Step-by-step explanation:
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=2x f - 1 ( x ) = 2 x is the inverse of f(x)=12x f ( x ) = 1 2 x .
Replace f(x)f(x) with yy.
y=12xy=12x
Interchange the variables.
x=12yx=12y
Solve for yy.
Rewrite the equation as 12y=x12y=x.
12y=x12y=x
Multiply both sides of the equation by 22.
2⋅12⋅y=2⋅x2⋅12⋅y=2⋅x
Simplify 2⋅12⋅y2⋅12⋅y.
Cancel the common factor of 22.
Cancel the common factor.
2⋅12⋅y=2⋅x2⋅12⋅y=2⋅x
Rewrite the expression.
1⋅y=2⋅x1⋅y=2⋅x
Multiply yy by 11.
y=2⋅xy=2⋅x
Solve for yy and replace with f−1(x)f-1(x).
Replace the yy with f−1(x)f-1(x) to show the final answer.
f−1(x)=2xf-1(x)=2x
Set up the composite result function.
g(f(x))
Fiona grows large pumpkins and wants to estimate the mean weight of the approximately 500 pumpkins in her
harvest. She takes a random sample of 11 of these pumpkins and finds they have a mean weight of 44 kg and a
standard deviation of 6.7 kg. The weights in the sample were roughly symmetric with no outliers.
Answer:
44+-3.169(6.7/root11)
Step-by-step explanation:
The 99% confidence interval for the mean weight in kg of pumpkins grown by Fiona in the harvest for the provided sample is,
[tex]44\pm 3.169\times\dfrac{6.7}{\sqrt{11}}[/tex]
What is mean and standard deviation?The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
Fiona grows large pumpkins and wants to estimate the mean weight of the approximately 500 pumpkins in her harvest.
She takes a random sample of 11 of these pumpkins. Here, the sample size is 11 which is less than 30. Thus, use the formula mentioned below.
[tex]\overline x\pm t\times\dfrac{\sigma}{\sqrt{n}}[/tex]
Here, (n) is the sample size, [tex]\overline x[/tex] is the mean of the sample.
Degree of freedom is,
[tex]DF=11-1=10[/tex]
For this, the value of t from the t table is 3.169 for 99% confidence interval.
The mean weight of 44 kg and a standard deviation of 6.7 kg they find. Put these values in the above formula,
[tex]\overline x\pm t\times\dfrac{\sigma}{\sqrt{n}}=44\pm 3.169\times\dfrac{6.7}{\sqrt{11}}[/tex]
Thus, the 99% confidence interval for the mean weight in kg of pumpkins in the harvest for the provided sample is,
[tex]44\pm 3.169\times\dfrac{6.7}{\sqrt{11}}[/tex]
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For the given table of values for a polynomial function, where must the zeros of the function lie?
A. between 2.0 and 2.5 and between 4.0 and 4.5
B. between 2.5 and 3.0 and between 4.0 and 4.5
C. between 2.0 and 2.5 and between 3.5 and 4.0
D. between 2.5 and 3.0 and between 3.5 and 4.0
Answer:
(B). between 2.5 and 3.0 and between 4.0 and 4.5.
Step-by-step explanation:
According to the Question,
If the value of the function is 0 at x=c, then c is a root or zero of the function. It means the graph of function intersects the x-axis at its zeroes.From the given table it is clear that the value of function are
x | f(x) | Sign
2.0 | 2.8 | Positive
2.5 | 1.1 | Positive
3.0 | –0.8 | Negative
3.5 | –1.2 | Negative
4.0 | –0.3 | Negative
4.5 | 0.7 | Positive
The sign of values of function changes in interval 2.5-3.0 and 4.0-4.5. It means the graph of function must intersect the x-axis in intervals 2.5-3.0 and 4.0-4.5. So, the zeros of the function lie between 2.5 and 3.0 and between 4.0 and 4.5.Therefore, the correct option is B.
pls help me this is due in 30 minnutes
Answer:
The surface area is 88ft.
Just to let you know just in case if you have the same question is that the formula of finding the surface area of a rectangular prism is A = 2(wl + hl + hw)
Question and choices are in the photo please explain the answer
Answer: The correct option is B.
Step-by-step explanation:
(x+5)(2x-1)=3(x+5)
Multiply the parentheses
2x^2 - x + 10x - 5 = 3x + 15
Collect like terms
2x^2 + 9x - 5 = 3x + 15
Move the expression to the left hand side and change its sign, then equate it to 0
2x^2 + 9x - 5 - 3x -15 = 0
Collect like terms
2x^2 + 6x - 20 = 0
Divide each term of the equation by 2
x^2 + 3x - 10 = 0
Rewrite the expression in factorized form
x^2 + 5x - 2x - 10 = 0
Factor the expression
x(x + 5) - 2(x + 5) = 0
(x + 5) (x - 2) = 0
Separate into possible cases but when the product of factors equals 0, at least one factor is 0.
x + 5 = 0———equation (1)
x - 2 = 0———-equation (2)
Solve the equations
x + 5 = 0———equation (1)
Make x the subject
x = 0 - 5
x = -5
x - 2 = 0———equation (2)
Make x the subject
x = 0 + 2
x = 2
Hence, the possible values of x are -5 and 2.
I need help solving these
roatate triangle p 90* clockwise about the point (2,-1)
Answer:
hope this helps
Step-by-step explanation:
Which of the following expressions can be used to calculate the area of a square with side lengths 5 inches?
- 5 + 4
- 5 x 4
- 5 x 5
- 5 + 5
Step-by-step explanation:
5x5
because 5^2 equals the area
DON'T UNDERSTAND SOMEONE CAN YOU HELP PLEASE
MY TEACHER IS ANNOYING ME TO DO THIS SUM
it is the linear equation
Jacob cuts 4 meters of a ribbon into 3 pieces, the length of the first piece is 1.28 meters.The length of the second one is 1.65 meters. Work out the length of the 3rd piece.
Answer:
1.07meters
Step-by-step explanation:
Given data
Lenght of ribbon= 4 meters
Number of pieces= 3 pieces
Length of first piece= 1.28meters
Length of second piece= 1.65meters
Let the length of the third piece be x meters
Hence
1.28+1.65+x= 4
2.93+x=4
x= 4-2.93
x=1.07meters
Hence, the length of the third piece is 1.07meters
please help me this is due in 30 minutes
Answer:
a
c
c
a
Step-by-step explanation:
Need help ASAP DUE SOON PLEASE AND SHOW WORK ?!!!
Answer: 804.25
Step by step explanation:
Write an equation of the line that passes through the points (2, -3) and (1,4).
please help! ten points! thank you
Maria thinks of a number double it and add 5 answer is 21 write as an equation in X and solve it to find Maria's number
Answer:
The number is 8
Step-by-step explanation:
2x +5 =21
2x= 21-5
2x=16
2x/2=16/2
x=8
To check
8×2=16
16+5=21
What is the x-intercept of the line shown below? Enter your answer as a coordinate pair.
Answer:
(1,0)
Step-by-step explanation:
Find the measure of the arc
Answer:
104, 52 degrees
Step-by-step explanation:
A whole circle is 360 degrees.
So ark YX = 360-110-146=104
Z=1/2*YX=52
Someone help with this please you have to classify and construct the triangles
Answer:
The first triangle would be D - Right.
Explanation :
Acute angles can't have a single angle greater or equal to [tex]90^o[/tex]
Equiangular triangles have every single angle equivalent.
Obtuse angles have only angles greater than [tex]90^o[/tex]
Right triangles have 1 right angle (90 degrees)
=============================================
The second triangle would be an obtuse triangle (A)
Here's an example of an obtuse angle :
(As you can see, it doesn't need to have all 3 sides obtuse, just one)
Graph inequality y< -3/2x -6
Answer:
Hope this helps...have a nice day/night!!Answer:
Step-by-step explanation:
You graph it
Helppp!!!and thanks.
Answer:
Step-by-step explanation:
12inches/foot , 12x132=1,584 inches
The selected accounts from the Blue Door Corporation's accounting records are presented below for the year ended December 31, 2015: Advertising expense $ 55,000 Interest revenue $ 30,000 Common stock 250,000 Inventory 67,000 Cost of goods sold 1,085,000 Rent revenue 24,000 Depreciation expense 125,000 Retained earnings 535,000 Dividends 150,000 Salaries and wages expense 675,000 Freight-out 25,000 Sales discounts 8,500 Income tax expense 70,000 Sales returns and allowances 41,000 Insurance expense 15,000 Sales revenue 2,400,000 Interest expense 70,000 Prepare a multiple-step income statement.
Solution :
Sales Revenue
Sales $ 2,400,000
Less:
Sales discount $ 8,500
Sales returns and allowances $ 41,000
$ 48,500
Net Sales $ 2,350,500
Cost of goods sold $ 1,085,000
Gross profit $ 1,265,500
Operating expense :
Salaries expenses $ 675,000
Advertising expenses $ 55,000
Depreciation expense $ 125,000
Freight expense $ 25000
Insurance expense $ 15,000
Total operating expenses $ 895,000
Operating income $ 370,500
Non operating income
Interest revenue $ 30,000
Rent revenue $ 24,000
$ 54,000
Non Operating expenses :
Interest expense $ 70,000
Income before income tax $ 354,500
Income tax expense $ 70,000
Net income $ 284,500
Ethan invests $3000 in a mutual fund that earns 6% interest per year compounded monthly. After 10 years, the investment is worth $5,458.19. How much interest did he earn?
Answer:
[tex]A = P(1 +\frac{r}{n} )^{nt}[/tex]
A = 3000(1 + .06/12)^120
strange the question did not want you to calculate the amount
that was given....
the interest is 5,458.19 - 3000 = 2,458.19
Step-by-step explanation:
8) what is the side ratio?. 9) what is the perimeter of RST?
Reflection: Across the line y = -1
The A’ is your reflected shape. The red line is y=-1, or your line right reflection. To solve, I counted the distance from the red line on the original triangle, and then the same on the opposite side of the red line, and counted the same distance, plotting the points at the final spot.
Find the measure of angle 1
Answer:
<1 is 45○
Step-by-step explanation:
180-90 = 90
90 / 2 = 45
Answer:
Each angle=60°
m∠1=180-(60+60)180- (120)=60°--------------------------hope it helps...have a great day!!Solve the rational equation by multiplying both sides by the LCD. Check your results for extraneous
solutions.
3
2 + 5x + 6
2-1
x + 2
7
x + 3
is a solution.
x=
0
is an extraneous solution.
RETRY
Intro
Answer:
x = 7 is a solution
x = -2 is an extraneous solution
^ CORRECT ANSWER
Step-by-step explanation:
The rational equation is solved and the solutions are 7 and the extraneous solution is x = -2
What is rational function equation?A rational equation can be defined as an equation that involves at least one rational expression
A rational function is a function of the form f( x )=P( x ) / Q( x ) ,
f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.
A rational function f ( x )=P( x ) / Q( x )
f( x ) = P( x ) / Q( x ) may have a vertical asymptote
The domain is the set of all real numbers for which Q( x ) ≠ 0
Given data ,
Let the rational equation be represented as A
Now , the value of A is
( 3 / ( x²+5x+6 ) ) + ( ( x-1) / (x+2) ) = 7 / (x+3) be equation (1)
On simplifying , we get
A rational function is a function of the form f( x )=P( x ) / Q( x ) ,
f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.
So , multiplying both sides by ( x²+5x+6 ) , we get
3 + x² + 2x - 3 = 7x + 14 be equation (2)
On further simplification , we get
x² - 5x - 14 = 0
On factorizing the equation , we get
x² - 7x + 2x - 14 = 0
Taking the common factors , we get
x ( x - 7 ) + 2 ( x - 7 ) = 0
( x + 2 ) ( x - 7 ) = 0
So , the two solutions of x are x = 7 and x = -2
Hence , the solutions of rational equation are x = 7 and x = -2
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The area of a circle is 3.14 square millimeters . What is the circle's radius ?
Answer:
Step-by-step explanation:Circle
Solve for radius
r≈1
A Area
3.14
d
r
r
r
d
d
C
A
Using the formula
A=
π
r
2
Solving forr
r=
A
π
=
3.14
π
≈
0.99975
Answer:
Radius of circle is 1 mm.
Step-by-step explanation:
Area of circle is 3.14 mm ²
Radius of circle
Area of circle = π × ( radius ) ²
substitute the values
3.14 mm² = 3.14 × ( radius )²
divide the values
3.14mm²/ 3.14 = ( radius) ²
1 mm²= ( radius)²
find the square root of 1 mm²
√1mm² = radius
1 mm = radius
Therefore the radius of circle is 1 mm.
i have absolutely no idea what this answer is i worked on it for 15 minutes could i get some help please
Answer:
40
Step-by-step explanation:
m<1 = (1/2)(50 deg + 30 deg)
m<1 = (1/2)(80 deg)
m<1 = 40 deg
Answer: 40
anyone help? Math infinite series
Which of the following infinite geometric sequences will have a related convergent series?
{16, 20.8, 27.04, 35.15,…}
{44, 44, 44, 44, …}
{5, 6, 7.2, 8.64,…}
(120, 96, 76.8, 61.44...)
=====================================================
Explanation:
A sequence is simply a list of values. There may or may not be a pattern to the list, though usually in a math class your teacher would use a pattern.
A series is where we add partial sums of a certain sequence to form a new sequence. For example, let's say A = {44, 44, 44, ...} is one sequence and we could form a list of partial sums to be B = {44, 88, 132, ...} The 88 is from adding the first two terms of sequence A together. The 132 is from adding the first three terms of sequence A. This process is continued forever.
For a series to be convergent, the terms must approach some finite single value. They likely won't actually reach this value but they should get closer and closer (think of it like an asymptote). When I formed series B shown above, note how the terms keep growing. It turns out they won't stop growing either and that means the series diverges to positive infinity. So we rule out choice B. The same happens for choices A and C as well.
To make sure the series approaches some finite value, the underlying sequence its based on must have the terms approaching 0. Choice D seems to have this happen. The terms of the sequence are getting smaller and smaller. Adding on smaller pieces will produce terms in a series that would likely get us closer to some finite target.
Keep in mind that not all decreasing sequences have a converging series. A famous example would be the harmonic sequence {1, 1/2, 1/3, 1/4, ...} which its series does not converge. The proof of this lengthy so I'll leave it out.
In the case of choice D, it is a geometric sequence with a = 120 as the starting term and r = 0.8 as the common ratio. The series converges to
S = a/(1-r) = 120/(1-0.8) = 600
✨HELP ASAP *Please*✨Theese figures are congruent. What series of transformations moves pentagon ABCDE onto pentagon A'B'C'D'E? Note: Rotations are clockwise Reflections are over the x-ory-axis.
A Rotation, translation
B. Reflection, translation
C. Reflection, rotation
D. Transation ansition
Answer: C
Brainliest Me
Solve the system of equations algebraically by using substitution method:
-3x+3y=9
-x+y=3
Answer:
This system has infinite solutions and it would be much easier to solve it by elimination but substitution it is.
Step-by-step explanation:
-3x+3y=9
-x+y=3
Isolate either x or y in any of the equations. I'll go with the second.
y = 3+x
Now substitute this for y in the first equation.
-3x+3(3+x)=9
Distribute the 3
-3x+9+3x=9
Combine like terms:
9=9
0=0
It's infinite