If you have been asked to assemble a two person team from among your five person team, then there are 10 different teams
Total number of members for the team = 5
Number of members that we need to assemble = 2
Here we have to use the combination
The combination is defined as the number of ways of selecting samples from the collection and the order of the collection does not matter
The number of combination of 2 members from a 5 member team = [tex]5C_2[/tex]
= 5! / 2!(5-2)!
= 5! / 2! × 3!
= (5 × 4 × 3!) /(2! × 3!)
= (5 × 4) / 2
= 20 / 2
= 10
Therefore, there are 10 different teams
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A kindergarten teacher has five books to distribute to 20 children in her class. (a) how many ways are there for her to distribute the books if they are all the same and no child gets more than one? (b) how many ways are there for her to distribute the books if they are different and no child gets more than one?
The ways in which a kindergarten teacher distributes the books are (a) 20 ways (b) 100 ways (c) 3,628,800 ways.
(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.
(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.
(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.
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The complete question is:
A kindergarten teacher has five books to distribute to 20 children in her class.
(a) How many ways are there for her to distribute the books if they are all the same and no child gets more than one?
(b) How many ways are there for her to distribute the books if they are different and no child gets more than one? If Charlie gets Green Eggs and Ham and Amanda gets The Cat in the Hat, that is a different distribution from the one in which Amanda gets Green Eggs and Ham and Charlie gets The Cat in the Hat.
(c) How many ways are there for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child?
A robot is on the surface of Mars. The angle of depression from a camera in the robot to a rock on the surface of Mars is 13.33 degrees. The camera is 196.0 cm above the surface. How far from the camera is the rock?
The distance between the rock and the surface is 827.20 cm.
Given data,
There is a robot on Mars' surface. 13.33 degrees of depression can be seen between a camera in the robot and a boulder on the surface of Mars. 196.0 cm is how high the camera is from the ground.
How far is the rock from the camera?
From the given data,
tan c = AB/BC
tan 13.33° = 196/BC
BC = 196/tan 13.33°
BC = 827.20 cm
Hence, the distance between the rock and the surface is 827.20 cm.
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the length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes what is the probability that a student will take no more than 40 minutes to complete fie examination? select one: a. 0.10 b. 0.00 c. 0.15 d. 0.05
The probability that a student will take no more than 40 minutes to complete tee examination is 0.00.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
The length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes.
We have to find the probability that a student will take no more than 40 minutes to complete the examination.
As the time required to complete the statistics examination is uniformly distributed and varies between 40 and 60 minutes so no any student will take less than 40 minutes to complete the examination.
P(X ≤ 40) = 0 where 40 ≤ x ≤ 60
Hence, the probability that a student will take no more than 40 minutes to complete tee examination is 0.00.
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how many ways can the letters of the word dancer be arranged in a row if d and a must remain together (in order) as a unit?
The number of ways the letters of the word DANCER can be arranged if D and A remain together is 120 ways .
In the question ,
it is given that the word is DANGER ,
the number of letters in the given word is = 6
it is given that the letters D and A are together ,
that means they are a single unit ,
So , the number of letters become = 5 letters
and 5 letters can be arranged in 5! ways ,
which can be simplified as
5! [tex]=[/tex] 5 * 4 * 3 * 2 * 1 [tex]=[/tex] 120 ways
Therefore , the number of ways of arrangement is 120 ways .
The given question is incomplete , the complete question is
How many ways can the letters of the word DANCER be arranged in a row if D and A must remain together (in order) as a unit ?
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A rectangle has a perimeter of 48 inches. If twice the length decreased by three is equal to three times the width, then find the length and width.
1. Write a system of equations that will solve the problem
2. Define your variables
3. Solve the problems SHOW YOUR WORK
4. Sketch a graph of your solution
1) The system of equations to solve the given problem are:
2l-3=3b
2(l+ b)=48
2) The variables l and w stands for length and width, respectively.
3) Length l=15 and Width w=9
4) The graph of the solution is shown below:
What is meant by perimeter?A perimeter is a closed path that covers, surrounds, or outlines a two-dimensional shape or a one-dimensional length.
The perimeter calculation has various practical uses. A calculated perimeter is the length of fencing required to encircle a yard or garden. The circumference of a wheel/circle specifies how far it will roll in one revolution. Similarly, the amount of string coiled around a spool is proportional to the spool's perimeter; if the length of the string were precise, it would equal the perimeter.
1) The system of equations to solve the given problem are:
2l-3=3b
2(l+ b)=48
2) Here the variables are l, w
The variables l and w stands for length and width, respectively.
3) Given, perimeter of the triangle=48 inches
2l-3=3b
l=(3(b+1))/2
So, 2(l+ b)=48
3b+3+2b=48
5b=45
b=9
l=(3(10))/2
l=15
Therefore, length l=15 and width w=9
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The perimeter of a triangle is 204 feet. The longest side of the triangle is 39 feet shorter than twice the shortest side. The sum of the lengths of the two shorter sides is 46 feet more than the length of the longest side. Find the lengths of the sides of the triangle.
The triangle has lengths of 59 feet, 66 feet, and 79 feet.
How to calculate for the sides of the triangle.Let us represent the length of the shortest side of the triangle with x feet, and that of the other shorter side with y feet
The longest side will be (2x - 39) feet
The length of the other shorter side will give us the equation;
y + x = 2x - 39 + 46
so that by subtracting x from both sides, we have
y = 2x - x + 46 - 39
y = (x + 7) feet
From the question,
x + x + 7 + 2x - 39 = 204 feet {which is the perimeter of the triangle}
4x - 32 = 204 {collect like terms}
4x = 203 + 32
4x = 236
x = 236/4
x = 59 feet
Therefore, as the length of the shortest side of the triangle is 48 feet,
the other shorter side is;
y = 59 + 7
y = 66 feet
and the longest side is;
2(59) - 39
118 - 39
79 feet.
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i honestly don’t know how to do this and if anyone could help it would be appreciated
How many solutions does the system of linear equations represented in the graph have?
Coordinate plane with one line that passes through the points negative 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 5 and 1 comma 3.
No solution
Infinitely many solutions
One solution at (−1, 3)
One solution at (3, −1)
The linear equations has one solution which is and the solution at (3, −1)
How to find the equations of the lineThe slope of the points (-3, -3) and (0, -2) is solved to get
m = (-2 - -3) / ( 0 - -3)
m = 1 /3
using point slope formula
y - -2 = 1/3(x - 0)
y + 2 = x/3
y = x/3 - 2
The slope of the points (0, 5) and (1, 3) is solved to get
m = (3 - 5) / (1 - 0)
m = -2
using point slope formula
y - 5 = -2(x - 0)
y - 5 = -2x
y = -2x + 5
solving simultaneously
y = -2x + 5
y = x/3 - 2
subtraction gives
0 = -7x/3 + 7
7x/3 = 7
x = 3 and y = -1
(3, -1) is the only solution
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An adult ticket to a museum costs $3 more than a children's ticket. When 200 adult tickets
is $2100. What is the cost of a
and 100 children's tickets are sold, the total revenue
children's ticket?
Tyrone likes to snack on his big bag of candy. He takes 8 pieces of candy from the bag each time
he snacks. After he has snacked 18 times, there
are only 6 pieces of candy remaining in the bag.
The number c of pieces of candy remaining in the bag is a function of s the number of snacks
Tyrone eats.
Write the function's formula.
C =
Answer:
c = s - (8×18)
Step-by-step explanation:
S = 8×18+6 = 150
c = s - (8×18)
Is it okay if ya'll can help me on number 5,8,9, and 10
The answer to the following algebra is;
b² at b = 4 is 16
y /5 at y = 15 is 3
27/s at s = 9 is 3
q/3 + 4 at q = 3 is 5
How to solve algebraic expression?Algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
Given the following:
b² at b = 4
substitute b = 4
= 4²
= 4 × 4
= 16
y /5 at y = 15
substitute y = 15
= 15/5
= 3
27/s at s = 9
substitute s = 9
= 27/9
= 3
q/3 + 4 at q = 3
substitute q = 3
= 3/3 + 4
= 1 + 4
= 5
In conclusion, the algebraic expression is solved by substituting the value of the variables.
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g given 2n letters, two of each of n types, how many arrangements are there with no pair of consecutive letters the same?
The arrangements are there with no pair of consecutive letters the same is ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k).
Explain arrangements are there with no pair of consecutive letters the same.Given 2n letters, two of every one of n types. What number of courses of action of these letters are there without any sets of sequential letters something similar? Kindly look at my answer and let me know where my mix-up is!
According to given information:So such plans where the sets of indistinguishable letters are discernible. Then, at that point, ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k) gives the quantity of such plans by incorporation avoidance (there are (2n−k)! ways for k given matches to be together (by combining the those sets into single components) and the rest randomly requested, 2k ways of requesting inside those given matches, and C(n,k) ways of picking those k pairs).So we can acquire the recipe
∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k)
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The graph shows the relationship between temperature y (in degrees
Fahrenheit) and altitude x (in thousands feet).
a. Find and interpret the slope of
the graph.
b. Write an equation of the line.
c.Interpret the x-intercept of the graph
Answer:answer will be more exact than the point you found in the first part
Step-by-step explanation:temperature in degrees Fahrenheit,
degrees Celsius
20
40
60
80 100 120 140 160 180 200 220 240
degrees Fahrenheit
a. Mark the point on the graph that shows the temperature in Celsius when it is 60
degrees Fahrenheit
b. Mark the point on the graph that shows the temperature in Fahrenheit when it
is 60 degrees Celsius.
c. Water boils at 100 degrees Celsius. Use the graph to approximate the boiling
temperature in Fahrenheit, or to confirm it, if you knew what it is.
d. The equation that converts Celsius to Fahrenheit is C = (F - 32). Use it to
calculate the temperature in Celsius when it is 60 degrees Fahrenheit. (This
answer will be more exact than the point you found in the first part
Be sure to show your work where possible-failure to show work will result in
deduction in grade
We know that modern medicine is rich with biology, chemistry and countless other
branches of science. While mathematics does not make a lot of headlines for changing
the way we think about our health and well-being, there are many ways in which
mathematics is informing and improving the way scientists and doctors approach the
world of medicine.
Consider the following data for a group of 2000 women. Of these women, 16 are known
to have breast cancer. All 2000 undergo the same test to determine whether or not they
have breast cancer, and 154 test positive. 14 of the 16 that have breast cancer test
positive and 140 of those that do not have breast cancer test positive.
1. Based on the data presented above, do you think the test for breast cancer is
effective at identifying women who have breast cancer?
The test for breast cancer is not effective at identifying women who have breast cancer.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
It is given that, out of 2000 women, 16 are known to have breast cancer.
But, through the test, the women who do not have breast cancer are also testing positive and the women who have breast cancer are also testing negative.
So, the test for breast cancer is not effective at identifying women who have breast cancer.
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Write the equation of the given line in slope-intercept form.
Answer:
SO... y=3x+0b
Or... y = -3x+0b
Step-by-step explanation:
Colleen took out a $48,000 student loan with a fixed interest rate to pay for college. Colleen did not make payments on her loan for a period of 7 years. After this time period interest had accrued, resulting in the loan balance increasing to $78,000. a. What is is the 7-year growth factor for the amount that Colleen owes on the loan? Preview b. What is the 7-year percent change for the amount that Colleen owes on the loan? % Preview c. What is is the 1-year growth factor for the amount that Colleen owes on the loan? Preview d. What is the 1-year percent change for the amount that Colleen owes on the loan? % Preview Submit
a)The 7-year growth factor for the amount on the loan is $4285.71 b) 7-year percentage change for the amount is 6.25% c) 1-year growth factor for the amount $612.244 and d) 1-year percent change for the amount is 0.894%.
a)We know very well that growth factor is ratio of difference of principal amount and loan amount to the time taken, or
Growth factor=(Final loan amount-Initial loan amount)/Total time
=>Growth factor=(78,000-48,000)/7
=>Growth factor=30,000/7=$4285.71
b)To find the percentage change in amount, we need to use initial loan amount and the difference between two amounts, or
percentage change=((78000-48000)/48000)×100
=>percentage change=[(30000)/48000)]×100
=>percentage change=300/48=6.25%
c)Now, we have already find the growth factor for 7 years, we need to find growth rate in 1 year. So, we use unitary method to find it
=>In 7 years growth factor is=$4285.71
∴In 1 years growth factor is=$4285.71/7=$612.244
d)In 7 years percentage change for the given amount is =6.25%
∴In 1 year percentage change for the given amount=6.25/7=0.894%
Hence, answers are a)$4285.71 b)6.25% c)$612.244 d)0.894%
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During a family vacation, the ratio of sunny days to rainy days was 12 to 5. What was the ratio of rainy days to the total number of days?
Answer: 5:17
Step-by-step explanation: Add both ratios together to get the complete amount of days.
Answer:
5:17
the rainy days amount is 5 and the total amount of days is 17 (12+5) so 5:17
ANSWER PLEASE
This scatter plot shows the number of siblings 14 students have and each student's grade level.
scatter plot shows the scores of 11 students that took the college algebra final exam and the hours they studied.
Choose the conclusion that is best supported by the data shown in the scatter plot
As hours spent studying increases, grades on the college algebra final exam increase.
As hours spent studying increases, grades on the college algebra final exam increase.
As hours spent studying increases, grades on the college algebra final exam decrease.
As hours spent studying increases, grades on the college algebra final exam decrease.
As hours spent studying increases, grades on the college algebra final exam stay the same.
As hours spent studying increases, grades on the college algebra final exam stay the same.
There is no relationship between the grade on the college algebra final exam and hours spent studying.
Answer:As hours spent studying increases, grades on the college algebra final exam increase.
Step-by-step explanation:
Jack's Car Rental rents out cars, trucks, and SUVs to both individuals and to businesses. For the month of June, they rented out 29 cars, 9 trucks, and 16 SUVs to individuals. They also rented out 13 cars, 22 trucks, and 4 SUVs to businesses. Which of the following matrices could represent this information?
The matrix that represents this information is
| 29 9 16 |
| 13 22 4 |
How to determine which matrices can represent the information?
Matrices (singular matrix) are rectangular arrays or tables where numbers or elements are arranged in rows and columns
Given that:
For the month of June, they rented out 29 cars, 9 trucks, and 16 SUVs to individuals. They also rented out 13 cars, 22 trucks, and 4 SUVs
A defined above, matrices can be viewed as a table. Thus, we can write:
Cars Trucks SUVs
29 9 16
13 22 4
In matrice form:
| 29 9 16 |
| 13 22 4 |
Therefore, the matrix that represents this information is
| 29 9 16 |
| 13 22 4 |
Option D. is the answer
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if the mean of 5 values equals 64, then what is the ∑x?
If the mean of the five values is equals to 64 then the sum of x values i.e., ∑x is 320.
Arithmetic mean:
Arithmetic mean is simply called mean or average. To calculate the arithmetic mean of a set of values, we need to add all the values and then divide the sum by the number of values in the set.
X-bar = ( a₁ + a₂ + -----+ aₙ )/n
Here, there are n items in the set, and each item is represented by one of the a's.
We have given that,
Mean of 5 values , X-bar = 64 , n = 5
we have to calculate the sum of x i.e ∑x
Using Arithmetic mean formula,
sum of x , ∑x = X-bar × n , where x is five values
so, ∑x = 64 × 5 = 320
Hence, the sum of x values is 320.
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What is 15% of a restaurant check for $65. 12? Explain how you calculated your answer. Round your answer to the nearest hundredth, if necessary.
Answer:
Step-by-step explanation:
if you do 65.12 * 15% you will get 9.768
subtract that from 65.12 you will get 55.352
round that to the nearest hundredth it is 55.35
increasing the difference between sample means will result in what outcome in an independent-measures t-test?
Increase the likelihood of rejecting the null hypothesis and increase measures of effect size.
What is the t - test?
When the population standard deviation is unknown, the student's t-test in statistics is a method for testing assumptions about the mean of a small sample taken from a population with a normally distributed sample size.
The independent samples t-test examines whether the two distinct values are different from one another when comparing two means, one of which is calculated from one set of scores and the other of which is calculated from another set of scores.
A two-sample t-test should be used to compare two independent means. The variances for both samples must be equal according to the test's premise.
Welch's test for unequal variances should be used if they are not.
Increase the probability of rejecting the null hypothesis and the size of the effect measurements.
Hence, Increase the likelihood of rejecting the null hypothesis and increase measures of effect size.
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You have 1 2/5 minutes left of
passing time. How many vines
can you watch if each vine is 6
seconds? (Hint: 6 seconds=
1/10 of a minute.)
Answer: You can watch 14 vines.
Step-by-step explanation: 1 2/5 is equal to 1 4/10
1 4/10 is equal to 14/10
So the amount of vines you could watch is 14 in 1 minute and 24 seconds.
Please answer this is due today
A 5-pound carton of oatmeal costs $6.25. What is the unit price? $__________ per pound (just type the number in the answer, not the $)
Answer: $1.25.
Step-by-step explanation: The unit price of the oatmeal is calculated by dividing the total cost by the weight of the carton. In this case, the unit price is $6.25 / 5 pounds = $1.25 per pound. This means that for every pound of oatmeal, the cost is $1.25.
Answer:
dang he beat me to it
Step-by-step explanation:
6.25/5 is 1.25 per pound
find the standard form of the equation of the circle with endpoints of a diameter at the points (3,8) (-5,6)
The equation of the circle with endpoints of a diameter at the points (3, 8) and (-5, 6) is x² + y² + 2x - 14y + 33 = 0.
How to determine the equation of a circleThese are the specified parameters:
Endpoints of a diameter at the points (3, 8) and (-5, 6).
Determine the center point of the circle (a, b).
(a, b) = ((x₁ + x₂)/2 , (y₁ + y₂)/2)
= ((3 + (-5))/2 , (8 + 6)/2)
= (-2/2 , 14/2)
= (-1, 7)
The center point is (-1, 7).
Determine the radius of the circle (r).
[tex]\begin{aligned} r & = \frac{1}{2} \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\r & = \frac{1}{2} \sqrt{(-5-3)^2 + (6-8)^2} \\ r& = \frac{1}{2} \sqrt{(-8)^2 + (-2)^2} \\ r& = \frac{1}{2} \sqrt{64 + 4} \\ r & = \frac{1}{2} \sqrt{68} \end{aligned}[/tex]
Determine of the equation of the circle
(x - a)² + (y - b)² = r²
(x - (-1))² + (y - 7)² = (1/2 √68)²
x² + 2x + 1 + y² - 14y + 49 = 1/4 × 68
x² + y² + 2x - 14y + 50 = 17
x² + y² + 2x - 14y + 50 - 17 = 0
x² + y² + 2x - 14y + 33 = 0
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Which graph represents function?
PLS HELP ASAP>>>>>>Write an equation in slope-intercept form for the line that passes through (3,1) and (1,2). Pls show work
The equation in slope-intercept form is found as; y = -x/2 + 5/2.
State the equation in slope-intercept form?When you understand the slope of a line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y frequency of the y intercept position is denoted by the symbol b in the formula.For the stated question.
Two point are-
(x1, y1) = (3,1)
(x2, y2) = (1,2)
Thus,
slope m = (y2 -y1)/(x2 - x1)
m = (2 - 1)/(1 - 3)
m = -1/2
Equation of line;
y - y1 = m(x - x1)
y - 1 = (-1/2)(x - 3)
y = -x/2 + 5/2
Thus, the equation in slope-intercept form is found as; y = -x/2 + 5/2.
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Trey lost 7 1/12 pounds in
8 weeks. If his weight loss
remained constant each week.
how many pounds did he
lose each week?
Answer:
about 15/16
Step-by-step explanation:
a study showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. to investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup. (a) formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the superma
As described in probability Null hypothesis is 0.64
what is probability?
Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is expressed. To forecast the likelihood of events, probability has been introduced in mathematics.
Solution:
Null hypothesis H0 : p = 0.64
Alternate hypothesis Ha : p ≠ 0.64
therefore Null hypothesis is 0.64
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a disease has hit a city. the percentage of the population infected t days after the disease arrives is approximated by p(t) for 0t. after how many days is the percentage of infected people a maximum? what is the maximum percent of the population infected?
The number of days would be 10 and the maximum percent of the population infected would be 25.752%.
What are exponential functions?
The exponential function, denoted by [tex]e^x[/tex], is a mathematical function. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.
[tex]p(t) = 7te^{-\frac{t}{10}}[/tex]
percentage of infected people a maximum when p '(t) = 0
[tex]p '(t) = 7(1)e^\frac{-1}{10} +7te^\frac{-t}{10}(\frac{-1}{10})\\\\p'(t)=e^{-\frac{t}{10}}(7 -\frac{7t}{10})\\\\e^{-\frac{t}{10}}(7 -\frac{7t}{10})=0\\\\7 -\frac{7t}{10}=0\\\\t = 10[/tex]
Hence percentage of infected people reaches a maximum after 10 days
maximum percent of the population infected = p(10)
[tex]p(10) = 7(10)e^{-\frac{10}{10}}\\\\p(10)=\frac{70}{e}\\\\P(10)=25.752\%[/tex]
Hence, the number of days would be 10 and the maximum percent of the population infected would be 25.752%.
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