The expected value of the above random variable is 11.15.
The expected value is a measure of the central tendency of a random variable. It represents the average value we would expect to obtain if we repeatedly observed the random variable over a large number of trials.
To find the expected value of a random variable, you multiply each value by its corresponding probability and sum them up. Let's calculate the expected value using the given probabilities and scores:
Expected value = (0.05 × 3) + (0.2 × 7) + (0.05 × 8) + (0.05 × 10) + (0.1 × 11) + (0.05 × 12) + (0.5 × 14)
Expected value = 0.15 + 1.4 + 0.4 + 0.5 + 1.1 + 0.6 + 7
Expected value = 11.15
Therefore, the expected value of the random variable is 11.15.
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Carlos rode his bike 1 2/3 miles to Tim's house then 1 2/3 to the park. What number line shows u the total number of miles that Carlos rode from house to the park
Number line wasn't added to the original question
Answer:
Carlos rode his bike 1 2/3 miles to Tim's house then 1 2/3 to the park. What number line shows u the total number of miles that Carlos rode from house to the park
Step-by-step explanation:
Distance biked to Tim's house = 1 2/3 miles
Distance biked to park = 1 2/3 miles
Total number of miles Carlos rode from house to park :
1 2/3 + 1 2/3
5/3 + 5/3
(5 + 5) / 3
10 /3
= 3 1/3 miles
how resolve it
plssss
Answer:
The answer is a
Step-by-step explanation:
Write the word sentence as an inequality.
A number y is less than 6.
Answer:
y - 6
Step-by-step explanation:
y is the number and it is less than 6 so 6 has to be negative:
y - 6
Which of the following are characteristics of a tortoise in a desert environment that distinguish the tortoise as a living thing?
Choose the THREE that apply.
A. It needs food.
B. It reproduces.
C. It uses energy.
D. It takes up space.
E. It is made up of atoms.
Answer:
A.
B.
E.
Step-by-step explanation:
hope this helps ❤️
What is the volume of a box with 385 cubes and 11/3 x 5/3 x 7/3
Answer:
y
=
x
2
−
2
x
,
y
=
x
Step-by-step explanation:
A local store owner is interested in finding the mean age of her customers. She randomly surveys 82 customers and records their age. Identify the population, sample, variable, type of variable, parameter, and statistic.
The statistic provides an estimate of the parameter based on the information obtained from the sample.
Identify the population, sample, variable, type of variable, parameter, and statistic in a customer satisfaction survey.In this scenario, the population refers to the entire group of customers of the local store.
The sample is a subset of this population and consists of the 82 customers who were randomly surveyed.
The variable of interest is the age of the customers, as the store owner wants to determine the mean age.
Age is a continuous numerical variable since it represents a quantitative measurement.
The parameter is the unknown mean age of all customers of the local store, while the statistic is the calculated mean age of the 82 surveyed customers.
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in cell b8, find the value from the appropriate probability table to construct a 90onfidence interval. Shipment Time to Deliver (Days)
1 7.0
2 12.0
3 4.0
4 2.0
5 6.0
6 4.0
7 2.0
8 4.0
9 4.0
10 5.0
11 11.0
12 9.0
13 7.0
14 2.0
15 2.0
16 4.0
17 9.0
18 5.0
19 9.0
20 3.0
21 6.0
22 2.0
23 6.0
24 5.0
25 6.0
26 4.0
27 5.0
28 3.0
29 4.0
30 6.0
31 9.0
32 2.0
33 5.0
34 6.0
35 7.0
36 2.0
37 6.0
38 9.0
39 5.0
40 10.0
41 5.0
42 6.0
43 10.0
44 3.0
45 12.0
46 9.0
47 6.0
48 4.0
49 3.0
50 7.0
51 2.0
52 7.0
53 3.0
54 2.0
55 7.0
56 3.0
57 5.0
58 7.0
59 4.0
60 6.0
61 4.0
62 4.0
63 7.0
64 8.0
65 4.0
66 7.0
67 9.0
68 6.0
69 7.0
70 11.0
71 9.0
72 4.0
73 8.0
74 10.0
75 6.0
76 7.0
77 4.0
78 5.0
79 8.0
80 8.0
81 5.0
82 9.0
83 7.0
84 6.0
85 14.0
86 9.0
87 3.0
88 4.0
This formula calculates the value corresponding to a 90% confidence level using the T.INV function. The first argument, 0.95, represents 1 minus the desired confidence level (0.05 for a 90% confidence level). The second argument, `COUNT(A2:A89)-1`, calculates the degrees of freedom by subtracting 1 from the count of data points.
To find the value from the appropriate probability table to construct a 90% confidence interval in cell B8, you can use the T.INV function in Excel. Here's how you can do it:
1. In cell B8, enter the formula:
```
=T.INV(0.95, COUNT(A2:A89)-1)
```
This formula calculates the value corresponding to a 90% confidence level using the T.INV function. The first argument, 0.95, represents 1 minus the desired confidence level (0.05 for a 90% confidence level). The second argument, `COUNT(A2:A89)-1`, calculates the degrees of freedom by subtracting 1 from the count of data points.
Make sure to adjust the cell references in the formula based on the actual location of your data in the spreadsheet.
Note: The T.INV function returns the value from the Student's t-distribution, which is used for small sample sizes or when the population standard deviation is unknown.
If you have a large sample size (usually considered more than 30), you can use the Z.INV function instead to calculate the value from the standard normal distribution.
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1.13 UNIT TEST GRAPH OF SINUSOIDAL FUNCTION PART 1
The true statements from the sinusoidal graph are:
The maximum height of the Ferris wheel is 64 ftThe radius of the Ferris wheel is 30 ftFrom the table, we have the following parameters:
Maximum height = 64 ftMinimum height = 4 ftSo, the radius (r) of the wheel is:
[tex]r = \frac{64 - 4}{2}[/tex]
This gives
[tex]r = \frac{60}{2}[/tex]
[tex]r = 30[/tex]
Also, from the table, the lowest point of the wheel is 4 ft;
The Ferris wheel is at this lowest point at 7.5 seconds and 17.5 seconds
Hence, the true statement is (c) and (d)
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what is the ratio of the length of red string to blue string written as a unit rate
Answer:2 to 3
Step-by-step explanation:
Answer:
Step-by-step explanation:
Solve the differential equation = -xy, given that when x=0, y=50. You may assume y>0. (4 marks) dx (b) For what values of x is y decreasing?
The solution to the differential equation is [tex]y = e^{-\frac{x^2}{2} + \ln(50)}[/tex]
The value of y is decreasing for x > 0.
Solving the differential equationFrom the question, we have the following parameters that can be used in our computation:
dy/dx = -xy
Rewrite as
dy/y = -x dx
Differentiate both sides
So, we have
ln|y| = -x²/2 + c
Take the exponent of both sides
[tex]|y| = e^{-\frac{x^2}{2} + c}[/tex]
Assume y > 0
So, we have
[tex]y = e^{-\frac{x^2}{2} + c}[/tex]
When x = 0, y = 50
So, we have
[tex]50 = e^{-\frac{0^2}{2} + c}[/tex]
Evaluate
c = ln(50)
So, we have
[tex]y = e^{-\frac{x^2}{2} + \ln(50)}[/tex]
For what values of x is y decreasing?Recall that dy/dx = -xy.
This means that if dy/dx < 0, then y is decreasing.
This means that, y is decreasing for x > 0.
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20 POINTS HELPIf these two rectangles are similar, what is the measure of the missing length d ?
Answer:
d (or V in the picture) = 16
Step-by-step explanation:
Because the two triangle are similar, the ratios of each of the side lengths should be equal. Therefore, 8/1 should be equal to d/2.
1.) Set up equality of ratios: 8/1 = d/2
2.) Cross multiply: 8*2 = d*1
3.) 16 = d
Which sentence is TRUE!!!!!!
The fixed costs for a company are $1,596.00 per month, and their variable cost per unit is $3.20. Suppose the company insists on producing 140 units, the selling price per unit required to break even is $
When the company insists on producing 140 units then the selling price per unit required to break even is approximately $14.60.
To calculate the selling price per unit required to break even, we need to consider the fixed costs, variable cost per unit, and the desired production quantity.
Given:
Fixed costs = $1,596.00 per month
Variable cost per unit = $3.20
Production quantity = 140 units
To break even, the total revenue should cover both the fixed costs and the variable costs.
The total cost can be calculated as follows:
Total cost = Fixed costs + (Variable cost per unit × Production quantity)
Plugging in the given values:
Total cost = $1,596.00 + ($3.20 × 140)
Total cost = $1,596.00 + $448.00
Total cost = $2,044.00
To break even, the total revenue should be equal to the total cost.
The selling price per unit required to break even can be calculated as:
Selling price per unit = Total cost / Production quantity
Plugging in the values:
Selling price per unit = $2,044.00 / 140
Selling price per unit ≈ $14.60
Therefore, the selling price per unit required to break even is approximately $14.60.
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The following differential equation describes the movement of a body with a mass of 1 kg in a mass-spring system, where y(t) is the vertical position of the body in meters) at time t. y" + 4y + 5y = -21 To determine the position of the body at time t complete the following steps. (a) Write down and solve the characteristic (auxiliary) equation. (b) Determine the complementary solution, yc, to the corresponding homogeneous equation, y" + 4y' + 5y = 0. (c) Find a particular solution, Yp, to the nonhomogeneous differential equation, Y" + 4y' + 5y = e-21. Hence state the general solution to the nonhomogeneous equation as y = Ye + yp. (d) Solve the initial value problem if the initial position of the body is 1 m and its initial velocity is zero.
After considering the given data we conclude that
a) r = -2 + i and r = -2 - i value generated after solving the auxiliary equation
b)[tex]y_c = c_1e^{(-2t)} cos(t) + c_2e^{(-2t)} sin(t)[/tex] complementary solution
c) general solution to the nonhomogeneous equation is [tex]y = y_c + Y_p = c_1e^{(-2t)} cos(t) + c_2e^{(-2t)} sin(t) + (1/26)e^{(-21)} .[/tex]
d) initial value problem is [tex]y(t) = e^{(-2t)} (cos(t) + 2sin(t))/2 + (1/26)e^{(-21)} .[/tex]
To determine the position of the body at time t, we can apply the given differential equation to solve for y(t). To do this, we can follow the steps below:
(a) the characteristic (auxiliary) equation is
The characteristic equation is obtained by setting the coefficients of the differential equation to zero, which gives us the equation [tex]r^2 + 4r + 5 = 0.[/tex]Solving this quadratic equation, we get r = -2 + i and r = -2 - i.
(b) evaluate the complementary solution, yc, to the corresponding homogeneous equation, [tex]y" + 4y' + 5y = 0.[/tex]
The complementary solution is given by[tex]y_c = c_1e^{(-2t)} cos(t) + c_2e^{(-2t)} sin(t),[/tex]where [tex]c_1[/tex] and [tex]c_2[/tex] are constants determined by the initial conditions.
(c) Calculate a particular solution, Yp, to the nonhomogeneous differential equation, [tex]Y" + 4y' + 5y = e^{(-21)}[/tex]. Hence state the general solution to the nonhomogeneous equation as [tex]y = y_c + y_p.[/tex]
To describe a particular solution, we can use the method of undetermined coefficients and guess a solution of the form [tex]Yp = Ae^{(-21)}[/tex], where A is a constant to be determined.
Staging this into the differential equation, we get A = 1/26. Therefore, the particular solution is [tex]Y_p = (1/26)e^{(-21)}[/tex]. The general solution to the nonhomogeneous equation is [tex]y = y_c + Y_p = c_1e^{(-2t)} cos(t) + c_2e^{(-2t)} sin(t) + (1/26)e^{(-21)}[/tex]
(d) Solve the initial value problem if the initial position of the body is 1 m and its initial velocity is zero.
Applying the initial conditions, we can solve for the constants [tex]c_1[/tex] and [tex]c_2[/tex] in the complementary solution. Since the initial velocity is zero, we have [tex]y'(0) = -2c_1 + c_2 = 0[/tex], which gives us [tex]c_2 = 2c_1.[/tex]
Applying the initial position, we have [tex]y(0) = c_1 = 1[/tex], which gives us [tex]c_2 = 2.[/tex]Therefore, the solution to the initial value problem is [tex]y(t) = e^{(-2t)} (cos(t) + 2sin(t))/2 + (1/26)e^{(-21)}[/tex]
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As an estimation we are told £3 is €4.
Convert £40.50 to euros.
Answer:
As per the conversion in the question, £40.50 = €54
Step-by-step explanation:
Here, we want to make a conversion;
from the question;
£3 = €4
£40.50 = €x
Thus;
3 * x = 4 * 40.5
x = (4 * 40.5)/3
x = €54
find the missing angle measurement
Answer: 56
Step-by-step explanation: According to AIA(Alternate Interior Angles Congruency) they are equal. So just solve the equation that they're both equal to each other and you get x=-6. Plug this back in to find the angle measure, 56! Hope this helped!
Answer:
x = -6
56 degrees
Step-by-step explanation:
Those two angles that are labeled are equal for a reason that I forgot (but trust me they are). So, -8x+8 = -6x+20
just solve the equation to get x = -6
after plugging in -6 for x, you get that the angles that are labeled are 56 degrees.
Listen In 2010 Glacial HVAC, Inc. sold 3,295 air conditioning units in Fulton County. Glacial's largest competitor, Estes Heating and Air, sold 2,759 units during 2010. Calculate Glacial's relative market share. Round your answer to two decimal places
Glacial HVAC, Inc. had a relative market share of 54.39% in Fulton County in 2010, based on the sale of 3,295 air conditioning units, compared to their largest competitor, Estes Heating and Air.
To calculate the relative market share, we need to divide Glacial HVAC's sales by the total market sales. The formula for relative market share is:
Relative Market Share = Glacial HVAC's Sales / Total Market Sales.
In this case, Glacial HVAC sold 3,295 units, and their largest competitor, Estes Heating and Air, sold 2,759 units. So the total market sales would be the sum of these two figures, which is 3,295 + 2,759 = 6,054 units.
Now, we can calculate the relative market share:
Relative Market Share = 3,295 / 6,054 * 100%.
Evaluating the expression, we find that Glacial HVAC's relative market share is approximately 54.39% when rounded to two decimal places.
This means that Glacial HVAC had a market share of 54.39% in Fulton County in 2010, indicating their position in the market relative to their largest competitor.
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Please help this is for a friend with co vid- 19
Answer:
Hey I know this isn’t an answer but your bf Jordan told me to tell you he is looking for you and he needs to talk to you. Sorry again for wasting ur time but he kinda worried
Step-by-step explanation:
What is the measure of the other acute angle ?
Answer:
58
Step-by-step explanation:
Answer: 58°
Step-by-step explanation:
We know it's a right triangle, one of them must be 90°. The sum of the three interior angles are 180°, so we know the sum of the other two angles is 180 - 90 = 90°.
If one of the angles is 32°, another angle is 90 - 32 = 58°
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the quadratic expression below.
Answer:
x = -3 and x = 2
Step-by-step explanation:
The expression for the quadratic equation is as follows:
(x+3)(x-2)
For (x+3)(x-2) to equal 0, either (x+3) or (x-2) must be equal to 0. So,
(x+3) = 0 and (x-2) = 0
It implies,
x = -3 and x = 2
So, the values of x are -3 and 2.
help i hate fractions pls
Answer:
the answer is B
Step-by-step explanation:
because you just put 100 underneath
Answer:
B, 71/100
Step-by-step explanation:
To do this, just put each fraction into a calculator, and whichever fraction results in the decimal you're looking for will be your answer.
28) (-5ưyA +9u) + (-5ư v4 - 8u + 8u²v2)+(-8u*v + 8uº4)=
Answer: good luck
Step-by-step explanation:
-23 = x - 23
A. Infinite number of solutions
B. No solution
C. 0
D. 5
Answer:
x=0
Step-by-step explanation:
have a nice day or evening
A mail order company has an 8% success rate. If it mails advertisements to 534 people, find the probability of getting less than 37 sales. Round z-value calculations to 2 decimal places and final answer to at least 4 decimal places. P(X<37)= 0.1814 Population of College Cities College students often make up a substantial portion of the population of college cities and towns. State College, Pennsylvania, ranks first with 71.1% of its population made up of college students. What is the probability that in a random sample of 138 people from State College, more than 50 are not college students? Round the final answer to at least 4 decimal places and intermediate z-value calculations to 2 decimal places. P(X>50) 0.1093 Residences of U.S. Citizens According to the U.S. Census, 67.5% of the U.S. population were born in their state of residence. In a random sample of 190 Americans, what is the probability that fewer than 114 were born in their state of residence? Round the final answer to at least four decimal places and intermediate z-value calculations to two decimal places. P(X<114)= Day Care Tuition A random sample of 54 four-year-olds attending day care centers provided a yearly tuition average of $3958 and the population standard deviation of $640. Part 1 of 2 Find the 99% confidence interval of the true mean. Round your answers to the nearest whole number. 3734 µ< $4182 Part: 1/2 Part 2 of 2 If a day care center were starting up and wanted to keep tuition low, what would be a reasonable amount to charge? Round your answer to the nearest hundred. would be a reasonable amount to charge.
The probability which is in a random sample of 133 people from State College, more than 50 are not college students is 0.0000313 (rounded to 4 decimal places).
Given that in State College, Pennsylvania, the proportion of college students in the population is 71.1%.
We need to find the probability that in a random sample of 133 people from State College, more than 50 are not college students.
We need to round the final answer to at least 4 decimal places and intermediate z-value calculations to 2 decimal places.
The proportion of college students in State College, Pennsylvania is 71.1%.
Therefore, the proportion of non-college students in State College, Pennsylvania is 100% - 71.1% = 28.9%.
Let X be the number of non-college students in a sample of 133 people from State College, Pennsylvania.
As the sample is random, X follows the binomial distribution with parameters n = 133 and p = 0.289.
The probability of getting more than 50 non-college students can be obtained using the normal distribution approximation to the binomial distribution.
Using the normal distribution approximation, we can convert the binomial distribution to a standard normal distribution using the following formula: Z = (X - np) / sqrt(npq)
Where q = 1 - p is the proportion of college students in the population, and np = 133 x 0.289
= 38.397 and npq = 133 x 0.289 x 0.711 = 9.728.
The probability of getting more than 50 non-college students is : P(X > 50)
= P(Z > (50 - 38.397) / sqrt(9.728))
= P(Z > 3.92)
= 0.0000313 (rounded to 4 decimal places).
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A rectangular garden has a width of 10 feet and a length of 14 feet. A cement
walkway is added around the outside of the garden. The area of the garden and the
walkway together are 252 square feet. What is the width of the walkway?
100 pts plz help!!!!!!1
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
Here,
The two lines l and m are parallel,
cut by a transversat line t
So The two angles are supplementary each other.
we know that,
The sum of two supplementary angles are 180°
According to the question,
(17x+14)°+(4x-2)°=180°17x+14°+4x-2°=180°17x+4x+14°-2°=180°21x+12°=180°21x=180°-12°21x=168°x=168°/21x=8°Therefore,
The value of x is 8°
If 55 yards of dirt costs $825.00 what is the constant of proportionality?
Answer:$15 per yard
Step-by-step explanation: $825 divided by 55 = $15
Find any vertical or slant asymptotes. Consider the following.
f(x) = x^3/ (x² - 49)
The function [tex]f(x) = x^3 / (x^2 - 49)[/tex]has a vertical asymptote at x = 7 and x = -7. There are no slant asymptotes. To find the vertical asymptotes of the function f(x), we need to identify the values of x for which the denominator becomes zero, as division by zero is undefined.
In this case, the denominator is (x² - 49). To determine when it equals zero, we set it equal to zero and solve for x:
x² - 49 = 0
This equation can be factored as the difference of squares:
(x - 7)(x + 7) = 0
Setting each factor equal to zero, we find that x = 7 and x = -7. Therefore, the function has vertical asymptotes at x = 7 and x = -7.
On the other hand, to determine if there are any slant asymptotes, we need to check if the degree of the numerator (x³) is greater than the degree of the denominator [tex](x^2 - 49)[/tex]. In this case, the degree of the numerator is 3, while the degree of the denominator is 2. Since the degree of the numerator is greater, there are no slant asymptotes for this function.
In summary, the function [tex]f(x) = x^3 / (x^2 - 49)[/tex] has vertical asymptotes at x = 7 and x = -7. There are no slant asymptotes.
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Can someone plz help this is my third time posting this question and I’m trying to get an 92
21 is the right answer.
180-138=42°
and since it is given in the question that the triangle is isoceles ,so half of 42 is 21°
Answer:
the last three answers is what i think
Step-by-step explanation:
Exercise 1: If tossing 4 coins identical and distinct. Find the number of macrostates and
microstates (explain the distribution in a table).
Exercise 2: Two particles distinct are to be distributed in three cells. Find the number of
macrostates and microstates ( explain the distrubition in a table)
Exercise 1: When tossing 4 identical and distinct coins, the number of macrostates and microstates are given below:MoleculesMacrostatesMicrostates4 coins16 states2^4=16Microstates: The number of ways in which the particles can be distributed among different energy levels is referred to as microstates. Macrostates: The number of ways in which the total energy of the system can be divided into different energy levels is referred to as macrostates. The distribution is represented in the following table: Distribution Microstates (W) Macrostates (Ω)TTTT1111HHHHT4C4,216HHHH3C4,715
Exercise 2:When distributing two distinct particles among three cells, the number of macrostates and microstates are as follows: Molecules Macrostates Microstates 2 particles10 states3^2=9Microstates: The number of ways in which the particles can be distributed among different energy levels is referred to as microstates. Macrostates: The number of ways in which the total energy of the system can be divided into different energy levels is referred to as macrostates. The distribution is represented in the following table: Distribution Microstates (W) Macrostates (Ω)2 in 11C21,23 in 11C31,33 in 11C32,310 in total 9.
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