Solve for z in the equation above.

the mean of a data set is the sum of the scores divided by the number of tests.

Total test scores =99+93+67+ 48+ 92+ 87=486

Number of tests =6

Mean test score =486/6=81

The mean test score is 81.

in this case, we express James’ uncle’s age in terms of James’ age. From the equation:

James’ age is n

James’s uncle’s age is m=3n-13

Thus, the relation that relates James’ uncle’s age in terms of James’ age is m=3n-13.

To find the greatest number from the given set, we first convert the decimal numbers into fractions.

12.35 becomes 1235/100

11.46 becomes 1146/10

Then, the LCM for the denominators of the given fractions of 2, 100, 3 and 10 is 300. Now we multiply each fraction with 300, which we will use to compare the give set.

25/2*300=3750

1235/100*300=3705

40/3*300=4000

1146/10*300=3438

From the calculated values, 4000 is the greatest value. Then, 40/3is the greatest value.

By inspection, we find the corresponding values of the given denominations in the following manner.

To answer this question, we need to convert the numbers into a similar form. Converting decimal numbers into fraction is appropriate to finding the greatest number.

-0.9 becomes 9/10

-1.9 becomes 19/10

Now we find the LCM of the denominators of the four fractions. The LCM of 5, 10 and 3 is 30. Multiply each fraction with the LCM to compare the fractions.

-3/5*30=-18

-9/10*30=-27

-19/10*30=-57

-8/3*30=-24

The greatest number is -18, meaning -3/5 is the greatest number.

The sides of a right-angled triangle are determined by the Pythagoras theorem. If we let the unknown side to x as in the figure below, then theory is applied as follows.  

The value of x is found as:

The value of the unknown leg side of a triangle is about 9.8 feet.

Choice A: 2 packs of Orange and 2 packs of Cream Soda

• Total drinks: 48 + 24 = 72 drinks
• Total cost: (2 * $15) + (2 * $5) = $30 + $10 = $40
• This choice not only meets the requirement of at least 60 drinks but also offers the best value in terms of cost per drink, making it the most cost-effective option.

Choice B: 3 packs of Root Beer

• Total drinks: 3 * 24 = 72 drinks
• Total cost: 3 * $14 = $42
• While this choice meets the requirement of at least 60 drinks, it's not the most cost-effective, as it costs $42for 72 drinks.

Choice C: 1 pack of Orange, 2 packs of Root Beer, and 1 pack of Cream Soda

• Total drinks: 24 + 48 + 12 = 84 drinks
• Total cost: $9 + (2 * $14) + $5 = $9 + $28 + $5 = $42
• This choice provides more than 60 drinks, but it's not the most cost-effective due to its higher cost of $42, same as choice B.

Choice D: 4 packs of Cream Soda

• Total drinks: 4 * 12 = 48 drinks
• Total cost: 4 * $5 = $20
• While this choice is the most cost effective, it falls short of providing the desired number of drinks.

We are asked to find the fraction of pizza the three friends shared equally.

First, the whole pizza is represented by 1. If one friend ate a quarter of the pizza, then:

First friend eats =1/4 of 1=1/4*1=1/4

Remaining fraction of the pizza=1-1/4=3/4

Now, the three friends share 3/4 amongst themselves equally. So, each friend gets

The three friends each gets 1/4 of the pizza.

The number of boxes to fit the room is found as volume of the room divided by the volume of the box.

Number of boxes:

\(\frac{volume\ of\ the\ room}{volume\ of\ the\ box} = \frac{12ft\ *\\ 12ft\ *\ 12ft}{2.5ft\ *\ 2.5t\ *\ 2.5ft}\ =\ 110.592\)

The approximate number of boxes that can be stored in the room is approximately 111 square feet.

The SI units of measuring length is meter. However, a meter can be a large unit or small quantity depending what is being measured. Therefore, derived units of meters are used to measure the length of an object. In our case, centimeters is the appropriate unit to measure the width of the window.