A student performs the following estimations.

35+192  230

258+350  610

947+1032  1980

Based on these estimations, which of the following is the student’s estimate of 694+7618?

 we are to find the selling price of the sweater from the marked price and the discount. The marked price is given as

Discount=mark off rate*original price

Discount=15%*$78

Convert 15% into a fraction, which become 15/100=0.15. Then

Discount=0.15*$78=$11.70

The selling price of the sweater will be the original price less the discount or mark off value. Then,

Thus, the approximate selling price of the sweater is $66.

An independent variable is a variable that when changed result in a change to other variables under investigation. From the given scenario, if the stock of the company increases, then the production, sales, and investment increase. Therefore, stock is the independent variable while other variables are dependent.

Looking at the give curve, we analyze each statement as:

• For statement 1: the points per game decreased five times between 1996 and 2015. So, the statement is false.
• For statement 2: the lowest points scored per game was in 1998-99 season and not in 2003-04 season. So, the statement is false.
• For statement 3: 2008-09 was the season the chargers scored the greatest number of points per game. So, this statement is false.
• For statement 4: the two season which no change in the points were 2012-13 and 2013-14. So this is true according to given curve.

from the given data, one gallon of cleaning solution requires 6 oz of ammonia. The mathematical expression of this statement can be expressed in two ways:

Or

The question requires we find the amount of ammonia needed to make 230 gallons of the solution. So, we use the second option and proceed as follows:

From the above equation, gallon of solution will cancel, and oz of ammonia is left.

Therefore, the solution will require 1380 oz of ammonia.

The length of the unknown side of the rectangle can be found by using the Pythagoras theorem. Letting the unknown side to be x, the labelled rectangle becomes: The unknown length of the triangle is about 16.7 feet.

The length of the unknown side of the rectangle can be found by using the Pythagoras theorem. Letting the unknown side to be x, the labelled rectangle becomes:

The unknown length of the triangle is about 16.7 feet.

: the question requires we find the cost of four syringes.

If we let x be the cost of four syringes, then we set up a proportion equation with cost as numerator and number of syringes as denominator. The proportion equation becomes

Cross-multiply to solve for x

Rearranging the above

Divide both sides of the equation by 55

Thus, the cost of 4 syringes is $48.

In this problem, we need to find the amount of gratuity the couple will leave. The gratuity is 16% of the total bill. Before solving the problem, the following are terms and their meaning in percent problems:

• Is means equals
• Of means multiply
• What means unknown (variable)

If we let x be the amount of gratuity, then translating the given problem into a mathematical equation becomes:

So, the value of x=9.376 and to the nearest cent, x=9.38

There, a couple will leave a gratuity of $9.38.

Explanation: We know that 1 L=1000 mL and to change between L and mL we use the following two options

We need to find how many mL are in 5.5 teaspoons. We are told that 1 teaspoon is about 4.93 mL, which we interpret as follows:

Or

Since we are looking for mL, we use the second option.

Thus, 5.5 teaspoons can hold approximately 27 mL.

To form an equation from the word problem, first break the given statement into smaller statements.

First, we are given the width of the rectangle as x. We are told, the length is two times width. Mathematically, this means

Length=2*width=2*x=2x

Now, the length is 6 less than 2 times width of the rectangle. Thus, the length of rectangle in terms of width becomes:

Length =2x-6

Thus, the length of the rectangle is 2x-6.