Answer/Step-by-step explanation:
Part A:
Yes, the given relation is a function
No, the given is not one-to-one.
The given relation is a function: True
The given one-to-one function: False
For the domain (3, + ∝) or the domain (- ∝,3)
the relation is one-to-one.
Part B:
[tex]y=2(x-3)^2-6[/tex]
[tex]y+6=2(x-3)[/tex]
[tex](x-2)^1=\frac{y}{2}+3[/tex]
[tex]x-2=[/tex] ±[tex]\sqrt{\frac{y}{2}+3}[/tex]
[tex]x=[/tex] ± [tex]\sqrt{\frac{y}{2}+2+2}[/tex]
So, [tex]y^-^1=[/tex] ± [tex]\sqrt{\frac{x}{2}+3}+3[/tex]
Part C:
[tex]y(y^-^1)=2([/tex]±[tex]\sqrt{\frac{x}{1}+3+3-3)^2-6}[/tex]
[tex]=2(\frac{x}{2}+3)-6[/tex]
[tex]x+6-6=x[/tex]
So y and y^-^1 are inverse function.
[RevyBreeze]
You have two cubes that
you fill with water
to make ice cubes. The first cube has a side
length of 3 units. The second cube has a
side length of 5 units. Write an
expression
that you can use to find the total volume of
ice you can make.
Answer:
V = 3^3 = 5^3
Volume of each cube is side^3. To find the volume of both cubes just add the two volumes together.
Step-by-step explanation: Your welcome.
Answer:
total volume = 152 units³
given:
first cube side: 3 unitssecond cube side: 5 unitsvolume of cube: side³using this formula:
total volume = first cube volume + second cube volume
total volume = 3³ + 5³
total volume = 27 + 125
total volume = 152 units³
Sarah normally earns £600 each month. In December she is given a bonus of 1/5 of her normal pay. How much will she now earn this month?
Answer:
She will earn 720 in December(Sorry, can't use the dollar sign.)
Step-by-step explanation:
1/5 of 600 is 120, so you want to add 120 to 600, which would be 720. Hope this helps!
Suppose you were to create a scatter plot of the data for speed and distance traveled. Would you expect to see a
positive, negative, or no relationship betwen the two variables. Explain your answer.
a. negative relationship, as the speed decreases, the distance increases.
b. positive relationship, as the speed decreases, the distance increases.
c. positive relationship, as the speed increases, the distance increases
d. no relationship.
Answer: its c. positive relationship; as the speed decreases, the distance increases.
Step-by-step explanation:
A clothing manufacturer would like to determine whether celebrity endorsements and length of commercial influence a customer's decision to buy its products. In order to estimate this potential influence, the manufacturer premieres its latest series of commercials privately to potential buyers. There are two types of commercials: commercials without celebrities, and commercials with celebrities. There are two lengths of commercials: 30 seconds and 60 seconds. Each potential buyer is randomly assigned a type and length of commercial to view. What are the factors of interest to the manufacturer
Answer:
The correct response will be "whether or not the viewer will buy the product".
Step-by-step explanation:
To consider its clients, the manufacturer requires conducting this research, but the only element of interest would be to figure out whether or not the consumer purchases the product after seeing the ad. The response variable or perhaps the predictor variables determine "not if the audience can buy the advertisement" as well as "whether another advertisement becomes 30 or 60 seconds" including "not when the commercial involves a brand personality" have become the explanatory variables or even just the relationship between the independent variable.The revenue, in thousands of dollars, of a new flavor of liquor is given below as function of the number of gallons (in hundreds), x, sold:
[tex]r(x) = 50x - {x}^{2} [/tex]
What is the maximum revenue? Use units
Answer:
$625,000
Step-by-step explanation:
The maximum revenue will be found where the derivative of the revenue function is zero.
r'(x) = 50 -2x = 0
50 = 2x
x = 25
When 2500 gallons are sold, the revenue is ...
r(25) = 50(25) -25(25) = (50 -25)(25) = 25(25) = 625 . . . thousands
The maximum revenue is $625,000.
what is the area of a triangle with vertices at (0,0), (0,4) and (4,5)?
Answer:
8
Step-by-step explanation:
Let us label these coordinates for our own ease:
A(0,0)
B(0,4)
C(4,5)
Area= [Ax(By-Cy)+Bx(Cy-Ay)+Cx(Ay-By)]÷2
Area = [0(4-5)+0(5-0)+4(0-4)]÷2
Area= [0+0-16]÷2
Area = -8
But since the value can not be negative we have consider a modulus in the formula, thus the value is 8
Kate wants to buy a new bicycle from a sporting goods stores the bicycle she wants normally sells for $440 the store has a sale? where all bicycle cost 3/4 of the regular price what is the sale price of the bicycle …
Given parameters:
Normal selling price off the bicycle = $440
Discount fraction = [tex]\frac{3}{4}[/tex]
Unknown:
Sale price of the bicycle = ?
Solution:
The discounted sale price of the bicycle;
= normal selling price x discount fraction
Input the parameters and solve;
Discounted sale price of the bicycle =[tex]\frac{3}{4}[/tex] x 440
= 3 x 110
= $330
The discounted sale price of the bicycle is $330
Colin’s piano lesson is 45 minutes, or Three-fourths of an hour, long. If he practices 6 different songs and spends an equal amount of time on each song, what fraction of an hour does he spend practicing each song?
Answer:
Colin spends 1/8 of an hour practicing each song
Step-by-step explanation:
Colin's piano lesson is 3/4 of an hour, long.
In that period, he practices 6 different songs, spending an equal amount of time on each one.
This means that each song gets the sixth part of the lesson duration. The fraction that expresses that amount is:
[tex]\displaystyle \frac{\frac{3}{4}}{6}=\frac{3}{24}=\frac{1}{8}[/tex]
Colin spends 1/8 of an hour practicing each song
Answer:
1/8
Step-by-step explanation:
can you help me for this m.c.m is of 10, 3 and 90.
Gracias (Thaks youuuuuuuuuuuuuuuuu)
Answer:
AR 27-10 supplements the MCM and is the ... available. The installation Trial Defense Service office will provide a military lawyer. If the. 3-1 ... away or assaulting you, enlist others to help.
Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. There are 15 questions on the test and the students have been given 55 minutes to complete it.
A Table titled Test Time, showing Number of Questions, Time per Item in minutes, and Total Time in minutes. The first row shows Multiple Choice, with m, 3, and 3 m. The second row shows Free Response, with 15 minus m, 8, and x. The third row shows Total, with 15, blank, and 55.
Which value could replace x in the table?
Answer:
8(15-m)
Step-by-step explanation:
just took the test
Which equation represents a linear function?
2xy +y=9
y= 124 – 5
3y + x2 + x = 0
4x + 2 (y - 1) = 0
A chocolatier makes chocolate bon-bons in the shape of a sphere with a radius of 2cm. The chocolate used in the bon-bons has a density of 1.31 g/cm^3. If the chocolate
used costs $0.06 per gram, how much would the chocolate for 140 bon-bons cost, to
the nearest cent?
We will get the mass of each chocolate sphere, and the cost of 140 of these is $368.56
How much would it cost?
A sphere of radius R has a volume:
V = (4/3)*3.14*R^3
The mass of a sphere of chocolate will be given by the volume times the density, then one ball of chocolate has a mass:
M = (4/3)*3.14*(2cm)^3*(1.31 g/cm^3) = 43.88 g
And we know that the cost is of $0.06 per gram, the cost for 140 of these spheres is:
cost = 140*(44.88 g)*$0.06 = $368.56
If you want to learn more about density, you can read:
https://brainly.com/question/1354972
Joseph earned $53 the first week he worked at Jim’s Candy Store and $62 the next week. How much did Joseph earn his first two weeks?
Explore:
Plan:
Solve:
Examine:
Answer:
$115
Step-by-step explanation:
Because the add does that like answer
I wait that you understand
one bath of cookies calls for 5 cups of flour for every 3 cups of chocolate chips how many cups of flour should be used for 27 cups of chocolate chips
Answer:
16.2
Step-by-step explanation:
0.6 * 27
Hope it helps!!!Brainliest pls!!!the roots of a polynomial equation are 0, 5, and -2. what is the equation written in a factored form and in standard form?
Answer:
Check the pic
Let g(x) = 2x and h(x) = x2 + 4.
Evaluate (h ∘ g)(−2).
20
−12
−16
16
Answer:
Option C, 20 is the answer.
Step-by-step explanation:
Let g(x) = 2x and h(x) = x² + 4
We have to evaluate (h ο g) ( -2 )
Since ( h ο g )x = h [ g(x) ]
= ( 2x)² + 4
= 4x² + 4
( h ο g ) ( -2 ) = 4 ( -2 )² + 4
= 4 × 4 + 4
= 16 + 4
= 20
Hope it helps!!!Brainliest pls!!!Pl ease help what is with give brainlist answer!
-5/6+6/18
1.-1/2
2.12/49
3.-1 and 1/6
4.12
Answer:
option 1 is true. -1/2=-0.5
Answer:
-1/2
Step-by-step explanation:
-5/6 + 6/18
Simplify the second fraction by dividing the top and bottom by 3 ( then we will have like denominators)
-5/6 + 2/6
Combine the numerators since the denominators are the same
-3/6
Divide the top and bottom by 3
-1/2
rewrite in simplest radical form 1 . show each step of your process.
—
-3/6
Answer:
what is this russian math?
Step-by-step explanation:
simplify without calculator(-5)(7)+4*5
Answer:
5*4=9 and if thats -5*7=35 and adding those together gets 35+9=44
Step-by-step explanation:
Answer:
Hello there buddy
Your answer is
35+9=44
Hope it’s helps you buddy
Step-by-step explanation:
~Awesome Jayden
1/5(12b+5) for b = 5/6
Answer:
3
Step-by-step explanation:
eq.
1/5(12×5/6+5)
=1/5×(10+5)
=1/5×15
=3
Answer:
3
Step-by-step explanation:
You bought a notebook for $2 and 6 packs of crayons. If you spent a total of $26, how much was each pack of crayons? *
Answer:
$4
Step-by-step explanation:
It was 4 dollars because you bought one notebook worth two dollars and six-packs of crayons. 26-2 is 24, and 6x4 is 24, so it is worth four dollars.
Find the union of A = {2,3,4} and B = {3,4,5)
Answer:
A U B = {2,3,4, 5}
Step-by-step explanation:
Union means join together
A U B = {2,3,4, 5}
The water level in a tank measures 15 inches and is decreasing 0.5 inches every minute. How many minutes, x, will it take for the water level to measure 9 inches deep?
Evaluate:
[tex] \\ { \displaystyle{ \rm \lim_{x \to1} \left \{ \frac{ {x}^{4 } - {3x}^{2} + 2 }{ {x}^{3} - {5x}^{2} + 3x + 1} \right \} }} [/tex]
[tex] \: [/tex]
Don't Spam
Answer:
To Evaluate:
[tex] \\ { \displaystyle{ \rm \lim_{x \to1} \left \{ \frac{ {x}^{4 } - {3x}^{2} + 2 }{ {x}^{3} - {5x}^{2} + 3x + 1} \right \} }}\\ \\[/tex]
Using L'Hospital's Rule
Let f(x) and g(x) be two common functions which are differentiable on an open Interval , at a point a where,
[tex]\\{ \displaystyle{ \lim_{x \to a}{ \rm{f(x)} = { \displaystyle{ \lim_{x \to a}}} \: { \rm{g(x)}} = 0 \: or \: \pm \infty}}}\\ \\[/tex]
Then,
[tex]\\{ \displaystyle{ \lim_{x \to a} \frac{{ \rm{f (x)}}}{{ \rm{g(x)}}} = { \displaystyle{ \lim_{x \to a }}} \frac{{ \rm{f '(x)}}}{{ \rm{g'(x)}}}}}\\ \\[/tex]
As x to 0 , we have:
[tex]\\{ \displaystyle{ \lim_{x \to 1}}} \left( \large\rm\frac{ {x}^{4} - {3x}^{2} + 2 }{ {x}^{3} - {5x}^{2} + 3x + 1} \right) = \frac{0}{0}\\ \\[/tex]
Therefore,
[tex]\\{ \large{ \displaystyle{ \lim_{x \to1}}} \left( \large \rm\frac{ {x}^{4} - {3x}^{2} + 2}{ {x}^{3} - {5x}^{2} + 3x + 1 } \right) = { \displaystyle{ \lim_{x \to1} { \small{\frac{ {4x}^{3} - 6x}{ {3x}^{2} - 10x + 3 }}} = { \small{\frac{4 - 6}{3 - 10 + 3} }} = - \frac{2}{ - 4} = - \frac{1}{2} }}}\\ \\[/tex]
Hence,
[tex]\\{ \displaystyle{ \lim_{x \to1}{\rm{ \left( \frac{ {x}^{4} - 3 {x}^{2} + 2 }{ {x}^{3} - 5 {x}^{2} + 3x + 1 } \right) = { \boxed{ \red{ - \frac{1}{2} }}}}}}}\\ \\[/tex]
Without using L'Hopital's rule:
Factorize the numerator.
[tex]x^4 - 3x^2 + 2 = (x^2 - 2) (x^2 - 1) = (x^2 - 2) (x + 1) (x - 1)[/tex]
Factorizing cubics is usually a bit trickier. But we know x = 1 makes the denominator vanish, so x - 1 is a factor of the cubic. So for some constants a and b,
[tex]x^3 - 5x^2 + 3x + 1 = (x - 1)^3 + a(x - 1)^2 + b(x - 1)[/tex]
Expanding the right side gives
[tex]x^3 - 5x^2 + 3x + 1 = x^3 + (a - 3)x^2 + (-2a + b + 3)x + a - b - 1[/tex]
Then
[tex]a - 3 = -5 \implies a = -2[/tex]
[tex]-2a + b + 3 = 3 \implies b = -4[/tex]
So we rewrite the limit as
[tex]\displaystyle \lim_{x\to1} \frac{x^4 - 3x^2 + 2}{x^3 - 5x^2 + 3x + 1} = \lim_{x\to1} \frac{(x^2 - 2) (x + 1) (x - 1)}{(x-1)^3 - 2(x-1)^2 - 4(x-1)}[/tex]
x is approaching 1 so x ≠ 1 and we can cancel out factors of x - 1 :
[tex]\displaystyle \lim_{x\to1} \frac{x^4 - 3x^2 + 2}{x^3 - 5x^2 + 3x + 1} = \lim_{x\to1} \frac{(x^2 - 2) (x + 1)}{(x-1)^2 - 2(x-1) - 4}[/tex]
The simplified limand is continuous at x = 1, so we can now evaluate the limit by direct substitution.
[tex]\displaystyle \lim_{x\to1} \frac{x^4 - 3x^2 + 2}{x^3 - 5x^2 + 3x + 1} = \frac{(1^2 - 2) (1 + 1)}{(1-1)^2 - 2(1-1) - 4} = -\frac24 = \boxed{-\frac12}[/tex]
Simplify:
22 - 3 × 6 + 52
A.
38
B.
139
C.
29
D.
65
Answer:
22 - 3 × 6 + 52 = 56
Step-by-step explanation:
Multiply
3×6 = 18
22-18+52
Add and subtract
22-18 = 4
4+52 = 46
Answer:
56
Step-by-step explanation:
To solve we must use the order of operations which is PEMDAS.
P-Parenthesis
E-Exponents
M-Multiplication
D-Division
A-Addition
and S-Subtraction
First we multiply -3 and 6 which gives us -18. So our equation is now 22-18+52.
Next we do addition. -18+52 is 34, plus 22 gives us 56.
Hope this helps :)
What is the answer to a
Answer: a = b*r/n
Step-by-step explanation: Hope this helps :^)
Represent the following expressions as a power of the number a (a≠0):
((a^2)^−2)^5÷(a^15)
Answer:
=0
Step-by-step explanation:
The thickness of photoresist applied towafers in a semiconductor manufacturing at a particular location onthe wafer is uniformly distributed between 0.2050 and 0.2150micrometers.(a) Determine the cumulative distributionfunction of photoresist thickness.(b) Determine the proportion of wafers that exceeds0.2125 micrometers in photoresist thickness.(c) What thickness is exceeded by 10% of thewafers?(d) Determine the mean and variance of photoresistthickness.
Answer:
a
[tex]f(x)= 100 [x - 0.2050][/tex]
b
[tex]P(X > 0.2125) = 0.25 [/tex]
c
[tex]a = 0.2140[/tex]
d
Mean [tex]\mu = 0.21[/tex]
Variance [tex]\sigma ^2 = 0.0000083 [/tex]
Step-by-step explanation:
From the question we are told that
The thickness of photoresist follows a uniform distribution
So
[tex]X\ \~{}\ U \{ 0.2050 , 0.2150 \}[/tex]
Generally the probability density function is mathematically represented as
[tex]F(x) = \left \{ \frac{1}{ 0.2150 - 02050} , 0.2150< x < 0.2150[/tex]
=> [tex]F(x) = \left \{ 100 , 0.2150< x < 0.2150[/tex]
Generally the cumulative distribution function is
[tex]f(x) = \int\limits^{x}_{- \infty} {F(x)} \, dx[/tex]
Here [tex]- \infty[/tex] means the lower limit which in this case is 02050
So
[tex]f(x) = \int\limits^{x}_{0.2050} {100} \, dx[/tex]
[tex]f(x) = 100 \int\limits^{x}_{0.2050} {1} \, dx[/tex]
=> [tex] f(x)=100 [ x ] | \left \ x} \atop {0.2050}} \right.[/tex]
=> [tex]f(x)= 100 [x - 0.2050][/tex]
Generally the proportion of wafers that exceeds 0.2125 is mathematically represented as
[tex]P(X > 0.2125) = 1 - F(0.2125)[/tex]
=> [tex]P(X > 0.2125) = 1- 100[0.2125 - 0.2050][/tex]
=> [tex]P(X > 0.2125) = 0.25 [/tex]
Generally the thickness which is exceeded by 10% of the wafers is mathematically represented as
[tex]P(X > a ) = 0.10[/tex]
=> [tex]1 - F(a) = 0.10[/tex]
=> [tex]1 -100 (a - 0.2050) = 0.10[/tex]
=> [tex]100(a -0.2050) = 0.90[/tex]
=> [tex]a - 0.2050 = 0.009[/tex]
=> [tex]a = 0.2140[/tex]
Generally the mean is mathematically represented as
[tex]\mu = \frac{ 0.2050 -0.2150 }{2}[/tex]
=> [tex]\mu = 0.21[/tex]
Generally the variance is mathematically represented as
[tex]\sigma ^2 = \frac{1}{12} [0.2150 - 0.2050]^2[/tex]
=> [tex]\sigma ^2 = 0.0000083 [/tex]
What's 5x5+6x3-1
Me brain is no working, please help
Answer:
42
Step-by-step explanation:
5*5+6*3-1
25+6*3-1
25+18-1
43-1
=42
I hope this helped, please give me Brainliest if it did. :)
HELP!!! 100 POINTS ANSWER FAST
Answer:
(x - 4)^2 = 9Step-by-step explanation:
Completing the square
x^2 - 8x + 7 = 0x^2 - 2*4x + 16 - 9 = 0(x^2 - 2*4x + 4^2) = 9 (x - 4)^2 = 9The blanks are
- 4 and 9Answer:
(x^2-4)^2 = 9
Step-by-step explanation:
First, isolate the constant:
x^2-8x = -7
Then, since (a-b)^2 = a^2-2ab+b^2, you should add 16(4^2) to both sides:
x^2-8x+16 = 9
Now, we can rewrite the right-hand side as (a-b)^2:
(x-4)^2 = 9