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3 years ago

What fraction is represented by the portion of the figure that is NOT shaded? (2 out of 10 are shaded)

1 answer:

OverLord2011 [107]3 years ago

8 0

Well let's see.

If the figure is split up into 10 pieces, then
each piece is 1/10 of the whole figure.

If 2 of the pieces are shaded, then
2/10 of the whole figure is shaded.

How many pieces are left ?

There were 10 pieces all together, and
2 of them are shaded. Hmmm. I think
there are probably (10 - 2) = 8 of them left
that are not shaded.

8 pieces makes 8/10 of the whole figure.

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PLEASE PLEASE HELP ME

Galina-37 [17]

Answer:

1. 110°

Step-by-step explanation:

Given angle - 610°

Coterminal angle is an angle in the interval 0°- 360° added or subtracted to multiples of 360°:

-610° + 2*360° = -610° + 720° = 110°

Correct option is 1.

7 0

3 years ago

A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

<em>So, the 95% confidence interval is (46.4, 53.6)</em>

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

<em>So, the 95% confidence interval is (47.9, 52.1)</em>

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

<em>Notice that the margin of error decreases when the sample size increases.</em>

4 0

3 years ago

An equation is shown below:

mart [117]

Multiple 6 with numbers inside paranthesis:
12x - 66 + 15 = 21
add 66 fhen substrack 15 from both sides :
12x = 72 divide both sides with 12:
x = 6

5 0

3 years ago

Read 2 more answers

A coat cost $ 131.61 with 9.5% sales tax

marysya [2.9K]

Calculating Total Cost. Multiply the cost of an item or service by the sales tax in order to find out the total cost. The equation looks like this: Item or service cost x sales tax (in decimal form) = total sales tax. Add the total sales tax to the Item or service cost to get your total cost. Multiply retail price by tax rate

Let's say you're buying a $100 item with a sales tax of 5%. Your math would be simply: [cost of the item] x [percentage as a decimal] = [sales tax]. That's $100 x .

6 0

3 years ago

Given that x and y are positive integers, solve the equation x² - 4y² = 13

zvonat [6]

<h3>Answer: x = 7 and y = 3</h3>

=====================================================

Explanation:

Apply the difference of squares rule

x² - 4y² = 13

x² - (2y)² = 13

(x - 2y)(x + 2y) = 13

Since x and y are positive integers, this means x-2y and x+2y are both integers as well.

The value 13 is prime. Its only factors are 1 and 13

Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:

A) x-2y = 1 and x+2y = 13
B) x-2y = 13 and x+2y = 1

----------------

Let's consider case A

We have this system of equations

$\begin{cases}x-2y = 1\\x+2y = 13\end{cases}$

Add the equations straight down

x+x becomes 2x
-2y+2y becomes 0y = 0 which goes away
1+13 becomes 14

Therefore we have 2x = 14 solve to x = 7

From here, plug this into either equation to solve for y

x-2y = 1

7 - 2y = 1

-2y = 1-7

-2y = -6

y = -6/(-2)

y = 3

You should get the same result if you used x+2y = 13

----------------

Since we've found that x = 7 and y = 3, notice how case B is not possible

Example: x-2y = 13 becomes 7-2(3) = 13 which is false.

Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.

-----------------

Let's check those x and y values in the original equation

x² - 4y² = 13

7² - 4*(3)² = 13

49 - 4(9) = 13

49 - 36 = 13

13 = 13

The answer is confirmed.

4 0

2 years ago