Answer:
75%
88.89%
Step-by-step explanation:
Given :
Mean = 70
Standard deviation = 12
Since the data is said to be extremely skewed, we apply Chebyshev's theorem rather than the empirical rule :
The minimum proportion of observation between 46 and 94
Chebyshev's theorem :
1 - 1 / k²
k = number of standard deviations from the mean
k = (94 - 70) / 12 = 24 / 12 = 2
Hence, we have ;
1 - 1/2²
1 - 1/4
1 - 0.25 = 0.75
Hence, The minimum proportion of observation between 46 and 94 is 75%
Between 36 and 106 :
k = (106 - 70) / 12 ;
k = 36/12 = 3
Hence,
1 - 1/3² = 1 - 1/9 = 8/9 = 0.8888 = 88.89%
The minimum proportion of observation between 34 and 106 is 88.89%
Hello! She earns a salary of $2,100, which is the fixed amount each month, plus 5% commission on her sales. To find out the amount of sales that will help her reach her goal, set up the inequality like this:
2,100 + 0.05x ≥ 2,400
We set it up like this, because $2,100 is the one-time price per month, and she earns 5% of her sales as commission. Plus, the key words "at least" means the inequality sign is greater than or equal to (≥)
How to solve this:
First off, subtract 2,100 from both sides, when you do, you get 0.05x ≥ 300. Now, divide each side by 0.05 to isolate the "x". 300/0.05 is 6,000. Let's check this. 6,000 * 5% (0.05) is 300. There. x = 6,000. Liz will need to sell $6,000 worth of items this month in order to meet her goal.
Answer:
<h2>infinitely many solutions</h2>
Step-by-step explanation:
5x - 6 = 3x - 6 + 2x <em>combine like terms</em>
5x - 6 = (3x + 2x) - 6
5x - 6 = 5x - 6 <em>subtract 5x from both sides</em>
-6 = -6 TRUE
Therefore the equation has infinitely many solutions.
The rate Ritz can eat apples is 8/15 apples per minute.
Set the rate (which is measured apples / minutes) equal to 16 apples / t minutes.
(8/15) = (16/t)
Cross multiply.
16*15 = 8t
t = 20
The answer is 30 minutes. You could solve the problem with basic reasoning as well. 16 is twice the number of apples as 8, so the time it takes to eat them will be double 15 minutes.
