25 math questions

7/20/23, 1:41 PM Week 1: Assignment - MyLab Homework-Natalie Banks

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Student: Natalie Banks Date: 07/20/23

Instructor: Keva Yarbrough Course: College Math-Summer 2023 (2)

Assignment: Week 1: Assignment - MyLab Homework

Evaluate the expression.

( − 4)2

( − 4)2 = 16

Use the order of operations to find the value of the given expression.

( ) ( )7 − 9 2 − 5 − 8 2

( ) ( )7 − 9 2 − 5 − 8 2 = − 5

Use the order of operations to find the value of the following expression.

12 ÷ 3 ÷ (9 − 6) − ( − 6)2

12 ÷ 3 ÷ (9 − 6) − ( − 6)2 = (Simplify your answer. Type an integer or a fraction.)

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Convert to standard decimal notation.6.34 10× 9

Select the correct answer below.

A. 6.34000000000

B. 0.00000000634

C. 6,340,000,000

D. 63,400,000,000

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The population of a country reached 317 million in August 2013. Write that number in scientific notation.

317 million = (Use scientific notation. Use the multiplication symbol in the math palette as needed.)

Evaluate the given expression for x = − 13.

− 7x − 3

The answer is .

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Evaluate the algebraic expression for the given value of the variable.

; − x + 62 x = 3

For , .x = 3 − x + 62 = (Simplify your answer.)

Evaluate the algebraic expression for the given values of the variables.

x − 6(x − y), for x = 6 and y = 12

When x and y , .= 6 = 1 x − 6(x − y) =2

The formula expresses the relationship between Fahrenheit temperature, F, and Celsius temperature, C. Use the formula to

convert to its equivalent temperature on the Celsius scale.

C = (F − 32) 5 9

95°F

= 95°F °C

A football is kicked vertically upward from a height of feet with an initial speed of feet per second. The formula describes the ball's height above the ground, h, in feet, t seconds after it was kicked. Use this formula to find the ball's height after it was kicked.

5 60 h = 5 + 60t − 16t2

3 seconds

The ball's height, after it was kicked, was feet.3 seconds

Simplify the given algebraic expression.

6x + 4x

6x + 4x =

Simplify the given algebraic expression.

5(4x − 9) + 5x

5(4x − 9) + 5x =

Simplify the algebraic expression.

3 − 3x + 3x − 5x − 3x2 2

(Simplify your answer. Do not factor.)3 − 3x + 3x − 5x − 3x2 2 =

The maximum heart rate, in beats per minute, that you should achieve during exercise is 220 minus your age, . Your exercise goal is to improve cardiovascular conditioning. Use the following formulas to answer parts (a) and (b).

220 − a

Lower limit of range H = (220 − a) 7 10

Upper limit of range H ( )= 4 5

220 − a

a. What is the lower limit of the heart range, in beats per minute, for a -year-old with this exercise goal?40

The lower limit of the heart range is beats per minute. (Round to the nearest integer as needed.)

b. What is the upper limit of the heart range, in beats per minute, for a -year-old with this exercise goal?40

Thus, the upper limit of the heart range is beats per minute. (Round to the nearest integer as needed.)

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(1) overestimates underestimates

The bar graph shows the estimated number of calories per day needed to maintain energy balance for various gender and age groups for sedentary lifestyles. (Sedentary means a lifestyle that includes only the light physical activity associated with typical day-to-day life.) The mathematical model

describes the number of calories needed per day, F, by females in age group x with sedentary lifestyles. According to the model, how many calories per day are needed by females between the ages of , inclusive, with this lifestyle? Does this underestimate or overestimate the number shown by the graph? By how much?

F = − 83x + 654x + 6162

9 and 13

           

0

800

1600

2400

3200

C al

or ie

s pe

r D ay

1114 1394

16651800 1910 2198

1825 2405

1733 2192

1482 2006Group 1

Group 2 Group 3 Group 4 Group 5 Group 6

Females Males

According to the model, how many calories per day are needed by females between the ages of , inclusive, with this lifestyle?9 and 13

(Type a whole number.)

Does the model underestimate or overestimate the number shown by the graph? By how much?

The model (1) the actual amount by approximately calories. F = − 83x + 654x + 6162

(Type a whole number.)

A business that manufactures small alarm clocks has weekly fixed costs of $ . The average cost per clock for the business to

manufacture x clocks is described by .

4000 0.5x + 4000

x a. Find the average cost when x 100, 1000, and 10,000.= b. Like all other businesses, the alarm clock manufacturer must make a profit. To do this, each clock must be sold for at least 50 more

than what it costs to manufacture. Due to competition from a larger company, the clocks can be sold for $1.50 each and no more. Our small manufacturer can only produce 2000 clocks weekly. Does this business have much of a future? Explain.

¢

a. The average cost when x 100 is $ .= (Type an integer or a decimal.)

The average cost when x 1000 is $ .= (Type an integer or a decimal.)

The average cost when x 10,000 is $ .= (Type an integer or a decimal.)

b. Does this business have much of a future?

A. Yes, the average cost to produce 2000 alarm clocks is much less than the selling price of the alarm clocks.

B. No, the average cost to produce 2000 alarm clocks is much greater than the selling price of the alarm clocks.

C. Yes, the average cost to produce 2000 alarm clocks is much greater than the selling price of the alarm clocks.

D. No, the average cost to produce 2000 alarm clocks is much less than the selling price of the alarm clocks.

Calories Needed to Maintain Energy Balance for Sedentary Lifestyles

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A company sells floats for children. An equation that models their profit is P 4x 10,000, where x is the number of floats sold.= −

If 5,000 floats are sold, what is the company's profit?

$

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Simplify 5(2x 3) 8x.− −

5(2x 3) 8x− − =

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Simplify .3 4x + 2x + 2 5x + x2 2

Enter your answer, using the menu on the left as needed.

3 4x + 2x + 2 5x + x2 2 =

Express the given set using the roster method.  

The set of natural numbers less than .8

Express the set of natural numbers less than in roster form.8

{ } (Use a comma to separate answers as needed. Use ascending order.)

Determine if the set is the empty set.

{ }x | x is a living U.S. president born before 1600

Choose the correct answer below.

The set is not the empty set.

The set is the empty set.

Determine whether the given statement is true or false.

13∉{ }1, 2, 3,... , 7

Choose the correct answer below.

True

False

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List all the subsets of the given set.

{g, n, s}

Choose the answer that lists all of the subsets of .{g, n, s}

A. {}, { }, { }, { }, { , }, { , }, { , }, { , , }g n s g n g s n s g n s

B. {}, { }, { }, { }, { , }, { , }, { , }g n s g n g s n s

C. { }, { }, { }, { , }, { , }, { , }g n s g n g s n s

D. { }, { }, { }, { , }, { , }, { , }, { , , }g n s g n g s n s g n s

Calculate the number of subsets and the number of proper subsets for the given set.

{ x | x N and x }∈ 10 < < 15

Number of subsets:

Number of proper subsets:

Explain why the empty set is a subset of every set.

Choose the correct answer below.

A. If there is at least one element of set A that is not an element of set B, then A is not a subset of B. If A is the empty set, which contains no elements, then there can never be any elements in A, much less elements in A that do not belong to B.

B. If there is at least one element of set A which is also an element of set B, then A is a subset of B. If A is the empty set, which contains no elements, then there can never be any elements in A, much less elements in A that belong to B.

C. If all elements in set A are also elements of set B and all elements in set B are also elements in set A, then A and B are subsets. If A is the empty set, then there can never be any elements in A, much less elements in A that belong to B.