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Related Questions
An accounting firm has 900 hours of on-the-clock staff time and 100 hours of reviewing time available to assign each week. The firm charges $300 for a tax return and $2000 for a small business audit. A small business audit requires 100 hours of staff time and 10 hours of review time. A tax return requires 12.5 hours of staff time and 2.5 hours of review time. In order to maximize their revenue for the week, how many small business audits and how many tax returns should the firm schedule? What is their maximum revenue for the week?
Constraints:
Objective Formula:
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Answer:
The maximum revenue for the week is $19,000.
Step-by-step explanation:
Denote the variables as follows:
X = small business audit
Y = tax return
The maximizing function is:
Z = 2000·X + 300·Y
The maximizing function is subjected to the constraints:
100·X + 10·Y ≤ 900
10·X + 2·Y ≤ 100
0 ≤ X and 0 ≤ Y
The problem can be solved using the simples method as follows:
Let s and t be slack variables.
Initial:
x y s t b Basic
100 10 1 0 900 s (departing)
12.5 2.5 0 1 100 t
Z -2000 -300 0 0 0
(entering)
Step 1:
x y s t b Basic
1 1/10 1/100 0 9 x
0 1 -1/10 1 10 t (departing)
Z 0 -100 20 0 18000
(entering)
Step 2:
x y s t b Basic
1 0 1/50 -1/10 8 x
0 1 -1/10 1 10 y
Z 0 0 10 100 19000
(entering)
The optimal solution is:
X = 8
Y = 10
The maximum revenue for the week is $19,000.
Lex be a random variable that represents the pH of arterial plasma (le, acidity of the blood). For healthy adults, the mean of the distribution is - 7.4.1 A new drug for arthritis has
been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with
sample standard deviations - 2.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.
USE SALT
(a) what is the level of significance?
what is the value of the sample test sisse? (Round your answer to three decimal places)
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Answer:
2.304
Step-by-step explanation:
Match the number with its opposite.
Match Term Definition
9.2 A) 2.9
−2.9 B) −9.2
−1.4 C) −4.1
4.1 D) 1.4
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-2.9 - A
-1.4 - D
4.1 - C
Explanation: the opposite of a number is the same number with the sign flipped
Answer:
9.2 - B
-2.9 - A
-1.4 - D
4.1 - C
Step-by-step explanation:hope this helps
Can someone please help?
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hope this helps
For how many different positive integers n is each of n, n+2, and n+4 a prime number?
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Answer:
3,5,7
Step-by-step explanation:
odd numbers is a multiple of three, at least one of them can't be prime
hope this helps there is 1 of them
3. A store manager reports that the mean grocery bill at her store on a Saturday is between
$28.25 and $36.75. To do this, she considered a random sample of customers that Saturday.
What was the sample mean? (Remember that the sample mean is the center of the confidence
interval). What was the margin of error?
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Answer:
Hope you understand, and never stop striving to learn!
Step-by-step explanation:
The sample mean is both values added together then divided by 2.
$46.63
The margin of error is the low value divided by the high value * 100% =76.8% (then you have to minus this from 100% so the margin of error is 23.2%)
Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water. Peggy made a 12-liter batch of iced tea with 90 tea bags.
What will Kermit think of Peggy's iced tea?
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Answer:
He will love the Tea
Step-by-step explanation:
12 divided by 2 is 6
We take 6 ( the liter that he likes ) and multiply it by 15. This gives us 90, exactly what Peggy made.
Answer:
It is just right!
Step-by-step explanation:
12 divided by 2 is 6 . We take 6 and multiply it by 15. This gives us 90, which is exactly what Peggy made.
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 36 x2 x dx
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We need to find the integration of (36x²)x.dx .
We know,
[tex]\int x^n.dx = \dfrac{x^{n+1}}{n+1} +c[/tex]
Now,
[tex]I=\int {36x^2x} \, dx \\\\I=36\int x^3.dx\\ \\I=36\times \dfrac{x^4}{4}+c\\\\I=9x^4+c[/tex]
Therefore, the integration of (36x²)x.dx is [tex]9x^4+c[/tex] .
Hence, this is the required solution.
Consider a tank in the shape of an inverted right circular cone that is leaking water. The dimensions of the conical tank are a height of 12 ft and a radius of 10 ft. How fast does the depth of the water change when the water is 10 ft high if the cone leaks at a rate of 8 cubic feet per minute?
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Answer:
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Step-by-step explanation:
Given
Represent radius with r and height with h
[tex]h = 12ft[/tex]
[tex]r = 10ft[/tex]
[tex]Rate = \frac{8ft^3}{min}[/tex] when [tex]h = 10ft[/tex]
Express radius in terms of height
[tex]\frac{r}{h} = \frac{10}{12}[/tex]
[tex]\frac{r}{h} = \frac{5}{6}[/tex]
[tex]r = \frac{5}{6}h[/tex]
First, we need to determine the volume of the cone in terms of height.
[tex]Volume = \frac{1}{3}\pi r^2h[/tex]
Substitute [tex]r = \frac{5}{6}h[/tex]
[tex]V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^3[/tex]
[tex]V = \frac{25}{108} \pi h^3[/tex]
Differentiate both sides w.r.t time (t)
[tex]\frac{dV}{dt} = 3 * \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}[/tex]
Solve for [tex]\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}[/tex]
At this point, [tex]h = 10[/tex] and [tex]\frac{dv}{dt} = \frac{8ft^3}{min}[/tex]
So, we have:
[tex]\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{864}{7500\pi}[/tex]
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Hence:
The rate is [tex]\frac{216}{1875\pi} ft/min[/tex]
Using implicit differentiation, it is found that the depth of water changes at a rate of -0.0764 feet per minute.
The volume of a cone of radius r and height h is given by:
[tex]V = \frac{\pi r^2h}{3}[/tex]
Applying implicit differentiation, we can find it's rate of change, thus:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
In this problem:
Height of 12 ft and radius of 10 ft, thus [tex]h = 12, r = 10[/tex].Radius does not change, thus [tex]\frac{dr}{dt} = 0[/tex].Water leaks at a rate of 8 cubic feet per minute, thus [tex]\frac{dV}{dt} = -8[/tex]Then:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
[tex]-8 = \frac{\pi (10)^2}{3}\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = -\frac{24}{100\pi}[/tex]
[tex]\frac{dh}{dt} = -0.0764[/tex]
The depth of water changes at a rate of -0.0764 feet per minute.
A similar problem is given at https://brainly.com/question/9543179
2/3 times 6/7 divided by 2/5
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Answer:
so the answer is 1 whole and 3/7 hope this helps :)
explanation:2/3× 6/7 = 4/74/7 ÷ 2/5 = 1 3/7Which of the following is not a rational number? (-12/35) (10) (2/0) (2 1/2)
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Answer:
(- 12/35) THIS IS THE MAIN ANSWER YOU CAN SEE IN THE GOOGLE
A food truck sells tacos $1.25 a piece. The truck operator earned $360.00 last night.
How many tacos did the food truck sell last night?
28.8 tacos
288 tacos
300 tacos
2.88 tacos
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Answer:
288
Step-by-step explanation:
Each taco is 1.25 dollars and you are trying to figure out how many tacos he sold to do this we make an equation.
Step 1
1.25 x = 360
x =is the amount of tacos sold.
Step 2
1.25 x = 360
/1.25 /1.25
to get x on its own we need to cancel out the 1.25 so we dived because it was multiplied to the x. we did the same on the other side to balance the equation.
Step 3
x = 288
we now need to identify what x is, we can see it is 288. If we trade x for what it means it is then this is your answer the amount of tacos sold=288
i hope this helps ;)
10times larger than 40
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Answer:400
Step-by-step explanation:10×40=400
Answer:400
Step-by-step explanation:
Evaluate 2x+6y when x= -4/5 and y= 1/3 Write your answer as a fraction or mixed number in simplest form.
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2/5 is a answer
in this we can se the answer is 2/5
One angle in a triangle measures twice the smallest angle, whereas the largest angle is nine times the smallest angle. Find the measures of all three angles.
° (smallest value)
°
° (largest value)
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Step-by-step explanation:
Let the smallest angle be x
2nd angle = 2x
3rd angle = 9x
By angle sum property
x+2x+9x=180°
x=180/12
x=15
Three angles are 15, 30 and 135
Solve the inequality.
2(4+2x)25x+5
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Answer:
[tex]100x^{2} +200x+5[/tex]
Step-by-step explanation:
Answer:
x ≤ 3
Step-by-step explanation:
A, B, C, or D???? Please help! Thank you!
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Answer:
Step-by-step explanation:
either the c or d
A 2 1/2 pound bag of grass seed covers 1/8 of an acre. How much grass seed is needed for 1 acre?
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Answer:
it needs 234 grass seeds for the acre
Name an equivalent ratio for One-half with a denominator of 8.
a. 4 Over 8
c. 5 Over 8
b. 1 Over 8
d. 3 Over 8
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Answer:
it is A
Step-by-step explanation:
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 ounces
How many ounces are in 4 gallons?
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Answer:
512
Step-by-step explanation
128 ounces in a gallon times that by 4. ====== ....... 512.
Ur welcome please heart this
Taylor is driving on the freeway at 55 miles per hour. What question finds her distance
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Answer:
distance(miles) = number of hours driven * 55
Step-by-step explanation:
Please help I will put brainliest
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Answer:
−64x12y12
Good Luck!!!
Answer:
[tex]-64x^{12} y^{12}[/tex]
Step-by-step explanation:
1. remove parentheses by multiplying factors.
2. use exponent rules to remove parentheses in terms with exponents.
3. combine like terms by adding coefficients.
4. combine the constants.
The school store sells 4 pencils for $0.80. What is the unit cost of a pencil?
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The midpoint M of QR has coordinates (6, 6). Point R has coordinates (5, 7). Find the
coordinates of point Q.
Write the coordinates as decimals or integers.
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Answer:
(7,5)
Step-by-step explanation:
match the simplified expressions to an equivalent expression
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Lines m and n are parallel. What is
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Answer:
Line m and m is a straight line
3 + 8 + 6 + 6 + 6 = 58 + 6
How do we solve this
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Answer:
93
Step-by-step explanation:
FIRST RIGHT GETS BRAINLIEST
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Answer:
-1 + 7 =-8
Step-by-step explanation:
Answer:
-6, -7
Step-by-step explanation:
-1 + -6 = -7
I need help ASAP please
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A circle is 360 degrees so 360 = b + 96 + 209
360 = b + 305
b = 55 degrees.
lines of best fit (regression lines) must touch all dada points on a scatter plot
true or false
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Answer:
False
Step-by-step explanation:
A regression line tries to average out all data points, so it may not touch any of them.