1.
To solve the following expression, which operation must you perform first?
8 + 12 (7 – 5) ÷ 6
Answer:

Explanation:
In the given expression, the operation that must be performed first is subtraction (). This is because the expression inside the parentheses (7 – 5) needs to be evaluated first. After subtracting 5 from 7, the expression becomes 2. Therefore, the expression becomes 8 + 12 * 2 ÷ 6.
2.
One way to find all the factors of 72 is to find its prime factorization. What is the prime factorization of 72?
Answer:
2 x 2 x 2 x 3 x 3
Explanation:
Start with the number 72.
Divide it by the smallest prime number, which is 2.
72 ÷ 2 = 36
Now, you have 36. Divide it by 2 again.
36 ÷ 2 = 18
Continue dividing by 2 until you can't divide by 2 anymore.
18 ÷ 2 = 9
Now, you have 9. 9 is not divisible by 2, so move on to the next prime number, which is 3.
9 ÷ 3 = 3
Continue dividing by 3 until you can't divide by 3 anymore.
3 ÷ 3 = 1
Now, you have reached 1, which is not divisible by any other prime numbers.
So, the prime factorization of 72 is:
72 = 2^3 * 3^2
This means that 72 can be expressed as the product of 2 raised to the power of 3 (2^3) and 3 raised to the power of 2 (3^2).
3.
A measuring cup has lines marking the fractions of a cup. In what order should the lines on the cup be labeled, starting with the bottom line of the measuring cup?
Answer:
Explanation:
The lines on the measuring cup should be labeled in increasing order, starting with the bottom line. This is because the bottom line represents the smallest fraction of a cup, and as you move up the cup, the lines represent larger fractions. Labeling the lines in increasing order ensures that the measurements are accurate and consistent.
4.
Frank and Joey ordered a large pizza. Frank ate 30% of the pizza, and Joey ate 2/5 of the pizza. What percentage of the pizza did they eat in all?
Answer:
70%
Explanation:
Frank ate 30% of the pizza, and Joey ate 2/5 of the pizza. To find the total percentage they ate, we add the two percentages together. 30% + 2/5 (which is equal to 40%) = 70%. Therefore, they ate 70% of the pizza in total.
5.
A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly?
Answer:
16
Explanation:
Since the student earned a grade of 80% on the math test, it means that they answered 80% of the problems correctly. To find out how many problems that is, we can calculate 80% of 20 (the total number of problems on the test). 80% of 20 is 16, so the student answered 16 problems correctly.
6.
A hotel is building a children’s wading pool in the shape of a square with a semicircle on one side. A diagram of the pool is shown below. What is the perimeter of the children’s pool?
Answer:
22.85 feet
7.
Wendy is taking a cab ride. The ride costs $1.20 for the first 0.5 km and $0.90 for each additional 0.5 km. If the trip costs $12.00, how many kilometers was the cab ride?
Answer:
6.5 km
Explanation:
To find out how many kilometers Wendy traveled in the cab, you can set up an equation based on the given information:
Let "x" be the number of additional 0.5 km increments beyond the first 0.5 km.
The cost for the first 0.5 km is $1.20, and for each additional 0.5 km, it's $0.90. So, the total cost can be expressed as:
Total cost = $1.20 (for the first 0.5 km) + $0.90x (for the additional increments)
Given that the trip costs $12.00, you can set up the equation:
$1.20 + $0.90x = $12.00
Now, solve for x:
$0.90x = $12.00  $1.20 $0.90x = $10.80
Now, divide both sides by $0.90 to find the number of additional 0.5 km increments:
x = $10.80 / $0.90 x = 12
So, Wendy traveled 12 additional 0.5 km increments beyond the first 0.5 km. To find the total distance, add the initial 0.5 km:
Total distance = 0.5 km + (12 * 0.5 km) = 0.5 km + 6 km = 6.5 km
Wendy traveled 6.5 kilometers in the cab ride.
8.
A student answered 76 problems on a test correctly and received a grade of 80%. How many problems were on the test if all the problems were worth the same number of points?
Answer:
95
9.
A woman put $580 into a savings account for three years. The rate of interest on the account was 6½%. How much was the interest in dollars and cents? (Use simple interest)
Answer:
$113.10
Explanation:
The correct answer is $113.10. To calculate the interest for the year, we need to use the formula for simple interest: Interest = Principal x Rate x Time. In this case, the principal is $580, the rate is 6.5% (or 0.065 as a decimal), and the time is 1 year. Plugging these values into the formula, we get: Interest = $580 x 0.065 x 1 = $37.70. However, since we are asked for the interest in dollars and cents, we round this to the nearest cent, which gives us $37.70. Therefore, the interest for the year is $113.10.
10.
A popular game at a carnival involves a spinner. There are five sections in total. The areas of sections 1, 2, 3, and 4 are equal. The area of section 5 is twice the area of any one of the other sections.
What is the probability that a player’s spin will be a 3?
Answer:
Explanation:
To find the probability of landing on section 3 when spinning the carnival wheel, we need to consider the relative areas of the sections.
Let's denote the area of each section as follows:
Area of sections 1, 2, 3, and 4: A
Area of section 5: 2A (since it's twice the area of any one of the other sections)
The total area of all sections is:
Total area = 4A (for sections 1, 2, 3, and 4) + 2A (for section 5) = 6A
Now, to find the probability of landing on section 3, we'll divide the area of section 3 by the total area:
Probability of landing on section 3 = Area of section 3 / Total area
Probability of landing on section 3 = A / (6A) = 1/6
So, the probability of landing on section 3 is 1/6.