By using the definition of inverse functions, we will see that:
g(g(f(f(f(36))))) = f(36) = 25.
What are inverse functions?Two functions f(x) and g(x) are inverses if:
f( g(x) ) = x
g( f(x) ) = x
Then we can rewrite:
g(g(f(f(f(36)))))
First, we can see that:
g(f(f(f(36)))) = f(f(36))
Replacing that in our expression, we get:
g(g(f(f(f36))))) = g(f(f(36)))
And the above expression is equal to f(36), to be sure of that, let's replace:
u = f(36)
Then we can rewrite:
g(f(f(36))) = g(f(u))
And by definition, the above thing is equal to u:
g(f(u)) = u = f(36).
Finally, we conclude that:
g(g(f(f(f(36))))) = f(36) = 3*√36 + 7 = 3*6 + 7 = 25
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How do I find x in this equation?
Answer:
Exact Form:
x
=29/20
Decimal Form:
x=1.45
Mixed Number Form:
x=1 9/20
Step-by-step explanation:
I did that before trust me I know
i’ll mark brainlest to whoever answers this question first! :)
Answer:
me
Step-by-step explanation:
i need help in geometry :(
9514 1404 393
Answer:
82 ft
Step-by-step explanation:
We can find the value of x by making use of the fact that corresponding angles have equal measures.
∠K = ∠N
20x -10 = 15x +15
5x = 25 . . . . . . . . . . add 10-15x
x = 5 . . . . . . . . . . . . divide by 5
Then the side lengths are ...
JK = (4x -4) ft = (4·5 -4) ft = 16 ft
KL = (5x +1) ft = (5·5 +1) ft = 26 ft
And the perimeter is the sum of side lengths:
16 ft + 26 ft + 40 ft = 82 ft
The perimeter of each pool is 82 feet.
Adam has $450. He spends $210 on food. Later he divides all the money into four equal parts. Then gives three parts to his friends, and he keeps one for himself. Later, he found $50 on the road.
Answer:
$110
Step-by-step explanation:
450-210= 240÷4= 60 +50=110
In an auditorium, the front 39 rows with 53 seats in each row are for kids while all 53 seats in each of the remaining 61 rows are for adults. How many seats are there in the auditorium?
Answer:
The auditorium has a total of 5,300 seats
Step-by-step explanation:
The seats for kids can be calculated by multiplying the number of rows by the number of seats per row:
Seats for kids=39*53 =2,067 seats
The seats for adults are calculated in a similar way:
Seats for adults = 61*53= 3,233 seats
Total seats: 2,067+3,233 = 5,300
The auditorium has a total of 5,300 seats
According to the Vivino website, the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New Englandâbased lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 56 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively.
Required:
a. Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.
b. Using the sample from the 60 bottles, what is the test statistic?
c. At α = 0.05, what is your conclusion?
Answer:
a
The null hypothesis is [tex]H_o : \mu = 32.48[/tex]
The alternative hypothesis is [tex]H_a : \mu < 32.48[/tex]
b
[tex]t = -1.504[/tex]
c
There is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48
Step-by-step explanation:
From the question we are told that
The mean price of is [tex]\mu = \$ 32.48[/tex]
The sample size is n = 56
The sample mean is [tex]\= x = \$30.15[/tex]
The standard deviation is [tex]\sigma = \$12[/tex]
The null hypothesis is [tex]H_o : \mu = 32.48[/tex]
The alternative hypothesis is [tex]H_a : \mu < 32.48[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{30.15 - 32.48 }{\frac{12 }{\sqrt{60} } }[/tex]
=> [tex]t = -1.504[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P (t < -1.504 )[/tex]
From the z-table
[tex]P(t < -1.504) = 0.066291[/tex]
So
[tex]p-value = 0.066291 [/tex]
From the value we obtain we see that
[tex]p -value > \alpha[/tex]
Then we fail to reject the null hypothesis
Hence there is no sufficient evidence to conclude that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48
In ΔUVW, u = 8 inches, v = 2.7 inches and w=5.9 inches. Find the measure of ∠W to the nearest 10th of a degree.
Answer:32.4
Step-by-step explanation:
The measure of ∠W to the nearest 10th of a degree is, 32.9°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know, The cosine rule of triangles, In a triangle, ABC with sides opposite to A is a and similar for b and c.
We have. cosA = (b² + c² - a²)/2bc.
Therefore, m∠W = (u² + v² - w²)/2uv.
m∠W = 0.84.
So, cosФ = 0.84.
Ф = cos⁻¹(0.84).
Ф = 32.9°.
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P= 2/ + 2w Find The Width
9514 1404 393
Answer:
W = P/2 -L
Step-by-step explanation:
Divide by 2 and subtract L.
P = 2L +2W
P/2 = L +W
P/2 -L = W
The width is ...
W = P/2 -L
I need help please! 7:44 est need rn
Answer:
B. [tex]3^{6}[/tex]
Step-by-step explanation:
[tex]3^{8} = 6561[/tex] [tex]3^{2} = 9[/tex] 6561 ÷ 9 = 729Option B, [tex]3^{6}[/tex], is equal to 729, so that is the right answer.I hope this helps!
If a dose of 100mg is contained in 4cc, how many cubic centimeter are in 40mg?
13+18 times 3 what does this equal
Answer:
93
Step-by-step explanation:
13+18 = 31
31x3= 93
Patty walked 2/5 of a mile in 5 1/2 minutes. At this rate, how long will it take Patty to walk 3 miles?
Answer:
41.25 minutes i think sorry if its wrong
what is l4x-4l+10=3x
Answer:
x=−6
Step-by-step explanation:
4x−4+10=3x
Step 1: Simplify both sides of the equation.
4x−4+10=3x
4x+−4+10=3x
(4x)+(−4+10)=3x(Combine Like Terms)
4x+6=3x
4x+6=3x
Step 2: Subtract 3x from both sides.
4x+6−3x=3x−3x
x+6=0
Step 3: Subtract 6 from both sides.
x+6−6=0−6
Answer:
l4x-
Step-by-step explanation:
Sorry I hope this is it I hoped it help sorry.
please leave a thanks.
three times a number m
Answer:
3n
Step-by-step explanation:
3 x n
simplifies to be
3n
hope this helps
Can someone help me I am confused
(9x-2y)/xy when x-4 and y=-2
Answer:
-5
Step-by-step explanation:
Answer:
GIVEN x=4 and y=-2
So, in (9x-2y)/xy when we apply x=4 and y=-2
{9(4)-2(-2)}/(4)(-2)
36+4/-8
40/-8
-5/1
=-5
Given the functions:
f(x) = x2 – 9, and g(x) = x3 + 4x² + 8x - 7, find h(x) = f(x) + g(2).
h(x) =
x3 + 5x2 + 80 -16
h(x) = x3 + 3x² + 80 + 2
h(x) = x3 + 5x2 + 8x - 16
h(x)
- 23 - 3x? 8.2 - 2
h(x)
x3 + 3x2 + 8x + 2
Answer:
h(x) = x² + 24
Step-by-step explanation:
First solve for g(2) in g(x) = x³ + 4x² + 8x - 7 by simply substituting 2 in x variable. The result is 33.
Then get the sum of f(x) and 33 to find h(x).
Find each key feature of the function shown in the graph. Enter all intervals using interval notation. Enter the x-intercepts as values of x only.
range=
domain=
x-intercepts=
average rate of change over the interval [0,2]=
the right-most interval where the graph is positive=
Answer:
Step-by-step explanation:
Range of the function is the set of y-values (output values) of the function on the graph.
Domain of the function is the set of x-values (input values) of the function.
Domain of the function : [-5, 4)
(including x = -5 and excluding x = 4)
Range : [-4, 2)
(Including y = -4 and excluding y = 2)
x - intercepts : x = -5, -2, 2
Average rate of change over the interval [0, 2]
= [tex]\frac{f(2)-f(0)}{2-0}[/tex]
= [tex]\frac{0-(-4)}{2-0}[/tex] [Since, f(2) = 0, f(0) = -4]
= 2
Right most interval where the graph is positive → [2, 4]
The key feature of a function include the intercepts and intervals of the function
The range is [-4,2)The domain is [-5,4)The x-intercepts are -2 and 2The average rate of change over the interval [0,2] is 2The right-most interval where the graph is positive is [2,4](a) The range
The least y value on the graph is at y = -4, and the maximum is at y = 2, with an open circle.
So, the range is:
[tex]\mathbf{Range = [-4,2)}[/tex]
(b) The domain
The least x value on the graph is at x = -5, and the maximum is at x = 4, with an open circle.
So, the domain is:
[tex]\mathbf{Domain = [-5,4)}[/tex]
(c) The x-intercepts
This is the point where the graph crosses the x-axis.
So, we have:
[tex]\mathbf{x-intercept =-2 \ and\ 2}[/tex]
(d) Average rate of change over [0,2]
From the graph, we have:
f(0) = -4
f(2) = 0
So, the average rate of change (m) is:
[tex]\mathbf{m = \frac{f(2) - f(0)}{2 - 0}}[/tex]
[tex]\mathbf{m = \frac{0 - -4}{2 - 0}}[/tex]
[tex]\mathbf{m = \frac{4}{2}}[/tex]
[tex]\mathbf{m =2}[/tex]
(d) The right-most interval where the graph is positive
The graph is positive from x = 2 to x = 4.
Hence, the right-most interval where the graph is positive is [2,4]
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Given:
A= The square root of 3
B= 2 times the square root of 3
C= The square root of 25
D= The square root of 16
Which expressions result in a rational number? Select all that apply.
a. a+b
b. c+d
c. a+d
d. a*b
e. b*d
f. c*d
g. a*a
Answer:
b, d, f, gStep-by-step explanation:
Given:
A= √3 B= 2 √3 C= √25 = 5D= √16 = 4Possible expressions resulting in a rational number are the product of A and B and any combination of C and D as they are rational
Correct choices
b. c+d = 5+4 = 9d. a*b = √3×2√3 = 2×3 = 6f. c*d = 5×4 = 20g. a*a = √3×√3 = 3A cyclist travels 10 km from home to the park.
She leaves home at 12:20 and arrives at the park at 12:50.
What is her average speed in km/h?
Answer:
20 km/hr
Step-by-step explanation:
The total time she takes to travel 10 km is 30 minutes of 0.5 hours.
To calculate speed, we can divide the distance traveled by the time it takes.
[tex]s = \frac{10}{0.5} = 20[/tex] km/hr
A local park is in the shape of a square. A map of the local park is made with the scale 1 inch to 200 feet.
If each side of the park on the map is 12 inches long, how long is each side of the actual square park?
1 inch to 100 feet
12 inches = 1200 feet.
Just multiply both sides by 12.
The answer is 1200 feet.
3^-3 find the value of power
Answer:
0.037
hope thats the answer
Answer:
Answer= 0.037
Step-by-step explanation:
([tex]3^{-3}[/tex]) is the same as [tex]\frac{1}{3^{3} }[/tex]
(the negative power rule states that [tex]x^{-y}[/tex] is the same as [tex]\frac{1}{x^{y} }[/tex])
which is equal to [tex]\frac{1}{27}[/tex]
or converted to decimals it will be equal to 0.037
i’ve been on this question for 22 minutes please help me
Answer:
F
Step-by-step explanation:
The pet store currently has 430 frogs. Last night 114 jumped out and
escaped. What was the inventory before the great frog escape?
Answer:
544
Step-by-step explanation:
430+114
passes through (0, 1) and (2, 5)
Answer:
y = 2x + 1
Step-by-step explanation:
1. Find the slope: change in y/change in x
[tex]\frac{5-1}{2-0}[/tex] = 2
Slope: 2
2. Find y-intercept by substituting in a point (0, 1)
y = 2x + b
1 = b
3. Put the equation together
y = 2x + 1
The equation of the line passing through the points (0, 1) and (2, 5) is y = 2x + 1.
What is y intercept?y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.
The equation of a line in slope intercept form is,
y = mx + c
Here m is the value of the slope and c is y intercept.
Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Given two points (0, 1) and (2, 5).
Slope, m = (5 - 1) / (2 - 0)
= 4 / 2
= 2
c is the y coordinate when x = 0.
We have that point given (0, 1).
So c = 1
Substituting m = 2 and c = 1 in the general form, we get,
y = 2x + 1
Hence the equation of the line is y = 2x + 1.
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Andre paid $13 for 3 books. Diego bought 12 books priced at the same rate.
How much did Diego pay for the 12 books?
PLEASE INCLUDE AN EXPLANATION
Answer:
$36
Step-by-step explanation:
i dont know how to explain it but heres the number answer
Answer:
well 3÷13= 4.33 and 4.33×12=52
4 pound tomato cost 14 dollar how much does 1 pound cost
Answer:$3.50
Step-by-step explanation:
14/4 =3.5. To check answer multiply 3.5 by 4. You get 14
(1-cos^2 60°)+(1-sin^2 60°)=tan^2 60°
nicholas started a canned food drive at school. the equation representing this is y=235=15, where x is the number of days, and y is the number of cans collected. explain how to determine how many days it would take to collect 2600 cans.
Answer:
195 cans will be left after 10 days
Sample Answer: I am given a number of cans, which is y, and I need to find the number of days, which is x. To do this, I would substitute 2600 for y, to get 2600 = 235x + 15. Solving for x, I would get x = 11. Thus, it would take 11 days to collect 2600 cans.
Step-by-step explanation:
i did the edge thing
Answer:
I am given a number of cans, which is y, and I need to find the number of days, which is x. To do this, I would substitute 2600 for y, to get 2600 = 235x + 15. Solving for x, I would get x = 11. Thus, it would take 11 days to collect 2600 cans.
Step-by-step explanation:
hope this helps
did it on edge
have a good day
What is the least common multiple of 9, 17, and 51? A. 51 B. 102 C. 153 D. 867
Answer:
C. 153Hope this helps
shshsgshsh
Answer:
C. 153
Step-by-step explanation:
I just did this quiz and got it right!! Hope this helps! :D