To calculate the volume of a chemical produced in a day a chemical manufacturing company uses the following formula below:
[tex]V(x)=[C_1(x)+C_2(x)](H(x))[/tex]
where represents the number of units produced. This means two chemicals are added together to make a new chemical and the resulting chemical is multiplied by the expression for the holding container with respect to the number of units produced. The equations for the two chemicals added together with respect to the number of unit produced are given below:
[tex]C_1(x)=\frac{x}{x+1} , C_2(x)=\frac{2}{x-3}[/tex]
The equation for the holding container with respect to the number of unit produced is given below:
[tex]H(x)=\frac{x^3-9x}{x}[/tex]
a. What rational expression do you get when you combine the two chemicals?
b. What is the simplified equation of ?
c. What would the volume be if 50, 100, or 1000 units are produced in a day?
d. The company needs a volume of 3000 How many units would need to be produced in a day?
Answers
Answer:
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
[tex]V(50) = 2548.17[/tex] [tex]V(100) = 10098.10[/tex] [tex]V(1000) = 999201.78[/tex]
[tex]x = 54.78[/tex]
Step-by-step explanation:
Given
[tex]V(x) = [C_1(x) + C_2(x)](H(x))[/tex]
[tex]C_1(x) = \frac{x}{x+1}[/tex]
[tex]C_1(x) = \frac{2}{x-3}[/tex]
[tex]H(x) = \frac{x^3 - 9x}{x}[/tex]
Solving (a): Expression for V(x)
We have:
[tex]V(x) = [C_1(x) + C_2(x)](H(x))[/tex]
Substitute known values
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
Solving (b): Simplify V(x)
We have:
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
Solve the expression in bracket
[tex]V(x) = [\frac{x*(x-3) + 2*(x+1)}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{x^2-3x + 2x+2}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
Factor out x
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * \frac{x(x^2 - 9)}{x}[/tex]
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * (x^2 - 9)[/tex]
Express as difference of two squares
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * (x- 3)(x + 3)[/tex]
Cancel out x - 3
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)}] *(x + 3)[/tex]
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Solving (c): V(50), V(100), V(1000)
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Substitute 50 for x
[tex]V(50) = [\frac{(50^2-50+2)(50 + 3)}{(50 + 1)}][/tex]
[tex]V(50) = \frac{(2452)(53)}{(51)}][/tex]
[tex]V(50) = 2548.17[/tex]
Substitute 100 for x
[tex]V(100) = [\frac{(100^2-100+2)(100 + 3)}{(100 + 1)}][/tex]
[tex]V(100) = \frac{9902)(103)}{(101)}[/tex]
[tex]V(100) = 10098.10[/tex]
Substitute 1000 for x
[tex]V(1000) = [\frac{(1000^2-1000+2)(1000 + 3)}{(1000 + 1)}][/tex]
[tex]V(1000) = [\frac{(999002)(10003)}{(10001)}][/tex]
[tex]V(1000) = 999201.78[/tex]
Solving (d): V(x) = 3000, find x
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
[tex]3000 = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Cross multiply
[tex]3000(x + 1) = (x^2-x+2)(x + 3)[/tex]
Equate to 0
[tex](x^2-x+2)(x + 3)-3000(x + 1)=0[/tex]
Open brackets
[tex]x^3 - x^2 + 2x + 3x^2 - 3x + 6 - 3000x - 3000 = 0[/tex]
Collect like terms
[tex]x^3 + 3x^2- x^2 + 2x - 3x - 3000x + 6 - 3000 = 0[/tex]
[tex]x^3 + x^2 -3001x -2994 = 0[/tex]
Solve using graphs (see attachment)
[tex]x = -54.783[/tex] or
[tex]x = -0.998[/tex] or
[tex]x = 54.78[/tex]
x can't be negative. So:
[tex]x = 54.78[/tex]
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Step-by-step explanation:
Answer:
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Answers
Answer:
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Given the equation;2x^2 - 9x -1 = 0
From the quadratic formula;
-b ±√ b^2 -4ac/2a
We have;
x= -(-9) ± √(-9)^2 - -4(2)(-1)/2(2)
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Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Three randomly selected computer engineers have following salaries (in $1000s): 70, 80, 90. The average and the standard deviation of the data in the sample are 80 and 10. Using hypothesis testing, determine if this sample provides a sufficient evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is different from $60,000.
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b. alternative hypothesis.
c. test statistic.
d. acceptance region.
Answers
Answer:
H0 : μ = 60000
H1 : μ ≠ 60000
Test statistic = 3.464
Step-by-step explanation:
Given :
Sample mean salary, xbar = 80000
Sample standard deviation, s = 10000
Population mean salary , μ = 60000
Sample size, n = 3
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H0 : μ = 60000
H1 : μ ≠ 60000
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Answers
Answer:
17 days
Step-by-step explanation:
as you see, 4=2^2
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so we have a number sequence:
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multiply (1) by 2 we have:
2^2+2^4 +...+2^(n+1)=520000 (2)
(2) minus (1) we have:
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It will take her about 17 days to buy the car worth 260000 cents
If a student decides she wants to save money to buy a used car that cost $2600 (260,000 cents)
If she saves 2 cents the first day and doubles the amount thereafter, the sequence of savings will be:
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This sequence is geometric in nature
In order to determine how long it will take her to save 260,000, we will use the sum of a GP formula expressed as:
[tex]S_n = \frac{a(r^n-1)}{r-1}[/tex]
Given the folowing
a = 2
r = 4/2 = 8/4 = 2
Sn = 260,000
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[tex]260000= \frac{2(2^n-1)}{2-1}\\260000/2=2^n-1\\130000 = 2^n - 1\\2^n = 130000 + 1\\2^n = 130001\\nlog 2=log130001\\n = \frac{log130001}{log2} \\n \approx 17[/tex]
This shows that it will take her about 17 days to buy the car worth 260000 cents
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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B) Yes, no two sets of ordered pairs occupy the same location.
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D) No, some of the ordered pair in this graph have the same first element.
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Answer:
D
Step-by-step explanation:
if you draw any vertical line through a function it should have a max of one intersection point so if the graph, reading from left to right doubles back on itself, it is not a function
Simplify 4(a + 1) + 5(a + 2).
Answers
Answer: [tex]9a+14[/tex]
Step-by-step explanation:
Simplify: [tex]4(a+1)+5(a+2)[/tex]
Step 1. Distribute 4 into a and 1. By distributing you would get 4a and 4.
[tex]4*a=4a. \\4*1=4[/tex]
Step 2. Plug 4a+4 back into the remaining equation, which can be viewed below:
[tex]4a+4+5(a+2)[/tex]
Step 3. Distribute, [tex]5(a+2)[/tex] again. Same principle as what you did previously. You should get 5a and 10.
[tex]5*a=5a.\\5*2=10.[/tex]
Step 4. Plug 5a+10 back into the leftover equation, which is as follows.
[tex]4a+4+5a+10[/tex]
Step 5. Combine like terms. Which is broken down below,
[tex]4a+5a=9a.\\4+10=14.[/tex]
Once you're done combining like terms, you'll get the simplified answer which is: [tex]9a+14[/tex]
Answer:
9a +14
Step-by-step explanation:
4(a + 1) + 5(a + 2)
Distribute
4a+4 +5a+10
Combine like terms
4a+5a +4+10
9a +14
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Answers
Answer:
4
Step-by-step explanation:
The given data is :
8, 10, 12,14,16,18,20
We need to find the standard deviation. Here,
Count = 7
Sum, Σx: 98
Mean, μ: 14
The standard deviation is given by :
[tex]\sigma=\sqrt{\dfrac{1}{N}\Sigma(x_i-\mu)^2}[/tex]
or
[tex]\sigma^2=\dfrac{1}{N}\Sigma(x_i-\mu)^2\\\\=\dfrac{(8-14)^2+...+(20-14)^2}{7}\\\\=\dfrac{112}{7}\\\\\sigma^2=16\\\\\sigma=4[/tex]
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Factor the following expressions completely. Show and check all work on your own paper.
x^2+169
Answers
Answer with rational numbers: Not Factorable
Answer with imaginary numbers: (x-13i)(x+13i)
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Answers
Answer:
B
Step-by-step explanation:
-2/3x<31/3
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x>-15 1/2
Answer:
x > - 15 1/2
Step-by-step explanation:
-2/3 x -10 < 1/3
Multiply each side by 3
3(-2/3 x -10 < 1/3)
-2x -30 < 1
Add 30 to each side
-2x-30+30 <1+30
-2x < 31
Divide by -2 remembering to flip the inequality
-2x/-2 > 31/-2
x > -31/2
x > - 15 1/2
need help on this math problem
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Answer:
[tex]-5, 18, \sqrt{13}[/tex]
Step-by-step explanation:
We can solve the first equation, f of -3. The value of the function f is [tex]\frac{1+x^2}{x+1}[/tex], and plugging in -3 gets us [tex]\frac{1+9}{1-3}[/tex], this results in 10 divided by negative 2, which is negative 5.
Now, we must solve g of negative one third. The function g is defined as [tex]|9x-15|[/tex]. Plugging in negative one third into the question gets us [tex]|9(-\frac{1}{3})-15|[/tex]
9 times negative one third is -3, and -3 minus 15 is -18. The absolute value of -18 is 18.
Now, we must solve h of negative 2, and h is defined as [tex]\sqrt{-3-8x}[/tex]. Plugging in negative 2, we have [tex]\sqrt{-3-8(-2)}[/tex]. Negative 8 times negative 2 is positive 16, and 16 minus 3 is 13. The answer is the square root of 13
SOMEONE PLEASE HELP ME!!!!!!!!
Answers
9514 1404 393
Answer:
PQ = 46
Step-by-step explanation:
Midsegment ST is half the length of base segment PQ.
2×ST = PQ
2×(5x -22) = 3x +19
10x -44 = 3x +19 . . . . . . . eliminate parentheses
7x = 63 . . . . . . . . . . . . add 44-3x
x = 9 . . . . . . . . . . . . divide by 7
PQ = 3x +19 = 3×9 +19
PQ = 46
Please help 20 points. I will give Brainly to who ever get it right.
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The range is the an interval on the y-axis where the function is defined.
You can see that your function is y-wise going all the way down to negative infinity but then stops and continues the path along 2 on the upper bound.
The inequality describing the interval is thusly B,
[tex]-\infty\lt y\lt2[/tex]
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Hi! I'd appreciate it if you could help me on this question. The question I need help with is question 42. Thank you If you could help me!!
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9514 1404 393
Answer:
19 hours
Step-by-step explanation:
Add up the numbers:
3×3.5 +2×2.0 +4.5 = 19
Jacob trains 19 hours per week.
During a 1966 Tabiona High School track meet, Levere ran the 100 yard dash in
10.63 seconds. Ross took second with a time of 10.98 seconds.
a. Levere’s time was _______% shorter than Ross’.
b. Ross’ time was _______% longer than Levere’s.
c. Levere’s time was _______% of Ross’.
Answers
Answer:
a) 3.19
b) 3.29
c) 96.81
Step-by-step explanation:
Question a:
Levere's: 10.63s
Ross: 10.98s
10.98 - 10.63 = 0.35s shorter than 10.98s, so:
0.35*100%/10.98 = 3.19% shorter.
Question b:
35s longer than 10.63s, so:
0.35*100%/10.63 = 3.29% longer.
Question c:
3.19% shorter, so 100 - 3.19 = 96.81% of Ross.
What error, if any, did Noah make?
Answers
Answer:
breathing, jk buddy
Step-by-step explanation:
what is the union of these two sets? E={-1,0,4,5,6,7} G={-2,-1,1,2,3,8}
Answers
Answer:
U={-2,-1,0,1,2,3,4,5,6,7,8}
Suppose 1 in 5 (1/5) JWU students own their own car. If four students are randomly selected, what is the probability that all four own their car?
Answers
Answer:
1/625 = 0.0016
Step-by-step explanation:
update, oh sorry, this is about 4 picks and not 5.
so, it is 1/5⁴ = 1/625 = 0.0016
1 in 5 own their own car.
that is 20% or a chance of 1/5 = 0.2 of picking a student owning a car.
let's assume that the total number of students is large enough that each pick does not change the individual probabilities.
each event (picking a student and checking the ownership of a car) is independent and non-overlapping.
so, the probability that all 5 own a car is the chance of picking the 5th student owning a car AND all 4 previous student picks owning a car.
the probability that all 4 previous picks own a car is the chance of picking the fourth student owning a car AND all 3 previous student picks owning a car.
the probability that all 3 previous picks own a car is the chance of picking the third student owning a car AND all 2 previous student picks owning a car.
the probability that all 2 previous picks own a car is the chance of picking the second student owning a car AND the previous student pick owning a car.
the probability that the first student pick owns a car is 1/5 or 0.2
so, we have a clean
1/5×1/5×1/5×1/5×1/5 = 1/5⁵ probability = 1/3125 = 0.00032
