Explanation

"3x" usually represents 3 rectangles (each representing x).

"+2" typically means 2 small unit squares (each representing 1).

So, a model showing 3 long bars and 2 small squares matches 3x + 2.

Explanation

Given A = p + prt, we need to solve for t.

Step 1: Subtract p from both sides

A - p = prt

Step 2: Divide both sides by pr

(A - p) / pr = t

The answer is A-p/pr.

Explanation

The initial population is 2¹⁶ insects.

If the population doubles, the new population will be 2 * 2¹⁶ = 2¹⁷.

Explanation

Step 1: Convert 2.5 × 10^-1 to a fraction

2.5 × 10^-1 = 0.25 = 1/4.

Step 2: Calculate 1/2 + 1/4

To add these fractions, find a common denominator, which is 4. 1/2 = 2/4. So, 2/4 + 1/4 = 3/4.

Explanation

The graph shows that Todd ate a significantly larger portion than Rick, then Rick 25% and Todd 75% is accurate.

Explanation

Length = x³ - x + 2

= (2)³ - 2 + 2

= 8 - 2 + 2

= 8

Width = x + x²

= 2 + (2)²

= 2 + 4

= 6

Area = Length * Width

= 8 * 6

= 48

Explanation

The scale factor can be found by dividing the actual width by the width in the scale drawing. Actual width = 18 cm, scale width = 1.2 cm. Scale factor = Actual width / Scale width = 18 / 1.2 = 15.

The length in the scale drawing is 3.6 cm. Actual length = Scale length * Scale factor = 3.6 * 15 = 54 cm.

Explanation

Let's identify the prime numbers from the list:

Given numbers:

7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

A prime number has only two divisors: 1 and itself.

Prime numbers are:

7

11

13

17

Total prime numbers = 4

Explanation

Tom has 3 more marbles than Bob.

Bob has 10 marbles, so Tom has 10 + 3 = 13 marbles.

So the correct equation is:

∆ - 3 = 10 (Because if Tom has ∆ marbles, and we subtract 3, it equals Bob's 10 marbles.)

Explanation

High temperatures:

Monday = 75°F

Tuesday = 82°F

Wednesday = 78°F

Thursday = 84°F

Friday = 81°F

Total = 75 + 82 + 78 + 84 + 81 = 400°F

Mean = Total ÷ Number of days = 400 ÷ 5 = 80°F