Rita promises her daughter on her 12th birthday that she will give her $12,000 for college on her 18th birthday. How much does R

Answer:

2×5×8 = 80

80 + 1 = 81

Thus, the total number of students in the camp is 81

Response:

Detailed explanation:

The spinner has four colors: red, blue, green, and yellow. Joaquin spins this spinner two times. The possible outcomes are represented as

S = {RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY}.

Considering the variable “yellow (Y),” let’s determine the potential values for Y.

From the aforementioned set, it appears that Y can assume only three values: 0, 1, or 2.

Within the 16 possible outcomes, Y appears 0 times in 9 instances, 1 time in 6 instances, and 2 times in 1 instance.

Therefore, the probability is calculated as the number of favorable outcomes divided by the total outcomes in the sample space.

This means

P(Y=0) = 9/16

P(Y=1) = 6/16 = 3/8

P(Y=2) = 1/16

Answer:

D. R(x) = 850x +9600

Detailed explanation:

Selling 10 additional machines increased revenue from $18100 to $26600, which reflects an increase of...

... $26,600 minus $18,100 equals $8,500

This indicates that revenue rose by $8500 divided by 10, which equals $850 per machine.

Only one option contains this value:

... D. R(x) = 850x+9600

_____

Verification

R(10) = 850·10 +9600 = 8500 +9600 = 18,100.... Correct

R(20) = 850·20 +9600 = 17000 +9600 = 26,600.... Correct

_____

Comments on choice selection

In multiple-choice scenarios, it's often not required to solve the entire problem accurately. Generally, it's enough to identify the single number that distinguishes the correct from the incorrect options.

In reality, problems are seldom multiple-choice. One must go through the process thoroughly and determine whether the answer is accurate.

Here, we delved deep enough to find the slope, representing the revenue gain when one unit increase in sales occurs. Different methods can determine the intercept. One such method is to identify the value that aligns revenue with one of the "x" values:

... R(10) = 850·10 +b = 18100

... b = 18100 -8500 = 9600

therefore...

... R(x) = 850x +9600

We can verify this answer by calculating R(20) as shown previously.

To determine the time interval δt, we must subtract the starting time from the ending time. In this scenario, the first value in the coordinates signifies time:

δt=50 - 0
δt= 50s

The time interval is 50s.

Answer:

Terrence's

Step-by-step explanation:

The cut length of the square corresponds to the box height.

1. a

In Anya's approach: 8.5 - 1.5 = 7, 11 - 1.5 = 9.5; with the height being 1.5, the volume calculates as height x length x width = 1.5 x 9.5 x 7 = 99.75 square inches.

Terrence's method: 8.5 - 3 = 5.5, 11 - 3 = 8. Volume = 5.5 x 8 x 3 = 132 square inches. Clearly, 99.75 < 132 square inches, indicating Terrence's approach would yield a larger volume.

1. b

The dimensions of the box rely on the length, width, and height of the cardboard cutout, thus varying cutting measurements for the same cardboard size can produce different box dimensions.

2. Squares are cut from each corner, thus the combined size of the two squares on the cardboard must be less than the shorter cardboard side. The shorter side is 8.5 inches, which divided by 2 results in 4.25 inches, therefore squares cannot exceed this size. If squares are taken out measuring 4.25 inches, it will leave a strip 2.5 inches wide that cannot form a box.

To cut out squares of 5 inches, how you position them can cause overlap or extend beyond the cardboard. While 5 + 5 equals ten, making the longer side of 11 inches adequate, the 8.5 inches side allows zero room for the 10 inches.