3.60*0.75

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

From the given data, we can draw the following triangle by letting the unknown length to be p.

We apply the Pythagoras theorem, the value of p:

The unknown length of the triangle is about 21.4 feet.

A whole pizza represents 1, and two friends eat ¼ of the pizza. The remaining fraction of pizza is:

Remaining amount = 

Thus, 3/4 of pizza is left for three friends to share equally.

Now, the other three friends will each get

So, the other three friends will each get 1/4 of the pizza.

We use 1 L =1000 mL to convert between the two units. The conversion options of interconversions are:

And

We want millimeters, use the second option to change L to mL as:

Therefore, 2.5 L is equivalent to 2500 mL.

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

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

We use the order of operation to solve for the unknown value of x.

3(3x+3)=8x+5

Multiply 3 with each number in the brackets

(3*3x)+(3*3)=8x+5

9x+9=8x+5

Subtract 9 from both sides

9x+9-9=8x+5-9

9x=8x-4

Subtract 8x on both sides

9x-8x=8x-8x-4

x=-4

Thus, the unknown value of x is -4.

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.

To convert 514 to a percentage:

Step 1: Convert the mixed number to a decimal

514=5+14=5+0.25=5.255

Step 2: Convert to a percentage

Multiply by 100:

5.25×100=525%

The selling price of the sweater is marked price less the mark off value.

Mark off value=mark off rate*original price

Mark of value=30% of $95

Mark of value=0.30*$95=$28.50

Now, find the selling price of the sweater

Selling price= marked price-mark off value

Thus, the sweater will be sold for 66.50 after applying a mark off of 30%. The selling price is about $67.

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.