Answer:
0.0062 = 0.62% probability that a randomly selected truck from the fleet will have to be inspected
Step-by-step explanation:
Z-score
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
What is the probability that a randomly selected truck from the fleet will have to be inspected?
Values of Z above 2.5. So this probability is 1 subtracted by the pvalue of Z = 2.5.
Z = 2.5 has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability that a randomly selected truck from the fleet will have to be inspected
For this case we have the following variables:
x: number of hours that it takes Mr. David to complete a job working alone.
y: number of hours it takes Mr. Ludwing to complete a job working alone.
k: number of hours it takes for both of them to do a job working together.
We now write the equation that models the problem.
To do this, we must add the work rate per hour of each and equal to the rate of work per hour of both.
We have then:
Answer:
The algebraic expression that models the problem is:
Answer:
306 seniors
Step-by-step explanation:
117 seniors who quit + 189 seniors who continued = 306 seniors who started taking dance classes in the fall.
Formula for the circumference of a circle.
<h3>How did Archimedes find the circumference of a circle?</h3>
Archimedes stated in his Proposition that the area of a circle is equal to the area of a triangle with a base equal to the circumference and a height equal to the radius: (1/2)(r · 2πr) = πr2. Archimedes arrived at his approximation of the circumference of the circle by increasing the number of sides of the hexagon. Archimedes claimed that the area of any circle is equal to the area of a right triangle, where the radius of the circle is represented by one side and the circumference by the other.
Archimedes demonstrated using a similar method that the area of a circle of diameter D is equal to the area of a right-angled triangle with one side equal to the radius and the other to the circumference of the circle on the right angle.
Formula for the circumference of a circle:
A circle's area is equal to pi times the radius squared (A = r2). Discover how to apply this formula to determine a circle's area given its diameter.
The circumference is diameter x pi, or 2 x radius x pi.
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Learn more about circumference of a circle here:
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The fractions in this equation are 3/4 and 5/6. The denominators of those fractions are 4 and 6. The lowest common multiple (LCM) of the numbers 4 and 6 is 12. The LCM is 12 because this is the smallest multiple 4 and 6 have in common
Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, ....
Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, ....
The LCM has been highlighted in bold to make it easier to spot
Therefore, the LCD (lowest common denominator) of the fractions is 12. If we were to multiply both sides of this equation by the LCD, then we will clear out the fractions entirely to have whole numbers only left over.
Check out the attached image below for the steps of this process.
Final Answer: 9x + 36 = 10