3.60*0.75

Simplify the expression above. Which of the following is correct?

Let x be the original price of the recliner.

Step 1: Apply the 30% discount

The recliner is on sale for 30% less than the original price:

SalePrice=x−0.3x=0.7x

Step 2: Apply the 25% coupon discount

The consumer gets an additional 25% off the sale price:

FinalPrice=0.7x−0.25(0.7x) = 0.525x

Step 3: Solve for x

The consumer paid $237, so:

0.525x=237

​ x≈451.43x

Rounding to the nearest dollar, the original price is $451.

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 three times width. Mathematically, this means

Length=3*width=3*x=3x

Again, the length is 4 less than 3 times width of the rectangle. Thus, the length of rectangle in terms of width becomes:

Length =3x-4

This is the required equation.

To solve this problem, we need to have all options in fraction form.

74  95 = 

7/8 = 3/8

0.72 = 72/100

74% = 74/100

Now, find the least common denominator of 95, 8, and 100. The least common denominator is 3800, which we multiply by each fraction as follows:

74/95*3800=2960

7/8*3800=3325

72/100*3800=2736

74/100*3800=2812

We can see that the fraction 7/8 is the greatest among the given options.

We are required to find the doctor’s earning in 4 weeks after taking off taxes.

The first step is to find the total weekly deductions as follows:

Total weekly tax=federal income tax + state income tax + Social Security tax

Total weekly tax=$(85.00+40.00+81.00)

Total tax=$206.00

The next step is to find the weekly income after deducting total taxes

Weekly net income=gross income-total tax

Weekly net income=$(980.00-206.00)=$774.00

In one week, the net income of the doctor is $774.00 and after 4 weeks, the net income will be 4 times his weekly earning

The first five months of the year are January, February, March, April, and May. We use to graph to find the amount of rainfall in each month as follows:

In the month of January, rainfall was between o and 1, which is halfway. Therefore, rainfall in January is 0.5 inches

On February, rainfall was 1 inch and on March the rainfall was 2 inches.

On April, the rainfall amount was 4 inches while on month of May, the rainfall was about 3.5 inches. Therefore, total rainfall in the first 5 months was:

Total rainfall=0.5 inches+1 inches+ 2 inches+4 inches + 3.5 inches =11 inches

An independent variable is a change that when modified brings a change in other variables. In this case, the person increases his climbing rate, calories burned, distance traveled and energy used increases. Therefore, the walking speed is the independent variable while other variables are dependent.

We need to find the radius of the circle from the given value of area. Then, the radius of the circle will be used to find the circumference of the circle.

The first step is to find the radius, r of the circle as

Thus, the circumference of a circle whose area is \(9\pi\ in\ ^2\)is 6 in.

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:

Now we evaluate the above equation noting that of means multiply.

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.

From the cost of 45 syringes, we are required to find the cost of 5 syringes. We set up a proportion equation by letting the cost of 5 syringes to y. Besides, we let the cost to be numerator and number of syringes to be denominator as follows.

Solve the value of y by cross products

Divide both sides by 45

Therefore, 5 syringes will cost $80.00.

We are asked to find mL equivalent in 1.5 teaspoons. To carry out the operations, we utilize dimensional analysis to solve this problem as follows.

Converting between teaspoon and mL uses the following conversions:

Or

Since we want to remain with mL, use the second option and proceed as follows.

Thus, 1.5 teaspoons is equal to 7.395 mL