Sarah is participating in a charity event where she can either walk or jog to raise money. The charity will donate based on how far she travels and the speed at which she moves. The donation rules are as follows:

For every kilometer Sarah walks (at a speed of 5 km/h), the charity will donate $2.

For every kilometer Sarah jogs (at a speed of 10 km/h), the charity will donate $3.

Sarah has two hours to complete the event. She needs to decide how much time to spend walking and how much time to spend jogging to maximize the total donation.

Question:

Based on the donation rules, which of the following best explains how the time spent?

Francis is planning to fill a cylindrical tank with water. The tank has a radius of 2 meters and a height of 5 meters. He initially wants to know the volume of water the tank can hold. After calculating, Francis realizes that if he doubles the radius of the cylinder but keeps the height the same, the tank can hold significantly more water.

Question:

What will be the effect on the volume of thecylinder if Francis doubles the radius, and how does this relate to theoriginal volume?

A student named Alex conducted an experiment by rolling a standard six-sided die 60 times. The results are recorded as follows:

1: 12 times

2: 8 times

3: 10 times

4: 10 times

5: 14 times

6: 6 times

Based on the experiment's results, Alex plans to roll the die 30 more times. Alex wonders how many times each number might appear in the next 30 rolls. Predict the number of times the number 4 will appear in the next 30 rolls based on the experiment's results.

A school's math club is organizing a fundraiser. They plan to sell t-shirts and caps. The profit      from selling t-shirts is given by the expression:

            P_t =5x + 3

            Where:

P_t is the profit from selling t-shirts in dollars.

x is the number of t-shirts sold.

            Theprofit from selling caps is given by the expression:

         P_c = 4y + 2

            Where:

P_c is the profit from selling caps in dollars.

y is the number of caps sold.

            Theclub has a goal of raising $100 in profit. Based on the expressions provided,which of          the following is thebest strategy to reach their goal?

Alex is working on a math problem where he needs to find the number of apples and oranges in two baskets. He knows the following information:

The total number of apples and oranges in both baskets is 50.

The number of apples in the first basket is twice the number of oranges in that basket.

The number of apples in the second basket is 10 less than the number of oranges in that basket.

     Alexsets up the following algebraic expressions based on the given information:

x=2y (apples in the first basket)

z=w−10 (apples in the second basket)

The total number of apples and oranges is x+y+z+w=50.

Question: Which of the following equations correctlyrepresents the relationship between the number of oranges in the first basket(y) and the number of oranges in the second basket (w)?

Maria bought a toy for $50. The toy was on sale, and the price was reduced by 20%.

After the sale, Maria decided to buy another toy of the same kind at the same reduced price.  To find the total amount that Maria will pay on both toys, she came up with an initial understanding about the problem and generate an incorrect hypothesis:

                                       1.     Initial Price: The original price of the toy is $50.

                                       2.     Percentage Decrease: The price is reduced by 20%.

     Incorrect Hypothesis: If the price of an item is reduced by a certain percentage, the total amount spent on two items will be equal to the original price of one item multiplied by two.

     Question: If you will modify the hypothesis which of the following is correct?

A school is planning to build a monument in the shape of a rectangular pyramid to celebrate its anniversary. The base of the pyramid is a rectangle with a length of 12 meters and a width of 8 meters. The height of the pyramid (the perpendicular distance from the base to the apex)will be 10 meters. 

     However, the school principal is considering a design change to make the base of the pyramid a square, with each side of the square equal to the width of the rectangular base. The height of the pyramid remains the same.

     Question:Which of the following istrue about the volume of the two pyramids?

A website features a diagram of two intersecting lines with the following angle measurements:

Angle ∠A = 50°

Angle ∠B = 130°

Angle ∠C = 50°

Angle ∠D = 130°

The website states: "Angles that are opposite each other when two lines intersect are always equal."

Which of the following statements best explains the relationship between the angles, confirming the website's statement?

A Grade 7 class conducted a survey on the number of books their classmates read over the summer. The results are as follows:

3 students read 1 book

5 students read 2 books

8 students read 3 books

2 students read 4 books

4 students read 5 books

3 students read 6 books

     Question:

     Based on the data provided, which of the following is the correct frequency distribution table?

A teacher asked the class to roll a standard six-sided die 30 times and record the number of      prime numbers obtained. The numbers on a standard die are 1, 2, 3, 4, 5, and 6.

The following is a list of the results from one student's experiment:

                   4, 2,6, 5, 3, 1, 4, 5, 2, 6, 3, 2, 5, 1, 4,6, 2, 5, 3, 1, 4, 6, 2, 3, 5, 4, 2, 1, 6, 5

Based on the data collectedby the student, What percentage ofthe rolls resulted in a prime number?

A teacher is conducting a survey to find out how many hours students in Grade 7 spend on homework each week. She decides to collect data from a random sample of students.

Which of the methods below is the best way tocollect a representative sample of Grade 7 students' homework habits?

A teacher is explaining howt o find the volume of a cylinder by relating it to the area of a circle. She says:

"Imagine stacking many thin circular disks on top of each other to make the shape of a cylinder. Each disk has the same area, and the height of the cylinder is the number of disks you stacked. By multiplying the area of one disk by the height, you can find the total volume of the cylinder."

Based on the teacher's explanation, which of the following shows how the volume of the cylinder is calculated?