1 ) 9 x + 18 > 9 x - 27
9 x - 9 x > - 27 - 18
0 * x > - 45
Always true
2 ) 6 x - 13 < 9 x - 12
6 x - 6 x < - 12 + 13
0 * x < 1
Always true
3 ) - 6 ( 2 x - 10 ) + 12 x ≤ 180
- 12 x + 60 + 12 x ≤ 180
0 * x ≤ 180 - 60
0 * x ≤ 120
Always true.
Answer:
to convert a fraction to a decimal, divide the numerator by the denominator
Answer:
See below.
Step-by-step explanation:
The theoretical probability of choosing a particular colour is 1/6 or 16.67% so for 625 picks we would expect 625/6 = 104 to be the result.
Part A Yellow. The experimental probability is 106/625 = 16.96% and the theoretical probability = 16.67%.
Part B Green. The experimental probability is 142/625 = 22.72% and the theoretical probability is 16.67%.
Answer:
AK = CN = 9.6 cm
BN = 8 cm
Step-by-step explanation:
AC is the base of the isosceles triangle, so N is the midpoint of AC. CN is 6 cm, so the Pythagorean Theorem tells us the altitude BN is
... BN = √(BC² -CN²) = √(100 -36) = 8 . . . . cm
The area of the triangle is ...
... Area = (1/2)(AC)(BN) = (1/2)(12 cm)(8 cm) = 48 cm²
The other altitudes (AK, CM) are to sides of length 10, so they can be found from the area formula as ...
... 48 cm² = (1/2)·altitude·(10 cm)
... 48 cm²/(5 cm) = altitude = 9.6 cm
Thus we have BN = 8 cm, AK = CM = 9.6 cm.
Complete Question
A peanut butter cookie recipe calls for 3 1/2 cups of flour to make 6 dozen cookies. How many cups of flour must be used to make 20 dozen?
Answer:
11 2/3 cups of flour
Step-by-step explanation:
From the above question:
6 dozen = 3 1/2 cups of flour
20 dozen = x
Cross Multiply
6 dozen × x = 20 dozen × 3 1/2 cups of flour
x = 20 dozen × 3 1/2 cups of flour/6 dozen
x = 20 × 7/2 /6
x = 140/2 ÷ 6
x = 140/2 × 1/6
x = 140/12 cups of flour
x = 11 8/12
= 11 2/3 cups of flour
Therefore, 11 2/3 cups of flour must be used to make 20 dozen.