Given:
A certain function h(x) contains the point (8,-2).
To find:
The value of [tex]h^{-1}(-2)[/tex].
Solution:
If a function is defined as
[tex]f(x)=\{(a,b):a\in R,b\in R\}[/tex]
Then, its inverse is defined as
[tex]f^{-1}(x)=\{(b,a):a\in R,b\in R\}[/tex]
It is given that, a certain function h(x) contains the point (8,-2). It means, its inverse [tex]h^{-1}(x)[/tex] contains the point (-2,8). So, the value of inverse function is 8 at x=-2, i.e.,
[tex]h^{-1}(-2)=8[/tex]
Therefore, the value of [tex]h^{-1}(-2)[/tex] is 8.
A factory process requires 3 steps to finish a product. The steps each have a mean completion time of μ=10 seconds and a standard deviation of σ=5 seconds. The time it takes to complete each step is independent from the other steps. Let T be the total completion time of the 3 steps on a randomly chosen product.
Find the mean of T.
Answer:
The mean of T is 10 seconds
Step-by-step explanation:
The given parameters are;
The mean completion time of each step, μ = 10 seconds
The standard deviation, σ = 5 seconds
Each step is independent from the other steps
The variable that represents the total completion time for the three steps = T
We have the mean of T, [tex]\overline T[/tex], given by the combined mean as follows;
[tex]\overline T = \dfrac{n_1 \cdot \overline x_1 + n_2 \cdot \overline x_2 + n_3 \cdot \overline x_3 }{n_1 + n_2 + n_3 }[/tex]
Where;
[tex]The \ mean \ completion \ time \ for \ each \ step \ is \ \overline x_1 = \overline x_2 = \overline x_3 = 10 \ seconds[/tex]
n₁ = n₂ = n₃ = 1, each step is taken only once, we have;
[tex]\overline T = \dfrac{1 \times 10 + 1 \times 10 + 1 \times 10 }{1 + 1 + 1 } = \dfrac{30}{3} = 10 \ seconds[/tex]
Therefore, the mean of T = 10 seconds
Using the normal distribution, it is found that the mean of T is of 30 seconds.
A normal distribution has two parameters: Mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex].
For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex].In this problem, the mean is [tex]\mu = 10[/tex] and the standard deviation is [tex]\sigma = 5[/tex].
For the total completion, there are 3 instances, hence [tex]n = 3, n\mu = 3(10) = 30[/tex], hence, the mean of T is of 30 seconds.
A similar problem is given at https://brainly.com/question/24085252
The price of a math book after a discount of 25% is $45, find the original price of the book.
Answer:
Step-by-step explanation:
let original price be x
x=45/(1-25/100)= 45/(1-0.25)=45/.75=60
x=60
Answer:
25 percent off 45.00 is 33.75. The difference is 11.25. Hope that helps :)
Step-by-step explanation:
Noam solved the equation for k using the following calculations. k-7.6 = 10.35 + 7.6 +7.6 k= 1741 What error, if any, did he make? He should have subtracted 7.6 instead of adding it. He should have subtracted 10.35 from both sides. O He made a computation error when he added 10.35+746. O He made a computation error when he added -7.6 and 7.6.
Answer: C- He made a computation error when he added 10.35+7.6.
Step-by-step explanation:
Noam did not line up the decimals when he was adding 10.35 and 7.6. So if you line up the decimals, you would get 17.95 instead of 17.41.
Answer
C.
Step-by-step explanation:
He made a computation error when he added 10.35+746.
*Cough* E d g e n u i t y *Cough*
Sorry I think I am coming down with something...
*Cough* It's right *Cough*
Please give me brainliest!!
Karl drove 612.9 miles. For each gallon of gas, the car can travel 41 miles. What is a reasonable estimate of the number of gallons of gas Karl used? Select all that apply.
A 1.4 gallons
B 15 gallons
C 14 gallons
D 1.5 gallons
E 140 gallons
Answer:
B. 15 gallons
Step-by-step explanation:
We don't need an exact answer, so we estimate
To do this, we round
41 is a tens number, so I'm going to round to the nearest 10
40
612.9 is a hundreds number, so I'm rounding to the nearest hundred
600
for EACH gallon, the car drives(roughly) 40 miles. If I have driven(roughly) 600 miles, that means I have used 600/40=15 gallons
A department store buys 100 shirts at a cost of $700 and sells them at a selling price of $10 each. Find the percent markup
Answer:
30%
Step-by-step explanation:
The price for each shirt to buy is: $ 700/100 = $ 7 / each
Selling price is: $ 10 / each
So the difference between the selling and buying prices is: $ 10 - $ 7 = $ 3
So 100 each, the interest is: $ 3 X100 = $ 300 => 30%
70 points!!! Which of the following is an arithmetic sequence with common difference –5?
A. 5, 25, 125, 626, ...
B. 5, -25, 125, -625 ...
C. 8, 3, -2, -7 ...
D. 0, 5, 10, 15 ...
Answer:
c
Step-by-step explanation:
This is c because the numbers in c are moving down by -5.
Answer:
I would say b
Step-by-step explanation:
-5 times 5 is -25
-5 times -25 is 125 ect
6x - 12 y = 24
-X-6y=4
Answer:
x=2
y=-1
Use the system of equations to solve for it
-5x + 20 <5
I need help!
Answer:
Step-by-step explanation:
I’d vhvhvmvjvhkvhvkfygjghk
Answer:
x>3
Step-by-step explanation:
-5x+20<5 (move the constant to the right)
-5x<5-20 (calculate)
-5x<-15 (divide both sides)
solution: x>3
hope this helps!
There are 50 carpenters in a crew. On a certain day, 15
were present. What percent showed up for work?
Answer:
30
Step-by-step explanation:
15:50*100 = ( 15*100):50 = 1500:50 = 30
Answer:
thirty
Step-by-step explanation:
cuz dis bussin. duh.
Chloe needed to get her computer fixed. She took it to the repair store. The technician
at the store worked on the computer for 3.5 hours and charged her $197 for parts.
The total was $389.50. What was the cost of labor, per hour?
Answer:
he took $55.8for 1hr
Step-by-step explanation:
it's because we should devid eit for calculation for minute
What goes on the lines I don’t understand the problem
Answer:
Step-by-step explanation:
a). Let the number of spoons = x
And number of forks = y
Total number of spoons and forks bought by Perry = 10
x + y = 10 --------(1)
Cost of one spoon = $5
Cost of one fork = $3
Therefore, total cost of x spoons and y forks = $(5x + 3y)
5x + 3y = 42 -------(2)
b). Now we can convert these equations into the slope-intercept form.
x + y = 10 ⇒ y = -x + 10
Table for input output values,
x 2 4 6
y 8 6 4
5x + 3y = 42
3y = -5x + 42
y = [tex]-\frac{5}{3}x+14[/tex]
x 0 3 6
y 14 9 4
Point of intersection of these lines will be (6, 4).
can you guys help me find the domain? (finding the domain graphically)
Answer:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
Step-by-step explanation:
Hope this helps i would give answer but i dont know what the answer is so sorry but hope this helps you.
please help it’s due today
What is the equation of the line in point-slope form that passes through the point (7,-4) and has a slope of 1/2 ?
a. y+ 7 = 1/2 (x – 4)
b.y-7= 1/2 (x + 4)
c.y - 4 = 1/2 (x + 7)
d.y+4 = 1/2(x - 7)
Answer:
d. [tex]y+4=\frac{1}{2}(x-7)[/tex]
Step-by-step explanation:
Here m=1/2 and (x1, y1)=(7, -4)
Equation of line in point slope form is given as
[tex]y-y_1=m(x-x_1)[/tex]
Therefore
[tex]y+4=\frac{1}{2}(x-7)[/tex]
2x + 22 4x – 2 3x + 3
find x
Answer:
?Incomplete question!!
By what means these algebraic expressions are related?
is 3 1/4 a rational number
Answer: Yes the mixed 3 1/4 is a rational number.
Step-by-step explanation:
Percents
Michael is leaving a 15% tip for his waitress. What percent of the
original price will he pay? Write your answer as a percent, decimal,
and fraction.
Given that,
Michael is leaving a 15% tip for his waitress.
To find,
What percent of the original price will he pay.
Solution,
Let the original price was 100%.
When he leaves a 15% tip for the waitress, he is really paying 100%+15%=115% of the original price.
[tex]115\%=\dfrac{115}{100}\\\\=1.15[/tex]
or
[tex]\dfrac{115}{100}=\dfrac{23}{20}[/tex]
So, this is the required solution.
Joseph drove to Carly’s house for dinner. He was away from his house for 2 hours. He spent 50minutes at Carly’s house. Driving to and from Carly’s house he drove at a speed of 45mph. How far away from Carly does Joseph live?
70 miles
Hope this helps
-Millie
Select three ratios that are equivalent to 5:2
Choose 3 answers:
(Choice A)
A
2:5
(Choice B)
B
10:4
(Choice C)
C
20:50
(Choice D)
D
35:14
(Choice E)
E
55:22
Answer:
B,D,E
Step-by-step explanation:
b-multiply by 2 for both
d- multiply by 7 for both
e-multiply by 11 for both
Tyson brought a bag of coins into the bank to be counted. The bag contained only nickels and
dimes. There were a total of 220 coins and the total value of those coins was $15.50.
Use what you have learned about systems of linear equations to determine how many of the coin
were nickels and how many were dimes. Then, fill in the blanks below with your answer.
number of nickels is
number of dimes is
There will be 130 nickels and 90 dimes. 100 nickels is 5 dollars. 90 dimes are 9 dollars. And then there will be 30 left. 30 dimes isn’t 1.50$ bur 30 nickels is 1.50$ so you add the 30 to the nickels and it’ll be exactly 15.50$.
Answer:
15 50..…......................
Veronica wants to buy a new bicycle. The bicycle costs $310. Veronica
opened a savings account with $50. She also got a job and plans to
save $20 a week. How long will it take her to save up enough money
for the bike?
Step-by-step explanation:
bicycle cost= 310
initial money in savings account= 50
additional money saved per week = 20
number of weeks = w
you have to set up an equation
The equation is...
bicycle cost = additional money saved × w + initial money
Substitute the values
310 = 20w + 50
Solve for w
310 - 50 = 20w +50 - 50
260 = 20w
260÷ 20 = 20w÷ 20
13 = w
It will take 13 weeks for her to have enough money for her bicycle
I hope this helps!!!
Characterize the slope of the line in the graph,
A. Positive
B. Negative
C. Zero
D. Undefined
1. Fill in the blank: When I text, I mostly misspell '----' as '---'.
2. Fill in the blank: When I text, my autocorrect changes '---' to '----'.
3. True or false: You have more than one Brainly account.
4. True or false: The Eiffel Tower is high like your grades.
5. (Optional) 3x+4=13 solve for x
6. What's your Hogwarts house?
7. Draco or Harry?
8. Remus Lupin or Serius Black?
9. True or False: KPOP is trash.
10. True or False: KPOP is everything.
When i text i mostly misspell, carrot as caroot
When i text, my autocorrect changes rat to fat.
False
True B)
Answer:
5 : x=3
Step-by-step explanation:
Which expression is equivalent to x^5 • x^2?
x^3
x^7
x^10
(x + x)^7
Answer: x^7
Step-by-step explanation: x5*x2
=(x*x*x*x*x)*(x*x)
=x*x*x*x*x*x*x
=x7
Determine the intercepts of the line.
Answer:
Y-intercept: (0, 0.4)
X-intercepts: (0.3, 0)
Answer:
The y-intercept is (0, 0.4), and the x-intercept is (0.3, 0)
Step-by-step explanation:
To find the intercepts of the line, you need to see what points lie on the x and y-axis.
What are the slope, m, and the y-intercept, B, of a line that pases through the points (-2,1)and (8,-5)?
A. m=-5/3 and b=-7/3
B. m=-3/5 and b=-1/5
C. m=-3/5 and b=11/5
D. m=5/3 and b=13/3
Answer:
B. m= -3/5 and b= -1/5Step-by-step explanation:
Given points:
(-2, 1) and (8, -5)Slope is:
m = (y2 - y1)/(x2 - x1)m = (-5 - 1)/(8 - (-2)) = -6/10 = -3/5m = -3/5Use formula y = mx + b, substitute x = -2, y = 1, m = -3/5, find y-intercept b:
1 = (-3/5)*(-2) + b1 = 6/5 + bb = 1 - 6/5b = - 1/5Correct option is B.
Step-by-step explanation:
[tex] m \: = \: -3/5 \: and \: b \: = \: -1/5[/tex]
At the instant when the radius of a cone is 3 inches, the volume of
the cone is increasing at the rate of 9 pi cubic inches per minute. If
the height is always 3 times the radius, find the rate of change of the
radius at that instant.
Answer:
The rate of change of the radius of the cone when the radius is 3 inches is 0.[tex]\overline 3[/tex] inch/minute
Step-by-step explanation:
The given parameters are;
The radius of the cone = 3 inches
dV/dt = 9·π in.³/min
The height, h = 3 × Radius, r
The formula for the volume of a cone, V is V = 1/3×π×r²×h = 1/3×π×r²×3×r = π·r³
Therefore, we have;
dV/dt = dV/dr × dr/dt
dV/dr =3·π·r²
∴ dr/dt = dV/dt/(dV/dr) = 9·π/(3·π·r²) = 3/r²
When r = 3 inches, we have;
dr/dt = 3/r² = 3/(3²) = 1/3 inch/minute
The rate of change of the radius of the cone when the radius is 3 inches = 0.[tex]\overline 3[/tex] inch/minute
What is the approximate area of the circle shown below?
A. 251 in
B. 5027 in 2
C. 126 in2
D. 20,106 in?
Answer:
B. 5027 in²Step-by-step explanation:
Area of a circle = π r²
where r = 80/2 = 40 in
plugin value of r=40in into the formula:
Area of a circle = π r²
= π (40)²
= 5027 in²
Please tell me how to do this or give me the answer either one is fine with me!!!!
:)
Answer:
16.85 cm²
Step-by-step explanation:
Find the area of the small circle then subtract the area of the large circle by the small circle
Area of small circle :
πr², where r = 4cm
π(4²) = 50.27 cm²
67.12 - 50.27 = 16.85 cm²
PLEASE ANSWER ASAP TY
In triangle ABC below, BD is the altitude. Find the length of DC. Leave your answer in
simplified radical form.
Answer:
Step-by-step explanation:
Step 1: Find AB Use Pythagoras Theorem
AB = [tex]\sqrt{AC^{2} -BC^{2} } = \sqrt{12^{2} -8^{2} } = \sqrt{80}[/tex]
Step 2: Find the Area of the triangle ABC
Area = [tex]\frac{1}{2}AB.BC = \frac{1}{2}\sqrt{80}.8 = 4\sqrt{80}[/tex] = [tex]16\sqrt{5}[/tex]
Step 3: Find BD. Use the area of the triangle above
Area = [tex]\frac{1}{2}BD.AC[/tex]
We already known the Area and AC so, we just plug all the number in
BD = [tex]\frac{2. Area}{AC}[/tex] = [tex]\frac{2.16\sqrt{5}}{12}[/tex] = [tex]\frac{8\sqrt{5}}{3}[/tex]
Step 4: Find DC. Use Pythagoras Theorem of the triangle BDC
DC = [tex]\sqrt{BC^{2}-BD^{2} }[/tex] = [tex]\sqrt{8^{2}-(\frac{8\sqrt{5}}{3})^{2}}[/tex] = [tex]\frac{16}{3}[/tex]
HELP PLEASE I ONLY NEED THESE LAST ONES
Answer:
For the first one its 600 yards...and for number 6 its 351.86