1 quart = 4 cups
7 quarts = 28 cups
1 guest needs 2 cups
12 guests need 24 cups
She has 28 and needs 24, yes there is enough
Answer:
a)P=0.42
b) 
Step-by-step explanation:
We have a binomial distribution, since the result of each experiment admits only two categories (success and failure) and the value of both possibilities is constant in all experiments. The probability of getting k successes in n trials is given by:

a) we have k=2, n=10 and p=0.01:

b) We have,
, Here P is the probability that at least one particle will penetrate the shield, this probabity has to be equal or greater than 0.95. Therefore, this will be equal to subtract from the total probability, the probability that the particles do not penetrate raised to the total number of particles.

Answer:
9.1 miles
Step-by-step explanation:
Answer:
Carlos is incorrect.
Step-by-step explanation:
We have been given that a line through the origin has a slope of
. Carlos thinks the slope of a perpendicular line at the origin will be 3.
We know that the slope of a perpendicular line to a given line is always negative reciprocal of the slope of the given line.
The slope of the perpendicular line at the origin will be negative reciprocal of
.
Let us find negative reciprocal of
as:

Since the slope of a perpendicular line at the origin is
, therefore, Carlos is incorrect.
The angles of a triangle always add up to 180°.
120 + x + 16 + x = 180
Add up the values.
136 + 2x = 180
Subtract 136 from both sides.
2x = 44
Divide both sides by 2.
x = 22