FREE THEA Math Questions and Answers
On three tests, a student received grades of 88, 82, and 84. What is the lowest score a student can receive on the following test to achieve an average score of at least 70 if tests count twice as much as quizzes?
Let's denote the score on the next test as "x."
Since tests count twice as much as quizzes, the total weightage for the quizzes is 3 (1 for each quiz) and the total weightage for the tests is 2 (because tests count twice as much). Therefore, the total weightage for all the scores is 3 + 2 = 5.
To find the lowest score the student can get on the next test to achieve an average score of at least 70, we can set up the following equation:
(88 + 82 + 84 + 2x) / 5 ≥ 70
Simplifying the equation, we have:
(254 + 2x) / 5 ≥ 70
Multiply both sides of the inequality by 5 to eliminate the denominator:
254 + 2x ≥ 70 * 5
254 + 2x ≥ 350
Subtract 254 from both sides:
2x ≥ 350 - 254
2x ≥ 96
Divide both sides by 2 to isolate x:
x ≥ 96 / 2
x ≥ 48
Therefore, the student must score at least 48 on the next test to achieve an average score of at least 70.
What is the angle between the lines (0, -1) and (3, -2)?
To find the slope of a line passing through two points, we can use the formula:
slope = (change in y) / (change in x)
Let's denote the coordinates of the two points as (x1, y1) and (x2, y2).
Given points:
Point 1: (x1, y1) = (0, -1)
Point 2: (x2, y2) = (3, -2)
Now, we can calculate the slope:
slope = (change in y) / (change in x)
= (y2 - y1) / (x2 - x1)
= (-2 - (-1)) / (3 - 0)
= (-2 + 1) / 3
= -1 / 3
Therefore, the slope of the line passing through (0, -1) and (3, -2) is -1/3.
Daisy is preparing cookies. She makes use of eggs, butter, sugar, and flour. What are the most combinations of ingredient orders she can try?
To determine the number of different orders of ingredients Daisy can try, we need to calculate the number of permutations.
Since there are 4 ingredients (sugar, flour, butter, and eggs), we have 4 options for the first ingredient, 3 options for the second ingredient (after choosing the first one), 2 options for the third ingredient (after choosing the first two), and 1 option for the last ingredient (after choosing the first three).
The total number of different orders is obtained by multiplying these options together:
4 * 3 * 2 * 1 = 24
Therefore, Daisy can try 24 different orders of the ingredients.
How many different ways are there to arrange five boys in a line?
To calculate the number of ways to arrange 5 boys in a straight line, we can use the concept of permutations.
Since there are 5 boys, there are 5 options for the first position, 4 options for the second position (after placing the first boy), 3 options for the third position (after placing the first two boys), 2 options for the fourth position (after placing the first three boys), and 1 option for the last position (after placing the first four boys).
The total number of arrangements is obtained by multiplying these options together:
5 * 4 * 3 * 2 * 1 = 120
Therefore, there are 120 different ways to arrange 5 boys in a straight line.
There will be 220 yards of fencing installed by a rancher. She constructs 80 yards of the fence in the morning, and the final 40 yards in the afternoon. In what proportion did she erect the fence that day?
The rancher initially has 220 yards of fencing. In the morning, she puts up 80 yards of fencing. Therefore, the remaining fencing to be put up is 220 - 80 = 140 yards.
In the afternoon, the rancher puts up 40% of the remaining fence, which is 40/100 * 140 = 56 yards.
The total fencing put up by the rancher that day is 80 + 56 = 136 yards.
To find the percentage of the fence she put up, we can divide the total fencing put up by the initial length of the fence and multiply by 100:
(136 / 220) * 100 = 61.82%
Therefore, the rancher put up approximately 61.82% of the fence that day.
Peter is making preparations for his trip. He desires to visit the beach, play volleyball, watch a movie, and visit a museum. How many options does he have for placing orders?
If Peter wants to order his activities (going to the museum, watching a movie, going to the beach, and playing volleyball), we can calculate the number of permutations.
Since there are 4 activities, he has 4 options for the first activity, 3 options for the second activity (after choosing the first one), 2 options for the third activity (after choosing the first two), and 1 option for the last activity (after choosing the first three).
The total number of different orders is obtained by multiplying these options together:
4 * 3 * 2 * 1 = 24
Therefore, Peter has 24 different ways of ordering his activities.
A nearby business agrees to donate $1.25 for every $4 raised by the public during a bike-a-thon. How much will the company donate every mile if the public donates a total of $156.00?
According to the pledge, the local company donates $1.25 for every $4.00 pledged by the public.
To find out how much the company will donate per mile, we can calculate the ratio of the company's donation to the public's pledge:
Company's donation / Public's pledge = $1.25 / $4.00
Simplifying this ratio, we get:
Company's donation / Public's pledge = 1.25 / 4
To determine the company's donation per mile, we multiply this ratio by the total public pledge per mile:
Company's donation per mile = (1.25 / 4) * $156.00
Calculating this expression gives us:
Company's donation per mile = 0.3125 * $156.00 = $48.75
Therefore, the local company will donate $48.75 per mile during the bike-a-thon.