By using the concept of function, it can be calculated that
[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here, the function is
[tex]f(x) = 2x + \frac{4}{3}\\[/tex]
Let f(x) = y
[tex]2x + \frac{4}{3} = y\\\frac{6x + 4}{3} = y\\[/tex]
6x + 4 = 3y
6x = 3y - 4
[tex]x = \frac{3y - 4}{6}[/tex]
[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]
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Essay for operation of sets
What is Set Theory Formula?
The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
In a set theory, there are three major types of operations performed on sets, such as: Union of sets (∪) Intersection of sets (∩) Difference of sets (–)
Set Operations include Set Union, Set Intersection, Set Difference, Complement of Set, and Cartesian Product of Set
Set Union
The union of sets A and B (denoted by A ∪ B) is the set of elements that are in A, in B, or in both A and B. Hence, A ∪ B = { x | x ∈ A OR x ∈ B }.
n(A∪B) = n(A) + n(B) − n(A∩B)
Set Intersection
The intersection of sets A and B (denoted by A ∩ B) is the set of elements which are in both A and B. Hence, A ∩ B = { x | x ∈ A AND x ∈ B }.
n(A∩B) = n(A)+n(B)−n(A∪B)
Set Difference
The set difference of sets A and B (denoted by A - B) is the set of elements that are only in A but not in B. Hence, A - B = { x | x ∈ A AND x ∉ B }.
Complement of a Set
The complement of a set A (denoted by A’) is the set of elements which are not in set A. Hence, A' = { x | x ∉ A }. More specifically, A'= (U - A) where U is a universal set that contains all objects.
The complement of a universal set is an empty set U′ = ϕ. The complement of an empty set is a universal set ϕ′ = U.
Cartesian Product / Cross Product
The Cartesian product of n number of sets A1, A2, ... An denoted as
A1 × A2 ... × An can be defined as all possible ordered pairs
De-Morgan's Law - The De Morgan's law states that for any two sets A and B, we have (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'
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Two customers went to a sports shop to buy baseball gloves. Each baseball costs the same amount, and each glove costs the same amount.
The first customer paid $60.00 for 4 baseballs and 2 gloves.
The second customer paid $84.00 for 5 baseballs and 3 gloves.
What was the cost, in dollars, of each baseball?
Question 7 options:
$8.50
$6.00
$5.25
$12.00
Hurry!!
The cost, in dollars, of each baseball is B. $6.00.
How to calculate the cost?The first customer paid $60.00 for 4 baseballs and 2 gloves. This will be expressed as:
4b + 2g = 60
The second customer paid $84.00 for 5 baseballs and 3 gloves. This will be:
5b + 3g = 84
Collect both expressions
4b + 2g = 60
5b + 3g = 84
Multiply equation i by 3
Multiply equation ii by 2
12b + 6g = 180
10b + 6g = 168
Subtract
2b = 12
Divide
b = 12/2
b = 6
The baseball is $6.
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help me 10 pnts thanks so much
The expression 3.2^2 - 1 and 10 - 0.33 * 2 should be joined by less than to form an inequality
What is inequality?Inequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.
The signs used in inequality are of 4 types namely
less thangreater thanless than or equal togreater than or equal toThe given expression is solved as follows
3.2^2 - 1
= 10.24 - 1
= 9.24
10 - 0.33 * 2
= 10 - 0.66
= 9.34
The two expressions can be joined as below
9.24 < 9.34
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Emi is a veterinarian. In a given week, 50% of the 16 dogs she saw were boxers. Antonio is also a veterinarian. In the same week, 7 of the 35 dogs he saw this week were Boxers. Each wants to record the part, the whole, and the percent.
Emi will need to locate the whole in this case because she already has the part and the percentage.
What is a whole?In mathematics, the total number of items being analyzed, in this case, the total number of dogs, is represented by a whole.
The term "part" refers to a quantity that is typically smaller than the total and describes particular qualities. For instance, 20 of the 30 students in a classroom enjoy playing basketball. The part is 20 then.
The relationship between the part and the whole is represented by the percentage, which is a number followed by the symbol%. In this instance, the proportion of boxers and overall dogs are related.
Emi already knows the percentage (50%), the part (16), and the total number of dogs, which in this case is 32, as a result of this.
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Which equation represents this statement?
3 times the sum of 4 and a number is 18.
O 3 +4n = 18
O 3n+ 4 = 18
O 3.4+ n = 18
O 3 (n+4)= 18
The equation represents the statement "3 times the sum of 4 and a number is 18 " is option (D) 3(n+4) = 18
The statement is
3 times the sum of 4 and a number is 18
The equation is the the mathematical statement the represents the relationship between two expression or variables with an equal sign.
Consider the unknown number = n
Sum of 4 and the number = n + 4
3 times the sum of 4 and the number = 3(n + 4)
3 times the sum of 4 and a number is 18
3(n + 4) = 18
Hence, the equation represents the statement "3 times the sum of 4 and a number is 18 " is option (D) 3(n+4) = 18
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You might need: Calculator
Solve for a.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
4x +49x+8
3. One batch of pancakes needs 1 1/4 cups of pancake mix. One box has 9 cups of pancake mix How many batches of pancakes can be made with one box of pancake mix?
A bag of fertilizer covers 3000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 170 feet. To cover the lawn bags of fertilizer are required
Answer: The correct answer is 17 bags of fertilizer to cover the lawn
Step-by-step explanation:
1 bag of fertilizer covers 3000 SF of lawn
How many bags are needed for an area of 290 feet x 170 feet
Calculate the Square Feet:
290 x 170 = 49,300 SF
Divide space (SF) by bag coverage (SF):
49,300 / 3,000 = 16.43 bags of fertilizer
Round up answer to 17 bags of fertilizer
please help 25points, please show how you did it
Answer:
Angle 1: 27
2: 153
3: 58
4: 138
Step-by-step explanation:
1. 180-(116+37)=27
2. 180-27=153
3. 180-(48+74)=58
4. 122+16=138
180-138=42
180-42=138
can you graph x+y greater than or equal to 500
A graph of the given inequality (x + y ≥ 500) is shown in the image attached below.
What is a graph?In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical axes of a cartesian coordinate, which are the x-coordinate and y-coordinate.
Next, we would translate the word sentence into an inequality as follows:
x + y greater than or equal to 500 ⇒ x + y ≥ 500
Subtracting x from both sides of the inequality, we have the following equation:
x + y - x ≥ 500 - x
y ≥ 500 - x
Rearranging the equation in slope-intercept form, we have:
y ≥ -x + 500
In conclusion, we can reasonably and logically deduce that both the x-intercept and y-intercept of this linear inequality (equation) is equal to 500.
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The population of a small town, P, as a function of time, t, in years past 1940 is given below.
P = 2,511 + 500t
For which of the following years was the population of the town 11,511?
A. 1928
B. 1958
C. 1968
D. 1918
The year for which the population of the small town is 11,511 is; Choice B; 1958.
Function evaluationIt follows from the task content that the year for which the population of the small town in discuss becomes 11,511 be determined.
Given the function: P = 2,511 + 500t
11,511 = 2511 + 500t
9,000 = 500t
t = 9,000 / 500
t = 18 years.
Hence, the year in which case the population of the small town is; 11,511 is; 1940 + 18 = 1958.
Therefore, the year in which the population of the small town in discuss becomes 11,511 as required in the task content is Choice B; 1958 is correct.
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Which equation is equivalent to the given equation
x = x² - 20
A) x^2 - x-20=0
B) x^2 +x -20 =0
C) x^2-x+20=0
D) x^2+x+20=0
Amanda has 5 office assistants. If A is the event that at least 4 of them are men and B is the event that at least 4 of them are women, are A and B mutually exclusive?
Choose the correct answer below.
O No
Yes
A and B are mutually exclusive events
The correct answer is yes
What are mutually exclusive events?
Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously. A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.
We are given that Amanda has 5 office assistants.
Events A is the event that at least 4 of them are men. this means that there is at most 1 female assistant
Events B is the event that at least 4 of them are women. this means that there is at most 1 male assistant.
Now one of the conditions is possible but both at the same time is not possible
Hence the both events are mutually exclusive.
The correct answer is yes
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what is the momentum of an automobile with a mass of 1200 kilograms moving at 6 meters per second
The momentum of the automobile is 7200 kgm/s
What is momentum?
Momentum can be described as the product of the velocity and mass of an object.
It is a vector quantity which is defined as a quantity having both magnitude and direction.
The formula for calculating momentum is expressed as;
p = mv
Where;
p is the momentum of the objectm is the mass of the objectv is the velocity of the objectNow, let's substitute the values
p = 1200(6)
expand the bracket
p = 1200 × 6
Multiply the values
p = 7200 kgm/s
Hence, the value is 7200 kgm/s
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what is:
s . s + 0.5s . s
if s=8.2
Answer:
100.86
Step-by-step explanation:
8.2*8.2+0.5(8.2)*8.2
find the smallest value of an expression
(without using a calculator)
[tex]\bf\sqrt{(x-8)^2+(y+4)^2} +|y+3x|[/tex]
Step-by-step explanation:
to eliminate the always positive absolute value at the end let's set y = -3x
that makes the absolute value term = 0 in all cases.
then we have
sqrt((x - 8)² + (-3x + 4)²)
the x-value that makes this a minimum result also makes
(x - 8)² + (-3x + 4)²
a minimum.
x² - 16x + 64 + 9x² - 24x + 16
10x² - 40x + 80
the x that makes this a minimum, also makes
x² - 4x + 8
a minimum.
we get the extreme value as zero of the first derivative :
0 = 2x - 4
4 = 2x
x = 2
so, we get the minimum of all these expressions for x = 2.
as y = -3x, we get y = -3×2 = -6.
the minimum value for the expression is with
x = 2
y = -6
so, the minimum value is
sqrt((2 - 8)² + (-6 + 4)²) + |-6 + 3×2| =
= sqrt((-6)² + (-2)²) + |-6 + 6| =
= sqrt(36 + 4) + 0 =
= sqrt(40) = 6.32455532...
Pam has worked for the same employer for 5 years. Her current salary is $73,500
which is 122.5% of her starting salary. What was Pam's starting salary?
What was Pam's starting salary?
Pam's current salary for 5 years = $73.500
Her salary went up for 122.5% in 5 years.
a = her starting salary
First, we will make an equation of this problem.
Let's use a as the symbol of her starting salary
equation that we are going to use
73500 = 122.5% x a
Next, we move a to the left and we want to divide 73500 with 122.5%
a = 73500 / (122.5/100)
Next, we want to divide 73500 with 1.225 since we've done dividing 122.5 with 100
a = 73500 / 1.225
a = 60000
Finally, we got the answer of Pam's starting salary was $60.000
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Sixth grade > P.9 Add and subtract rational numbers GDR Add.
[tex] \frac{ - 3 \10{ + }{ - 9 \times \ \frac{910}{?} {?}{?} ?} {?} [/tex]
-
[tex] \frac{ - 3}{10 } + - 9 \times \frac{9}{10} =[/tex]
The result of the expression (-3/10) + -9 × 9/10 is -42/5
The expression is
(-3/10) + -9 × 9/10
The expression is the mathematical statement that consist of different variables, numbers and the mathematical operators.
The expression is
(-3/10) + -9 × 9/10
Here we have to do the suitable arithmetic operations
First do the multiplication in the given expression
= (-3/10) + (-9×9)/10
= (-3/10) + -81/10
Add the terms in the expression
Here the denominator of the both term is equal so we just need to add the numerators
= (-3 + -81) / 10
= (-3 - 81) / 10
= -84 / 10
Divide both numerator and denominator by 2
= -42/5
Hence, the result of the expression (-3/10) + -9 × 9/10 = -42/5
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Find the value of the expression:
3x^0 for x=2.6
Answer:
1
Step-by-step explanation:
We don't even need to calculate 3 x 2.6 considering any number raised to the power of zero equals 1.
Hank rents 9 cases of plates.He has 250 guests attending the banquet. There are 30 plates in each case. Did Hank rent enough plates? Explain
Answer:
yup
Step-by-step explanation:
so to find the amount of plates he has we :
30*9 = 270
How many guests :
250
Hank has 20 extra plates,
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The scale on a map states that 1 centimeter corresponds to 15 kilometers Find how far apart two cities are if their corresponding points on the map are 13 centimeters apart
In this case, they are both centimetres, so they remain constant. The true size, 15km, is then multiplied by 13/ 1. Then, 20 × 13 = 195. As a result, the answer is 195 kilometres.
What is scale?The term scale refers to the relationship that exists between a measurement on a model and the corresponding measurement on the actual object. A scale of 1:5 means that the size of one unit in the drawing represents five units in reality. A scale of 1:5 is used, for example, if a giraffe with a real-world height of 150 inches is represented as 30 inches on the drawing. A ratio, such as 1:100, is used to represent a scale.A drawing at a scale of 1:100 indicates that the object is 100 times smaller than it would be in real life. You could also say that one unit in the drawing equals one hundred units in real life.Therefore,
The map has a scale = 1 cm
Corresponds to = 15 kilometers
Map centimeters apart = 13 cm
Then you simply multiply the true size
= 15km, by 13/ 1.
Then, 20 x 13 = 195.
Hence, the answer is 195 kilometers.
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Find the average for the set of numbers 7, 6, 12, 5, 7, 6, 13. Average:
Answer:
Add up all the numbers and divide the product of that by the numbers there are.
7+6+12+5+7+6+13 = 56
There are 7 numbers in these set of numbers hence we divide the product (56) by 7.
56/7 = 8
The answer is 8; The average of all these numbers is 8.
Step-by-step explanation:
Tina has 5345 beads . She has 3687 fewer beads than her sister . How many beads does her sister have ?
Answer:
Her sister has 9032 beads
Step-by-step explanation:
All you have to do is Tina's beads plus the extra number of beads that her sister has
5345 + 3687 = 9032
Solve the following 2(x + 3) = x - 4
Answer:
x = - 10
Step-by-step explanation:
2(x + 3) = x - 4
==> distribute the 2
2x + 6 = x - 4
==> subtract 6 from both sides
2x = x - 10
==> subtract x from both sides
x = - 10
Fill in the blank, rounding the result to exactly three significant digits when necessary
81 m = ___ ft
10. Reduce the fraction 36/48 to its lowest terms.
O A. 114
O B. %
O C. 112/48
O D.34
Answer:
if D is 3/4 then it is the answer
Step-by-step explanation:
Because both 36 and 48 can be divided by 12 and 36/12 = 3 and 48/12=4 so the answer is 3/4
Solve: √x-4= -2
a) x=2
b) x=8
c) There is no solution.
d) x=0
The solution of the square root equation is x = 8
What is a square root?A square root is a number such that when multiplied by itself, it gives another number.
The square root of a number x is given by √x
How to solve the square root equation?Given the square root equation above, we have that
√(x - 4) = - 2
To solve this equation, first, we remove the square root by squaring both sides of the equation. So, we have that
√(x - 4) = - 2
√(x - 4)² = (- 2)²
x - 4 = 4
Adding the number 4 to both sides of the equation, we have that
x - 4 + 4 = 4 + 4
x + 0 = 8
x = 8
So, the solution of the equation is x = 8
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Differentiate the function with respect to x.
When we differentiate the given function with respect to x we get
(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
what is Differentiation?
Differentiate is used for calculating rates of change.
How to Differentiate function?
Some of the formulas are; Power Rule: (d/dx) (xn ) = nxn⁻¹. Derivative of a constant, a: (d/dx) (a) = 0.
Here, we have
y = 2x⁵ + 2x⁴ / 5x² -3
when we differentiate a given function with respect to x, we get
dy/dx = {(5x² -3)(10x⁴ + 8x³)} - {(2x⁵ + 2x⁴)(10x -3)}/(5x -3)²
dy/dx = (30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
Hence, after differentiating the given function with respect to x, we get
(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
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A Finnish registration consists of 3 letters and 3 numbers with empty spaces possible.
Numbers do not have leading zeroes and the number part cannot be only zero (for example AAA-001 isn't a valid plate but AAA-1 is). The registration plate must have at least one letter and one number. How many possible Finnish registration plates are possible to exist when the letters used are the 26 letters of the latin alphabet?
Answer:
How many possible plates there could be if we also allowed the letters Å, Ä and Ö?
Answer:
Using the Fundamental Counting Theorem, the number of plates for each case is obtained as follows:
Latin Alphabet: 17,558,424.Extra Letters: 24,364,611.What is the Fundamental Counting Theorem?The Fundamental Counting Theorem is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
With the Latin letters, it is found that for the letters, there are 26 outcomes, hence:
[tex]n_1 = n_2 = n_3 = 3[/tex]
With one number, the number of outcomes for the digit is:
[tex]n_4 = 9[/tex]
(as the digit cannot be zero).
With two numbers, the number of outcomes for the digit are:
[tex]n_4 = 9, n_5 = 10[/tex]
With three numbers, the parameters are:
[tex]n_4 = 9, n_5 = 10, n_6 = 10[/tex]
Hence the total number of plates is obtained as follows:
T = 26³ x (9 + 9 x 10 + 9 x 10 x 10) = 17,558,424.
With the extra letters, each letter can assume 29 outcomes, hence the number of plates is:
T = 29³ x (9 + 9 x 10 + 9 x 10 x 10) = 24,364,611.
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Amount Desired at End of Period
$17,600.00
Length of Time
7
1. Period Used
2. Rate Used
23. PV factor used
3 4. PV of amount desired at end of period
Rate
2%
Compounded
Quarterly
Required:
Complete the following using the information above and the present value Table 12.3
or the present value table in the Business Math Handbook or the present value
formula to answer the following:
Note: Use cells A2 to D3 from the given information to complete this question.
A percentage is a number or ratio expressed as a fraction of . It is often denoted using the percent sign, "%" and PV factor used is 0.62026 .
Hence,
The amount desired at end of a period is $9400.
The length of time is 4 years .
The rate is 2%.
Compounded is monthly.
The period used is 48.
The rate used is 1%.
The PV factor used is 0.62026 .
The PV of the amount desired at the end of the period is $5830.45
What is the percentage?
A percentage is a number or ratio expressed as a fraction of . It is often denoted using the percent sign, "%".
Here from the question,
PV factor = (1 + i) ----(1)
where, i = 12/12 % , i =1
and
n = 4(12)
n = 48
Substituting the values in the equation , we get
PV factor = (1 + 0.01)^ -48
PV factor = 0.62026
Hence,
the amount desired at end of a period is $9400.
The length of time is 4 years.
The rate is %.
Compounded is monthly.
The period used is 48 .
The rate used is 1%.
The PV factor used is 0.62026.
The PV of the amount desired at the end of the period is $5830.45
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