Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the following table. 1 2 3 4 5 6 7 p(x) 0.02 0.03 0.09 0.25 0.40 0.16 0.05 It can be easily verified that u = 4.66 and 0 = 1.20. (a) Because u-o = 3.46, the x values 1, 2, and 3 are more than 1 standard deviation below the mean. What is the probability that x is more than 1 standard deviation below its mean? P(x cu- o) = (b) What x values are more than 2 standard deviations away from the mean value (either less than u - 20 or greater than u + 20)? (Select all that apply.) x = 2 <= 3 = 4 x = 5 x = 7 (c) What is the probability that is more than 2 standard deviations away from its mean value? P( x4-20 or 4 + 20 < x) =
Answers
Hence, the probability that x is more than 2 standard deviations away from its mean value is 0.
Answer: (a) P(x cu- o) = 0.347(b) None of the options apply to this situation(c) P(x < 0.5742 or x > 8.7459) = 0
(a) Because u-o = 3.46, the x values 1, 2, and 3 are more than 1 standard deviation below the mean.
What is the probability that x is more than 1 standard deviation below its mean? P(x cu- o)
=Here, we know that the standard deviation is σ = √((∑(p(x - μ)²)) =
√((0.02(1 - 4.66)² + 0.03(2 - 4.66)² + 0.09(3 - 4.66)² + 0.25(4 - 4.66)² + 0.40(5 - 4.66)² + 0.16(6 - 4.66)² + 0.05(7 - 4.66)²))
= √(4.1744) = 2.0431.
So, the mean and standard deviation of x are μ = 4.66 and σ = 2.0431, respectively.
Then, z = (x - μ) / σ and z = (1 - 4.66) / 2.0431
= -1.7761, z = (2 - 4.66) / 2.0431 = -1.2959, and z =
(3 - 4.66) / 2.0431 = -0.8062.
Now, we need to calculate the probability that x is more than 1 standard deviation below its mean.
So, P(x cu- o) = P(z < -1) + P(z < -1.2959) + P(z < -0.8062) = 0.0386 + 0.0988 + 0.2096 = 0.347.
Therefore, the required probability is 0.347.
(b) What x values are more than 2 standard deviations away from the mean value (either less than u - 20 or greater than u + 20)? (Select all that apply.)
x = 2 <= 3 = 4 x
= 5 x = 7
Here, we need to find out the x values that are more than 2 standard deviations away from the mean value.
We already know that the standard deviation is σ = 2.0431.
So, we can calculate the values of u - 2σ and u + 2σ as follows: u - 2σ =
4.66 - 2(2.0431)
= 0.5742 and u + 2σ
= 4.66 + 2(2.0431)
= 8.7459.
Therefore, the x values that are more than 2 standard deviations away from the mean value are less than 0.5742 or greater than 8.7459.
As we can see from the table, there are no such values that satisfy this condition.
So, none of the options x = 2, <= 3, = 4,
x = 5, and x = 7 apply to this situation.
(c) What is the probability that is more than 2 standard deviations away from its mean value? P( x4-20 or 4 + 20 < x)
=We already know that u - 2σ = 0.5742 and u + 2σ = 8.7459.
Now, we need to calculate the probability that x is less than 0.5742 or greater than 8.7459.
So, P(x < 0.5742 or x > 8.7459)
= P(x < 0.5742) + P(x > 8.7459).
Since there are no x values less than 0.5742 or greater than 7, we can write P(x < 0.5742) = 0 and P(x > 8.7459) = 0.
Therefore, P(x < 0.5742 or x > 8.7459) = 0 + 0 = 0.
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Related Questions
which quarter has the smallest spread of data? 3−6 6−13 13−15 15−16 correct: your answer is correct. what is that spread?
Answers
The fourth quarter having the range of 15-16 has the smallest spread of data, with the range of 1.
In order to determine which quarter has the smallest spread of data, we are required to calculate the range of each quarter. The range of each quarter can be defined as the difference between the highest and lowest values in the each quarter.
The first quarter is 3-6, so the range is 6-3 = 3.
The second quarter is 6-13, so the range is 13-6 = 7.
The third quarter is 13-15, so the range is 15-13 = 2.
The fourth quarter is 15-16, so the range is 16-15 = 1.
Therefore, after comparing the ranges of all the quarters, it can be concluded that the fourth quarter having the range of 15-16 has the smallest spread of data, with the range of 1.
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What is 30% of 60? A. 0.18 B. 1.8 C. 18 D. 180
Answers
Answer:
C ) 18 hope this helps !!!
Answer:
C. 18
Step-by-step explanation:
If you multiply 30%, or .3 by 60, you get 18.
Consider the following primal problem:
Maximize
subject to:
z=7x
1
−5x
2
−2x
3
x
1
−x
2
+x
3
=10
2x
1
+x
2
+3x
3
≤16
3x
1
−x
2
−2x
3
≥−5
x
1
≥0,x
2
≤0,x
3
unrestricted in sign
Write down the dual problem of the above primal problem.
Answers
The first constraint is a linear equation that relates the variables x1, x2, and x3, and the second constraint is an inequality constraint involving x1 and x2The given problem is a linear programming problem in its primal form.
The objective is to maximize the expression z = 7x1 - 5x2 - 2x3, subject to two constraints.. The goal is to find the values of x1, x2, and x3 that maximize the objective function while satisfying the given constraints.
In the primal problem, the objective is to maximize the expression z, which is a linear combination of the decision variables x1, x2, and x3. The coefficients 7, -5, and -2 represent the weights assigned to each variable in the objective function. The constraints represent the relationships and limitations imposed on the variables. The first constraint is an equality constraint, which means that the left-hand side of the equation must equal the right-hand side. The second constraint is an inequality constraint, indicating that the value of the expression 2x1 + x2 must be less than or equal to a certain value.
To solve this linear programming problem, various optimization techniques such as the simplex method or interior point methods can be applied. These methods iteratively adjust the values of the decision variables to find the optimal solution that maximizes the objective function while satisfying the given constraints. By solving the primal problem, the values of x1, x2, and x3 can be determined, leading to the maximum value of the objective function z.
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Classify the marked triangle in the object by its angles and by its sides
Answers
Answer:
a isosceles triangle because it has two sides that are paarrelell
Step-by-step explanation:
mention about angles of a triangle
Answers
Griffiths Fig. 5.48 is a handy "triangle" summarizing the mathematical connections between and But there's a missing link; he has nothing for the left arrow from to Note the equations defining are very analogous to the basic Maxwell's equations for B: So depends on in the same way (mathematically) that depends on (Think Biot-Savart!) Use this idea to just write down a formula for in terms of B to finish off that triangle. In Griffiths Ex. 5.9 he found the B field everywhere inside (and outside) an infinite solenoid (which you can think of as a cylinder with uniform surface current flowing azimuthally around it. See Griffiths. Fig 5.35. Use the basic idea from part 1a to, therefore, quickly and easily just write down the vector potential in a situation where looks analogous to that, i.e. with C constant. Sketch What physical situation creates such a B field?
Answers
Formula for A in terms of B: A = ∫(B × r') / ||r - r'|| dr'
The missing link in the triangle summarizing the mathematical connections between A and B can be filled by writing down a formula for A in terms of B. This can be done by using the analogy between the equations defining A and the basic Maxwell's equations for B, and applying the Biot-Savart law. By using the basic idea from the first part, the vector potential in a situation where B is constant can be quickly found.
Physical situation creating constant B field:
A constant B field can be created by a current-carrying wire in the form of a straight line or a circular loop. The vector potential for this configuration can be found using the formula derived above.
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Find the sale price of a $45 item after a 20% discount.
Answers
Answer:
36$
Step-by-step explanation:
Find the 92nd term of the arithmetic sequence 8, 25, 42
Answers
The 92nd term of the arithmetic sequence is 1555
What is an arithmetic sequence?An arithmetic sequence is defined as an ordered set of numbers having a common difference that is between each consecutive term.
The formula for calculating arithmetic sequence is expressed as;
Tn = a + (n -1) d
Where;
Tn is the last term of the sequencea is the first term of the sequencen is the number of termsd is the common difference between successive termsNow, substitute the values
T92 = 8 + ( 92 - 1) 17
expand the bracket
T92 = 8 + 91(17)
expand the bracket further
T92 = 8 + 1, 1547
Add the values
T92 = 1555
Hence, the value is 1555
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Procter and Gamble (PG) paid an annual dividend of $2.95 in 2018. You expect PG to increase its dividends by 7.4% per year for the next five years (through 2023), and thereafter by 2.6% per year. If the appropriate equity cost of capital for Procter and Gamble is 8.6% per year, use the dividend-discount model to estimate its value per share at the end of 2018.
Answers
The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.
To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.
First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:
Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22
After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)
where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.
In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:
PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.
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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.
To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:
Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22
After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.
In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.
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a+5= -5a+5 I am confused on how to solve this equation.
Answers
Answer
a = 0
Explanation
a + 5 = -5a + 5
We will bring the terms with a togther and the terms without together
a + 5 = -5a + 5
a + 5a = 5 - 5
6a = 0
Divide both sides by a
(6a/6) = (0/6)
a = 0
Hope this Helps!!!
They are 3 trucks for every 7 cars in a parking lot. How many trucksand cars could it be in their parking lot
Answers
Answer:
Um..... 6 trucks?
Step-by-step explanation:
6. What is the value of x?
A. 14
B. 28
C. 24
D. 17
Please help asap
Answers
Answer:
A
Step-by-step explanation:
draw a hexagon of equal sides and unequal angles
Answers
Answer:
This is a picture of a hexagon of equal sides and unequal angles.
A rule of thumb used by nutritionist is that to lose one LB of body fat, you need to burn three, 500 cal about what you take in. If you burn 450 more calories than you take in each day, how long will it take to lose one LB? What about 10 LB?
Answers
If you consistently burn 450 more calories than you consume each day, it will take approximately 8 days to lose one pound of body fat. To lose 10 pounds, it would take around 80 days.
To lose one pound of body fat, you need to create a calorie deficit of 3,500 calories (500 calories x 7 days). If you burn 450 more calories than you consume each day, you would have a daily deficit of 450 calories. Dividing 3,500 calories by 450 calories (deficit per day) gives us approximately 7.8 days. This means it would take about 8 days to lose one pound of body fat.
To calculate the time it would take to lose 10 pounds, we multiply the time taken to lose one pound (8 days) by the desired weight loss. Therefore, 8 days x 10 pounds equals 80 days. So, if you consistently maintain a daily deficit of 450 calories, it would take around 80 days to lose 10 pounds of body fat. It's important to note that individual results may vary due to factors such as metabolism, body composition, and activity level.
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Im struggling in math rn and i need help with this problem 3 1/4 = 1/2 + w
Answers
Answer:
w= 2 3/4
Step-by-step explanation:
First, we need to find what can equal w. So, we can subtract 1/2 form both sides, so one sides has just w and one side has just a number. 3 1/4-1/2= 2 3/4. So w= 2 3/4
Answer:
2 3/4
Step-by-step explanation:
3 1/4 = 1/2 + w
Transfer 1/2 to other side
3 1/4 - 1/2 = w
Solve
w = 2 3/4
Hope this helps!! Please give Brainliest!!
Which equation represents the line that passes through points B and C on the graph?
Answers
Answer:
i will help but i need to see the options first
Step-by-step explanation:
post another question with options pls
VERY EASYYYYYYYYY!!!!!!!!!!!!!! ASAPPPPPP
Answers
Answer:
yes
Step-by-step explanation:
Answer:
In your opinion, is Netflix a waste of time?
I hope this helps you
Which system of equations has the same solution as the system below?
5+2g = 45
4x + 4y = 48
-
Submit Answer
O
5x – 4y = –90
4x + 4y = 48
O
-10x – 4y = -90
4x + 4y = 48
--
-10x + 2y = -90
4x + 4y = 48
-10x – 4y = 45
4x + 4y = 48
Answers
Answer: (1) (2) (4)
Step-by-step explanation:
someone please help 20 points!
Answers
The two linear inequalities that represent this situation are,
5x + 10x ≥ 80 and x + y ≤ 14.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
let, The no. of hours the student babysits is 'x' and the no. of hours the student teaches be 'y'.
Therefore, From the given information the two linear inequalities will be formed as,
5x + 10x ≥ 80 (as he wants to make at least).
And,
x + y ≤ 14 (as he can work almost)
From the graph of these two inequalities, the solution or the intersecting point is (2, 12).
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What is the area of the figure?
(PLEASE GIVE A EXPLANATION!)
Answers
assume the mass hanger (before we add anything to it) is about 5g. how much mass will you need to add to the mass hanger in order to get a total single mass hanger system equal to 90 grams?
Answers
We will need to add 85 grams of mass to the mass hanger in order to get a total single mass hanger system equal to 90 grams.
To get a total single mass hanger system equal to 90 grams, you will need to add 85 grams of mass to the mass hanger. This is because the mass hanger is already 5 grams, and you need to add enough mass to get to 90 grams.
Here's the step-by-step explanation:
1. Start with the mass of the mass hanger: 5 grams
2. Subtract this from the desired total mass: 90 grams - 5 grams = 85 grams
3. The result is the amount of mass you need to add to the mass hanger: 85 grams
The combination of slotted masses and mass hanger allows a student to quickly create any desired amount of mass.
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What is the circumference of a circle with a diameter of 4.2 cm?
Answers
Answer:
it would be C≈13.19cm
hope this helps :)
Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals.
f(x)= 9x
f(1/2) =
f(square root of 6)=
f(-2)=
f(0.4)=
Answers
Given function is: f(x)= 9xTo find the values of the given function at the indicated values: Round off the answer to 3 decimal places.1. f(1/2).
f(1/2):
Plug x = 1/2 into the function:
f(1/2) = 9(1/2)
Simplifying, we find that f(1/2) = 4.5.
Similarly, for the remaining parts,
Substitute x = 1/2 in the given function. f(1/2) = 9 (1/2) = 4.5002. f(√6).
Substitute x = √6 in the given function. f(√6) = 9 √6 = 27.7123. f(-2). Substitute x = -2 in the given function. f(-2) = 9 (-2) = -18.0004. f(0.4).
Substitute x = 0.4 in the given function. f(0.4) = 9 (0.4) = 3.600. The required values of the given function are: f(1/2) = 4.500f(√6) = 27.712f(-2) = -18.000f(0.4) = 3.600.
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Solve the system by graphing.
y = −x + 3
y = −3x − 1
The solution of the system
Answers
Answer:
A(-2,5)
x= -2 , y=5
Step-by-step explanation:
draw the lines for both equations and that will be by finding any points in the lines:
1. sub any value for x to find y in the equation (y=-x+3) :
When x=0 ⇒ y=-0+3, y=3 (the point is: (0,3)When x=1 ⇒ y= -1 +3 , y=2 (the point is: (1,2)When x=2 ⇒ y=-2+3, y=1 (the point is: (2,1)When x=-1 ⇒ y=-(-1)+3, y=4 (the point is: (-1,4)When x=-2 ⇒ y=-(-2)+3, y=5 (the point is: (-2,5)plot the points in the graph and match them to get the first line for equation(1).
2. sub any value for x to find y in the equation (y=-3x-1) :
When x=0 ⇒ y=-3(0)-1, y=-1 (the point is: (0,-1)When x=1 ⇒ y=-3(1)-1, y=-4 (the point is: (1,-4)When x=2 ⇒ y=-3(2)-1, y=-7 (the point is: (2,-7)When x=-1 ⇒ y=-3(-1)-1, y=2 (the point is: (-1,2)When x=-2 ⇒ y=-3(-2)-1, y=5 (the point is: (-2,5)Now again plot the points in the same graph and match them to get the second line for equation(2).
When you finish you will have two lines drawn in a graph, the solution will be were the two points intercept, and that will be:
A(-2,5)
x= -2 , y=5
(note: you can check your answer by subbing the value of x in both equations and you should get the answer 5 as the value of y)
suppose that all of the 1000 first-year students at a certain college are enrolled in a math or an english course. suppose 400 are taking both math and english and 600 are taking english. how many are taking a math course?
Answers
As per the set theory, the number of student who take math course is 800
Set:
In math, set means an organized collection of objects and can be represented in set-builder form or roster form.
Given,
Here we know that suppose that all of the 1000 first-year students at a certain college are enrolled in a math or an English course. suppose 400 are taking both math and English and 600 are taking English.
Now, we need to find the number of students who take math course.
While looking into the given question we have identified that,
Total Number of students = 1000
Number of students in both course = 400
Number of students taking English = 600
Then the number of students who take math course is calculated as
=> 1000 - 600 + 400
=> 800
Therefore, the resulting number of students is 800.
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Given u = 3i − 8j and v = −4i + 8j, what is u • v
Answers
the dot product of u and v is -76.
What is Dot product?
The product of two vectors can refer to several different types of products, but the two most common ones are the dot product and the cross product.
Dot product: The dot product of two vectors u and v is a scalar (i.e., a single number) given by the formula:
u • v = ||u|| ||v|| cos(θ)
To find the dot product of u and v, we can use the formula:
u • v = (3i − 8j) • (−4i + 8j)
Expanding the dot product using the distributive property, we get:
u • v = 3i • (−4i) + 3i • (8j) − 8j • (−4i) − 8j • (8j)
The dot product of two orthogonal vectors (i.e., vectors that form a 90-degree angle) is zero, because the cosine of 90 degrees is 0. We can use this fact to simplify the above expression, since the second and third terms involve the product of i and j, which are orthogonal unit vectors:
u • v = (3i • (−4i)) + (−8j • (8j))
Simplifying further using the fact that i • i = j • j = 1, we get:
u • v = −12 − 64
u • v = -76
Therefore, the dot product of u and v is -76.
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00:00
Which number correctly completes the ratio table?
2
8
13
14
16
104
112
O A. 64
о
B. 48
O
C. 40
O D. 32
Answers
Answer:
D
Step-by-step explanation:
in my head
Answer:
A. 64
Step-by-step explanation:
BRAINLIEST ANSWER!! ASAP
3(x+1)+6=-9
PLEASE EXPLAIN HOW YOU GOT THE ANSWER
Answers
Answer:
x=-6
Step-by-step explanation:
use distributive property on the () and times x and 1 by three
then you subtract 6 from both sides
then subtract three from both sides
then divide both sides by 3
your work would look like this:
3(x+1)+6=-9
3x+3+6=-9
3x+3=-15
3x=-18
x=-6
Hope this helps!
Answer:
X=6
Step-by-step explanation:
3(x+1)+6=−9
Step 1: Simplify both sides of the equation.
3(x+1)+69(3)(x)+(3)(1)+6=−9
(Distribute)
3x+3+6=−9(3x)+(3+6)=−9
(Combine Like Terms)
3x+9=−93x+9=−9
Step 2: Subtract 9 from both sides.
3x+9−9=−9−93x=−18
Step 3: Divide both sides by 3.
3x3=−18/3
x=−6
I need help on homework.
Answers
J = (3,0)
K = (3,negative two)
L = [ 0, negative two]
I apologise for the way this is set out, half of the keys on my laptop do not work
Answer:
J- (3,0)
K- (3,-2)
L- (1,-2)
Reasoning- Just move the points to where it's asking.
The Martinez family picked 3 lb of apples. Ana picked for those apples,
How many pounds of apples did Ana pick?
Answers
Answer:
C. 7/8
Step-by-step explanation:
The Martinez family picked 3 and one-half pounds of apples. Ana picked one-fourth of those apples. How many pounds of apples did Ana pick?
options
A. 1/4
B. 3/4
C. 7/8
D. 1 1/4
E. 3 1/8
Total apples the Martinez family picked = 3 1/2 pounds
Ana picked one-fourth of those apples.
Number of apples Ana picked = 1/4 × 3 1/2 pounds
= 1/4 × 7/2 pounds
= (1 * 7) / (4 * 2) pounds
= 7/8 pounds
Ana picked 7/8 pounds of apples