Answer:
[tex]f^{-1}(x) = \frac{x+8}{8}[/tex]
Domain of f(x): All real values.
Range of f(x): All real values.
Domain of f -1(x): All real values.
Range of f -1(x): All real values
Step-by-step explanation:
We are given the following function:
[tex]f(x) = 8x + 8[/tex]
Since it is a line, we have that both the domain is the range is the real set.
Inverse function:
The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.
Finding the inverse function:
Exchange x and y in the original function, and isolate y. So
Original
[tex]y = 8x + 8[/tex]
Exchanging:
[tex]x = 8y - 8[/tex]
Isolating y:
[tex]8y = x + 8[/tex]
[tex]y = \frac{x+8}{8}[/tex]
[tex]f^{-1}(x) = \frac{x+8}{8}[/tex]
A certain department store keeps track of an age and an annual income of customers who have its credit card. From a sample of 820 of such customers the following descriptive statistics had been obtained: the average age was 41 years with the standard deviation of 16 years and the average annual income was $37,290 with the standard deviation of $2,850. The correlation between the age the annual income was found to be 0.34. Answer the following questions. (Round your answers to 2 places after the decimal point).
Calculate the value of a slope.
a) 309.23 $ per year of age
b) 60.56 $ per year of age
c) 192.43$ per year of age
d) None of the above
Answer: b) $60.56 per year of age
Step-by-step explanation: If the scatterplot of two variables shows a line and the correlation between them is strong, we can calculate a regression line.
Regression line is a line graph that best fits the data. Like any other line, its formula is given by
y = mx + b
with
m being the slope
b the y-intercept
The slope of the line, correlation and standard deviations of the two variables have the following relationship:
[tex]m=r\frac{S_{y}}{S_{x}}[/tex]
where
r is correlation
[tex]S_{y}[/tex] is standard deviation for the y data
[tex]S_{x}[/tex] is standard deviation for the x data
For our problem:
r = 0.34
[tex]S_{y}=[/tex] 2850
[tex]S_{x}=[/tex] 16
Calculating
[tex]m=0.34(\frac{2850}{16})[/tex]
m = 60.56
Slope for the regression line of annual income per year of age is 60.56.
someone help me please
Answer:
all real numbers greater than but not equal to 0
A convenience store sells a coffee mug that comes
with a special price for refills using the mug. The
equation C = 2.3r + 6.5 represents the cost C, in
dollars, of the mug and r refills. What is the cost of
the mug?
Answer:
The cost of the mug is of $6.50.
Step-by-step explanation:
The cost of the mug and r refills is given by the following equation:
[tex]C(r) = 2.3r + 6.5[/tex]
Cost of the mug:
The cost of the mug is found when no refills are bought, that is, C when [tex]r = 0[/tex], which is [tex]C(0)[/tex]
[tex]C(0) = 2.3*0 + 6.5 = 6.5[/tex]
The cost of the mug is of $6.50.
Find the value of tan Θ is sin Θ = 1/2 90° ≤ Θ ≤ 180°
a. -√3/2
b. -√3/3
c. √3/2
d. √3/3
9514 1404 393
Answer:
b. -√3/3
Step-by-step explanation:
From your knowledge of the values of trig functions of special angles, you know sin(30°) = 1/2. For an angle in the second quadrant, this means the reference angle is 30° and the actual angle measure is 180° -30° = 150°.
The corresponding value of the tangent function is -√3/3, negative in the second quadrant.
Answer:
sin theta=p/h=1/2 let p=1k and h=2k
tan theta=p/b=1k/(√(2k)²-k²)=1k/k√3=1/√3
=tan 30
therefore theta =30°
your answer is 1/√3=√3/3
5 & 2/8 - 3 &7/8 = ?
Answer:
11/8 or 1 & 3/8
Step-by-step explanation:
5 & 2/8=21/4
3&7/8=31/8
21/4-31/8=11/8 or 1 & 3/8
Answer:
[tex]1\frac{3}{8}[/tex]
Step-by-step explanation:
Convert to improper fractions.
[tex]\frac{42}{8} -\frac{31}{8}[/tex]
Subtract.
[tex]\frac{11}{8} = 1\frac{3}{8}[/tex]
good luck, i hope this helps :)
in a recent year, the number of homes with tablets grew 43 3/4% from the previous year. What decimal is equivalent to 43 3/4?
Answer:
43.75
Step-by-step explanation:
Laci is filling a circular kiddie play pit with balls. The play pit has a radius of 7ft and each bag of balls covers 15 square feet. How many bags would she need to buy to have enough to cover the play pit
Answer:
10.26 bags
Step-by-step explanation:
Area of circle :
A = πr²
radius, r = 7ft
A = π * 7²
A = π * 49
A = 153.93804 ft²
Since a bag covers 15 ft² ;
Number of bags needed will be :
Area / number of square feet per bag
153.93804 ft² / 15 ft²
= 10.262536 bags
= 10.26 bags
Answer:
10.21
this is the correct answer because 10.21 is right
Prokaryotic cells are cells that _____. Select all that apply.
1.are simple
2.have no nucleus
3.have cell walls with peptidoglycan
4.have membrane-covered organelles
probably 1 and 2, I'm only in 6th grade tho so I forgot (love the pfp btw)
Math question 35 points please help
Answer:
It's D 100%
Step-by-step explanation:
If im right mark me brainliest if im wrong report me
Expand and simplify the following
5(m – 8) - 4(m – 7)
Step-by-step explanation:
5(m – 8) - 4(m – 7)
5m-40-4m+28
m -12
Answer:
5(m - 8) - 4(m - 7)
= 5m - 40 - 4m +28
= m - 12
m = 12
hope it helps
distance of -2,-6 and 4,2
Step-by-step explanation:
distance = -6-(-2) and 4-2
-6+2 and 2
-4 and 2 is distance
Answer:
[tex]d = \sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]
d = √(4 - (-2))² + (2 - (-6))²
d = √36 + 64
d = 10
5-x=3
Work out the value of x
Answer:
x = 2
Step-by-step explanation:
5 - x = 3
- x = 3 - 5
- x = - 2
x = 2
At practice, Diego does twice as many push-ups as Noah, and also 40 jumping jacks. He does 62 exercises in total. The equation 2x + 40 = 62 describes this situation. What is the value of x?
The value of x would be 11.
Step-by-step explanation:
We can simply just isolate x in the equation to solve:
2x + 40 = 62
(Subtract 40 from both sides) 2x = 22
(Divide each side by 2) x = 11
Hope this helps! :)
============================================================
Explanation:
If we knew the value of x, we would use PEMDAS to evaluate 2x+40 to get some single number value. For instance, if x = 4, then 2x+40 becomes 2(4)+40 which evaluates to 48 when you use PEMDAS.
However, we don't know the value of x. To find x, we follow PEMDAS in reverse to undo everything happening to x.
Note the order in which stuff is happening to x
multiply by 2add 40To undo this, we follow this process in reverse. So we need to undo the "add 40" part first, which was the last thing done. That means we'll subtract 40 from both sides
2x+40 = 62
2x+40-40 = 62-40
2x = 22
Then we undo the "multiply by 2" part. We'll divide both sides by 2
2x = 22
2x/2 = 22/2
x = 11
Let's check the answer.
2x+40 = 62
2(11)+40 = 62 ... x replaced with 11
22+40 = 62
62 = 62
Since we get the same thing on both sides, we get a true equation and this confirms we have the correct x value.
Q2
A painter has exactly 32 units of yellow dye and 54 units of green dye.
He plans to mix as many litres possible of colour A and colour B.
Each litre of colour A requires 4 units of yellow dye and 1 unit of green dye.
Each litre of colour B requires 1 unit of yellow dye and 6 units of green dye.
Find the maximum number of litres he can mix.
Q3.
A farmer can plant up to 8 hectares of land with wheat and barley. He can earn $5,000 for every
hectare he plants with wheat and $3,000 for every hectare he plants with barley. His use of a
necessary pesticide is limited by federal government regulations to 10 litres for his entire 8
hectares. Wheat requires 2 litres of pesticide for every hectare planted and barley requires just 1
litre per hectare.
(a)
(b)
What is the maximum profit he can make in this scenario?
How many hectares of wheat and how many hectares of barley will give the maximum
profit?
I did not understand Q3 and I could not, but I understood Q2
The answer is Q2: 12 liters
Heyyyy can someone help me ?? is for today ;-;
Zuleima puts her pebbles on the table. Make groups of 3 and have 1 left. Then make groups of 5 and have 2 left. How many stones does Zuleima have?
a) 32 b) 10 c) 26 d) 1000 e) 22
Answer:
E) 22
Step-by-step explanation:
To solve this, use process of elimination. (If they are both '☆'s, it is the answer.)
A)32
3n+1 x 5n+2 ☆
B) 10
3n+1 ☆ 5n+2 x
C) 26
3n+1 ☆ 5n+2 x
D) 1000
3n+1 ☆ 5n+2 x
E) 22
3n+1 ☆ 5n+2 ☆
The answer is E) 22
Cary and his brother took a road trip together. The total number of miles they drove was more than 200. Cary drove for 50 miles. Which distances could his brother have driven? Check all that apply.
50 miles
100 miles
150 miles
200 miles
250 miles
Answer:
D and E
Step-by-step explanation:
Got it right hope this helps
Answer:
200 miles or 250 miles.
Step-by-step explanation:
They both have 200+ miles. 200+50=250 miles. 250+50=300 miles. Hippity hoppity gimme that brainliest pls
what is the value of cos x°
Answer:
15÷17
Step-by-step explanation:
C A/H....adjacent over hypotenuse
Answer:
Well, I got B. Because it seems the most reasonable answer to this question.
Step-by-step explanation:
en una fiesta de disfraces dos quintos de los invitados van disfrazados de superhéroes un quinto de animales y el resto de zombis. si hay 180 invitados ¿cuantos hay disfrazados de cada cosa?
solo un quinto que sería 90 disfrazaos
Order the cars based on how far they drive on 1 gallon of gas. Place the car that travels
farthest on top.
0.2 gallons used for 7 miles
0.5 gallons used for 12 miles
0.9 gallons used for 25 miles
Step-by-step explanation:
First car.
0.2 gallons used for 7 miles.
Distance drive on 1 gallon of gas [tex]=\dfrac{7}{0.2}=35\ \text{miles}[/tex]
Second car.
0.5 gallons used for 12 miles.
Distance drive on 1 gallon of gas [tex]=\dfrac{12}{0.5}=24\ \text{miles}[/tex]
Third car.
0.9 gallons used for 25 miles.
Distance drive on 1 gallon of gas [tex]=\dfrac{25}{0.9}=27.8\ \text{miles}[/tex]
So, the first car traveled fast while the second car traveled least. Hence, the sequence is first car > third car > second car.
Identify the number of moles of each element present in one mole of NH NO3.
# moles N:
# moles H:
# moles O:
Answer:
no se jejfjekqkznbeoqnzne
caleb got $60 for birthday and put it in savings account. after he deposited money, he now has $139 write an equation and show work
Answer:
Equation 60+x=139 and the answer is x=79
Step-by-step explanation:
60+x=139
139-60=x
79=x
x=79
Hope this helps! :)
Colbert's backyard has two trees, shown below. The height of shorter tree is 3/5 of the height of the taller tree. If the height of the shorter tree is 4 1/2 feet tall, what is the height, in feet, of the taller tree?
Answer:
The height of the taller tree is 7.5 feet.
Step-by-step explanation:
I am going to say that:
The height of the shorter tree is x.
The height of the taller tree is y.
The height of shorter tree is 3/5 of the height of the taller tree.
This means that [tex]x = \frac{3y}{5}[/tex]
If the height of the shorter tree is 4 1/2 feet tall, what is the height, in feet, of the taller tree?
This means that [tex]x = 4 + \frac{1}{2} = \frac{8+1}{2} = \frac{9}{2}[/tex]
We want to find y.
[tex]x = \frac{3y}{5}[/tex]
[tex]\frac{9}{2} = \frac{3y}{5}[/tex]
[tex]6y = 45[/tex]
[tex]y = \frac{45}{6}[/tex]
[tex]y = 7.5[/tex]
The height of the taller tree is 7.5 feet.
3x ^ 2 = 1 / 3 x + 1
Answer:
What are you to find?
Step-by-step explanation:
Please state in your question and I will help you solve it. Thanks for your cooperation.
need help i get stuck these will give BRAINLIST
Answer:
D
Step-by-step explanation:
Look at the measurements that they give, then look at the line plots and see which ones have the same as the measurements that they gave you.
Answer:The 3rd option
Step-by-step explanation:
solve for x and y
7x+14y=28 5x+10y=20
Answer:
7x2 + 14x1
5x2 + 10x1
x = 2
7 =1
Step-by-step explanation:
plz help with 24-28!!!!!!!!!!!!!!
Answer:
4
Step-by-step explanation:
3х – 5y = 15
у = 2х + 4
Answer:
the answer is m equals 3 over 5
Right triangle ABC is shown below with the dimensions given in units. Which measurement is closest to BC in units?
4.4
4.6
7.0
3.9
Answer: 7.0
Step-by-step explanation: Tan 29 = x/8 than you multiple 8 by tan 29 and you will get 7.0
The Length of BC is 4.4.
What is Trigonometry?The branch of mathematics concerned with specific functions of angles and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).
Given:
B = 8
Using Trigonometry
tan 29 = P/ B
0.554 = P / 8
P = 8 x 0.554
P = 4.432
Hence, the measure for BC is 4.432
Learn more about Trigonometry here:
https://brainly.com/question/29002217
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Can you Graph the image A(4,-1) after a translation 7 units up?
There are 30 female performers in a dance recital. The ratio of men to women is 4:5. How many men are in the dance recital?
