Answer:
a:b = 3:5 it can be also written as 3 x 6 : 5 x 6 = 18 : 30.
b: c = 6 :7 ' '' '' '' '' 6 x 5 : 7 x 5 = 30 : 35.
a:b:c = 18 : 30 : 35
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 is the answer to a
Answer: a = b*r/n
Step-by-step explanation: Hope this helps :^)
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 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?
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.
Write an equation that can be described by the statement: y is equal to 1/3 of x.
Enter the correct answer in the box.
Answer: [tex]y=\frac{1}{3} x[/tex]
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.
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
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:
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. :)
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!
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:
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!!!Which equation represents a linear function?
2xy +y=9
y= 124 – 5
3y + x2 + x = 0
4x + 2 (y - 1) = 0
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}
You can work a total of no more than 10 hours each week at your iwo jobs. House cleaning pays $5 per hour and
your sales job pays $8 per hour. You need to earn at least $56 each week to pay your bills. Write a system of
inequalities that show the various numbers of hours you can work at each job.
I'm not 100% sure but it's not u
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:
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
Which of the following are factor pairs for 72? You will select two.
2 x 36
3 x 18
6 x 12
8 x 8
Answer:
The two factor pairs for 72 are the following:
2 × 366 × 12Step-by-step explanation:
Of you take the answer to each equation only these two equal 72, leaving them as factors.
3 × 18 is equal to 54
8 × 8 is equal to 65
Which leaves them being the wrong answer
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
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 :)
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
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]
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
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
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:
Elsa earns 5140 for working 20 hours
1) What is Elsa's rate of pay for each hour she works?
A) 5650 per hour
B) $7.00 per hour
$7.25 per hour
D) $2.00 per hour
Answer:
$2.57
Step-by-step explanation:
divide 5,140 by 20,
5,140/20=257=2.57
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
What is the quotient when 7.8 is divided by 6 ?
Answer:
the anser is 1.3
have a nice day!
4/7×4/5×7/9
Write your answer in fraction in simplest form
Answer:
16/45 for fraction, or 0.35 for decimal
Step-by-step explanation:
4/7 x 4/5 × 7/9
reduce numbers with greatest common factor 7
4 × 4/5 × 1/9
calculate the product = 4 × 4 × 1 = 16
5 × 9 = 45
16/45 or 0.35