Answer:
[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]
The inverse function is to calculate the number of rides; given the amount paid
Step-by-step explanation:
Given
[tex]Admission = 15[/tex]
[tex]Ride = 3[/tex] per ride
Required
Explain the inverse function
First, we calculate the function
Let x represents the number of rides
So:
[tex]f(x) = Admission + Ride * x[/tex]
[tex]f(x) = 15 + 3 * x[/tex]
[tex]f(x) = 15 + 3x[/tex]
For the inverse function, we have:
[tex]y = 15 + 3x[/tex]
Swap x and y
[tex]x = 15 + 3y[/tex]
Make 3y the subject
[tex]3y = x - 15[/tex]
Make y the subject
[tex]y =\frac{x}{3} - 5[/tex]
Replace y with the inverse function
[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]
The above is to calculate the number of rides; given the amount paid
The table shows the displacement-time data for a ship relative to a shore.
t(hours) 2.95 3.15 3.75 3.95 3.99 4.00
s(0 (miles) 14.95 17.61 27.23 31.01 31.80 32.00
Estimate the instantaneous velocity of the ship at t = 4 hours.
A.
20.00 mi./h.
B.
20.15 mi./h.
C.
20.25 mi./h.
OD.
20.50 mi./h.
Answer:
Step-by-step explanation:
f(x) = 4x² + 3x - 2 g(x) = 6x³ - 3x²-4 Find (f +g) (x)
Answer:
6x^3+x^2+3x-6
Step-by-step explanation:
f(x) = 4x² + 3x - 2
g(x) = 6x³ - 3x²-4
(f +g) (x) =4x² + 3x - 2+6x³ - 3x²-4
Combine like terms
=6x^3+4x^2-3x^2+3x-2-4
=6x^3+x^2+3x-6
(x-2)(-5x^2+x)=(x)(-5x^2)+(x)(x)+(-2)(-5x^2)+(-2)(x) is an exsample of
this is an example of linear equations is one variable
Khanacademy Unit:Sequences
What does g(2)=?
Answer:
g(2) = -42
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationAlgebra II
SequencesStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \left \{ {{g(1) = 50} \atop {g(n) = 8 - g(n - 1)}} \right.[/tex]
Step 2: Evaluate
Substitute in x [Function g(n)]: g(2) = 8 - g(2 - 1)(Parenthesis) Subtract: g(2) = 8 - g(1)Substitute in function value: g(2) = 8 - 50Subtract: g(2) = -42Evaluate the function.
f(x)=2x^2+8x
Find f(−1)
PLease help!
a:-10
b:-6
c:6
d:10
Answer:b
Step-by-step explanation:
What the cubic inches…
Step-by-step explanation:
The radius r is 5 in (r = D/2). so the volume V of the beach ball is
[tex]V= \dfrac{4 \pi}{3}r^3 = \dfrac{4 \pi}{3}(5\:\text{in})^3[/tex]
[tex]\:\:\:\:\:= 523.6\:\text{in}^3[/tex]
GIVING OUT BRAINLIEST HELP PLEASE ❤️
Answer:
C
Step-by-step explanation:
Which angels are corresponding angles? Check all that apply
Answer:
Only A and B.
Step-by-step explanation:
Corresponding angles are angles in the same position and are the same size. The others are wrong as they are not the same sizes or are not the same
Linda is doing car wash with her teammates to collect money for their trip. They can
get $12 for the car that they wash. In order to start their work, they spent $155 to buy
supplies needed for the work.
Part A:
Create a function f(c) to represent the profit that they make for washing c cars.
f(c) =
(b)
Part B:
Use the function rule that you created on Part A to find the value of f '(145)
f-? (145)
9514 1404 393
Answer:
(a) f(c) = 12c -155
(b) f⁻¹(145) = 25
Step-by-step explanation:
(a) Profit is the difference between revenue (12c) and cost (155). The profit function is ...
f(c) = 12c -155
__
(b) The number of cars Linda's team must wash to achieve a profit of $145 is found from ...
145 = 12c -155
300 = 12c . . . . . . add 155
25 = c . . . . . . . . . divide by 12
f⁻¹(145) = 25 . . . . the team must wash 25 cars for a profit of $145
PLS HELP ASAP.!
THANK YOU, WILL MARK BRAINLIEST
Answer:
Explanation:
The volume of the triangular prism:
The base area of the prism = 1/2 x 4 x 6 = 12 ft2
Height = 6 ft
The volume of the triangular prism = 12 x 6 = 72 ft3
The volume of the rectangular prism:
The base area of the prism = 4 x 6 = 24 ft2
Height = 12 ft
The volume of the triangular prism = 12 x 24 = 288 ft3
Volume of the composite figure = (288 + 72)ft3 = 360 ft3
Step-by-step explanation:
Miguel borrowed $1,800 for 2 years and ended up paying $180 in simple interest what was the interest rate
Answer: 103.534%
I used a calculator and everything
Can someone answer with steps and explanation? Thanks.
Answer:
[tex]BC=9\sqrt{3}\approx15.59\text{ units}[/tex]
Step-by-step explanation:
Since Segment BOA is a diameter:
[tex]m\angle ACB=90[/tex]
Arc Ac and Arc CB are in a ratio of two to four. Since Segment BOA is a diameter, Arc ACB measures 180°. Letting the unknown value be x, we can write that:
[tex]2x+4x=180[/tex]
Hence:
[tex]x=30[/tex]
Thus, Arc CB = 120°. By the Inscribed Angle Theorem:
[tex]\displaystyle m\angle A=\frac{1}{2}\left(\stackrel{\frown}{CB}\right)=\frac{1}{2}\left(120)=60[/tex]
Therefore, ΔABC is a 30-60-90 triangle. Its sides are in the ratios shown in the image below.
Since AC is opposite from the 30° triangle, let AC = a.
We are given that AC = 9. Hence, a = 9.
BC is opposite from the 60° angle and it is given by a√3. Therefore:
[tex]BC=9\sqrt{3}\approx15.59\text{ units}[/tex]
You are ordering a new home theater system that consists of a TV, surround sound system, and DVD player. You can choose from 66 different TVs, 1212 types of surround sound systems, and 1818 types of DVD players. How many different home theater systems can you build
Answer:
You can build 1296 different home theater systems.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
There are:
6 different TVs
12 types of surround sound systems.
18 types of DVD players.
How many different home theater systems can you build?
The components are independent, so, by the fundamental counting principle:
6*12*18 = 1296
You can build 1296 different home theater systems.
Which point represents the value of -(-2) on the number line?
Answer:
2
Step-by-step explanation:
-(-2)
negative x negative always give positive .
=>2
You can easily represent 2 on number line
2 times the difference between 49.5 and 37.5
Answer:
24
Step-by-step explanation:
diff is 12
12x2 is 24
Exhibit 11-10 n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 At 95% confidence, the null hypothesis _____. a. should not be rejected b. should be revised c. should be rejected d. None of these answers are correct
Answer:
Option C
Step-by-step explanation:
n = 81
s2 = 625
H0: σ2 = 500
Ha: σ2 ≠ 500
Test Statistics X^2 = (n-1)s^2/ σ2 = (81-1)*625/500
X^2 = 100
P value = 0.0646 for degree of freedom = 81-1 = 80
And X^2 = 100
At 95% confidence interval
Alpha = 0.05 , p value = 0.0646
p < alpha, we will reject the null hypothesis
At 95% confidence, the null hypothesis
Tích các nghiệm của phương trình Log(x-1)²=2 là
Answer:
-99
Step-by-step explanation:
Log(x-1)²=2
Log(x-1)²=Log(100)
(x-1)²=100
x-1=10 and x-1=-10
x₁=11 and x₂=-9
x₁ × x₂ = 11 × (-9) = -99
PLEASE HELP W THIS I WILL Give YOU THE BRAINLIEST PLEASE ! - What does it mean to have a skewed distribution? What causes a skew in statistical terms? And how does one deal with skewed data when conducting research? Are there specific types of
research questions and types of data where one would expect the data to be skewed?
Answer:
Explained below
Step-by-step explanation:
A) A skewed distribution in a dataset is when the median is not equal to the mean in such a manner that the bell curve is tilted to the left or right.
B) If in a data set, if there are outliers which are extremely large or extremely small in comparison to other values in that same dataset, then we can say that such a curve will be pulled towards the outlier and thus the distribution is skewed.
Also, if the curve is inclined to the left, it means there are few extreme values to the left and it is negatively skewed.
Similarly, if the curve is inclined to the right, it means there are few extreme values to the right and is positively skewed.
C) Example of a research question is;
If in a developed country where the poverty level is about 0%, if we collect the data of income of the households, we will discover majority of people with average income and very few people with extreme high levels of income. This condition means the data is positively skewed.
−12 as a ratio of two integers.
Answer:
-12 can be written as the ratio of -24 and 2, for example.
Step-by-step explanation:
Ratio of a to b:
The ratio of a to b is given by the division of a by b, that is:
[tex]r = \frac{a}{b}[/tex]
−12 as a ratio of two integers.
Here, we want any division in which the result is -12. One example is:
[tex]-12 = \frac{-24}{2}[/tex]
-12 can be written as the ratio of -24 and 2, for example.
Choose the correct Set-builder form for the following set written in Roster form: { − 2 , − 1 , 0 , 1 , 2 }
Step-by-step explanation:
{x:x is an integer where x>-3 and x<3}
The mapping shows a relationship between input and output values.
Answer:
where is the photo
Step-by-step explanation:
What is the other number to this math equation?
Answer:
You need to ask yourself what times 20 gives you 600. Then ask yourself what times 20 gives you 160. Then that will give you your answer.
Step-by-step explanation:
PLEASE HELP ASAP!!
Q: Use the graph of f below. Assume the entire function is graphed below. Find where f(x)<0.
(graph and answers pictured.)
Answer:
Option (4)
Step-by-step explanation:
From the graph attached,
We have to find the interval in which the function is less than zero or negative.
Value of the function are along the y-axis and negative value of the function means negative side of the y-axis.
In the graph, function is below the x-axis in the interval x > 4 and x = 6 only.
Therefore, in the interval (4, 6] function f(x) < 0.
Option (4) is the correct option.
circle o has diameter ab and chord ac. calculate the measure of cab id bc = 62⁰
Answer:
sin62 =0.883Step-by-step explanation:
0.883=1/0.836=1.133
The measure of ∠CAB is 31⁰.
Given that,
Circle O has diameter AB and chord AC.
We have to determine,
The measure of ∠CAB if BC is 62⁰.
According to the question,
The measurement of the required angle by using circle properties following all the steps given below.
The measure of the BC is 62 degrees.
If the circle has diameter AB and chord AC,
Then,
By the property of the circle,
[tex]\rm m\angle CAB = \dfrac{1}{2} \times BC \\[/tex]
Substitute the value of the BC in the equation,
[tex]m\angle CAB = \dfrac{1}{2} \times BC \\\\ m\angle CAB = \dfrac{1}{2} \times 62 \\\\ m\angle CAB = 31 \ degree \\\\[/tex]
Hence, The measure of ∠CAB is 31⁰.
For more details refer to the link given below.
https://brainly.com/question/1319201
The graph of the function f(x) = 4 over 5 square root x is shown. What is the domain of the function?
Answer:
all real numbers greater than or equal to 0
Step-by-step explanation:
The domain of the function is whatever the input (in this case, x) can be. As you cannot take the square root of a negative number, x cannot be negative. Because you can take the square root of 0 (which is 0), x can be anything postive or 0, meaning anything greather than or equal to 0. The domain is all real numbers greater than or equal to 0.
Solve the system by graphing. Write the solution as an ordered pair.
y = 13x + 2
y = –x – 2
PLEASE HELP!!!!!
Answer:
the answer to the question is - 2 over 7 and - 12 over 7
A student uses the ratio of 4 oranges to 6 fluid ounces to
find the number of oranges needed to make 24 fluid
ounces of juice. The student writes this proportion:
4 24
616
Explain the error in the student's work.
A student uses the ratio of 4 oranges to 6 fluid ounces to find the number of oranges needed to make 24 fluid ounces of juice. The student writes the proportion:4/6=24/16
Find the value of
[tex]3 \frac{1}{5} \div \frac{8}{20} [/tex]
Answer:
[tex]{ \bf{3 \frac{1}{5} \div \frac{8}{20} }} \\ = \frac{16}{5} \div \frac{8}{20} \\ { \boxed{ \tt{reciprocal \: of \: \frac{8}{20} = \frac{20}{8} }}} \\ \therefore \: = \frac{16}{5} \times \frac{20}{8} \\ = \frac{320}{40} \\ { \bf{ answer : 8}} \\ \\ {\underline{\tt {\blue{becker \: jnr}}}}
[/tex]
What is the distance between [(3 + 4i) + (2 - 3i)] and (9 - 2i)?
Answer:
5
Step-by-step explanation:
(3 + 4i) + (2 - 3i) = 3 + 4i + 2 - 3i = 5 + i
distance between (5 + i) and (9 - 2i) is the difference between them. and difference means subtraction.
(9 - 2i) - (5 + i) = 9 - 2i - 5 - i = 4 - 3i
and since we are looking for a distance, we are looking for the absolute value of that subtraction.
after all, we could have done the subtraction also in the other direction
(5 + i) - (9 - 2i) = -4 + 3i
and this must be the same distance.
|(-4 + 3i)| = |(4 - 3i)|
and that is done by calculating the distance of any of these 2 points from (0,0) on the coordinate grid of complex numbers.
|(a +bi)| = sqrt(a² + b²)
in our case here
distance = sqrt(4² + (-3)²) = sqrt(16 + 9) = sqrt(25) = 5
as you can easily see, this is (as expected) the same for the result of the subtraction in the other direction :
sqrt((-4)² + 3²) = sqrt(16+9) = sqrt(25) = 5
Rachel is driving to visit her mother, who lives 250 miles away. How long will the
drive be, round-trip, if Rachel drives at an
average speed of 40 mph?
Answer:
Time for a round trip = 12.5 hours
Step-by-step explanation:
Mother's house = 250 miles
Total distance for the round trip = 250 + 250 = 500 miles
Given speed = 40 mph
Find time .
[tex]Speed = \frac{distance }{Time }\\\\Time = \frac{distance }{speed } = \frac{500}{40} \\\\Time = 12.5 \ hours[/tex]
