Find each difference. If you get stuck, consider drawing a number line diagram. HELP ASAP

Mathematics

1 answer:

liq [111]3 years ago

4 0

1.) 5
2.) 13
3.) -350
4.) 150
5.) -520
6.) 200
7.) 5
8.) -9
9.) -3
10.) 13
hope this helped

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IQ scores based on the Stanford-Binet IQ test are normally distributed with a mean of 100 and standard deviation 15. If you wer

lianna [129]

Answer:

95 intervals

Step-by-step explanation:

Given that

population mean = 100

standard deviation = 15

number of interval that involve the mean for 95% confidence interval is calculated as

We know that when we measure the 99 percent confidence interval, 99 outof 100 confidence interval are required to provide the mean population.

similarly

Assuming we measure a confidence interval of 95 percent, then we should expect 95 out of 100 confidence interval to provide the mean population therefore, answer is 95

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3 years ago

at an amusement park a person spends $30 on admission and food and then goes on r number of rides that cost $2 each

stepladder [879]

The question is find the equation, in the function and standard notations, that represent the amount spent in the range of 0 to 5 rides.

Constant cost: $30
Independent variable, number of rides: r
Variable cost: $2r

Total spend, s(r): 30 + 2r

Function: s(r) = 30 + 2r, for 0 ≤r ≤ 5 ----- this is the function notation

Standard form: s(r) is the dependent variable = s

s = 30 + 2r => s - 2r = 30 =>

s + (-2)r = 30, for 0 ≤ r ≤ 5 ------ this is the standard form

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3 years ago

Show that the points (0.-1).(2, 1).(0.3) and (-2, 1) are the vertices of a square ABCD.

Inessa05 [86]

The diagram is below

A = (0,-1)
B = (2,1)
C = (0,3)
D = (-2,1)

Let's find the distance from A to B using the distance formula.

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-2)^2 + (-1-1)^2}\\\\d = \sqrt{(-2)^2 + (-2)^2}\\\\d = \sqrt{4 + 4}\\\\d = \sqrt{8}\\\\d \approx 2.828\\\\$

The distance from A to B is exactly $\sqrt{8}$ units or approximately 2.828 units. This is the length of side AB.

Through very similar steps, you should find that the other side lengths of BC, CD and AD are all the same.

Since AB = BC = CD = AD, this means we have a rhombus. Recall a rhombus is any quadrilateral with all four sides the same length.

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

Let's find the slope of line AB

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-1)}{2 - 0}\\\\m = \frac{1 + 1}{2 - 0}\\\\m = \frac{2}{2}\\\\m = 1\\\\$

Line AB has a slope of 1.

Through similar steps, you should find the slope of line BC is -1.

Rule: Whenever two slopes multiply to -1, then their corresponding lines are perpendicular.

Based on that rule, lines AB and BC are perpendicular. This means they meet up at a right angle (aka 90 degree angle).

You should find that line CD has a slope of 1, so BC and CD are perpendicular. Lastly, line AD has a slope of -1. So all the slopes mentioned are either +1 or -1. The slopes alternate as you move around the figure. This all shows that any two adjacent sides meet at a 90 degree angle.

Therefore, this figure is a rectangle. Any rectangle has all four angles of 90 degrees.

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

The first section showed that we have a rhombus. The second section afterward showed that we also have a rectangle. The combination of a rhombus and a rectangle at the same time leads to a square.

Therefore, quadrilateral ABCD is a square.