Answer:
42 squared is 1764
Step-by-step explanation:
Answer: (x + 42)(x - 42)
Step-by-step explanation:
factorise: x^2 - 42^2
. x^2 - 42^2 have ^2 in common (so you can ignore that).
. put in brackets (x - 42)(x + 42)
. +/- any order really doesn't matter :D
The price of a floor tile is $3 per square foot, and the cost of shipping is $20. You are adjusting the size of your bathroom according to the space availability. You would like to estimate the rate of change of cost for flooring that you expect when you change the size of the square bathroom of current length 10 feet. Assume xx to be the length of a square shaped bathroom. Include units in all parts. a. Calculate the average rate of change of cost when you change your bathroom from 10 feet to 12 feet long. b. Calculate the instantaneous rate of change of cost at length 10 feet. c. If the cost of shipping also depends on the length according to \$20(1 \sin{x})$20(1 sinx), what is the instantaneous change of cost at length 10 feet.
Answer:
a
[tex]A = \$66 \foot [/tex]
b
tex]C(10)' = \$60 / feet[/tex]
c
[tex]C(10)' = \$79.696 \ feet [/tex]
Step-by-step explanation:
From the question we are told that
The price per square foot of a floor tile is [tex]p = \$ 3[/tex]
The cost of shipping is [tex]s = \$ 20[/tex]
The current length of the square bathroom is x = 10 ft
The new length is [tex]x_ 1 = 12 \ ft[/tex]
Generally the equation representing the cost of the square tile is mathematically represented as
[tex]C(x) = 3x^2 + 20[/tex]
Generally the average rate of change of cost is mathematically represented as
[tex]A = \frac{ cost \ for\ a \ 12 feet \ bathroom - cost \ for\ a \ 10 feet \ bathroom }{12 feet - 10 feet}[/tex]
Generally the cost for flooring a 12 feet square bathroom is mathematically represented as
[tex]C(12) = 3(12)^2 + 20[/tex]
=> [tex]C(12) = \$ 452 [/tex]
Generally the cost for flooring a 10 feet square bathroom is mathematically represented as
[tex]C(10) = 3(10)^2 + 20[/tex]
=> [tex]C(10) = \$320[/tex]
So
[tex]A = \frac{ 452- 320 }{12 feet - 10 feet}[/tex]
=> [tex]A = \$66 \foot [/tex]
Generally the instantaneous rate of change of cost is obtained by the differentiating the cost function as follows
[tex]C(x) = 3x^2 + 20[/tex]
[tex]C(x)' = \frac{dC(x)}{dx} = 6x[/tex]
So the instantaneous rate of change of cost at length 10 feet is mathematically represented as
[tex]C(10)' = 6(10)[/tex]
=> [tex]C(10)' = \$60 / feet[/tex]
Generally given that the new cost function is
[tex]C(x) = 20(1 + sinx) + 3x^2[/tex]
Now the instantaneous rate of change of cost will now be
[tex]C(x)' = 20cos(x) + 6x[/tex]
So the instantaneous rate of change of cost at length 10 feet is mathematically represented as
[tex]C(10)' = 20cos(10) + 6* 10 [/tex]
=> [tex]C(10)' = \$79.696 \ feet [/tex]
The concentration of particles in a suspension is 50 per mL. A 5 mL volume of the suspension is withdrawn. a. What is the probability that the number of particles withdrawn will be between 235 and 265? b. What is the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52? c. If a 10 mL sample is withdrawn, what is the probability that the average number per mL of particles in the withdrawn sample is between 48 and 52? d. How large a sample must be withdrawn so that the average number of particles per mL in the sample is between 48 and 52 with probability 95%?
Answer:
(a) 0.6579
(b) 0.2961
(c) 0.3108
(d) 240
Step-by-step explanation:
The random variable X can be defined as the number of particles in a suspension.
The concentration of particles in a suspension is 50 per ml.
Then in 5 mL volume of the suspension the number of particles will be,
5 × 50 = 250.
The random variable X thus follows a Poisson distribution with parameter, λ = 250.
The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.
The mean of the approximated distribution of X is:
μ = λ = 250
The standard deviation of the approximated distribution of X is:
σ = √λ = √250 = 15.8114
Thus, [tex]X\sim N(250, 250)[/tex]
(a)
Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:
[tex]P(235<X<265)=P(\frac{235-250}{15.8114}<\frac{X-\mu}{\sigma}<\frac{265-250}{15.8114})[/tex]
[tex]=P(-0.95<Z<0.95)\\=P(Z<0.95)-P(Z<-0.95)\\=P(Z<0.95)-[1-P(Z<0.95)]\\=2P(Z<0.95)-1\\=(2\times 0.82894)-1\\=0.65788\\\approx 0.6579[/tex]
Thus, the value of P (235 < X < 265) = 0.6579.
(b)
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{5}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{5}})[/tex]
[tex]=P(-0.28<Z<0.28)\\=P(Z<0.28)-P(Z<-0.28)\\=P(Z<0.28)-[1-P(Z<0.28)]\\=2P(Z<0.28)-1\\=(2\times 0.64803)-1\\=0.29606\\\approx 0.2961[/tex]
Thus, the value of [tex]P(48<\bar X<52)=0.2961[/tex].
(c)
A 10 mL sample is withdrawn.
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{10}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{10}})[/tex]
[tex]=P(-0.40<Z<0.40)\\=P(Z<0.40)-P(Z<-0.40)\\=P(Z<0.40)-[1-P(Z<0.40)]\\=2P(Z<0.40)-1\\=(2\times 0.65542)-1\\=0.31084\\\approx 0.3108[/tex]
Thus, the value of [tex]P(48<\bar X<52)=0.3108[/tex].
(d)
Let the sample size be n.
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{n}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{n}})[/tex]
[tex]0.95=P(-z<Z<z)\\0.95=P(Z<z)-P(Z<-z)\\0.95=P(Z<z)-[1-P(Z<z)]\\0.95=2P(Z<z)-1\\P(Z<z)=\frac{1.95}{2}\\\\P(Z<z)=0.975[/tex]
The value of z for this probability is,
z = 1.96
Compute the value of n as follows:
[tex]z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}\\\\1.96=\frac{48-50}{15.8114/\sqrt{n}}\\\\n=[\frac{1.96\times 15.8114}{48-50}]^{2}\\\\n=240.1004\\\\n\approx 241[/tex]
Thus, the sample selected must be of size 240.
Which of the following expressions is not equivalent to -4.5 • -8?
-8 • -4.5
8 • 4.5
(8)(-4.5)
(4.5)(8)
Answer: (8)(-4.5)
Step-by-step explanation:
If you were to multiply-4.5 • -8 that would equal a positive number but if you were to divide (8)(-4.5) it would equal a negative number
Answer:
(8)(-4.5)
Step-by-step explanation:
please mark brainliest
A city has a population of 38802500 people. Estimate this population to the nearest ten million
Answer:
40,000,000 or 40 million
Step-by-step explanation:
Classify the following triangle. Check all that apply.
A. Right
B. Acute
C. Equilateral
D. Scalene
E. Obtuse
F. Isosceles
What is the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5?
What is the answer to 6x + 7= -x + 70
Answer:
x = 9
Step-by-step explanation:
6x + 7 = -x + 70
~Subtract 7 to both sides
6x = -x + 63
~Add x to both sides
7x = 63
~Divide 7 to both sides
x = 9
Best of Luck!
SUPER EASY, ILL GIVE A BRAINLIEST THINGY TO FIRST ANSWER. At the store, two brands are sold. Brand A is offered as 6 for $0.85. Brand B is offered as 8 for $1.00. Which brand is the better buy?
Answer:
8 for $1.00
step by step explanation:
Simplify: b3·b−5·b11
A) b9
B) b15
C) b19
D) b-165
A = 2/3 * (B + C)
Solve for C
Find all solutions of the equation x^2+3x+5=0 and express them in the form a+ bi
Answer:
in you question there is the ans hibben
Step-by-step explanation:
x^2+3x+5=0 =a+ bi
what is 10 times 20,00x
what is meaning of integers
whole numbers, plus their counterparts less than zero, and zero
Negative integers(less than 0) being: –1, –2, –3 exc.
Positive integers(more than 0) being: 1, 2, 3 exc.
Answer:
Integers are whole numbers like -3, -2, -1, 1, 2, 3, 4. They can't be fractions or decimals though
A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 31% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution?
Answer:
Explained below.
Step-by-step explanation:
A Binomial experiment has the following properties:
There are a fixed number of trials (n). Each trial are independent of the others. Each trial has only two outcomes: Success and Failure Each trial has the same probability of success (p).If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.
The number of employees selected is, n = 20.
Every employees response is independent of the others.
Each employees response is either: Yes or No.
The probability of an employee responding as "yes" is, p = 0.31.
Thus, the experiment being performed is a binomial experiment.
So, the probability distribution for the number of employees believing their company president has low ethical standards can be modelled by a binomial probability distribution.
But the number of years of experience cannot be modelled by a binomial probability distribution. Because every employee will have different answer for this question.
Solve for x: 2x-1-x+3=5
Answer:
given
2x-1-x+3=0
x+2=0
x= -2
hope it helps you mate
please mark me as brainliast...
Answer:
2x-1-x+3=5
subtract 3 both sides
add 1 both sides
after that now its
2x-x=3
2x-x= x
x=3 thats the answer
SOMEONE PLEASE HELP ME... GOD WILL BLESS U...
Kavitha is 9 years younger than Lizzy. 8 years ago, Lizzy was 2 times as old as Kavitha reduced by 1. How old are they now?
Answer: Kavitha is 18 and Lizzy is 27
Step-by-step explanation: 8 years ago, Kavitha was 10 and Lizzy was 19.
10 × 2 = 20
20 - 1 = 19
Kavitha is 9 years younger than Lizzy because 27 - 9 = 18
9514 1404 393
Answer:
Kavitha is 19 and Lizzy is 28
Step-by-step explanation:
Let k and l represent the current ages of Kavitha and Lizzy.
k = l -9 . . . . . Kavitha is 9 years younger
l -8 = 2(k -8 -1) . . . . 8 years ago, Lizzy was 2 times as old as Kavitha was 9 years ago
l -8 = 2(l -9 -9) . . . . substitute for k
l -8 = 2l -36 . . . . . . eliminate parentheses
28 = l . . . . . . . . . . . add 36 - l
k = 28 -9 = 19
Kavitha is 19; Lizzy is 28.
Determine whether the lines are parallel, perpendicular, or neither. EM has the
slope of 5/6 and TC has the slope of 6/5
Answer:
Not sure, not good with lines, but I think I did it correctly. EM = Neither TC= Perpendicular.
Two points that are on the same line are called what?
A
coplanar
B
collinear
C
supplementary
D
parallel
Answer:
That would be B Collinear
Answer:
B: Collinear
Step-by-step explanation:
Let's look at the answer choices, shall we?
-Coplanar is two lines or points on the same plane.
-Supplementary is where two angles measure to 180 degrees
- Parallel lines are where two lines have the same slope and will never intersect
The only other option is collinear, which happens to have the definition of two points on the same line.
I think #1 is wrong but i can't figure it out
Answer:
Step-by-step explanation:
x=6
y=4
5x-y^2 :2
5×6 - 4 ^2 :2
30 - 16 :2
30 - 8
22 (the wright answer)
Circle the mistake :x =6 and y =4 it's not x=4 and y=6
Explain the mistake :when you calculed with x=4 and y=6 the final answer is wrong.
Solve for x. Show each step of the solution 4.5 ( 8 - x ) + 36 = 102 - 2.5 ( 3x + 24)
Answer:
X=-10
Step-by-step explanation:
Answer:
x = -10
Step-by-step explanation:
4.5(8-x) + 36 = 102 - 2.5(3x+24)
36 - 4.5x + 36 = 102 - 7.5x - 60
72 - 4.5x = 42 - 7.5x
72 + 3x = 42
3x = -30
x = -10
(2x+4) + (3x-9) simplify
Four friends went to the movies.
Each person bought a movie ticket, and the total the four friends spent on the tickets was $52.
Which equation can be used to find the cost of each tickets
A) 4+x=52
B) x - 4= 52
C) 4x=52
D)x/4=52
The equation that can be used to find the cost of each ticket is 4x = 52.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 6 is an equation.
We have,
Number of people who bought the tickets = 4
The total cost of tickets = $52
Now,
The cost of each ticket.
= 52 ÷ 4
= 13
Now,
Cost of one ticket = x
4x = 52
x = 52/4 = 13
Thus.
The cost of each ticket is $13.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
Expand the expression
3(x-6)
Answer:
3x-3(6) = 3x-18
Step-by-step explanation:
We want to factor the following expression: 25x^6-30x^3+9 We can factor the expression as (UVwhere Uand are either constant integers or single-variable expresSions 1) What are U and V?
Answer:
U = 5x^3
V = 3
(5x^3 - 3)^2
Step-by-step explanation:
(1) The value of U and V are U = 5x³ and V = 3.
(2) The factored form of 25x⁶ - 30x³ + 9 is (5x³3 - 3)²
What is a quadratic equation?A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
We can factor the expression 25x⁶ - 30x³ + 9 by first noticing that each term is a perfect square:
25x⁶ = (5x³)²
30x³ = 2(15x³)
9 = 3²
Now we can write the expression as the difference of two squares:
25x⁶ - 30x³ + 9 = (5x³)² - 2(5x³)(3) + 3²
Let U = 5x³ and V = 3. Then we have:
(5x³3 - 3)²
Therefore, the factored form of 25x⁶ - 30x³ + 9 is (5x³3 - 3)².
To learn more about the quadratic equation;
https://brainly.com/question/17177510
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which is the equation of the line that passes through the points (-4,-8) and (1,3)
Answer:
−5x+13y=84
Step-by-step explanation:
I hope this is good :)
I buy a printer for $125 and ink cartridges cost $15 each. Explain the relationship between the cost of ink cartridges and the total cost.
Answer:
125+15c=t
Step-by-step explanation:
Every cartridge is worth $15, so that would be 15c aka 15 x however many cartridges you purchase. Then the printer is $125, and its not changing so there will be no variable. Put those two amounts together and you'll get the total cost. (Hopefully I explained this well enough.)
During the years 1992 through 1996, the average number of
green
grapes, g, sold at a farmer's market can be modeled by
g=-0.1312 + 1.12t + 54.33.
The average number of red grapes, r, sold by the farmer's market can
be modeled by
r=0.00772
0.6787+77.18. Determine the model representing the total
number of grapes, n, sold from 1992 through 1996.
Answer:
133.18522
Step-by-step explanation:
g=55.3188
r=77.86642
77.86642+55.3188
133.18522
Ming li spent $15 at the movies. She then earned $30 babysitting. She spent $12 at the bookstor. She now has $18 left. How much money did ming li have to begin woth
Answer:
$15
Step-by-step explanation:
30 - (12+15)
30-27=3
18-3=15
Hope this helps ;)
Solve the following system of equations.
6x -5y=13 & 9y-15+2x=0
x = 3
y = 1
Step-by-step explanation:Hi !
6x - 5y = 13
9y - 15 + 2x = 0
6x - 5y = 13
2x + 9y = 15 | ×(-3)
6x - 5y = 13
- 6x - 27y = - 45
add
6x - 6x - 5y - 27y = 13 - 45
- 32y = - 32 | ×(-)
32y = 32
y = 1
replace y = 1
6x - 5(1) = 13
6x - 5 = 13
6x = 13 + 5
6x = 18
x = 3
Good luck !
Is the function even, odd, or neither?
You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even. If you end up with the exact opposite of what you started with (that is, if f (–x) = –f (x), so all of the signs are switched), then the function is odd.
In all other cases, the function is "neither even nor odd".
Let's see what this looks like in action:
Determine algebraically whether f (x) = –3x2 + 4 is even, odd, or neither.
If I graph this, I will see that this is "symmetric about the y-axis"; in other words, whatever the graph is doing on one side of the y-axis is mirrored on the other side:
graph of y = –3x^2 + 4
This mirroring about the y-axis is a hallmark of even functions.
Also, I note that the exponents on all of the terms are even — the exponent on the constant term being zero: 4x0 = 4 × 1 = 4. These are helpful clues that strongly suggest to me that I've got an even function here.
But the question asks me to make the determination algebraically, which means that I need to do the algebra.
So I'll plug –x in for x, and simplify:
f (–x) = –3(–x)2 + 4
= –3(x2) + 4
= –3x2 + 4
I can see, by comparing the original function with my final result above, that I've got a match, which means that:
f (x) is even