A teacher has asked all the students in the class what is their favorite color is and separates the responses into five categories. The results are shown in the table below. which of the following is the best way to display the frequency for each color?

Color	Red	Black	Green	White	Other
Number of students	12	25	8	5	10

In this task, we use the relation from the given scenario to compare the number of dimes to quarters.

If we let p be number of pennies in the bottle. Then,

Number of quarters in the bottle = 2p

Number of nickels in the bottle = 3p

Number of dimes in the bottle =6(3p)=18p

Now relating dimes to quarters, we have

Thus, there are 9 times as many dimes as quarters in the box.

Let the unknown length of the x. The resulting triangle is shown below.

We use the Pythagoras theorem as follows to find the unknown value of x as:

Thus, the value of unknown side of the triangle is 21.8 feet.

The length of the chair could be appropriately measured in centimeters. Kilometers are used to measure long distances while micrometers could be used to measure the length of small microorganism in microbiology lab. However, milligrams are used to measure the masses of small quantities.

We are asked to find the number of cups of flour that will be used to make 90 cookies.

First, we convert 2 ¼ into improper fraction as:

Letting x to be the number of cups of flour, we set up a proportion equation with number of cookies on numerator and number of cups of flour on the denominator becomes:

Solve the value of x by cross-products

Dividing both sides by 60, the above equation result to

Thus, the number of cups of flour needed to make 90 cookies is 81/16 cups, which is equal to 5 1/16 cups.

Before finding the greatest number from the data set, the numbers need to be in fraction form.

-0.5=-5/10

-1.5=-15/10

The set of numbers becomes -2/3, -5/10, -15/10, -4/9

Now the least common denominator for 3, 10, and 9 is 90, which will be used to multiplied by the given fractions as follows:

-2/3*90=-60

-5/10*90=-45

-15/10*90=-135

-4/9*90=-40

From the above evaluations, the resulting numbers arranged from the smallest to the largest is -135, -60, -45, -40. Thus, the greatest number from the data set is -40, with a corresponding fraction of -4/9.

The percentage change in weight is found in three steps below:

Absolute change in weight=final weight-initial weight

Absolute change in weight=(left|120-153 ight|=left|-33 ight|=33)

Relative change in weight=(frac{absolute change}{initial weight}=frac{33}{153}=0.216)

Percent change=relative change * 100%

Percent change=0.216*100%=21.6%

The percent change in weight lost is 21.6 %, which is about 22%.

Percentages are fractions with denominator equal to 100. To convert a percent to decimal form, divide the value by 100.

The decimal form of 98.2% is 0.982.

Given the equation A(f)=92+2f

To find the value of A(f), we need to manipulate the value of f. In this case, f is the independent variable while A(f) is the dependent variable.

A dependent variable is one that depends on the independent variable. An independent variable is one that when changed result in a change of another variable.

In this problem, if we change the brand of laptop, tax rate, and memory size, the price of the laptop changes. Thus, the cost of the laptop is the dependent variable.

We follow the order of operations to solve the given expression. The order of operations is PEMDAS:

• Parentheses
• Exponents
• Multiplication and Division (in order from left to right)
• Addition and Subtraction (in order from left to right)

First, we start with the numerator and solve it as follows

[3(6+5*4)]

We start with multiplication in parenthesis, 5*4=20. The expression becomes

[3(6+20)]

Then, we conduct the addition in parenthesis 6+20=26. Then, the expression becomes

[3(26)]=3*26=78

Now, we solve for denominator, which is 26/2=13.

Thus, the expression is reduced into

The expression reduces into 6.