Answer:
0.337 = 33.7% probability that one of the eight children has a food allergy.
Step-by-step explanation:
For each children, there are only two possible outcomes. Either they have a food allergy, or they do not. The probability of a child having food allergy is independent of any other child. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
7% of U.S. children 4 years of age or younger have a food allergy.
This means that 
A day care program has capacity for 8 children in that age range.
This means that 
What is the probability that one of the eight children has a food allergy?
This is P(X = 1).
0.337 = 33.7% probability that one of the eight children has a food allergy.
I think it's the Multiplication Property of Equality.
Hope this helps you! :)
The distance from the sun is option 2 5.59 astronomical units.
Step-by-step explanation:
Step 1; To solve the question we need two variables. P which represents the number of years a planet takes to complete a revolution around the Sun. This is given as 13.2 years in the question so P = 13.2 years. The other variable is the distance between the planet and the sun in astronomical units. We need to determine the value of this using the given equation.
Step 2; So we have to calculate the value of 'a' in Kepler's equation. But the exponential power 
is on the variable we need to find so we multiply both the sides by an exponential power of 
to be able to calculate 'a'.
P = 
, 
= 
, = a, 
= a = 5.58533 astronomical units.
Rounding it over to nearest hundredth we get 5.59 astronomical units.
Answer:
3. x-2
Step-by-step explanation:
Let's start with 1. we know that 2-x is the same as -2+x and since addition can be written as -2+x or x+(-2) and equal the same thing, we know that x-2 is the one that is not equivalent.
200,000 = 158,000(1.06)^x
Divide both sides by 158,000
1.2658 = 1.06^x
Take the log of both sides and use the power rule to bring down the exponent (x) to the front.
log 1.2658 = x log 1.06
Divide both sides by log 1.06
log (1.2658)/log(1.06) = x
x = 4 years
CHECK
y = 158,000(1.06)^4
y = 199,471.36
