Solve the following DE using Power series around xo = 0. Find the first eight nonzero terms of this DE. y" + xy' + 2y = 0.
Answers
The first eight nonzero terms of the solution by substituting the values of the coefficients in the power series expression for y(x) are:
\(a_0 = 0\\a_1 = -a_2/2\\a_2 = -3a_1/2\\a_3 = -(4a_2 + 6a_1)/2\\a_4 = -(5a_3 + 7a_2)/2\\a_5 = -(6a_4 + 8a_3)/2\\a_6 = -(7a_5 + 9a_4)/2\\a_7 = -(8a_6 + 10a_5)/2\\a_8 = -(9a_7 + 11a_6)/2\)
To solve the given differential equation y" + xy' + 2y = 0 using power series method around xo = 0, we assume a power series solution of the form:
y(x) = ∑[n=0 to ∞] \(a_n x^n\)
Now, let's find the first eight nonzero terms of this power series solution.
First, we'll calculate the derivatives of y(x) with respect to x:
y'(x) = ∑[n=0 to ∞] a_n * n * \(x^{(n-1)\)
y''(x) = ∑[n=0 to ∞] a_n * n * (n-1) * \(x^{(n-2)\)
Substituting these expressions into the original differential equation, we have:
∑[n=0 to ∞] \(a_n\) * n * (n-1) * \(x^{(n-2)\) + x * ∑[n=0 to ∞] \(a_n\) * n * \(x^{(n-1)\) + 2 * ∑[n=0 to ∞] \(a_n * x^n\) = 0
Now, we'll rearrange the terms and combine them:
∑[n=2 to ∞]\(a_n\) * n * (n-1) * \(x^{(n-2)\) + ∑[n=1 to ∞] \(a_n\) * n * \(x^n\) + 2 * ∑[n=0 to ∞] \(a_n * x^n\) = 0
Let's break down each summation separately:
For the first summation term, n starts from 2:
∑[n=2 to ∞] \(a_n\) * n * (n-1) * \(x^{(n-2)\) = a_2 * 2 * 1 * \(x^0\) + \(a_3\) * 3 * 2 * x^1 + \(a_4\) * 4 * 3 * \(x^2\) + ...
For the second summation term, n starts from 1:
∑[n=1 to ∞] \(a_n\) * n * \(x^n\) = \(a_1\) * 1 * \(x^1\) + \(a_2\) * 2 * \(x^2\) + \(a_3\) * 3 * \(x^3\) + ...
For the third summation term, n starts from 0:
2 * ∑[n=0 to ∞] \(a_n * x^n\) = 2 * \(a_0 * x^0\) + 2 * \(a_1 * x^1\) + 2 *\(a_2 * x^2\) + ...
Combining these terms, we have:
2\(a_0\) + (2\(a_1 + a_2\))x + (2\(a_2 + 3a_1\))\(x^2\) + \((2a_3 + 4a_2 + 6a_1)x^3\) + ...
Since the equation should hold for all values of x, each coefficient of \(x^n\)should be zero. Therefore, we equate each coefficient to zero and find the recurrence relation for the coefficients:
2\(a_0\) = 0 => \(a_0 = 0\)
\(2a_1 + a_2 = 0\) => \(a_1 = -a_2/2\)
\(2a_2 + 3a_1 = 0\) => \(a_2 = -3a_1/2\)
\(2a_3 + 4a_2 + 6a_1 = 0\)
Using these recurrence relations, we can calculate the first eight nonzero terms of the solution.
Starting from \(a_0 = 0\), we can find the values of \(a_1, a_2\), and so on:
\(a_0 = 0\)
\(a_1 = -a_2/2\)
\(a_2 = -3a_1/2\)
\(a_3 = -(4a_2 + 6a_1)/2\)
\(a_4 = -(5a_3 + 7a_2)/2\)
\(a_5 = -(6a_4 + 8a_3)/2\)
\(a_6 = -(7a_5 + 9a_4)/2\)
\(a_7 = -(8a_6 + 10a_5)/2\)
\(a_8 = -(9a_7 + 11a_6)/2\)
Therefore, these are the first eight nonzero terms of the solution by substituting the values of the coefficients in the power series expression for y(x).
Learn more about Power Series at
brainly.com/question/32614100
#SPJ4
Related Questions
The time spent (in days) waiting for a kidney transplant for people with ages 35-49 can be approximated by the normal distribution with a mean of 1667 and a standard deviation of 207.4. What waiting time represents the first quartile?
Answers
The waiting time represents the first quartile is approximately 1530.4 days. Given that the time spent (in days) waiting for a kidney transplant for people with ages 35-49 can be approximated by the normal distribution with a mean of 1667 and a standard deviation of 207.4.
The formula for the normal distribution is:z = (x - μ) / σWhere,z is the standard score,μ is the mean,σ is the standard deviation,x is the observation whose standard score, z, is to be found. First quartile (Q1) is the 25th percentile and it divides the distribution into 25% and 75%
So,We have,μ = 1667σ = 207.4Q1 = 25th percentile = 0.25
From the Z- table, the value corresponding to 0.25 is -0.67z = -0.67
Let the waiting time be x days.So,-0.67 = (x - 1667) / 207.4
Multiplying by 207.4 on both sides of the equation,-0.67 × 207.4 = x - 1667-136.6 = x - 1667x = 1530.4
Therefore, the waiting time represents the first quartile is approximately 1530.4 days.
For more question on quartile
https://brainly.com/question/28169373
#SPJ8
(10 +13)2 + 7y)
Which expression is equivalent to the expression above?
Answers
Answer:
23+9y
Step-by-step explanation:
hope that helped :)
(46 + 7y) is equivalent to the linear expression((10 +13)2 + 7y).
What is the general form of a linear expression?
Ax + By + C is the general form of a linear expression. Here, x and y are variables and A, B, and C are constants.
Given,
(10 +13)2 + 7y)
= 23 × 2 + 7y
= 46 + 7y
Learn more about linear expression here: https://brainly.com/question/21835898
#Tag #SPJ2
f(x)=log5x what Is the range of the function
Answers
The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.
The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.
The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm
log5(�)log 5 (x) for �>0 x>0.
Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).
In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.
For more such questions on Logarithm:
https://brainly.com/question/31117877
#SPJ8
Answer: All real numbers
Step-by-step explanation:
Edge
Two bacteria cultures are being studied in a lab. At the start, bacteria A had a population of 60 bacteria and the number of bacteria was tripling every 8 days. Bacteria B had a population of 30 bacteria and was doubling every 5 days. Determine the number of days it will take for both bacteria cultures to have the same population. Show all work for full marks and round your answer to 2 decimal places if necessary. [7]
Answers
Two bacteria cultures are being studied in a lab. The initial population of bacteria A is 60, and it triples every 8 days. The initial population of bacteria B is 30, and it doubles every 5 days.
Let's start by finding the population of bacteria A at any given day. We can use the formula:
Population of bacteria A = Initial population of bacteria A * (growth factor)^(number of periods)
Here, the growth factor is 3 since the population triples every 8 days.
Now, let's find the population of bacteria B at any given day. We can use the same formula:
Population of bacteria B = Initial population of bacteria B * (growth factor)^(number of periods)
Here, the growth factor is 2 since the population doubles every 5 days.
To find the number of days it will take for both bacteria cultures to have the same population, we need to solve the following equation:
Initial population of bacteria A * (growth factor of bacteria A)^(number of periods) = Initial population of bacteria B * (growth factor of bacteria B)^(number of periods)
Substituting the given values:
60 * 3^(number of periods) = 30 * 2^(number of periods)
Now, let's solve this equation to find the number of periods, which represents the number of days it will take for both bacteria cultures to have the same population.
To make the calculation easier, let's take the logarithm of both sides of the equation. Using the property of logarithms, we can rewrite the equation as:
log(60) + number of periods * log(3) = log(30) + number of periods * log(2)
Now, we can isolate the number of periods by subtracting number of periods * log(2) from both sides of the equation:
log(60) - log(30) = number of periods * log(3) - number of periods * log(2)
Simplifying further:
log(60/30) = number of periods * (log(3) - log(2))
log(2) = number of periods * (log(3) - log(2))
Now, we can solve for number of periods by dividing both sides of the equation by (log(3) - log(2)):
number of periods = log(2) / (log(3) - log(2))
Using a calculator, we can calculate the value of number of periods, which represents the number of days it will take for both bacteria cultures to have the same population.
Finally, rounding the answer to 2 decimal places if necessary, we have determined the number of days it will take for both bacteria cultures to have the same population.
To know more about "Population":
https://brainly.com/question/28103278
#SPJ11
69. 18 + x = 43
How do you do this ? Please help
Answers
Solve for x
X=25
Answer:
x=-26.18
Step-by-step explanation:
69.18+x=43
-69.18 -69.18
x=-26.18
A group of friends wants to go to the amusement park. They have $201.75 to spend on parking and admission. Parking is $5.75, and tickets cost $24.50 per person, including tax. How many people can go to the amusement park?
Answers
Answer:
8 friends
Step-by-step explanation:
The group of friends will park only once, so you only need to add $5.75 once, but you still need to add the amount of money for all the people who are in the car, 24.50 x 8 is equal to exactly 196 dollars, so 196 + 5.75 is equal to exactly 201.75, which is the amount of money the group has, so 8 people can come.
Answer: The answer is 8 :)
Step-by-step explanation: Hope this helps!
Employees spin a reward wheel. The wheel is equally likely to stop on each of six rewards labeled A–F. Design and use a simulation to find the experimental probability that fewer than two of the next three spins land on reward A.
Answers
The experimental probability that fewer than two of the next three spins land on reward A is 1/6
Here is the fundamental probability formula: The number of possible outcomes divided by the number of ways an event could occur is the probability of that item happening. Let's examine how to get the data you require and determine the probability of an event.
In theory, there is a 25% chance that the spinner will land on reward A.
\(P(A) =\frac{The Number Of Ways Event A Can Occur}{The total number Of Possible Outcomes}\)
\(P(A)=\frac{1}{6}\)
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
Learn more about probability here:
https://brainly.com/question/28049826
#SPJ4
Consider the following function call round(3.14159, 3) what is the return value? a.3.14159 b.3.141 c.3.14 d.3.1
Answers
The return value of the function call round(3.14159, 3) is c. 3.14. The round function rounds the first argument (3.14159) to the number of decimal places specified in the second argument (3). In this case, it rounds to 3.14.
The function call in your question is round(3.14159, 3). The "round" function takes two arguments: the number to be rounded and the number of decimal places to round to. In this case, the number to be rounded is 3.14159 and the desired decimal places are 3.
The return value is the result of the rounding operation. In this case, rounding 3.14159 to 3 decimal places gives us 3.142.
So, the correct answer is:
b. 3.142
Visit here to learn more about function call:
brainly.com/question/25762866
#SPJ11
A rectangular prism has a legnth of 9 in., a width of 4 in., and a height of 1 1/2 in.
The prism is filled with cubes that have edge lengths of 1/2 in.
How many cubes are needed to fill the rectangular prism?
Enter your answer in the box.
TO FILL THE RECTANGULAR PRISM, _____ CUBES ARE NEEDED
Answers
Answer:
432 cubes
Step-by-step explanation:
V = 9 x 4 x 1.5 = 54 in³
V = 1/2 x 1/2 x 1/2 = 1/8 in³
54/(1/8) = 432 cubes
R + c = 100
R= 14 + 3c
Answers
Answer is in a photo. I can only upload it to a file hosting service. link below!
bit.\(^{}\)ly/3a8Nt8n
x+y=24
75x+60y=1710
Solve using any method
Answers
Answer:
\(x=18,\:y=6\)
Step-by-step explanation:
Solve by substitution
\(\begin{bmatrix}x+y=24\\ 75x+60y=1710\end{bmatrix}\)
\(\mathrm{Substitute\:}x=24-y\)
\(\begin{bmatrix}75\left(24-y\right)+60y=1710\end{bmatrix}\)
\(\begin{bmatrix}1800-15y=1710\end{bmatrix}\)
\(\mathrm{For\:}x=24-y\)
\(\mathrm{Substitute\:}y=6\)
\(x=24-6\)
\(x=18\)
\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)
\(x=18,\:y=6\)
Write the set of all real numbers except 100 in set-builder notation.
The set-builder notation is {x||
Answers
In set builder notation, if we assume that x is a variable, then the set of all real numbers other than 100 is: where the first x is the variable.
It's the one with the R in the middle, which is the numerical representation. This is a place where only integers and decimals are acceptable.
As conclusion, let's focus on the third, which acts as a limit. We're looking for non-zero real numbers below 100.
This is further explained below.
Write the set of all real numbers except 100 in set-builder notation.?Generally,
In set builder notation, the set of all real numbers other than 100 is represented as follows (it is assumed that the variable to be used is x): The very first x stands for the variable.
The second, which begins with an R, is the representation of the number. In this context, only real numbers will do
.
In conclusion, the third factor is the limitation. We are interested in all actual numbers other than 100.
Read more about real numbers
https://brainly.com/question/551408
#SPJ1
I swimsuit is on sale for $45.50. If the sale price is discounted 5% from the original price, what was the original price? Round to the nearest sent.
Answers
The percentage is the indicating hundredth of the original price of the given swimsuit such that the price of $45.50 is 5% less than the original price will be $47.90.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
Let's suppose the original price of the swimsuit was $x.
5% of x → (5/100)x = 0.05x
Price after 5% discount = x - 0.05x = 0.95x
0.95x = 45.50
x = $47.90
Hence "The original price of the given swimsuit such that the price of $45.50 is 5% less than the original price will be $47.90".
For more about the percentage,
brainly.com/question/13450942
#SPJ5
3) (10 points) Find all r e 2 satisfying simultaneously): (mod 6). 129 (mod 10) If there is no such r, simply justify why Note: You need to show work that can be used in general. Finding the solution by tinkering" is not enough.)
Answers
The only value of r that satisfies both congruences is r = 49(mod 60).
To find all values of r that satisfy the given congruences simultaneously, we can apply the Chinese Remainder Theorem (CRT).
Let's analyze each congruence separately:
r ≡ 1 (mod 6)
r ≡ 9 (mod 10)
The first congruence implies that r leaves a remainder of 1 when divided by 6. Therefore, we can write r as:
r = 1 + 6k, where k is an integer.
Substituting this expression for r into the second congruence:
1 + 6k ≡ 9 (mod 10)
We can simplify this congruence as:
6k ≡ 8 (mod 10)
Now, we need to find the inverse of 6 modulo 10. Since 6 and 10 are coprime, the inverse exists. We can find it using the Extended Euclidean Algorithm:
10 = 6× 1 + 4
6 = 4× 1 + 2
4 = 2 ×2 + 0
The last nonzero remainder obtained is 2, and the coefficient of 6 in the previous step is -1. Therefore, the inverse of 6 modulo 10 is -1 (or 9).
Multiplying both sides of the congruence by the inverse:
9 ×6k ≡ 9× 8 (mod 10)
54k ≡ 72 (mod 10)
4k ≡ 2 (mod 10)
Now, we can solve this congruence for k. We can see that k = 8 satisfies this congruence since:
4×8 ≡ 32 ≡ 2 (mod 10)
Therefore, k = 8.
Now, substituting the value of k back into the expression for r:
r = 1 + 6k
r = 1 + 6× 8
r = 1 + 48
r = 49
So, the only value of r that satisfies both congruences is r = 49.
To summarize, the solution is r ≡ 49 (mod 60).
Learn more about chinese remainder theorem here:
https://brainly.com/question/30806123
#SPJ11
-3x - 4y = 2
x + y = -1
use substitution or elimination (show solving steps!)
will mark brainliest
Answers
Answer:
(-3, 2)
Step-by-step explanation:
x + y = -1 = x = -1 - y
-3( -1 -y ) -4y = 2
4 + 3y - 4y = 2
-y + 4 = 2
-y = -2
y = 2
x + 2 = -1
x = -3
Given circle O , m∠EDF=31° . Find x .
Answers
The calculated value of x in the circle is 59
How to calculate the value of xFrom the question, we have the following parameters that can be used in our computation:
The circle
The measure of angle at the center of the circle is calculated as
Center = 2 * 31
So, we have
Center = 62
The sum of angles in a triangle is 180
So, we have
x + x + 62 = 180
This gives
2x = 118
Divide by 2
x = 59
Hence, the value of x is 59
Read more about circles at
https://brainly.com/question/32192505
#SPJ1
Find the equation of the line.
Use exact numbers.
y=
Answers
Answer:
y = -2x+5
Step-by-step explanation:
y = mx+c
\(m=\frac{0-5}{2.5-0} \\m=\frac{-5}{2.5}\\m=-2\)
\(y=mx+c\\y=-2(0)+c\\5=0+c\\c=5-0\\c=5\)
will mark as brainliest plz help
Answers
Answer:
30 is answer bro
Step-by-step explanation:
hope it wI'll help u
Sorry dude, diagram not visible, send a clear pic so I will help uh.
The sum of two numbers is 40 and the difference of these numbers is 14. Write a system of equations to represent this scenario and solve it by elimination. What are the two numbers?
Answers
Answer:
26
Step-by-step explanation:
Find the area of the figure
Answers
Answer:
11000
Step-by-step explanation:
6361.20 = 0.062 (x)
solve for x
please help.
Answers
Answer: 102600
Step-by-step explanation:
6361.20 = 0.062 x
x = 6361.20/0.062
x = 102600
(when you divide a number with a decimal you get a larger number because you are, in fact, dividing by less than 1.)
(Immagine you divide 10 cookies with 1 friend you both get 5 cookies, but if you divide with less than 1 friend [let's pretend that it's possible] you will have to give less because now there are essentially fewer people).
Hope this helps =)
convert 2 Bigha into kattha
Answers
Answer:
To convert 2 Bigha into Kattha:
If 1 Bigha = 20 Kattha:
2 Bigha = 2 * 20 Kattha = 40 Kattha
If 1 Bigha = 16 Kattha:
2 Bigha = 2 * 16 Kattha = 32 Kattha
One liter (1000 cm3 ) of oil is poured onto a lake and spreads out into a circle one molecule thick. Estimate the diameter of the circle assuming the molecules are 2 x 10-10m in size.
Answers
The estimated diameter of the circle formed by the oil layer is approximately 2 micrometers (2 μm).
To estimate the diameter of the circle formed when one liter (1000 cm³) of oil spreads out into a circle one molecule thick, we need to determine the number of oil molecules and then calculate the diameter based on their size.
Given that the size of each oil molecule is 2 x 10⁻¹⁰ m, we can convert the volume of the oil into the number of molecules:
1 liter = 1000 cm³ = 1000 x 10⁻⁶ m³
Number of oil molecules = Volume of oil / Volume of one oil molecule
The volume of one oil molecule can be calculated using its size:
Volume of one oil molecule = (4/3)πr³, where r is the radius of the molecule.
Since the thickness of the oil layer is described as one molecule thick, we can assume the height of the oil layer is equal to the diameter of one oil molecule.
Thus, the volume of one oil molecule can be approximated as (4/3)π(2 x 10⁻¹⁰/2)³.
Now, we can calculate the number of oil molecules:
Number of oil molecules = (1000 x 10⁻⁶) / [(4/3)π(2 x 10⁻¹⁰/2)³]
Once we have the number of oil molecules, we can calculate the diameter of the circle formed by the oil layer:
Diameter = 2 x radius
Radius = (Number of oil molecules / π)^(1/2)
Therefore, the estimated diameter of the circle can be calculated using the formula:
Diameter = 2 x [(Number of oil molecules / π)^(1/2)]
Please note that the calculation involves approximation and estimation based on assumptions about the thickness and arrangement of oil molecules.
The actual behavior of the oil spreading may vary in real-world conditions.
For similar question on circle.
https://brainly.com/question/28162977
#SPJ8
David bought 4.75 pounds of chicken for $11.40.
How much did he pay per pound?
HURRYYYY
Answers
Answer:
2.4 so B
Step-by-step explanation:
you will divide 11.40 by 4.75
2.4 so B
Step-by-step explanation
you will divide 11.40 by 4.75
What percentage of the large circle does the small circle take up?
Please please help
Answers
Answer:
25 percent.
Step-by-step explanation:
To begin we want to find the area of the small circle. That would be pi(r)^2 or 9pi after plugging in the 3 for the radius. We can only assume that the large circle is double the radius of the smaller circle so it would be 6. Plug 6 in and get 36pi for the area of that circle. 9pi/36pi will equal 0.25 and that will be your percentage. I hope this helped.
Ram's salary decreased by 4 percent and reached rs. 7200 per month. how much was his salary before?
a. rs. 7600
b. rs7500
c. rs 7800
Answers
Ram's original salary was rs. 7500 per month before it decreased by 4 percent to rs. 7200 per month.
Explanation:The given question is based on the concept of percentage decrease. Here, Ram's salary has decreased by 4 percent and reached rs. 7200 per month. So, we have to find the original salary before the decrease. We can set this up as a simple equation, solving it as follows:
Let's denote Ram's original salary as 'x'.
According to the question, Ram's salary decreased by 4 percent, which means that Ram is now getting 96 percent of his original salary (as 100% - 4% = 96%).
This is formulated as 96/100 * x = 7200.
We can then simply solve for x, to find Ram's original salary. Thus, x = 7200 * 100 / 96 = rs. 7500.
So, Ram's original salary was rs. 7500 per month before the 4 percent decrease.
Learn more about Percentage Decrease here:https://brainly.com/question/35705707
#SPJ2
Please help me thanks a lot
Answers
Answer:
Refer to the attachment
Given the figure, find the total area of the shaded region.
-4
A
D
8.
6-
4-
2-
O
-2-
-4
2
G
S
B
The area of the shaded region is
R
6 8
-U
X
square units.
Answers
Answer:
what was one survival event you experienced
It costs mrs. richardson $13.67 to arrange a flower bouquet for a wedding. she charges the bride $35 for the arrangement. how much money does mrs. richardson profit from each arrangement?
Answers
Mrs. Richardson makes a profit of $21.33 from each flower arrangement for the wedding.
To calculate the profit, we subtract the cost from the selling price. Mrs. Richardson's cost for arranging the bouquet is $13.67, and she charges the bride $35 for the arrangement.
Profit = Selling Price - Cost
Profit = $35 - $13.67
Profit = $21.33
Therefore, Mrs. Richardson makes a profit of $21.33 from each flower arrangement for the wedding.
In this scenario, the profit is calculated by subtracting the cost of arranging the bouquet from the selling price. The cost incurred by Mrs. Richardson is $13.67, which includes the expenses for materials, labor, and any other associated costs. On the other hand, the selling price is $35, which is what the bride pays for the arrangement.
By subtracting the cost from the selling price, we find that the profit per arrangement is $21.33. This means that Mrs. Richardson earns $21.33 for each bouquet she arranges for a wedding, after covering her costs.
LEARN MORE ABOUT profit here: brainly.com/question/32864864
#SPJ11
Kenisha is about to call a Bingo number in a classroom game from 1-
75.
1. Describe an event that is likely to happen, but not certain, for the
number she calls.
2. Describe an event that is unlikely to happen, but not impossible, for
the number she calls.
3. Describe an event that is certain to happen for the number she calls.
PLEASE HELP WILL VOTE BRANLIEST ONLY IF ANSWER IS CORRECT 10 POINTS !!!!!!!!!
Answers
1. An event that is likely to happen, but not certain, for the number Kenisha calls is that it is a prime number. While there are several prime numbers between 1 and 75, it is not guaranteed that the number she calls will be prime. However, given the range of numbers, the probability of calling a prime number is relatively high.
2. An event that is unlikely to happen, but not impossible, for the number Kenisha calls is that it is a perfect square. Perfect squares are numbers that can be expressed as the square of an integer. In the range of 1 to 75, there are only a few perfect squares, so the chances of calling one as the bingo number are relatively low, but not impossible.
3. An event that is certain to happen for the number Kenisha calls is that it will be an integer. Since the game is played with whole numbers from 1 to 75, the number called will always be an integer, as it represents a specific whole number in the given range.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
The solution is given below.
1. An event that is likely to happen, but not certain, for the number Kenisha calls is that it will be an odd number. Since there are 75 numbers in total and half of them are odd, there is a higher probability that the number called will be odd.
2. An event that is unlikely to happen, but not impossible, for the number Kenisha calls is that it will be a perfect square. There are only a few perfect square numbers between 1 and 75, so the chances of calling a perfect square number are lower compared to other numbers.
3. An event that is certain to happen for the number Kenisha calls is that it will be a number between 1 and 75. Since the numbers in the game range from 1 to 75, any number called by Kenisha will definitely fall within this range.
To learn more on probability click:
brainly.com/question/11234923
#SPJ1