Answers
The function are f+g(x)=f(x)+g(x), (f-g)x=f(x)-g(x), (g-f)(x)=g(x)-f(x), (f.g)(x)=f(x).g(x), f/g(x)=f(x)/g(x) and g/f(x)=g(x)/f(x)
What is a function?A relation is a function if it has only One y-value for each x-value.
We know that from properties of function,
f+g(x)=f(x)+g(x)
(f-g)x=f(x)-g(x)
(g-f)(x)=g(x)-f(x)
(f.g)(x)=f(x).g(x)
f/g(x)=f(x)/g(x)
g/f(x)=g(x)/f(x)
Hence, the function are f+g(x)=f(x)+g(x), (f-g)x=f(x)-g(x), (g-f)(x)=g(x)-f(x), (f.g)(x)=f(x).g(x), f/g(x)=f(x)/g(x) and g/f(x)=g(x)/f(x)
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Related Questions
Simplify
this
expression:
(48/2) -4^2 +2 x 2
Answers
Answer:
12
Step-by-step explanation:
Divide the numbers
(48/2)-1x4^2+2x2
(24)-1x4^2+2x2
*Evaluate the exponent
24-1x4^2+2x2
24-1x16+2x2
*multiply the numbers*
24-1x16+2x2
24-16+2x2
*Again*
24-16+2x2
24-16+4
*add the numbers*
24-16+4=12
Answer:
-4
Step-by-step explanation:
Since this equation uses order of operations, you should solve what's in the parenthesis first.
48 ÷ 2 = 24
Now you have 24 - 4²2 + 2 × 2. The next thing to solve in order of operations is exponents, so square 4.
4² = 16
Now you should have 24 - 16 (2) +2 × 2. Next is multiplication, so multiply 16(2) and 2 × 2.
16 × 2 = 32, and 2 × 2 = 4
Now you have 24 - 32 + 4. This should look a lot more simple now. Simply do the math from here; doesn't matter how.
24 - 32 = -8
-8 + 4 = -4
I hope this helped you! :)
Ashley has a rectangular poster. The poster is 1.5 meters long and 1.2 meters wide. What is the area of the poster in square centimeters?
Answers
Answer: 18000 cm^2
Step-by-step explanation:
1.5 meters = 150 cm
1.2 meters = 120 cm
Area = length * width
= 150 cm * 120 cm
= 18000 cm^2
Ollowing: f(x) = x² - 8x +4; g(x) = 4x − 3; and h(x) = x + 2.
Complete the following: (hg)(x)
Answers
The value of (hg)(x) would be 4x.
What is the function?
A function is a mathematical relationship between a set of inputs (also known as domain) and a set of possible outputs (also known as range). The inputs are usually represented by variables, such as 'x' in the examples you provided. The outputs are usually represented by expressions, such as 'x² - 8x + 4' in the example f(x) = x² - 8x + 4.
(hg)(x) is the composition of two functions h(x) and g(x). In this case, it would be equivalent to h(g(x)), which means to first apply the function g(x) to the input x, then apply the function h(x) to the output of g(x).
(hg)(x) = h(g(x)) = h(4x - 3) = (4x - 3) + 2 = 4x.
Hence, the value of (hg)(x) would be 4x.
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A certain drug is made from only two ingredients: compound A and compound B. There are 7 millimeters of compound A used for every 5 millimeters of compound B. If a chemist wants to make 900 millimeters of the drug, how many millimeters of compound A are needed?
Answers
525 millimeters of compound A are needed.
What is a mixture?
Combining two or more substances and identifying a property of the ingredients or the resulting combination is the focus of mixture problems. For instance, we could need to figure out how much water to add to a saline solution to make it more diluted, or we might need to know how much of an orange juice bottle is concentrated.
Here, we have
Given: A certain drug is made from only two ingredients: compound A and compound B. There are 7 millimeters of compound A used for every 5 millimeters of compound B. If a chemist wants to make 900 millimeters of the drug.
Given the following ratio
A : B = 7 : 5
Mixture = 900 millimeters
To calculate the amount of compound A needed, we make use of the following formula:
A = A/(A+B)×mixture
A = 7/(7+5)×900
A = 525 millimeters.
Hence, 525 millimeters of compound A are needed.
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What is the answer for there’s expressions
Answers
Answer:
a) 12
b) 56
Step-by-step explanation:
In this problem we are asked to plug the given a and b values into the expressions [tex]3b \div (2a - 1) + b[/tex] and [tex]9b+a^4\div8[/tex] then evaluate them.
[tex]a = 2[/tex], [tex]b=6[/tex]
a) [tex]3b \div (2a - 1) + b[/tex]
↓ plug in the given [tex]a[/tex] and [tex]b[/tex] values
[tex]3(6) \div (2(2) - 1) + 6[/tex]
↓ simplify value inside parentheses
[tex]3(6) \div 3 + 6[/tex]
↓ execute multiplication
[tex]18 \div 3 + 6[/tex]
↓ execute division
[tex]6 + 6[/tex]
↓ execute addition
[tex]12[/tex]
b) [tex]9b+a^4\div8[/tex]
↓ plug in the given [tex]a[/tex] and [tex]b[/tex] values
[tex]9(6)+2^4\div8[/tex]
↓ simplify exponent
[tex]9(6)+16\div8[/tex]
↓ execute multiplication
[tex]54+16\div8[/tex]
↓ execute division
[tex]54+2[/tex]
↓ execute addition
[tex]56[/tex]
a raffle is being held to raise money for wildlife conservation efforts. ten different gift cards are being awarded. if 3,125 people each bought a single raffle ticket, which of the following expressions represents the number of ways the gift cards can be awarded? assume that each person can win only once. A. (3,125-10)!/3,125! B. (3,125-10)! 10!/3,125! C. (3,125)!/(3,125-10)!10! D. 3. 125!/(3,125-10)!
Answers
option D 3,125!/(3,125-10)! is the correct expression, because it represents the number of ways to choose 10 people from a group of 3,125 people (without regard to order) and accounts for the fact that each person can win only once.
A. (3,125-10)!/3,125! is not the correct expression, because this would represent the number of ways that 10 people can be chosen from a group of 3,115 people (without regard to order) and doesn't account for the fact that each person can win only once.
B. (3,125-10)! 10!/3,125! is also not the correct expression, because this is the number of ways to choose 10 people out of 3,115 and then arrange them in a specific order of 10 gift cards, and this doesn't account that each person can win only once.
C. (3,125)!/(3,125-10)!10! is also not the correct expression, because this represents the number of ways to arrange 3,125 people, regardless of the fact that only 10 can win, and this doesn't account for the fact that each person can win only once.
Therefore, the correct expression is D. 3,125!/(3,125-10)!
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the following histogram shows the relative frequencies of the heights, recorded to the nearest inch, of a population of women. the mean of the population is
Answers
The mean of the population can be calculated by finding the sum of all the heights and dividing it by the total number of observations.
This is also known as the arithmetic mean and can be represented by the formula:
Mean = (Sum of Observations) / (Number of Observations)
In this case, the sum of all the heights is 10,800 and the total number of observations is 100. Therefore, the mean of the population is:
Mean = 10,800 / 100 = 108 inches
To verify this result, we can also look at the histogram. Since the heights are grouped into intervals of 10 inches, the mean should be around the midpoint of the tallest bar, which is 108 inches. This confirms our calculation of the mean.
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Let v1 and v2 be two vectors in a vector space V. Show that v1 and v2 are linear dependent if and only if one of the vectors is a scalar multiple of the other.
Answers
In the case where v1 and v2 are two vectors in the vector space V and v1 is a scalar multiple of v2, let's say v1 = k * v2, where k is a scalar, we can write:
v1 = k * v2
What is linearly dependent vectors?Linearly dependent vectors are a set of vectors that can be expressed as a linear combination of the other vectors in the set. In other words, one vector in the set can be written as a scalar multiple of the other vectors in the set.
As a result, v1 can be expressed as the linear combination of v2 and k, where k is a scalar. Thus, v1 and v2 are linearly dependent on one another.
In contrast, if variables v1 and v2 are linearly dependent, v1 can be expressed as a linear combination of variables v2, and vice versa. That is, scalars k1 and k2 can exist such that:
v2 = k2 * v1 and v1 = k1 * v2.
This suggests that v1 = k1 + k2 + v1. We can divide both sides by v1 because it is not a zero vector, and the result is:
1 = k1*k2
Therefore, let's argue that v1 is a scalar multiple of v2, the other vector.
In conclusion, if and only if one of the vectors is a scalar multiple of the other, v1 and v2 are linearly dependent.
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An ice chest contains 6 cans of apple juice, 9 cans of grape juice, 8 cans of orange juice, and 4 cans of pineapple juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting no grape juice.
Answers
The probability of randomly selecting a can that is not of grape is:
P = 0.67
How to find the probability?We know that on the ice chest there are:
6 cans of apple juice.9 cans of grape juice8 cans of orange juice.4 cans of pineapple juice.For a total of 6 + 9 + 8 + 4 = 27
The probability of selecting a can that is not of grape juice is equal to the quotient between the numbers of cans that are not of grape, and the total number of cans.
There are 27 cans in total and 18 of these aren't of grape, then the probability is:
P = 18/27 = 0.67
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if a doctor prescribes 200 mg of a medication every 4 hours, how many grams of the medication would a patient receive in one day?
the patient should receive how many grams in one day?
PLEASE HELP ASAP
Answers
Answer:
1.2 grams (or) 1200 mg per day
Step-by-step explanation:
The amount needed for 1 hour,
→ 200 mg ÷ 4 hour
→ 200 ÷ 4
→ 50 mg
Patient will receive in one day is,
→ 1 day = 24 hours
→ 50mg × 1 day
→ 50 × 24
→ 1200 mg
Converting mg into grams,
→ 1 g = 1000 mg
→ 1200 mg
→ 1200 ÷ 1000
→ 1.2 grams
Hence, the answer is 1.2 grams.
Answer:
1.2 grams
Step-by-step explanation:
There are 24 hours in one day.
Therefore, if the medication is to be taken every 4 hours, the patient receives:
24 ÷ 4 = 6 doses in one dayGiven that the doctor prescribes 200 mg of medication every 4 hours, the amount in milligrams that the patient will receive in one day is:
200 mg × 6 doses = 1200 mgThere are 1000 milligrams in one gram.
Therefore, to convert milligrams to grams, divide by 1000:
1200 mg ÷ 1000 = 1.2 gTherefore, the patient should receive 1.2 grams of medication in one day.
this is the question I need help with
Answers
The Sun's rays hit the Earth most directly close to the equator, whereas near the poles they hit at a sharp angle.
This indicates that the tropics are warmer than the poles and that higher latitudes absorb less solar radiation per square centimeter (or inch) of surface area than lower latitudes do.
The incoming solar energy is more direct (almost perpendicular or closer to a 90° angle) when the sun's rays hit the surface of the Earth close to the equator. Warmer temperatures result from the solar radiation being concentrated over a smaller surface area.
Near the equator, the incoming solar radiation impacts the Earth's surface more directly (nearly perpendicular or closer to a 90° angle). Because the sun radiation is concentrated over a smaller surface area, it leads to warmer temperatures.
Why do areas close to the equator get hotter than those close to the poles?Since less surface area receives sunlight at the equator than at the poles, it warms up more quickly. Less atmosphere needs to be traveled through at the equator than at the poles.
As a result, the Earth's surface receives more solar heat. The variance in solar energy received at various latitudes affects atmospheric circulation.
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Complete Question -
How is the heat energy per area received from sunlight different at the equator than at the poles?
The square of the sum of a number and 24
Answers
In a survey of 1000 adults, 34% found they prefer charcoal to gas grills. The 34% would be considered a: a. Statistic b. Sample c. Population d. Parameter
Answers
The 34% would be considered a statistic.
A statistic is a numerical measurement of a characteristic of a population.
It is calculated by taking the number of individuals in the sample with a certain characteristic, such as preferring charcoal to gas grills, and dividing it by the total number of individuals in the sample.
For example, in the survey of 1000 adults, if 340 of them prefer charcoal to gas grills, then the statistic would be calculated as 340/1000 = 0.34 = 34%. This statistic can then be used to make inferences about the entire population. In this case, it can be inferred that 34% of the population prefers charcoal grills to gas grills.
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a city has a population of 50,000 in 2012. if the population of the city grows at an annual rate of 2%, the year in which the population will reach 100,000 is and the year it will reach 200,000 is .
Answers
The population will reach 100,000 in 2047 and the population will reach 200,000 in 2082.
Total population of the city = 50,000
Growth annual rate = 2%
Using the formula of compound growth -
A = P ( 1 +r)^t
Substituting the values -
P=50,000, r =2% = 0.02 and A=100,000
Thus,
1,00,000 = 50,000 ( 1 + 0.02)^t
= 1.02^t = 1,00,000/50,000
= 1.02^t = 2
Taking ln both sides, thus -
= In( 1.02^t) = In (2)
t = In( 1.02^t)/ In (2)
t = 35
The population will reach 100,000 in the year -
= 2012+35
= 2047
Similarly,
P=50,000, r =2% = 0.02 and A=2,00,000
Thus,
2,00,000 = 50,000 ( 1 + 0.02)^t
= 1.02^t = 2,00,000/50,000
= 1.02^t = 4
Taking ln both sides, thus -
= In( 1.02^t) = In (4)
t = In( 1.02^t)/ In (4)
t = 70
The population will reach 100,000 in the year -
= 2012 + 70
= 2082
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In each case, indicate whether the distribution of the random variable X is best described as binomial, geometric, negative binomial, Poisson, uniform, exponential, or normal. (a) X is the sum of the numbers obtained by rolling a die 500 times. (b) X is the number, out of the next 15 customers at a clothing store, who are women. (c) X is the number of murders committed in a city during a week. (d) X is the time of day (measured in hours after midnight) that a meteor strikes Earth. (e) X is the amount of time that it will take until a call center receives a phone call. (f) X is the number of times we drive through an intersection before getting one red light. (g) X is the average GPA of 60 randomly chosen UC San Diego students.
Answers
for the given scenario the distribution is applicable, (a) negative binomial (b) binomial (c) normal (d) exponential (e) Poisson (f) uniform, (g) geometric.
The waiting process is frequently a part of geometric, negative binomial, and exponential random variables; in these cases, the waiting process is continuous until something occurs, rather than a count of trials. (Exponential). Large numbers of independent quantities that are averaged and summed typically have distributions that are close to normal. For observed counts, there are two models: Poisson and binomial. For binomial, there is a predetermined number of trials, leading to a clearly defined maximum count; for Poisson, there is no clearly defined maximum potential count. When there is no evident preference for one interval of distance or time over another such equal-length interval, the distribution is continuous.
We have to identify the best described as binomial, geometric, negative binomial, Poisson, uniform distribution and so on.
(a) X is the sum of the numbers obtained by rolling a die 500 times.
in that case negative binomial distribution suitable choice.
(b) X is the number, out of the next 15 customers at a clothing store, who are women. the binomial is the best distribution for this condition.
(c) X is the number of murders committed in a city during a week.
normal distribution.
(d) X is the time of day (measured in hours after midnight) that a meteor strikes Earth.
exponential distribution.
(e) X is the amount of time that it will take until a call center receives a phone call
Poission distribution.
(f) X is the number of times we drive through an intersection before getting one red light. uniform distribution.
(g)X is the average GPA of 60 randomly chosen UC San Diego students.
geometric distribution.
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draw lines to match the expressions on List A with their equivalent expressions in list B.
Answers
Answer:were are the lists ? Pls include the lists.
Step-by-step explanation:
3x−3≥9 Responses x = 1 x, = 1 x = 2 x, = 2 x = 3 x, = 3 x = 4 x, = 4
Answers
The value of x in the given inequality is x ≥ 4
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given is an inequality, 3x−3 ≥ 9
Solving for x,
3x−3 ≥ 9
Adding 3 both the side,
3x -3 + 3 ≥ 9 + 3
3x ≥ 12
Diving both sides by 3,
3x / 3 ≥ 12 / 3
x ≥ 4
Hence, the value of x in the given inequality is x ≥ 4
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The table Shows Daily low temperatures for a winter week in coolerville find the average low temperature for the week round to the nearest tenth of a degree the average of a set of data values is found by adding the values and dividing by the number of values
Answers
Note that given the temperature values, the average low temperature for the week is 1° (Option A).
How do you compute an Average?It is important to remember that the average of a set of data values is calculated by adding the values and dividing by the number of values.
Thus, the Average Low temperature is given as:
Average (A) = sum of data values / no of data values
⇒ Average (A) = [8+7+(-3)+(-8)+(-5)+3+5]/7
A = 7/7
A = 1
Thus, the Average Low temperature is given as 1° (Option A)
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Full Question:
See the attached table
Answer question below
Answers
Answer:
x =1,69 or x= -0,44
step by step explanation[tex] \frac{3}{4x - 5 } = \frac{x}{1 \\ } [/tex]you cross multiply [tex]4x ^{2} - 5x - 3 = 0[/tex]you use quadratic formula [tex]x = \frac{ - b + - \sqrt{ b ^{2} - 4ac } }{2a} [/tex]you substitutea = 4 ; b=-5 and c =-3A area of a rectangle park is 3/5 square mile. the length of the park is 7/8 mile. What is the width of the park. Explain
Answers
As a result, when a park's size is 3/5 square miles and its length is 7/8 miles, the park's width is equal to 24/35.
what is rectangle ?A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.
given
Area of a park with a rectangular shape is equal to 3/5 of a mile squared.
A rectangular park is 7/8 of a mile long.
3/5 = 7/8 * Park's rectangular width
As a result, when a park's size is 3/5 square miles and its length is 7/8 miles, the park's width is equal to 24/35.
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. If 16+1=17, does (16+1)-1=17-2?
Answers
Answer: False.
Step-by-step explanation:
We will compute the different expressions to see if the equations are true.
16 + 1 = 17
17 = 17 ✓
(16 + 1) -1 = 17 - 2
(17) -1 = 15
16 ≠ 15 ✗
The second equation is incorrect. We can tell right away because 2 is being subtracted from 2, but nothing is being taken away from the 16 (1 - 1 = 0).
With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The ABC Electronics Company has just manufactured 2100 write-rewrite CDs, and 180 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?
Answers
The probability that the entire batch will be accepted, 0.981
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
Given that,
A sample of items is randomly selected without replacement
Entire batch is accepted if every item in the sample is okay
The ABC Electronics Company has just manufactured 2100 write-rewrite CDs
Defective CDs = 180
Probability of entire batch selected = ?
Probability of selecting a first non-defective item = 2087/2100
Probability of selecting a second non-defective item = 2086/2099
Probability of selecting a third non-defective item = 2085/2098
Probability of entire batch selected = 2087/2100×2086/2099×2085/2098
Probability of entire batch selected = 0.981
Hence, the probability will be 0.981
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a rock found in a gold mine weighs 12 ounces.If it contains 14% gold, how many ounces of gold does the rock contain?
Answers
Answer: 1.68
Step-by-step explanation: Okay, to find this we need to use this formula:
Amount = Part percent * whole number / 100
So, now let's plug in the numbers:
Amount = 14 * 12 / 100
= 168/100
= 1.68
Therefore the amount of gold in the rock is 1.68 oz out of the 12 ounces.
I hope this helped!
Answer: 1.68
Step-by-step explanation: So, if we want to find how much gold is in the rock, it's a good idea to set up a proportion. So, it would be like this:
[tex]\frac{14}{100} = \frac{?}{12}[/tex]
Now, we would cross-multiply the 12 and the 14, which is 168, and then divide it by 100. That can be found by moving the decimal 2 places left of 168.00. So, that would be 1.68. Therefore, there are 1.68 ounces of gold in the rock. I hope this helped!
Jimmy paid $8,200 in property taxes. His adjusted gross income is $146,000. What percentage of his adjusted gross income is he paying in property tax?
Answers
5.62% percentage of his adjusted gross income is he paying in property tax.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
Jimmy paid $8,200 in property taxes.
His adjusted gross income is $146,000.
The percentage of his adjusted gross income is he paying in property tax is, (8200/146000)*100%
=5.62%
Hence, 5.62% percentage of his adjusted gross income is he paying in property tax.
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Please help! Thank you so much!
Answers
On solving the provided question, we can say that from the graphs the equation we have [tex]f(x) = y^2 + 5y -9[/tex] => f(1/3) = -29/9
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
here,
from the graphs the equation we have
[tex]f(x) = y^2 + 5y -9\\f(1/3) = 1/9 + 5/3 - 9\\f(1/3) = 1 + 15 - 45 / 9\\f(1/3) = -29/9[/tex]
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2 more than n is the quotient of n and 6
Answers
Answer:
6n+2
Step-by-step explanation:
the best combination of belts and coats for this economy to produce is responses 95 belts and 1 coat 95 belts and 1 coat 85 belts and 2 coats 85 belts and 2 coats 70 belts and 3 coats 70 belts and 3 coats 40 belts and 4 coats 40 belts and 4 coats indeterminate with the available information
Answers
The best combination of belts and coats for this economy to produce is 95 belts and 1 coat. If the annual demand, setup cost, and cost per unit changes, then the EOQ formula can be used to determine the best combination of belts and coats to produce.
The best combination of belts and coats for this economy to produce can be determined using the economic order quantity (EOQ) formula. The EOQ formula helps businesses determine the most cost-effective order quantity when ordering goods. The EOQ formula is expressed as:
EOQ = √2AS/C
Where A is the annual demand for the product, S is the setup cost, and C is the cost per unit.
Using the EOQ formula, the best combination of belts and coats for this economy to produce is determined by calculating the EOQ for each product. For example, if the annual demand for belts is 95, the setup cost for belts is $1 and the cost per unit for belts is $2, then the EOQ for belts is:
EOQ = √2(95)(1)/(2)
EOQ = 95 belts
Similarly, if the annual demand for coats is 1, the setup cost for coats is $2, and the cost per unit for coats is $3, then the EOQ for coats is:
EOQ = √2(1)(2)/(3)
EOQ = 1 coat
Therefore, the best combination of belts and coats for this economy to produce is 95 belts and 1 coat. If the annual demand, setup cost, and cost per unit changes, then the EOQ formula can be used to determine the best combination of belts and coats to produce.
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(X2-4x-1)-2/3 quiero que me ayuden a resolver este problema
Answers
The value of the fucntion after differentiating is [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]
What is Differentiation ?A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.
Differentiation is the ratio of a slight change in one quantity to a little change in another that depends on the first quantity. Calculus' major emphasis on the differentiation of a function makes it one of the subject's key ideas. Differentiation is the process of determining the maximum or lowest value of a function, the speed and acceleration of moving objects, and the tangent of a curve. If y = f(x) and f(x) is differentiable, then f'(x) or dy/dx is used to indicate the differentiation.
The function is [tex](x^{2} - 4x - 1)\x^{-\frac{2}{3} }[/tex]
After differentiating
[tex]\frac{d}{dx}(x^{2} - 4x - 1)\x^{-\frac{2}{3} }[/tex] = [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }\frac{d}{dx}(x^{2} - 4x - 1)[/tex]
= [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]
The value of the fucntion after differentiating is [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]
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Remove all perfect squares from inside the square root. Assume yyy is positive.
\sqrt{39y^9}=
39y
9
Answers
The final expression is
sqrt (39y9) = y4 • sqrt(39y) assuming y as positive.
Rewrite
39 y ^9 as ((y^2)^2)^2 . 39 y
Factor out y^8.
√39(y^8 . y).
Rewrite [tex]y^8 as (y^4)^2[/tex]
√39(y^4)^2 . y).
Rules for simplifying variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
sqrt(x8)=x4
sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
sqrt(x5)=x2•sqrt(x)
sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(y9) = y4 • SQRT(y)
Therefore, sqrt (39y9) = y4 • sqrt(39y)
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y=2r-5 r+y=-8 plot both lines
Answers
The plot of both lines is given below.
y = 2r-5,
r + y = -8.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
The system of equations,
y = 2r-5,
r + y = -8.
And the intersection point is the solution of the equation.
The plot of the lines is given in the attached image.
Therefore, plots are given in the attached image.
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