Answer:
e = 29.0 will be the answer.
Step-by-step explanation:
Use the sine rule in the given triangle,
\(\frac{EF}{\text{sin}(\angle D)}=\frac{DE}{\text{sin}(\angle F)}=\frac{DF}{\text{sin}(\angle E)}\)
\(\frac{d}{\text{sin}(35)}=\frac{16}{\text{sin}(30)}=\frac{e}{\text{sin}(115)}\)
\(d=\frac{16\times \text{sin}(35)}{\text{sin}(30)}\)
d = 18.35
\(\frac{16}{\text{sin}(30)}=\frac{e}{\text{sin}(115)}\)
\(e=\frac{16\times \text{sin}(115)}{\text{sin}(30)}\)
e = 29.002
e ≈ 29.0
Therefore, e = 29.0 will be the answer.
4. Consider a regression model y i
=β 1
+β 2
x i
+e i
. Suppose that based on a theoretical argument we know that β 2
=0. (a) What does the regression model look like, algebraically, if β 2
=0 ? (b) What does the regression model look like, graphically, if β 2
=0 ? (c) If β 2
=0, the sum of squares function becomes S(β 1
)=∑ i=1
n
(y i
−β 1
) 2
. Using calculus, show that the formula for the least squares estimator of β 1
in this model is β
^
1
=(∑ i=1
n
y i
)/n.
Algebraically, this means that the dependent variable y is a linear function of the independent variable x, with no coefficient multiplying x.
When β₂=0, the regression model simplifies to yᵢ = β₁xᵢ + eᵢ. This means that the dependent variable y is solely determined by the intercept β₁ and the error term e, with no effect from the independent variable x.
This means that the best estimate for β₁, when β₂ = 0, is the mean of the dependent variable y.This is because when β₂ = 0, the value of x does not contribute to the variation in y. The line is parallel to the x-axis and has a constant intercept β₁
.
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The data in this table is going to be plotted on a dual bar chart. If the grid is 16 rows tall, what number should replace A to give the best scale for the vertical axis of this data?
The number should replace A to give the best scale for the vertical axis of this data is 15.75
How to find the number?From the given parameters and graphs, we notice that we should find the mean of the set of data.
The scale should be chose in a way that the center shows the the mean of the frequencies
Recall that mean is the average of all the frequencies, then we have to find the mean of the means of the two frequencies.
(30+12+10)/2 52/3 = 17.3
Also, (27+6+13)/3 = 14.2
Then we find the average of the two averages to have
(17.3+14.2)/2 = 31.5/215.75
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Determine the dependence between the quantities for the given graph.
A coordinate plane linear graph, titled package delivery charges with weight of package in pounds labeled on X-axis total cost in dollars on Y-axis. A line begins from origin, goes linearly upward and slight to the right.
The
depends on the
.
if you could help me that would be nice
Answer:
it is -5
Step-by-step explanation:
it is 5 so the opposite is -5
A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?"
What are the unknowns in this problem?
Responses
the total number of people in the room
the total number of people in the room
the total number of parents in the room
the total number of parents in the room
the total number of children in the room
the total number of children in the room
the total number of children and the total number of parents in the room
By solving a system of equations, we can see that there are 17 children and 8 parents in the room.
How to get the total number of children in the room?Let's define the variables:
x = number of children.
y = number of parents.
We know that there are 9 more children than parents, then:
x = y + 9
And there is a total of 25 people, so:
x + y = 25
So we have a system of equations:
x = y + 9
x + y = 25
Replacing the first equation into the second one, we get:
(y +9) + y = 25
2y + 9 = 25
2y = 25 - 9 = 16
y = 16/2 = 8
then the value of x is:
x = y + 9 = 8 + 9 = 17
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2. Realiza la siguientes sumas de números enteros usando el método de tener y deber
a) –4 + 5 –3 =
b ) +3 –5 +7 =
c) –3 + 5 –8 =
d) +4 – 7 –8 = 9.
Answer:
a is the answer
Step-by-step explanation:
mean absolute deviation of 290
Answer:
3.5555555555556
Step-by-step explanation:
you cannot find the Mean Absolute Deviation of one number. This answer is the data set 2, 9, and 0. 3.5555555555556 is the Mean Absolute Deviation of 2, 9, 0.
A donut shop has made 36 chocolate donuts, 27 strawberry donuts and 18 caramel donuts. The donut shop wants to sell boxes with a combination of the three types of donuts. How many boxes will there be and how many of each donut will there be in each box if each box has the same total number of donuts? Pls show working. Thx.
Each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut, there will be a Total of 4 boxes, and each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut.
The number of boxes and the distribution of donuts in each box, we need to find the greatest common divisor (GCD) of the total number of chocolate, strawberry, and caramel donuts available. The GCD will represent the maximum number of donuts that can be included in each box.
First, let's find the GCD of 36, 27, and 18. By calculating the GCD, we can determine the maximum number of donuts that can be included in each box.
GCD(36, 27, 18) = 9
Therefore, the maximum number of donuts that can be included in each box is 9.
Next, we need to determine the number of boxes. To do this, we divide the total number of each donut type by the maximum number of donuts per box.
Number of boxes for chocolate donuts = 36 / 9 = 4 boxes
Number of boxes for strawberry donuts = 27 / 9 = 3 boxes
Number of boxes for caramel donuts = 18 / 9 = 2 boxes
Since each box contains the same total number of donuts, we can conclude that there will be 4 boxes with chocolate donuts, 3 boxes with strawberry donuts, and 2 boxes with caramel donuts.
To find the distribution of donuts in each box, we divide the maximum number of donuts per box by the GCD:
Distribution in each box: 9 = 1 × 9
Therefore, each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut, there will be a total of 4 boxes, and each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut.
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Can someone explain how to do this?
Answer:
20 6 12 38
5 20 7 32
25 26 19 70
I need help with this
1. Since triangle ABC and DEF are congruent, the value of x is -3
2. length AB = 24
length DE = 24
What are congruent triangles?If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE
therefore;
12- 4x = 15-3x
collect like terms
12 -15 = -3x +4x
x = -3
therefore the value of x is -3 and
AB = 12 - 4x
AB = 12 -4( -3)
AB = 12 +12 = 24
DE = 15-3x
= 15-3(-3)
= 15 + 9
= 24
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the m and p genes are 14 m.u. apart on an autosome. an mp/mp woman mates with an mp/mp man. what is the probability that their first child will be mp/mp
The probability that their first child will be mp/mp is is 1 (certain).
How to determine probability that their first child will be mp/mpIf the m and p genes are 14 m.u. apart on an autosome, it means that the chance of recombination between them during meiosis is 14%.
Therefore, the chance of the two alleles remaining together in the same gamete is 86%.
If an mp/mp woman mates with an mp/mp man, their possible gametes are:
mp/mp woman: mp, mp
mp/mp man: mp, mp
The probability of the woman producing an mp gamete is 1, and the probability of the man producing an mp gamete is also 1.
Therefore, the probability of their first child being mp/mp is the product of the probabilities of each parent producing an mp gamete, which is:
P(mp/mp) = P(mp from woman) x P(mp from man) = 1 x 1 = 1
So the probability of their first child being mp/mp is 100%.
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y = x + 1 y = − 4x − 4
Answer:
2y=3x=-4
Step-by-step explanation:
grouping like terms
y+ly =4x-x=-4
2y=3x=-4
(a) Determine a cubic polynomial with integer coefficients which has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.
(b) Prove that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational.
Answer:
(a) \(x\³ - 6x - 6\)
(b) Proved
Step-by-step explanation:
Given
\(r = $\sqrt[3]{2} + \sqrt[3]{4}$\) --- the root
Solving (a): The polynomial
A cubic function is represented as:
\(f = (a + b)^3\)
Expand
\(f = a^3 + 3a^2b + 3ab^2 + b^3\)
Rewrite as:
\(f = a^3 + 3ab(a + b) + b^3\)
The root is represented as:
\(r=a+b\)
By comparison:
\(a = $\sqrt[3]{2}\)
\(b = \sqrt[3]{4}$\)
So, we have:
\(f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3\)
Expand
\(f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)
\(f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)
\(f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)
\(f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)
Evaluate like terms
\(f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)\)
Recall that: \(r = $\sqrt[3]{2} + \sqrt[3]{4}$\)
So, we have:
\(f = 6 + 6r\)
Equate to 0
\(f - 6 - 6r = 0\)
Rewrite as:
\(f - 6r - 6 = 0\)
Express as a cubic function
\(x^3 - 6x - 6 = 0\)
Hence, the cubic polynomial is:
\(f(x) = x^3 - 6x - 6\)
Solving (b): Prove that r is irrational
The constant term of \(x^3 - 6x - 6 = 0\) is -6
The divisors of -6 are: -6,-3,-2,-1,1,2,3,6
Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values
\(f(-6) = (-6)^3 - 6*-6 - 6 = -186\)
\(f(-3) = (-3)^3 - 6*-3 - 6 = -15\)
\(f(-2) = (-2)^3 - 6*-2 - 6 = -2\)
\(f(-1) = (-1)^3 - 6*-1 - 6 = -1\)
\(f(1) = (1)^3 - 6*1 - 6 = -11\)
\(f(2) = (2)^3 - 6*2 - 6 = -10\)
\(f(3) = (3)^3 - 6*3 - 6 = 3\)
\(f(6) = (6)^3 - 6*6 - 6 = 174\)
For r to be rational;
The divisors of -6 must divide f(x) without remainder
i.e. Any of the above values must equal 0
Since none equals 0, then r is irrational
A group of 75 math students were asked whether they
like algebra and whether they like geometry. A total of
45 students like algebra, 53 like geometry, and 6 do
not like either subject.
Algebra vs. Geometry
Likes Algebra
Does Not
Like Algebra
Total
Likes
Geometry
Mark this and return
a
3
53
Does Not
Like Geometry
b
6
e
Total
45
P
75
What are the correct values of a, b, c, d, and e?
a 16, b = 29, c = 22, d = 30, e = 24
a = 29, b = 16, c = 30, d = 22, e = 24
a 16, b = 29, c = 24, d = 22, e = 30
H
a = 29, b = 16, c = 24, d = 30, e = 22
The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.
For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:
We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.
75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)
Simplifying this equation, we have:
75 = 98 + 6
75 = 104
This equation is incorrect, so we can eliminate options c and d.
Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.
Using the correct values for a and b, we have:
16 + b = 6
b = 6 - 16
b = -10
Since we can't have a negative value for the number of students, option a is also incorrect.
The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.
Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)
Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)
Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)
Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)
All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.
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graph of f(x)=0.5(4)^x
The graph of the exponential function is on the image at the end.
How to find the graph of the exponential function?Here we want to graph the function:
f(x) = 0.5*(4)ˣ
To graph this (or any function) we can find some points on the function, and to do so, we need to evaluate it.
when x = 0:
f(0) = 0.5*(4)⁰ = 0.5
Then the point is (0, 0.5)
when x = 1
f(1) = 0.5*(4)¹ = 2
So we have the point (1, 2)
if x = 2
f(2) = 0.5*(4)² = 8
So we have the point (2, 8)
Now we can graph these points and connect them with a general exponential curve.
The graph of the exponential function is shown below.
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The Question Is Above
Answer:
b
Step-by-step explanation:
(a) Attendance at the Accra Sports Stadium was alysed by the General Secretary, Prosper Harrison Addo. The analysis demonstrated that spectators consisted of 70% males. If seven people are randomly selected from the spectators during a football match, What is the probability that 4 of them are males? (3 marks) i 11. Find the probability that at most 5 of them are females (4 marks)
a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.
b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.
a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- n is the total number of trials (number of people selected)
- k is the number of successful trials (number of males selected)
- p is the probability of success in a single trial (probability of selecting a male)
- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)
In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:
P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)
b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.
P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).
Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.
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Factor completely. 4x^2-x-5
The factors of the given equation 4x^2-x-5 are 5/4 and -1.
What is referred as the factors of the polynomial?Factoring polynomials is the inverse procedure of multiplying polynomial factors. Factors of polynomials are zeros of polynomials that take the form of some other linear polynomial. If we divide a given polynomial by any of its factors after factorisation, the remainder would be zero.Factors are integers which are multiplied together to create the original number. The factors in the particular instance of polynomials are the polynomials that are multiplied to generate the original polynomial.For the given question, the expression is given as;
= 4x^2-x-5
as, 4×5 = 20, break the number such that on subtraction we will get -1.
= 4x^2 - 5x + 4x -5
Taking x common from first two digit.
= x(4x - 5) + (4x - 5)
Taking common again.
= (4x - 5)(x + 1)
Put the equation equal zero to find the factor.
4x - 5 = 0
x = 5/4
and, x + 1 = 0
x = -1
Thus, the factors are found as 5/4 and -1.
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a waiter believes the distribution of his tips has a model that is slightly skewed to the right, with a mean of $9.60 and a standard deviation of $5.40. i. explain why you cannot determine the probability that a given party will tip him at least $20.
Here the data is slightly right skewed which means there is no symmetry in the distribution of waiter tips. We, cannot determine the probability for this case.
Now, we will look into the details of distribution,
Mean of distribution = $9.60
The standard deviation of the skewed data = $5.40
Tip to the waiter = $20
Now, understand a few terms,
Normal distribution, also known as Gaussian distribution, is very commonly used for randomly generated variables.
The graph of normal distribution has some parameters: the average or mean which is the maximum point of the graph and it is the point about which the graph is symmetrical, and the standard deviation which tells how much each data point is away from the mean.
As the data is skewed so we can,t use the normal distribution, and no other details about the model and distribution are given in the problem. So, we cannot determine the Probability for this case.
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what would this one be?
Answer:
I believe it's 6/10
Step-by-step explanation:
3/5 times 2 = 6/10
You receive an unexpected gift of $500. Is it better to put it in savings or pay down credit card give an explanation
It depends on interest rates, emergency fund, credit utilization, and other financial goals. If credit card interest is high, pay it off, otherwise put the money in savings.
Whether it's better to put an unexpected gift of $500 in savings or pay down credit card debt depends on a few factors
If the interest rate on your credit card debt is higher than the interest rate you're earning on your savings account, it's generally better to pay down the debt. This is because the interest you're paying on your debt is likely higher than the interest you're earning on your savings, so paying down the debt will save you more money in the long run.
If you don't have an emergency fund, it's generally better to put the money in savings. An emergency fund is important to have in case unexpected expenses arise, such as medical bills or car repairs. If you don't have an emergency fund and an unexpected expense comes up, you may have to put it on your credit card and go further into debt.
If you're using a high percentage of your available credit, paying down your credit card debt can improve your credit score. This is because credit utilization is an important factor in determining your credit score, and a high credit utilization ratio can negatively impact your score.
If you have other financial goals, such as saving for a down payment on a house or a vacation, it may be better to put the money in savings to work towards those goals.
Ultimately, the decision of whether to put an unexpected gift of $500 in savings or pay down credit card debt depends on your individual financial situation. If you're unsure, it may be helpful to speak with a financial advisor or planner to determine the best course of action for your specific circumstances.
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probability of rolling a
number less than 3 or rolling an odd number.
Answer:
1/3
that is the answer
A dth tv connection provides channels in english and other languages in the ratio 7:13. what percentage of the channels are in english
A DTH TV connection provides channels in English and other languages in the ratio 7:13. To find out what percentage of the channels are in English, you need to divide the number of English channels by the total number of channels and then multiply the result by 100.
Let's assume that there are a total of 100 channels available on this DTH TV connection. According to the given ratio, 7 out of every 20 channels will be in English. So, the percentage of channels in English will be:
(7/20) x 100 = 35%
Therefore, 35% of the channels on this DTH TV connection are in English.
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There are 20 trash cans along Claiborne Street, and 12 of them are full.
What percent of the trash cans are full?
12 out of 20 are full.
Divide full by total cans and then multiply by 100:
12/20 = 0.6 x 100 = 60 %
Answer: 60% are full
will the sampling distribution of x always be approximately normally distributed? Explain. Choose the correct answer below 0 ?. Yes, because the Central Limit Theorem states that the sampling distribution of x is always approximately normally distributed O B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough O C. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the population being sampled is normally distributed O D No, because the Central Limit Theorem states that the sampling d bution of x is approximately no aly distribui d only i the sa le sae is mere than 5% of the population.
B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.
The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that as the sample size increases, the sampling distribution of the sample means will approach a normal distribution. However, this is only true if certain conditions are met, one of which is having a large enough sample size.
The CLT states that the sampling distribution of x will be approximately normally distributed if the sample size is large enough (usually greater than 30). If the sample size is small, the sampling distribution may not be normally distributed. In such cases, other statistical techniques like the t-distribution should be used.
Furthermore, the CLT assumes that the population being sampled is not necessarily normally distributed, but it does require that the population has a finite variance. This means that even if the population is not normally distributed, the sampling distribution of x will still be approximately normal if the sample size is large enough.
In conclusion, the answer is B, as the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.
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Find the area of the circle .Round your answers the nearest whole number if necessary.use 3.14 or 22/7
Please help
Please help me with this proof i don’t understand
The two-column proof are:
Statements Reasons
ABCD is a parallelogram | Given CEFD is a parallelogram | Given AB || CD and AD || BC | Definition of a parallelogram FE || CD and FD || CE | Definition of a parallelogram ABCD and CEFD have the same base CD | Given AB and FE are corresponding sides of ABCD and CEFD, respectively | Definition of corresponding sides of parallelograms AB || FE | Transitive property of parallel lines.AD = BC | Opposite sides of a parallelogram are congruent (1)ED = FC | Opposite sides of a parallelogram are congruent (2)What are the parallelograms?To begin the proof, we list our given information in the left column of the two-column format. The first two statements are simply the given parallelograms, so we can write them down as statements 1 and 2.
Next, we use the properties of parallelograms to make some additional statements about the sides of these shapes. Statements 3 and 4 use the fact that opposite sides of a parallelogram are parallel to one another. Statement 3 tells us that AB is parallel to CD and AD is parallel to BC, and statement 4 tells us that FE is parallel to CD and FD is parallel to CE.
Now that we have made some statements about the sides of the parallelograms, we can start to relate them to one another. Statement 5 tells us that the two parallelograms have the same base, CD. This means that the distance between CD and AB is equal to the distance between CD and FE.
Therefore, we have proven that AB = FE based on the given information and the properties of parallelograms.
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Mark incorrectly says that 3 1/3 is the same as 3.13. convert 3 1/3 to a decimal correctly. what did he do wrong
Answer:
3.33
Step-by-step explanation:
3 1/3 is equal to ((3*3)+1)/3
= 10/3
= 3.33 ---------> Final answer
Evaluate the expression, using a calculator if necessary. Round
your answer to four decimal places. cot(3pi/11)
The value of cot(3π/11), rounded to four decimal places, is approximately 0.1724.
To evaluate the expression, cot(3π/11), using a calculator, we can follow the steps below:
Step 1: Convert the angle to radiansπ radians = 180 degrees1 radians = (180/π) degrees
To convert degrees to radians, multiply the degree measure by π/180 radians.
3π/11 radians = (3π/11) × (180/π) degrees= (540/11) degrees.
Step 2: Evaluate the cotangent function using a calculator
cot(540/11)≈ 0.1724 (rounded to four decimal places)
Therefore, the value of cot(3π/11), rounded to four decimal places, is approximately 0.1724.
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The volume of a cone with height 29 cm is 1758 CM3, find the radius of the conw
Answer:13.77 cm.
Step-by-step explanation:
r = sqrt((3V)/(pih))
= sqrt((31758)/(pi29))
= sqrt((5274)/(pi*29))
= sqrt(182.16)/(pi/29)
= 13.77 cm