Simplify the expression. Which of the following is correct?

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 median of a data set is a number that falls in the middle of the data set. To find the median, the numbers in the data set are arranged from the smallest to the largest. In the given data set, the organized arrangement is:

-5, -1, 0, 3, 9

There are five elements in the data set, and the median falls in the third position from either side. Thus, 0 falls in the third position.

C organizes the collection correctly.

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.

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.

We are asked to determine Japheth’s uncle’s age relating to Japheth’s age.

First, express Japheth’s uncle’s age in terms of Japheth’s age as follows

Japheth’s age=k

Japheth’s uncle’s age, u = 3k-10.

Thus, the relationship between Japheth’s uncle’s age to that of Japheth is u=3k-10.

We use the relation 1 L=1000 mL to convert L to mL.

The two options for converting between L and mL are

And

We use the first option to convert 6.5 L to mL as follows:

Thus, 6.5 L is 6500 mL.

we are asked to find the number of gallons a full tank can hold. A full tank is equivalent to 1.

Convert the mixed fraction into proper fraction as follows

(2frac{2}{5}=frac{left(2ast5 ight)+2}{5}=frac{10+2}{5}=frac{12}{5})

If we let x be the number of gallons in full tank, and setting up the proportion equation with the number of gallons on the numerator and fraction of tank on denominator as follows.

(frac{x gallons}{1 full tank}=frac{frac{12}{5} gallons}{frac{4}{7}full tank})

Cross-multiply to find the value of x.

(frac{x }{1 full tank}=frac{frac{12}{5} gallons}{frac{4}{7}full tank})

(x astfrac{4}{7}full tank=frac{12}{5} gallonsast1 full tank)

(x =frac{frac{12}{5} gallonsast1 full tank}{frac{4}{7}full tank}=frac{12}{5}divfrac{4}{7} gallons=frac{12}{5}astfrac{7}{4}gallons=frac{21}{5}gallons)

Converting 21/5 to a mixed fraction is 4 1/5. Thus, when the tank is full, it holds 4 1/5 gallons of water.

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.

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.