A firm has two plants (X and Y) producing the same product which sells for $12 each. The total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.
To solve the problem, first translate the given problem into equations.
The formula for profit is:
profit = revenue from sales - total cost
total cost = fixed cost + variable cost
revenue = selling price x number of units sold
Let:
x = the number of units sold in plant X
y = the number of units sold in plant Y
From the problem, we can conclude:
Profit X = profit Y
x = y
Profit X = 12x - (5000 + 3x) (equation 1)
Profit Y = 12 y - (7000 + 2y) (equation 2)
Substitute y = x into equation 2
Profit Y = 12 x - (7000 + 2x)
Hence,
12x - (5000 + 3x) = 12 x - (7000 + 2x)
3x - 2x = 7000 - 5000
x = 2,000
Therefore, total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.
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In a recent survey, 78% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 10 of them favor the building of the health center. Use binomial probability distribution formula and write your answer with four decimal places.
The probability that exactly 10 of the citizens favor the building of the health center is;
P(X = 10) = 0.0355
This question is a binomial probability distribution question that takes the formula;
P(X = x) = ⁿCₓ * pˣ * q⁽ⁿ ⁻ ˣ⁾
Where
p = chance of success
q = chance of failure
n = number of trials
We are given;
p = 78% = 0.78
q = 1 - 0.78 = 0.22
n = 14
Thus, probability that exactly 10 of them favor the building of the health center is;
P(X = 10) = ¹⁴C₁₀ × 0.78¹⁰ × 0.22⁽¹⁴ ⁻ ¹⁰⁾
P(X = 10) = 182× 0.78¹⁰ × 0.22⁴
P(X = 10) = 0.0355
Therefore, the probability that exactly 10 of the citizens favor the building of the health center is;
P(X = 10) = 0.0355
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What are 3 materials that do not conduct electricity?.
Plastic, wood, and rubber are the three materials that do not conduct electricity.
Conductors are materials that conduct heat or electricity. Insulators are the materials that do not allow to conduct heat or electricity.
Electrical insulators are materials that do not allow to pass electricity through them.
Glass, wood, rubber and plastic are examples of these materials. Air also acts as an insulator.
Thus,these non-conductors/insulators are useful in a variety of applications.
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For 0 ≤ t ≤ 6 seconds, a screen saver on a computer screen shows two circles that start as dots and expand outwards. 1) At the instant that the first circle has a radius of 9 centimeters, the radius is increasing at a rate of 3/2 cm/sec. Find the rate at which the area of the circle is changing at that instant. 2)The radius of the first circle is modeled by g(t) = 12 - 12e-0.5t for 0 ≤ t ≤ where g(t) is measured in centimeters and t is measured in seconds. At what time t is the radius of the circle increasing at a rate of 3 cm/sec. 3) A model for the radius of the second circle given b the function f for 0 ≤ t ≤ 6, where f(t) is measured in cm and t is measured in seconds. The rate of change of the radius of the second circle is given by f1(t) = t2-4t+4. Based on this model, by how many cm is the radius of the second circle increasing from time t =0 to t = 3?
The rate of change of area is given as 27 π. The time at which radius of circle is increasing is 1.386 sec and change in radius is 3 cm.
What is rate of change?
The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another.
a) Given, radius of circle = 9 cm
rate of change of radius = 3/2
We know area of circle = πr^2
change in area =2πrr'
we get 2×π×9×2/3=27π
B) Given,
g(t) = 12 - 12e^0.5t
derivate it
g'(t) =-12×-1/2e^t/2
g'(t)=3
3= 6e^t/2
t = 1.386
c) f1(t) = t2-4t+4.
Integrate it we get
radius =3.
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suppose sixty percent of people at a company picnic got food poisoning. what percent of the people at the picnic did not get food poisoning? a. 40% b. 60% c. 20% d. 80%
a. 40%
the total amount of people is 100%
assume a person gets either food poisoning or doens't get food poisoning
100% - 60% = 40%
yang company sold merchandise for $4,000. the event is subject to a state sales tax of 9%. based on this information, yang would be required to
Sales revenue will be recorded at $4,000 and yang Yang would be required to Recognize sales tax liability of $360.
What is sales revenue?
The terms revenue and sales revenue are sometimes used synonymously. However, the concept of revenue includes income derived from sources other than those directly connected to the primary business, such as interest on savings or money distributed as dividends. Revenue comprises income derived from the sale of goods and services. The classification of this is "non-operating income."Sales = $4,000
State sales tax rate = 9%
State sales tax = Sales x State sales tax rate
= 4,000 x 9%
= $360
Sales revenue will be recorded at $4,000 and sales revenue is not affected by the sales tax amount.
Hence, Yang would be required to Recognize sales tax liability of $360.
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scarlett is younger than nasim. their ages are consecutive integers. find scarlett's age if the sum of scarlett's age and 5 times nasim's age is 185.
Given ages represent the consecutive integers and sum of Scarlett's age and five times Nasim age is 185 , then Scarlett age is equal to 30 years.
As given in the question,
Age represents the consecutive integers and Scarlett age is less than Nasim's age.
Let 'x' represent the age of Scarlett
And ' x + 1' represents the age of Nasim
As per the given condition of their ages we have,
x + 5 ( x + 1 ) = 185
⇒ x + 5x + 5 = 185
⇒ 6x + 5 = 185
⇒ 6x = 185 - 5
⇒ 6x = 180
⇒ x = 180 / 6
⇒ x = 30 years
Therefore, for the given ages represent the consecutive integers and sum of Scarlett's age and five times Nasim age is 185 , then Scarlett age is equal to 30 years.
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Kilometer and inche are ome meaurement ued to meaure length. What are ome other unit ued to meaure length
Some other measurements used to measure length are meter, centimeter millimeter, decameter, decimeter, hectometer, foot, etc
What is length of an object?
Length of an object is the distance between one end point to another end point of the object.
The concept of length is a very important tool in mathematics, especially in geometry and mensuration. Concept of length is very important in physics also
Kilometer and inches are some measurements used to measure length.
Some other measurements used to measure length are meter, centimeter millimeter, decameter, decimeter, hectometer, foot, micrometer, nanometer, angstrom, picometer, Fermi, etc
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The length of a certain insect is 7/8 inches. What is length of the tail if it's half the insects total length
The length of the tail if it's half the insects total length as described in the task content is; 7/16 inches.
What is the length of the tail of the insects?It follows from the task content that the length of the tail of the insect whose length is as given is to be determined.
Since the given length of the insect is; 7/8 inches.
Also, the tail of the insect is half the insects to tak length.
Consequently, the expression which holds true for the length of the tail is;
(1/2) × (7/8)
= 7/16.
The length of the insect's tail is therefore; 7/16 feet.
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Can someone help me with this DeltaMath question? I have no idea what to do but I've gotten this far...
The proof as explained below shows that ΔBAD ≅ ΔCDA by the side-side-side (SSS) congruence theorem.
What is the Side-side side (SSS) Congruence Theorem?The Side-side-side (SSS) congruence theorem states that two triangles are congruent to each other if the three sides of one triangle are equal or congruent to the corresponding three sides of the other.
The proof that shows triangles BAD and CDA are congruent is explained below.
Statement Reason
1. BD ≅ AC; BA ≅ DC 1. Given
2. AD ≅ AD 2. Reflexive property
3. ΔBAD ≅ ΔCDA 3. Side-side-side (SSS)
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the following for loop calculates the amount of money in a savings account after numberyears given an initial balace of savingsbalance and an annual interest rate of 2.5%. complete the for loop to iterate from 1 to numberyears (inclusive).
The loop will be written in Matlab.
Simply setting the years' range will allow the for loop to run its course and complete the task. To allow the loop to iterate from 1 to the number of years, we add the expression 1:number years.
function savingsBalance = CalculateBalance(numberYears,savingsBalance)
% numberYears: Number of years that interest is applied to savings
% savingsBalance: Initial savings in dollars
interestRate = 0.025;
% 2.5 percent annual interest rate
% Complete the for loop to iterate from 1 to numberYears (inclusive)
for n = 1:numberYears
savingsBalance = savingsBalance + (savingsBalance * interestRate);
end
end
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7.81 for the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment.
The maximum absolute values of the shear and bending moments are
Cy = 1800 lbs
Ay = 4800 lbs
Max absolute BM = 14400 lbs-feet
Given,
Draw the shear and bending moment diagrams for the beam and the indicated loading, and then figure out the highest absolute values of the shear and bending moment.
(a) The shears and bending-moment diagrams,
Ay + Cy = 800 * 9 - 600
Ay + Cy = 6600 lbs
Ay
∑Ma = 0
Cy * 15 + 600 * 9 = 800 * 9²/2
Cy = 1800 lbs
Ay = 4800 lbs
(b) Determine the maximum absolute values of the shear and bending moment,
Map absolute B.M:
Map positive B.M occurs, when SF = 0 is at 'x'
4800 - 800x = 0
x = 6ft
Positive map = 4800 * 6 = 800 * 6²/2
Max absolute BM = 14400 lbs-feet and it developed at 6ft from support A.
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Which graph is not a function?.
The graphs with consist of nonuniform points are not functions.
Given that,
To determine which graph is not a function.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
The only graph that cannot be a function, whose expression is not able to be determined, one example is that points are drawn non-uniformly and do not have a relation with each other, that type of relationship is not a function on a graph.
Thus, the graphs with consist of nonuniform points are not functions.
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aplicarán 6/3 kg de Nitrógeno, 2/5 kg de Fósforo y 6/4 kg de Potasio. ¿Cuál es la cantidad total de fertilizante que se aplicará?
Addition of the fractions showed that the total amount applied is 39/10 kg
Addition of FractionsThe addition of fractions is a little different from the normal addition of numbers since a fraction has a numerator and a denominator which is separated by a bar. The addition of fractions can be easily done if the denominators are equal. While like fractions have common denominators, unlike fractions are converted to like fractions to make addition easier.
In this case, we simply need to add the fraction of nitrogen, phosphorous and potassium.
This becomes;
6/3 + 2/5 + 6/4 = 2 + 2/5 + 3/2 = 39/10 = 3.9kg
The amount added is 39/10kg or 3.9kg
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Translation: 6/3 kg of Nitrogen, 2/5 kg of Phosphorus and 6/4 kg of Potassium will be applied. What is the total amount of fertilizer to be applied?
The graph of a quadratic function has the y-intercept A (0, 7.5), anf the zeros of the function are -10 and 3. Write the equation of the function.
The equation of the function is f(x) = (-1/4)(x+10)(x-3)
The y intercept of the function = A(0, 7.5)
The zeros of the function are
-10 and 3
The equation in intercept form
y = a(x - p)(x - q)
Where the value of p = -10
The value of q = 3
Then the function will be
f(x) = a(x + 10)(x - 3)
The point A = (0, 7.5)
Substitute the values of x and y in the equation
7.5 = a(0+10)(0-3)
Do the arithmetic operation
7.5 = a(10)(-3)
Multiply the terms
7.5 = -30a
a = 7.5 / -30
Divide the terms
a = -1/4
Hence, the equation of the function is f(x) = (-1/4)(x+10)(x-3)
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the values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.481, 1.611, and 0.294, respectively. does this data suggest that the true average percentage of organic matter in such soil is something other than 3%? carry out a test of the appropriate hypotheses at significance level 0.10. [note: a normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.]
True average percentage of organic matter in such soil is different from 3%.
What is Statistics?
Statistics is the study of data collection, analysis, presentation, and interpretation. Much of the early push for the subject of statistics came from government demands for census data as well as information about a range of economic operations.
Solution:
We are given that the values of the sample mean and sample standard deviation are 2.481 and 1.611 respectively.
Suppose we know the population distribution is normal, we have to test the hypothesis that does this data suggest that the true average percentage of organic matter in such soil is something other than 3%.
Let μ = true average percentage of organic matter in such soil
SO, Null Hypothesis : μ = 3% {means that the true average percentage of organic matter in such soil is equal to 3%}
Alternate Hypothesis : μ ≠ 3% {means that the true average percentage of organic matter in such soil is different than 3%}
The test statistics that will be used here is One-sample t test statistics because we don't know about the population standard deviation;
TS = (0.02481 - 0.03)/(0.01611)/√30
TS = 4.6% (approx)
Therefore, we conclude that the true average percentage of organic matter in such soil is different from 3%.
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which measure captures the variation in ressponses? multiple choice the frequency distribution the median the mode the standard deviation the mean
the measure that captures the variation in responses is mean and it is the weighted average
What is the meaning of mean in math?
In mathematics and statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations), the geometric mean, and the harmonic mean.
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the findings from a study of young single mothers at a university can be generalized to the population of: the findings from a study of young single mothers at a university can be generalized to the population of: all young single mothers in that society all young single mothers at that university all single mothers in all universities all young women in that university
All young single mothers in that society is correct.
Given that
The findings from a study of young single mothers at a university can be generalized to the population of:
1. all young single mothers in that society
2. all young single mothers at that university
3. all single mothers in all universities
4. all young women in that university
It can be generalized to all young single mother at the University. Because the findings might not be through for adults and at the same time might not be through for those outside the University.
Hence the answer is all young single mothers in that society is correct.
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What is the rule of obtuse angle?.
The rule of obtuse angle is that one angle measures more than 90° and total sum og angle should be 180°.
How many angles are there in total?Acute, obtuse, right, straight, reflex, and complete rotation are some of the terms used to describe fundamental angles. Two rays are joined at their termini to form the geometric shape known as an angle. The most common way to express an angle is in degrees.
What does the word "angle" mean?A measure of an angle or the amount of turning required to bring one line or plane into coincidence with or parallel to another angled is represented by two lines extending from the same point.
A triangle is said to have an obtuse angle if one of the inner angles is greater than 90 degrees. If one of the angles of an obtuse triangle is greater than 90°, then the total of the other two angles is also less than 90°.
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Waim want to buy weet to ditribute on hi birthday. He want to give 3 weet to each of
hi 28 friend and have 10 weet extra. How hould he calculate the number of weet to
buy?
The number of weet to buy is 84.
We have amount given to one friend and we need to find number of weet given to all of his friends. We use unitary methods to calculate the number of weets.
Let total number of weet be X
Number of weet given to 1 friend = 3
Number of weet given to 28 friend = 28 X 3
= 84
Therefore X = 84
84 weet will be distributed among 28 friend.
Wasim wants 10 weet extra
So, total number of wee he will purchase =
Total weet given to his 28 friends + total extra weet
= 84 + 10
= 94
Hence, Waim will buy 94 weets.
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(a) Strawberries cost $4.20 per kilogram and cream costs $8.56 per litre. Venus buys 1.2 kg of strawberries and 125 ml of cream. Work out the total cost.
What is the geometric means between 5 and 125?.
The geometric mean between 5 and 125 will be 25.
What is geometric mean?
The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.
The Geometric Mean (GM) is the average value or mean that, in mathematics, represents the centre tendency of a group of numbers by calculating the product of their values. In essence, we multiply the numbers collectively and take the nth root of the resulting multiplied numbers, where n is the total number of data values.
The given number is 5, 125.
So the Geometric Mean willl be (5*125)[tex].^{1/2}[/tex]
So [tex](625)^{1/2}[/tex]
= 25
Hence, the geometric mean between 5 and 125 will be 25.
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use the distance formula and algebra to show that the set of all points (x, y) that are equidistant from the point (f, k) and the line x
We have proved that the set of all points (x, y) that are equidistant from the point (f, k) and the line x.
What is a parabola?
A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.
That’s a parabola in the usual orientation. y=1 is the directrix. (f, k) is the focus. Squared distance, as usual, is the fundamental quantity.
If (x,y) is a point in the set, the squared distance to y=1 is (y−1)². The squared distance to (f, k).
(y - 1)²=(x - f)²+(y - k)²
Hence, we can say that the set of all points (x, y) is equidistant from the point (f, k) and the line x.
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Solve; round to the nearest hundredth.
a 2x² = 24
b x² - 4 = 14
Answer:
Step-by-step explanation:
a
2/2 x^2 = 24/2
x^2 = 12
x = √12
x = 3.464102 = 3.46
x = -√12 = -3.46
b
x^2 = 14 + 4
x^2 = 18
x = √18
x = 4.242641 = 4.24
x = -√18 = -4.24
a customer at cavallaro's fruit stand picks a sample of 3 oranges at random from a crate containing 40 oranges, of which 5 are rotten. what is the probability that the sample contains 1 or more rotten oranges?
The probability that the sample contains 1 or more rotten oranges be, 1/8.
Given, a customer at cavallaro's fruit stand picks a sample of 3 oranges at random from a crate containing 40 oranges, of which 5 are rotten.
we have to find the probability that the sample contains 1 or more rotten oranges,
first we will find the probability that the sample contains no rotten oranges,
P(E) = 35/40
P(E) = 7/8
Now, the probability that the sample contains 1 or more rotten oranges be,
1 - 7/8
P(E) = 1/8
Hence, the probability that the sample contains 1 or more rotten oranges be, 1/8.
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A computer scientist is investigating the usefulness of twodifferent design languages in improving programming tasks. Twelve expert programmers, familiar with both languages, are askedto code to code a standard function in both languages, and asked tocode a standard function in both languages, and time (in minutes)is recorded. The data follow:
(a) Is the assumption that the different in coding time isnormally distributed reasonable?
Time
Programmer Design Language 1 Design Language 2
1 17 18
2 16 14
3 21 19
4 14 11
5 18 23
6 24 21
7 16 10
8 14 13
9 21 19
10 23 24
11 13 15
12
18
20
(b) Find a 95% confident interval on the different in meancoding times. Is there any indication that one designlanguages is preferable?
The 95% confidence interval for the mean coding time difference is (-1.2169,2/5502) one design language is better than another.
Given that,
A computer scientist is looking into how two different design languages may make programming chores better. Twelve experienced programmers who are fluent in both languages are given the task of creating a standard function in each language, and the time taken (in minutes) is recorded.
We have to identify the 95% confidence interval for the mean coding time difference. Is there any evidence that one design language is better than another.
We know that,
The attached file's histogram demonstrates that the distribution of differences is roughly normal.
It follows that the distribution must be regular.
The 95% confident level for μ=μ₁-μ₂
We get,
=d±t(S/√n)
=0.666667±2.201(2.964436/√12)
=0.666667±2.201(0.85576)
=0.666667±1.883525474
We get (-1.2169,2.5502)
Therefore, The 95% confidence interval for the mean coding time difference is (-1.2169,2/5502) one design language is better than another.
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a bottle of lemonade normally contains 400 ml. special edition bottles have 10 % extra free. how much lemonade is in the special edition bottles?
Answer:360ml
Step-by-step explanation:
400/10=10%=40
400-40=360ml
find the area of the polygon below. 15cm 9cm 10cm 5cm
A= blank cm^2
Answer:
95
Step-by-step explanation:
15 * 5 = 75
5 * 4 = 20
20 + 75 = 95
What is the experimental probability of rolling a single die ten times and landing on 6?
The experimental probability of landing on a 6 is 1/10.
What is the probability?Probability is used to calculate the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
Result of the experiment:
Face Frequency
1 2
2 1
3 0
4 5
5 1
6 1
Probability of landing on a 6 = 1 /10
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the water utility (an enterprise fund) has just sent out a purchase order to a vendor for some new equipment. which of the following would be included in the journal entry to record this event?
For the water utility (an enterprise fund) has just sent out a purchase order to a vendor for some new equipment, of the following that would be included in the journal entry to record this event is none of the above. (Option D)
An enterprise fund refers to a fund which may be used to report any activity for which a fee is charged to external users for goods or services. An enterprise fund uses a separate accounting and financial reporting mechanism for which revenues and expenditures are segregated into a fund with financial statements separate from all other governmental activities. Enterprise funds provide goods and services to customers outside the reporting entity. Hence, from the options of journal entry records, none of the given options will be used.
Note: The question is incomplete as it is missing options which are A) A credit to Accounts Payable. B) A debit to Encumbrances. C) A debit to Expenditures. D) None of the above.
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the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base. find the altitude.
If the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inch
The area of a triangle is 96 sq. inches
Let base be b
Its altitude is 2 inches greater than five times its base.
a=5b+2
ab/2=A
(5b+2)b/2=96
(5b+2)b=192
5b²+2b=192
5b²2+2b-192=0
On solving the quadrartic equation,
we get
b=6
a=32
Therefore, if the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inchs
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