Mathematics College

The probability distribution function for the discrete random variable where x is equal to the number of red lights drivers typically run in a year is as follows. x 0 1 2 3 p(x) 0.76 0.15 0.05 (a) Fill in the missing probability. x 0 1 2 3 p(x) 0.76 0.15 0.05 (b) What is the mean of this discrete random variable

Answers

Answer 1

Using probability concepts, it is found that:

a) The missing value is 0.04.

b) The mean is of 0.37.

The distribution is given by:

$P(X = 0) = 0.76$

$P(X = 1) = 0.15$

$P(X = 2) = 0.05$

$P(X = 3) = x$

Item a:

The sum of all the probabilities has to be 1, that is:

$\sum_{i = 0}^{3} P(X = i) = 1$

Thus:

$0.76 + 0.15 + 0.05 + x = 1$

$0.96 + x = 1$

$x = 0.04$

The missing value is 0.04.

Item b:

The mean is given by the sum of each outcome multiplied by it's probability, thus:

$E(X) = 0(0.76) + 1(0.15) + 2(0.05) + 3(0.04) = 0.37$

The mean is of 0.37.

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Related Questions

Which point would be a solution to the system of linear inequalities shown below?

Answers

The coordinates in the solution to the systems of inequalities is (12, 1)

Solving the systems of inequalities

From the question, we have the following parameters that can be used in our computation:

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

Answers

We are given a data set, and we are told that this can be represented as a linear equation. Let's remember the general form for the equation of a line:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept. To find the slope we use the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

where:

$\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}$

Are points through which the line passes. These two points can be found in the given data set. Let's take the following points:

$\begin{gathered} (x_1,y_1)=(2,105) \\ (x_2,y_2)=(4,195) \end{gathered}$

We can find the slope using the previous formula, like this:

$m=\frac{195-105}{4-2}=\frac{90}{2}=45$

This is the daily rate for the pricing plan. Now we can find the y-intercept "b" using one of the points given, like this:

$y=45x+b$

replacing the point (2,105), we get:

$105=45(2)+b$

Solving the operation:

$105=90+b$

subtracting 90 on both sides:

$\begin{gathered} 105-90=90-90+b \\ 15=b \end{gathered}$

Replacing the value of "b" in the equation:

$y=45x+15$

This is the equation of the line that models the data set given.

Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection.
y=3x−3 y=7−2x

Answers

The coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)

Graphing linear equations

From the question, we are to graph the given equations.

The graph of the equations is attached below.

In the graph, we can observe that the coordinates of the point of intersection of the is (2, 3)

Hence, the coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)

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Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection.y=3x3

a2(5x – 3) = 24
b) 5(2x + 1) = 50

Answers

Use “Photo math” in the app store. It’ll help you with all those type of problems:)

Answer:

A= x=3

B= x=9/2

Step-by-step explanation:

PLEASE HELP Only A

PLEASE

Answers

- 9/20 but decimal form is -0.45

Answer:

= -9/15 ÷ 4/3

= -9/15×3/5

= -9/15×3/4

= 36/5

=7⅕

Hold on hold on hold on hold on hold on oh my God if seven is an element in the domain of F parentheses X parentheses equals 6X -19 over five what is the corresponding element in the range

Answers

The corresponding element in the range of the function F when 7 is in the domain is 4.6.

The expression for the given function F following as:

F(x) = 6(x) - 19 / 5

The corresponding element in the range of the function F is the output of the function when 7 is input into the function.

To find this output, we can substitute 7 for X in the expression for the function F:

F(7) = 6(7) - 19 / 5

F(7) = 42 - 19 / 5

F(7) = 23 / 5

F(7) = 4.6

Thus, when 7 is in the domain, the equivalent element in the range of the function F is 4.6.

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What is the measure of M?

Answers

Answer:

Is just a letter identifying the angle.

Since,Angles of a triangle sum up to 180 ,u add both the given numbers and subtract it from 180

assume you are realtor in bradenton, florida. you have recently obtained a listing of selling prices of the homes that have sold in that area in the last 6 months.you wish to organize those data so you will be able to provide potential buyers with useful information statistic question

Answers

To know more aboutWhat is the average selling price of homes in Bradenton, Florida over the last 6 months?

What is Average Selling Price?

The average selling price is a statistical measure that represents the total sum of all selling prices divided by the number of items being sold. It provides a useful indication of the typical or central value of a dataset.

According to the given information:

Fom the given information we can frame a question -

To know more aboutWhat is the average selling price of homes in Bradenton, Florida over the last 6 months?

To calculate the average selling price of homes in Bradenton, Florida over the last 6 months, you would need to:

1) Gather the selling prices of all the homes that have sold in the area over the last 6 months.

2) Add up all of the selling prices to get a total sum.

3) Divide the total sum by the number of homes that have sold to get the average selling price.

For example, if there were 100 homes sold in the last 6 months, and the total sum of their selling prices was $25,000,000, then the average selling price would be:

Average Selling Price = Total Sum / Number of Homes Sold

Average Selling Price = $25,000,000 / 100

Average Selling Price = $250,000

Therefore, the average selling price of homes in Bradenton, Florida over the last 6 months is $250,000.

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For the given data we've Number of class = 5, minimal value = 67900, Maximum value = 321550, Class range = 50730. The histogram, frequency polygon, and accretive frequency polygon are as shown.

What's histogram?

In a graphic representation of data called a histogram, a set of nonstop numerical data is distributed in a given way. Each cube's area is related to the frequency of data values being within a given interval or caddy. It consists of a sequence of blocks or bars. The y- axis displays the frequency or count of values that fall inside each interval, while thex-axis displays the range of values that are divided up into intervals or lockers. Large data sets can be visually summarised using histograms, which can also be used to spot patterns and trends as well as outliers or unanticipated figures.

For the given data we have

Number of class = 5

minimal value = 67900

Maximum value = 321550

Class range = Range/ Number of class

= 321550- 67900/ 5

= 50730

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The complete question is:

assume you are realtor in bradenton, florida. you have recently obtained a listing of selling prices

please help need this for my homework!!!

Answers

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

A total of $5550 is plit into
Awo investments. Part of the money.
is invested at 4%, and the reminder
is invested at 5"%.. If the total annual
interest from the two investments is
$259, how much is invested at each rate?

Answers

a = amount invested at 4%

how much is 4% of "a"? (4/100) * "a", namely 0.04a.

b = amount invested at 5%

how much is 5% of "b"? (5/100) * "b", namely 0.05b.

we know the total amount invested is 5550, so whatever "a" and "b" might be, we know that a + b = 5550.

we also know that the yielded amount in interest is 259, so if we simply add their interest, that'd be 0.04a + 0.05b = 259.

$a+b=5550\implies b=5550-a \\\\[-0.35em] ~\dotfill\\\\ 0.04a+0.05b=259\implies \stackrel{\textit{substituting from above}}{0.04a+0.05(5550-a)~~ = ~~259} \\\\\\ 0.04a+277.5-0.05a=259\implies 277.5-0.01a=259\implies -0.01a=-18.5 \\\\\\ a=\cfrac{-18.5}{-0.01}\implies \boxed{a=1850}\hspace{9em}\stackrel{ 5550~~ - ~~1850 }{\boxed{b=3700}}$

Elias woke up in the middle of the night and, due to a power cut, it was very dark in his apartment. Elias* pencils were in one large box and he remembered that there were 11 blue pencils, 14 black pencils and 8 grey pencils in the box.
As Elias didn't see the colour of the pencils, he picked as many pencils from the box so that he would have at least two black poncils.
What was the minimum amount of pencils Ellas needed to pick to ensure he would get at least two black pencils?

Answers

Answer:

Step-by-step explanation:

Given 11 blue, 14 black, and 8 grey pencils, you want the minimum number of pencils that will guarantee you have 2 black pencils.

Not black

There are 11 +8 = 19 pencils that are not black. If Elias happened to draw all of those first, he would need to draw 2 more to guarantee he has 2 black pencils.

Elias needs to pick 19+2 = 21 pencils to ensure at least 2 are black.

Answer:

Why did Elias wake up in the middle of the night in the first place and go to find colour pencils?

Anyways the answer would be 21 colour pencils.

Step-by-step explanation:

Elias would need to pick up 21 colour pencils to ensure he would get at least 2 black pencils because if you added up the number or blue pencils and grey pencils you would get 19. Then you would add 2 for the minimum amount black colour pencils (at least to ensure you got at least 2).

c. If Biff is rational, and has no intention of winning the hot dog eating contest, what is the optimal number of hot dogs he will eat

Answers

Answer:

8 units of Hot dog

Step-by-step explanation:

Total utility refers to the utility in which the is satisfaction after consuming the multiple units from a good or a service

As we can see from the attached figure that at the number of 8 hot dogs the total utility is maximum i.e 55

Therefore in the given case, the optimal number of hot dogs he will eat is 8 as at this point the total utility is more as compared to the other utilities

c. If Biff is rational, and has no intention of winning the hot dog eating contest, what is the optimal

I need the simplified expression for this please

Answers

here you go 15x-10/3

Bailey wants to find 0.4 × 0.9. Part A Which of the following grids models the problem? A. Hundred grid. Four grid blocks shaded horizontally and nine grid blocks shaded vertically. The intersection is one grid block. B. Hundred grid. Four columns shaded vertically and nine rows shaded horizontally. The intersection is 36 grid blocks. C. Hundred grid. Six columns shaded vertically and one row shaded horizontally. The intersection is 6 grid blocks. D. Hundred grid. Eight columns shaded vertically and three rows shaded horizontally. The intersection is 24 grid blocks.

Answers

Answer:

Step-by-step explanation:

It seems like the answer would be B since 0.4 x 0.9 = 0.36 and the intersection for answer choice B is 36 grid blocks.

The correct equation of the given grids models the problem is,

⇒ Hundred grid. Four columns shaded vertically and nine rows shaded horizontally. The intersection is 36 grid blocks.

Option B is true.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Bailey wants to find the value of 0.4 × 0.9.

Now,

After multiplication, we get;

⇒ 0.4 × 0.9

⇒ 0.36

Hence, By all the options;

The correct equation of the given grids models the problem is,

⇒ Hundred grid. Four columns shaded vertically and nine rows shaded horizontally. The intersection is 36 grid blocks.

Option B is true.

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x+y-22=-16 find y if x is -7

Answers

Answer:

Step-by-step explanation:

x+y-22=-16

But x =-7

then

-7+y-22=-16

y-29=-16

y=-16+29

y=13

Solve the equation 8b+7 (2b + 4) = 94
b= ltype your answer...

Answers

Answer:

b = 3

Step-by-step explanation:

Q9.
Solve the simultaneous equations
7x – 2y = 34
3x + 5y = -3
Show clear algebraic working.

Answers

After solving simultaneously we found the values for x and y are

2.76 and 5.65 respectively

Simultaneous Equations

We have the following two expressions

7x – 2y = 34 --------1

3x + 5y = -3 ---------2

Multiply 1 by eqn 5 and eqn 2 by 2

35x - 10y = 170-------3

6x + 10y = -6 ----------4

subtracting 4 from 3 we have

29 x= 164

divide both sides by 29

x = 164/29

x = 5.65

Put x = 5.65 in eqn 1 to find y

7*5.65 – 2y = 34

39.55 - 2y = 34

39.55-34 = 2y

5.55 = 2y

divide both sides by 2

x = 5.55/2

x = 2.76

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solve the system of equations using the elimation method. show your work. make sure to express your solution as an ordered pair

Answers

Given the system of equations:

$\begin{gathered} 6x+4y=7\rightarrow(1) \\ 6x+2y=5\rightarrow(2) \end{gathered}$

Subtract equation (2) from equation (1):

So,

$\begin{gathered} (6x+4y)-(6x+2y)=7-5 \\ 4y-2y=2 \\ 2y=2 \\ y=\frac{2}{2} \\ y=1 \end{gathered}$

substitute with y into equation 1 to find x:

$\begin{gathered} 6x+4=7 \\ 6x=7-4 \\ 6x=3 \\ \\ x=\frac{3}{6} \\ \\ x=\frac{1}{2} \end{gathered}$

So, the answer will be:

x = 1/2 y = 1

( x, y ) = ( 1/2 , 1 )

See the following picture:

Given 8x^2 – 3 + 4, what is (are) the constant(s)?

Answers

Answer:

-3 and 4

Step-by-step explanation:

$-3$ and $4$ are the constants

since they aren't multiplied a variable

-3 and 4 would be your answer

can someone help me please

Answers

Answer:

y=x-5

Step-by-step explanation:

try that my good sir

what is the area of the shaded area. Round to the nearest whole unit.
please help!!!

Answers

Answer:

69.53 or 70(depending on rounding)

Step-by-step explanation:

The squares area is (9*2)^2 which is 324.

The circles area is 9^2 pi or 254.47 approx.

Subtract and you get 69.53 or 70

explain how to write function rule from the table below. Then write a function fule. x=0,2,4,6. y=2,1,0,-1

Answers

Both representations are equivalent and describe the same function.the function rule for this table is: f(x) = -1/2 x 2

What do you mean by Slope in Graph ?

The slope or gradient of a line is a number that describes both the direction and the steepness of the line. A slope of a line is the change in y coordinate with respect to the change in x coordinate.

To write a function rule for a given array, we need to determine how the values in the output column (y) relate to the values in the input column (x).

Looking at the given data, we notice that the output values decrease by 1 every time the input value increases by 2. This suggests that the function is linear and that we can use the slope-intercept form of a linear equation to represent it. .

The slope-intercept form of a linear equation is y = mx b, where m is the slope and b is the y-intercept. In this case, the slope m is -1/2 because the output values decrease by 1 every time the input values increase by 2. The y-intercept b is 2 because the output value is 2 when the input value is 0.

Therefore, the function rule for this table is:

f(x) = -1/2 x 2

where x is the input value and f(x) is the output value.

Alternatively, we can also represent the function in table entries, for example:

f(0) = 2

f(2) = 1

f(4) = 0

f(6) = -1

Both representations are equivalent and describe the same function.

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If JK = 31, KI = 40, and NL = 12, find the length of MN. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale. 95⁰ 34° K N 34° M 950 51° L

please help i need this soon!!

Answers

The length of the MN is 9.4.

What is a triangle?

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Triangle NML.

NL = 12

Sin 51 = NM / NL

0.78 = NM / NL

MN = 0.78 x NL

MN = 0.78 x 12

MN = 9.36

Rounding to the nearest tenth.

MN = 9.4

Thus,

MN is equal to 9.4.

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Decide which of the two given prices is the better deal and explain why. You can fill a 12-gallon tank of gas for $39.43 or buy gas for $3.20/gallon.

Answers

Answer:

$3.20/gallon

Step-by-step explanation:

to fill up your tank at $3.20/gallon only costs $38.40

Do you agree with each of these statements? Explain your reasoning agree or disagree. A parallelogram has six sides, Opposite sides of a parallelogram are parallel. A parallelogram can have one pair or two pairs of parallel sides. All sides of a parallelogram have the same length. All angles of a parallelogram have the same measure.

Answers

1) A parallelogram has six sides.

False, because a parallelogram has four sides.

2) Opposite sides of a parallelogram are parallel.

True, this is part of the definition of a parallelogram.

3) A parallelogram can have one pair or two pairs of parallel sides.

False, the parallelogram must have two pairs of parallel sides.

4) All sides of a parallelogram have the same length

False, the sides have the same length in pairs.

5) All angles of a parallelogram have the same measure.

False, the angles have the same measure in pairs.

Dose anyone know how to solve this?

Answers

Answer:

what are the solution dropdown choices for the one that's marked wrong cause I'm getting -2 as a solution and also 5

Mary Beth uses 7/12 yards of fabric to make a pillow. How much fabric will she need? Between what two whole numbers

Answers

The range of whole numbers between which the decimal falls is 0 yards to 1 yard.

What is a whole number?

The whole number is set to positive integers including 0. i.e 0, 1, 2, 3, and so on.

To find the total amount of fabric Mary Beth needs to make a pillow, we first need to convert 7/12 yards into a decimal. To do this, we can divide the numerator by the denominator:

7/12 = 7 / 12 = 0.5833...

So, Mary Beth needs approximately 0.5833 yards of fabric to make a pillow.

To determine the range of whole numbers between which the decimal falls, we can round up to the next whole number (1 yard) and round down to the previous whole number (0 yards). Therefore, the range of whole numbers between which the decimal falls is 0 yards to 1 yard.

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How many two or three-digit numbers can you make using the digits 1, 7, 8, 5, and 2?

Answers

Answer:

the are so many numbers but here's one of them

Step-by-step explanation:

Since the number is less than 700, it cannot begin with a 7 or an 8.

So the hundreds digit can only be a 2 or a 5.

Now the tens digit can be any digit not occupying the hudreds digit. So there would be 3 possibilities, and there remain two possibilities for the units digit.

Hence, the number of such numbers is 2x3x2 which is 12.

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 will be 150.

What is a sample?

A sample is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The number of two-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5

⇒ 25

The number of three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5 x 3

⇒ 125

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 125 + 25

⇒ 150

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17. Rob purchased a boat three years ago. The boat decreased by 7% each year. Three years
later, the value of the boat was $32,174.28. Which equation initially models the value of Rob's
boat?
A. y = 40,000(0.93)*
B. y = 40,000(1.07)*
C. y = 32,174.28 (0.93)*
D. y = 32,174.28 (1.07)*

Answers

Answer:

The correct equation that initially models the value of Rob's boat is option A, y = 40,000(0.93)*.

Since the value of the boat decreased by 7% each year, the value of the boat after three years can be represented by:

y = 40,000(0.93)^3

where y is the value of the boat after three years, and 40,000 is the initial value of the boat.

Simplifying this equation, we get:

y = 40,000(0.7951)

y = 31,804

However, we know that the actual value of the boat after three years was $32,174.28. This means that our initial assumption that the boat decreased by 7% each year is incorrect and we need to adjust the equation accordingly.

To find the correct equation, we can use the formula for exponential decay:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the rate of decay (expressed as a decimal), and t is the time in years.

In this case, we know that the final value of the boat is $32,174.28, and that the boat was owned for three years. We also know that the value of the boat decreased by 7% each year.

So we can set up an equation:

32,174.28 = 40,000(0.93)^3

Simplifying this equation, we get:

32,174.28 = 31,804.00

This equation is approximately true, which means that the initial value of the boat was $40,000 and the correct equation that initially models the value of Rob's boat is:

y = 40,000(0.93)^t

where t is the time in years.

Write a recursive formula for an, the nth term of the sequence 50, -10, 2, ....
a1
an
11

Answers

Answer:do homework

Step-by-step explanation:

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