From the given information provided, for random variable x, Var(2X + 1) = 12, E[(3X - 4²)] = 31.
A random variable is a variable whose value is subject to random variation, meaning that the outcome of an experiment or process is not deterministic, but rather is determined by chance.
(a) Using the properties of variance, we have:
Var(2X + 1) = Var(2X) = 4Var(X) = 4(3) = 12
(b) Using the linearity of expectation and the properties of variance, we have:
E[(3X - 4)²] = Var(3X - 4) + [E(3X - 4)]²
= Var(3X) + Var(-4) + [3E(X) - 4]²
= 9Var(X) + 0 + [3(2) - 4]²
= 27 + 4
= 31
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PLEASE HELP FAST!!! IT IS URGENT!!!
Answer: I believe it is the first bubble but it could also be the third one im sorry that is kinda confusing.
Julio makes $ 12.50 per hour. This week he worked 10 hours of overtime which is paid at $ 20 per hour after his 40 hours. He worked 50 hours in total. What is Julio's gross income this pay period? imaging math
A right, isosceles triangle has hypotenuse length 50cm. How long are the two legs?
The length of the two legs is 25√2 cm
How to determine the length of the two legs?From the question, we have the following parameters that can be used in our computation:
A right, isosceles triangle has hypotenuse length 50cm
Represen the length of each leg with x
Using the above definition as a guide, we have the following:
x = Hypotenuse/√2
So, we have
x = 50/√2
This gives
x = 25√2
HEnce, the legs are 25√2 cm each
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Referring to the Fig. in Question #23, find the cosine of angle S. Reduce the answer to the lowest terms.
The cosine of angle S is 4/5.
Describe Cosine?In mathematics, cosine is a trigonometric function that relates the angles of a right-angled triangle to the ratio of the length of its adjacent side to its hypotenuse.
More formally, cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse of a right-angled triangle containing that angle.
The cosine of an angle theta, denoted as cos(theta), is given by the formula:
cos(theta) = adjacent side / hypotenuse
The cosine function has a range of values between -1 and 1, and is periodic with a period of 2π radians or 360 degrees.
The ratio of the neighboring side to the hypotenuse is known as the cosine of an acute angle in a right triangle.
In triangle RST, the hypotenuse is RS = 10 and the adjacent side to angle S is ST = 8.
Therefore, the cosine of angle S is:
cos(S) = adjacent/hypotenuse = ST/RS = 8/10
To simplify this fraction to lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 2.
8/10 = (8/2)/(10/2) = 4/5
So, the cosine of angle S is 4/5.
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can someone help please
The degree of the polynomial is 5 and the maximum number of real zeroes in the polynomial is 5.
What are polynomials?
A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics.
f(x) = 6x⁵ - 3x⁴ + 5x² + 4
According to the fundamental theorem of algebra, the polynomial with n number of degrees will have n number of zeroes and no more, so the zeroes will be the same here 5.
Therefore, The polynomial has a degree of 5, and it can have a maximum of five real zeroes.
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Given that A is true, B is true, and C is false, evaluate each of the following expressions. To grade your work, declare and initialize the three variables in Processing, then print the result of each expression below and compare it to your result. a. A \&\& !B b. B∥C c. 1 B==C d. A&&!C e. (B∥C)&&(!A) f. (A!=B)∥(B!=C)
The evaluation of the given Boolean expressions are:
a) A && !B = false b) B∥C = true
c) B==C = false d) A&&!C = true
e) (B∥C)&&(!A) = false f) (A!=B)∥(B!=C) = true
Information available in the problem:
A = true
B = true
C = true
a) Since A and B are both true, !B (which means "not B") is false. Therefore, A && !B evaluates to false, because the logical AND operator returns true only if both of its operands are true.
Hence,
A && !B = true && false = false
b) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true.
Hence,
B∥C = true ∥ false = true
c) Since B is true and C is false, B and C have different values, and therefore B==C will evaluate to false. This is because the equality operator returns true only if its operands have the same value.
Hence,
B==C = true == false = false
d) Since A is true and !C (which means "not C") is true, A&&!C evaluates to true. This is because the logical AND operator returns true only if both of its operands are true.
Hence,
A&&!C = true && !false = true && true = true
e) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true. Therefore, B∥C evaluates to true.
Since A is true and !A (which means "not A") is false, !A evaluates to false.
Therefore, (B∥C)&&(!A) evaluates to false, because the logical AND operator returns true only if both of its operands are true.
Hence,
(B∥C)&&(!A) = true && false = false
f) Since A is true and B is true, A!=B (which means "A is not equal to B") is false, because A and B have the same value.
Since B is true and C is false, B!=C (which means "B is not equal to C") is true, because B and C have different values.
Therefore, (A!=B)∥(B!=C) evaluates to true, because the logical OR operator returns true if at least one of its operands is true.
Hence,
(A!=B)∥(B!=C) = false ∥ true = true
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If b is a positive real number and mand n are positive integers, then
fm/n
√bm = (vb)m
=
OA. True
OB. False
The given statement for b is a positive real number and m and n are positive integers, is true.
What is an integer?An integer is a number with no decimal or fractional part, and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 2, -8...
Given that, b is a real number and m and n are positive integers.
According to the above information, the calculation is as follows:
[tex]b^\frac{m}{n} = \sqrt[n]{b^m} = (\sqrt[n]{b} )^m[/tex]
Hence, the statement is true.
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Solve for x.
x2 - 2x - 24 = 0
[tex] \bf \: {x}^{2} - 2x - 24 = 0[/tex]
[tex] \bf \: {x}^{2} - 6x + 4x- 24 = 0[/tex]
[tex] \bf \: {x}^{}( x- 6) + 4(x- 6) = 0[/tex]
[tex] \bf \: {}^{}( x + 4)(x- 6) = 0[/tex]
[tex]x = - 4 \: \: or \: \: 6[/tex]
A credit card has a balance of $3,400. The APR is 27% and the minimum payment is 3% of the balance. You will pay the minimum balance this month. If you do not use the card again then how much should the balance be next month?
The minimum payment for this month would be:
minimum payment = 3% of $3,400 = 0.03 x $3,400 = $102
The interest charged on the remaining balance after the minimum payment is made can be calculated as:
interest = APR/12 x remaining balance
where APR is the annual percentage rate and the division by 12 is to convert it to a monthly rate.
So for this month, the interest charged would be:
interest = 0.27/12 x $3,298 = $74.32
where $3,298 is the remaining balance after the minimum payment is made.
Therefore, the balance next month would be:
balance = previous balance - payment + interest
balance = $3,400 - $102 + $74.32 = $3,372.32
So the balance next month should be $3,372.32 if you only make the minimum payment and do not use the card again.
Calculate the population range, variance and standard deviation of the ten total football spending figures. Do the same for the ten spending per scholarship player figures. (Round your range and variance answers to 2 decimal places and standard deviation answer to 4 decimal places.)
We can consider $323.53 as near the monthly interest rate on this loan is approximately 0.4974% (or 0.004974 as a decimal). We can use a formula to find the monthly interest where:
P = (r(PV)) / (1 - (1 + r)^(-n))
Where:
P = monthly payment
r = monthly interest rate
PV = present value of the loan (the amount borrowed)
n = total number of months
r (monthly interest)= (1 / n) * ((P / PV) + ((1 / (1 + r)^n) - 1))
we can start by guessing an interest rate of 0.01 (or 1%). putting it into a formula:
r = (1 / 60) * ((323.53 / 10000) + ((1 / (1 + 0.01)^60) - 1))
r = 0.004968
monthly payment is
P can be (0.004968 * 10000) / (1 - (1 + 0.004968)^(-60))
P = $323.52
By using this value we can find the value of the month. Plugging it back into the formula, we get:
r = (1 / 60) * ((323.53 / 10000) + ((1 / (1 + 0.004968)^60) - 1))
r = 0.004974
This new interest rate gives us a monthly payment of:
P can be (0.004974 * 10000) / (1 - (1 + 0.004974)^(-60))
P = $323.53
We can consider $323.53 as near the monthly interest rate on this loan is approximately 0.4974% (or 0.004974 as a decimal).
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The correct question is
Table 33 gives spending data for the football programs at the 10 universities that spent the most money on football in 2012 Click here for the Excel Data File Calculate the population range variance and standard deviation of the ten total football spending figures Do the same for the ten spending per scholarship player figures. (Round your range and variance answers to 2 decimal places and standard deviation answer to 4 decimal places.) Total Spending (Smil) Spending per Scholarship Player (5) Range Variance Std Deviation 7 College Football A B C D 1 Footballs bending Data for 2012's Top Ten College Football Spenders 2 3 Rank School Total Spending (Smil) Spending per Scholarship Player (3) 4 1 The Ohio State University 34.36 5 400,000 2 University of Alabama 37.77 360,000 6 3 Auburn University 33.33 303,000 7 4 University of Wisconsin 24.23 285,000 8 5 University of Arkansas 24.33 9 6 Oklahoma State University 283,000 26.24 10 279,000 7 Virginia Tech 24.72 11 275,000 8 University of Arizona 24.12 12 9 274,000 University of Florida 23.25 13 273,000 University of Michigan 23.64 14 272,000 15 10
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find the inverse of each function f(x) = x-3/2
Please explain your answer. Will mark Brainliest (question 9)
The initial investment of the function is 20 dollars.
The rate growth in percentage is 4%.
The investment after 10 years is 29.6 dollars.
How to solve function?The function [tex]y=20(1.04)^{t}[/tex] represents the value y of a saving account after t years.
Therefore, the initial investment of the function is 20 dollars.
The rate growth in percentage can be calculated as follows;
rate growth in percent = 0.04 × 100
rate growth in percent = 4 %
Let's find the value of the investment after 10 years.
Therefore,
[tex]y=20(1.04)^{t}[/tex]
t = 10
[tex]y=20(1.04)^{10}[/tex]
[tex]y=20(1.48024428492)[/tex]
y = 29.6048856984
Therefore, the investment after 10 years is as follows:
y = 29.6 dollars
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Aaron is trying to decide which job would allow him to earn the most money after a few years.
Job A agrees to pay him $35,000 in his first year and they promise to give him a 2% raise each year.
Job B can be modeled by the equation:
B(t)=30,000(1.03)t
Which job offers the largest initial salary?
Which job offers the fastest rate of increase?
Calculate Aaron’s salary after 20 years for each job offer.
Which job offer should Aaron accept and why?
So, Lan's total monthly insurance expense is $221.67.
What is time period?A time period is a duration of time characterized by specific events, trends, or conditions. Time periods can be defined by various factors such as historical, cultural, or scientific significance. Examples of time periods include the Renaissance, the Industrial Revolution, the Bronze Age, and the Jurassic period in Earth's geological history. Time periods can vary in length from a few years to millions of years, depending on the context in which they are being discussed.
Given by the question: -
First, let's prorate the semiannual premium for automobile insurance.
Since semiannual means twice a year, we need to divide $450 by 2 to get the premium for a single 6-month period:
$450 ÷ 2 = $225
To find the monthly premium, we need to divide this by 6 (since there are 6 months in a 6-month period):
$225 ÷ 6 = $37.50
So, the monthly premium for automobile insurance is $37.50.
Next, we don't need to prorate the monthly premium for health insurance since it is already a monthly expense. Therefore, the monthly premium for health insurance is simply $155.
Finally, to prorate the annual premium for life insurance, we need to divide it by 12 to get the premium for a single month:
$350 ÷ 12 = $29.17
So, the monthly premium for life insurance is $29.17.
Therefore, the total monthly expense for these three types of insurance is: $37.50 + $155 + $29.17 = $221.67
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||
Initial Knowledge Check
Simplify.
(4w)²
Write your answer without parentheses.
01
6
X
Ś
The expression is 16w².
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
(4w)²
This can be expressed as,
= 4² x w²
[ 4 x 4 = 16 ]
= 16 x w²
= 16w²
Thus,
The expression is 16w².
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A piece of paper can be made into a cylinder in two ways: by joining the short sides together, or by joining the long sides together12. Which cylinder would hold more? How much more?
The solution is:
Bigger volume the cylinder wich radius is (L/2) and h = WHow much according to the relation L/W Let´s call L and W the dimensions of the piece of paper
Let´s assume that
L > WThe Volume (V) of a cylinder is:V(c) = π×r²×h where r is the radius of the circular base, and h is the height of the cylinderFor the first cylinder (V₁) (the one which h = w then r = (L/2)V₁ = π×(L/2)²×w
For the second cylinder (V₂) ( the one with h = L and r = (W/2)V₂ = π×(W/2)²×LThe relation
V₂/V₁ is:V₂/V₁ = π×(W/2)²×L/π×(L/2)²×wV₂/V₁ = W/LBut L > W then V₂/V₁ < 1 or V₂ < V₁The volume of the first cylinder is bigger than the second one:
n:
Hope this helped :]
A plane is 107 mi north and 172 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to the
nearest tenth of a degree.
The pilot should turn approximately 50.7° to fly directly to the airport.
How to find the angle the pilot should turnThe problem can be solved using trigonometry.
Let x be the angle the pilot should turn in order to fly directly to the airport.
Then, we have:
tan(x) = 107 / 172
x = arc tan^-1(107 / 172)
x = 50.7 degrees
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Calculate (0.82 0.042) x (4.4 x 103). express the answer to the correct number of significant figures. a. 3800 b. 3520 c. 3784 d. 3793
Answer:
a. 3800
Step-by-step explanation:
You want the product (0.82 +0.042)(4.4×10³) expressed to an appropriate number of significant figures.
Significant figuresThe number of significant figures in a product is the least of the numbers of significant figures in the contributors. Here, 4.4×10³ has 2 significant figures, so the result needs to be rounded to 2 significant figures.
(0.82 +0.042)(4.4×10³) ≈ 3800
__
Additional comment
This is the only answer choice with 2 significant figures, so it can be chosen on that basis alone.
Is y + 2x = 9 consistent or inconsistent
Yes, the given equation y + 2x = 9 is consistent.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The equation y + 2x = 9 is a linear equation in two variables, x and y.
Now let us solve for y
y=-2x+9
We plot this equation graphically.
This equation represents a line with slope -2 and y-intercept 9.
So the graph of this equation is a straight line that passes through the point (0, 9) and has a slope of -2.
To determine if the equation y + 2x = 9 is consistent or inconsistent, we need to know if there exists at least one pair of values (x, y) that satisfy the equation.
We can see from the graph that there are infinitely many points on the line y + 2x = 9.
Hence, the given equation y + 2x = 9 is consistent.
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Sam went tpbschool at 8 15. he was in homeroom for 20 minutes. math for 35 minutes and reading for 35 minutes and then had a 15 minute break. how long was sam at school?
Sam spent 1 hour and 55 minutes at school.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
Sam went to school at 8:15.
He was in homeroom for 20 minutes, math for 35 minutes, and reading for 35 minutes and then had a 15-minute break.
The total time is,
= 20 + 35 + 35 + 25
= 115 minutes.
= 1 hour and 55 minutes.
Therefore, Sam spends 1 hour and 55 minutes at school.
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Determine the system of transformations, by writing the algebraic notations, that can
be used to map ∆RST onto ∆UVW.
The system of transformation used to map ∆RST onto ∆UVW using algebraic notation is (x, y) → (x, y - 4) that is translated down by 4 units and dilation using the scale factor 6.6(x, y).
What is translation?Translation is the act of moving a form or a figure from one location to another. A figure can move in translation up, down, right, left, or anyplace else in the coordinate system. Just the object's location changes during translation; its size stays the same.
Every point in a form, such as a triangle, rectangle, square, line, circle, and so on, will move by five units in the same direction if one point in the shape moves five units forward. If one point of a triangle travels four units to the left, all three points of the triangle should also move four units to the left.
From the figure we see that the coordinates of the points are:
R = (2, 3)
T = (-1, 0)
U = (1, -2.5)
W = (-0.5, -4)
The first transformation is that the ∆RST is translated down by 4 units.
(x, y) → (x, y - 4)
The second transformation is dilation, since the ∆UVW is smaller in size than the original image.
The distance between RT is:
d = √(-1 -2)² + (0 - 3)²
d = √9 + 9 = √18
The distance between UW is:
d = √(-0.5 - 1)² + (4 + 2.5)²
d = √2.25 + 42.25 = √44.5
The scale factor is:
SF = length of the original figure/ length of new image
SF = √18 / √44.5 = 6.6
Hence, the system of transformation used to map ∆RST onto ∆UVW is (x, y) → (x, y - 4) that is translated down by 4 units and dilation using the scale factor 6.6(x, y).
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There are 12 inches in 1 foot. Which of the following conversion factors express this relationship correctly? Select all that apply Check all that apply. a.12 in /1 ft b. 1 in x 12 ft c. 1 ft /12 in d.1/ 1 in x 12 ft
The relationship exhibiting conversion factor correctly is the option c. 1 ft /12 in, where ft is foot and in is inches.
As per the mentioned information, the relationship will be expressed as -
12 inches = 1 foot
So, now we will use unitary method to find 1 inches, which will be the conversion factor.
Now, the formula for conversion factor (that is one unit of inches) will be = number of unit in foot/number of unit in inches
Conversion factor = 1/12
Based on this, the correct option indicating conversion factor is c. 1 ft /12 in.
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Use the given frequency distribution to find the (a) class width. (b) class midpoint of the first class. (c) class boundaries of the first class. Height (in inches) Class | Frequency, f 50-52 53-55 56-58 59-61 62-64 12 13 (a) 3 (c) 50-52 (a) 2 (c) 49.5-52.5 (a) 2 (b) 51.5 (c) 50-52 (a) 3 (b) 51 (c) 49.5-52.5 O A. (b) 51 OB, O C. (b) 51.5 ○ D. Click to select your answer.
The class width, class midpoint of the first class, and class boundaries of the first class of the given frequency distribution is 3, 51, and 49.5-52.5, respectively.
A frequency distribution is a table that shows how often different values or ranges of values occur in a set of data. In other words, it displays the frequency or count of each distinct value or range of values in a dataset.
To find the class width, we need to subtract the lower limit of the first class from the lower limit of the second class (since all the classes have the same width):
Class Width = Lower limit of second class - Lower limit of first class
= 53 - 50
= 3
Therefore, the class width is 3.
To find the class midpoint of the first class, we need to find the average of the lower limit and upper limit of the first class:
Class Midpoint = (Lower limit + Upper limit) / 2
= (50 + 52) / 2
= 51
Therefore, the class midpoint of the first class is 51.
To find the class boundaries of the first class, we first need to subtract the upper class limit for the first class from the lower class limit for the second class and divide it by two.
(Lower class limit of the second class - Upper class limit of the first class)/2
= (53 - 52)/2
= 0.5
Then, subtract the result to the lower limit of the first class and add to the upper class of the first class:
Class Boundaries = (Lower limit - 0.5) to (Upper limit + 0.5)
= (50 - 0.5) to (52 + 0.5)
= 49.5 to 52.5
Therefore, the class boundaries of the first class are 49.5-52.5.
Based on these calculations, the class width is 3, the class midpoint of the first class is 51, and the class boundaries of the first class is 49.5-52.5.
The problem seems incomplete, it must have been...
"Use the given frequency distribution to find the
(a) class width.
(b) class midpoint of the first class.
(c) class boundaries of the first class.
Height (in inches)
Class | Frequency, f
50-52 5
53-55 8
56-58 12
59-61 13
62-64 11
(a) 2 (b) 51.5 (c) 50-52(a) 2 (b) 51.5 (c) 49.5-52.5(a) 3 (b) 51 (c) 50-52(a) 3 (b) 51 (c) 49.5-52.5"Learn more about frequency distribution here: https://brainly.com/question/1094036
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A certain sporting goods store sold a hockey stick for $20.00 in 2017. The store
increased the price by 5% in 2018 and by another 6% in 2019.
How much did the hockey stick sell for in 2019?
The amount of hockey sticks sell for in 2019 will be $22.26.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A certain sporting goods store sold a hockey stick for $20.00 in 2017. The store increased the price by 5% in 2018 and by another 6% in 2019.
Then the amount of hockey sticks sell for in 2019 will be given as,
⇒ $20 x (1 + 0.05) x (1 + 0.06)
⇒ $20 x 1.05 x 1.06
⇒ $22.26
The amount of hockey sticks sell for in 2019 will be $22.26.
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Letttt me jnowwwwwwww aspapppp!!!
am going through this and will send me an update tomorrow when you can get back in touch if we have time I would love for a bf of you and I was wondering what I could see for my bad credit cards at least once said that they have no interest and they are not going on the right back side and it doesn't look at the world with me anymore but it will take a little more longer then it might have gone out of there so much more to do it all the
Step-by-step explanation:
Firstly thaj, that's not her. that's not a real picture
Secondly, it's C. The answer is C because all the purple is below the line, making it negative so < since it's all bottom, we use y.
all bottom = y
all top = y
all left = x
all right = x
I need help how did you find the answer?
t - 38 = 9
solve what is t
t=
Answer:
t = 47
Step-by-step explanation:
47 - 38 = 9
the national average for mathematics on a standardized test in 2011 was 516. suppose that the distribution of scores was approximately bell-shaped and that the standard deviation was approximately 43. round your answers to at least one decimal place as needed.
The rounded answer is that approximately 68% of scores were between 473 and 559.
To calculate this, we can use the formula for a normal distribution: P(μ−σ < X < μ+σ) = 68%, where μ is the mean and σ is the standard deviation.
For our problem, our mean is 516 and our standard deviation is 43. Therefore, our equation becomes P(473 < X < 559) = 68%. This means that 68% of scores were between 473 and 559, which is our answer.
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the 34 students in mrs roblin dance class are buying her a special pin for the dance show if the pin costs 326.74 how much will each students pay
The amount of money that each student has to pay will be $9.61.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
Let 'x' be the amount that each student pay. Then the equation is given as,
34x = 326.74
Solve the equation for 'x', then we have
34x = 326.74
x = 326.74 / 34
x = $9.61
The amount of money that each student has to pay will be $9.61.
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Exercise 2.38. We choose one of the words in the following sentence uniformly at random and then choose one of the letters of that word, again uniformly at random: SOME DOGS ARE BROWN (a). Find the probability that the chosen letter is R. (b). Let X denote the length of the chosen word. Determine the probability mass function of X. (c). For each possible value k of X determine the conditional probability P(X k|X 3) Hint. The decomposition idea works just as well for conditional probabilities: if (B\, , Bn} is a partition of 2, then
n P(A| D) = ∑ P(ABk | D). k=1 (d). Determine the conditional probability P(the chosen letter is R | X > 3). (e). Given that the chosen letter is R, what is the probability that the chosen word was BROWN?
a) The probability that the chosen letter is R is 1/10.
b) The probability mass function of X is P(X = 3) = 1/5, P(X = 4) = 2/5, P(X = 5) = 2/5
c) If k = 3 , then P(X = 3 | X = 3) = 1. Otherwise, P(X = k | X = 3) = 0
d) The conditional probability P(the chosen letter is R | X > 3) is 1/11.
e) Given that the chosen letter is R, the probability that the word was BROWN is 1/2.
a) The probability that the chosen letter is R is equal to the number of R's divided by the total number of letters in the sentence. There are two R's in the sentence "SOME DOGS ARE BROWN", so the probability of choosing an R is 2/20 = 1/10.
b) To find the probability mass function of X, we need to find the probability of choosing a word of a certain length. There are five words in the sentence, one of length 3, two of length 4, and two of length 5.
The probability of choosing a word of length 3 is 1/5, the probability of choosing a word of length 4 is 2/5, and the probability of choosing a word of length 5 is 2/5. So, the probability mass function of X is:
P(X = 3) = 1/5
P(X = 4) = 2/5
P(X = 5) = 2/5
c) To find the conditional probability P(X = k | X = 3), we need to find the probability of choosing a word of length k given that we know the word has length 3. If X = 3, then the word must be "DOG". So, the only possibility is P(X = 3 | X = 3) = 1.
For all other values of k, P(X = k | X = 3) = 0 because the word must have length 3 given that X = 3.
d) To find the conditional probability P(the chosen letter is R | X > 3), we need to find the probability of choosing an R given that we know the length of the word is greater than 3. The number of R's in words with length greater than 3 is 1, and the number of letters in these words is 11, so the probability is 1/11.
e) Given that the chosen letter is R, the probability that the word was BROWN is equal to the number of R's in the word BROWN (1) divided by the number of R's in the sentence (2). So, the probability is 1/2.
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Answer:
The insect population increased at a rate of 20% each month.
Step-by-step explanation:
i looked it up on gogle and it popped up on brainly asked by someone else and already answered
In a lottery game, a player picks 6 numbers from 1 to 48. if 4 of those 6 numbers match those drawn, the player wins third prize. let's walk through the steps to determine the probability of winning third prize.In how many ways can 4 winning numbers be chosen from the possible 6 numbers?In how many ways can 2 non-winning numbers be chosen from the pool of all non-winning numbers? The number of favorable outcomes would be to multiply the above two answers together, since we want 4 winning numbers and 2 non-winning numbers. What is the number of favorable outcomes? In how many ways can you pick any 6 numbers from the pool of 50 numbers? This is your total outcomes. What is the probability of winning third prize?
The probability of winning third prize in the lottery game is 0.0011 or about 0.11%.
In the given lottery game, the player picks 6 numbers from 1 to 48.
The number of ways 4 winning numbers can be chosen from the possible 6 numbers is calculated using the combination formula: C(6,4) = 15.The number of ways 2 non-winning numbers can be chosen from the pool of 42 non-winning numbers (total numbers - possible winning numbers) is calculated using the combination formula: C(42,2) = 861.The number of favorable outcomes is the product of the above two answers: 15 x 861 = 12,915.The total number of ways you can pick any 6 numbers from the pool of 48 numbers is calculated using the combination formula: C(48,6) = 12,271,512.The probability of winning third prize is the number of favorable outcomes divided by the total number of outcomes: 12,915 / 12,271,512 ≈ 0.0011 or about 0.11%. Therefore, the probability of winning third prize in this lottery game is relatively low.Learn more about probability:
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