Answer:
X=(-1.5, 7.5)
Step-by-step explanation:
Simplifying
4x2 + -24x + -45 = 0
Reorder the terms:
-45 + -24x + 4x2 = 0
Solving
-45 + -24x + 4x2 = 0
Solving for variable 'x'.
Factor a trinomial.
(-3 + -2x)(15 + -2x) = 0
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:
Simplifying
-3 + -2x = 0
Solving
-3 + -2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3
Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3
Combine like terms: 0 + 3 = 3
-2x = 3
Divide each side by '-2'.
x = -1.5
Simplifying
x = -1.5
Set the factor '(15 + -2x)' equal to zero and attempt to solve:
Simplifying
15 + -2x = 0
Solving
15 + -2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-15' to each side of the equation.
15 + -15 + -2x = 0 + -15
Combine like terms: 15 + -15 = 0
0 + -2x = 0 + -15
-2x = 0 + -15
Combine like terms: 0 + -15 = -15
-2x = -15
Divide each side by '-2'.
x = 7.5
Simplifying
x = 7.5
Solution
x = {-1.5, 7.5}
The total ratio is 5
The number of comedy movies watched is 12
The number of other movies watched is 18
<h3>What is a ratio?</h3>
Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. Therefore,
He has watched 2 comedy movies for every 3 other movies. The total movies he has watched is 30. Therefore,
Ratio of comedy to total movies is as follows:
number of comedy movies watched = 2 / 5 × 30 = 60 / 5 = 12
number of other movies watched = 3 / 5 × 30 = 90 / 5 = 18
Therefore,
total ratio = 5
number of comedy movies watched = 12
number of other movies watched = 18
learn more on ratios here: brainly.com/question/10080852
Answer:
They are proportional
Step-by-step explanation:
Y/X represents coordinates Y being rise X being run. So Y/X is equal to rise/run. If there was a coordinate grid, if the two points created a straight line that slant to the right I would be proportional. Since all I see is rise/run= 5 they are proportional. 5 represents the slope.
Answer:
X= -7
Step-by-step explanation:
-25 + 8x +20 = -61
8x -5 = -61
8x = -56
x = -7
This question is incomplete, the complete question is;
The owners of Spiffy Lube want to offer their customers a 10-minute guarantee on their standard oil change service. If the oil change takes longer than 10 minutes to complete, the customers is given a coupon for a free oil change at the next visit. Based on past history, the owners believe that the timer required to complete an oil change has a normal distribution with a mean of 8.6 minutes and a standard deviation of 1.2 minutes.
Suppose management could improve the process by reducing the mean time required for an oil change (but keeping the standard deviation the same). How much change in the mean service time would be required to allow for a 10-minute guarantee that gives a coupon to no more than 1 out of every 25 customers on average
Answer:
Required change in the mean service time is 7.8988
Step-by-step explanation:
Given the data in the question;
How much change in the mean service time would be required to allow for a 10-minute guarantee that gives a coupon to no more than 1 out of every 25 customers on average
let mean = μ
p( x > 10 ) ≤ (1/25)
p( x > 10 ) ≤ 0.4
p( x-μ / 1.2 > 10-μ / 1.2 ) ≤ 0.4
(10-μ / 1.2 ) ≤ 0.4
(10-μ / 1.2 ) ≥ 
( 0.96 )
(10-μ / 1.2 ≥ 1.751
10-μ = ≥ 1.751 × 1.2
10-μ ≤ 2.1012
μ ≤ 10 - 2.1012
μ ≤ 7.8988
Therefore, required change in the mean service time is 7.8988
