Answers
The composite functions are (f · g) (x) = (x + 2)² and (f / g) (x) = 1, whose domains are all real numbers. The value of each function at x = 2 is listed below:
(f · g) (2) = 16 (f / g) (2) = 1How to find and to analyze composite functions
In this problem we must determine and analyze composite functions. Composite functions can be found by combining two simpler functions thanks to operators. There are four operators to make composite functions:
Addition: (f + g) (x) = f(x) + g(x)Subtraction: (f - g) (x) = f(x) - g(x)Multiplication: (f · g) (x) = f(x) · g(x)Division: (f / g) (x) = f(x) / g(x)The domain of a function is the set of all possible of x-values.
First, we determine the two composite functions: f(x) = g(x) = x + 2.
Case A:
(f · g) (x) = (x + 2)²
Case B:
(f / g) (x) = 1
Second, determine the domain for each case:
Case A:
All real numbers.
Case B:
All real numbers.
Third, evaluate each case at x = 2:
Case A:
(f · g) (2) = (2 + 2)² = 4² = 16
Case B:
(f / g) (2) = 1
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Related Questions
(1000 8 13. DIG DEEPER A 4,500-gram bag of soil costs $3, and an 18-kilogram bag of soil costs $10. Which is the less expensive way to buy 18,000 grams of soil? Explain.
Answers
It is cheaper to buy 18-kilogram bag of soil. The cost of the 18-kilogram is $10 and the cost of the cost of the other option is $12.
What is the cheaper way of buying 18,000 grams of soil?Cost of buying 18,000 grams of soil using the 4500 gram bag = (18,000 / 4,500) x $3 = $12
The second step is to convert 18 kilogram to grams.
1 kg = 1000 grams
18 x 1000 = 18,000 grams
18,000 grams cost $10.
Thus, it is cheaper to buy 18-kilogram bag of soil.
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During certain time periods at a hospital, patients arriving at the emergency room have waiting times that are uniformly distributed between 0 and 7 minutes. Assume that a patient is randomly selected, and find the probability that the waiting time is less than 0.75 minutes. (Round to three decimal places)
Answers
Since the waiting times are uniformly distributed between 0 and 7 minutes, the probability density function (PDF) of the waiting time is:
f(x) = 1/7 for 0 ≤ x ≤ 7
0 otherwise
To find the probability that the waiting time is less than 0.75 minutes, we need to integrate the PDF from 0 to 0.75:
P(X < 0.75) = ∫[0,0.75] f(x) dx
P(X < 0.75) = ∫[0,0.75] 1/7 dx
P(X < 0.75) = [1/7 * x] [0,0.75]
P(X < 0.75) = 1/7 * 0.75
P(X < 0.75) = 0.1071
Therefore, the probability that the waiting time is less than 0.75 minutes is 0.1071 (rounded to three decimal places).
Can you help me answer this question?
How many different outfit combinations can San create with 3 shirts, 3 pants and 3 pairs of shoes.
Answers
3x3x3=27
A combined total of $33,000 is invested in two bonds that pay 5% and 6.5% simple interest. The annual interest is $2,010.00. How much is invested in each bond?
Answers
Answer: $9,000 is invested in the 5% bond, and $24,000 is invested in the 6.5% bond.
Step-by-step explanation: x + y = 33,000 (the full sum contributed)
We too know that the yearly intrigued earned is $2,010.00, which is the whole of the intrigued earned from each bond. Utilizing the equation for basic intrigued:
intrigued = principal x rate x time
ready to calculate the intrigued earned from each bond:
0.05x (for the 5% bond)
0.065y (for the 6.5% bond)
So we have another condition:
0.05x + 0.065y = 2,010
Presently we have two conditions with two factors, which we are able illuminate utilizing substitution or end.
Let's utilize substitution:
x + y = 33,000 --> y = 33,000 - x
0.05x + 0.065y = 2,010 --> 0.05x + 0.065(33,000 - x) = 2,010
Streamlining:
0.05x + 2,145 - 0.065x = 2,010
-0.015x = -135
x = 9,000
So the sum contributed within the 5% bond is $9,000, and the sum contributed within the 6.5% bond is:
y = 33,000 - x = 33,000 - 9,000 = $24,000
Lenny bought a motorcycle. He paid 10.5% in tax. The Tax added $1260 to the price of the motorcycle.
What is the price of the motorcycle not including tax?
Answers
The price of the motorcycle not including tax will be $12,000.
Given that:
Lenny bought a motorcycle. He paid 10.5% in tax.
The percentage is given as,
Percentage (P) = [Tax] / Initial value x 100
The price of the motorcycle not including tax is calculated as,
10.5 = (1260 / Initial value) x 100
0.105 = 1260 / Initial value
Initial value = 12,000
The price of the motorcycle is $12,000.
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is there another square other than the own drawn to make a reflective symmetry?
Answers
Mona pays $1.00 for the first call of the day on her mobile phone plus $0.15 per minute of the call. She paid $2.95 for her first call today. Write an expression that you could use to calculate the length in minutes of the phone call.
Answers
The requreid Mona's phone call was 13 minutes long.
Let's let the variable "m" represent the length of the phone call in minutes.
We know that Mona pays $1.00 for the first call of the day plus $0.15 per minute of the call. So the total cost of the call can be represented by the expression:
$1.00 + $0.15m
We also know that Mona paid $2.95 for her first call today. So we can set the expression for the total cost of the call equal to $2.95:
$1.00 + $0.15m = $2.95
To solve for the length of the call in minutes, we can first subtract $1.00 from both sides of the equation:
$0.15m = $1.95
Then we can divide both sides by $0.15:
m = 13
Therefore, Mona's phone call was 13 minutes long.
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What is the volume of this figure?
Enter your answer in the box.
ft³
Answers
Answer: 76 cubic feet
Step-by-step explanation:
Think about breaking it into two rectangular prisms:
Total volume = Volume of longer prism + volume of shorter prism
Total volume = 8x4x2 + 2x2x3
Total volume = 76 cubic feet
Eating at the all-you-can-eat buffet at your favorite restaurant currently costs
$18.50, and increases in cost by 6% each year. What will this buffet cost in 6 years?
$26.24
$30.23
$27.13
$31.64
Answers
A = P(1 + r)^n
where A is the final amount, P is the initial amount, r is the annual interest rate as a decimal, and n is the number of years.
In this case, P = 18.50, r = 0.06, and n = 6. Plugging these values into the formula, we get:
A = 18.50(1 + 0.06)^6
A = 18.50(1.06)^6
A = 18.50(1.4185)
A = 26.23
Therefore, the cost of the all-you-can-eat buffet in 6 years will be approximately $26.23, which is closest to option A.
7. Based on an exponential model of the data, what is the predicted value of Variable 2 when
Variable 1 = 2?
Round your answer to the nearest whole number.
Variable 1:
10
20
30
40
50
60
70
80
90
100
variable 2:
100
80
52
40
35
25
17
11
10
7
Answers
Answer:
128
Step-by-step explanation:
You want a prediction for x=2 when the given data is modeled by an exponential model.
x = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100y = 100, 80, 52, 40, 35, 25, 17, 11, 10, 7ModelA graphing calculator's exponential regression function models this data with the formula ...
y = 135.7 · 0.9711^x
y = 137.7 · 0.9711^2 ≈ 127.94 . . . . when x=2
This model gives a value for variable 2 of approximately 128 when variable 1 = 2.
<95141404393>
Suppose log 2 = r, log, 3= s, and log 5 = t. Which algebraic expression represents log 75?
Answers
log(75) = log( 3 • 5 • 5 )
= log(3) + log(5) + log (5)
= s + t + t
= s + 2t
To go from log( 3 • 5 • 5 ) to log(3) + log(5) + log (5), we use the log rule that says log( a • b ) = log(a) + log(b).
Melissa drew a right triangle.
The perimeter of the triangle is 9+√41.
The hypotenuse is of length ✓41.
Using this information, what is the length of the other
two sides of the triangle?
Answers
Answer:
Let's denote the two legs of the right triangle as a and b, and the hypotenuse as c. We know that c = √41, so we can use the Pythagorean theorem to relate a and b to c:
c^2 = a^2 + b^2
Substituting c = √41, we get:
(√41)^2 = a^2 + b^2
41 = a^2 + b^2
We also know that the perimeter of the triangle is:
perimeter = a + b + c = 9 + √41
Substituting c = √41, we get:
a + b + √41 = 9 + √41
a + b = 9
Now we have two equations with two unknowns (a and b):
a^2 + b^2 = 41
a + b = 9
We can solve this system of equations by substitution. Solving the second equation for a, we get:
a = 9 - b
Substituting this into the first equation, we get:
(9 - b)^2 + b^2 = 41
81 - 18b + 2b^2 = 41
2b^2 - 18b + 40 = 0
b^2 - 9b + 20 = 0
(b - 4)(b - 5) = 0
So we have two possible solutions: b = 4 and b = 5. We can find the corresponding value of a using a = 9 - b:
a = 5 and b = 4 or a = 4 and b = 5
Therefore, the two legs of the right triangle are 4 and 5.
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answers
The calculated area of this triangle is 43.50 sq units
What is the area of this triangle?From the question, we have the following parameters that can be used in our computation:
The triangle
The area of the triangle is calculated as
Area = 1/2 * Product of adjacent legs * sin of middle angle
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 12 * 8 * sin(65)
Evaluate
Area = 43.50
Hence, the area is 43.50 sq units
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solve the inequality and graph the solution on the line provided.
5x - 15 < 10
Answers
Add 15 to both sides of the inequality to isolate the term with x:
5x - 15 + 15 < 10 + 15
5x < 25
Divide both sides of the inequality by 5 to solve for x:
5x/5 < 25/5
x < 5
Therefore, the solution for the inequality is x < 5.
To graph the solution on the number line, we can draw a line with an open circle at 5 (since the inequality is less than, not less than or equal to), and shade the part of the line to the left of the circle to represent all the values of x that satisfy the inequality. Here's a rough sketch:
<-------------------o------------------->
5
The shaded region is on the left side of the open circle.
Answer: x < 5, see attached for the graph.
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
5x - 15 < 10
Add 15 to both sides of the equation:
5x < 25
Divide both sides of the equation by 5:
x < 5
For the graph, we will use an open circle because this is only less than (<), not less than and equal to.
Then, since x is all values less than 5, we will shade our arrow to the left of 5. See attached.
Darcy is tiling a square area of her bathroom floor. For every 13 white tiles used, she wants to use 12 gray tiles.
Answers
The ratio to show the relationship is 13 : 12
Writing the ratio to show the relationshipFrom the question, we have the following parameters that can be used in our computation:
For every 13 white tiles used, she wants to use 12 gray tiles.
This means that
Ratio = White : Gray
Substitute the known values in the above equation, so, we have the following representation
Ratio = 13 : 12
Hence, the ratio of white tiles and the number of gray tiles is 13 : 12
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Complete question
Demetria is tiling a square area of her bathroom floor. For every 13 white tiles used, 'she wants to use 12 gray tiles.
Write a ratio to show the relationship between the number of white tiles and the number of gray tiles.
Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
<[tex]\sqrt{74}[/tex]
Answers
The inequality is -8 < √74 < 9. A mathematical expression that's values on the left and right are not equal is referred to as having an inequality.
A mathematical expression that's values on the left and right are not equal is referred to as having an inequality. In essence, an inequality analyses any two values that demonstrates whether one is bigger than, less than, or neither greater nor equal to the other quantity. Numbers are compared using inequalities to determine a range of quantities that are contained inside the parameters of a variable.
Let A = √74
A² = 74
8² < A² < 9²
Hence, the inequality is -
8 < √74 < 9
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2 Mike and Anna are having a weight loss competition. Mike wants to practice kickboxing to burn calories while Anna
prefers to run. Mike records his calories burned in the table below and Anna graphs her calories burned in the graph.
Who burns more calories per hour?
Anna's Calories Burned:
Running
A. Mike and Anna burn the same amount
of calories per minute
B. Mike burns more calories per minute
thank Anna.
C. Anna burns more calories per minute
than Mike.
D. There is not enough information
to determine who burns more calories
per minute.
Mike's Calories Burned:
Kickboxing
Minutes
0
12
24
36
Calories
0
150
300
450
Calories Burned
y
500
450
400
350
300
250
200
150
100
50
5
10 15 20 25 30 35
Minutes
40 45
50
Answers
Based on the information regarding the data, B. Mike burns more calories per minute than Anna
How to explain the dataThe calorie consumption of Mike was between 12.5 and 16.67, averaging out at nearly 13.75 per minute.
In contrast, Anna burned around 13.33 each minute.
So the answer is B - Mike burns more calories per minute than Anna.
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what is half of 9min and 28 sec
Answers
Answer:
4 minutes and 44 seconds.
dr
15
3-
13 1
-6
-9
-12
-15
2 3 4 5
X
Which lists all of the x-intercepts of the graphed
function?
O(0.6)
O(1, 0) and (2, 0)
O(1, 0), (2, 0), and (-3, 0)
O(1.0), (2, 0), (-3,0), and (0, 6)
Answers
Answer:
not sure sorry -(1,0)and (2,0)
PLEASE HELP ITS URGENT ILL GIVE YOU BRAINLIEST.
The following are daily high temperatures (°F) in Auckland, New Zealand: 75 67 83 90 79 74 70 71 72 78 76 67 66 80 77 77 84 74
Using the data above, make a box-and-whisker plot. If the set has outliers, use an * to show them.
if you answer as a troll I will report
Answers
Answer: The box goes from Q1 to Q3, with the middle spoken to by a line interior the box at Q2. The bristles expand from the box to the least and most extreme values. There's one exception, spoken to by an bullet (*), at the esteem of 90.
Step-by-step explanation: box and whisker plot:
|
90 ---| *
84 ---|
83 ---|
80 ---|_____
79 ---| |_____
| | |
76 ---| | |
| | |
72 ---|_____| |
71 ---| |
70 ---|___________|
66 75
Katrina is building a wall around her backyard using bricks that are 18 inches long. The wall needs to be 36 feet, or 432 inches, long.
Answers
Katrina will need 24 bricks to build the wall around her backyard.
We have,
To determine the number of bricks needed for the wall, we need to divide the total length of the wall (432 inches) by the length of each brick (18 inches):
So,
Number of bricks = Total length of the wall / Length of each brick
Number of bricks = 432 inches / 18 inches
Number of bricks = 24 bricks
Therefore,
Katrina will need 24 bricks to build the wall around her backyard.
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The complete question:
Katrina is building a wall around her backyard using bricks that are 18 inches long. The wall needs to be 36 feet, or 432 inches, long.
Find the number of bricks needed to build around he backyard.
Everyone in the population must have an of being selected in order for a sample to be an
Answers
Answer: Everyone in your population must have an equal, non-zero chance of being selected. (In other words, everyone has an equal chance of receiving a survey.) You must know, specifically, what that chance of being selected is for each person.
23=-8v-7+2v????????????????????
Answers
Answer:
v=-5
Step-by-step explanation:
Answer:
[tex]23 = 10v - 7 \\ 23 + 7 = 10v \\ 30 = 10v \\ v = 3 \\ \\ [/tex]
The profit equation for the sale of pressure cookers for the company Kitchen Masters is PP = −120pp2 + 19,800pp − 727,450. Which of the following is a sale price for the immersion blenders, p, that will allow Kitchen Masters to achieve a profit, P, of $89,300?
Answers
Where the above factors are given, a sale price of approximately $84 for the immersion blenders will allow Kitchen Masters to achieve a profit of $89,300.
Why is this so?The profit equation for the sale of pressure cookers for the company Kitchen Masters is:
P = −120p² + 19,800p − 727,450
To find the sale price for the immersion blenders, p, that will allow Kitchen Masters to achieve a profit, P, of $89,300,
Let the profit equation = 89,300.
Now, we solve for p:
89,300 = −120p² + 19,800p − 727,450
Adding 727,450 to both sides:
816,750 = -120p² + 19,800p
Dividing both sides by -120:
-6,805 = p² - 165p
Rearrange the equation to make it Quadratic
p² - 165p + 6,805 = 0
Now we can solve for p using the quadratic formula:
p = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = -165, and c = 6,805.
p = (-(-165) ± √((-165)² - 4(1)(6,805))) / 2(1)
p = (165 ± √((27,225 - 27220)) / 2
p ≈ 83.618 or p ≈ 81.382
Therefore, a sale price of approximately $84 for the immersion blenders will allow Kitchen Masters to achieve a profit of $89,300.
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Willa sells cars. Last month, she had 124,000 dollars in sales. Her commission rate is 1.3 percent. How much did Willa earn for the month?
Answers
Her commission rate is 1.3%, which can be written as a decimal as 0.013.
Multiplying her sales by her commission rate, we get:
0.013 * 124,000 = 1,612
Therefore, Willa earned $1,612 for the month.
Can you round off 20.900156 to 1 decimal place?
Answers
Answer:
Step-by-step explanation:
20.9 is solution
. Amanda lets her new pony exercise by letting the pony run in circles while
attached to a rope, which Amanda holds in the center of the ring. If the part of
the rope between Amanda's hand and the pony is 30 feet long, how far does
the pony run in one circle. Round your answer to the nearest tenth. (Draw a sketch to help.
Answers
Answer:
188.5 ft
Step-by-step explanation:
One Circle = perimeter
= 2 nr
= 2 x 3.14 x 30
= 188.5 ft
Rotations : If the point (6,2) was on a figure that was rotated 180 degrees clockwise what would be the coordinates of the new point on this figure
Answers
The coordinates of the new point is (-6, -2)
What would be the coordinates of the new pointFrom the question, we have the following parameters that can be used in our computation:
Point = (6, 2)
Rule: 180 degrees rotation
The rule of 180 degrees rotation is
(x, y) = (-x -y)
substitute the known values in the above equation, so, we have the following representation
image = (-6, -2)
Hence, the image = (-6, -2)
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Simplify the expression: 8y + 4 - 3y + 12
Answers
The simplified value of 8y + 4 - 3y + 12 is 5y+16
What is simplification of expression?An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. For example , 4x+5 , 2x²+2, 10y³+5y²+6
To simplify an expression means to write the expression Ina simpler form. for example 6y²+2y can be written as 2y( 3y+1)
Simplifying 8y + 4 - 3y + 12,
collecting like terms
8y-3y+4+12
= 5y+16
therefore the simplification of 8y + 4 - 3y + 12 is 5y+16
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2. A gift is packed in a rectangular box (rectangular prism) of dimensions 15 in, 10 in, and 8 in and it needs to be wrapped with gift paper. How much gift paper is required to wrap the gift box?
length= 5 in , width= 4 in, height= 3 in
Answers
length, l=16in
width, b=13in
thickness, t=3in
To Find:-
Area of wrapping paper required.
Explanation:-
Since, wrapping paper is to be wrapped over the whole rectangular box.Therefore, we have to calculate the total surface area of the rectangular box.

Therefore, 590 of paper is required to wrap the whole rectangular box.
=700 sq in
= 94 sq in
Step-by-step explanation:
To find the amount of gift paper required to wrap the gift box, we need to find the total surface area of the rectangular prism. The total surface area is the sum of the areas of all six faces of the rectangular prism.
The formula for the surface area of a rectangular prism is:
Surface area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
For the given rectangular prism with dimensions 15 in, 10 in, and 8 in, we have:
l = 15 in, w = 10 in, h = 8 in
Substituting these values into the formula, we get:
Surface area = 2(15)(10) + 2(15)(8) + 2(10)(8)
Surface area = 300 + 240 + 160
Surface area = 700
Therefore, the amount of gift paper required to wrap the gift box is 700 square inches.
For the second part of the question, we need to find the surface area of the rectangular prism with dimensions 5 in, 4 in, and 3 in. Using the same formula, we have:
l = 5 in, w = 4 in, h = 3 in
Surface area = 2(5)(4) + 2(5)(3) + 2(4)(3)
Surface area = 40 + 30 + 24
Surface area = 94
Therefore, the amount of gift paper required to wrap the second gift box is 94 square inches.