "the whole thing",
and "is" can be replaced by "is equal to".

You have said "The whole thing of a number is equal to 61."
or
"61 is equal to the whole thing of a number."

The only number that 61 can be equal to is 61.

3 0

3 years ago

Read 2 more answers

Here are three stories:

aev [14]

Answer:

1)

a) 6x+3 = 27

b) x=4

c) We know that x is price of each ticket, so The price of each ticket is $4. They bought 6 tickets, so total cost of ticket = 24 and $3 for parking so, total money spent = $27.

2)

a) 3x + 6 = 27

b) x= 7

c) We know that x is amount of juice poured, so 3 friends of Diego will get 7 ounces of Juice, while Diego will get 6 ounces of juice.

3)

a) 27x + 3 = 6

b) x= 1/9

c) We know that x is time spend on each picture, so Jada spend 1/9 hour on each picture

Step-by-step explanation:

1. A family buys 6 tickets to a show. They also pay a $3 parking fee. They spend $27 to see the show.

a) Decide which equation represents each story. What does x represent in each equation?

Let x be price of one ticket.

The equation will be: 6x+3 = 27

b. Find the solution to each equation. Explain or show your reasoning,

Now solving the equation:

6x+3=27

6x=27-3

6x=24

x=24/6

x=4

So, we get x = 4

c. What does each solution tell you about its situation?

We know that x is price of each ticket, so The price of each ticket is $4. They bought 6 tickets, so total cost of ticket = 24 and $3 for parking so, total money spent = $27.

2. Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself.

a) Decide which equation represents each story. What does x represent in each equation?

Let x be amount of juice poured.

The equation will be: 3x+6 = 27

b. Find the solution to each equation. Explain or show your reasoning,

Now solving the equation:

3x+6=27

3x=27-6

3x=21

x=21/3

x=7

So, we get x = 7

c. What does each solution tell you about its situation?

We know that x is amount of juice poured, so 3 friends of Diego will get 7 ounces of Juice, while Diego will get 6 ounces of juice.

3. Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself.

a) Jada works for 6 hours preparing for the art fair. She spends 3 hours on a sculpture and then paints 27 picture frames.

Let x be time spend on each picture frame.

The equation will be: 27x+3=6

b. Find the solution to each equation. Explain or show your reasoning,

Now solving the equation:

27x+3=6

27x=6-3

27x=3

x=3/27

x=1/9

So, we get x = 1/9

c. What does each solution tell you about its situation?

We know that x is time spend on each picture, so Jada spend 1/9 hour on each picture

8 0

3 years ago

Read 2 more answers

What is the value of (16^3/2)^1/2

Alika [10]

<u><em>Answer: =1024. *The answer must be have positive sign.*</em></u>

Step-by-step explanation:

This question's it's about the order of operations. p-parenthesis, e-exponents, m-multiply, d-divide, a-add, and s-subtract. It can also go left to right.

do exponents first.

16³/2=4098=2048¹/2

2048¹=2048

2048/2

divide left to right.

2048/2=1024

Hope this helps!

Thanks!

Have a great day!

4 0

3 years ago