Sarah wanted to buy a TV. She had $390 in her pocket. The TV she wanted was $415; however she had a 10% off coupon. The sales ta
x is 6%. Does she have enough money to purchase the TV?
2 answers:
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Answer:
we choose f(x) = π cos(πx)
Step-by-step explanation:
Given the information:
- f(0) = 0
- f(2) = π
Let analyse all possible answers;
1/ f(x) = -2 sec(x)
when x= 0 we have: f(0) = -2 sec(0) = -2 = -2 wrong
2. f(x) = 7sin(x/4 - 1/29)
when x= 0 we have: f(0) =7sin(0/4 - 1/29) = 7sin(-1/29) = -0.00421 wrong
3. (x) = π cos(πx)
when x= 0 we have: f(0) = πcos(π0) = cos(0) = π0 = 0
when x= 2 we have: f(2) = πcos(π2) = πcos(0) = π
True
4. f(x) = 2π cos(x - π/2)
when x= 0 we have: f(0) = 2π cos(0 - π/2) = 2π cos(-π/2) = 0
when x= 2 we have: f(2) =2π cos(2 - π/2) = 2π0.034 = 0.0697π Wrong
So we choose f(x) = π cos(πx)
Answer:
Probability that the average mileage of the fleet is greater than 30.7 mpg is 0.7454.
Step-by-step explanation:
We are given that a certain car model has a mean gas mileage of 31 miles per gallon (mpg) with a standard deviation 3 mpg.
A pizza delivery company buys 43 of these cars.
<em>Let </em><em> = sample average mileage of the fleet </em>
<em />
The z-score probability distribution of sample average is given by;
Z = ~ N(0,1)
where, = mean gas mileage = 31 miles per gallon (mpg)
= standard deviation = 3 mpg
n = sample of cars = 43
So, probability that the average mileage of the fleet is greater than 30.7 mpg is given by = P(<em> </em>> 30.7 mpg)
P(<em> </em>> 30.7 mpg) = P(
>
) = P(Z > -0.66) = P(Z < 0.66)
= 0.7454
<em>Because in z table area of P(Z > -x) is same as area of P(Z < x). Also, the above probability is calculated using z table by looking at value of x = 0.66 in the z table which have an area of 0.7454. </em>
Therefore, probability that the average mileage of the fleet is greater than 30.7 mpg is 0.7454.