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

We use the calculator to find the positive square root of 19, which is then multiplied by 3.

Using the calculator,

Multiplying the square root above with 3 becomes

The approximate value of 3 times the square root of 19 is 13.1.

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%.

Here, we are required to find the unit of measuring mass. The SI unit of mass is kilogram but other derived units are grams, milligrams, microgram and more.

A kilogram is a large quantity for measuring heavier objects but grams can used to measure small and light objects such as the mass of the mobile phone. Therefore, gram is the appropriate unit for measuring weight of a mobile phone.

The number of cups of milk to make a bigger batch, we proceed as follows:

First convert the mixed number 1 2/5 as

Then, we let the unknown number of cups of milk to be x and we set a proportion equation with number cups of floor as numerator and cups of milk as denominator

Find the value of x by cross-products

2 as a fraction is 2/1 which is then used to find the product of the numerator as follows.

Per means division. The above equation becomes

When dividing fractions, we multiply the first fraction with the reciprocal of the second. The reciprocal of 2/9 is 9/2. Thus

The numbers of cups of milk required is 63/5, which when converted to mixed fraction becomes 12 3/5.

We use the given slope to find the minimum length of the ramp. In this case, slope is the ratio of height to length of the lamp. Thus,

If we let x be the minimum length of the ramp. Then,

Substituting the value of slope into the above equation results in,

Solve for value of x by cross-products

X = 18 Feet

Thus, the minimum length of the ramp needed to provide access to a door that is 1.5 high is 18 feet.

To find the greatest number from the given options, convert the decimal numbers into fractions.

6.98 becomes 698/100

9.2 becomes 92/10

The least common denominator for the denominators of 7, 100 and 10 is 700. Now we can multiply each fraction with 700 as follows:

3/7*700=300

698/100*700=4886

10/7*700=1000

92/10*700=6440

In order from the smallest to largest, we organize the number set as follows:

3/7, 10/7, 6.98, 9.2.

Thus, 9.2 is the greatest of all.

we find the value of x by applying the absolute conditions to the given equation.

First, add 2 to both sides of equation

The absolute conditions are:

If   , a>0, then u=a or u=-a

In this case a=10, which is greater 0.

The first condition becomes

Add 2 to both sides of the equation

Divide both sides by 4

The second condition becomes

Add 2 to both sides of the equation

Divide both sides by 4

Then, the value of x is 3 or -2.

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.

A histogram is used to visualize the frequency of a one variable over the other while a line graph is used to compare two variables.

A scatter plot used to show the correlation between two variables.

A pie chart is used to show the proportion of the given information in circle, with each section of a circle representing a given fraction of a whole.

From the given information, a pie chart is an appropriate tool show the frequency of the students choosing their favorite color.

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.