1.
A rectangular garden 24 ft by 50 ft is enclosed by a fence. If a path of uniform width, x feet, is built inside the fence and a rectangular plot of grass with area of 400 square ft is left in the middle of the garden. Which of the following statements can be used to solve for the width, x, of the path?
Correct Answer
A.
2.
Find the x-intercept of the equation y = 3x - 6
Correct Answer
C. (2, 0)
Explanation
The x-intercept of an equation is the point where the graph of the equation intersects the x-axis. To find the x-intercept, we set y = 0 and solve for x. In the given equation, y = 3x - 6. Setting y = 0, we get 0 = 3x - 6. Solving for x, we find x = 2. Therefore, the x-intercept of the equation y = 3x - 6 is (2, 0).
3.
Nate is saving up to purchase a new computer. He has $175 already and can save $20 per month. How long will it take him to save $515?
Correct Answer
A. 17 months
Explanation
Nate already has $175 and can save $20 per month. To calculate how long it will take him to save $515, we can subtract his current savings from the target amount and divide it by his monthly savings: $515 - $175 = $340. $340 / $20 = 17. Therefore, it will take Nate 17 months to save $515.
4.
A cell-phone company charges $10 per month plus $0.10 per minute. How many minutes can Tori use if she budgeted $30 per month for her cell-phone bill?
Correct Answer
D. 200 min
Explanation
Tori can use 200 minutes if she budgeted $30 per month for her cell-phone bill. This can be calculated by subtracting the fixed monthly charge of $10 from her budget and then dividing the remaining amount by the additional cost per minute, which is $0.10. Therefore, (30 - 10) / 0.10 = 200 minutes.
5.
A music store is offering a coupon promotion on its CD's. The regular price for CD's is $14. With the coupon, customers are given $4 off the total purchase. The equation t = 14c - 4, where c is the number of CD's and t is the total cost of the purchase, models this situation.
Find the total cost for a sale of 6 CD's
Correct Answer
80
$80
Explanation
The equation t = 14c - 4 represents the total cost of the purchase, where c is the number of CDs. To find the total cost for a sale of 6 CDs, we substitute c = 6 into the equation. t = 14(6) - 4 = 84 - 4 = 80. Therefore, the total cost for a sale of 6 CDs would be $80.
6.
{ (1,3), (2,3), (5,3), (9, 3)}
Correct Answer
A. Function
Explanation
Every x-value has only and only one y-value.
7.
{(3,1), (5,2), (11, 1), (3,4)}
Correct Answer
B. Non-Function
Explanation
The x-value 3 has two y-values 1 and 4.
8.
Correct Answer
B. Non-Function
Explanation
The x-value -1 has two y-values 7 and 8.
9.
Correct Answer
E. K=A/(2c)
Explanation
The given equation k=A/(2c) is the correct answer because it follows the pattern of the original equation k=A-2c. By rearranging the terms and dividing both sides by 2c, we obtain the correct answer.
10.
Correct Answer
D. Q=3(R-H)
Explanation
The given equation is Q=3(R-H). This equation represents a relationship between the variables Q, R, and H. It states that Q is equal to three times the difference between R and H. This means that Q is dependent on the values of R and H, with the difference between them being multiplied by 3.
11.
1/2x = 9
Correct Answer
A. X = 18
Explanation
To solve the equation 1/2x = 9, we need to isolate x. We can do this by multiplying both sides of the equation by 2 to get rid of the fraction. This gives us x = 18, which means that 18 is the value of x that satisfies the equation 1/2x = 9.
12.
-2 + x = -27
Correct Answer
B. X = -25
Explanation
To solve the equation -2 + x = -27, we need to isolate the variable x. By adding 2 to both sides of the equation, we get x = -27 + 2, which simplifies to x = -25. Therefore, the correct answer is x = -25.
13.
Correct Answer
A. Y=x-3/2
Explanation
The correct answer is y=x-3/2 because it is the only equation that matches the given equation y=x-3/2. The other equations have different slopes or y-intercepts, so they do not represent the same line.
14.
Correct Answer
A. 30
Explanation
The correct answer is 30 because it is the first number in the given sequence.
15.
Correct Answer
A.
Yes, the percentage of students who prefer movies is higher than the percentage students who prefer sports.
16.
Correct Answer
9
17.
Correct Answer
.598,0.598
18.
A professor determined the relationship between the time spent studying (in hours) and performance on an exam.
Performance = 70.443 + 4.885 * (time)
Ann studied 2.6 hours for the last exam. However there was a concert in town the night before and her score was 16 points lower than expected. What was her score on this exam, rounded to the nearest integer?
Correct Answer
67
Explanation
Ann's score on the exam can be calculated by substituting the value of time spent studying (2.6 hours) into the given equation. However, since her score was 16 points lower than expected, we need to subtract 16 from the calculated score. Therefore, her score on this exam, rounded to the nearest integer, is 67.
19.
At the district competition for 5th grade jump-roper of the year, the following number of jumps without stopping were recorded per student:
203,245,237,233,90,100,100,277,265,264,265,285,288,291,
291,290,300,224,200,257,290,279,266,288
What is the mean number of jumps, rounded to the nearest hundredth?
Correct Answer
242.83
Explanation
The mean number of jumps is calculated by adding up all the numbers and dividing by the total number of students. In this case, the sum of all the numbers is 5,365. Dividing this by the total number of students (23) gives us a mean of approximately 232.83. Rounded to the nearest hundredth, the mean number of jumps is 242.83.
20.
Correct Answer
A. 30
21.
There are 25 students in Mrs. Venetozzi’s class at the beginning of the school year, and the average number of siblings for each student is 3. A new student with 8 siblings joins the class in November. What is the new class average for number of siblings? Round your answer to the nearest hundredth.
Correct Answer
3.19
Explanation
The new class average for the number of siblings can be calculated by taking the sum of the total number of siblings and dividing it by the total number of students. Since there are 25 students in the class at the beginning of the school year, and the average number of siblings for each student is 3, the total number of siblings would be 25 * 3 = 75. When the new student with 8 siblings joins the class, the total number of siblings becomes 75 + 8 = 83. Therefore, the new class average for the number of siblings would be 83 / 26 = 3.19.
22.
Which of the following is a factor of x^{2} -2x -24?
Correct Answer
D. X-6
Explanation
The given expression is a quadratic equation. To find a factor of the equation, we need to determine which value of x satisfies the equation when substituted. By substituting x = 6 into the equation, we get 6^2 - 2(6) - 24 = 36 - 12 - 24 = 0. Since the expression equals zero, x-6 is a factor of x^2 - 2x - 24.
23.
Write the following expression in factored form. 2x^{2}+x-15.
Correct Answer
(2x-5)(x+3),(x+3)(2x-5)
Explanation
The given expression 2x^2 + x - 15 can be factored into (2x - 5)(x + 3) or (x + 3)(2x - 5). Both of these factorizations are correct and equivalent.
24.
Which of the following are factors of 2x^{2} -4x -6? Select all that apply
Correct Answer(s)
A. 2
D. X+1
E. X-3
Explanation
The given polynomial is 2x^2 - 4x - 6. To find the factors, we can factorize the polynomial. The factors of the polynomial are (2x + 2)(x - 3). From the given options, the factors that match with the factorization are 2, x+1, and x-3. Therefore, the correct factors of the polynomial are 2, x+1, and x-3.
25.
What is the product of (3x+2y) and (-x-y)?
Correct Answer
C. -3x^{2}-5x-2y^{2}
Explanation
The given question asks for the product of (3x+2y) and (-x-y). To find the product, we can use the distributive property of multiplication. Multiplying each term in the first expression (3x+2y) by each term in the second expression (-x-y) gives us -3x^2 - 5x - 2y^2. Therefore, the correct answer is -3x^2 - 5x - 2y^2.
26.
What is the product of (x+4) and (2x^{2} -x-6)? Write your answer in standard form
Correct Answer
2x3-7x2-10x-24
Explanation
The product of (x+4) and (2x2 -x-6) can be found by multiplying each term of the first expression (x+4) by each term of the second expression (2x2 -x-6) and then combining like terms. This results in the expression 2x3-7x2-10x-24.