Answer:
C
Step-by-step explanation:
Calculate AC using Pythagoras' identity in ΔABC
AC² = 20² - 12² = 400 - 144 = 256, hence
AC = 
= 16
Now find AD² from ΔACD and ΔABD
ΔACD → AD² = 16² - (20 - x)² = 256 - 400 + 40x - x²
ΔABD → AD² = 12² - x² = 144 - x²
Equate both equations for AD², hence
256 - 400 + 40x - x² = 144 - x²
-144 + 40x - x² = 144 - x² ( add x² to both sides )
- 144 + 40x = 144 ( add 144 to both sides )
40x = 288 ( divide both sides by 40 )
x = 7.2 → C
To find the z-score for a weight of 196 oz., use
A table for the cumulative distribution function for the normal distribution (see picture) gives the area 0.9772 BELOW the z-score z = 2. Carl is wondering about the percentage of boxes with weights ABOVE z = 2. The total area under the normal curve is 1, so subtract .9772 from 1.0000.
1.0000 - .9772 = 0.0228, so about 2.3% of the boxes will weigh more than 196 oz.
Answer:
In your change cup you have 28 coins. All of which are nickels and quarters. Together they add up to $4. How many coins do you have of each.
It is easier to solve by substitution.
75: 1, 3, 5, 15, 25, 75
90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
GCF(75, 90) = 1, 3, 5, 15
1 × 3 × 5 × 15
3 × 75
225
