Given the following:
Demand = 1050Ordering cost = 15Holding cost = 55The economic order quantity is 24.
What is the economic order Quantity?Eoq = √2 * demand * ordering cost / holding cost)
= √(2 * 1050 * 15 / 55)
EOQ = 24
What is the average number of bags on-hand?The Average inventory = EOQ / 2
= 24 / 2
= 12
How many orders per year will there be?Expected number of orders = demand / EOQ
= 1050 / 24
= 44
What is the total cost of ordering and carrying flour?Annual holding cost (AHC) = (EOQ / 2) * Holding cost
= (24 / 2) * 55
= 660
Annual ordering cost (AOC) = (demand / EOQ) * ordering cost
= (1050 / 24) * 15
= 656
Thus,
Total cost of managing = AHC + AOC
= 660 + 656
TCM = 1,316
If holding costs were to increase by $5 per year, how much would the minimum total annual cost?5. For holding cost of 60
EOQ= √(2 * demand * ordering cost / holding cost)
= √(2 * 1050 * 15 / 60)
= 23
Annual holding cost = (EOQ / 2) * holding cost
this gives us
= (23 / 2) * 60
= 690
Annual ordering cost = (demand / EOQ) * ordering cost
= (1050 / 23) * 15
= 685
Total cost of managing = AHC+ AOC
= 690 + 685
= 1375
Change in total annual cost = new - old
= 1375 - 1316
= 59
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If an event has a 55% chance of happening in one trial, how do I determine the chances of it happening more than once in 4 trials?
The chances of it happening more than once in 4 trials is 13%
How to determine the numberFrom the information given, we have can deduce that;
Probability of 1 trial = 55%
= 55/ 100
Find the ratio
= 0. 55
We are to find the probability of it happening more than once in 4 different trials
If the probability of it happening in one trial is 555 which equals 0. 55
Then the probability of it happening in 1 in 4 trials is given as;
P(1/4 trials) = 1/ 4 × 55%
P(1/4 trials) = 1/ 4 × 0. 55
Put in decimal form
P(1/4 trials) = 0. 25 × 0. 55
P(1/4 trials) = 0. 138
But we have to know the percentage
= 0. 138 × 100
Multiply the values, we have
= 13. 8 %
Thus, the chances of it happening more than once in 4 trials is 13%
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An unknown radioactive element decays into non-radioactive substances. In 340
days the radioactivity of a sample decreases by 61 percent.
(a) What is the half-life of the element?
half-life: ? (days)
(b) How long will it take for a sample of 100 mg to decay to 81 mg?
time needed: ? (days)
(a) The half-life of the unknown radioactive element is 250.28 days.
(b) The time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.
Half life of the unknown radioactive elementN(t) = N₀(0.5)^t/h
where;
t is time of decayh is half lifeN₀ is initial massN(t) remaining mass at time, tin 340 days; N(340) = N₀(0.39);
1 - 0.61 = 0.39
N(340) = N₀(0.5)^340/h
N(340)/N₀ = 0.5^340/h
0.39 = 0.5^340/h
log(0.39) = 340/h x log(0.5)
log(0.39) /log(0.5) = 340/h
1.358 = 340/h
h = 340/1.358
h = 250.28 days
Time taken for the sample to decay 81 mg81 = 100(0.5)^t/250.28
81/100 = (0.5)^t/250.28
0.81 = (0.5)^t/250.28
log(0.81) = t/250.28 x log(0.5)
log(0.81) / log(0.5) = t/250.28
0.304 = t/250.28
0.304(250.28) = t
76.1 days = t
Thus, the half-life of the unknown radioactive element is 250.28 days and the time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.
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simplify 12x^6-4x^4+6x^2 over 2x^2
Answer:
6x⁴ - 2x² +3
Step-by-step explanation:
[tex]\frac{12x^6-4x^4+6x^2}{2x^2}=6x^4 - 2x^2 + 3[/tex]
Consider an urn containing 8 white balls, 7 red balls and 5 black balls.
1)Randomly select 2 balls without replacement. The probability of getting 2 white balls is equal to:
2)Randomly select 5 balls without replacement. the probability of getting 2 white balls is equal to:
3) randomly select 150 balls with replacement. The probability of getting at least 72 white balls is:
Answer + Step-by-step explanation:
1) The probability of getting 2 white balls is equal to:
[tex]=\frac{8}{20} \times \frac{7}{19}\\\\= 0.147368421053[/tex]
2) the probability of getting 2 white balls is equal to:
[tex]=C^{2}_{5}\times (\frac{8}{20} \times \frac{7}{19}) \times (\frac{12}{18} \times \frac{11}{17} \times \frac{10}{16})\\=0.397316821465[/tex]
3) The probability of getting at least 72 white balls is:
[tex]=C^{72}_{150}\times \left( \frac{8}{20} \right)^{72} \times \left( \frac{7}{20} \right)^{78} +C^{73}_{150}\times \left( \frac{8}{20} \right)^{73} \times \left( \frac{7}{20} \right)^{77} + \cdots +C^{149}_{150}\times \left( \frac{8}{20} \right)^{149} \times \left( \frac{7}{20} \right)^{1} +\left( \frac{8}{20} \right)^{150}[/tex]
[tex]=\sum^{150}_{k=72} [C^{k}_{150}\times \left( \frac{8}{15} \right)^{k} \times \left( \frac{7}{15} \right)^{150-k}][/tex]
First of all, we would determine the total number of balls in the urn as follows:
Total number of balls = 8 + 7 + 5
Total number of balls = 20 balls.
Next, we would determine the probability of getting two (2) white balls without replacement:
P(2 white balls) = 8/20 × 7/19
P(2 white balls) = 2/5 × 7/19
P(2 white balls) = 0.1474.
Part 2.When 5 balls are selected without replacement, the probability of getting two (2) white balls would be calculated as follows:
P = [⁵C₂ × (8/20 × 7/19) × (12/18 × 11/17 × 10/16)]
P = [5!/(2! × (5 - 2)!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [5!/(2! × 3!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [20/2 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = [10 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]
P = 0.3456.
Part 3.When 150 balls are randomly selected with replacement, the probability of getting at least seventy two (72) white balls would be calculated by applying binomial probability equation. Mathematically, binomial probability is given by this equation:
[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]
Substituting the given parameters into the formula, we have;
P = [¹⁵⁰C₇₂ × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]
P = [150!/(72! × (150 - 72)!) × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]
P = [150!/(72! × (78)!) × (4/5)⁷² × (4/5)⁽⁷⁸⁾]
P = 0.7948.
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I need the answers to this question
Answer: Madison can travel 2.2 miles less than Anthony on one gallon of gas.
Step-by-step explanation:
The equation y = 39.1[tex]x[/tex] represents the number of miles, [tex]y[/tex], that madison can drive her car for every x gallons of gas.
Question: Madison can travel _ miles _ than Anthony on one gallon of gas.
Lets find how much Madison travels on 1 gallon of gas.
39.1(1) = 39.1
Therefore, Madison travels 39.1 miles on one gallon of gas.
Now lets solve for Anthony
Anthony travels 380.7 miles on 9 gallons of gas.
Therefore we can set up the equation:
9x = 380.7 to show that 9 gallons equates to 380.7 miles
to solve divide 9 from both sides
[tex]\frac{9x}{9} =\frac{380.7}{9}[/tex]
x = 41.3
So, Anthony travels 41.3 miles on one gallon of gas
Now find whether Madison travels more or less than Anthony on one gallon.
39.1 - 41.3 = -2.2
This means that Anthony can travel 2.2 miles more than Madison.
For your answer, this means that:
Madison can travel 2.2 miles less than Anthony on one gallon of gas
Hope this helped and have a nice day :)
The length of line segment AG is 17 m and the line segment AD is 25 m. What is the length of line segment GD?
Answer:
AG = 17 m
AD = 25 m
GD = ?
AD = AG + GD
GD = AD - AG
= 25 - 17
= 8 m
the answer to your question is 8m
PLEASEEEEEEEEEE HELPPPP. which of the following system of inequalities would produce the region indicated on the graph below?
Answer: C
Step-by-step explanation:
The line [tex]y=x+2[/tex] is shaded below and is solid.
This eliminates all the options except for C.
Talia noticed that she does not have a common factor. What should she do?
Talia needs to leave the polynomial as is because it is prime and cannot be factored.
Talia needs to factor out a 3x from the first group and a 4x from the second group.
Talia needs to factor out a negative from one of the groups so the binomials will be the same.
Talia needs to apply the distributive property to get the expression (3x + 4)(5x – 1).
The correct option regarding Talia factoring is given by:
Talia needs to factor out a negative from one of the groups so the binomials will be the same.
Which expression is Talia tying to factor?The expression is given by:
(15x² - 3x) + (-20x + 4).
Her first step was:
3x(5x - 1) + 4(-5x + 1)
After that, she did not factor out anything more out of the expression. However, looking at the two terms of the addition, we can realize that:
(-5x + 1) = -(5x - 1), hence she should factor out the negative.
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61% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 46 owned dogs are randomly selected, find the probability that
a. Exactly 29 of them are spayed or neutered.
b. At most 29 of them are spayed or neutered.
c. At least 28 of them are spayed or neutered.
d. Between 28 and 32 (including 28 and 32) of them are spayed or neutered.
A good calculator is found at: Stattrek Binomial Calculator Round answers to at least 4 decimal places.
Using the binomial distribution, the probability that:
(a) Exactly 29 of them are spayed or neutered, that is, P(X = 29) = 0.1163.
(b) At most 29 of them are spayed or neutered, that is, P(X ≤ 29) = 0.6648.
(c) At least 28 of them are spayed or neutered, that is, P(X ≥ 28) = 0.5714.
(d) Between 28 and 32 (including 28 and 32) of them are spayed or neutered, that is, P(28 ≤ X ≤ 32) = 0.48345.
A binomial distribution, with a success rate of p on each trial, gives us the probability of x number of success in n number of trials, using the formula:
P(X = x) nCx.pˣ.qⁿ⁻ˣ, where q = 1 - p.
In the question, we are informed that 61% of owned dogs in the United States are spayed or neutered, and are given that 46 owned dogs are randomly selected.
This can be seen as a binomial probability distribution, with n = 46, and p = 61% = 0.61, q = 1 - p = 1 - 0.61 = 0.39.
(a) We are asked for the probability of exactly 29 of them being spayed or neutered.
Thus, x = 29, and we need to find P(X = 29).
Using the given calculator, P(X = 29) = 0.1163.
(b) We are asked for the probability of at most 29 of them being spayed or neutered.
Thus, we need to find P(X ≤ 29).
Using the given calculator, P(X ≤ 29) = 0.6648.
(c) We are asked for the probability of at least 28 of them being spayed or neutered.
Thus, we need to find P(X ≥ 28).
Using the given calculator, P(X ≥ 28) = 0.5714.
(d) We are asked for the probability between 28 and 32 of them are spayed or neutered.
Thus, we need to find P(28 ≤ X ≤ 32), which can be shown as;
P(28 ≤ X ≤ 32) = P(X ≤ 32) - P(X < 28).
Using the given calculator, P(X ≤ 32) = 0.91209.
Using the given calculator, P(X < 28) = 0.42864.
Thus, P(28 ≤ X ≤ 32) = P(X ≤ 32) - P(X < 28) = 0.91209 - 0.42864 = 0.48345.
Thus, using the binomial distribution, the probability that:
(a) Exactly 29 of them are spayed or neutered, that is, P(X = 29) = 0.1163.
(b) At most 29 of them are spayed or neutered, that is, P(X ≤ 29) = 0.6648.
(c) At least 28 of them are spayed or neutered, that is, P(X ≥ 28) = 0.5714.
(d) Between 28 and 32 (including 28 and 32) of them are spayed or neutered, that is, P(28 ≤ X ≤ 32) = 0.48345.
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If h(x) = 3x - 1 and j(x) = -2x, solve h[j(2)]
Answer:
-13
Step-by-step explanation:
First, we will find the value of j(2) first.
j(2) = -2(2) = -4
next, we will solve h[j(2)].
h[j(2)] = h(-4) = 3(-4) - 1 = -12 - 1 = -13
Look for a pattern in the data set to determine which kind of model best describes the data.
Running Speed of a Human
Distance Traveled
(miles)
1
2
3
4
Average Speed
(miles per hour)
7
6.3
5.67
5.103
The data appear to be linear.
The data appear to be quadratic.
The data appear to be cubic.
The data appear to be exponential.
On looking for a pattern in the given data set, the quadratic model best describes the data.
2nd option is correct.
A data model represents the type of relationship between the variables of a data set.
Data models are of four types, namely, Linear, Cubic, Quadratic and Exponential data models.
Given data is:
Distance Traveled Average Speed(miles per hour)
(miles)
1 7
2 6.3
3 5.67
4 5.103
A quadratic model is the best data model for the given data set.
The pattern observed in the given data set observes the properties of a quadratic function.
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Answer:
Exponential is the correct answer.
Step-by-step explanation:
What is the largest prime number p such that 8 times p is less than 1000?
Answer:
113
Step-by-step explanation:
first we need to divide 1000 by 8 to get 125.
Our prime number has to be less than 125.
The largest prime number less than 125 is 113.
The angle bisectors of a triangle intersect at a point called the
Answer:
incenter
Step-by-step explanation:
Question: 1 An analysis of an unknown compound found it contained 40 g potassium, 52 g chromium and 56 g of oxygen. a) What is the empirical formula for this compound? b) What type of compound is it, ionic, covalent or a combination of both? Explain your choice.
1) The empirical formula for this compound is; K₂Cr₂O₇
2) It is an Ionic compound because it has two potassium ions (K+) and a negatively charged dichromate ion (Cr2O7-).
How to find the Empirical Formula?
1) Elements of the unknown compound are;
Potassium = 40 g
Chromium = 52 g
Oxygen = 56 g
Let us find the number of moles of each element;
Number of moles of Potassium = 40/39 = 1.026 mol K
Number of moles of Chromium = 52/52 = 1 mol Cr
Number of moles of oxygen = 56/16 = 3.5 mol O
Multiply through the number of moles by 2 and round up to the nearest whole number to get the empirical formula at; K₂Cr₂O₇
2) The compound K₂Cr₂O₇ is called Potassium dichromate. It is classified as an ionic compound because it has two potassium ions (K+) and a negatively charged dichromate ion (Cr2O7-).
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DETAILS BASSELEMMATH7 9.PP1.035. 0/1 Submissions Used The measure of the smallest angle of a right triangle is 10° less than the measure of the other small angle. Find the measures of all three angles in degrees. smallest angle largest angle.
Answer:
40°, 50°, and 90°
Step-by-step explanation:
Let the smallest angle be x.
Then, the other small angle is x+10.
The acute angles of a right triangle are complementary, so x+x+10=90, and thus x=40.
So, the acute angles measure 40° and 50°.
Therefore, the three angles are 40°, 50°, and 90°.
Reagan has a part-time job walking dogs. She makes $12.20 per hour. If she earns $106.75 this week, how many hours does she work?
Answer:
8.75
Step-by-step explanation:
106.75 divided by 12.20= 8.75
To reduce their expected estate tax liability prior to either spouse's death, the Hansens could?
If the Hansens want to reduce their expected estate tax liability prior to the death of either of the spouses, they could initiate a Marital Transfer.
What is a marital transfer?A Marital transfer simply means that the Hansens should bequest their assets to each each other in case either of them die.
If this happens, the surviving spouse will not be charged any estate taxes because bequests to spouses are not subject to taxation.
To do this, the Hansens should put it into both of their wills that they plan to gift/ bequest their assets to their spouse if they die.
The big disadvantage of using a marital transfer however, is that the estate will still be subject to taxes when the surviving spouse dies. All the estate taxes that had been avoided would then be incurred by the estate but only after the death of both spouses.
In conclusion, they should use a marital transfer.
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Describe the translation.
y=(x−5)2+5 → y=(x−0)2+0
A. T<−5,5>
B. T<5,−5>
C. T<−5,−5>
D. T<5,5>
Answer:
C
Step-by-step explanation:
This is a translation 5 units left and 5 units dowh.
Here, the translation is [tex]T < 5,-5 >[/tex].
What is translation?The translation is a coordinate transformation operation in which a point or a figure moves left/right/up or down in a coordinate system or a set of axes. After applying translation, the size of the figure remains unchanged, just the position changes. For example, consider a function [tex]y=f(x)[/tex]. If we translate it to the new function [tex]y'=f(x+a)+b[/tex], then the graph of [tex]y[/tex] moves [tex]a[/tex] units to the right and [tex]b[/tex] units to the up and in this case the translation is denoted by [tex]T < a,b >[/tex]Here, the translation is given as: [tex]y=2(x-5)+5\longrightarrow y=2(x-0)+0[/tex].
i.e. [tex]y=2(x-5)+5\longrightarrow y=2(x-5+5)+(5-5)[/tex].
So, the graph of [tex]y[/tex] moves 5 units to the right and (-5) units to the up i.e., 5 units to the down.
Therefore, here, the translation is [tex]T < 5,-5 >[/tex].
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PLEASE HELP ASAPP PLEASE
Answer: Interior Angle
Step-by-step explanation:
The angle BAD is fully enclosed, it is on the inside
Help me with this question asap please !
Answer:
BA
CB
CA
Step-by-step explanation:
this simply means that such a letter combination stands for a line that goes through the points with these letters.
and a "ray" means a straight line (not one that goes around a corner). "from this figure" means lines (or connections between points) that are drawn in this graphic.
BA yes
B is just a point, no line. therefore, no.
DBA guys around a corner (from D to B, and then from there to A). therefore, no.
AD would be a straight line, but it is not drawn in the graphic. therefore, no.
ADB is partly not drawn, and it goes around a corner. therefore, no.
CB, CA are both straight lines in the graphic. yes.
According to a recent poll at a university,70.7 % of high school seniors in a certain region had a driver's license. A sociologist thinks this rate has declined. The sociologist surveys randomly selected high school seniors and finds that have a driver's license. a. Pick the correct null hypothesis. b. Pick the correct alternative hypothesis. c. In this context, what does the symbol p represent?
your mother i swear
Step-by-step explanation:
ask yo mom
The volume of a sphere is 4500π m3. What is the surface area of the sphere to the nearest square meter?
Answer:
2827 m²
Step-by-step explanation:
The equation for volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Using this equation and the given volume of the sphere, we can find the radius of the sphere.
Finding the Radius[tex]V=\frac{4}{3}\pi r^3[/tex]
[tex]4500\pi = \frac{4}{3}\pi r^3[/tex]
Divide both sides by π
[tex]4500=\frac{4}{3}(r^3)[/tex]
Multiply both sides by 3
[tex]13500=4( r^3)[/tex]
Divide both sides by 4
[tex]3375=r^3[/tex]
Take the cube root of both sides
[tex]r=15[/tex]
Thus the radius of the sphere is 15m. We can use this information to find the surface area of the sphere.
Finding the Surface AreaThe equation for surface area of a sphere is [tex]4\pi r^2[/tex]. Substituting the value we found for the radius into the equation, we find:
[tex]SA=4\pi r^2\\SA=4\pi 15^2\\SA=4\pi 225\\SA=900\pi\\SA\approx2827$ m^2[/tex]
The surface area of the sphere, rounded to the nearest square meter, is 2827 m².
To begin to better understand personal experiences of headache pain, a drug manufacturer has asked 18 adults to rate their most recent headache on a scale of 0 to 100 (with 0 corresponding to no pain and 100 corresponding to the greatest pain the person has ever felt). Here are the 18 ratings.
The answers to these questions are:
Non of the abovemeanmean and medianmean is greater.How to solve for the solutionsa. In the question we have the existence of the mean, the mode and the median hence the answer to this question is none.
b. if the measurement 14 is replaced by 2, the data that it is going to have the most effect on is going to be the mean. It would reduce the mean.
c. If the largest measurement is removed, it is going to have the most effects on the mean and the median.
d. If the data is skewed then the mean of the data set is going to be greater.
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Prove: In an equilateral triangle the three medians are equal
Step-by-step explanation:
Let ABC be the equilateral triangle. Let AE, BD and CF be the medians. A meridian divides a side into two equal parts. Hence, proved that medians of an equilateral triangle are equal .
Select the correct answer. The graph of function f is shown. An exponential function passes through (minus 4, 9), (0, 1), (1, 0), and (5, minus 2). Function g is represented by the table. x -1 0 1 2 3 4 g(x) 24 6 0 -2 Which statement correctly compares the two functions? A. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. C. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞. D. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
The answer choice which correctly draws a comparison between the end behaviours of the functions is; Choice C; They have the same end behavior as x approaches -∞ and same end behavior as x approaches ∞.
Which answer choice correctly compares the end behaviour of the functions?As given in the task content; the graph of the exponential function passes through (-4, 9), (0, 1), (1, 0), and (5, -2).
It therefore follows that as; x reduces (approaches -∞), the y value increases.
And, as x -increases (approaches +∞), the y-value decreases.
For the table, the values can be written as coordinates as follows; (-1,2), (0,4), (1,6), (2, 0), (3,-2).
Consequently, as x reduces (approaches -∞), the y- values decrease.
And, as x increases (approaches +∞), the y-values decrease.
Ultimately, the two functions in discuss can be concluded to have; Choice C.
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look at the screenshot and explain your answer pls
Answer:
f(x) = g(x) + 9 because it is shifted 9 to the right
please help with the first one
Answer:
y = x +5
Step-by-step explanation:
The equation of a parallel line will have the same x- and y-coefficients, but a different constant. You need to find the constant that makes the line go through the given point.
ApplicationThe given line is y = x +1. The equation you're looking for is
y = x +c . . . . . . for some new constant c
We want this equation to be true for (x, y) = (-2, 3). Putting these values into the equation, we can solve for c.
3 = -2 +c
5 = c . . . . . . add 2
The desired equation is y = x +5.
Consider the curve C in the Cartesian plane described in polar coordinates by given:
See picture:
a. Determine a Cartesian equation that describes curve C. Hint: first multiply (c) by r.
b Describe this curve and use this description to obtain the area inside C.
c Use (c) to set up an integral that computes the area inside C that is also within the rst quadrant.
d Evaluate this integral to determine the area.
a. Recall that in polar coordinates, we can parameterize [tex]x=r\cos(\theta)[/tex] and [tex]y=r\sin(\theta)[/tex]. So, doing as the hint suggests, we have
[tex]r = 6\cos(\theta) + 8 \sin(\theta)[/tex]
[tex]\implies r^2 = 6r\cos(\theta) + 8r\sin(\theta)[/tex]
[tex]\implies \boxed{x^2 + y^2 = 6x + 8y}[/tex]
b. By completing the square, we get
[tex]x^2 + y^2 = 6x + 8y[/tex]
[tex]x^2 - 6x + y^2 - 8y = 0[/tex]
[tex]x^2 - 6x + 9 + y^2 - 8y + 16 = 25[/tex]
[tex](x-3)^2 + (y-4)^2 = 5^2[/tex]
which is the equation of the circle centered at (3, 4) with radius 5. Thus the area bounded by [tex]C[/tex] is [tex]\pi\cdot5^2 = \boxed{25\pi}[/tex].
c. This is made easier if you can consult a plot (attached). In the first quadrant, we have [tex]0\le\theta\le\frac\pi2[/tex], while the radial coordinate [tex]r[/tex] runs uninterrupted from the origin [tex]r=0[/tex] to the circle [tex]r=6\cos(\theta)+8\sin(\theta)[/tex]. So the area is
[tex]\displaystyle \int_0^{\pi/2} \int_0^{6\cos(\theta) + 8\sin(\theta)} r\,dr\,d\theta = \boxed{\frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta}[/tex]
d. Evaluate the integral.
[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(36\cos^2(\theta) + 96\sin(\theta)\cos(\theta) + 64 \sin^2(\theta)\right) \, d\theta[/tex]
Simplify the integrand with the help of the identities
[tex]\cos^2(x) + \sin^2(x) = 1[/tex]
[tex]\sin(x)\cos(x) = \dfrac12 \sin(2x)[/tex]
[tex]\sin^2(x) = \dfrac{1 - \cos(2x)}2[/tex]
[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(50 + 48\sin(2\theta) - 14 \cos(2\theta)\right) \, d\theta[/tex]
The rest is easy. You should end up with
[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta = \boxed{24 + \frac{25\pi}2}[/tex]
a) The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.
b) The area inside C is A = π · 5² = 25π square units.
c) The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].
d) The integral evaluated at the given limits is equal to an area of 20.139π square units.
How to analyze a polar equation and find its area by geometric and calculus means
In this question we find a polar equation in explicit form. a) To find the equivalent form in rectangular coordinates, we must apply the following substitutions x = r · cos θ, y = r · sin θ:
r = 6 · cos θ + 8 · sin θ
r² = 6 · r · cos θ + 8 · r · sin θ
x² + y² = 6 · x + 8 · y (1)
The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.
b) Perhaps the equation represents a conic section, possibly a circunference. To prove this assumption, we must apply algebraic handling until standard form is obtained:
x² - 6 · x + y² - 8 · y = 0
x² - 6 · x + 9 + y² - 8 · y + 16 = 25
(x - 3)² + (y - 4)² = 5² (1b)
Which indicates a circumference centered at point (h, k) = (3, 4) and with a radius of 5 units. By the area formula for a circle we find that the area inside C is A = π · 5² = 25π square units.
c) The polar form of the area integral is presented herein:
A = ∫ ∫ r dr dθ, for r ∈ [0, r(θ)] and θ ∈ [0, 0.5π]
A = (1 / 2)∫ [r(θ)]² dθ, for θ ∈ [0, 0.5π]
A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π]
The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].
d) By algebraic handling, trigonometric formulas and integral properties:
A = 25 ∫ dθ + 24 ∫ sin 2θ dθ - 14 ∫ cos 2θ dθ, for θ ∈ [0, 0.5π]
A = 25 · θ - 12 · cos 2θ - 7 · sin 2θ, for θ ∈ [0, 0.5π]
A = 20.139π
The integral evaluated at the given limits is equal to an area of 20.139π square units.
To learn more on circumferences: https://brainly.com/question/4268218
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please help.
A report by the NCAA states that 57.5% of football injuries occur during practices. A head trainer claims that this is too high for this conference, so he randomly selects 36 injuries and founds that 17 occurred during practices. Is his claims correct at a=0.05?
Answer:
he is more likely incorrect.
Step-by-step explanation:
Z = (ps - p0)/sqrt(p0(1-p0)/n)
ps = proportion sample
p0 = proportion null hypothesis (NCAA)
n = sample size
ps = 17 / 36/100 = 17/1 / 36/100 = 1700/36 =
= 47.22222222...%
Z = (0.47222... - 0.575)/sqrt(0.575(1 - 0.575)/36) =
= -0.10277777... /sqrt(0.244375 / 36) =
= -0.10277777... / 0.0823905... =
= -1.247446952... ≈ -1.25
p(-1.25) = 0.10565
0.10565 > 0.05
the null hypothesis is therefore likely, or at least cannot be rejected.
so, his claims are not supported, as surprising as this might feel given that the sample result itself is 10 points off the NCCA result, which feels to be a solid difference.
List all elements of B that belong to specified set B={10, square root of 5, -14, 2/3, square root of 16, 0.81
The irrational number on set B is given by: [tex]\sqrt{5}[/tex]
What are irrational numbers?Irrational numbers are numbers that cannot be represented by fractions. The two most common examples are:
Non-exact roots.Non-terminating decimal.In the set B given in this problem, the only number that is irrational is [tex]\sqrt{5}[/tex], as it is a non-exact root.
More can be learned about irrational numbers at https://brainly.com/question/2236338
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