a. The unconditional mean of X = 1.75 cars.
b. Conditional Mean of X Given Y=1 is 1.38 cars.
c. Probability of Rachel Selling 1 Car Given Rebecca Selling 3 is 1.07.
d. The covariance COV (X,Y) is 0.23. COV(X,Y) ≠ 0, X,Y not independent.
e. The correlation coefficient is 0.52, The strength is (0.3-0.5) and the direction is positive correlation.
f. The expectation and variance of Z are 10.25 cars and 6.66 cars².
Step-by-Step Joint Probability Distribution of Cars Sold:
a. Unconditional Mean of X:
1. Calculate marginal probabilities of X:
P(X=1) = 0.57, P(X=2) = 0.29, P(X=3) = 0.14
Calculate expected value of X:
E(X) = Σ(xi × P(xi)) = (1 × 0.57) + (2 × 0.29) + (3 × 0.14) = 1.75 cars
b. Conditional Mean of X Given Y=1:
1. Calculate conditional probability:
P(X=1|Y=1) = 0.40 / 0.52
2.Calculate conditional mean:
E(X|Y=1) = (1 × 0.806) + (2 × 0.194) = 1.38 cars
c. Probability of Rachel Selling 1 Car Given Rebecca Selling 3:
1. Calculate conditional probability:
P(Y=1|X=3) = 0.15 / 0.14 = 1.07 (impossible, probabilities must be between 0 and 1)
d. Covariance and Independence:
1. Calculate joint expected values:
[tex]E(XY) = \sum (x_i \times y_i \times P(x_i,y_i)) = 2.74[/tex]
2. Calculate individual variances:
Var(X) = 0.74, Var(Y) = 0.24
3. Calculate covariance:
COV(X,Y) = E(XY) - E(X)E(Y) = 2.74 - (1.75 × 0.88) = 0.23
Since COV(X,Y) ≠ 0, X and Y are not independent.
e. Correlation Coefficient:
1. Calculate correlation coefficient:
ρ(X,Y) = COV(X,Y) / (σ(X) × σ(Y)) = 0.23 / (√0.74 × √0.24) ≈ 0.52
2. Strength: weak positive correlation (0.3-0.5)
3. Direction: positive correlation (positive coefficient)
f. Expectation and Variance of Z:
1. Use properties of mean:
E(Z) = E(3X+5) = 3E(X) + 5 = 3 × 1.75 + 5 = 10.25 cars
2. Use properties of variance:
Var(Z) = 9Var(X) = 9 × 0.74 = 6.66 cars²
Complete and correct question:
The joint probability distribution of variables X and Y is shown in the table below. Rebecca and Rachel are car salespeople. Let X denote the number of cars that Rebecca will sell in a month, and let Y denote the number of cars Rachel will sell in a month.
x=1 x=2 x=3
Y=1 0.40 0.18 0.15
Y=2 0.12 0.11 0.04
a. Find the unconditional mean of X.
b. Find the conditional mean number of cars that Rebecca will sell in a month given Rachel sells 1 car in a month.
C. What is the probability that Rachel will sell 1 car in a month given that Rebecca sold 3?
d. Find covariance COV (X, Y). Are X and Y independent? Explain why.
e. Find the correlation coefficient between X and Y. Discuss the strength and the direction of its relationship.
f. Chris, another salesperson, sells a car better than Rebecca. Let Z denote the number of cars that Rebecca will sell in a month, where Z = 3X +5. Get the expectation and variance of Z using the properties of the mean and the variance.
What expression is equal to (3x^2yz) (5xy^3z^2)
find the distance between two points. Round answers to the nearest tenth (1,5), (7,9)
To find the distance between two points (1,5) and (7,9), you can use the distance formula sqrt((x2 - x1)^2 + (y2 - y1)^2). Rounding to the nearest tenth, the distance is approximately 7.2.
Explanation:To find the distance between two points, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the given points (1,5) and (7,9), we substitute the values into the formula:
d = sqrt((7 - 1)^2 + (9 - 5)^2) = sqrt(36 + 16) = sqrt(52)
Rounding to the nearest tenth, the distance between the two points is approximately 7.2.
What is the intersection of plane TUYX and plane VUYZ?
I have attached an image with the diagram and answers.
Answer:
A) UY
Step-by-step explanation:
From the given figure, TUYX is one of the side of the rectangular prism and UVYZ is another side of the rectangular prism.
The both sides are intersecting perpendicular in one edge, that is the line segment UY.
You can see it on the figure.
Therefore, the intersecting line is UY.
how many 3/8 are in 6
The number of the fraction 3/8 that we can get in 6, is: 16.
We are asked to find how many of the fraction, 3/8, we will have in 6.
This implies that, what number would we need to multiply with 3/8 to get 6?
To determine this, all we need to do is to divide 6 by the fraction, 3/8.
Thus:[tex]6 \div \frac{3}{8}[/tex]
To solve this, multiply 6 by the reciprocal of 3/8, which is 8/3[tex]6 \times \frac{8}{3} \\\\= \frac{6 \times 8}{3} \\\\= \frac{48}{3} \\\\\mathbf{= 16}[/tex]
Therefore, the number of the fraction 3/8 that we can get in 6 is: 16.
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Twelve people join hands for a circle dance. in how many ways can they do this?
The average polar bear weighs 1,200 pounds. The average grizzly bear weighs 800 pounds. The average black bear weighs 400 pounds. The average polar bear weighs how many times more than the average black bear?
The average polar bear weighs is 800 times more than the average black bear.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have given that the average polar bear weighs 1,200 pounds.
Average grizzly bear weighs is 800 pounds.
The average black bear weighs is 400 pounds.
To find the average polar bear weighs of x times more than the average black bear.
We need to subtract ;
1,200 - 400 = 800
That is 800
Hence, The average polar bear weighs is 800 times more than the average black bear.
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6.5x – 14.5 = 7.75x – 12
....................
the denominator of a fraction is five more than twice the numerator. if both of the numerator and denominator are decreased by two,the simplified is 1/3
Write a for loop that assigns summedvalue with the sum of all odd values from 1 to usernum. assume usernum is always greater than or equal to 1.
Firstly, define a variable `usernum` and let's use 10 as an example. Then, define another variable `summedvalue` and set it as 0 initially. This variable will hold the sum of all odd numbers up to `usernum`.
Next, we start a for loop. This loop will go through each number in the range from 1 to `usernum` inclusive. That's why in the range function we provide `usernum + 1` as the second parameter.
Now, for every number `i` in this range, we check whether it is odd. A number is odd if it gives a remainder of 1 when divided by 2. In other words, we're checking if `i % 2` is not equal to 0 (`i % 2 != 0`).
If the current number `i` is indeed odd, we add it to `summedvalue` (`summedvalue += i`). Then, the loop goes to the next number and the process repeats itself until we've considered all numbers from 1 to `usernum`.
Finally, when the loop ends, the value of `summedvalue` is the sum of all odd numbers from 1 up to (and including) `usernum`. Return this `summedvalue`.
In the case of `usernum = 10`, the odd numbers between 1 to `usernum` are 1, 3, 5, 7, and 9. When you add them together, you get 25. That's why in this case, the result will be 25.
There are approximately 3.5 million deaths per year in a country express this quantity as deaths per minute
Order these numbers from least to greatest.
14325
,
5.753
,
534
,
5.34
Mr. Li records the measures of the lengths of his students’ handprints. The lengths, in centimeters, are shown in the table.
14.0 , 11.5 , 12.1 , 16.2 , 13.5 , 14.3 , 16.8
12.4 , 13.7 , 12.0 , 14.7 , 15.2 , 11.9 , 15.6
13.8 , 14.2 , 12.5 , 15.0 , 16.0 , 13.1 , 11.7
If the class creates a histogram of the data in the table, how many students are in the range 12 cm to 13.9 cm?
1) 3
2) 4
3) 7
4) 8
In the given data set, there are 7 values in the given range.
What is data set?A data set is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question.
Given is a set of data we need to determine how many students are in the range 12 cm to 13.9 cm,
So,
Here we just need to find the number of values between 12cm and 13.9 cm, from the given table, these are:
12.1 cm, 13.5 cm, 12.4 cm, 13.7 cm, 13.8 cm, 12.5 cm, 13.1 cm
So, there are 7 values in the given range, which means that 7 students are in the range of 12cm and 13.9cm.
Then the correct option is 7.
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What type of number is −0.5/-0.5?
The number -0.5 divided by itself equals to 1. In general, any number (except zero) divided by itself will always equal to 1.
Explanation:To find the answer to the given number −0.5/-0.5, you should simply divide the negative number -0.5 by itself (-0.5). Here, a negative number divided by another negative number results in a positive result. Therefore, -0.5/-0.5 equals 1.
In general terms, any non-zero number divided by itself will always equal 1. This is because the division operation is asking 'how many times does this number fit into itself?', and the answer is invariably 'once'.
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One number is four times another number. The sum of their reciprocals is 1/4 . What are the numbers?
Answer:
The numbers are 5 and 20.
Step-by-step explanation:
To find : What are the numbers?
Solution :
Let the one number be 'x'.
The reciprocal is [tex]\frac{1}{x}[/tex]
The another number be 'y'.
The reciprocal is [tex]\frac{1}{y}[/tex]
One number is four times another number.
i.e. [tex]x=4y[/tex] .....(1)
The sum of their reciprocals is [tex]\frac{1}{4}[/tex].
i.e. [tex]\frac{1}{x}+\frac{1}{y}=\frac{1}{4}[/tex] ....(2)
Substitute (1) in (2),
[tex]\frac{1}{4y}+\frac{1}{y}=\frac{1}{4}[/tex]
[tex]\frac{1+4}{4y}=\frac{1}{4}[/tex]
[tex]4y=20[/tex]
[tex]y=5[/tex]
One number is 4y=4(5)=20.
Therefore, the numbers are 5 and 20.
Please help me Estimate 476-269
Simplify -(-7y+12) and explain
The Hampton family has a fish tank holding 10450 ml of water. The water is leaking at a rate of 270ml per minute. Write a function to model this situation
Anna has 10 to the 2nd power quarters. Jazmin has 10 to the second power dimes Who has more money, Anna or Jasmine? How much more? Explain
is a relation a function if it passes through the y-axis twice
A relation that passes through the y-axis twice is not considered a function. A function, by definition, can only output one 'y' value for each unique 'x' value. This relation fails the 'vertical line test' which checks that each 'x' value only connects to a single 'y' value.
Explanation:In mathematical terms, a relation is a set of ordered pairs, where each first element is related to the second element. A function, on the other hand, is a special type of relation where every input (or 'x' value) corresponds to exactly one output (or 'y' value).
Now, if a relation passes through the y-axis twice, it means that there are two 'y' values for a single 'x' value (which in this case, is zero). This violates the definition of a function. Hence, a relation that passes through the y-axis twice is not a function. It is simply a relation because it doesn't pass the 'vertical line test' (a vertical line passing through more than one point on the graph of a relation means that the relation is not a function).
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how do I solve (7-6i)(-8+3i)?
A hospital has three independent fire alarm systems, with reliabilities of 0.95, 0.97, and 0.99. in the event of a fire, what is the probability that a warning would be given?
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability that a warning would be given is 0.97.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
A hospital has three independent fire alarm systems, with reliabilities of 0.95, 0.97, and 0.99.
This means,
The probability that one alarm will give a warning = 0.95
The probability that one alarm will give a warning = 0.97
The probability that one alarm will give a warning = 0.99
Combining each of them we get,
0.95 + 0.97 + 0.99 = 2.91
Divide by 3.
= 2.91 / 3
= 0.97
This means,
The probability that a warning would be given is 0.97.
Thus,
The probability that a warning would be given is 0.97.
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In Your own words, explain the place-value relationship when the same two digits are next to each other in a multi-digit number
PLEASE HELP! DUE in 4 hours!
calculate the slopes
3-0 / -2 - 2 = 3/-4 = -3/4
3 - -4 / -2 - -1 = 7/-1 = -7/1
0 - -4 / 2 - -1 = 4/3
-3/4 and 4/3 are negative reciprocals so this is a right triangle
Answer is A
BRAINLEIEST!!! To make 112 dozen muffins, a recipe uses 312 cups of flour. How many cups of flour are needed for every dozen muffins made? Enter your answer in the box as a mixed number in simplest form.
To find out the number of cups of flour needed for each dozen muffins, you need to divide the total quantity of flour used by the total number of dozens. Therefore, about 2 11/14 cups of flour are required for each dozen muffins.
Explanation:To find out how many cups of flour are needed for every dozen muffins made, we need to divide the total amount of flour used by the total number of dozens of muffins. The recipe used 312 cups of flour to make 112 dozens of muffins. So, we divide 312 by 112:
312 ÷ 112 = 2.78571428571429
To convert this to a mixed number in simplest form, you can say that approximately 2 11/14 cups of flour are needed for every dozen muffins made.
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For every dozen muffins made, the recipe requires [tex]\(2 \frac{11}{14}\)[/tex] cups of flour. This is determined by simplifying the ratio of 312 cups of flour needed for 112 dozen muffins to its simplest form.
To find the cups of flour needed for every dozen muffins, we can set up a ratio between the cups of flour and the number of dozens of muffins.
[tex]\[ \text{Cups of Flour} : \text{Dozens of Muffins} \][/tex]
Given that 112 dozen muffins require 312 cups of flour, the ratio becomes:
[tex]\[ \frac{312 \text{ cups}}{112 \text{ dozens}} \][/tex]
Now, simplify this ratio by dividing both the numerator and the denominator by the greatest common factor, which is 8.
[tex]\[ \frac{39 \text{ cups}}{14 \text{ dozens}} \][/tex]
Now, express this ratio as a mixed number in simplest form. Since 39 and 14 share no common factors other than 1, the mixed number is [tex]\(2 \frac{11}{14}\).[/tex]
Therefore, the answer is [tex]\(2 \frac{11}{14}\)[/tex] cups of flour for every dozen muffins made.
99 POINTS AND BRAINLIEST
ECONOMICS
Economics affects nearly everything we do in some way. Someone else has produced most items we consume, or use, in our daily lives, from food to clothes to music to gas for our cars. Chances are, when we purchase these daily items, we don't question the price with the producer. But in the United States, the interactions between the consumers and producers determine quite a lot in terms of business and economics.
Think about the items and services that you and your family buy or consume. What causes you to pay the prices that you do for these goods and services? What determines the price that's on the price tag? What goes into determining, or setting, that price? Consider all the possible elements that could influence the prices you pay.
There are currently 3 students signed up for a trip. The van can transport only 7 students.
Which graph shows all the possible values for the extra number of students that need to sign up so that more than one van is needed to transport them?
Number line with closed circle on 4 and shading to the right.
Number line with closed circle on 4 and shading to the left.
Number line with open circle on 4 and shading to the right.
Number line with open circle on 4 and shading to the left.
Answer:
Answer:
Number line with an open circle on 4 and shading to the right.
Explanation:
Call x the number of students that need to sign up so that more than one van is needed to transport them =>
x + 3 > 7
=> x > 7 - 3
=> x > 4
That is the number greater than 4, without including the number 4.
That is the number line is the set of numbers to the right of 4, and the open circle is used to indicate that the number 4 is not included (a closed circle would indicate that the number 4 is included, which is not the case).
Step-by-step explanation:
which sets of numbers represent geometric sequences check all that apply
Will the first digit of the quotient of 2589 divided by 4 be in the hundreds or thousands place? Explain how you can decide without finding the quotient.
Actually we can directly check if the quotient has equal or one less amount of places than the given number. This can be checked by looking at the number on the biggest place of the dividend, if it is less than the divisor, the answer will have one less digits place. So in this case since the divisor is 4 and the greatest place of the dividend is thousands and the number is 2, so the quotient will be in the hundreds place.
Hundreds place
Answer:
Step-by-step explanation:Actually we can directly check if the quotient has equal or one less amount of places than the given number. This can be checked by looking at the number on the biggest place of the dividend, if it is less than the divisor, the answer will have one less digits place. So in this case since the divisor is 4 and the greatest place of the dividend is thousands and the number is 2, so the quotient will be in the hundreds place.
If f(x) is discontinuous, determine the reason.
f(x) = {x^2 -4, x<1
{ x+4, x>1
f(x) is continuous for all real numbers
The limit as x approaches 1 does not exist
f(1) does not equal the limit as x approaches 1
f(1) is not defined
Answer:
F(1) is not defined
Step-by-step explanation: