When using the department allocation method for allocating overhead costs, there is typically one cost pool per department. This means that all the overhead costs associated with a particular department are combined into a single pool.
The department allocation method is one of several ways to allocate overhead costs to products or services. With this method, overhead costs are allocated based on the department or functional area that incurs them. For example, a manufacturing company might have separate departments for production, maintenance, and administration. Each of these departments incurs overhead costs such as rent, utilities, and supplies.
To use the department allocation method, the first step is to identify the cost pools associated with each department. This involves grouping all the overhead costs incurred by each department into a single pool. For instance, all the overhead costs incurred by the production department might be combined into a single production cost pool.
Once the cost pools have been established, the next step is to allocate them to the products or services produced by each department. This is typically done using a predetermined overhead rate, which is calculated by dividing the total overhead costs in a cost pool by a measure of activity, such as direct labor hours or machine hours. The predetermined overhead rate is then used to allocate overhead costs to each product or service based on the amount of activity it requires.
Overall, the department allocation method can be a useful way to allocate overhead costs in organizations that have multiple departments or functional areas. By grouping overhead costs into separate cost pools for each department, it becomes easier to identify the costs associated with each area of the organization and to allocate those costs fairly to the products or services that each department produces.
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Find the surface area of a square pyramid with side length 1 mi and slant height 3 mi.
Surface area of the square pyramid is 7 square mi.
What is a square pyramid?A square pyramid is a three-dimensional geometric figure which has a square base and four lateral faces, The lateral faces are triangular faces with a common vertex.
How to calculate the surface area of a square pyramid?Let us consider a square pyramid, whose side length is "a" and slant height is "h".
Then the area of the base, i.e. area of square shaped base = square unit and the area of each triangular face is (1/2 × a × h) square unit.
So, the sum of areas of 4 triangular faces is 4 × (1/2 × a × h)=2ah square unit.
∴ Surface area of a square pyramid = Area of base + Area of 4 side face
[tex]\sf = (a^2+2ah) \ square \ unit[/tex]
Given that, Side length (a) = 1 mi
And Slant height (h) = 3 mi
∴ Surface area of the given square pyramid = [tex]\sf (1)^2+(2\times1\times3) \ square \ mi[/tex]
[tex]\sf = 1+6 \ square \ mi[/tex]
[tex]\sf = 7 \ square \ mi[/tex]
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if z = f(x, y) and fx(3, 2) = 4, fy(3, 2) = −6 , find dz dt at t = 5 when x = g(t), y = h(t) and g(5) = 3 , g ′ (5) = 2 . h(5) = 2 , h′ (5) = 4 .
The rate of change of z with respect to time at t = 5 is -16.
Using the chain rule, we can express the total differential of z as dz = fx(3, 2) dx + fy(3, 2) dy. At t = 5, x = g(5) = 3 and y = h(5) = 2, and we know that g′ (5) = 2 and h′ (5) = 4.
Thus, we have dx/dt = g′ (5) = 2 and dy/dt = h′ (5) = 4. Plugging in these values and the given partial derivatives, we have dz/dt = 4(2) + (-6)(4) = -16.
Therefore, the rate of change of z with respect to time at t = 5 is -16.
To explain, we use the chain rule to express the total differential of z as dz = fx(3, 2) dx + fy(3, 2) dy, where fx and fy are the partial derivatives of z with respect to x and y, respectively, evaluated at the point (3, 2).
Then, at t = 5, we use the given information to find the values of x, y, dx/dt, and dy/dt, and we plug these values and the partial derivatives into the total differential to get dz/dt.
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seyall industries recently conducted drug tests on selected employees. it is likely that these tests were not random, but that reasonable suspicion or probable cause led to the tests. group of answer choices false true
Seyall Industries recently tested some of its employees for drug use. It's likely that these tests weren't conducted at random, but rather because of a solid suspicion or solid evidence. This statement is false.
Employers may have reasonable suspicion or probable cause to conduct drug tests on employees in a variety of situations, such as when an employee exhibits behavior that suggests drug use or when an employee has been involved in an accident or incident that may be related to drug use.
Additionally, some industries may require drug testing as a condition of employment or as part of safety regulations. It is important for employers to have a clear drug testing policy in place that outlines the circumstances under which testing may be conducted, the procedures for conducting tests, and the consequences for positive results.
Employers should also ensure that they comply with any applicable laws and regulations regarding drug testing in the workplace. This is because drug testing in the workplace is typically conducted based on specific criteria and is not usually done at random.
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*PLS MUST ANSWER ASAP*
Answer:the 3rd option
Step-by-step explanation:
Kasey is thinking of two numbers. The sum of the two numbers is -18. Their difference is 38. Write
a system of equations that can be used to find the numbers.
Equation 1:
Equation 2:
Solve:
A system of equations that can be used to find the numbers.
Equation 1: x + y = -18
Equation 2: x - y = 38.
The two numbers that Kasey is thinking of are 10 and -28.
To find the two numbers that Kasey is thinking of, we can set up a system of equations based on the given information.
Let's denote the two numbers as x and y.
Equation 1: The sum of the two numbers is -18.
This can be represented as:
x + y = -18
Equation 2: The difference between the two numbers is 38.
This can be represented as:
x - y = 38.
Now, we have a system of two equations with two variables. We can solve this system to find the values of x and y.
One approach to solve this system is by using the method of substitution or elimination.
In this case, we will use the method of elimination.
Adding Equation 1 and Equation 2, we eliminate the y variable:
(x + y) + (x - y) = -18 + 38
2x = 20
x = 10
Substituting the value of x into Equation 1:
10 + y = -18
y = -28
Therefore, the two numbers that Kasey is thinking of are 10 and -28.
By solving the system of equations, we found that one number is 10 and the other number is -28.
These values satisfy the conditions given in the problem, where their sum is -18 and their difference is 38.
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11. DO IT YOURSELF A homeowner is updating her front porch by painting stenciled patterns on the floor. If her floor measures 8 feet by 20 feet, and she has 13 different stencils to use, how many stencil patterns per square feet will she have when completed?
The stencil patterns per square feet she have when completed are:
[tex]\[ \text{Number of stencil patterns per square foot} = \frac{{13n}}{{160}} \text{ patterns/ft}^2 \][/tex]
To find the number of stencil patterns per square foot, we first need to calculate the total area of the floor in square feet. The floor measures [tex]8[/tex] feet by [tex]20[/tex] feet, so its total area is given by:
[tex]\[ \text{Area of the floor} = \text{Length} \times \text{Width} = 8 \text{ ft} \times 20 \text{ ft} = 160 \text{ ft}^2 \][/tex]
Next, we need to determine the total number of stencil patterns that will be used. The homeowner has [tex]13[/tex] different stencils. However, we don't know how many times each stencil will be repeated, so we'll assume that each stencil is used an equal number of times.
Let's denote the number of times each stencil is used as [tex]n[/tex]. Then the total number of stencil patterns used is given by [tex]\( 13 \times n \)[/tex].
To find the number of stencil patterns per square foot, we divide the total number of stencil patterns by the total area of the floor:
[tex]\[ \text{Number of stencil patterns per square foot} = \frac{{13 \times n}}{{\text{Area of the floor}}} = \frac{{13 \times n}}{{160 \text{ ft}^2}} \][/tex]
Since we don't have a specific value for [tex]n[/tex], we can express the answer in terms of [tex]n[/tex]:
[tex]\[ \text{Number of stencil patterns per square foot} = \frac{{13n}}{{160}} \text{ patterns/ft}^2 \][/tex]
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Which of the following code blocks are used to report that a newborn is affected by maternal factors and by complications of pregnancy, labor and delivery?
a. P90-96
b. P00-P04
c. P10-P15
d. P50-P61
Based on the International Classification of Diseases, 10th Revision (ICD-10), the correct code block to report that a newborn is affected by maternal factors and complications of pregnancy, labor, and delivery is:
b. P00-P04
The code block P00-P04 specifically pertains to Newborn affected by maternal factors and by complications of pregnancy, labor, and delivery. This code block includes various conditions and complications that can arise during the perinatal period related to the maternal factors and the process of pregnancy, labor, and delivery. These codes are used to document and classify specific conditions or complications affecting the newborn that are attributable to maternal factors and the events surrounding childbirth.
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[tex]8a+17=5a+5[/tex]
The value of a in the expression is -4.
We have,
8a + 17 = 5a + 5
Combine the like terms.
8a - 5a = 5 - 17
3a = -12
Divide 3 on both sides.
3a/3 = -12/3
a = -4
Thus,
The value of a in the expression is -4.
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a and b are relations on s×s, where s={1,2,3} a={(1,1),(1,3),(2,1),(3,1),(3,2)} b={(1,3),(2,2),(2,3),(3,2),(3,3)} compute a∘b.
The composition of relations a and b on s×s is a∘b={(1,2),(2,2),(2,3),(3,2)}.
To compute the composition of relations a and b, we need to perform the following steps.
First, we need to write out the ordered pairs that are in both a and b. In this case, the only ordered pair that is in both a and b is (1,3).
Next, we need to find all ordered pairs of the form (x,z) such that there exists a y in s such that (x,y) is in b and (y,z) is in a.
In this case, the only such ordered pair is (1,2), since (1,3) is already accounted for.
Finally, we combine the two sets of ordered pairs to get the composition a∘b={(1,2),(2,2),(2,3),(3,2)}.
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what is the probability that a 3 standard deviation event never occurs out of n trials? what assumption would you make to estimate that?
The probability that a 3 standard deviation event never occurs out of 1000 trials is approximately 2.3 × 10^-6.
Assuming that the probability of a 3 standard deviation event occurring in a single trial is low, we can use the binomial distribution to estimate the probability that such an event never occurs out of n trials.
Let p be the probability of a 3 standard deviation event occurring in a single trial. Since a 3 standard deviation event is defined as an event that is 3 standard deviations away from the mean, we can use the standard normal distribution to calculate this probability. The probability of a standard normal random variable being greater than 3 is approximately 0.0013. Therefore, we can assume that p = 0.0013.
Let X be the number of trials out of n in which a 3 standard deviation event occurs. Then X has a binomial distribution with parameters n and p. The probability that a 3 standard deviation event never occurs out of n trials is given by:
P(X = 0) = (1 - p)^n
Substituting p = 0.0013, we get:
P(X = 0) = (1 - 0.0013)^n
To calculate the probability that a 3 standard deviation event never occurs out of n trials, we need to know the value of n. If n is large, we can use the normal approximation to the binomial distribution. The normal approximation to the binomial distribution states that if n is large and p is not too close to 0 or 1, then X has approximately a normal distribution with mean np and variance np(1-p). In this case, we can use the following formula to estimate the probability that a 3 standard deviation event never occurs out of n trials:
P(X = 0) ≈ Φ((0.5 - np) / sqrt(np(1-p)))
where Φ is the cumulative distribution function of the standard normal distribution.
For example, if we take n = 1000, then np = 1.3 and np(1-p) ≈ 1.2987. Using the above formula, we get:
P(X = 0) ≈ Φ((0.5 - 1.3) / sqrt(1.2987)) ≈ Φ(-4.51) ≈ 2.3 × 10^-6
Therefore, the probability that a 3 standard deviation event never occurs out of 1000 trials is approximately 2.3 × 10^-6.
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In a survey of 1500 residents of a city, 34% said that they regularly eat organic foods. The margin of error is ±2.6% Give an interval that is likely to contain the exact percentage of residents in the city who regularly eat organic foods.
The interval that is likely to contain the exact percentage of residents in the city who regularly eat organic foods is given as follows:
The interval is from 31.4% to 36.6%.
How to obtain a confidence interval?A confidence interval for a parameter is defined as the estimate of the parameter plus/minus the margin of error.
For this problem, we have that:
The estimate is of 34%.The margin of error is of 2.6%.Hence the lower bound of the interval is given as follows:
34 - 2.6 = 31.4%.
The upper bound of the interval is given as follows:
34 + 2.6 = 36.6%.
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Answer:
Step-by-step explanation:
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exam scores were normal in mis 200. jason's exam score was 1.41 standard deviations above the mean. what percentile is he in? a. 68th.b. 75th.c. 84th.d. 92nd
This means that Jason is in the 92nd percentile. The answer is d. 92nd.
What is mean?
In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.
To calculate the mean of a set of numbers, you add up all the values in the set, and then divide the sum by the total number of values.
Assuming a normal distribution, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Since Jason's exam score is 1.41 standard deviations above the mean, we can say that approximately 92% of the data falls below his score (since 1.41 standard deviations above the mean is approximately the same as the mean plus 1.41 standard deviations). This means that Jason is in the 92nd percentile.
Therefore, the answer is d. 92nd.
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the population of a town today is 20000 people. (a) if the population decreases linearly and the decrease is 7% in the first year, what will the town's population be in 10 years?
The population of the town in 10 years as per given rate of decrease is equal to approximately 9,566 people.
Todays population of a town = 20,000
Time period = 10 years
To find the town's population in 10 years if it decreases linearly by 7% each year,
Use the formula for linear decrease,
P = P₀ × (1 - r)ⁿ
Where
P is the population after n years
P₀ is the initial population
r is the rate of decrease expressed as a decimal.
n is the number of years
In this case, the initial population P₀ is 20,000,
the rate of decrease r is 7% or 0.07,
and the number of years n is 10.
Substituting these values into the formula,
P = 20,000 × (1 - 0.07)¹⁰
Calculating the expression,
⇒ P ≈ 20,000 × (0.93)¹⁰
⇒ P ≈ 20,000 × 0.4783
⇒ P ≈ 9,566
Therefore, the town's population in 10 years, if it decreases linearly by 7% each year, will be approximately 9,566 people.
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4. let a = 0.3 0 0 0.2 0.1 0.4 0.1 0 0.4 . (a) (3 points) find the eigenvalues of a
To find the eigenvalues of matrix a, we can start by finding the characteristic polynomial det(a - λI), where I is the identity matrix and λ is an unknown constant.
Using the cofactor expansion method along the first row, we get:
det(a - λI) = (0.3 - λ)(-1)^(1+1) det(0.1 0.4 0 0.4) + (-1)^(1+2) (0 - λ) det(0 0.4 0.1 0.4) + (0.2)(-1)^(1+3) det(0 0.1 0.4 0.1; 0.4 0 0.4 0; 0 0.4 0.1 0.4; 0.4 0 0 0.1)
Simplifying this expression, we get:
det(a - λI) = (0.3 - λ)[(0.1)(0.4)(0.4) + (0.4)(0.4)(0.1) + (0.4)(0.1)(0.4)] - (0.2)(0.4)(0.1)(0.4) - (0.4)(0.4)(0.1)(0.1)
det(a - λI) = -λ^3 + 1.2λ^2 - 0.4λ
Next, we can solve for the roots of this polynomial by setting it equal to zero:
-λ^3 + 1.2λ^2 - 0.4λ = 0
Factorizing out a λ term, we get:
λ(-λ^2 + 1.2λ - 0.4) = 0
Using the quadratic formula to solve for the roots of -λ^2 + 1.2λ - 0.4, we get:
λ = 0.2, 0.4, 0.6
Therefore, the eigenvalues of matrix a are λ = 0.2, 0.4, and 0.6.
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State if the three numbers can be the measures of the sides of a triangle:
1. 10, 12, 8
3. 9, 17, 6
2. 12, 5, 12
4. 9,7,5
Two sides of a triangle have the following measures. Find the range of possibl
The three numbers that can form a triangle are as follows:
10, 12, 812, 5, 129, 7, 5How to find the length of a triangle?The triangle inequality theorem states that in a triangle the sum of lengths of any two sides is greater than the length of the third side.
Therefore, the triangle inequality theorem can be used to check if the length of the three number can form a triangle.
Hence, if the lengths of a triangle are a, b and c, the triangle inequality theorem states that:
b + c > a
a + c > b
a + b > c
Therefore, the measure that forms a triangle are as follows:
10, 12, 812, 5, 129, 7, 59, 17, 6 can't form a triangle because 9 + 6 < 17.
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the death rate from a particular form of cancer is 23% during the first year. in a randomly assigned treatment group, only 15 out of 84 patients die during the initial year. what conditions are met?
We fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the death rate for the treatment group is different from the overall death rate of 23%.
What is null hypothesis?The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.
To determine if any conditions are met, we need to perform a hypothesis test.
Null Hypothesis (H₀): The death rate for the treatment group is the same as the overall death rate of 23%.
Alternative Hypothesis (Hₐ): The death rate for the treatment group is different from the overall death rate of 23%.
We can use a one-sample proportion z-test to test this hypothesis. The test statistic is calculated as:
z = (p - P) / √(P(1-P) / n)
where p is the sample proportion (15/84), P is the hypothesized proportion (0.23), and n is the sample size (84).
Using these values, we get:
z = (0.1786 - 0.23) / √(0.23 * 0.77 / 84) = -1.76
The corresponding p-value for this test statistic is 0.0788, which is greater than the standard significance level of 0.05. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the death rate for the treatment group is different from the overall death rate of 23%.
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Please help me!
Use the quadratic formula, (image) to solve the equation. 2x2 − 8x + 7 = 0. Round to the nearest hundredths place.
x = −2.71 and x = −1.29
x = 1.29 and x = 2.71
x = −5.25 and x = 9.25
x = 5.17 and x = 10.83
The value of x in the quadratic equation using quadratic formula to the nearest hundredths place is x = 1.29 and x = 2.71.
The correct answer choice is option B.
How to solve quadratic equation?2x² - 8x + 7 = 0
[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
[tex]x = \frac{ -(-8) \pm \sqrt{(-8)^2 - 4(2)(7)}}{ 2(2) }[/tex]
[tex]x = \frac{ 8 \pm \sqrt{64 - 56}}{ 4 }[/tex]
[tex]x = \frac{ 8 \pm \sqrt{8}}{ 4 }[/tex]
[tex]x = \frac{ 8 \pm 2\sqrt{2}\, }{ 4 }[/tex]
[tex]x = \frac{ 8 }{ 4 } \pm \frac{2\sqrt{2}\, }{ 4 }[/tex]
[tex]x = 2 \pm \frac{ \sqrt{2}\, }{ 2 }[/tex]
[tex]x = 2.70711[/tex]
or
[tex]x = 1.29289[/tex]
Hence,
Approximately, x = 1.29 or x = 2.71
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the westridge city planners track the city's population each year. this year, the population is 15,400. a large tech company just opened their headquarters in westridge, so the city planners expect the city's population to grow by about 5% each year. write an exponential equation in the form y=a(b)x that can model the population of westridge, y, x years after the arrival of the new headquarters.
Step-by-step explanation:
so, from year 0 to year 1 after arrival the population grows by 5% (= factor 1.05).
as growth means the number of people before plus the additional 5%.
so, we multiply 15,400 by (1 + 0.05) or simply by 1.05.
and in year 2 after arrival we multiply that result again by 1.05.
which is the year 0 number multiplied by 1.05 × 1.05 or simply 1.05².
in year 3 after arrival that result gets multiplied by 1.05. or year 0 multiplied by 1.05×1.05×1.05 or simply 1.05³.
and so on, and so on.
so, we get an exponential function with starting value of 15,400 :
y = 15,400 × (1.05)^x
to calculate the local population x years after the arrival of the large company.
for x = 0 we get the starting value of 15,400.
mr. adams divides 183 markers equally among the 24 students in his class. he puts the extra markers in a box. what is the least number of extra markers in a box?
Mr. Adams divides 183 markers equally among the 24 students in his class. To find the least number of extra markers in the box, divide the total markers (183) by the number of students (24). The result is 7 with a remainder of 15. So, the least number of extra markers in the box is 15.
Mr. Adams divides 183 markers equally among the 24 students in his class, which means each student gets 7 markers. However, since 7 does not divide evenly into 183, there will be some markers left over. To determine the least number of extra markers in a box, we need to find the remainder when 183 is divided by 24.
Using long division, we get:
24 | 183
-----
7 6
-----
This means that there are 6 markers left over that Mr. Adams puts in a box. Therefore, the least number of extra markers in a box is 6.
Mr. Adams divides 183 markers equally among the 24 students in his class. To find the least number of extra markers in the box, divide the total markers (183) by the number of students (24). The result is 7 with a remainder of 15. So, the least number of extra markers in the box is 15.
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PLEASE HELP!!
A blender has an efficiency of 72%. What happened to the other 28%?
Answer in one to three complete sentences.
The other 28% represents the energy loss or inefficiency of the blender.
What is the energy loss or inefficiency of the blender?This means that only 72% of the input energy is effectively converted into useful work, while the remaining 28% is dissipated in the form of heat or other forms of energy loss. This energy loss is typically attributed to factors such as mechanical friction, heat generation, and
It could be due to factors such as friction, heat generation, or mechanical losses within the blender's components. This energy is not effectively converted into the desired blending action and is instead lost as waste.
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Write the equation of a line perpendicular to7x-8y=-5 that passes through the point (-7,3).
Step-by-step explanation:
7x-8y = - 5 arrange to y = mx+ b form m is the slope of this line
8y = 7x+5
y = 7/8 x = 5/8 <====== m, slope = 7/8
perpendicular slope = - 1/m = - 8/7
Now use point ( -7,3) slope (-8/7) form:
y-3 = - 8/7 ( x - - 7) simplify
y = -8/7 x + 5 re-arrange , add 8/7 x to both sides of the equation
8/7 x + y = 5 multiply through by 7 to get integer values
8x + 7y = - 35
suppose a function f: x → y is onto but not one-toone. is f−1 (the inverse relation for f) a function? explain your answer
An "onto" function, also known as a surjective function, maps every element of the domain to at least one element of the codomain. A "one-to-one" function, or injective function, maps each element of the domain to a unique element in the codomain. If f: x → y is onto but not one-to-one, it means that some elements in x have the same corresponding element in y.
To determine if the inverse relation, f^(-1), is a function, let's recall the definition of a function: for every input, there must be exactly one output. Since f is not one-to-one, multiple elements in x correspond to a single element in y. Thus, when considering the inverse relation f^(-1), a single element in y would correspond to multiple elements in x.
In conclusion, f^(-1) would not be a function because it does not satisfy the requirement of having a unique output for each input.
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Find the total surface area of the cylinder shown. Leave the answer in terms of π The radius is 3.5 and the height is 6
The solution is: the total surface area of the cylinder is: 208.92 unit^2.
Here, we have,
we know that,
Area of ends:
Area of Circle = πr²
given, radius is 3.5 and the height is 6
so, we get,
Area of end = π3.5²=49/4π
There are two ends so we multiply that by 2 to get 49/2π
Area of Rest:
First, we need to find the circumference using the equation: πd
πx7=7π
Then to find the area we just need to multiply 7π by the height
7π x 6 = 42π
Total surface area
we now just need to add them together
49/2π + 42π = 133/2π
= 208.92
Hence, The solution is: the total surface area of the cylinder is: 208.92 unit^2.
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The surface area of the given cylinder is 208.81 square units.
Given that, the radius of a cylinder is 3.5 units and the height is 6 units.
We know that, the total surface area of a cylinder is 2πr(r + h).
Here, surface area = 2×3.14×3.5×(3.5+6)
= 2×3.14×3.5×9.5
= 208.81 square units
Therefore, the surface area of the given cylinder is 208.81 square units.
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Find the first partial derivatives of the function. f(x,y)=x 4+6xy 5
So, the first partial derivatives of the function f(x,y)=x^4+6xy^5 is ∂f/∂y = 30xy^4.
To find the first partial derivatives of the function f(x,y)=x^4+6xy^5, we need to take the partial derivative with respect to x and y separately.
Starting with the partial derivative with respect to x, we treat y as a constant and differentiate x^4 to get:
∂f/∂x = 4x^3 + 6y^5
Next, we take the partial derivative with respect to y, treating x as a constant and differentiating 6xy^5 to get:
∂f/∂y = 30xy^4
So the first partial derivatives of the function f(x,y)=x^4+6xy^5 are:
∂f/∂x = 4x^3 + 6y^5
∂f/∂y = 30xy^4
Thus, the first partial derivatives of the function f(x,y)=x^4+6xy^5 is ∂f/∂y = 30xy^4.
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If a creature is a chimpanzee then it is a primate. If a creature is a primate then it is a mammal. Bobo is a mammal. Therefor Bobo is a chimpanzee. Use a Venn diagram or truth table or common form of an argument to decide whether each argument is valid or invalid.
The required given argument is invalid.
The argument states that if a creature is a chimpanzee, then it is a primate. This is true, because all chimpanzees are primates. The argument also states that if a creature is a primate, then it is a mammal. This is also true, because all primates are mammals. The argument then concludes that if a creature is a mammal, then it is a chimpanzee. This is not necessarily true, because not all mammals are chimpanzees. For example, humans are mammals, but we are not chimpanzees.
Here is a truth table that shows the validity of the argument:
Chimpanzee? | Primate? | Mammal? | Conclusion?
------- | -------- | -------- | --------
Yes | Yes | Yes | Yes
Yes | Yes | No | No
No | Yes | Yes | No
No | No | Yes | No
As you can see, the conclusion is true only in the first row of the truth table. In all other rows, the conclusion is false. Therefore, the argument is invalid.
Here is a common form of the argument:
All A are B.
All B are C.
Therefore, all A are C.
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This is called a syllogism. The first statement is the major premise, the second statement is the minor premise, and the third statement is the conclusion. The syllogism is valid because the conclusion follows logically from the premises.
In the case of set theory, the argument about Bobo, the major premise is "All chimpanzees are primates." The minor premise is "Bobo is a primate." The conclusion is "Bobo is a chimpanzee." The conclusion does not follow logically from the premises. Therefore, the argument is invalid.
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help pls ill give u brainliest
Step-by-step explanation:
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If a population of scores is normally distributed and has a mean of 300 and a standard deviation of 50, then what proportion of scores would you expect to find between 250 to 350?
The population scores with a mean of 300 and a standard deviation of 50, approximately 68% of the scores would be expected to fall between 250 and 350.
If a population of scores is normally distributed with a mean of 300 and a standard deviation of 50, we can use the properties of the normal distribution to determine the proportion of scores that would be expected to fall within a certain range.
In this case, we want to find the proportion of scores that fall between 250 and 350.
To do this, we can use the standard normal distribution and the z-score formula.
The z-score is a measure of how many standard deviations a particular score is from the mean. We can calculate the z-scores for 250 and 350 using the formula:
z = (x - μ) / σ
where x is the score we want to find the z-score for, μ is the mean, and σ is the standard deviation.
For 250: z = (250 - 300) / 50 = -1
For 350: z = (350 - 300) / 50 = 1
Once we have the z-scores for 250 and 350, we can use a z-score table or a calculator to find the proportion of scores that fall between these values.
From a standard normal distribution table, we can find that the proportion of scores between -1 and 1 is approximately 0.6827.
Therefore, we would expect to find approximately 68.27% of scores between 250 and 350 in a normally distributed population with a mean of 300 and a standard deviation of 50.
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Find the standard form of the complex number, then represent the complex number graphically: 5(cos(135°) + i sin(135°))
To find the standard form of the complex number, we can use Euler's formula which states that e^(ix) = cos(x) + i sin(x). Using this formula, we can rewrite 5(cos(135°) + i sin(135°)) as 5(e^(i * 135°))
We can then use the fact that e^(ix) = cos(x) + i sin(x) to simplify this expression:
5(cos(135°) + i sin(135°)) = 5(e^(i * 135°)) = 5(cos(135°) + i sin(135°))
So the standard form of the complex number is:
5(cos(135°) + i sin(135°))
To represent this complex number graphically, we can plot the point (5 cos(135°), 5 sin(135°)) in the complex plane. This point has a magnitude of 5 and an angle of 135° (measured counterclockwise from the positive real axis). So the graphical representation of the complex number is a point in the second quadrant of the complex plane, 5 units away from the origin, and making an angle of 135° with the positive real axis.
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Select the inequality that describes each sentence.
Jason ran for less than 3 miles.
If D is the distance that Jason ran (in miles), the inequality will be:
D < 3.
Which inequality describes this sentence?Here we want to write an inequality for the given sentence:
"Jason ran for less than 3 miles."
Let's define the variable D as the distance that Jason ran in miles, now we want to write an inequality that says that D is less than 3 miles.
To do so, we will use the symbol <, it is used to say that the thing in the left is smaller than the thing in the right, then the inequality will be:
D < 3.
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Solve the simultaneous equation 24n+9m=8 and 3n-2m=6
Answer:
We can solve the simultaneous equation 24n + 9m = 8 and 3n - 2m = 6 by using the elimination method.
First, we need to multiply the second equation by 3 to eliminate n:
24n + 9m = 8
(3n - 2m) × 3 = 6 × 3
9n - 6m = 18
Now we have two equations with the same n coefficient, so we can subtract the second equation from the first to eliminate n:
24n + 9m = 8
-(9n - 6m = 18)
-----------------
15n + 15m = -10
We can simplify this equation by dividing both sides by 5:
3n + 3m = -2
Now we have two equations with the same m coefficient, so we can subtract the second equation from the first to eliminate m:
24n + 9m = 8
-(3n + 3m = -2)
----------------
21n + 6m = 10
We can simplify this equation by dividing both sides by 3:
7n + 2m = 10/3
Now we have two equations with only one variable, so we can solve for one variable and substitute the value into one of the original equations to solve for the other variable:
7n + 2m = 10/3
2m = 10/3 - 7n
m = (10/3 - 7n)/2
Substitute this expression for m into the first equation:
24n + 9m = 8
24n + 9[(10/3 - 7n)/2] = 8
24n + (30/2 - 63n/2)/2 = 8
24n + 15 - 63n/4 = 8
24n - 63n/4 = 8 - 15
(96n - 63n)/4 = -7
33n/4 = -7
n = -28/33
Substitute this value of n into the second equation:
3n - 2m = 6
3(-28/33) - 2m = 6
-28/11 + 2m/11 = 2
2m/11 = 2 + 28/11
2m/11 = 50/11
Answer:
n = 14 / 15
m = -8 / 5
Step-by-step explanation:
24n + 9m = 8 ------- (1) x 2
3n - 2m = 6 -----------(2) x 9
48n + 18m = 16 ------- (3)
27n - 18m = 54 --------(4)
Adding two eqn , we get ;
______________
75n = 70
n = 14 / 15
Putting value of n in eqn (2) , we get ;
14 / 5 - 2m = 6
2m = 14 / 5 - 6
2m = -16 / 5
m = -8 / 5