Answer:
The number of favorable outcomes is 5
Step-by-step explanation:
<u><em>The correct question is</em></u>
How many favorable outcomes are expressed in the fraction 5/12
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the event space is the number of outcomes in the event you are interested in or the number of favorable outcomes
The size of the sample space is the total number of possible outcomes
In this problem we have
therefore
The number of favorable outcomes is 5
The total number of possible outcomes is 12
<h3>
Answer: 6 inches</h3>
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Explanation:
x = amount (in inches) the spring is stretched
y = force applied (in pounds)
y = kx for some constant k, since x and y vary directly
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Plug in the given info that x = 5 and y = 150 pair up together
Solve for k
150 = k*5
150/5 = k
k = 30
The equation goes from y = kx to y = 30x. Whatever the stretching distance (x) is, you multiply by 30 to get the force needed (y) to pull the spring.
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Plug in y = 180 to solve for x
y = 30x
180 = 30x
30x = 180
x = 180/30
x = 6
The spring will be stretched 6 inches if you apply a force of 180 pounds.
Answer:
B
Step-by-step explanation:
14x - 3x + 11 = -22
-11 -11
14x - 3x = -33
11x = -33
/11 /11
x = -3
In this item, we are given with the amounts of both the flour and sugar.
Part A:
First, we determine the total amount of recipes needed for the batch.
total amount = (4 1/5 cup) + (2 3/7 cup)
total amount = 232/35 cup
To determine the total amount of sugar needed for 4/9 of the recipe, we multiply the given amount of sugar by 4/9. That is,
amount of sugar = (4/9)(2 3/7)
<em> amount of sugar = 68/63 cups of sugar</em>
Part B: To determine the amount of flour needed is 3 times the given amount for each batch.
amount of flour = (3)(4 1/5 cups of flour)
<em> amount of flour = 63/5 cups or 12.6 cups of flour</em>
The value of F(G(x)) is 2x^2 - 13
<h3>How to solve the composite functions?</h3>
The functions are given as:
F(x)=2x+1
G(x)=x^2-7
To find (FxG)(x), we make use of
(FxG)(x) = F(G(x))
So, we have:
F(G(x))=2G(x)+1
Substitute G(x)=x^2-7
F(G(x))=2(x^2-7)+1
Expand
F(G(x))=2x^2 - 14 + 1
Evaluate the like terms
F(G(x))=2x^2 - 13
Hence, the value of F(G(x)) is 2x^2 - 13
Read more about composite functions at:
brainly.com/question/20379727
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