Answer:
probability that he or she will answer at least 4 problems correctly = 0.5
Step-by-step explanation:
probability that he or she will answer at least 4 problems correctly is given as;
P (at least 4 correctly) = P (exactly 4 correctly) + P (all 5 correctly)
Since there are 10 problems. 4 is from the 7 problems chosen and 1 is from the 3 problems we can't figure out. Thus, P(exactly 4 correctly) = 7C4 x 3C1
Thus, P (at least 4 correctly) = [ (7C4) x (3C1) ] / (10C5)] + [(7C5)/(10C5)]
= [(35 x3)/252 ] + [21/252]
= [ 105/252 ] + [ 21/252 ]
= 126 / 252
= 0.5
Answer: 
Step-by-step explanation:
Given
Length L=15 feet
width b=2 feet
Volume V=375 cubic feet
Suppose h is the height
Volume is given by 
Answer:
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).
We are dividing:
So, a polynomial by a binomial factor.
Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.
We want our remainder to be 3. So, P(a)=P(-k)=3.
Therefore:
Simplify:
Solve for <em>k</em>. Subtract 3 from both sides:
Factor:
Zero Product Property:
Solve:
So, either of the two expressions:
Will yield 3 as the remainder.
Answer:
x = 1 or x = -5
Step-by-step explanation:
Solve for x over the integers:
8 abs(x + 2) - 6 = 5 abs(x + 2) + 3
Subtract 5 abs(x + 2) - 6 from both sides:
3 abs(x + 2) = 9
Divide both sides by 3:
abs(x + 2) = 3
Split the equation into two possible cases:
x + 2 = 3 or x + 2 = -3
Subtract 2 from both sides:
x = 1 or x + 2 = -3
Subtract 2 from both sides:
Answer: x = 1 or x = -5
Answer:
B
Step-by-step explanation:
It all starts whether the Knave of Hearts tells the truth or not. You can decide yourself.
Hearts: H
Clubs: C
Diamonds: D
Spades: S
If H lies, C tells the truth, therefor D lies. So S tells the truth
If H tells the truth, C lies. Therefore D tells the truth and S lies
