Answer:
D. 0.5256
Step-by-step explanation:
Use binomial probability:
P = nCr p^r q^(n-r)
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
Given n = 10, p = 0.25, and q = 0.75.
If r = 0:
P = ₁₀C₀ (0.25)⁰ (0.75)¹⁰⁻⁰
P = 0.0563
If r = 1:
P = ₁₀C₁ (0.25)¹ (0.75)¹⁰⁻¹
P = 0.1877
If r = 2:
P = ₁₀C₂ (0.25)² (0.75)¹⁰⁻²
P = 0.2816
So the total probability is:
P = 0.0563 + 0.1877 + 02816
P = 0.5256
Answer:
C.
Step-by-step explanation:
Answer:
length = 48 feet , width = 32 feet
Step-by-step explanation:
Using
2W + 2L = 160 with W = L - 16 , then
2(L - 16) + 2L = 160 ← distribute and simplify left side
2L - 32 + 2L = 160
4L - 32 = 160 ( add 32 to both sides )
4L = 192 ( divide both sides by 4 )
L = 48
Substitute L = 48 into W = L - 16
W = 48 - 16 = 32
Thus length = 48 feet and width = 32 feet
6. One variable only so pretty straightforward.
length-x+4
width-x
x+x+4=80
2x=76
x=38
x+4=42
answer: length 42cm and width 38cm
7. Another money problem!
n-# of nickels
q-# of quarters
n=3+q
0.05n+0.25q=2.85
Substitution works like a charm!
0.05(3+q)+0.25q=2.85
0.15+0.05q+0.25q=2.85
0.3q=2.7
q=9
n=3+q
n=3+9
n=12
answer: 9 nickels and 12 quarters
8. One variable situation again.
Ann's money-2b+9
Betty's money-b
b+2b+9=60
3b=51
b=17
2b+9=43
answer: Ann has $43 and Betty has $17.
9. # of red m&m's-x+1
# of blue m&m's-x
x+1+x=13
x=6
x+1=7
answer: 6 blue and 7 red m&m's
10. a-number of adult tickets
s-number of student tickets
a+s=785 ----> a=785-s
5a+2s=3280
5(785-s)+2s=3280
-3s=-645
s=215
a+s=785
a+215=785
a=570
answer: 215 children tickets and 570 adult tickets
Answer:
The second option: 3 (6 - 5n)/20n
Step-by-step explanation:
Make sure all fractions have a common denominator:
Step 1. Find a common multiple between all three denominators
5, 4, and 10 all have a common multiple of 20. Proof: 5 × 4 = 20, 4 × 5 = 20, and 10 × 2 = 20
Step 2. Multiply the denominators to get to 20. Whatever you do to the bottom (denominator) must be done to the top (numerator).
1/5n × 4/4 = 4/20n
3/4 × 5n/5n = 15n/20n
7/10n × 2/2 = 14/20n
Your fractions now all have a common denominator of 20n.
Rewrite the equation using the new fractions:
4/20n - 15n/20n + 14/20n
Only focus on adding/subtracting the numerators; the denominators will stay the same: 20n.
(4 - 15n + 14)/20n
Combine like terms:
(18 - 15n)/20n
Factor out any numbers possible:
3(6 - 5n)/20n
Note* 3 go into both 18 and 15, which allows us to factor 3 out. 18 ÷ 3 = 6 and 15 ÷ 3 = 5, giving us our new numbers inside the parentheses.
