The requried, inverse of a function is a function for which the values or the domain and the range are interchanged. Option C is correct.
What is an inverse function?The inverse of a function is a new function that results from interchanging the input (domain) and output (range) of the original function.
Here,
if f(x) is a function, its inverse function is denoted by f⁻¹(x), and it is defined such that f⁻¹(y) = x, where y = f(x) is the original function.
For example, if f(x) = 2x + 3, the inverse function f⁻¹(x) is found by interchanging x and y, and solving for y:
x = 2y + 3
2y = x - 3
y = (x - 3)/2
Therefore, f⁻¹(x) = (x - 3)/2, and it is the inverse of the original function f(x). Note that the domain and range of the inverse function are interchanged with respect to the original function.
Learn more about inverse functions here:
https://brainly.com/question/30350743
#SPJ1
A chef had to fill up ⅘ of a container with mashed potatoes. He ended up using 2 4/6 pounds of mashed potatoes. How many pounds would he use if he had to fill up the entire container?
question: A chef had to fill up ⅘ of a container with mashed potatoes. He ended up using 2 4/6 pounds of mashed potatoes. How many pounds would he use if he had to fill up the entire container?
Step-by-step explanation: I don't know, u figure it out lol
What is the algebraic expression of 2 ( x + 7 ) +10
Answer:
2(x+12)
Step-by-step explanation:
Internet
Which answer is equal to cot(x)?
The cotangent of an angle is obtained dividing the cosine of the angle by the sine of the angle, that is:
cot(x) = cos(x)/sin(x).
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The cotangent function is the inverse of the tangent function, that is:
cot(x) = 1/tan(x)
cot(x) = 1/(sin(x)/cos(x))
cot(x) = cos(x)/sin(x).
More can be learned about trigonometric ratios at brainly.com/question/24349828
#SPJ1
At a local preschool there is a ratio of 3 boys to every 4 girls if there are 245 total preschoolers enrolled then how many boys are there
Answer:
105
Step-by-step explanation:
B:G=3:4
Add 3 and 4 to get 7
then divide 245 by 7 to get 35.
after you will need to times 35 by the ratio of boys which is 3.
35 ×3 =105.
So your answers is 105 boys.
Answer: 105 preschoolers are boys
The first thing we must do is add up our total to get a starting fraction. 3+4 is 7. Which means 3/7 of our students are boy and 4/7 of our students are girls.
Next we must multiply our total students "245" into the number of boys and girls.
3/7 x 245 is 105. 4/7 x 245 is 140.
105+140 is 245, which means our numbers are correct.
And finally that leads us with our answer.
105 of the students are boys.
I hope this helped & Good Luck <3!!
A mechanic charger a flat rate of $30 per hour. You have already bought all the parts needed and only have $120 to fix your car. How many hours can the machine work on your car? Find the y-intercept and slope
Answer: 4 hours
Step-by-step explanation: y int = 120, slope = 30
Let Si and S2 be subsets of a vector space V. Prove that span(Si n S2) C span(S1) nspan(S2). Give an example in which span(S1nS2) and span(Si)nspan(S2) are equal and one in which they are unequal.
Let S₁ and S₂ be subsets of a vector space V. So, proves are shown as well.
What is vector space?A vector space, also known as a linear space, is a collection of vectors that have been put together and multiplied ("scaled") by integers known as scalars. Real numbers are frequently seen as being scalars. Scalar multiplication by rational numbers, complex numbers, etc., on the other hand, seldom occurs. The term "subspace" refers to a vector space that is enclosed within another vector space. Each subspace is a vector space in and of itself, but it also has a definition in relation to another (bigger) vector space. We'll soon find out that there are a lot of different subspaces from earlier parts that we already know about.
Let, S₁ and S₂ be subsets of vector space V
Now, S₁ ⊆ V, S₂ ⊆ V
(S₁ ∩ S₂) ⊆ V
Let, x ⊆ span (S₁ ∩ S₂)
x ∈ span (S₁) and x ∈ span (S₂)
x ∈ span (S₁ ∩ S₂)
∴ span (S₁ ∩ S₂) ⊆ span (S₁) ∩ span (S₂)
span (S₁ ∩ S₂) = span (S₁) ∩ span (S₂)
where either S₁ ⊆ S₂ or, S₂ ⊆ S₁
span (S₁ ∩ S₂) ≠ span (S₁) ∩ span (S₂)
where, (S₁ ⊆ S₂) = ∅ but span (S₁) ∩ span (S₂)
(S₁ ∩ S₂) = ∅ i.e. span (S₁ ∩ S₂)
but span (S₁) = R₁²
span (S₂) = R₁²
Thus, span (S₁) ∩ span (S₂) = R₁²
To know more about vector space refer to:
https://brainly.com/question/11383
#SPJ4
in a class of 24 students, 23 of them took an exam in class and 1 student took a make-up exam the following day. the professor graded the first batch of 23 exams and found an average score of 78 points with a standard deviation of 6.4 points. the student who took the make-up the following day scored 62 points on the exam
The average score for the class on the exam was 78 points with a standard deviation of 6.4 points. The student who took the make-up exam scored 79.25points.
1. Calculate the mean of the first 23 exams:
Mean = 78 points
2. Calculate the standard deviation of the first 23 exams:
Standard Deviation = 6.4 points
3. Calculate the mean of the entire class:
Mean = (78 x 23) + 62 = 1840 + 62 = 1902
Total = 24
Mean = 1902 / 24 = 79.25 points
The average exam score for the class of 24 students was 78 points with a standard deviation of 6.4 points. This means that most students in the class scored between 71.6 and 84.4 points on the exam. The student who took the make-up exam the following day scored 79.25points. This score is significantly lower than the average score of the class, suggesting that the student may have not done as well on the exam compared to the other students. It is also possible that the student faced additional challenges that the other students did not have to face, such as taking the exam on a different day. Regardless, the student's score was significantly lower than the average score of the class.
Learn more about average here
https://brainly.com/question/24057012
#SPJ4
Can you help me with this
Answer:
two plus two equals five
Step-by-step explanation:
arallel lines s and t are cut by a transversal r. Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed by lines r and s are 1, 2, 3, 4; formed by lines r and t are 5, 6, 7, 8. Which angles are alternate interior angles? Angle3 and Angle5 Angle1 and Angle7 Angle3 and Angle7 Angle4 and Angle5
The angles are alternate interior angles
<4 and <6
<3 and <5.
What are Parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
As, from the property of parallel line we have the following properties
Alternate Interior angleCorresponding AngleCo- interior angle.So, from the figure the pair angles shows alternate interior angle
<4 and <6
<3 and <5.
Learn more about Parallel line here:https://brainly.com/question/16701300
#SPJ1
K
Consider the numbers
Select all that apply.
Which are rational numbers?
A. 8
7
D. 0
G. √9
J.-√34
5
M. √3
8
4,√3, -2.57, 22, 19.2.-19, 125, 27.131331333-34. √2.-7.0,√/9.
B. 4
E.125
H. 7.131331333...
K. -2.57
N. 2
C.-19
OF. 22
1. 5
9
OL.
26
0. 19.2
The rational numbers in this problem are given by these following letters:
A, B, C, D, E, G, I, K, L, O.
What are rational and irrational numbers?Rational numbers are the whole numbers plus decimals that can be represented by fractions, involving both positive and negative numbers.
The set of irrational numbers is composed by numbers that cannot be represented by fractions, such as non-exact roots, which are non-terminating and non-repeating decimal numbers.
The irrational numbers are justified as follows:
7.1313313333... is a non-terminating decimal.The remaining are non-exact roots.More can be learned about rational numbers at brainly.com/question/12088221
#SPJ1
Andrew collects stamps. he collected a total of 150 stamps. is 84% of the stamps he collected were foreign, how many other stamps did he collect?
Answer:
24
Step-by-step explanation:
If 84% of the stamps he collected were foreign, that means he collected 150 * 0.84 = 126 foreign stamps.
So, he collected 150 - 126 = 24 stamps that were not foreign.
_______ is the error due to the particular sample selected being an imperfect representation of the population of interest. it may be defined as the variation between the true mean value for the sample and the true mean value of the population.
Random sampling error is the error due to the particular sample selected being an imperfect representation of the population of interest.
What is random sampling error?When an analyst selects a sample that is not a true representation of the entire population of data, they commit a statistical error known as a sampling error. The results of the sample therefore do not fairly represent the results of the entire population.
Sampling is a type of analysis where a small sample of observations are selected from a larger population. The selection process has the potential to result in both sampling errors and non-sampling errors.
According to the definition, random sampling error is the error that results from the particular sample being chosen not accurately representing the population of interest. It could be described as the difference between the true mean value for the sample and the true mean value of the population.
Learn more about error here:
https://brainly.com/question/5290588
#SPJ4
The length of a rectangular pool is 4 meters less than twice the width. if the pool's perimeter is 94 meters, what is the width?
Answer:
see below
Step-by-step explanation:
length = x
width = y
x = 2y -4
2*(x+y) =94
x+y = 47
so x = 47-y
so 47-y= 2y -4
so 3y = 51
y = 17
x=30
the number of marbles peter had to be the number of marbles ravi had was in the ratio 8:5. after giving 18 marbles to his friends, peter had the same number of marbles as ravi. how many marbles did ravi have?
Answer:
30
Step-by-step explanation:
before
p:r
=8:5
after
p:r
=5:5
3 units=18
1 unit=6
no. of marbles Ravi has=5 units=6×5=30
suppose that {~v1, ~v2, ~v3} is a linearly dependent set of vectors in rn and ~v4 is vector in rn. show that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.
True, that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.
What is a linearly independent set?
A collection of vectors is said to be linearly independent in vector space theory if no nontrivial linear combination of the vectors equals the zero vector. The vectors are considered to be linearly dependent if such a linear combination occurs.
(i.e., all coefficients = 0). A single element set {v} is linearly independent if and only if v ≠ 0.
Now,
As given that
x1v1 + x2v2 + x3v3 = 0 with x1, x2, x3 not all zero, then x1v1 + x2v2 + x3v3 + 0 v4 = 0 and still the coefficients are not ALL zero.
Hence,
It is True that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.
To know more about linearly independent set visit the link
https://brainly.com/question/29646890?referrer=searchResults
#SPJ4
Translate into a proportion: What number is 63% of 107? Let n= the number.
Answer:
look at the picture.......................
A tank originally holds 10 grams of salt, mixed into 100 gallons of water. Water containing 1.5 g of salt/gallon
is entering at the rate of 5 gallons/minute. I water is exiting the tank at the same rate, find the amount of salt Q in
the tank after time t.
The absolute value of the sum of two Integers does not exceed the sum of the absolute values of these integers. əziou? aydunu le O V x Vy( ]z +y] 5 [+/+ 1y1) (18) + (0) 5126+2EXE O (18) + |3| 5] +31 ANEXE 0 (IAI + 3 + x| -) AXA
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
This inequality, sometimes called as the triangle inequality.
To learn more about the inequality from the given link
https://brainly.com/question/25275758
#SPJ4
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
This inequality, sometimes called as the triangle inequality.
To learn more about the inequality from the given link
brainly.com/question/25275758
#SPJ4
Mensa is an organization that allows people to join only if their IQs are in the top 2% of the population. (You may need to use Table 8.1.)
(a)
What is the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa? (Remember that the mean is 100 and the standard deviation is 15. Round your answer to two decimal places.)
(b)
Mensa also allows members to qualify on the basis of certain standard tests. If you were to try to qualify on the basis of the quantitative reasoning part of the GRE exam, what score would you need on the exam? (Remember that the mean is 151.3 and the standard deviation is 8.7. Round your answer to the nearest whole number.)
(a) To be eligible for Mensa, an individual's IQ must be in the top 2% of the population. This means that the IQ score must be greater than or equal to the 97th percentile of the normal distribution. We can use the standard normal distribution table to find the 97th percentile.
Since the mean IQ score is 100 and the standard deviation is 15, we can standardize the IQ score to find the z-score:
z = (IQ - mean) / standard deviation
z = (IQ - 100) / 15
The 97th percentile corresponds to a z-score of 2.33. To find the IQ score, we can reverse the standardization formula:
IQ = z x standard deviation + mean
IQ = 2.33 x 15 + 100
IQ = 146.95
So, the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa is 147.
(b) To be eligible for Mensa on the basis of the quantitative reasoning part of the GRE exam, an individual's score must be in the top 2% of the population. This means that the score must be greater than or equal to the 97th percentile of the normal distribution. We can use the standard normal distribution table to find the 97th percentile.
Since the mean score on the quantitative reasoning part of the GRE is 151.3 and the standard deviation is 8.7, we can standardize the score to find the z-score:
z = (score - mean) / standard deviation
z = (score - 151.3) / 8.7
The 97th percentile corresponds to a z-score of 2.33. To find the score, we can reverse the standardization formula:
score = z x standard deviation + mean
score = 2.33 x 8.7 + 151.3
score = 162.291
So, the score required to be eligible for Mensa on the basis of the quantitative reasoning part of the GRE exam is approximately 162. Round to the nearest whole number, the score would be 162.
To know more about Normal distribution check:
https://brainly.com/question/29509087
#SPJ1
If 1 mile equals 1,760 yards, then how many miles are in 11,088 yards? 0.6 miles 1.8 miles 6.3 miles 110 miles
Answer:
6.3 miles
Step-by-step explanation:
We are given 11088 yards.
Use the conversion factor 1 mile equals 1,760 yards.
11088 yards * 1 mile/ 1,760 yards
11088 / 1760 miles
6.3 miles
Subsets
What is the symbol for subset?
Step-by-step explanation:
I honestly don't know how to put it sideways but the symbol for subset is "⊂" with a line right under it. (So like the quotation marks but have the line underneath the sideways U.
"⊂
_"
A shop tech earns a base pay of $18.48 per hour, plus "time-and-a-half for overtime (time exceeding 40 hours). If he works 44.5 hours during a particular week, what
is his gross pay?
The gross pay is $
Answer: Gross pay = $733.04
Step-by-step explanation:
The half-life of Carbon is 5730 years. If 10 grams of Carbon are present at time t = 0, how many will be present in 2,000 years?
The amount of Carbon that will be presented in 2,000 years is given as follows:
7.85 grams.
What is an exponential function?An exponential function is defined as follows:
y = a(b)^(x/n).
In which:
a is the initial amount.b is the rate of change.n is the time needed for the rate of change.Considering the initial amount of 10 grams and the half life of 5730 years, the parameters for this problem are given as follows:
a = 10, b = 0.5, n = 5730.
Hence the function is defined as follows:
y = 10(0.5)^(x/5730)
Then the amount after 2,000 years is given as follows:
y = 10(0.5)^(2000/5730)
y = 7.85 grams.
More can be learned about exponential functions at https://brainly.com/question/30113628
#SPJ1
If the hot-tub heater provides 5900 kJ/min, how long, in hours, will it take to heat the water in the hot tub from 65 °F to 104 °F?
Express your answer to two significant figures and include the appropriate units.
HÅ
Value
20
Provide Feedback
Units
Submit Request Answer
?
P Pearson
Copyright © 2023 Pearson Education Inc. All rights reserved. | Terms of Use | Privacy Policy | Permissions | Contact Us |
So, using a heater with a heating output of 5900 kJ/min, it will take roughly 9.05 hours to heat the water in the hot tub from 65°F to 104°F.
What kind of energy does heating use?When the temperature rises, atoms and molecules move faster and collide, creating thermal energy (also known as heat energy). Thermal energy is the energy that results from the heated substance's temperature.
How do you calculate kW for heating?Calculate the square footage or square metres of your room. The room's dimensions are then multiplied by its width, height, and length. Then double this amount by 6. For BTUs or 0.0606 for kW, respectively.
To know more about Heating visit:
https://brainly.com/question/1429452
#SPJ1
There are five boxes. The weight of the first box is 200 kg and the weight of the second box is 20% higher than the weight of the third box, whose weight is 25% higher than the first box's weight. The fourth box at 350 kg is 30% lighter than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.
The difference in the average weight of the four heaviest boxes and the four lightest boxes is 75 Kg.
Given:
The weight of boxes is :
1st box = 200 kg
2nd box = 300 kg
3rd box = 250 kg
4th box = 350 kg
5th box = 500 kg
Since , heavier weight = 500 Kg
lighter weight = 200 Kg
Average weight of four heaviest boxes =1400/4=350kg
Average weight of four lightest boxes =1100/4=275kg
∴ Difference =(350−200)/2=150/2=75kg
Hence , the difference in the average weight of the four heaviest boxes and the four lightest boxes is 75 Kg.
Learn more about Average at:
https://brainly.com/question/20118982
#SPJ1
Nolan buys a $12,000, 13-week treasury bill at 5%. What’s his effective rate? Round your answer to the nearest hundredth of a percent.
As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.
what is interest ?Divide the original by the lending rates, the duration of time, and other factors to arrive at simple interest. Simple gain = principal + interested + hours is the marketing formula. This system makes it simpler to calculate interest. The most popular technique to figure out this is as a portion of the principal sum. He can only pay his share of the 100% interest, for example, if he borrow $100 from a friend he agrees to repay him with 5% interest. $100 (0.05) = $5. When you borrow more money, you should pay interest, and when you give it out, you must make payments. Interest is often determined as an indicator of the overall of the loan total. The interest on the loan is this percentage.
given
Simple interest = $12,000 × 0.05 × 13/52 = $150
Simple discount note = ($12,000 - $150) × 13/52 = $2962.5
Effective rate of interest = $150 / $2962.5
Effective rate of interest = 0.0506 or 5.06%
As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.
To know more about interest visit:
https://brainly.com/question/28792777
#SPJ1
Adam invests $1,051 in a savings account with a fixed annual interest rate that is compounded continuously. After 8 years, the account balance reaches $1,698.49. What is the interest rate of the account?
The account has an annual interest rate of 6.80%, compounded continuously.
What is interst rate?Interest is the cost associated with the boring money or to return on for lending money it is typically expressed as a percent of the principal amount borrowed or lent and usually the paid periodically over the life of loan interest can also be on from investment such as saving account bonds and the other financial instrument.
The interest rate of the account can be calculated as follows:
Rate = ln(1,698.49/1,051)/(8×ln(1))
Rate = 0.0680 or 6.80%
This means that the account has an annual interest rate of 6.80%, compounded continuously.
To know more about intrest rate click-
https://brainly.com/question/16134508
#SPJ1
Business acumen is the ability to make decisions based on principles of business that will most likely
lead to positive outcomes.
Which course of action would be the least effective in helping you to develop business acumen?
A) Find an internship in your field.
B) Ask a professional in your field to mentor you.
C) Interview experienced people in your field.
D) Ask trusted friends their opinions of your field.
Business acumen, often referred to as business savviness, business sense, and business knowledge, is the keenness and rapidity with which one perceives and responds to a business issue in a way that is most likely to produce a favorable result.
What are the 4 disciplines of business acumen?The success of an organization depends heavily on the four pillars of business acumen: planning, operations, finance, and strategy. Business savvy individuals use their abilities and leadership to foster success in each field.Business acumen, often referred to as business savviness, business sense, and business knowledge, is the keenness and rapidity with which one perceives and responds to a business issue in a way that is most likely to produce a favorable result. Understanding business difficulties is a sign of someone with business acumen. It is the accumulation of information on how things are done and why, both generally and within the context of the organization. It is a crucial quality for leadership and manifests in both one's inquiries and their choices.A combination of knowledge, technical skills, and soft skills called "business acumen" is utilized to improve an organization and its workforce.To learn more about Business acumen refer to:
https://brainly.com/question/29517196
#SPJ1
A sugar solution was made by mixing 11qt. of a 70% sugar solution and 4 qt. of a 85% sugar solution. Find the concentration of the new mixture.
Answer:
Step-by-step explanation:
To find the concentration of the new mixture, we need to find the total amount of sugar in the mixture, and then divide it by the total volume of the mixture.
Let's first find the amount of sugar in each of the two original solutions:
70% solution: 11 qt. * 70% = 7.7 qt. of sugar
85% solution: 4 qt. * 85% = 3.4 qt. of sugar
Now we add the volume of the two original solutions to find the total volume of the new mixture:
Total volume: 11 qt. + 4 qt. = 15 qt.
And add the amount of sugar in the two original solutions to find the total amount of sugar in the new mixture:
Total sugar: 7.7 qt. + 3.4 qt. = 11.1 qt.
Finally, we divide the total amount of sugar by the total volume to find the concentration of the new mixture:
Concentration: 11.1 qt. / 15 qt. = 0.7407 (rounded to four decimal places).
So the new mixture is approximately 74.07% sugar.
What is an equation for the linear function whose graph contains the point (2, 5) with a slope of -5?
Answer:
y=-5x+15.
Step-by-step explanation:
1. if the given slope is (-5), then it is possible to make up the required equation in slope-interception form: y=-5x+interception, where 'interception' is unknown number;
2. in order to calculate the 'interception' it is enought to substitute the given coordinates of the point into the last equation (y=5; x=2):
5=-5*2+interception; ⇒ interception=15. Then
3. finally, the required equqaiton is y=-5x+15.