Answer:
2. Cecilia uses 3 cups of flour for 36 cookies
4. Cecilia is making 3/4 of the original recipe
Step-by-step explanation:
Recipe for 48 cookies
Flour = 4 cups
Sugar = 1 1/3 cups
Recipe for 36 cookies
48 cookies : 36 cookies
= 4 : 3
Flour used in 36 cookies = x cups
Flour used in 48 cookies = 4 cups
4 cups : x cups
4 : 3 = 4 : x
4/3 = 4/x
4*x = 3*4
4x = 12
x = 12/4
x = 3 cups
Sugar = 1 1/3 cups
Sugar used in 36 cookies = y cups
Sugar used in 48 cookies = 1 1/3 cups
4 : 3 = 1 1/3 : y
4/3 = 4/3 ÷ y
4/3 = 4/3 × 1/y
4/3 = 4/3y
4*3y = 3*3
12y = 9
y = 9/12
= 3/4
y = 3/4
The true statement are:
2. Cecilia uses 3 cups of flour for 36 cookies
4. Cecilia is making 3/4 of the original recipe
Answer:
30
Step-by-step explanation:
40/100 x 50= 20
50-20=30
Answer: -6.7
Step-by-step explanation:
64.3−(3)(23)−2
=−6.7
Answer:
Step-by-step explanation:
In this problem, we have the following linear equations:
y=3x+5
y=ax+b
We know that a linear equation is an equation for a line. In a system of linear equations, two or more equations work together.
1. What values for a and b make the system inconsistent?
A system is inconsistent if and only if the lines are parallel in which case the system has no solution. This is illustrated in the first Figure bellow. Two lines are parallel if they share the same slope. So, the system is inconsistent for:
a=3
for any value of b
2. What values for a and b make the system consistent and dependent?
A system is consistent if and only if the lines are the same in which case the system has infinitely many solutions. This is illustrated in the second Figure bellow. So, the system is consistent and dependent for:
a=3 and b=5
Answer: 0.421
Step-by-step explanation:
Heavy smoker = 20%
Light smoker = 30%
Non smokers = 50%
We can assume that the probability that a non-smoker is going to die in the next 5 years be y.
Since light smokers were twice as likely as nonsmokers to die during the five-year study, the probability will be:
= 2 × y = 2y
Probability for the Heavy smokers will be:= 2 × 2y = 4y
The expected number of people that will die for each in the next 5 years will be:
Non smoker:
= 50% × y
= 0.5 × y
= 0.5y
Light smoker:
= 30% × 2y
= 0.3 × 2y.
= 0.6y
Heavy smoker:
= 20% × 4y.
= 0.2 × 4y
= 0.8y
Total = 0.5y + 0.6y + 0.8y = 1.9y
The probability that the participant was a heavy smoker will be:
= 0.8y/1.9y
= 0.421
