<span>You are given a rectangular picture measuring 8 inches by 7 inches. Also, Alistair wants this to be framed and that the total area is 34 square inches. The width of the frame is x inches. To solve the dimension of the frame with value of x we have:
We have to assume that x here will be equal to all sides of the frame and so, using the area of the rectangle, we can model the equation like this:
A = LW (where A is the area, L is the length and W is the width)
36 = (8 - x)(7 - x)
36 = 56 - 8x - 7x + x</span>²
<span>x</span>² - 15x +20 = 0 → model of our equation and in quadratic form
x² - 15x + 20 = 0
using a calculator, x = 1.48 inches
<span>
3.Use the equation you created in part A to find the width of the picture frame</span>
These two lines create vertical angles, which are congruent. That means angle z = 60 degrees. Since angle z and the angle represented by the expression 6x + 60 are supplementary (they are adjacent angles that add to equal 180 degrees), you can set up the following equation to find x:
6x + 60 + 60 = 180
6x + 120 = 180
6x = 60
x = 10
Answers:
x = 10
z = 60
75+ 15x ≥ 140
⇒ 15x ≥ 140-75
⇒ 15x ≥ 65
⇒ x ≥ 65/15
⇒ x ≥ 13/3
⇒ x ≥ 4 1/3
Final answer: x ≥ 4 1/3~
18333/10000
Convert to a fraction by placing the decimal number over a power of 10
Answer:
So about 95 percent of the observations lie between 480 and 520.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviations of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
The mean is 500 and the standard deviation is 10.
About 95 percent of the observations lie between what two values?
From the Empirical Rule, this is from 500 - 2*10 = 480 to 500 + 2*10 = 520.
So about 95 percent of the observations lie between 480 and 520.
