First translate the English phrase "Four times the sum of a number and 15 is at least 120" into a mathematical inequality.
"Four times..." means we're multiplying something by 4.
"... the sum of a number and 15..." means we're adding an unknown and 15 and then multiplying the result by 4.
"... is at least 120" means when we substitute the unknown for a value, in order for that value to be in the solution set, it can only be less than or equal to 120.
So, the resulting inequality is 4(x + 15) ≤ 120.
Simplify the inequality.
4(x + 15) ≤ 120
4x + 60 ≤ 120 <-- Using the distributive property
4x ≤ 60 <-- Subtract both sides by 60
x ≤ 15 <-- Divide both sides by 4
Now that we have the inequality in a simplified form, we can easily see that in order to be in the solution set, the variable x can be no bigger than 15.
In interval notation it would look something like this:
[15, ∞)
In set builder notation it would look something like this:
{x | x ∈ R, x ≤ 15}
It is read as "the set of all x, such that x is a member of the real numbers and x is less than or equal to 15".
Answer:
0.6247
Step-by-step explanation:
The formula for calculating a Z-score is Z = (X - μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question,
μ = 51, σ = 10. We are to find P(36 ≤ X ≤ 56)
Step 1
Find the Probability of X ≤ 36
μ = 51, σ = 10
Z = (X - μ)/σ
Z = 36 - 51/ 10
Z = -15/10
Z = -1.5
We find the Probability of Z = -1.5 from Z-Table
P(X <36) = P(X = 36) = P(Z = -1.5)
= 0.066807
Step 2
Find the Probability of X ≤ 56
μ = 51, σ = 10
Z = (X - μ)/σ
Z = 56 - 51/ 10
Z = 5/10
Z = 0.5
We find the Probability of Z = 0.5 from Z-Table:
P(X < 56) = P(X = 56) = P(Z = 0.5)= 0.69146
Step 3
Find P(36 ≤ X ≤ 56)
P(36 ≤ X ≤ 56) = P(X ≤ 56) - P(X ≤ 36)
= P( Z = 0.5) - P(Z = -1.5)
= 0.69146 - 0.066807
= 0.624653
Approximately to 4 decimal places , P(36 ≤ X ≤ 56) = 0.6247
Answer:
7.5 miles per hour.
Step-by-step explanation:
We have been given that Mr. Ward runs a lot. He ran 45 minutes each day, 5 days each week, for 16 weeks.
First of all, we will find time for that Mr. Ward ran in 16 weeks.
We will multiply 5 by 16 to find number of days for that Mr. Ward ran and then we will multiply the result by 45 minutes to find the time.
Now, we will divide 3600 minutes by 60 minutes to convert time into hours as:
Now, we will divide 450 miles by 60 hours to find Mr. Ward's average speed as:
Therefore, Mr. Ward's average speed in 7.5 miles per hour.
Answer:
A. make a point on the line to the right 2 units from 0
B. the opposite of 2 isn't located at the same place as point P on the number line because the opposite of 2 is -2 and the point P is the opposite of negative 2 which would be positive 2. So the two points are not in the same place because they have different signs.
Step-by-step explanation:
hope this helps
I know the wording is a bit complicated lol <3
Answer: I think it's D
Step-by-step explanation:
