The answer of the given question based of a suggestive survey the answer is "What do you like and don’t like about the CEO?"
Who is CEO?The CEO or Chief Executive Officer is highest-ranking executive in company who is responsible for making major corporate decisions, managing overall operations, and leading organization towards achieving its goals and the objectives. The CEO reports to board of directors and is responsible for success or failure of company.
The suggestive survey question is: "What do you like and don’t like about the CEO?"
This question is suggestive because it implies that the respondent should have opinions about the CEO, and it encourages the respondent to share both positive and negative opinions. This can bias the responses towards certain answers, rather than allowing the respondent to express their own thoughts freely.
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Find the interquartile range (IQR) of the data set.
2. 6, 3, 2004. 9, 5, 5, 6, 6, 7. 9, 8, 2008. 2
The interquartile range (IQR) of the given data set is 4, calculated by subtracting the third quartile (Q3) from the first quartile (Q1).
An indicator of a data set's statistical dispersion is the interquartile range (IQR). The third quartile (Q3) is subtracted from the first quartile to compute it (Q1). The middle 50% of the data's spread is measured by the IQR.In the given data set, the data points are 2, 3, 5, 5, 6, 6, 7, 8, 9, 9, 2004, 2008. We first need to arrange the data points in ascending order, which will be 2, 3, 5, 5, 6, 6, 7, 8, 9, 9, 2004, 2008. To calculate the IQR, we first need to calculate the first quartile and the third quartile. The first quartile is the median of the lower half of the data set, which is 5. The third quartile is the median of the upper half of the data set, which is 9. The IQR is calculated by subtracting the third quartile (Q3) from the first quartile (Q1). Therefore, the IQR of the given data set is 4 (9 - 5 = 4).
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Let \( A=\left[\begin{array}{rrr}-2 & -5 & -13 \\ 4 & 5 & 11 \\ 1 & 2 & 6\end{array}\right] \) Find the third column of \( A^{-1} \) without computing the other two columns. How can the third column o
The third column of the inverse of the matrix, A = [tex]\begin{bmatrix}-2 & -5 & -13 \\4 &5 &11 \\1 &2 &6 \\\end{bmatrix}[/tex], obtained using the product of A and the third column of A⁻¹ is; [tex]\begin{bmatrix} 1 \\ -3\\ 1 \\\end{bmatrix}[/tex]
What is an inverse of a matrix?The product of a matrix and the inverse of the matrix is the multiplicative identity.
The specified matrix can be presented as follows;
A = [tex]\begin{bmatrix}-2 & -5 & -13 \\4 & 5 & 11 \\1 &2 & 6 \\\end{bmatrix}[/tex]
The third columns of the inverse of the matrix, A, A⁻¹, can be obtained without computing the other two columns, as follows;
The inverse of the matrix A, A⁻¹ is the solution of the following matrix equation;
Ax = [tex]e_i[/tex]
Where;
[tex]e_i[/tex] = The column i of the identity matrix
x = The third column of the inverse matrix
Therefore, for the third column, we get;
[tex]e_i[/tex] = [tex]e_3[/tex] = [tex]\begin{bmatrix}0 \\ 0\\1\\\end{bmatrix}[/tex]
Ax = [tex]e_3[/tex] = [tex]\begin{bmatrix}0 \\ 0\\1\\\end{bmatrix}[/tex]
Therefore;
x = [tex]e_i[/tex]/X, which using a graphing calculator, indicates;
[tex]x = \frac{\begin{bmatrix}0 \\ 0\\1\\\end{bmatrix}}{\begin{bmatrix}-2 & -5 & -13 \\4 & 5 & 11 \\1 &2 & 6 \\\end{bmatrix}} = \begin{bmatrix}1 \\ -3\\1\\\end{bmatrix}[/tex]
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the iron bank offers a range of financial services and investment opportunities. of its customers, 36% invest in stocks, 22% invest in futures, and 15% invest in both stocks and futures. use this information and the rules of probability to answer the following:Part A: What proportion of Iron Bank customers invest in neither Stocks nor Futures? Part B: Of the Iron Bank customers who invest in Futures, what percentage invest in Stocks? Part C: What is the probability that a randomly selected Iron Bank customer invests in Stocks aud does not invest in Futures?
Part A: The proportion of Iron Bank customers who invest in neither stocks nor futures is 27%.
Part B: Of the Iron Bank customers who invest in futures, 61.54% also invest in stocks.
Part C: The probability that a randomly selected Iron Bank customer invests in stocks and does not invest in futures is 18.18%.
Part A: This can be calculated by subtracting the combined proportion of those who invest in stocks (36%) and those who invest in futures (22%) from 100%.
Part B: This can be calculated by dividing the proportion of those who invest in both stocks and futures (15%) by the proportion of those who invest in futures (22%).
Part C: This can be calculated by subtracting the proportion of those who invest in both stocks and futures (15%) from the proportion of those who invest in stocks (36%).
Given, that 36% of the customers are investing in stocks and 15% of those customers are also investing in futures.
So, 21% of the customers invest in stocks and not futures, while 79% of the customers either invest in futures, or in neither stocks nor futures.
Therefore, the probability is 21/100, or 18.18%.
In conclusion, the probability that a randomly selected Iron Bank customer invests in stocks and does not invest in futures is 18.18%. This is calculated by subtracting the proportion of those who invest in both stocks and futures (15%) from the proportion of those who invest in stocks (36%).
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coloca los números del 1 al 5 y del 7 al 11 de tal manera de que la suma de cada línea sea 18.
Help with Graded Assignment
Unit Test, Part 2: Measurement of Two-Dimensional Figures
The capacity of Leo's container is (WH x L) / 2, where W, H, and L represent the width, height, and length of the container, respectively.
To find the capacity of Leo's container, we need to calculate its volume. The volume of a rectangular prism is calculated by multiplying its length, width, and height. We can express this formula mathematically as:
Volume = Length x Width x Height
Since we do not have the exact measurements of the container, we cannot determine the exact volume.
The surface area of a rectangular prism is given by the formula:
Surface Area = 2 x (Length x Width + Width x Height + Length x Height)
Therefore, we can set the equation for surface area equal to the equation for the total surface area of the container:
Surface Area = 2 x (Length x Width + Width x Height + Length x Height) = Total Surface Area of Container
Then we have:
Total Surface Area of Container = 2LW + 2WH + 2HL Surface Area of Material = 6LW
Since the material covers all six sides, we can set the surface area of the material equal to the total surface area of the container:
6LW = 2LW + 2WH + 2HL
Simplifying this equation, we get:
4LW = 2WH + 2HL
Dividing by 2, we get:
2LW = WH + HL
Multiplying by the height, we get:
2LWH = WH² + HL²
Now, we can rearrange this equation to get the volume of the container:
Volume = Length x Width x Height = (WH x L) / 2
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Complete Question:
Leo made a container to store his camping gear. The container is in the shape of a rectangular prism. The container has material covering all six sides.
What is the capacity of the container?
For each statement below, state whether the lengths, angles or both are invariant.
Translation
Reflection
Rotation
Enlargement
The average cost of a large pizza in the United States is roughly $ 12.50, with a standard deviation of 51.50. Use that information to answer the following questions.
a) Use the Empirical Rule to make an interval that should include 99.7% of the data
b) Use the Empirical Rule to make an interval that would be considered usual
c) Find the z-score of a pizza that cost $10
a) The interval would be:Interval = $12.50 ± ($51.50 x 3)Interval = $12.50 ± $154.50 Interval = ($12.50 - $154.50, $12.50 + $154.50)Interval = (-$142.00, $179.00)
b) The interval would be:Interval = $12.50 ± ($51.50 x 1)Interval = $12.50 ± $51.50 Interval = ($-39.00, $64.00)This interval can be considered usual since it includes about 68% of the data.
c) A pizza that costs $10 is about 0.049 standard deviations below the mean.
Use the Empirical Rule to make an interval that should include 99.7% of the data.The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical rule that states that for a normal distribution, about 68% of observations will fall within one standard deviation of the mean, about 95% will fall within two standard deviations, and about 99.7% will fall within three standard deviations.To make an interval that should include 99.7% of the data, we need to find the mean plus/minus three standard deviations. The mean is given as $12.50, and the standard deviation is given as $51.50. Therefore, the interval would be:Interval = $12.50 ± ($51.50 x 3)Interval = $12.50 ± $154.50Interval = ($12.50 - $154.50, $12.50 + $154.50)Interval = (-$142.00, $179.00)
Use the Empirical Rule to make an interval that would be considered usual.Again, we can use the Empirical Rule to find an interval that would be considered usual. This would be the interval that falls within one standard deviation of the mean. The mean is given as $12.50, and the standard deviation is given as $51.50. Therefore, the interval would be:Interval = $12.50 ± ($51.50 x 1)Interval = $12.50 ± $51.50 Interval = ($-39.00, $64.00)This interval can be considered usual since it includes about 68% of the data.
Find the z-score of a pizza that costs $10.The z-score is a measure of how many standard deviations a data point is from the mean. To find the z-score of a pizza that costs $10, we first need to find the difference between $10 and the mean of $12.50, and then divide that difference by the standard deviation of $51.50.z-score = (10 - 12.50) / 51.50z-score = -0.049 This means that a pizza that costs $10 is about 0.049 standard deviations below the mean.
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Find a polynomial \( f(x) \) of degree 4 with leading coefficient 1 such that both \( -4 \) and 2 are zeros of multiplicity 2 . \[ f(x)=x \]
Polynomial with a degree 4 and leading coefficient 1 is to be found. Also, -4 and 2 are the zeros of multiplicity 2.
Given the roots, the polynomial can be expressed in factored form as:
\[f(x) = (x + 4)^2(x - 2)^2\]
Expanding this:
\begin{align*}
f(x) &= (x + 4)^2(x - 2)^2\\
&= (x^2 + 8x + 16)(x^2 - 4x + 4)\\
&= x^4 + 4x^3 - 4x^3 - 32x^2 + 16x^2 + 128x + 64\\
&= x^4 - 16x^2 + 128x + 64
\end{align*}
Thus, the polynomial is:
\[f(x) = x^4 - 16x^2 + 128x + 64\]Therefore, the answer is \[f(x) = x^4 - 16x^2 + 128x + 64\].
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The cone-shaped paper cup is 2/3 full of sand. What is the volume of the part of the cone that is filled with sand?
The volume of the part of the cone that is filled with sand is 2/9 times the total volume of the cone.
To do this, we need to first determine the total volume of the cone. The formula for the volume of a cone is:
V = 1/3 x π x r² x h
Where V is the volume, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant (approximately equal to 3.14).
Since we know that the paper cup is cone-shaped, we can assume that it has a circular base. Let's say that the radius of the base of the cone is r and the height of the cone is h.
The total volume of the cone can be calculated using the formula above:
V = 1/3 x π x r² x h
Now we need to determine the volume of the part of the cone that is filled with sand. We know that the cup is 2/3 full of sand, so the volume of sand in the cup is 2/3 of the total volume of the cup. We can express this as:
V = 2/3 x V
We can substitute the formula for V into this equation to get:
V = 2/3 x (1/3 x π x r² x h)
Simplifying this equation, we get:
V = 2/9 x π x r² x h
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Find the value of the unknown in the figure below
b =(17,6x 8,9):19,7=7,95
f:g → 10 - g. Find f-1: g
pls i need this
The inverse function is [tex]f^{-1} (g) = 10 - g[/tex]
What is the Composition function?Composition function is a type of function that is formed by combining two or more functions, where the output of one function becomes the input of another function. Composition function shown by the symbol "∘".
The composition function is a mathematical operation that combines two functions to produce a new function. Specifically, given two functions f and g, the composition function (also called function composition) creates a new function h(x) = f(g(x)) that applies the function g to an input x, and then applies the function f to the output of g(x).
We can start by finding the inverse function of f(g), which is [tex]f^{-1} (g)[/tex]. To do so, we need to solve the equation:
[tex]f(g) = x = 10 - g[/tex]
for g, in terms of x:
x = 10 - g
g = 10 - x
This gives us the inverse function:
[tex]f^{-1} (x) = 10 - x[/tex]
Now we can find f^-1(g) by replacing x with g in the above equation:
[tex]f^{-1} (g) = 10 - g[/tex]
Therefore, the function [tex]f^{-1} (g)[/tex] is given by:
[tex]f^{-1} (g) = 10 - g[/tex]
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Complete question is: f:g → 10 - g. Find f-1: g.
What is the best comparison between the theoretical and experimental probability of tossing heads?
Answer: Theoretical probability is based on mathematical analysis and predictions, while experimental probability is based on actual data collected through repeated trials or experiments.
For example, the theoretical probability of tossing a fair coin and getting heads is 1/2, because there are two equally likely outcomes (heads and tails) and only one of them is heads.
On the other hand, the experimental probability of tossing heads can be found by conducting multiple trials of coin flips and recording the frequency of getting heads. As the number of trials increases, the experimental probability should approach the theoretical probability.
Therefore, the best comparison between theoretical and experimental probability of tossing heads is that the theoretical probability is based on mathematical analysis and predictions, while the experimental probability is based on actual data collected through repeated trials or experiments. The two probabilities may be similar or different, but as the number of trials increases, the experimental probability should converge to the theoretical probability.
Step-by-step explanation:
A diameter of a circle is 78 cm
WHat is the area
since it has a diameter of 78, then its radius is half that, or 39.
[tex]\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=39 \end{cases}\implies A=\pi (39)^2\implies A\approx 4778.36~cm^2[/tex]
A golf coach bought g golf balls. The balls came in 7 packages. Write an expression that shows how many golf balls were in each package.
Answer:
g/7
Step-by-step explanation:
Answer:G/7
Step-by-step explanation:G/7
Thuli wants to buy TV R8 500 A bank offers to loan her the money at an interest of 5 percent she decide to pay her TV off 3 years. Calculate the simpled interest she will have to pay also calculate the total she will pay
The simple interest she will have to pay equals R 1275, and the total she will pay equals R 9775 for her TV over the past 3 years.
Thuli wants to buy TV, and a bank offers to loan her the money at an interest rate.
Principal, P = R 8,500
Interest Rate, R = 5%
Time, t = 3 year
Simple interest is defined as an interest charge that borrowers pay their lenders for a loan. It is calculated using the principal only. Formula for SI is written as SI = (P×T×R)/100
Here, SI = Simple interest
P = Principal (sum of money borrowed)
R = Rate of interest p.a
T = Time (in years)
We have to calculate simpled interest she will have to pay also calculate the total she will pay.
So, Simple interest = (8500×3×5)/100
= 85× 15 = R 1275
Now, total she will have to pay = Principle + SI
= 8500 + 1275
= R 9775
Hence, required total she will pay is R9775.
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PLEASE HELP WITH THE PROBLEM !!
Answer:
the answer is 18
Step-by-step explanation:
volume of triangular prism =l×w×h
9×2×1=18
Whats the distance between (-1,-2) and (3,4)
Answer:
the answer is 7,21
Step-by-step explanation:
Distance formula is d=√(x1-x2)²+(y1-y2)²√(-1-3)²+(-2-4)²√(-4)²+(-6)²√16+36√527.21Solve the following equations . a² = 64. 2x-2 = 16. 3y² = 27
Answer:
-3
Step-by-step explanation:
a² = 64
Taking the square root of both sides, we get:
a = ±√64
a = ±8
Therefore, the solutions to the equation a² = 64 are a = 8 and a = -8.
2x-2 = 16
Adding 2 to both sides, we get:
2x = 18
Dividing both sides by 2, we get:
x = 9
Therefore, the solution to the equation 2x-2 = 16 is x = 9.
3y² = 27
Dividing both sides by 3, we get:
y² = 9
Taking the square root of both sides, we get:
y = ±√9
y = ±3
Therefore, the solutions to the equation 3y² = 27 are y = 3 and y = -3.
find the perimeter of 18.6 18.9 6.9
The perimeter of the polygon with sides of lengths 18.6, 18.9, and 6.9 is 44.4 units.
What is the perimeter?
The perimeter of a polygon is the total distance around its boundary, which is equal to the sum of the lengths of all its sides. To find the perimeter of a polygon, you simply add up the lengths of all its sides.
The perimeter of any polygon is the sum of the lengths of its sides. In this case, we have three sides of lengths 18.6, 18.9, and 6.9.
To find the perimeter, we simply add these lengths together:
Perimeter = 18.6 + 18.9 + 6.9
Perimeter = 44.4
Therefore, the perimeter of the polygon with sides of lengths 18.6, 18.9, and 6.9 is 44.4 units.
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In rectangle QRST , QS=30-2x and RT=9+x . Find the lengths of the diagonals of QRST
Answer:
Each of the diagonals is 16
Step-by-step explanation:
The diagonals of a rectangular are equal
The two diagonals are QS and RT
QS = RT
→ 30 - 2x = 9 + x
Subtract 30 both sides:
30 - 30 - 2x = 9 - 30 + x
- 2x = -21 + x
Subtract x both sides
-2x - x = -21 + x - x
-3x = -21
x = -21/-3 = 7
So the diagonal RT = 9 + 7 =16
should be the same as diagonal QS
Qs = 30 - 2(7) = 30 - 14 = 16
Solve for Vtotal help me out please TT TT
Using Pythagorean theorem to calculate the distance of the charges, the electric potential is -93V
What is the electric potentialThe electric potential at point P can be calculated using the formula:
[tex]V=\frac{1}{4\pi\epsilon_0}\frac{q_1}{r_1}+\frac{1}{4\pi\epsilon_0}\frac{q_2}{r_2}[/tex]
where [tex]\epsilon_0[/tex] is the vacuum permittivity, q1 and q2 are the charges, and r1and r2 are the distances from the charges to point P.
To find r1 and r2, we can use the Pythagorean theorem:
[tex]r_1=\sqrt{(0.1\text{ m})^2+(0.15\text{ m})^2}=0.18\text{ m}[/tex]
[tex]r_2=\sqrt{(0.1\text{ m})^2+(0.25\text{ m})^2}=0.27\text{ m}[/tex]
Substituting the values into the formula, we get:
[tex]V=\frac{1}{4\pi\epsilon_0}\frac{-5.0\times10^{-6}\text{ C}}{0.18\text{ m}}+\frac{1}{4\pi\epsilon_0}\frac{5.0\times10^{-6}\text{ C}}{0.27\text{ m}}[/tex]
Using the value of vacuum permittivity
[tex]\epsilon_0=8.85\times10^{-12}\text{ F/m}[/tex] we get:
[tex]V=-267\text{ V}+174\text{ V}= -93\text{ V}[/tex]
Therefore, the electric potential at point P is -93 V.
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what is the value of 12.5-31/2 +1 1/4?
The value for the expression is obtained as -7/4.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
To evaluate the expression 12.5 - 31/2 + 1 1/4, we need to convert the mixed number 1 1/4 to an improper fraction -
1 1/4 = 5/4
Now we can substitute the values into the expression and simplify -
Substitute 1 1/4 with 5/4 -
= 12.5 - 31/2 + 1 1/4
= 12.5 - 31/2 + 5/4
Convert 12.5 to an improper fraction with a denominator of 2 -
= 25/2 - 31/2 + 5/4
Get a common denominator of 4 -
= (50)/(4) - (62)/(4) + 5/4
= 55/4 - 62/4
= -7/4
Therefore, the value is -7/4.
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60% of all Americans live in cities with population greater than 100,000 people. If 34 Americans are randomly selected, find the probability that
a. Exactly 23 of them live in cities with population greater than 100,000 people.
b. At most 23 of them live in cities with population greater than 100,000 people.
c. At least 22 of them live in cities with population greater than 100,000 people.
d. Between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people.
a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is 0.095.
b. The probability that at most 23 of them live in cities with population greater than 100,000 people is 0.0332.
c. The probability that at least 22 of them live in cities with population greater than 100,000 people is 0.9876.
d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is 0.8782.
What is the probability of selecting the required numbers?Let X be the number of Americans out of 34 who live in cities with population greater than 100,000 people.
Then X follows a binomial distribution with n = 34 and p = 0.6.
a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is:
P(X = 23) = (34C₂₃) x (0.6)²³ x (0.4)¹¹ = 0.095
b. The probability that at most 23 of them live in cities with population greater than 100,000 people is:
P(X <= 23) = P(X = 0) + P(X = 1) + ... + P(X = 23)
= ∑(34Ci) x (0.6)^i x (0.4)^(34-i), i = 0 to 23
= 0.0332
c. The probability that at least 22 of them live in cities with population greater than 100,000 people is:
P(X >= 22) = 1 - P(X < 22) = 1 - P(X <= 21)
= 1 - ∑(34Ci) * (0.6)^i x (0.4)^(34-i), i = 0 to 21
= 0.9876
d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is:
P(18 <= X <= 24) = P(X <= 24) - P(X < 18)
= ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 24
- ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 17
= 0.8782
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ANSWER FAST!!!
find the missing y value in the table
x y
4 2.5
11 9.5
15 13.5
21 y
The missing y value in the table can be found to be 19. 5.
How to find the missing value in the table?To find the missing value, you need to find the relationship that x and y have with each other on the table.
We find that when 4 increases to 11, 2. 5 as y, increases to 9. 5. The difference in both is:
= 11 - 4 = 9. 5 - 2.5
= 7 = 7
We see this common difference again with 15 and 11 being 4 and the difference between the y - values of 13. 5 and 9. 5 being 4 as well.
The y value corresponding to 21 as x would be:
= ( 21 - 15 ) + 13. 5
= 19. 5
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7. Solve the system: ( 4 points ) 3a−2b=1
7a−b=17
and show all step
Answer:
a = 3, b = 4
Step-by-step explanation:
[tex]3a-2b=1\\7a-b=17\\\\[/tex]
Multiply second equation by 2
[tex]3a-2b=1\\14a-2b=34\\[/tex]
Subtract the equations
[tex]3a-2b=1\\-(14a-2b=34)\\\\-11a=-33\\a=3[/tex]
Plug back in to either original equation to solve for b
[tex]3(3)-2b=1\\9-2b=1\\-2b=-8\\b=4[/tex]
Solution:
(3,4)
Find the volume of the cone in cubic feet. Use 3.14 for π and round your answer to the nearest tenth.
HELPPPPPPPPP
Answer:
third option
Step-by-step explanation:
Volume of a cone = V = πr²(h/3)
Where,
r = radiush = heightHere we are given the following :
Height = 54m Radius = 38m π = 3.14Note that we are asked to find the volume in square feet so we must first convert the height and radius into feet
Converting given values
Height = 54 * 3.2808 = 177.1632 ftRadius = 38 * 3.2808 = 124.6704 ftπ = 3.14By plugging these values into the formula we acquire
V = (3.14)(124.6704²)(177.1632/3)
==> evaluate exponent
V = (3.14)(15542.7086362)(177.1632/3)
==> divide 177.1632 by 3
V = (3.14)(15542.7086362)(59.0544)
==> multiply 3.14 and 15542.7086362
V = 48804.1051175(59.0544)
==> multiply 48804.1051175 and 59.0544
V = 2882097.1 ft² (rounded to the nearest tenth)
The volume of the cone is 2882097.1 so the correct answer choice is the third option.
Important note : Its important to note that we must convert meters to feet before finding the volume. If we try to convert after finding the volume, our answer will be incorrect.
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Please answer the Bonus question.
Answer:
FG = 25.6
Step-by-step explanation:
ABC to DEC = 5:2
DEC to FEG = 1:4
so,
ABC to FEG = 5/2 × 1/4 = 5:8
that means the scaling factor from small to large is 8/5.
therefore,
EG = BC × 8/5 = 10×8/5 = 2×8 = 16
the side length ratio for ABC tells us
AB:BC:AC = 5 : 2 1/2 : 4
BC = 10
so,
AB:BC = 5 : 2 1/2 = 5 : 2.5
AB:10 = 5 : 2.5
2.5AB = 50
AB = 50/2.5 = 20
AC:AB = 4:5
AC:20 = 4:5
AC = 20×4/5 = 80/5 = 16
FG = AC × 8/5 = 16 × 8/5 = 128/5 = 25.6
A study of the amount of time it takes a specialist to repair a mobile MRI shows that the mean is 8. 4 hours and the standard deviation is 1. 8 hours. If 40 broken mobile MRIs are randomly selected, find the probability that their mean repair time is less than 8. 9 hours
Using the normal distribution, it is found that there is a 0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
[tex]Z=\frac{x-u}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean.
Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s=\frac{\sigma}{\sqrt n}[/tex]
u=8.4, sigma=1.8 n=32 s=0.3182
The probability that their mean repair time is less than 8.9 hours is the p-value of Z when X = 8.9, hence:
Z=1.57
Z = 1.57 has a p-value of 0.9418.
1 - 0.9418 = 0.0582.
0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.
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Statistics grades: In a statistics class of 42 students, there were 11 men and 31 women. Six of the men and seven of the women received an A in the course. A student is chosen at random from the class.
Give all answers as decimals rounded to 4 digits after the decimal point
(a) Find the probability that the student is a woman.
(b) Find the probability that the student received an A.
(c) Find the probability that the student is a woman or received an A.
(d) Find the probability that the student did not receive an A.
A is 0.8218
A is 0.6905.
(a) The probability that the student is a woman.The number of women in the class is 31 while the total number of students is 42. The probability of a randomly selected student being a woman is given as:P(woman) = (Number of women in the class) / (Total number of students in the class)P(woman) = 31 / 42P(woman) = 0.7381(b) The probability that the student received an A.The number of men and women that received an A is given as follows:Men that received an A = 6Women that received an A = 7The total number of students that received an A is:Total number of students that received an A = (Number of men that received an A) + (Number of women that received an A)Total number of students that received an A = 6 + 7Total number of students that received an A = 13The probability of a randomly selected student receiving an A is given as:P(A) = (Number of students that received an A) / (Total number of students in the class)P(A) = 13 / 42P(A) = 0.3095(c) The probability that the student is a woman or received an A.The probability of the student being a woman or received an A is given as:P(woman or A) = P(woman) + P(A) - P(woman and A)From parts (a) and (b), we know that:P(woman) = 0.7381P(A) = 0.3095Now, we have to determine the probability that the student is a woman and received an A.The number of women that received an A = 7 while the total number of women in the class is 31.The probability of a woman receiving an A is given as:P(woman and A) = (Number of women that received an A) / (Total number of women in the class)P(woman and A) = 7 / 31P(woman and A) = 0.2258Therefore:P(woman or A) = P(woman) + P(A) - P(woman and A)P(woman or A) = 0.7381 + 0.3095 - 0.2258P(woman or A) = 0.8218(d) The probability that the student did not receive an A.The probability that the student did not receive an A is given as:P(not A) = 1 - P(A)From part (b), we know that:P(A) = 0.3095Therefore:P(not A) = 1 - P(A)P(not A) = 1 - 0.3095P(not A) = 0.6905Therefore, the answers are given as follows:(a) The probability that the student is a woman is 0.7381.(b) The probability that the student received an A is 0.3095.(c) The probability that the student is a woman or received an A is 0.8218.(d) The probability that the student did not receive an A is 0.6905.
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A number has three prime factors. Two of its prime factors are 3 and 5. The other prime factor is even
what is the number?
The other prime factor is even, the number is 30, and its prime factors are 2, 3, and 5.
To find the third prime factor and ultimately the number, we can use the fact that any integer greater than 1 can be expressed as a unique product of prime factors. We know that the number has three prime factors, and two of them are 3 and 5. So, we need to find the third prime factor.
Since the other prime factor is even, it must be 2 (the only even prime number). Therefore, the number can be calculated as:
Number = 3 x 5 x 2 = 30
So, the number is 30, and its prime factors are 2, 3, and 5.
Prime factors are the prime numbers that divide a given number exactly without leaving any remainder. For example, the prime factors of 12 are 2, 2, and 3, because 2 x 2 x 3 = 12 and these are the only prime numbers that divide 12 exactly. To factorize a number into its prime factors, we can use a method called prime factorization. We start by dividing the number by the smallest prime number that divides it exactly. We keep dividing the quotient by the smallest prime number that divides it exactly until we obtain only prime numbers. The prime factors are then the product of these prime numbers
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