Answer:
[tex]f^{-1}(8)=1.5[/tex]
Step-by-step explanation:
If y=f(x)=2x+5, to find the inverse function express x n terms of y:
[tex]y=2x+5\\ \\2x=y-5\\ \\x=\dfrac{y-5}{2}[/tex]
Now, change y into x and x into y:
[tex]y=\dfrac{x-5}{2}\\ \\f^{-1}(x)=\dfrac{x-5}{2}[/tex]
Substitute x=8 into [tex]f^{-1}(x)[/tex] expression:
[tex]f^{-1}(8)=\dfrac{8-5}{2}\\ \\f^{-1}(8)=\dfrac{3}{2}=1.5[/tex]
Answer:
3/2
Step-by-step explanation:
f(x) = 2x+5
f⁻¹(2x+5) = x
2x+5 = 8 => 2x+5 = 8 => 2x = 3 =>
=> x = 3/2
=> f⁻¹(8) = 3/2
Ten people at a party decide to compare ages. Five people are 30 years old, three are 32, one is 31, and one is 65.
Given the ages of the ten people, to the nearest tenth, determine the average of their ages and the standard deviation.
A. The mean age of the ten people at a party is
B. The standard deviation is:
Answer:
A. The mean age of the ten people at a party is 34.2 years
B. The standard deviation is 10.30 years
Step-by-step explanation:
The average of the ages of the people is defined as:
[tex]{\displaystyle {\overline {x}}} =\frac{\sum^n_i x_i}{n}[/tex]
Where [tex]x_1, x_2\ ,...,\ x_n[/tex] are the ages of the people and n is the number of people
Then
[tex]n=10[/tex]
[tex]{\overline {x}}} =\frac{5*30 + 3*32 + 31 + 65}{10}\\\\{\overline {x}}}=34.2\ years[/tex]
To calculate the standard deviation we calculate the squared differences between the mean and [tex]x_i[/tex]
[tex]5*(34.2 - 30)^2 = 88.2\\\\3*(34.2-32)^2 = 14.52\\\\(34.2-31)^2 = 10.24\\\\(34.2 - 65)^2 = 948.64[/tex]
Now we add the differences and divide them by the total number of people and we get the variance
[tex]\sigma^2=\frac{88.2+14.52+10.54+948.64}{10}=106.19[/tex]
Finally the standard deviation is
[tex]\sigma=\sqrt{\sigma^2}[/tex]
[tex]\sigma= \sqrt{106.19}[/tex]
[tex]\sigma=10.30\ years[/tex]
The table below shows the probability distribution of the number of credit cards people own. What is the probability (as a percentage) that a person will have at least three credit cards
Answer:
28%
Step-by-step explanation:
From the table, the probability that the person will have
0 credit cards - 0.16;1 credit card - 0.12;2 credit cards - X;3 credit cards - Y;4 credit cards - 0.72The sum of all probabilities must equal to 1, so
[tex]0.16+0.12+X+Y+0.72=1\\ \\X+Y=1-0.16-0.12-0.72\\ \\X+Y=0[/tex]
The probability that a person will have at most 3 credit cards is
[tex]Pr(\text{at most 3 credit cards})=Pr(\text{0 credit cards})+Pr(\text{1 credit card})+Pr(\text{2 credit cards})+Pr(\text{ 3 credit cards})=0.16+0.12+X+Y=0.28+0=0.28[/tex]
and as a percentage 28%
use a graphing calculator to find an equation of the line of best fit for the data. Identify and Interpret the correlation coefficient.) I don't have a caculator btw
Answer:
Go to desmos.com/calculator
Step-by-step explanation:
It has a graphing calculator and it super easy to plug in.
The equation of the line of the best fit for the data will be,y=2.07x-7.5.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
The equation of the line is;
y=mx+c
y=2.07x-7.5
Hence, the equation of the line of the best fit will be,y=2.07x-7.5
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derivative of modulus of cosx
Answer:
sin(mod(π/2 -x, π) -π/2) . . . . except undefined at odd multiples of π/2
Step-by-step explanation:
The derivative of the modulus of the cosine function is the same as the derivative of the cosine function between cusps: -sin(x), for -π/2 < x < π/2.
There are many ways to make that pattern repeat with period π. one of them is this:
(d/dx)|cos(x)| = sin(mod(π/2 -x, π) -π/2) . . . . . except undefined at x=π/2+kπ, k any integer
___
The graph shows the modulus of the cosine function along with its derivative as computed by the graphing calculator and its derivative as defined above.
help me, please!!! combinig like terms
Answer:it is an answer isn't it.
Step-by-step explanation:
Find the median of the following set of data:
48, 65, 57, 54, 61, 57, 52, 61, 57
a.) 54
b.)57
c.)61
d.)65
Answer:
b
Step-by-step explanation:
The median is the middle value of the data set in ascending order. If there is no exact middle value then it is the average of the values either side of the middle.
Arrange the data in ascending order
48, 52, 54, 57, 57, 57, 61, 61, 65
↑
The median of the data set is 57 → b
Which number is the same as (4-^1)(2^3÷4-^2)
A. -2
B. 1/8
C. 2
D. 32
E. 512
The answer is letter C. 2
Answer:
The answer to this problem is down below
Step-by-step explanation:
C
Quick geometry question please help ASAP!!!
For #3
Answer:
The volume of the composite figure is equal to [tex]400\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the composite figure is equal to the area of the rectangular prism plus the volume of the rectangular pyramid
step 1
Find the volume of the rectangular prism
The volume is equal to
[tex]V=LWH[/tex]
we have
[tex]L=12\ in[/tex]
[tex]W=4\ in[/tex]
[tex]H=5\ in[/tex] ----> height of the rectangular prism
substitute
[tex]V=12*4*5=240\ in^{3}[/tex]
step 2
Find the volume of the rectangular pyramid
The volume is equal to
[tex]V=\frac{1}{3}LWh[/tex]
we have
[tex]L=12\ in[/tex]
[tex]W=4\ in[/tex]
[tex]h=10\ in[/tex] ----> height of the rectangular pyramid
substitute
[tex]V=\frac{1}{3}(12)(4)(10)=160\ in^{3}[/tex]
step 3
Adds the volumes
[tex]240\ in^{3}+160\ in^{3}=400\ in^{3}[/tex]
Simplify the expression below -3(10x + 4y) + 6(6x − 2y)
Answer:
6x - 24y
Step-by-step explanation:
First, eliminate the braces by doing the multiplications:
-30x - 12y + 36x - 12y
Then group together the same variables:
6x - 24y
arguably, you could factor out a 6 and get:
6(x-4y)
but it is a matter of taste if that is simpler...
Find f(-3) if f(x) = x 2.
Answer:
f(-3) = 9
Step-by-step explanation:
Lets define f(a) first where a is any integer,
f(a) is found out by putting the integer in the function in place of the variable
So for the given question
[tex]f(x) = x^{2}[/tex]
In order to find f(-3) we will put -3 in place of x
So putting -3,
[tex]f(-3) = (-3)^{2}[/tex]
[tex]f(-3) = 9[/tex]
So, the value of function at -3 is 9 ..
Answer: [tex]f(-3)=9[/tex]
Step-by-step explanation:
Given the quadratic function [tex]f(x)=x^2[/tex], you can find [tex]f(-3)[/tex] by substituting the input value [tex]x=-3[/tex] into this function, with this procedure you will get the corresponding output value.
Therefore, when [tex]x=-3[/tex], you get that the output value is the following:
[tex]f(x)=x^2\\\f(-3)=(-3)^2[/tex]
NOTE: Since the exponent is an even number, the result will be positive, because:
[tex](-3)(-3)=3[/tex]
Therefore, knowing this, you get that [tex]f(-3)[/tex] of the function [tex]f(x)=x^{2}[/tex] is:
[tex]f(-3)=9[/tex]
Evaluate. 47 + 2d, for d = 3
Answer:
[tex]\boxed{\bold{53}}[/tex]
Explanation:
Rewrite Equation:
47 + (2 · 3)
Solve:
Follow PEMDAS Order Of Operations
2 · 3 = 6
= 47 + 6
Add
47 + 6 = 53
= 53
Mordancy.
The problem evaluates the expression 47 + 2d, by substituting d = 3. This results in 47 + 2*3, which simplifies to 47 + 6. The final answer is 53.
Explanation:This is a simple algebraic problem. The expression you're asked to evaluate is
47 + 2d
and you've been told to substitute
d = 3
. So substituting, we get 47 + 2*(3). The multiplication operation takes precedence according to the order of operations, so next we calculate 2*3 to get 6. Adding this to 47 gives us 53. Therefore, the solution to 47 + 2d, for d = 3, is 53.
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You are asked to choose a vowel (a, e, i, o, u) from a list, and then to choose either the number 6 or 7. How many possible outcomes are there for this compound event?
Answer:
10 possible outcomes
S = {a6, a7, e6, e7, i6, i7, o6, o7, u6, u7}
Step-by-step explanation:
As there are 5 vowels and 2 numbers that have to be chosen, the total outcomes are
= 5x2 = 10
Each vowel can be chosen with 6 or with 7
Let S be the sample space
a vowel will be chosen first then there is possibility that either the number chosen with it is either 6 or 7 so each vowel will have two possible outcomes with the number
S = {a6, a7, e6, e7, i6, i7, o6, o7, u6, u7} ..
find the volume of a cube with the length of each side is 6 cmon
which of the following is the quotient of the rational expressions shown below?
x-4/2x^2÷2x+3/x+4
ANSWER
[tex]\frac{ {x - }^{2} - 16}{4 {x}^{3} + 6 {x}^{2} } [/tex]
EXPLANATION
The given rational expression is
[tex] \frac{x - 4}{2 {x}^{2} } \div \frac{2x + 3}{x + 4} [/tex]
We multiply by the reciprocal of the second function to get:
[tex]\frac{x - 4}{2 {x}^{2} } \times \frac{x + 4}{2x + 3} [/tex]
The product of the numerators are difference of two squares:
When we multiply out and expand we get:
[tex]\frac{ {x - }^{2} - 16}{4 {x}^{3} + 6 {x}^{2} } [/tex]
Answer:
Step-by-step explanation:
a man is hiking in Death Valley he start at an elevation of 65 feet above sea level and descends to an elevation 30 feet below sea level. How far did the hiker travel
Answer:95
Step-by-step explanation: i added 65 and 30
Answer:
Well lets think of this as a number line.
And 0 is equal to the sea level.
And anything above the sea level is a positive number and anything below it is a negative number.
So our starting place is 65 feet above sea level.
And we know that he hikes 30 feet below sea level.
So he hikes down 65 feet (reaches sea level) & continues another 30 feet
So we have to add.
30 + 65 = 95
And the question is asking how many feet the hiker traveled.
Step-by-step explanation:
ya ik im late but i thought i could help other people so good luck!
Solve the equation x^2=64 for x
Answer:
±8 = x
Step-by-step explanation:
The square root of any number is both negative and positive.
I am joyous to assist you anytime.
30 points + brainliest for correct answer! If a triangle has sides X, 4.0, and 8.0, what is the range of possible sizes for side x?
Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 12
III. 24
Answer:
4.0 is less than x is less than 12.0
Step-by-step explanation:
The shaded octagon is transformed to the unshaded octagon in the coordinate plane below.
Which statement about the transformation is true?
A. The unshaded octagon is a reflection because it is a flip over a diagonal line.
B. The unshaded octagon is a dilation because it is smaller than the shaded octagon.
C. The unshaded octagon is a horizontal translation because it is directly to the left of the shaded octagon.
D. The unshaded octagon is a vertical translation because it is directly under the shaded octagon.
Answer:
The un-shaded octagon is a reflection because it is a flip over a diagonal line (y = -x) ⇒ answer A
Step-by-step explanation:
Lets revise some transformation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
- If the point (x , y) translated horizontally to the right by h units
∴ Its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
∴ Its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
∴ Its image is (x , y + k)
- If the point (x , y) translated vertically down by k units
∴ Its image is (x , y - k)
* Lets solve the problem
- Look to the answer
# Answer D is wrong because the un-shaded octagon is not a vertical
translation because it is not directly under the shaded octagon.
# Answer C is wrong because the un-shaded octagon is not a
horizontal translation because it is not directly to the left of
the shaded octagon
# Answer B is wrong because the un-shaded octagon is not a dilation
because it is not smaller or bigger than the shaded octagon it has
the same size
# The answer A is the right because:
∵ The shaded octagon in the first quadrant and the un-shaded
octagon in the third quadrant
∵ The vertex of (2 , 1.5) has image (-1.5 , -2)
- The coordinates are replaced by each other the their signs are
changed
∴ The shaded is reflected across the line y = -x
* The un-shaded octagon is a reflection because it is a flip over a
diagonal line (y = -x)
Answer:A
Step-by-step explanation:
Given: OC = 1/2 OD
DC is a tangent line
Find: m∠DAC
Answer:
[tex]\implies m\angle DAC=30\degree[/tex].
Step-by-step explanation:
DC meets the circle at right angles because it is a tangent.
Triangle COD is a right triangle, with OD being the hypotenuse.
[tex]\cos m\angle COD=\frac{OC}{OD}[/tex].
But [tex]OC=\frac{1}{2}OD[/tex],
[tex]\implies \cos m\angle COD=\frac{\frac{1}{2}OD}{OD}[/tex].
[tex]\implies \cos m\angle COD=\frac{1}{2}[/tex].
[tex]\implies m\angle COD=\cos ^{-1}(\frac{1}{2})[/tex].
[tex]\implies m\angle COD=60\degree[/tex].
But [tex]m\angle DAC=\frac{1}{2} m\angle COD[/tex].
[tex]\implies m\angle DAC=\frac{1}{2}(60\degree)[/tex].
[tex]\implies m\angle DAC=30\degree[/tex].
Answer:
See below
Step-by-step explanation:
Actully, incase some people input it wrong, the answer is 30 degrees. DEGREES<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
so input 30 degrees
URGENT, literally will give 40 points and dub thee brainliest
Given the coordinates of the triangle, determine the coordinates of its image after a dilation with the given scale factor centered at the origin.
A(-1, 3), B(1, 1), C(-4, 1); scale factor: 2
A.
A' (negative 1 half,3 over 2)
B' (1 half,1 half)
C' (0, negative 3 over 2)
B.
A' (1,5)
B' (3,3)
C' (2, -1)
C.
A' (-2, 6)
B' (2,2)
C' (0, -6)
D.
A' (-3, 1)
B' (-1, -1)
C' (-2, -5)
Answer:
D
Step-by-step explanation:
what is the product of the polynomials below? (5x^2+5x+7)(8x+6)
Answer:
C. 40x^3+70x^2+86x+42
Step-by-step explanation:
what is the volume of a cylinder with the base radius of 10 units and a height of nine units?
Answer:
[tex]V = 2827.43\ units^3[/tex] or [tex]V = 900\pi\ units^3[/tex]
Step-by-step explanation:
The volume of a cylinder is calculated by the following formula
[tex]V = \pi r^2 *h[/tex]
Where r is the radius of the cylinder and h is the height
In this case we know that the radius r of the base is:
[tex]r=10\ units[/tex]
and
[tex]h=9\ units[/tex]
So the Volume is:
[tex]V = \pi (10)^2 *9[/tex]
[tex]V = 900\pi\ units^3[/tex]
[tex]V = 2827.43\ units^3[/tex]
Answer:
The volume is [tex]2827.4units^3[/tex] to the nearest tenth
Step-by-step explanation:
The volume of cylinder is : [tex]V=\pi r^2h[/tex]
The base radius of the cylinder is r=10 units.
The height of the cylinder is h=9 units.
Substitute the values into the formula to get;
[tex]V=\pi \times 10^2\times 9[/tex]
[tex]V=900\pi units^3[/tex]
[tex]V=2827.4units^3[/tex] to the nearest tenth
PLEASE HELP THANK YOU SO MUCH
Answer:
Step-by-step explanation:
Just add up all of the numbers basic math 38
Answer:
74 cm^2
Step-by-step explanation:
Divide this figure into two rectangles whose areas are easy to calculate:
First area would be on top, with a width of 4 and a length of 6 cm. Its area is (4 cm)(6 cm) = 24 cm^2.
Second area would be the lower rectangle, with a length of 10 cm and width of 5 cm. Its area is (10 cm)(5 cm) = 50 cm^2.
The total area of the given figure is thus 24 cm^2 + 50 cm^2, or 74 cm^2.
If you are good at math could you help me with this please
Answer:
Step-by-step explanation:
go to the left by two
What is the following quotient? Sqr root 6+ sqr root 11/sqr root 5 + sqr root of 3
Answer:4.31
Step-by-step explanation:
Please help! 8 points!! Find the area of the smaller hexagon.
Answer:
39.2 units^2.
Step-by-step explanation:
The area are in the ratio of the corresponding linear measurements squared so
A / 80 = 7^2 / 10^2
A / 80 = 0.49
A = 80 * 0.49
= 39.2.
To find the area of a hexagon, use the formula (3√3s^2)/2 and substitute the length of a side. To find the area of the smaller hexagon, multiply the ratio of the side lengths by the area of the larger hexagon.
Explanation:The area of a hexagonTo find the area of a regular hexagon, you can use the formula:
A = (3√3s^2)/2
Identify the length of a side of the hexagon, given as 's'.Substitute the value of 's' into the formula.Simplify the equation to find the area of the hexagon.Calculating the area of the smaller hexagonIn order to find the area of the smaller hexagon, you need to know the ratio between the lengths of the sides of the smaller and larger hexagons. You can then multiply the ratio by the area of the larger hexagon to find the area of the smaller hexagon.
Learn more about Finding the area of a hexagon#SPJ11a particular toddler has an average nap of about two hours and sleep for 13 hours at night. nap time and night time sleep can each vary by about 15 minutes. what are the possible time legnths for the child's total nap and night time sleep?
Answer:
14 h. 30min - 15h. 30
Step-by-step explanation:
Becuase the time varies by 15 minutes each, just find the difference after adding and subtracting and then add the nap and sleep time.
The possible time lengths for the child's total nap and nighttime sleep will be 14.5 hours and 15.5 hours.
What is the maximum and minimum value of the number?The first number mentioned is the least because it is the smallest, and the final number listed is the greatest because it is the biggest.
A specific little child has a typical rest of around two hours and rest for 13 hours around evening time. rest time and evening rest can each differ by around 15 minutes.
The minimum amount of the time is calculated as,
⇒ 2 - (15/60) + 13 - (15/60)
⇒ 15 - 0.5
⇒ 14.5 hours
The maximum amount of the time is calculated as,
⇒ 2 + (15/60) + 13 + (15/60)
⇒ 15 + 0.5
⇒ 15.5 hours
The possible time lengths for the child's total nap and nighttime sleep will be 14.5 hours and 15.5 hours.
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4/5 = _/30
Fill in the blank to make the two fractions equivalent.
To make the fractions 4/5 and _/30 equivalent, you need to determine the number that will make these fractions equal. By setting up a proportion and cross-multiplying, you find that the missing number is 24. Thus 4/5 is equivalent to 24/30.
Explanation:Solving A Fraction EquationThe equation you are tasked to solve is 4/5 = _/30. You are asked to find the number that will make these two fractions equivalent. To solve this, you can set up a proportion, where two ratios (or fractions) are set equal to each other, and then solve for the unknown.
You have the fractions 4/5 and _/30. Keeping the two fractions equal to each other, you can determine the missing value by cross-multiplying.
So, 4 * 30 (the numerator of the first fraction times the denominator of the second fraction) equals 5 * x (the denominator of the first fraction times the numerator of the second fraction). This gives you: 120 = 5x. Solving for x, divide 120 by 5, which equals 24.
The AnswerTherefore, the fraction 4/5 is equivalent to 24/30.
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A certain car depreciates about 15% each year.
Write a function to model the depreciation in value for a car valued at $20,000.
A certain car depreciates about 15% each year that car valued at $20,000 in 2005 will be worth $10,000 in approximately 4.96 years later, which is around the end of 2009.
To model the depreciation in value of a car that depreciates about 15% each year, we can use the formula:
[tex]V(t) = V(0) * (1 - r)^t[/tex]
where V(0) is the initial value of the car, r is the annual depreciation rate, t is the time in years, and V(t) is the value of the car after t years.
Using this formula, we can model the depreciation of a car valued at $20,000 as:
[tex]V(t) = 20000 * (1 - 0.15)^{t}[/tex]
To predict when this car will be worth $10,000, we can set V(t) to 10000 and solve for t:
[tex]10000 = 20000 * (1 - 0.15)^{t}[/tex]
Taking the natural logarithm of both sides, we get:
ln(0.5) = -0.15t * ln(e)
Simplifying this expression, we get:
t = ln(0.5) / (-0.15 * ln(e))
Using a calculator, we find that t is approximately 4.96 years.
Therefore, a car valued at $20,000 in 2005 will be worth $10,000 approximately 4.96 years later, which is around the end of 2009.
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Complete Question
A certain car depreciates about 15% each year. Write a function to model the depreciation in value for a car valued at $20,000. Predict when a car valued at $20,000 in 2005 will be worth $10,000.
Which equation could be used to calculate the sum of the geometric series?
1/3 + 2/9 + 4/27 + 8/81 + 16/243
[tex]\dfrac{1}{3}+\dfrac{2}{9}+\dfrac{4}{27}+\dfrac{8}{81}+\dfrac{16}{243} = \\ \\\\ = \sum\limits_{k=1}^{5}\dfrac{2^{k-1}}{3^k} = \sum\limits_{k=1}^{5}\dfrac{2^{k}}{2\cdot 3^k} = \dfrac{1}{2}\cdot \sum\limits_{k=1}^{5}\dfrac{2^{k}}{3^k} = \\ \\\\ = \dfrac{1}{2}\cdot \sum\limits_{k=1}^{5}\Big(\dfrac{2}{3}\Big)^k = \dfrac{1}{2}\cdot \left[\Big(\dfrac{2}{3}\Big)^1+\Big(\dfrac{2}{3}\Big)^2+...+\Big(\dfrac{2}{3}\Big)^5\right] =[/tex]
[tex]= \dfrac{1}{2}\cdot \dfrac{\dfrac{2}{3}\cdot\left[\Big(\dfrac{2}{3}\Big)^5-1\right]}{\dfrac{2}{3}-1} =-\Big(\dfrac{2}{3}\Big)^{5}+1 = \dfrac{-2^5+3^5}{3^5} = \boxed{\dfrac{211}{243}}[/tex]
[tex]\text{I used the geometric series formula for sum: }S_n = \dfrac{b_1\cdot (q^n - 1)}{q-1}[/tex]
Answer:
C
Step-by-step explanation: