Simplify each expression blow:

(a). 18.5 - (4.8 + 0.2)² + 4.1  2=

(b). 11.35 + (0.2  3.5 )² - 3.7=

©. On a business trip, Jason bought the following amounts of gasoline: 15.4, 12.2, 13.8, and 10 gallons (gal). How much gasoline did he purchase on the trip?

(d). If Jason paid for the above purchases of gasoline, the amounts of $42.95, $34.05, $38.50, and $27.90 with two $100 bills. How much cash does he have left?

(e). Multiply the numbers without a calculator: 3.75  0.73 =

Problem #8.

(a). 1.257 x 10²=

(b). Round the number 23.5724 to two decimal places.

(c). Round the number 2.5976 to the thousandths.

(d). 7² + 9²  10²=

(e). We find the circumference of a circle by multiplying the diameter of the circle by 3.14. If a circle has a diameter of 4.2 ft. What is its circumference, to the nearest hundredth of a foot.

Problem #9.

(a). Divide: 4.983  1,000

(b). Divide: 523  105

(c ). A street improvement project will cost $58,350, and that cost is to be divided among the 100 families in the area. What will be the cost to each individual family?

(d). Find the decimal equivalents of the common fraction . Round to the thousandths place value.

(e). The area of a whole circle is 3.14 multiply the square of its radius. Find the area of a semicircle (half of a circle) of radius R=2.

Problem #10.
(a). Write the decimal 0.235 as common fraction or mixed numbers. Simplify your answer.

(b). Write the decimal 2.25 as a mixed number. Simplify your answer

(c). Insert < or > to form a true statement. 0.124 ______

(d). Which of the numbers and terminate and which repeat. Explain your answer.

(e). A baseball team has a winning percentage of 0.275. Write this as a fraction in simplest form.

I don't think there is much of a chance you will find a volunteer here to do your test for you. If you have a specific q

I don't think there is much of a chance you will find a volunteer here to do your test for you. If you have a specific question about it, ask.

Round the number 23.5724 to two decimal places

(a). To simplify the expression 18.5 - (4.8 + 0.2)² + 4.1  2, we need to follow the order of operations, which is also known as BIDMAS (Brackets, Indices, Division and Multiplication, Addition and Subtraction).

First, parenthesize the numbers inside the parentheses: 4.8 + 0.2 = 5.

Then square the result: 5² = 25.

Next, multiply 4.1 by 2: 4.1  2 = 8.2.

Now, substitute the values back into the expression: 18.5 - 25 + 8.2.

Finally, perform the subtraction: 18.5 - 25 + 8.2 = 26.7 - 25 = 1.7.

(b). To simplify the expression 11.35 + (0.2  3.5)² - 3.7, we again follow the order of operations.

First, multiply 0.2 by 3.5: 0.2  3.5 = 0.7.

Then square the result: 0.7² = 0.49.

Next, substitute the values back into the expression: 11.35 + 0.49 - 3.7.

Finally, perform the addition and subtraction: 11.35 + 0.49 - 3.7 = 11.84 - 3.7 = 8.14.

(c). To find the total amount of gasoline Jason purchased on the trip, we need to sum up the amounts he bought.

Add the amounts of gasoline: 15.4 + 12.2 + 13.8 + 10 = 51.4 gallons.

(d). To find out how much cash Jason has left after paying for the gasoline purchases, we need to subtract the total cost of gasoline from the amount he paid with the two $100 bills.

Add up the amounts Jason paid for gasoline: $42.95 + $34.05 + $38.50 + $27.90 = $143.40.

Subtract the total cost of gasoline from the amount Jason paid: $200 - $143.40 = $56.60.

(e). To multiply the numbers 3.75 and 0.73 without a calculator, we can use long multiplication.

Write the numbers vertically and start by multiplying the digits in the ones place:
3.75
x 0.73
_______

Next, multiply the digits in the tenths place, remembering to add a placeholder zero for the tenths digit:
3.75
x 0.73
_________
2625
+ 2625
_________
= 27.37

Problem #8.

(a). To simplify the multiplication 1.257 x 10², we multiply 1.257 by 100:
1.257 x 100 = 125.7.

(b). To round the number 23.5724 to two decimal places, we look at the digit in the thousandths place (4). Since it is less than 5, we round down. Therefore, 23.5724 becomes 23.57.

(c). To round the number 2.5976 to the thousandths place, we look at the digit in the ten-thousandths place (6). Since it is 5 or greater, we round up. Therefore, 2.5976 becomes 2.598.

(d). To simplify the expression 7² + 9²  10², we need to follow the order of operations.

First, square 7 and 9: 7² = 49 and 9² = 81.

Next, multiply 81 by 100: 81  100 = 8100.

Finally, add 49 and 8100: 49 + 8100 = 8150.

(e). To find the circumference of a circle with a diameter of 4.2 ft, we multiply the diameter by 3.14.

Multiply 4.2 by 3.14: 4.2  3.14 = 13.188

Round the result to the nearest hundredth: 13.188 rounded to the nearest hundredth is 13.19.

Problem #9.

(a). To divide 4.983 by 1,000, we move the decimal point three places to the left: 0.004983.

(b). To divide 523 by 105, we perform the division: 523 ÷ 105 = 4.981.

(c). To find the cost to each individual family for a street improvement project that costs $58,350 divided among 100 families, we divide the total cost by the number of families: $58,350 ÷ 100 = $583.50.

(d). To find the decimal equivalents of the common fraction , we divide 3 by 8: 3 ÷ 8 = 0.375.

(e). To find the area of a semicircle with radius R = 2, we use the formula for the area of a circle divided by 2: 0.5 x π x (2²) = 0.5 x 3.14 x 4 = 6.28.

Problem #10.

(a). To write the decimal 0.235 as a common fraction, we use the place value of each digit: 0.235 = 235/1000.

(b). To write the decimal 2.25 as a mixed number, we look at the whole number part (2) and the decimal part (0.25). The decimal part can be expressed as a fraction: 0.25 = 25/100. Therefore, 2.25 = 2 + 25/100 = 2 + 1/4 = 2 1/4.

(c). To determine whether 0.124 is < or > another number, we need context. Without another number to compare it to, we cannot say whether it is less than or greater than.

(d). The numbers and terminate, as they have a finite number of decimal places. The number terminates because the digit in the hundredths place is 0, and the number terminates because the digit in the thousandths place is 0.

(e). To write the winning percentage 0.275 as a fraction in simplest form, we express it as 275/1000. Simplifying the fraction, we divide both the numerator and denominator by their greatest common factor, which is 25: 275/1000 = 11/40.