show that the properties of a probability distribution for a discrete random variable are satisfied.
Answers
The properties of a probability distribution for a discrete random variable ensure that the probabilities assigned to each possible value of the variable are consistent with the axioms of probability and allow for meaningful inference and prediction.
The properties of a probability distribution for a discrete random variable are.
The probability of each possible value of the random variable must be non-negative.
The sum of the probabilities of all possible values must equal 1.
The probability of any event A is the sum of the probabilities of the values in the sample space that correspond to A.
These properties are satisfied because the probabilities of each possible value of a discrete random variable are defined in such a way that they are non-negative and sum to 1. Additionally, any event A can be expressed as a collection of possible values of the random variable, and the probability of A is then computed as the sum of the probabilities of those values.
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Related Questions
In the following expression, the 2 distributes to the 3 and to the 4:
(2) (3+4) = (2) (3) + (2) (4)
true or false
Answers
Answer:
True
Step-by-step explanation:
(2) (3+4) = (2) (3) + (2) (4)
(2) (3+4)=2(7)=14
(2) (3) + (2) (4)=6+8=14
14=14 √
Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x)= 1= ² + 4
X-4
Answers
To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:
\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)
To simplify this expression, we can expand the square:
\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)
Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)
Next, let's find g(f(x)). We substitute f(x) into the function g(x):
\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)
Hence, g(f(x)) simplifies to 1/x^2.
In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.
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Jason is buying wings and hot dogs for a party. One package of wings costs $7. Hot dogs cost $5 per package. He must spend no more than $40. Write and inequality to represent the cost of Jason’s food for the party. Jason knows that he will be buying at least 5 packages of hot dogs. Write an inequality to represent this situation. Graph both inequalities. Give two options for Jason when buying wings and hot dogs.
Answers
An inequality to represent the cost of Jason’s food for the party is
An inequality to represent this situation "Jason knows that he will be buying at least 5 packages of hot dogs" is
The two options for buying wings and hot dogs include the following:
One (1) package of wings and five (5) packages of hot dogs.Two (2) packages of wings and five (5) packages of hot dogs.How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of wings respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of packages of wings.Let the variable y represent the number of packages of hot dogs.Since one package of wings costs $7 and Hot dogs cost $5 per package, and he must spend no more than $40, a linear inequality which represents this situation is given by;
7x + 5y ≤ 40
Additionally, since Jason knew he would buy at least 5 packages of hot dogs, a linear inequality which represents this situation is given by;
y ≥ 5
Next, we would use an online graphing calculator to plot the above system of linear inequalities as shown in the graph attached below.
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Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$38,737, $50,463]. The population standard deviation used for the analysis is known to be $14,300.
a. What is the point estimate of the mean salary for all college graduates in this town?
Point estimate
b. Determine the sample size used for the analysis.
Sample size
Answers
Answer:
a. The point estimate was of $44,600.
b. The sample size was of 16.
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the difference between the two bounds, divided by 2.
a. What is the point estimate of the mean salary for all college graduates in this town?
Mean of the bounds, so:
(38737+50463)/2 = 44600.
The point estimate was of $44,600.
b. Determine the sample size used for the analysis.
First we need to find the margin of error, so:
\(M = \frac{50463-38737}{2} = 5863\)
Relating the margin of error with the sample size:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.9}{2} = 0.05\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.64.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
For this problem, we have that \(\sigma = 14300, M = 5863\). So
\(M = z\frac{\sigma}{\sqrt{n}}\)
\(5863 = 1.645\frac{14300}{\sqrt{n}}\)
\(5863\sqrt{n} = 1.645*14300\)
\(\sqrt{n} = \frac{1.645*14300}{5863}\)
\((\sqrt{n})^2 = (\frac{1.645*14300}{5863})^2\)
\(n = 16\)
The sample size was of 16.
Which function has an amplitude that is twice the size and a period that is three times the size of the function
y = 3 cos (-1) + 2?
OB.
O D.
=sin(+3)-1
y = 6 cos (3-1) + 3
>
y =
y = 6 sin(-3) +1
- cos (+1)-3
y =
Answers
As per the given data, y = 6 cos (3x - 1) + 3 is the function that has an amplitude that is twice the size and a period that is three times the size of the function.
The given function is y = 3 cos (-1x) + 2.
To find a function with an amplitude twice the size and a period three times the size, we can modify the amplitude and period in the original function.
Amplitude:
The amplitude of the original function is 3. To double the amplitude, we multiply it by 2: 3 * 2 = 6.
Period:
The period of the original function is determined by the coefficient of x, which is -1. To make the period three times larger, we divide the coefficient by 3: -1 / 3 = -1/3.
Putting it all together, we have:
y = 6 cos (3x - 1) + 3
Thus, this function has an amplitude of 6 (twice the size of the original function) and a period of 3 times the size of the original function.
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Determine whether each quadrilateral is a parallelogram. Justify your answers.
And
Explain why the quadrilateral with the given vertices is a parallelogram. Use the indicated theorem.
Answers
The given quadrilaterals, 1 and 2, are parallelograms because the pair of opposite sides are parallel and the other pairs are congruent.
3. According to Theorem 7.9, quadrilateral ABCD is a parallelogram.
4. According to Theorem 7.12, quadrilateral PQRS is a parallelogram.
What is the proof for the parallelograms?3. Quadrilateral ABCD with vertices A(0,0), B(7,1), C(5,6), D(-2,5), and Theorem 7.9:
Theorem 7.9 states that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Using the distance formula, we can calculate the lengths of the sides of quadrilateral ABCD:
AB = √((7 - 0)² + (1 - 0)²) = √50
BC = √((5 - 7)² + (6 - 1)²) = √29
CD = √((-2 - 5)² + (5 - 6)²) =√50
DA = √((0 - (-2))² + (0 - 5)²) = √29
We can see that AB = CD and BC = DA, indicating that the opposite sides are congruent.
Quadrilateral PQRS with vertices P(-2,0), Q(3,1), R(4,4), S(-1,3), and Theorem 7.12:
Theorem 7.12 states that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
Using the slope formula, we can calculate the slopes of the sides of quadrilateral PQRS:
Slope of PQ = (1 - 0) / (3 - (-2)) = 1/5
Slope of RS = (4 - 3) / (4 - (-1)) = 1/5
Slope of QR = (4 - 1) / (4 - 3) = 3
Slope of SP = (3 - 0) / (-1 - (-2)) = 3
The lengths of opposite sides can be calculated using the distance formula:
PQ = √((3 - (-2))² + (1 - 0)²) = √(25 + 1) = √26
RS = √((4 - 4)² + (4 - 1)²) = √(9) = 3
QR = √((4 - 3)² + (4 - 1)²) = √(1 + 9) = √10
SP = √((-1 - (-2))² + (3 - 0)²) = √(1 + 9) = √10
We can see that PQ = RS and QR = SP, indicate that the opposite sides are parallel and congruent.
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Is the relation shown in the table below a function? (type in yes or no)
Answers
Answer:
Yes
Step-by-step explanation:
To know if a table is a function or not, we have to see if 1 input only has 1 output.
Looking at the table each input only has 1 output, so it is a function.
Can anyone plz answer the question?? It's in the photo. Thanks!
Answers
Answer:
11 because 10x2=20 and the 220 divided by 20 =11
Step-by-step explanation:
Let the speed of the train going from Boston to New York = X
Let the distance from Boston to when the trains meet = Y
The distance to New York when they meet would be 220 - Y
The Boston to New York train would be: Y = (2X-10)*2
New York to Boston train would be : 220 -Y = 2X
Using substitution:
220-(2X-10)*2 = 2X
Simplify the left side:
220 - 4X+20 = 2X
Add 4x to both sides and combine like terms:
240 = 6X
Divide both sides by 6:
x = 40
Now find distance from Boston by replacing x with 40"
Y = (2(40)-10)*2
Y = 160 -20
Y = 140 miles
\(2i+3x=4-ix\)
Show work.
No wrong answers or you will be reported. I will mark Brainliest! Thank you!
Answers
Answer:
Step-by-step explanation:
I am assuming i is the imaginary number:
Factor:
(3 + i)x - (4-2i) = 0.
In order for this to equal 0, x must be equal to 1-i.
I don't want to be reported to so take my word for it.
Also I plugged it into wolfram alpha so if it is wrong, blame the most powerful math equation solver available on the internet.
Using BTS he properties, find the unit's digit of the cube of each of the following numbers
![[tex]2i+3x=4-ix[/tex]Show work.No wrong answers or you will be reported. I will mark Brainliest! Thank](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/ePVOgZfDCYvFelov6pJo7QFVwEbEVQYI.jpeg)
A farmer harvested 21 1/4
fewer bushels of sweet corn this year than the previous year. If the farmer's sweet corn crop is planted across acres, what is the average loss per acre?
Answers
Answer:
85/12 fewer bushels per acre
Step-by-step explanation:
Hi, to answer this question we have to write an expression with the information given and solve it:
We simply have to divide the total loss (21 1/4) by the number of acres (3):
Mathematically speaking:
21 1/4 ÷3 = (21(4) +1)/4 ÷3 = 85/4 ÷ 3= 85/12 fewer bushels per acre
Feel free to ask for more if needed or if you did not understand something
Another day, another math problem 3
Answers
Answer:
\(2\sqrt{x+1}-3\\domain:[-1, \infty)\)
Step-by-step explanation:
\(g(h(x)) = 2(\sqrt{x+1})-3\\g(h(x)) = 2\sqrt{x+1} - 3\\\)
the function is only defined when (x+1) >= 0 (since square root) so the domain is when x >= -1
I need help with reading
Answers
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
A coordinate plane with points at negative 4 comma 4, negative 2 comma 0, 0 comma negative 3, 3 comma 1, and 5 comma negative 2.
What is the domain of the relation?
{−4, −3, −2, 0, 1, 3, 4, 5}
{−4, −2, 0, 3, 5}
{−3, −2, 0, 1, 4}
{0, 3, 4, 5}
Answers
The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.
How to determine domain relation?The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.
Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.
Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.
Hence, the correct option is {−4, −2, 0, 3, 5}.
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⦁ A $10,000 certificate of deposit earns simple interest of 8 percent per year. Calculate the total earned money over the 5 year period?
Answers
Answer:
The total earned money over the 5 year period=$14,000
Step-by-step explanation:
We are given that
Principle amount, P=$10000
Rate of interest, r=8%
Time, t=5 years
We have to find the total earned money over the 5 year period.
We know that
Simple interest=\(\frac{P\times r\times t}{100}\)
Using the formula
S.I=\(\frac{10000\times 8\times 5}{100}{/tex]
S.I=$4000
Now,
Amount=P+S.I
Amount=10000+4000
Amount=$14000
Hence, the total earned money over the 5 year period=$14000
15)
136⁰
2
S
?
R
Find the measure of the arc or angle indicated
Answers
Answer:
224
Step-by-step explanation:
360.-136.
What is the answer I’m dumb
Answers
Answer:
9units
Step-by-step explanation:
NEED HELP ASAPPPPPPPPP Luis deposits $1000 in savings account A earning 8%
simple interest, and $800 in savings account B earning 5%
compound interest. Which account has more after 10 years,
and what is the difference?
A: Account A will have 496.88 more
B: Account A will have 400 more
C: Account B will have 503.12 more
D: Account B will have $200 less
Answers
9514 1404 393
Answer:
A: A has $496.88 more
Step-by-step explanation:
A graphing calculator works this problem nicely.
The balance in the simple interest account after t years is ...
A = 1000(1 + 0.08t)
The balance in the compound interest account after t years is ...
B = 800(1 +0.05)^t
The larger starting balance and the higher interest rate keep the A account balance higher than the B account balance for more than 29 years. Then, the effect of interest compounding takes over. Until then, account A has more money in it. The calculator shows Account A has $496.88 more after 10 years.
Select the two binomials that are factors of this trinomial.
x2 + 6x + 8
O A. X+4
O B. x+8
O C. X-4
O D. x+ 2
SUBMIT
Answers
Hey there! :)
Answer:
A. x + 4
D. x + 2
Step-by-step explanation:
Starting with:
x² + 6x + 8
Find numbers that add up to 6 and multiply to 8. We get:
2, 4.
Put these into the factors:
(x + 2)(x + 4)
Therefore, the correct answers are:
A. x + 4
D. x + 2
Help math math math
Answers
Answer:
160
Step-by-step explanation:
Answer:
160
Step-by-step explanation:
multiply (d + 4) (d - 4)
Answers
Answer:
\(d^{2}\) - 16.
Step-by-step explanation:
To solve for the product of (d + 4) and (d - 4), we can use the FOIL method.
What does 'FOIL' Stand for?First Outer Inner LastThis means we multiply the first terms, then the outer, then the inner, and finally the last terms, then we add all the products together.
So, (d + 4) (d - 4) can be expanded like this:
First: d × d = \(d^{2}\) Outer: d × -4 = -4d Inner: 4 × d = 4d Last: 4 × -4 = -16Adding all of them together, we get: \(d^{2}\) - 4d + 4d - 16, which simplifies to \(d^{2}\) - 16.
Therefore, (d + 4)(d - 4) = \(d^{2}\) - 16.
pls help a gurlll out
Answers
Answer:
x = 15°
Step-by-step explanation:
165 and x are on a straight line which means they are supplementary.
Set up the equation and solve for x:
165 + x = 180
x = 180 - 165
x = 15
The House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
Answers
The percent error of the house of the pizza would be 2.
How to calculate the percent error?Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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I NEEEEED HELP!!!!!!
Answers
Tasha used the pattern in the table to find the value of 4 Superscript negative 4.
Powers of 4
Value
4 squared
16
4 Superscript 1
4
4 Superscript 0
1
4 Superscript negative 1
One-fourth
4 Superscript negative 2
StartFraction 1 Over 16 EndFraction
She used these steps.
Step 1 Find a pattern in the table.
The pattern is to divide the previous value by 4 when the exponent decreases by 1.
Step 2 Find the value of 4 Superscript negative 3.
4 Superscript negative 3 = StartFraction 1 Over 16 EndFraction divided by 4 = StartFraction 1 Over 16 EndFraction times one-fourth = StartFraction 1 Over 64 EndFraction
Step 3 Find the value of 4 Superscript negative 4.
4 Superscript negative 4 = StartFraction 1 Over 64 EndFraction divided by 4 = StartFraction 1 Over 64 EndFraction times one-fourth = StartFraction 1 Over 256 EndFraction
Step 4 Rewrite the value for 4 Superscript negative 4.
StartFraction 1 Over 256 EndFraction = negative StartFraction 1 Over 4 Superscript negative 4 EndFraction
Answers
The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.
In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.
To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.
Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.
Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.
Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction
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Consider parallelogram QRST below. Use the information given in the figure to find m
Answers
The missing values are
<UTQ = 41 degree
x= 1
<UQT = 47 degree
We have a parallelogram QRST.
We know that the opposite sides of the parallelogram is equal and parallel then
QR || ST
QT || SR
Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)
<UTQ = 41
Similarly, <UQT = <SRQ = 47
Now, RU = UT
2x + 1= 3
2x = 2
x= 1
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Which is the slope of the line that passes through the points (2,10) and (5,8)?
Answers
Answer:
Slope = (Y2 - Y1) / (X2 -X1)
Slope = (8 -10) / (5 -2)
Slope = -2 / 3
————————
What is the area of a rectangle with a length of Four and two-fourths meters and a width of Seven and five-sixths meters?
Answers
Answer:
the area of the rectangle is 35.25 square meters.
Step-by-step explanation:
To find the area of a rectangle, we multiply the length by the width.
First, we need to convert the mixed numbers to improper fractions to make the multiplication easier:
4 and 2/4 = 4 + 2/4 = 16/4 + 2/4 = 18/4
7 and 5/6 = 7 + 5/6 = 42/6 + 5/6 = 47/6
Now we can multiply the length and width:
Area = (18/4) * (47/6)
Area = (9/2) * (47/6) (canceling the common factor of 2 between 18/4 and 6 in 47/6)
Area = (9 * 47) / (2 * 6)
Area = 423/12
Area = 35.25
Therefore, the area of the rectangle is 35.25 square meters.
Elizabeth runs a farm stand that sells apples and raspberries. Each pound of apples sells for $2.25 and each pound of raspberries sells for $1.50. Elizabeth sold 32 more pounds of raspberries than pounds of apples and made $108 altogether. Graphically solve a system of equations in order to determine the number of pounds of apples sold, x, and the number of pounds of raspberries sold,y.
Answers
Answer:
Im confused?
Step-by-step explanation:
The number of pounds of apples is 16 and the number of pounds of raspberries is 48.
Given that, the cost of a pound of apples = $2.25 and the cost of a pound of raspberries = $1.50.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of pounds of apples be x, then the number of pounds of raspberries(y) be y=x+32.
Now, the total cost of apples = The number of pounds of apples × The cost of a pound of apples
=x × 2.25
= 2.25x
The total cost of raspberries = The number of pounds of raspberries × The cost of a pound of raspberries
=(x+32) × 1.50
=1.50x+48
So, the total cost = The total cost of apples + The total cost of raspberries
⇒108 = 2.25x+1.50x+48
⇒3.75x=60
⇒x=16
So, y=x+32=48
The graph is plotted below for y=x+32=48
Therefore, the number of pounds of apples is 16 and the number of pounds of raspberries is 48.
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How many 4-digit numbers can you write if you are not allowed to use any other digits except one and two?
Answers
Step-by-step explanation:
ans = 1212 ,2121,2222,1111,2211,1122
Final Exam Review Quiz 1
Which equation best represents a line that has a slope of and passes through the point (3, 5)?
Answers
Answer:
y = \(\frac{2}{3}\) x + 3
Step-by-step explanation:
y = mx + b is the slope intercept form of a line. You need to know the m (slope) and the b (y intercept) to write the equation.
We are given the m (slope) to be \(\frac{2}{3}\). We will use 3 from the point given for our x and the 5 from the point given for our y. We will use these to solve for the b (y-intercept)
y = mx + b
5 = \(\frac{2}{3}\) (3) + b
5 = \(\frac{2}{3}\) · \(\frac{3}{1}\) + b
5 = \(\frac{6}{3}\) + b
5 = 2 + b Subtract 2 from both sides
3 = b
We can now write the equation. Our slope (m) is \(\frac{2}{3}\) and our y-intercept (b) is 3.
y = \(\frac{2}{3}\) x + 3
Helping in the name of Jesus.