9. During the past week, Mr. Hamilton gave one quiz and one exam to his high school algebra class.
1 answer:
<em>Missing Information:</em>
<em>It takes Mr. Hamilton 1/15 of an hour to grade one student’s exam and 1/30 of an hour to grade one student’s quiz.</em>
Answer:
Step-by-step explanation:
Given
Required
Determine the time spent on x students
First, we need to determine the total time spent on 1 student
Take LCM
Next is to determine the total time on x students:
You might be interested in
The given number sentence is simplified as 1 3/5
<u>Step-by-step explanation:</u>
The given number sentence is 2-4/5 x 1/2
- In order to solve this, the operations must be performed based on the BODMAS rule.
- This means that, the operations should be performed in the order of Bracket, Of, Division, Multiplication, Addition and Subtraction.
Here, based on that above rule, the multiplication must be done in the first step and then subtraction should be done in the next step.
⇒ 2 - 4/5 × 1/2
⇒ 2 - 4/10
⇒ 2 - 2/5
Therefore, the given expression is reduced to 2- 2/5
cross multiply the denominator 5
⇒ (10-2) / 5
⇒ 8/5
Now, the expression is reduced to single term 8/5.
To further reduce the term, divide 8 by 5.
- The quotient is 1.
- The remainder is 3.
- The divisor is 5.
The answer is written in the form of
⇒ 1 3/5
Answer:
0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct?
This is the pvalue of Z when X = 48101. So
By the Central Limit Theorem
has a pvalue of 0.0091
0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct
Answer:
Step-by-step explanation:
Instead of using the standard form, we can use the vertex form of a quadratic equation:
Where a is the leading coefficient, and (h, k) is our vertex.
Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:
Now, we need to determine a.
We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:
Solve for a. Subtract within the parentheses:
Add 4 to both sides:
Square:
Solve:
Thererfore, the value of a is 4.
So, our function is:
Now, let’s find our roots. Set the equation to 0 and solve for x:
So, our roots are 1 and 3.
The greater root is 3 and the lesser root is 1.
Therefore, m-n, where m>n, is 3-1 or 2.
Our final answer is 2.
Answer:
Step-by-step explanation:
Given equation:
Since 5 is the greatest common factor of 65 and 60 in the given expression.
Therefore, the above expression can be written as
Hence, by factoring the side that contains the variable p we have the expression .