Answers
y = f (x)
The domain of the function is:
values of x for which it is defined.
The range is:
values of and for which it is defined.
The inverse is:
x = f (y)
The domain of the function is:
values of and for which it is defined.
Answer:
TRUE
option A
Domain of the function is Range of its Inverse.
Range of the function is Domain of its Inverse.
This is because the function and its inverse are a reflection about the line x= y, as a result the x values get translated to y values.
Related Questions
A sample of 4 different calculators is randomly selected from a group containing 13 that are defective and 26 that have no defects. what is the probability that at least one of the calculators is defective? (hint: think complement)
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In how many ways can 6 people be selected from 7 men and 8 women if the selection must have a majority of women?
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Number of women = 8
Number of people to be selected = 6
Condition: Women must be majority
Options: 6 women, 0 men; 5 women, 1 man; 4 women, 2 men
Number of ways = [(8C6)*(7C0)]+[(8C5)*(7C1)]+[(8C4)*(7C2)] = 28+392+1470 = 1890 ways
Kris wanted to understand whether students at her school were in favor of an extended school day. She surveyed some students and displayed the results in the table below: In favor Opposed Undecided Grade 9 6 4 8 Grade 10 10 11 9 Grade 11 12 15 11 Grade 12 15 6 14 If the principal randomly selects a student in grade 10 from this survey, what is the probability that the student is opposed to extending the school day? (1 point) Question 9 options: 1) 0.09 2) 0.29 3) 0.30 4) 0.37
Answers
Answer:
4) 0.37
Step-by-step explanation:
If the principal randomly selects a student in grade 10 from this survey, the probability that the student is opposed to extending the school day is a division of the number of students that opposed from 10 Grade by the total number of students of the 10 Grade.
The table of the question is as:
Grade In favor Opposed Undecided
9 6 4 8
10 10 11 9
11 12 15 11
12 15 6 14
So, there are 10 students in 10 grade that are in favor of the extended school day, 11 students that are Opposed and 9 students that are undecided about the extended school day. then, there are 30 student in 10 Grade
Then, the probability is:
[tex]\frac{11}{10+11+9} =\frac{11}{30}=0.37[/tex]
Enter a recursive rule for the geometric sequence. 4, −16, 64, −256, ...
Answers
Answer:
The recursive rule is an = (-4) · an-1
Step-by-step explanation:
* Lets explain recursive formula for a geometric sequence:
1. Determine if the sequence is geometric (Do you multiply, or divide, the same amount from one term to the next?)
2. Find the common ratio. (The number you multiply or divide.)
3. Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term.
# a1 = first term;
# an= r • an-1
- Where:
a1 = the first term in the sequence
an = the nth term in the sequence
an-1 = the term before the nth term
n = the term number
r = the common ratio
Ex: {3, 6, 12, 24, 48, 96, ...}
first term = 3, common ratio = 2
The recursive formula an = 2 · an-1
* In our problem:
- a1 = 4
- r = -16/4 = -4
- The recursive rule is
# an = (-4) · an-1
Answer:
here is the correct answer.
Step-by-step explanation:
find the are of each circle round nearest tenth use 3.14 11ft
Answers
Identify the random variable as discrete or continuous: number of passengers in a car that enters a uh parking garage.
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The number n of aluminum cans used each year is directly proportional to the number of people using the cans. if 250 people use 60,000 cans in one year, how many cans are used each year in dallas, which has a population of 1,008,000.
Answers
________________________________________________________
Explanation:
_______________________________________________________
(60,000) / (250) = "n" / (1,008,000) ;
Solve for "n" ; {number of cans used each year in Dallas} ;
(250) n = (60,000)(1,008,000) ;
Divide each side of the equation by "250" ;
to isolate "n" on one side of the equation; & to solve for "n" ;
→ { (250) n} / 250 = [ (60,000)(1,008,000) ] / 250 ;
to get:
→ n = (60,480,000,000) / (250) ;
→ n = 241,920,000
________________________________________________________
The answer is: " 241,920,000 cans " .
________________________________________________________
If a household has at least one cat, there is a 30% probability that the household has at least one dog. thirty percent of households have at least one cat and 33% of households have at least one dog. given that a household does not have at least one dog, the probability that the same household does not have at least one cat is
Answers
The probability that a household does not have a cat, given that it doesn't have a dog is 70%. This is a question about conditional probability, and can be solved by applying Bayes theorem and the concept of complements in probability.
Explanation:Given the question, we need to calculate the probability that a household does not have a cat if it is known that the same household does not have a dog. This question applies to the concept of conditional probability in mathematics.
Let's consider the event of a household having at least one cat as C and the event of a household having at least one dog as D. The question tells us that the probability of a household having a dog given it has a cat P(D|C) = 0.30 and the probability of a household having a cat P(C) = 0.30, and the probability of having a dog P(D) = 0.33. We are asked to find the probability of a house not having a cat given it does not have a dog, P(C'|D').
Using Bayes theorem, the conditional probability P(C'|D') can be calculated using the formula: P(C' | D') = P(D' | C') * P(C') / P(D'), where P(C') is the probability of not having a cat and P(D'| C') is the probability of not having a dog given that there is no cat.
First, find the complement percentages. P(C') = 1 - P(C) = 0.70 and P(D') = 1 - P(D) = 0.67. Then, because P(D'| C') = P(D') (as having a dog does not depend on whether or not you have a cat), the formula simplifies to: P(C' | D') = P(C'). So the probability that a household does not have a cat, given that it doesn't have a dog is 0.70 or 70%.
Learn more about Conditional Probability here:https://brainly.com/question/32171649
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minimize the objective function P=20x+16y
Answers
A mathematical expression that compares one number to another is called a ____.
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A mathematical expression that compares one number to another is called a ratio or proportion, which includes concepts such as inequalities and proportional relationships.
A mathematical expression that compares one number to another is called a ratio or proportion. Ratios express the relationship between two quantities, while a proportion indicates that two ratios are equivalent. For example, the expression 1/2 = 3/6 signifies a proportion because the two ratios 1/2 and 3/6 are equivalent. A unit rate is a specific kind of ratio where one of the measurements is 1, such as 55 miles per hour (55/1 miles/hour). Additionally, there are other mathematical expressions used for comparison, such as inequalities, which show how two values differ, or the concept that one value 'x' is proportional to another, often used in scientific and engineering contexts.
A combination lock requires three numbers from 1 to 25. how many combinations are possible? did you use the sum rule or the product rule? (note that although we use the term combination with locks, order matters.)
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The point is that numbers can be reused. 1 5 1 is a valid combination as is 4 4 4
20 * 5 * 1 is a valid combination as is 1 25 5
So the answer is 15625 "combinations" are possible <<<<< answer
On the trip you and your friends stop for gas and decide to drinks 1.05, and snacks, which are 2.20, if they spend a maximum of 25$ and wish to buy at least 12 items , write a system of inequalities that show the range of drinks and snacks you can buy with 25.00, 2 inequalities are needed, and a data table for each
Answers
x + y ≤ 12
Furthermore, the total amount spent would be equal to the sum of the products of the number of the cost of each as represented in the inequality below.
1.05x + 2.2y ≤ 25
how to multiply fractions
Answers
Question: How to multiply fractions?
Answer: well, in order to multiply fractions, you need to simply the particular fraction with the lowest terms (if they have any of course), then we multiply our numerators from each other so we can get a brand new numerator. (you do the same thing with denominators.
Example:
[tex] \frac{6}{8} ( \frac{6}{7} ) \\ \\ \frac{6(6)}{8(7)} \\ \\ 6(6) =36 \\ \\ 8(7) = 56 \\ \\ \\ Answer: \frac{36}{54}[/tex]
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
Hello There!
To multiply fractions, you first want to line up the numerator and the denominator together so they line up with each other.
Next, you want to multiply across. This includes multiplying the numerators together and then multiplying the denominators together.
Finally, you want to find the greatest common factor but only if the fraction can be simplified.
That Is How To Multiply Fractions
$1,000 is invested at a rate of 3.25%, compounded annually. Identify the compound interest function that models the situation. Then find the balance after 8 years.
Answers
A=P(1+r)^n
P=principle
r=rate
n=time
But:
P=$1000, r=3.25%, n=time
thus the function representing this will be:
A=1000(1+3.25/100)^n
A=1000(1.0325)^n
Thus the amount after 8 years will be:
A=1000(1.0325)^8
A=1,291.58
ANSWER: 1,291.58
please help with this word problem
Answers
(corner to top)² = (113 m)² +(188 m)²
(corner to top)² = 48,113 m²
Then, taking the square root, we find ...
(corner to top) = √(48,113 m²)
(corner to top) ≈ 219 m
The distance from the corner of the base to the top of the pyramid was about ...
219 m
If i = −1 and a and b are non-zero real numbers, what is 1a+bi ?
Answers
1a + b(-1)
a - b is your answer <<<< answer
A coin is flipped three times. James is declared the winner if there are at least two tails. Peter is declared the winner if there is a head flipped.
a. How many different outcomes are there?
b. What is the probability that James wins?
c. What is the probability that Peter wins?
d. Is the game fair?
e. Are there any outcomes where the game would be tied?
f. Are there any outcomes where no one would win?
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QF Q3c.) Find the following function
Answers
f(-3) = 4(-3) -3 = -15
(f◦g)(0) = f(g(0)) = -15
what is the maximum for
f(x)= 625-16x^2
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If the racetrack publishes that the odds in favor of a horse winning a race are 5 to 9, what is probability that the horse will not win the race?
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Josiah has a piece of wood that measures 10 1 / 8 feet he wants to make 5 shelves if each shelf is 1 3/4 fuel long does he have enough to make 5 shelves explain
Answers
To find the amount of feet to make 5 shelves, we must multiply the amount to make one shelf by 5
1.75 * 5 = 8.75
(1.75 is the decimal form for one shelf)
Because 8.75 is less than 10, he has enough to make 5 shelves
I saved $100 to spend over the summer. I decide to budget $20.00 to spend each week, how can I write an equation that represents this situation
Answers
x is the number of weeks
100 is the amount you have
20 is your budget
the price of a video game was reduced from $60 to $45.by what percentage was the price of video Gamers reduced
Answers
Equation wise:
60x = 45
Divide both sides by 60:
x = 45 / 60
0.75
But, we need to find the percent reduced,
so it will be:
1 - 0.75
0.25
25%
Hope this helps!
Use the quadratic function to predict y if x equals 7. Y=2x^2 -3x +3
Answers
f(7)=2(7)^2-3(7)+3
f(7)=2(49)-3(7)+3
f(7)=98-21+3
f(7)=80
Hence we conclude that when x=7, y=80
stuffed animals each weigh 1/4 pound are on a scale. the scale shows 1 1/2 pounds how many stuffend animals are on the scale
Answers
0.25 and 1.5
To figure this out, we divide:
1.5/0.25
6
There are 6 stuffed animals on the scale.
Answer: The answer is: 6
Step-by-step explanation: I have my ways ;>
Have a nice day!
-Sunny
What is the 95% confidence interval for the mean life expectancy in the entire population of siberian tigers? (use the t-test to answer the question)?
Answers
Randy buys a pair of shoes that were originally priced at $147. He receives a 35% discount and pays 8.5% sales tax. How much does Randy pay? (Work shown)
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Then multiply
147 * 0.67 = 98.49
Now for a sales tax you would want to multiply by 108.5% (or 1.085) as you are paying the previous price and them some
98.49 * 1.085 = 106.86165
You can round to the second decimal place since you can't have a monetary value less than a penny
your answer would be $106.86
Answer: $103.67
Step-by-step explanation:
Based on the given conditions, formulate: 147 x (8.5% + 1) x (1 - 35%)
Calculate the sum or difference: 147 x 1.085 x (1 - 0.35)
Calculate the sum or difference: 147 x 1.085 x 0.65
Calculate the product or quotient: 159.495 x 0.65
Calculate the product or quotient: 103.67175
Round: 103.67
Answer: $103.67
Marcus is selling lemonade in peanuts each cup of lemonade cost $0.75 in each bag of peanuts cost $0.35 on Saturday market so 5 more cups of lemonade then bags of peanuts here in $7.05 how many cups of lemonade did Marcus sell on Saturday
Answers
0.75L + 0.35(L -5) = 7.05
1.10L -1.75 = 7.05 . . . . . . . . . . eliminate parentheses
1.10L = 8.80 . . . . . . . . . . . . . . .add 1.75
L = 8 . . . . . . . . . . . . . . . . . . . . .divide by 1.10
Marcus sold 8 cups of lemonade on Saturday.
Lesson 6.04 in this lesson you will: 1. write the introdcution paragraph for your argument using the same topic you chose and researched in lesson 6.02.
Answers
The introduction paragraph should start with an opening statement introducing your chosen topic and providing some context, followed by your thesis statement that clearly states your argument. The given example shows how to create an introduction paragraph for an argument on 'Climate Change'.
Explanation:In order to write the introduction paragraph for your argument, first remember your chosen topic from lesson 6.02. Your opening statement must introduce the topic and provide some general context about it. For instance, if your topic is 'Climate Change', then your introductory paragraph might start like this:
'In today's rapidly changing world, one issue that stands in prominence is climate change. During the last century, human activities have accelerated this process unnaturally, leading to unpredictable weather and extreme disasters.'
Then present your thesis statement that clearly expresses your stance on the issue. It could be something like:
'This essay aims to argue that proactive international cooperation is crucial in mitigating the detrimental effects of climate change.'
Make sure this paragraph is captivating and clear as it sets the tone for the rest of your essay.
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a dump truck weighs 11.25 tons. a conveyor belt pours sand into the truck at a constant rate of 1/4 ton per minute. the dump truck weighs 18 tons when filled. at the same time the dump truck is being filled, an identical truck filled to capacity is being emptied at a rate of 1/8 ton per minute. how much sand is in each dump truck when the trucks are the same weight?
Answers
W1B = Weight of the truck 1 before starting the filling.
W1A = Weight of the truck 1 when filled.
R1F = Rate of change (Truck 1 being filled)
W2B = Weight of the truck 2 before starting the filling.
W2A = Weight of the truck 2 when filled.
R2F = Rate of change (Truck 2 being filled)
Given that a conveyor belt pours sand into the truck and stops when filled, then the amount of sand, when the truck is filled to capacity, is:
[tex]S = W_{1B} - W_{1A} = 18-11.25 = 6.75Tons[/tex]
Let's analyze Truck 1:
Given that the rate of change is:
[tex] \frac{1}{4} ton/min[/tex]
This means that in 1min the amount of sound poured is 1/4Ton, then the time elapsed when filled using rule of three is:
[tex]t = \frac{6.75}{ \frac{1}{4} } = 27min[/tex]
A similar analysis happens with Truck 2:
Given that the rate of change is:
[tex] \frac{1}{8} ton/min[/tex]
Then:
[tex]t = \frac{6.75}{ \frac{1}{8}} = 54min[/tex]
Now we can find two straight lines:
Truck 1:
[tex]\left \{ {{t=0min} \atop {S=0Ton}} \right. [/tex]
[tex] \left \{ {{t=27min} \atop {S=6,75Ton} \right[/tex]
[tex]S-S_{0} = m(t-t_{0})[/tex]
[tex]S-0 = \frac{6.75-0}{27-0} (t-0)[/tex]
∴ [tex]S = 0.25t[/tex]
Truck 2:
[tex] \left \{ {{t=0min} \atop {S=6.75Ton}} \right[/tex]
[tex] \left \{ {{t=54min} \atop {S=0Ton}} \right[/tex]
[tex]S-S_{0} = m(t-t_{0})[/tex]
[tex]S-6.75 = \frac{6.75-0}{0-54} (t-0)[/tex]
∴ [tex]S = -0.125t+6.75[/tex]
The trucks are the same weight when they have the same amount of sand, so solving for t:
[tex]0.25t = -0.125t+6.75[/tex]
[tex]0.375t = 6.75[/tex]
[tex]t = 18min[/tex]
Finally, the amount of sand in each truck:
[tex]S = 0.25(18) = 4.5Ton [/tex]
To find out how much sand is in each dump truck when they are the same weight, we can set up an equation based on the given information. Let's assume that the amount of sand in the first truck is x tons. We can then find the value of t that makes the weight of both trucks the same and substitute it into the equation to find x.
Explanation:To find out how much sand is in each dump truck when they are the same weight, we can set up an equation based on the given information.
Let's assume that the amount of sand in the first truck is x tons. Since the conveyor belt pours sand into the truck at a constant rate of 1/4 ton per minute, the weight of the sand will increase by (1/4) * t tons, where t is the time in minutes.
Similarly, the second truck is being emptied at a rate of 1/8 ton per minute. So, the weight of sand in the second truck will decrease by (1/8) * t tons.
We know that the dump truck weighs 11.25 tons initially and 18 tons when filled. Therefore, we can set up the equation:
11.25 + (1/4) * t - (1/8) * t = 18 - x
Simplifying the equation:
(1/4) * t - (1/8) * t = 18 - 11.25 - x
(1/8) * t = 6.75 - x
t = 6.75 * 8 - 8x
Now, we need to find the value of t that makes the weight of both trucks the same. Let's substitute that value into the equation to find x.