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Janaisa Harris, BA-Mathematics |
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Ms. Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher. She is now broadening her educational impact by engaging in curriculum mapping for her county. This endeavor enriches her understanding of educational strategies and their implementation. With a strong commitment to quality education, she actively participates in the review process of educational quizzes, ensuring accuracy and relevance to the curriculum.
, BA-Mathematics
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Quizzes Created: 1 | Total Attempts: 38,599
Questions: 10 | Viewed: 38,599

1.

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

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:
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?

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?

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?

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.

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?

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.

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)

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?

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.

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