Answers:
- <u>20 pounds</u> of the 95% concrete mix
- <u>10 pounds</u> of the 80% concrete mix
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Explanation:
x = amount of the 95% concrete mix
y = amount of the 80% concrete mix
Type A mix has 95% concrete. If we have x pounds of this, then 0.95x pounds is pure concrete. Type B mix has 80% concrete. If there are y pounds of this, then 0.80y pounds is pure concrete.
So far we have 0.95x+0.80y pounds of pure concrete from the two mixes
Divide this over 30 to get (0.95x+0.80y)/30
Setting this equal to 0.90 means we want the final mix to be 90% concrete.
Since we want 30 pounds total, we can say x+y = 30 which solves to y = 30-x. We'll use this later
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(0.95x+0.80y)/30 = 0.90
0.95x+0.80y = 30*0.90 .... multiply both sides by 30
0.95x+0.80y = 27
0.95x+0.80(30-x) = 27 ..... plug in y = 30-x
0.95x+0.80*30-0.80*x = 27
0.95x+24-0.80x = 27
0.15x+24 = 27
0.15x = 27-24 ..... subtracting 24 from both sides
0.15x = 3
x = 3/0.15 ........... dividing both sides by 0.15
x = 20
y = 30-x
y = 30-20
y = 10
Answer:
D. Alice used empirical probability, Mark used theoretical probability.
Step-by-step explanation:
Alice used empirical probability because she actually flipped the coin 100 times but Mark assumed the coin was fair and didn't actually test it, using theoretical probability.
50 + (15 × 15), 50 + 15 × 50 + 15, (10 × 5) + 225, 10 × 225 + 5 × 225
Solution:
Given expression is 50 + 225.
To find the equivalent expressions for 50 + 225.
(1) 225 can be written as 15 × 15.
⇒ 50 + 225 = 50 + (15 × 15)
(2) Using distributive law, we find the another equivalent expression
a + (b × c) = a + b × b + c
⇒ 50 + (15 × 15) = 50 + 15 × 50 + 15
(3) Now, 50 can be written as 10 × 5.
⇒ 50 + 225 = (10 × 5) + 225
(4 Using distributive law, we find the another equivalent expression
a + (b × c) = a + b × b + c
⇒ (10 × 5) + 225 = 10 × 225 + 5 × 225
Hence the equivalent expressions for 50 + 225 are:
50 + (15 × 15)
50 + 15 × 50 + 15
(10 × 5) + 225
10 × 225 + 5 × 225
That's simplied already, unless they want a decimal then it's .6 or something
