The inverse of y = 3x is f⁻¹(x) = 1/3x.
The inverse is a function or an operation which reverses the order of operation of another function or an operation”.
There are a few steps to find the inverse of a number:
Write the number as the denominator of a fraction that has 1 as a numerator to find the reciprocal of an integer.Place a decimal number as the denominator of a fraction with 1 as the numerator, then divide to calculate the reciprocal of a decimal.Reverse the placement of the numerator and denominator for the reciprocal of a fraction.We will be using the concept of inverse function to solve this.
Given that, y=3x
Let f(x) =y=3x
Switch x and y
x=3y
Express y in terms of x.
y = 1/3x
From the definition of the inverse function. f(x)=y⇒x=f⁻¹(y)
⇒ f⁻¹(y)=1/3x
Thus, the inverse of y = 3x is f⁻¹(x)=1/3x.
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In a certain tate about 3/5 of regitred voter particated in 2016 election what fraction of regitred voter did not
The fraction of registered voter that did not participate was 2/5
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
To solve this exercise we have to perform a mathematical operation with fractions:
Information about the problem:
Total = 1Registered voter participated= 3/5No. did not participate = ?Calculating the fraction of the registered voter that did not vote we get:
No. did not participate = Total - Registered voter participated
No. did not participate = 1 - 3/5
No. did not participate = (5 - 3) /5
No. did not participate = 2/5
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Is the inverse of a function always a function example?.
Every function has an inverse, but not every inverse will be a function.
A function takes a starting value, performs some operation on this value, and creates an output answer.
The inverse function takes the output answer, performs some operation on it, and arrives back at the original function's starting value.
An inverse relation is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.
A function is a one-to-one function if and only if each second element corresponds to one and only one first element.
Example:
consider the inverse of the function an f(x)=2x-4.
y=2x-4
x=y-4
x+4=y
f⁻¹(y)=x+4
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Select the correct answer
Nia wants to check whether the finance charge applied in her credit card statement is correct. To do this, she needs to calculate the average daily
balance in her account for the previous billing cycle. She made a table to do the calculation. The billing cycle is 31 days
What was Nia's average daily balance in this billing cycle?
Balance
Days
7
10
$745. 00
$585. 15
$245 20
$90. 75
A. $13,420. 00
B. $13,418. 00
c. $800. 00
D. $432. 84
E. $430. 48
The Nia's average daily balance in this billing cycle was equals to the $432.85. So, correct choice is option(D).
Nia wants to check whether the finance charge applied in her credit card statement is correct or not. For this she made a table to do this calculation. The billing cycle is 31 days is present in above figure. We have to calculate the Nia's average daily balance in billing. Average daily balance of Nid is represented by:
Average mean = (Days x Balance)/Total Number of days
So, Days × balance = (745.0 x 7) + (1555. 15 × 10) + (245.20 × 7) + (90.75 × 7)
= 5215 + 5851.5 +1716.4 + 635.25
= $13418.15
Total number of days = 7+ 10 + 7 + 7 = 31 days
Hence, the Average = 13418.15/31
= $432.84
Hence, required average daily balance is $432.84.
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Which equation is true?
A.
3
4
=
9
16
B.
6
8
=
4
3
C.
3
5
=
8
10
D.
12
16
=
36
48
Answer: a and c
Step-by-step explanation:
Jayden invests $2,644.93 in a retirement account with an interest rate of 8% compounded annually. What will the account balance be after 5 years?
The balance in the account of Jayden after 5 years will be $3,886.27.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Jayden invests $2,644.93 in a retirement account with an interest rate of 8% compounded annually. Then the amount after 5 years is calculated as,
A = $2,644.93 x (1 + 0.08)⁵
A = $2,644.93 x (1.08)⁵
A = $2,644.93 x 1.469
A = $3,886.27
The balance in the account of Jayden after 5 years will be $3,886.27.
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What’s 900+900
Just doing this cause it’s fun
FV of $600 each 6 month for 4 year at a nominal rate of 8%, compounded emiannually. Do not round intermediate calculation. Round your anwer to the nearet cent
The future value of the $600 invested semi-annually at 8% nominal interest rate for 4 years is $1369.44 rounded to the nearest cent.
The formula to use in this case is FV = PV(1 + r/n)^nt, where FV is the future value, PV is the present value, r is the nominal interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Given the information in the problem, we know that:
PV = $600 (the present value)
r = 0.08 (the nominal interest rate as a decimal)
n = 2 (the interest is compounded semi-annually)
t = 4 (the number of years)
Plugging these values into the formula, we get:
FV = $600(1 + 0.08/2)^(2*4)
To solve for FV, we need to calculate (1 + 0.08/2)^(2*4)
= (1.04)^8
=2.2824
FV = $600*2.2824
FV = $1369.44
Thus, the future value of the $600 invested semi-annually at 8% nominal interest rate for 4 years is $1369.44 rounded to the nearest cent.
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PV = $600 (the present value)
r = 0.08 (the nominal interest rate as a decimal)
n = 2 (the interest is compounded semi-annually)
t = 4 (the number of years)
Plugging these values into the formula, we get:
FV = $600(1 + 0.08/2)^(2*4)
To solve for FV, we need to calculate (1 + 0.08/2)^(2*4)
= (1.04)^8
=2.2824
FV = $600*2.2824
FV = $1369.44
Subtract 33 1/3% of 36 from 50% of 88.
Add explanation.
The value of the expression is 32.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
50% of 88 - 33(1/3)% of 36
This can be written as,
= 50/100 x 88 - (100/3)/100 x 36
= 44 - 12
= 32
Thus,
The value is 32.
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A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six months, the subjects' symptoms are studied and compared. Answer parts (a) through (c) below.
After six months, the subjects' symptoms are studied and compared. Answer parts are given below.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
A pharmaceutical company wants to test the effectiveness of a new allergy drug.
The company identifies 250 females 30–35 years old who suffer from severe allergies.
The subjects are randomly assigned into two groups.
One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.
After six months, the subjects' symptoms are studied and compared.
Here, 30-35 year-old girls are used to test the new allergy medication's effects.
(a)
Females between the ages of 30 and 35 who are the test subjects are the experimental units.
The new allergy medication, whose results are being studied, is the remedy.
It's best to choose C.
(b)
A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.
In this case, choice B is preferable.
(c)
If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.
In this case, choice A is preferable.
Therefore, all the correct choices are given above.
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The complete question is given in the image.
There are 16 ounces in one pound.
A box of nails weighs 4 pounds. Using
the variable w. Write and solve a
division equation to find how many
ounces the box weighs.
According to the equation, the weight of box in ounces is 64.
Firstly let us represent the weight of box with w. Now, the formula to be used for calculation of the weight of box is -
The weight of box in ounces = weight of box in pounds × number of ounces in one pound/one
Keeping the values in formula to find the value of weight of box in ounces.
The weight of box in ounces = 4 × 16/1
Performing multiplication and division on Right Hand Side of the equation to find the weight of box in ounces
The weight of box in ounces = 64 ounces
Thus, the weight of box in ounces is 64.
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a pet store gives away 3 dog treats with every food bowl sold. write an expression to represent this situation please help asap tysm
Can some please help I need to get this answer?
The hypotenuse square in a right-angled triangle is equal to the sum of the squares of the two shorter sides, according to the Pythagorean theorem.
Pythagoras, a Greek philosopher who was born around 570 BC, is honored in the name of the theorem. Perhaps more than any other mathematical theorem, the theorem has been demonstrated numerous times using a variety of techniques. There are many different types of proofs, some of which go back thousands of years, including both geometric proofs and algebraic proofs.
The Pythagorean relation holds true when Euclidean space is represented by a Cartesian coordinate system in analytical geometry: the squared distance between two points equals the sum of squares of the difference in each coordinate between the points.
[tex]c=\sqrt{ a2+b2}= \sqrt{ 3.92+82}=8.9[/tex]
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How do i solve this?
Answer:
x = 45/2 or 22.5
Step-by-step explanation:
Since we are given CDE ~ KLM, we know that C is similar to K, D is similar to L, and E is similar to M. The problem asks to find DE, so by comparison, it is known that DE is similar to LM.
From the two triangles, KM is similar to CE, and we can see that the ratio between the two is 8:15. We are given LM, which is 12, so we can find x using this equation to compare the smaller triangle to the bigger one:
KM/CE = LM/DE
Plug in your given values:
8/15 = 12/x
Find x:
x = 45/2 or 22.5
The ratio of markers to crayons in an artist's collection is 4:3. Which of the following ratios is equivalent to 4:3?
Answer:
A
Step-by-step explanation:make brainiest
A plane rises from take-off and flies at an angle of 14 with the horizontal runway. When it has gained 950 feet, find the distance, to the nearest foot, the plane has flown.
The distance, to the nearest foot, the plane has flown is 3926.887 feet.
What are Angles?Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.
Angles are usually measured in degrees or radians
The horizontal runway, the distance plane flied and the height gained forms a right angled triangle.
Let x be the distance plane flied.
Height gained = 950 feet
Angle that plane makes with the horizontal runway = 14°
Sin 14 = Opposite side / Hypotenuse
Sin 14 = 950 / x
x = 950 / sin 14
x = 3926.887 feet
Hence the distance plane flied is 3926.887 feet.
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What is range and X range?.
The range of a set of numbers is the difference between the maximum and minimum values in the set. X range is a type of range chart used to identify patterns in data points over a period of time.
The Range of a dataset is determined by subtracting the smallest value from the largest value in that dataset, providing an indication of the total spread of the data points. Range is a useful metric for understanding the variability of data points and for comparing different datasets.
X Range is a type of range chart used to identify patterns in data points over a period of time. It is a graphical representation of the range of data points and can help to identify trends and seasonal patterns. X Range charts are particularly useful for understanding how data points fluctuate over time, and can be used to identify any outliers in the data that may require further investigation.
X Range charts can be used to identify any clusters of data points, and to compare different data sets. X Range charts are also useful for understanding the overall volatility of a dataset and for making predictions about future data points.
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Use 4 of the 5 numbers shown to make the equations true.
Each number can be used only once.
The answers to the two blank portions are, √64 = 8 and ∛1000 = 10.
What are surds and indices?We are aware that there are two different sorts of radicals. Surds are created when a number is raised to a power that makes it greater than zero but less than one. Indices are created when a number is raised to a power that makes it bigger than one.
We know 10×10 = 100.
10¹×10¹ = 100.
10² = 100.
√100 = 10.
Similarly ∛1000 = 10.
As ∛1000 = ∛(10×10×10) = ∛10³ = 10.
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a+b=b-a
what are some numbers to make this equation true?
Answer:
b =0nand a =0 simple beacaes3 0-0=0and 0+0=0
The ratio of peanuts to raisins is 2:8. What percent of the peanuts and the raisins are peanuts? I need this ASAP.
Answer:
20%
Step-by-step explanation:
2+8=10
10*10=100
2*10=2
Please can you give me brainliest?
What is the solution to y 6 =- 3y 26?.
The solution to y+6 =- 3y-26 is 8.
The solution to the equation y+6 =- 3y-26 is to solve for y. This can be done by rearranging the equation and combining like terms. The equation can be rearranged to -3y-y+6 = -26.
Combining the like terms yields -4y+6 = -26.
To solve for y, subtract 6 from both sides.
These yields -4y = -32.
Finally, divide both sides by -4 to obtain y = 8.
Therefore, the solution to the equation y+6 =- 3y-26 is y = 8.
Understanding the solution to an equation is a critical part of algebra and can be used to solve a variety of problems. There are many methods for solving equations, and it is important to understand each type and how to employ them appropriately. Solving equations like y+6 =- 3y-26 requires rearranging the equation and combining like terms to obtain the solution. Once the equation is in a simpler form, the solution can be found by applying basic math operations.
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What is the value of ƒ(g(3)) when ƒ(x) = x³ + 5x² − 2x − 1 and g(x) = x² –
- -
- 4?
The value of the function ƒ(g(3)) is 239, when ƒ(x) = x³ + 5x² − 2x − 1 and g(x) = x² – 4.
What is function?A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output.
Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.
We have given to find ƒ(g(3))
when ƒ(x) = x³ + 5x² − 2x − 1
and g(x) = x² – 4
When g(3) = (3)² – 4
= 9 - 4
= 5
For
ƒ(g(3)) = (5)³ + 5(5)² − 2(5) − 1
= 125 + 125 - 10 - 1
= 239
Thus, the value of the function ƒ(g(3)) is 239, when ƒ(x) = x³ + 5x² − 2x − 1 and g(x) = x² – 4.
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What are the 4 properties of multiplication examples?.
The 4 properties of multiplication are Associative Property, Commutative Property, Distributive Property, and Identity Property.
The properties of multiplication are particular rules that are used while multiplying numbers. These properties help simplify expressions easily and, hence, have a significant role in solving all kinds of mathematical expressions, whether algebraic expressions, fractions, or integers.
Associative Property: (P × Q) × R = P × (Q × R)
For example, (4 × 5) × 3 = 4 × (5 × 3) = 60.
Commutative Property: P × Q = Q × P
For example, 3 × 4 × 2 = 2 × 3 × 4 = 24.
Distributive Property: P(Q + R) = PQ + PR; P(Q - R) = PQ - PR
For example, 3(2 + 4) = (3 × 2) + (3 × 4) = 6 + 12 = 18.
Identity Property: P × 1 = P
For example, 4 × 1 = 4, or 1 × 27 = 27.
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How do you solve systems by elimination with multiplication?.
To solve the given system of equations using elimination method following steps need to follow:
Equate the coefficient in opposite sign by multiplying the equation by required number for the variable you want to eliminate.
As given in the question,
Steps required to solve the given system of equations by elimination method with multiplication:
To eliminate x-term equate the coefficient of x in opposite sign.
4x + 3y = 1 __(1)
3x + 4y = 1 __(2)
1. Multiply 3 to (1) and -4 to (2) to eliminate the x-term.
12x + 9y = 3 __(3)
-12x - 16y = -4 __(4)
2. Now add (4) from (3) and eliminate x-term.
12x + 9y = 3
-12x - 16y = -4
0x -7y = -1
⇒ y = 1 / 7.
Therefore, solution of the system of equation using elimination method with multiplication is:
Equate the coefficient in opposite sign by multiplying the equation by required number for the variable you want to eliminate.
The above question is incomplete , the complete question is :
How do you solve systems of equations by elimination method with multiplication?.
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1. You have always wanted to learn how to juggle, so you decide to buy a brand new chainsaw that retails for $153. If sales tax is 6%, what is the total price you pay?
2. You are a real estate agent, and you sell your client's house for $350,000, earning a 5% commission. How much did you earn?
3. You fail out of school and are forced to become a traveling hamster salesperson. You earn 4% commission on all sales, and after two grueling weeks you manage to sell $710 worth of product. How much do you make?
Answer:
1. The total price you pay is $162.18
2. You earn $17,500
3. You earn $28.40
Step-by-step explanation:
1. 153 times 6% or 153 times 0.06 = 9.18
153 + 9.18 = 162.18
2. 350,000 times 5% or 350,000 times 0.05 = 17500
3. 710 times 4% or 710 times 0.04 = 28.4
For what values of k is the quadratic equation 9x2?.
The possible values of k for the quadratic equation 9x² - 5kx + 1 = 0 has equal roots are 6/5 and -6/5.
The standard form of an quadratic equation is, ax² + bx + c = 0, a ≠ 0 and a,b,c --> constants. The quadratic formula for solution of above equation is, x = ( - b ±√b² - 4ac)/2a , where Discriminate, D is equals to b² - 4ac . We have an quadratic equation, 9x² - 5kx + 1 = 0 --(*)
Step 1 : Determining the discriminant of the quadratic equation : After comparing the equation (*) with standard one , a = 9 , b = - 5k and c = k . So, discriminate formula , D = b² - 4ac
=> D = (- 5k)² - 4×9×1
=> D = 25 k² - 36
Step 2: Determining the values of k : We have equation (*) has equal roots then according to the nature of the roots of an quadratic equation When the value of discriminant, D = 0, then the quadratic equation has real and equal roots.
So, 25 k²- 36 = 0
=> 25 k² = 36
=> k² = 36/25
=> k = ±√36/25
=> k = ± 6/5
Hence, the values of k are ± 6/5.
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Complete question:
For what values of k is the quadratic equation 9x² - 5kx + k = 0, has equal roots?
The average temperature during the winter in the Arctic tundra i -34C. You can convernt Celete C to degree farenhite F uing the formula F=9\5C 32
The average temperature during the winter in the Arctic tundra i -34C which is also 93.2 degrees Fahrenheit
The difference between the freezing point of water and its boiling point at normal atmospheric pressure is divided into exactly 100 equal parts to determine the temperature in degrees Celsius (degrees). Water has a freezing point set at 0° and a boiling point set at 100°.
Therefore, a 100°C difference is precisely equivalent to a 180°F difference. As a result, each degree in Celsius is equivalent to 1.8 degrees Fahrenheit.
The 34 Celsius to Fahrenheit formula is a linear function:
[°F] = ([34] x 9 ⁄ 5) + 32.
Therefore, we get:
34 C to F = 93.2 °F
34 °C in °F = 93.2 Fahrenheit
34 C in F = 93.2 degrees Fahrenheit
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A bracelet has two colors of beads. The ratio of green beads to blue beads is 2:7. There are 18 green beads. How many beads are there in total?
Answer:
81 Bead in total
Ratio: 18:63
Step-by-step explanation:
2*9 = 18
7*9 = 63
Use the Distributive Property to simplify the expression.
9(2n+1) =
PLs help me fast .
Which data set could be represented by the boxplot shown?
A. {6, 6, 8, 8, 9, 12, 13, 13, 14}
B. {6, 6, 7, 9, 9, 12, 13, 14, 16}
C. {6, 7, 8, 9, 10, 11, 12, 13, 14}
D. {6, 7, 9, 9, 9, 12, 13, 14, 14}
A data set which could be represented by the boxplot shown include the following: A. {6, 6, 8, 8, 9, 12, 13, 13, 14}.
What is a box-and-whisker plot?In Mathematics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided above, the five-number summary for the given data set include the following:
Minimum = 6First quartile = 7.Median = 9.Third quartile = 13.Maximum = 14.For the median, we have:
Median = 6, 6, 8, 8, 9, 12, 13, 13, 14
Median = 9.
In conclusion, we can logically deduce that the median of the given data set is equal to 9 while the first quartile is 7 and the third quartile is 13.
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What is 30% of 85  URGENT
Answer: 30 percent of 85 is 25.5
Answer:
the answer is 25.5
Step-by-step explanation:
this is because 85 in our question is equivalent to thus you just need to cross multiply
