A type II error would occur if the candidate is actually a drug user, but the drug test incorrectly classifies them as a nonuser.
A type II error occurs when the null hypothesis is not rejected, even though it is false.
In this case, the null hypothesis is that the job candidate is not a drug user.
Therefore, a type II error would occur if the candidate is actually a drug user, but the drug test incorrectly classifies them as a nonuser.
In other words, a type II error would occur if the drug test fails to detect drug use in a job candidate who is actually a drug user.
This means that the organization would mistakenly hire a drug user, which could have negative consequences for the workplace and potentially put the safety of others at risk.
To minimize the risk of type II errors, organizations should use drug tests that are as accurate as possible and consider using multiple types of tests or follow-up testing to confirm results.
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A small submarine starts at –1,260 feet in relation to sea level. Then it descends 5 feet per minute for 12 minutes.
What expression represents the new position of the submarine in relation to sea level?
–5(12) + 1,260
–1,260 + (–5)(12)
–1,260 + (5)(12)
1,260 – (–5)(12)
Both expressions are equivalent and represent the same result. So the final answer is that the new position of the submarine in relation to sea level is -1,320 feet.
To find the new position of the submarine in relation to sea level, we need to take into account its initial position and the rate at which it descends.
The submarine starts at a depth of -1,260 feet, so this will be our starting point.
We know that the submarine descends at a rate of 5 feet per minute for 12 minutes. To calculate how far it descends in total, we can multiply the rate by the time:
5 feet/minute x 12 minutes = 60 feet
So the submarine descends 60 feet in total. However, since it is descending, we need to subtract this value from the initial depth of -1,260 feet:
-1,260 feet - 60 feet = -1,320 feet
Therefore, the expression that represents the new position of the submarine in relation to sea level is:
-1,260 - (5 x 12) = -1,320
Alternatively, we could also write this as:
-1,260 + (-5 x 12) = -1,320
Both expressions are equivalent and represent the same result. So the final answer is that the new position of the submarine in relation to sea level is -1,320 feet.
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Answer:
Step-by-step explanation:
the answer is B
if one u.s. dollar buys 1.59 canadian dollars, how many u.s. dollars can you purchase for one canadian dollar (cad)?
U.S. dollars can be purchased for one Canadian dollar is 0.63 U.S. dollar.
One U.S. dollar buys 1.59 Canadian dollar
1 U.S. dollar = 1.59 CAD dollar
By using the unitary method to calculating the value of 1 Canadian dollar.
The unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit .
Value of one Canadian dollar
1/1.59 U.S. dollar = 1 CAD dollar
1 CAD dollar = 0.63 U.S. dollar
1 CAD dollar can buy 0.63 U.S. dollar.
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acme toy company sells baseball cards in packages of 100. three types of players are represented in each package -- rookies, veterans, and all-stars. the company claims that 30% of the cards are rookies, 60% are veterans, and 10% are all-stars. cards from each group are randomly assigned to packages. suppose you bought a package of cards and counted the players from each group. what method would you use to test acme's claim that 30% of the production run are rookies; 60%, veterans; and 10%, all-stars.
To test Acme's claim that 30% of the production run are rookies, 60% are veterans, and 10% are all-stars, you would use a hypothesis test. The null hypothesis would be that the claimed proportions are true (pR = 0.3, pV = 0.6, pA = 0.1) and the alternative hypothesis would be that at least one of the claimed proportions is incorrect.
You could use a goodness-of-fit chi-square test to compare the observed frequencies of each group of players in the package to the expected frequencies based on the claimed proportions. If the chi-square test statistic is large enough to reject the null hypothesis, then there is evidence that the claimed proportions are not accurate. The significance level would need to be chosen and the appropriate critical value for the chi-square distribution with 2 degrees of freedom would need to be calculated or looked up.
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find the gcf of the following literal terms. m 7 n 4 p 3 and mn 12 p 5
The GCF of the given literal terms m⁷ n⁴ p³ and mn¹² p⁵ is mn⁴p³.
To find the greatest common factor (GCF) of the given literal terms, we need to identify the highest power of each variable that appears in both terms.
The variables present in both terms are m, n, and p.
For m, the highest power is m⁷ in the first term and m¹ in the second term. Therefore, the common factor for m is m¹.
For n, the highest power is n⁴ in the first term and n¹² in the second term. Therefore, the common factor for n is n⁴.
For p, the highest power is p³ in the first term and p⁵ in the second term. Therefore, the common factor for p is p³.
Combining these common factors, we get the GCF of the given literal terms:
GCF = m¹ * n⁴ * p³
Therefore, the GCF of the given literal terms m⁷ n⁴ p³ and mn¹² p⁵ is mn⁴p³.
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Conditional Probability
A card is chosen at random from a standard deck. What is the probability that the card is a spade or a king, given that it is black?
Find each probability as a fraction (in simplest form), decimal, and percent.
The probability that a card is a spade or a king, given that it is black is 3/26 or 0.1154 or 11.54%
The probability that a card is a spade or a king, given that it is black?In a standard deck of cards, we have the following readings
Black cards = 26
Black spade or king = 3
So, we have the probability formula to be
Probability = Black spade or king/Black cards
This gives
Probability = 3/26
Evaluate
Probability = 0.1154
Express as percentage
Probability = 11.54%
Hence, the probability that a card is a spade or a king, given that it is black is 3/26
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Volume of a cone rh, curved surface area of a cone = xr!] [Volume of a spheresurface area of a sphere 4ar']
The solid is formed from a hemisphere of radius rcm fixed to a cone of radius rcm and height hem. The volume of the hemisphere is one third of the volume of the solid.
(a) Find h in terms of r
(b) The slant height of the cone can be written as Vk cm, where k is an integer.
Find the value of k
(c) Find an expressionin terms of r and x, for the total surface area, in cm², of the solid
Answer:
Long solution
Step-by-step explanation:
(a) Let the height of the cone be h cm. The volume of the hemisphere is given by (1/2)(4/3)πr³ = (2/3)πr³. The volume of the solid is the sum of the volumes of the hemisphere and the cone, which is (2/3)πr³ + (1/3)πr²h. Since the volume of the hemisphere is one third of the volume of the solid, we have:
(2/3)πr³ = (1/3)πr²h
Simplifying, we get:
2r = h
Therefore, h is expressed in terms of r as h = 2r.
(b) The slant height of the cone can be found using the Pythagorean theorem. Let l be the slant height, then we have:
l² = r² + h²
Substituting h = 2r, we get:
l² = r² + (2r)² = 5r²
Taking the square root of both sides, we get:
l = r√5
Since k is an integer, we can write:
l = Vk cm, where k is an integer
Comparing the two expressions, we get:
Vk = r√5
Therefore, the value of k is k = ⌊r√5⌋, where ⌊x⌋ denotes the largest integer less than or equal to x.
(c) The total surface area of the solid is the sum of the curved surface area of the cone, the curved surface area of the hemisphere, and the area of the circular base of the cone. We have:
Curved surface area of the cone = πr l = πr(r√5) = πr²√5
Curved surface area of the hemisphere = 2πr²
Area of the circular base of the cone = πr²
Therefore, the total surface area of the solid, in cm², is given by:
πr²√5 + 2πr² + πr² = (πr²)(√5 + 3)
(1/4) ^ -4 =256
but when we use the 1/a^n there is already a one over the four.. also why do we end up with a whole number when its 1/256 at a point
From the power rules, it is possible to prove that [tex](\frac{1}{4})^{-4 }[/tex]=256.
Power RulesThe main power rules are presented below.
Multiplication with the same base: you should repeat the base and add the exponents.Division with the same base: you should repeat the base and subtract the exponents.Power. For this rule, you should repeat the base and multiply the exponents.Exponent negative - For this rule, you should write the reciprocal number with the exponent positive.Zero Exponent. When you have an exponent equal to zero, the result must be 1.For proving the exercise, you should follow the steps below.
Apply the Power Rule - Exponent negativeFor this, you should write the reciprocal number with the exponent positive. Thus,[tex](\frac{1}{4})^{-4 }= 4^{4 }[/tex]
Solve the power Rule -In the previous step, you found [tex]4^{4 }[/tex]. This represents that 4 x 4 x 4 x 4= 16 x 16=256.
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use a proportion to estimate each animal population total ducks counted:1,100 marked ducks counted:257 total marked duck:960
The total population of ducks is 960.
To estimate the total population of ducks, we can set up a proportion using the marked ducks as a sample.
Let's use the following proportion:
Total Ducks / Marked Ducks = Total Marked Ducks / Marked Ducks Counted
Total Ducks / 257 = 960 / 257
Total Ducks x 257 = 960 x 257
Divide both sides by 257 to solve for Total Ducks:
Total Ducks = (960 x 257) / 257
Total Ducks = 960
Based on the proportion, we estimate that the total population of ducks is 960.
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What is the maximum vertical distance between the line
y=2x+63
and the parabola y=x^2 for -7
The maximum vertical distance between the line y = 2x + 63 and the parabola y = x^2 for -7 ≤ x ≤ 7 is 32 units.
To find the maximum vertical distance between the line y = 2x + 63 and the parabola y = x^2 for -7 ≤ x ≤ 7, we need to determine the points on the parabola that have the maximum vertical distance from the line.
Let's start by finding the points of intersection between the line and the parabola. Setting the equations equal to each other, we have:
2x + 63 = x^2
Rearranging the equation, we get:
x^2 - 2x - 63 = 0
Solving this quadratic equation, we find that x = -7 and x = 9 are the x-coordinates of the points of intersection.
Now, let's calculate the corresponding y-values for these x-coordinates on the parabola:
For x = -7, y = (-7)^2 = 49
For x = 9, y = (9)^2 = 81
Next, we can calculate the y-values for the line at these x-coordinates:
For x = -7, y = 2(-7) + 63 = 49
For x = 9, y = 2(9) + 63 = 81
Since the y-values of the line and the parabola are the same at the points of intersection, the maximum vertical distance occurs at the point (-7, 49) and (9, 81).
The maximum vertical distance between the line and the parabola is the difference in y-coordinates at these points:
81 - 49 = 32
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Brainleist and 50 points to first correct answer!!!!!!
Answer:
If we are using the Triangle Inequality Theorem the answer would be:
Step-by-step explanation:
1: Yes
2: Yes
3: Yes
4: No
5: Yes
6: No
7: No
I hope this helps! :)
Step-by-step explanation:
Due to the triangle side length rule :
any two sides summed must be greater than the remaining side
yes
yes
yes
no 3+4 is not greater than the remaining side 8
yes
no 8+3 not greater than 15
no 4 + 8 not greater than 15
The time the player spends on storytelling must be two times of
combatting. The time spent on exploring must be six times that of
combatting. The time for puzzle solving is the same amount as
combatting, and players should spend 15 minutes on the Hero
character creation. We need to create a game that has 615
minutes (more than 10 hours) in total playtime. What is the total
combat time in this game we should set? Write the equation
The total combat time in the game should be set as 60 minutes.
Let's denote the time spent on combatting as "c" (in minutes).
Based on the given information:
Storytelling time is two times combatting time: 2cExploring time is six times combatting time: 6cPuzzle-solving time is the same as combatting time: cHero character creation time: 15 minutesTo find the total playtime, we add up all the components:
Total playtime = Combat time + Storytelling time + Exploring time + Puzzle-solving time + Hero creation time
or, Total playtime = c + 2c + 6c + c + 15
We know that the total playtime is 615 minutes, so we can set up the equation:
615 = 10c + 15
Simplifying the equation:
10c = 615 - 15
10c = 600
c = 60
Therefore, the total combat time in the game should be set as 60 minutes.
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What is one change you can make to one value in Dylan's plan to ensure that he completes his assignment in time? Justify your response.
One change that can be made to one value in Dylan's plan to ensure the assignment is completed is to change hours worked to 4. 20 hours a day.
How to find the change ?The current number of paper flowers that the team can make is:
= 4 x 3 hours a day x 12 people x 5 days per week x 2 weeks
= 1, 440 flowers
One change that can be made would be to increase the number of hours worked to 4. 20 hours.
This would give a total number of flowers of :
= 4 x 4. 20 hours a day x 12 people x 5 days per week x 2 weeks
= 2, 016 flowers
They would then meet the target.
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what is the perimeter of an oval
Answer:
To find the perimeter (or arc length) of an ellipse, you'll need to use an elliptic integral
The perimeter is a distance around the outlines or edge of any shape. A practical example of measuring the perimeter of an ellipse would be the distance you cover when you walk along the edges of an elliptical-shaped field. Or the length of fence you need to surround it
You deposit $2500 in an account that pays 6% annual interest. Calculate the account balance after one ye: when the interest is compounded annually, semiannually, quarterly, monthly, and continuously
If you deposit $2500 in an account that pays 6% annual interest, the account balance after one year can be calculated using the following formulas for different compounding periods:
- Annually: A = P(1 + r)^n, where A is the account balance, P is the principal, r is the annual interest rate, and n is the number of years. Substituting the given values, we get A = 2500(1 + 0.06)^1 = $2650.
Semiannually: A = P(1 + r/n)^(n*t), where n is the number of times the interest is compounded in a year and t is the time period in years. Substituting the given values, we get A = 2500(1 + 0.06/2)^(2*1) = $2659.51.
- Quarterly: A = P(1 + r/n)^(n*t), where n is 4 (number of times compounded in a year) and t is 1 (one year). Substituting the given values, we get A = 2500(1 + 0.06/4)^(4*1) = $2664.90.
- Monthly: A = P(1 + r/n)^(n*t), where n is 12 (number of times compounded in a year) and t is 1 (one year). Substituting the given values, we get A = 2500(1 + 0.06/12)^(12*1) = $2668.21.
- Continuously: A = Pe^(r*t), where e is the base of the natural logarithm. Substituting the given values, we get A = 2500*e^(0.06*1) = $2671.00.
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Which of the following causes changes in the CPI to overstate the true inflation rate?
a. new product bias
b. substitution bias
c. increase in quality bias
d. all of the above
Answer:
Step-by-step explanation:
The correct answer is d. All of the above causes changes in the CPI to overstate the true inflation rate.
Find the final amount of money in an account after 5 years if $2, 400 is deposited at 6.5% interest rate
compounded annually.
Use the exponential formula A(t) = P(1 + r/n)^nt, where A is the future value, P is the principal
(present value), r is the interest rate, n is the number of times each year that the interest is compounded,
and t is the time in years.
The final amount of money in the account after 5 years is $3,316.08.
We have,
P = 2400 (the initial deposit)
r = 0.065 (the annual interest rate expressed as a decimal)
n = 1 (compounded annually)
t = 5 (5 years)
Plugging these values into the exponential formula, we get:
A(5) = 2400(1 + 0.065/1)⁽¹ ˣ ⁵⁾
= 2400(1.065)⁵
≈ $3,316.08
Therefore, the final amount of money in the account after 5 years with an initial deposit of $2,400 and a 6.5% interest rate compounded annually is $3,316.08.
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question 8 a gym wants to start offering exercise classes. a data analyst plans to survey 10 people to determine which classes would be most popular. to ensure the data collected is fair, what steps should they take? select all that apply.
Main Answer:The applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.
Supporting Question and Answer:
Why is random sampling an important step in ensuring fair data collection for determining popular exercise classes?
Random sampling is important in fair data collection as it helps ensure that the selected participants represent the larger population of the gym. By randomly selecting participants, the data analyst reduces the risk of bias and ensures that the survey results are more likely to be representative of the preferences of the entire gym population.
Body of the Solution: To ensure the data collected for determining the most popular exercise classes is fair, the data analyst should consider the following steps:
Random sampling: The analyst should randomly select the 10 people to participate in the survey. This helps ensure that the sample is representative of the gym's population and reduces bias.Informed consent: The analyst should obtain informed consent from the participants, explaining the purpose of the survey, how the data will be used, and ensuring that participants are willing to participate voluntarily.Confidentiality and anonymity: The analyst should assure the participants that their responses will be kept confidential and anonymous. This encourages honest and unbiased responses, as individuals may feel more comfortable sharing their preferences without fear of judgment or repercussions.Clear and unbiased questions: The survey questions should be clear, unbiased, and directly related to determining the most popular exercise classes. The questions should avoid leading or suggestive language that could influence participants' responses.Sufficient sample size: While surveying 10 people can provide some insights, a larger sample size would increase the reliability and representativeness of the data. The analyst may consider increasing the sample size to obtain a more robust understanding of class preferences.Therefore, the applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.
Final Answer: Hence,the applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.
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The applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.
Why is random sampling an important step in ensuring fair data collection for determining popular exercise classes?Random sampling is important in fair data collection as it helps ensure that the selected participants represent the larger population of the gym. By randomly selecting participants, the data analyst reduces the risk of bias and ensures that the survey results are more likely to be representative of the preferences of the entire gym population.
To ensure the data collected for determining the most popular exercise classes is fair, the data analyst should consider the following steps:
The analyst should randomly select the 10 people to participate in the survey. This helps ensure that the sample is representative of the gym's population and reduces bias.
Informed consent: The analyst should obtain informed consent from the participants, explaining the purpose of the survey, how the data will be used, and ensuring that participants are willing to participate voluntarily.
Confidentiality and anonymity: The analyst should assure the participants that their responses will be kept confidential and anonymous. This encourages honest and unbiased responses, as individuals may feel more comfortable sharing their preferences without fear of judgment or repercussions.
Clear and unbiased questions: The survey questions should be clear, unbiased, and directly related to determining the most popular exercise classes. The questions should avoid leading or suggestive language that could influence participants' responses.
Sufficient sample size: While surveying 10 people can provide some insights, a larger sample size would increase the reliability and representativeness of the data. The analyst may consider increasing the sample size to obtain a more robust understanding of class preferences.
Therefore, the applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.
Hence, the applicable steps to ensure fair data collection would be: Random sampling, informed consent, confidentiality and anonymity, and clear and unbiased questions.
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What is the least common multiple of x^2+3x-4 and 2x^2-2
2(x-4)(x+1)^2(x-1)
(x+1)
2(x+4)(x-1)^2(x+1)
(x-1)
The LCM of the two polynomials is (x - 1)(x + 4)(x + 1).
Let's factorize the given polynomials:
Polynomial 1:
x² + 3x - 4 can be factored as (x - 1)(x + 4).
Polynomial 2:
2x² - 2 can be factored as 2(x - 1)(x + 1).
Now, we identify the highest power of each distinct factor:
The highest power of (x - 1) is (x - 1).
The highest power of (x + 4) is (x + 4).
The highest power of (x + 1) is (x + 1).
Therefore, the LCM of the two polynomials is (x - 1)(x + 4)(x + 1).
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d(4)=45e^-0.15(4) I got my answer but I was told it was wrong need help please.
"The approximate value of D(4) is 24.6976." Please double-check your calculations and ensure that you correctly evaluated e^(-0.6) in your initial attempt. If you received a different answer, there may have been an error in the calculation.
To evaluate the expression D(4) = 45e^(-0.15(4)), we can follow the order of operations.
First, we simplify the exponent inside the parentheses:
-0.15(4) = -0.6
Next, we substitute this value back into the expression:
D(4) = 45e^(-0.6)
Using the properties of exponential functions, we can rewrite this as:
D(4) = 45 * e^(-0.6)
Now, we can calculate the value of e^(-0.6) using a calculator or mathematical software:
e^(-0.6) ≈ 0.5488 (rounded to four decimal places)
Finally, we substitute this value back into the expression:
D(4) ≈ 45 * 0.5488 ≈ 24.6976.
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EMERGENCY. help please
The probability of getting $800 or $1000 is 0.125.
Sample space = {Bankrupt, $350, $400, $600, $800, Lose a turn, $700, $300, $450, $900, Bankrupt, $600, $900, $400, $750, $300, $500, $450, $1000, $250, $800, $600, $200, $550}
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Here, total number of outcomes = 24
a) P(bankrupt) = 2/24 = 1/12
b) P(at least $500) = 12/24 = 1/2
c) P($800) = 2/24
P($1000) = 1/24
P($800 or $1000) = 2/24 + 1/24
= 3/24
= 1/8
= 0.125
d) P(a maximum of $700) = 4/24 = 1/6
e) P(less than $400) = 5/24
f) P(lose a turn) = 1/24
Therefore, the probability of getting $800 or $1000 is 0.125.
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A sciencetist used 90 grams of sodium nitrate during an experament One ounce is approximately equal to 28. 3 grams which measurement is closets to the number of ounces of sodium nitrate the scienctist used
The measurement closest to the number of ounces of sodium nitrate the scientist used is 3.17 ounces.
We are given that the scientist used 90 grams of sodium nitrate. To convert this measurement to ounces, we can divide the grams by the conversion factor of 28.3 grams per ounce.
90 grams / 28.3 grams per ounce ≈ 3.17 ounces
Since 3.17 ounces is the result of the conversion, it is the measurement closest to the number of ounces of sodium nitrate the scientist used.
It's worth noting that the conversion factor given, 28.3 grams per ounce, is an approximation, and the actual value may vary slightly depending on the specific substance being measured. However, for the purpose of this calculation and using the given conversion factor, 3.17 ounces is the closest measurement to the grams provided.
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Choose the INCORRECT statement below.
Answer:
#2
Step-by-step explanation:
Circle A'B'C'D' is smaller than circle ABCD. This means the scale factor must be less than one. 7/3 is greater than one, so it is false.
What is the value of X on the number line?
Answer:
1/3
Step-by-step explanation:
X is exactly halfway between 1/6 and 1/2, ie it is the average of those values.
average of 1/6 and 1/2 = (1/6 + 1/2) /2
= (1/6 + 3/6) /2
= (4/6) /2
= (2/3) /2
= 1/3
evaluate the iterated integral by converting to polar coordinates. 1 0 2 − y2 5(x + y) dx dy y
We have the iterated integral:
∫
�
=
0
2
∫
�
=
1
5
5
(
�
+
�
)
(
2
−
�
2
)
�
�
�
�
∫
y=0
2
∫
x=1
5
5(x+y)(2−y
2
)dxdy
To convert this to polar coordinates, we need to express $x$ and $y$ in terms of $r$ and $\theta$. Since the region of integration is defined by $0 \leq y \leq 2$ and $1 \leq x \leq 5$, we see that $1 \leq r \leq 5$ and $0 \leq \theta \leq \pi$. Then we have:
�
=
�
cos
�
and
�
=
�
sin
�
x=rcosθandy=rsinθ
The Jacobian of the transformation is $\frac{\partial(x,y)}{\partial(r,\theta)} = r$, so we have:
\begin{align*}
\int_{y=0}^{2} \int_{x=1}^{5} 5(x+y)(2-y^2) ,dx,dy &= \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5(r\cos \theta + r\sin \theta)(2 - r^2\sin^2 \theta) ,r,dr,d\theta \
&= \int_{\theta=0}^{\pi} \int_{r=1}^{5} 10r^2\cos \theta ,dr,d\theta + \int_{\theta=0}^{\pi} \int_{r=1}^{5} 10r^2\sin \theta \cos \theta ,dr,d\theta \
&\quad + \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5r^3\sin \theta ,dr,d\theta - \int_{\theta=0}^{\pi} \int_{r=1}^{5} 5r^5\sin^3 \theta ,dr,d\theta \
&= \int_{\theta=0}^{\pi} \left[ \frac{10}{3}r^3\cos \theta \right]{r=1}^{r=5} ,d\theta + \int{\theta=0}^{\pi} \left[ \frac{5}{2}r^3\sin^2 \theta \right]{r=1}^{r=5} ,d\theta \
&\quad + \int{\theta=0}^{\pi} \left[ \frac{5}{4}r^4\sin \theta \right]{r=1}^{r=5} ,d\theta - \int{\theta=0}^{\pi} \left[ \frac{5}{6}r^6\sin^4 \theta \right]{r=1}^{r=5} ,d\theta \
&= \int{\theta=0}^{\pi} \frac{1240}{3}\cos \theta + \frac{60}{2}\sin^2 \theta + \frac{155}{4}\sin \theta - \frac{2480}{6}\sin^4 \theta ,d\theta \
&= \left[ \frac{1240}{3}\sin \theta - \frac{60}{2}\frac
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If in a mixture 75%milk and 25% water how much percentage of mixture has to taken away and replace with same amount of water so that milk and water quantity will be half and half
To achieve an equal mixture of milk and water, we need to remove and replace some of the mixture with water. Let's assume that we start with a certain amount of the mixture, and we remove x% of it and replace it with an equal amount of water.
To determine the value of x, we can use the following approach:
First, let's assume that we start with 100 units of the mixture. Therefore, we have 75 units of milk and 25 units of water in the mixture.
If we remove x% of the mixture, we will have (100 - x)% of the original amount left. After removing x%, the amount of milk in the mixture will still be 75 units, but the amount of water will be (75/25)*x = 3x units.
Now, we replace the removed x% of the mixture with an equal amount of water. Therefore, the amount of water in the mixture will increase by x% of the original amount, which is 25x/100. After the replacement, the amount of milk in the mixture will still be 75 units, but the amount of water will be (25 + 25x/100) units.
To achieve an equal mixture of milk and water, we need the amount of milk to be equal to the amount of water. Therefore, we can set up the following equation:
75 = (25 + 25x/100)/(2)
Solving for x, we get x = 33.33%.
Therefore, we need to remove and replace 33.33% of the mixture with water to achieve an equal mixture of milk and water.
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Expand and simplify (3h + 2) (5h + 4)
a tank initially contains 100 gallons of water containing 40 pounds of salt. a salt solution containing 2 pound of salt per gallon is added to the tank at the rate of 3 gallons per minute, and the solution in the tank is drained off at the rate of 2 gallons per minute. how much salt is in the tank after 30 minutes?
After 30 minutes, there will be 100 pounds of salt in the tank.
Initially, the tank contains 40 pounds of salt.
For every minute, the amount of salt being added is 2 pounds/gallon * 3 gallons/minute = 6 pounds/minute.
The amount of salt being drained off is 2 pounds/gallon * 2 gallons/minute = 4 pounds/minute.
After 30 minutes, the total amount of salt added is 6 pounds/minute * 30 minutes = 180 pounds.
The total amount of salt drained off is 4 pounds/minute * 30 minutes = 120 pounds.
Therefore, the net increase in the amount of salt in the tank is 180 pounds - 120 pounds = 60 pounds.
The final amount of salt in the tank after 30 minutes is 40 pounds (initial amount) + 60 pounds (net increase) = 100 pounds.
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Pls Find the volume of this shape for me
The volume of the triangular prism is 18.9 yd³.
The volume of a triangular prism is given by the formula:
V = (1/2) x base x height x length
where base is the area of the triangular base, height is the height of the triangular base, and length is the height of the prism.
In this case, the base area is:
= (1/2) x 9yd x 2.1
= 9.45 yd²
So the volume of the prism is:
V = (1/2) x 9.45 x 4
= 18.9 yd³
Therefore, the volume of the triangular prism is 18.9 yd³.
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The start of an arithmetic sequence is shown below. what is the nth term in the sequence 10, 12, 14 ,16
Answer:
[tex]a_{n}[/tex] = 2n + 8
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 10 and d = a₂ - a₁ = 12 - 10 = 2 , then
[tex]a_{n}[/tex] = 10 + 2(n - 1) = 10 + 2n - 2 = 2n + 8
due now!!!!!!!!!!!!!!!!!!!!!!!
Answer:
5, -4
Step-by-step explanation:
