Grade 8 Math Trivia

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.

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).

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.

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.

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.

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.

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.

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.