Express 29 and 37 as the sum of two squares.
If you can answer the correct answer first, then I will mark brainliest.
Answers
Answer:
See below
Step-by-step explanation:
\( {5}^{2} + {2}^{2} = 25 + 4 = 29 \\ \\ {6}^{2} + {1}^{2} = 36 + 1 = 37\)
The values are 29 = 5² + 2² and 37 = 6² + 1².
What is square of number?The definition of a square number states that they are numbers that have been multiplied by themselves. In other terms, a natural number is referred to as a square number if it is multiplied by itself.
Decimal squares are fairly simple to calculate, and the process is the same for both whole numbers (integers) and decimals.
Given numbers 29 and 37
to express in form of sum of two square
let = 29 = a² + b²
the perfect square number near 29 is 25
29 = 25 + 4
29 = 5² + 2²
and 37 = a² + b²
the perfect square near 37 is 36
37 = 36 + 1
37 = 6² + 1²
Hence the numbers in sum of two squares are,
29 = 5² + 2² and 37 = 6² + 1²
Learn more about square of number;
https://brainly.com/question/28610159
#SPJ2
Related Questions
What is the solution m<1?
Answers
Answer: D
Step-by-step explanation: becaus elook at it bitlkjmnjhnnjh
Determine if the following statement is true or false. Alex calculated a correlation coefficient of -1.5. He made a mistake in his calculation since the correlation coefficient has to be between - 1 and 1. The statement is
(1) false
(2) true.
Answers
Answer:
(2) The statement is true.
-1 < r < 1
Out of 1,200 students that attend Norman Rockwell Middle School, how many would most likely sign up for after school tutoring, if 48 out of 80 students randomly surveyed said they would like to have extra help after school?
Answers
Answer:
720
Step-by-step explanation:
Out of 80 students the no. of students who sign up=48
So, out of 1200 students 48×1200÷80=720 students sign up.
What is the solution of the system? Solve using matrices. 25 points
x+2y=9
x+y=1
Answers
Answer:
x = -7 and y=8Step-by-step explanation:
solnusing by elimination method 1|x+2y=9 1| x+y=1 |x+2y=9 -|x+y=1 x-x+2y-y=9-1 0+y=8 y=8 1|x+2y=9 2|x+y=1 |x+2y=9 -|2x+2y=2x-2x+2y+2y=9-2-x=7divide -1 both side with the make value of xx=-7therefore x=-7 and y=8. this is my answerWhat is the coefficient in the expression x² - 6?
Answers
Your answer would be 1/x^2 -6
in a haplodiploid system, calculate the relatedness of a son to a maternal aunt.
Answers
In a haplodiploid system, the relatedness of a son to a maternal aunt is 75%.
In a haplodiploid system, males develop from unfertilized eggs and are haploid, while females develop from fertilized eggs and are diploid. This means that sons inherit all of their genetic material from their mother, including her alleles from both her haploid sets of chromosomes. Maternal aunts, on the other hand, share one set of haploid chromosomes with their nephew (the son), as they are the sister of his mother. Therefore, the relatedness between a son and his maternal aunt in a haplodiploid system is 0.75 or 75%.
In a haplodiploid system, the relatedness of a son to a maternal aunt can be calculated using the following steps:
1. Determine the relatedness of the son to his mother: In haplodiploid systems, sons are haploid and inherit their single set of chromosomes from their mother. This means that they are 100% related to their mother, as they share all her genes.
2. Determine the relatedness of the maternal aunt to the son's mother: The maternal aunt is a sister of the son's mother. In haplodiploid systems, sisters share 75% of their genes, as they get half of their genes from their mother and the other half from their father (who, as a haploid male, gives all his genes to his daughters).
3. Calculate the relatedness of the son to his maternal aunt: To determine the relatedness of the son to his maternal aunt, multiply the son's relatedness to his mother (100%) by the maternal aunt's relatedness to the son's mother (75%).
Relatedness of son to maternal aunt = (1.0) * (0.75) = 0.75 or 75%
So, in a haplodiploid system, the relatedness of a son to a maternal aunt is 75%.
Learn more about haplodiploid system here: brainly.com/question/31081669
#SPJ11
Type the correct answer in each box. Use numerals instead of words for numbers. If necessary, use / for the fraction bar(s). The amount of time it takes a water pump to empty a tank varies directly as the capacity of the tank. If it takes a water pump 2. 5 hours to empty a tank containing 60,000 gallons of water, how long does it take the same pump to empty a tank containing 108,000 gallons of water? it will take hours to empty the second tank.
Answers
An equation is formed when two equal expressions. The time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.
What is an equation?When two equal expressions are added together with the aid of the equal sign "=," an equation is created.
Given that the time it takes a water pump to empty a tank directly correlates with the tank's capacity. Consequently, the relationship can be expressed as,
V ∝ T
V = kT
Substituting the volume and time in the equation,
60,000 gallons = 2.5 hours × k
Solving the equation for k,
k = 60,000 gallons / 2.5 hours
k = 24,000 gallons per hour
Now, the equation for the relationship can be written as,
V = 24,000 gallons per hour × T
Now, the time the same pump will take to empty a tank containing 108,000 gallons of water is,
V = 24,000 gallons per hour × T
108,000 gallons = 24,000 gallons per hour × T
108,000 gallons / 24,000 gallons per hour = T
T = 4.5 hours
Hence, the time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.
In order to learn more about Equation,visit:
https://brainly.com/question/14437949
#SPJ4
rachel got prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 22 cents per yard. If after that purchase there was $19.88 left on the car, how many yards of ribbon did rachel buy.
Answers
Answer:
46 yards.
Step-by-step explanation:
Subtract the new balance from the original balance:
30.00 - 19.88 = 10.12
Therefore, Rachel spent $10.12
Divide the result by the cost of ribbons per yard:
10.12 ÷ 0.22 = 46
Therefore, Racheal bought 46 yeards of ribbon.
A line passes through the points (-10, -3) and (-5, 1). What is the slope of the line?
Answers
Answer:
m= 4/5
Step-by-step explanation:
use the formula (y2 - y1)/ (x2 - x1)
(-10, -3) (-5, 1)
1-( -3)/-5-( -10)= 4/5
Suppose triangle ABC will be dilated using the rule D Subscript Q, two-thirds.
Point Q is the center of dilation. Triangle A B C is 6 units away from point Q. The length of A B is 3, the length of B C is 7, and the length of A C is 8.
What will be the distance from the center of dilation, Q, to the image of vertex A?
2 units
3 units
4 units
6 units
Answers
The distance from the center of dilation, Q, to the image of vertex A will be 4 units.
According to the given rule of dilation, D subscript Q, two-thirds, the triangle ABC will be dilated with a scale factor of two-thirds centered at point Q.
Since point Q is the center of dilation and the distance from triangle ABC to point Q is 6 units, the image of vertex A will be 2/3 times the distance from A to Q. Therefore, the distance from A' (image of A) to Q will be (2/3) x 6 = 4 units.
By applying the scale factor to the distances, we can determine that the length of A'B' is (2/3) x 3 = 2 units, the length of B'C' is (2/3) x 7 = 14/3 units, and the length of A'C' is (2/3) x 8 = 16/3 units.
Thus, the distance from the center of dilation, Q, to the image of vertex A is 4 units.
For more such answers on the Center of dilation
https://brainly.com/question/13173812
#SPJ8
SOMEONE PLEASE HELP ME! I promise i will mark brainlest, but i need the right answer for this. help is much appreciated <3
Answers
Answer:
the third choice
Step-by-step explanation:
I haven't done those questions in a long time so I would double check. But I think its choice C because 0 has two functions, and I'm pretty sure that a number can only have 1 output, therefore C is not a function..
-1 0 1 2 3
g(x) 15 30 -1
X
Which statement correctly compares the two functions?
OA. They have different x- and y-intercepts but the same end behavior
as x approaches 0.
OB. They have the same x- and y-intercepts.
OC. They have the same y-intercept and the same end behavior as x
approaches.
OD. They have the same x-intercept but different end behavior as x
approaches.
K
Answers
The statement that correctly compares the two functions is "OD. They have the same x-intercept but different end behavior as x approaches."
To compare the two functions, we look at the given points and their corresponding values for each function.
The points provided are (-1, 15), (0, 30), (1, -1), and (2, x).
From the given points, we can see that both functions have the same x-intercept at x = 2. This means that both functions intersect the x-axis at the same point.
However, when we analyze the end behavior of the functions as x approaches infinity or negative infinity, we can see that they differ.
For function g(x), as x approaches infinity, the value of g(x) also approaches infinity since it has a positive slope and continues to increase. On the other hand, as x approaches negative infinity, g(x) approaches negative infinity because of its negative slope.
For function f(x), we do not have enough information to determine its end behavior, as the value for f(x) is not provided for x values beyond 3.
Therefore, the correct statement is "OD. They have the same x-intercept but different end behavior as x approaches." This statement captures the fact that the functions have the same x-intercept at x = 2, but their end behaviors differ based on the given information.
Hence, the correct statement is OD. They have the same x-intercept but different end behavior as x approaches.
For more such questions on functions , click on:
https://brainly.com/question/10439235
#SPJ8
A 2-column table with 9 rows. The first column is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 6, negative 2, 0, 4, 4, 0, negative 2, negative 6, negative 10. Based on the table, which best predicts the end behavior of the graph of f(x)? As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞. As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞. As x → ∞, f(x) → –∞, and as x → –∞, f(x) → ∞. As x → ∞, f(x) → –∞, and as x → –∞, f(x) → –∞.
Answers
Answer:
As x → ∞, f(x) → –∞, and as x → –∞, f(x) → –∞Step-by-step explanation:
First, you need to graph all given points in the table, that way you will be able to determine the end behavior.
Remember, the end behavior of a function is the behavior of f(x) as x approaches to positive infinity and negative infinity.
So, based in the graph, we can say that as x approaches to positive infinity, f(x) approaches to negative infinity, and as x approaches to negative infinity, f(x) approaches to negative inifinity. In other words, in either case, f(x) always approaches to negative infinity.
Therefore, the right answer is the last choice.
Answer:
As x → ∞, f(x) → –∞, and as x → –∞, f(x) → –∞
Step-by-step explanation:
Just took the test!!!
Question 1 2 pts Logic Puzzle: A certain clock runs fast; it indicates that 1 hour has passed when actually only 56 minutes have passed. If it is set correctly at 10:00am, what is the correct time when it reads 10:30pm?
Answers
Using proportions, it is found that the correct time when it reads 10:30pm is of 9:40 pm.
What is a proportion?A proportion is a fraction of total amount, and the measures are related using a rule of three.
In this problem, when 56 minutes have passed, the clock indicates that 60 minutes have passed. Hence, what is the time passed when the clock indicates that 12 hours and 30 minutes, that is, 60 x 12 + 30 = 750 minutes have passed?
Hence, the rule of three is:
56 minutes - 60 minutes
x minutes - 750 minutes
Applying cross multiplication:
\(60x = 56 \times 750\)
\(x = \frac{56 \times 750}{60}\)
\(x = 700\)
700 minutes is 660/60 = 11 hours + 40 minutes after 10:00 am, hence the correct time is of 9:40 pm.
You can learn more about proportions at https://brainly.com/question/24372153
There are 1942 students at West High School.
Use the information in the table to determine how many students study less than 2 hours each day.
Answers
Answer:
68
Step-by-step explanation:
The students who study less than 2 hours are the students who study less than 1 hour and the students who study 1.5 hours.
Less than 1 hours: 0.5%
1 hour: 3%
Total percent less than 2 hours: 3.5%
3.5% of 1942 = 0.035 × 1942 = 67.97
Answer: 68
find the value of given expression
\( \sqrt{(60 \div 10) {}^{2} } \)
Answers
Step-by-step explanation:
\( \sqrt{(60 \div 10) {}^{2} } \\ = \sqrt{(6) {}^{2} } \\ = \sqrt{36 } \\ = 6\)
6 is your answer
Answer:
\(\sqrt{\left(\frac{60}{10}\right)^2}\)
\(\sqrt{\left(\frac{60}{10}\right)^2}=\frac{60}{10}\)
\(\frac{60}{10}=6\)
----------------------
hope it helps..
have a great day!!
please help with congruence
Answers
1. The two triangles are congruent.
2. The two triangles are not congruent.
3. The two traingles are congruent.
What are congruent triangles?Congruent triangles are triangles having corresponding sides and angles to be equal. For two triangles to be equal, the corresponding angles must be equal and the corresponding sides of the triangles are equal.
1. For the first set of triangles, though the sides are not shown but the corresponding angles are equal, therefore the triangles are congruent.
2. For the second set of triangles, though the angles are equal , the corresponding sides are not equal, this means the triangles are not congruent.
3. For the third set of triangles, The angle are equal and one side is showing that the corresponding sides are also equal.
learn more about congruent triangles from
https://brainly.com/question/2938476
#SPJ1
Regression equation: y = 3. 915(1. 106)x The pond can hold 400 water lilies. By what day will the pond be full? Write and solve an equation. The pond will be full by the end of day.
Answers
The equation given, y = 3.915(1.106)x, represents the number of water lilies (y) in the pond on day x. To find the day on which the pond will be full, we need to solve for x when y reaches 400. By substituting y = 400 into the equation, we can solve for x using algebraic manipulation.
The equation y = 3.915(1.106)x represents the growth pattern of water lilies in the pond over time. The coefficient 3.915 represents the initial number of water lilies, and the factor 1.106 represents the growth rate per day. By substituting y = 400 into the equation, we get 400 = 3.915(1.106)x.
To solve for x, we need to isolate the variable. Divide both sides of the equation by 3.915, resulting in 400/3.915 = (1.106)x. Next, take the natural logarithm of both sides to eliminate the exponent: ln(400/3.915) = ln(1.106)x. Applying the logarithmic property, we can bring the exponent down: x = ln(400/3.915) / ln(1.106).
Using a calculator, we can evaluate the expression on the right-hand side to find x. The resulting value of x represents the number of days it will take for the pond to be full. Note that since the equation is a continuous function, we may need to round up the value of x to the nearest whole number, as the pond can only be full at the end of a day.
Learn more about equation here: brainly.com/question/29538993
#SPJ11
How many solutions does the equation 6x + 12 = 2(3x + 6) have? Explain.
Answers
Answer: No solution
Step-by-step explanation:
6x + 12 = 2(3x + 6)
Expand the right side:
6x + 12 = 6x + 6
Subtract 6x from both sides:
12 = 6
This is obviously not true, so there are no solutions to this equation :>
F = 1.8 C + 32
(a) Work out the value of F when C = -8
Answers
Answer:
17.6°
Step-by-step explanation:
1.8x-8=-14.4
-14.4 + 32= 17.6°C
Find y.
B
C
Зу
A
8 D
м
2
4
15
10
Answers
Answer:
y=4
Step-by-step explanation:
The question is asking what is the value of y:
Since all lengths have a dash on them they are all equal :
So 3y = y+8
3y = y + 8
First we subtract y from both sides:
3y-y = y+8-y
2y = 8
Divide both sides by 2:
2y÷2 = 8÷2
y = 4
pls help me i need to finish.
Answers
Answer:
C. 1.725*10^-2
Step-by-step explanation:
Simplify exponent
0.017+0.00025 = 0.01725
Scientific notation is 1.725*10^-2
How to solve this math equation
Answers
Answer:
125 degrees
Step-by-step explanation:
If I am reading the drawing correctly you have angles in matching corners. These are called Corresponding Angles and are equal to each other. So we know that the angle labelled (2x - 115) is equal to 135. So we set that up and solve for x
2x - 115 = 135
2x = 250
x = 125
D Let R be the region bounded by the graph of y = 2x – 2, the horizontal line y = 2, and the vertical line x = 1. Which of the following gives the volume of the solid generated when region R is revolved about the vertical line x 1
A π∫_1^2▒〖((y+2)/2〗-1 ) ^2 dy
B π∫_0^2▒〖((y+2)/2〗-1 ) ^2 dy
C π∫_1^2▒〖(2-(2x-〗 2))^2 ^2 dy
D π∫_0^2▒〖((y+2)/2〗)^2-1^2 ) ^2 dy
Answers
The correct option is B: V = π ∫[0,2] ((y + 2)/2 - 1)^2 dy
This integral will give us the Volume of the solid generated when region R is revolved about the vertical line x = 1.
The volume of the solid generated when region R is revolved about the vertical line x = 1, we can use the method of cylindrical shells.
The formula for the volume of a solid generated by revolving a region R about a vertical line is given by:
V = 2π ∫[a,b] x * f(x) dx
In this case, since we are revolving the region R about the vertical line x = 1, the limits of integration will be from y = 2 (where the horizontal line y = 2 intersects the graph y = 2x - 2) to y = 0 (where the graph y = 2x - 2 intersects the x-axis).
Let's analyze the options provided:
A. π ∫[1,2] ((y + 2)/2 - 1)^2 dy
B. π ∫[0,2] ((y + 2)/2 - 1)^2 dy
C. π ∫[1,2] (2 - (2x - 2))^2 dy
D. π ∫[0,2] ((y + 2)/2)^2 - 1^2 dy
Option A: The limits of integration are incorrect. We need to integrate with respect to y, not x.
Option B: This appears to be the correct integral setup, integrating with respect to y and using the correct limits of integration.
Option C: This option incorrectly uses the expression (2 - (2x - 2))^2, which doesn't match the function y = 2x - 2.
Option D: The limits of integration are incorrect. We need to integrate from y = 2 to y = 0.
Therefore, the correct option is B:
V = π ∫[0,2] ((y + 2)/2 - 1)^2 dy
This integral will give us the volume of the solid generated when region R is revolved about the vertical line x = 1.
For more questions on Volume .
https://brainly.com/question/27535498
#SPJ8
Kelsey’s driveway is sketched on the grid with each square having side lengths of 10 feet.
On a coordinate plane, a figure covers approximately 47 squares.
If a paving company will resurface her driveway at a cost of $0.08 per square foot, what is the approximate cost to resurface her driveway?
$26.40
$38.40
$264.00
$384.00
Answers
The cost of resurfacing her driveway will be $384.00.
What is a square?
A square is a quadrilateral having all equal sides and the sum of the for angles is equal to 360. the lines of the square are perpendicular to each other.
It is given in the question that:-
On a coordinate plane, a figure covers approximately 47 squares.The Paving Company will resurface her driveway at a cost of $0.08 per square foot.The total area of the squares will be:-
A = Side² x 48 = 10² x 48 = 4800 square feet
The total cost will be:-
Cost = 4800 x 0.08 = $384.00
Hence the cost of resurfacing her driveway will be $384.00.
To know more about squares follow
https://brainly.com/question/25870256
#SPJ1
John has a 3/4 of a quart of orange juice and needs to fill it equally in cups that hold 1/10 of a quart. how many cups can he fill?
Answers
Answer: 7 1/2 cups
Step-by-step explanation:
We first need to make both fractions have an equal denominator. Cross Multiply 3/4 and 1/10. You will end up with 30/40 and 4/40.
Next we divided 30 by 4, and we will end up with 7 1/2. 7 times 4 is 28, and half of 4 is 1/2, or in this case 2/10. John can fill 7 and 1/2 cups of orange juice.
A triangle has two sides of lengths 4 and 7. What value could the length of the third side be? Check all that apply
A.7
B.17
C.11
D.5
E.9
F.3
Answers
Answer: E
Step-by-step explanation:
4 x 4 = 16
7 x 7 = 49
16 + 49 = 65
8.062 is the square root of 65.
Round 8.062 I guess you could round it to 9 but I believe the actual answer should be 8.
From the following categories of variables, which of them are mutually exclusive and exhaustive?
a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday
b. Days: Weekday and Weekend
c. Letters: Vowels and Consonants
d. Letters: Alphabets and Consonants
Answers
The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.
Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.
Learn more about exhaustive here:
https://brainly.com/question/30239943
#SPJ11
If f(x)=(1)/(3)x-5,g(x)=-4x^(2)-5x+9, and h(x)=(1)/(x-8)+3, find g(-2). Type your exact answer, simplified if necessary, in the empty text box.
Answers
To find g(-2), we'll substitute -2 for x in the equation g(x) = -4x² - 5x + 9. So,g(-2) = -4(-2)² - 5(-2) + 9g(-2). The value of g(-2) is -6.
To find g(-2), substitute -2 for x in the equation
g(x) = -4x² - 5x + 9 to get
g(-2) = -6 + 9g(-2)
We are given three functions as follows:
f(x) = (1/3)x - 5, g(x)
= -4x² - 5x + 9, and
h(x) = 1/(x - 8) + 3.
We are asked to find g(-2), which is the value of g(x) when x = -2.
Substituting -2 for x in the equation g(x) = -4x² - 5x + 9, we get
g(-2) = -4(-2)² - 5(-2) + 9.
This simplifies to g(-2) = -16 + 10 + 9 = -6.
Hence, g(-2) = -6.
The value of g(-2) is -6.
To know more about substitute visit:
brainly.com/question/29383142
#SPJ11
Fantasy 5 is being played. The objective is to match at least two of the winning five numbers chosen from 40 possible ones. Each ticket costs $1. The following prizes will be awarded:
all 5 of 5 winning numbers - $unknown
4 of the 5 winning numbers - $500
3 of the 5 winning numbers - $5
2 of the winning numbers - $1
Determine the following probabilities.
a) Matching exactly 5 out of 5.
b) Matching exactly 4 out of 5.
c) Matching exactly 3 out of 5.
d) Matching 2 out of 5.
Answers
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1
a) The probability of matching exactly 5 out of 5 winning numbers is given by the number of ways to choose 5 winning numbers out of 40, divided by the total number of possible outcomes:
Probability of matching 5 out of 5 = (Number of ways to choose 5 winning numbers out of 40) / (Total number of possible outcomes)
The number of ways to choose 5 winning numbers out of 40 is given by the combination formula:
C(40,5) = 40! / (5! * (40-5)!) = 40 * 39 * 38 * 37 * 36 / (5 * 4 * 3 * 2 * 1) = 658008
The total number of possible outcomes is the number of ways to choose any 5 numbers out of 40, which is also given by the combination formula:
C(40,5) = 40! / (5! * (40-5)!) = 40 * 39 * 38 * 37 * 36 / (5 * 4 * 3 * 2 * 1) = 658008
Therefore, the probability of matching exactly 5 out of 5 winning numbers is:
Probability of matching 5 out of 5 = 658008 / 658008 = 1
b) The probability of matching exactly 4 out of 5 winning numbers is given by the number of ways to choose 4 winning numbers out of 5 and one non-winning number out of 35, divided by the total number of possible outcomes:
Probability of matching 4 out of 5 = (Number of ways to choose 4 winning numbers out of 5) * (Number of ways to choose 1 non-winning number out of 35) / (Total number of possible outcomes)
The number of ways to choose 4 winning numbers out of 5 is 5, since there are 5 different ways to choose which of the 5 winning numbers will not be matched.
The number of ways to choose 1 non-winning number out of 35 is given by the combination formula:
C(35,1) = 35
The total number of possible outcomes is the same as before:
C(40,5) = 40 * 39 * 38 * 37 * 36 / (5 * 4 * 3 * 2 * 1) = 658008
Therefore, the probability of matching exactly 4 out of 5 winning numbers is:
Probability of matching 4 out of 5 = 5 * 35 / 658008 = 0.000189
c) The probability of matching exactly 3 out of 5 winning numbers is given by the number of ways to choose 3 winning numbers out of 5 and two non-winning numbers out of 35, divided by the total number of possible outcomes:
Probability of matching 3 out of 5 = (Number of ways to choose 3 winning numbers out of 5) * (Number of ways to choose 2 non-winning numbers out of 35) / (Total number of possible outcomes)
The number of ways to choose 3 winning numbers out of 5 is given by the combination formula:
C(5,3) = 5! / (3! * (5-3)!) = 10
The number of ways to choose 2 non-winning numbers out of 35 is given by the combination formula:
C(35,2) = 35! / (2! * (35-2)!) = 35 * 34 / (2 * 1) = 595
The total number of possible outcomes is the same as before:
C(40,5) = 40 * 39 * 38 * 37 * 36 / (5 * 4 * 3 * 2 * 1) = 658008
Therefore, the probability of matching exactly 3 out of 5 winning numbers is:
Probability of matching 3 out of 5 = 10 * 595 / 658008 = 0.00905
d) The probability of matching exactly 2 out of 5 winning numbers is given by the number of ways to choose 2 winning numbers out of 5 and three non-winning numbers out of 35, divided by the total number of possible outcomes:
Probability of matching 2 out of 5 = (Number of ways to choose 2 winning numbers out of 5) * (Number of ways to choose 3 non-winning numbers out of 35) / (Total number of possible outcomes)
The number of ways to choose 2 winning numbers out of 5 is given by the combination formula:
C(5,2) = 5! / (2! * (5-2)!) = 10
The number of ways to choose 3 non-winning numbers out of 35 is given by the combination formula:
C(35,3) = 35! / (3! * (35-3)!) = 35 * 34 * 33 / (3 * 2 * 1) = 6545
The total number of possible outcomes is the same as before:
C(40,5) = 40 * 39 * 38 * 37 * 36 / (5 * 4 * 3 * 2 * 1) = 658008
Therefore, the probability of matching exactly 2 out of 5 winning numbers is:
Probability of matching 2 out of 5 = 10 * 6545 / 658008 = 0.0998
Learn more about total number of possible outcomes here brainly.com/question/2883198
#SPJ4