The expected counts for each possible outcome are given by Ei = npi
What is mutually exclusive outcomes?
When two events cannot happen simultaneously or at the same time, they are said to be mutually exclusive in probability theory. In other words, discontinuous occurrences are described as being mutually exclusive. The likelihood of two events occurring simultaneously is 0 if they are regarded as disjoint events. Events that do not occur simultaneously are said to be mutually exclusive. When a coin is tossed, for instance, the outcome will either be head or tail, but we cannot get both outcomes.
The expected counts for each possible outcome are given by Ei = npi
Suppose there are n independent trials of an experiment with k > 3 mutually exclusive outcomes,
where pi represents the probability of observing the ith outcome.
The expected counts for each possible outcome are given by Ei = npi
Where, pi is the probability of observing the ith outcome
Ei is the expected count of the ith outcome.
Hence, The expected counts for each possible outcome are given by Ei = npi.
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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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i honestly don’t know how to do this and if anyone could help it would be appreciated
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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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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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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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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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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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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Fifteen percent of cellphone users use their cell phones to access the Internet. In a random sample of 10 cell phone users, what is the probability that:
Exactly 2 have used their phones to access the Internet?
More than 2 have used their phones to access the Internet?
At least 8 have used their phones to access the Internet?
No more than 5 have used their phones to access the Internet?
Between 1 and 3 people, exclusive, have used their phones to access the Internet?
1) Probability that Exactly 2 have used their phones to access the Internet is; P(X = 2) = 0.2759
2) Probability that more than 2 have used their phones to access the Internet is; P(X > 2) = 0.1798
3) Probability that at least 8 have used their phones to access the Internet is; P(X ≥ 8) = 0.00001
4) Probability that no more than 5 have used their phones to access the Internet is; P(X ≤ 5) = 0.99862
How to solve binomial probability distribution?The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.
The formula for binomial probability distribution is;
P(X = x) = nCx * p^(x) * (1 - p)^(n - x)
Where;
P(X = x) = binomial probability
x = number of times for a specific outcome within n trials
nCx = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trials
1) We are given;
p = 15% = 0.15
n = 10
Thus;
P(X = 2) = 10C2 * 0.15^(2) * (1 - 0.15)^(10 - 2)
P(X = 2) = 0.2759
2) Probability that more than 2 have used their phones to access the Internet is;
P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
Using binomial probability calculator, we have;
P(X > 2) = 0.1798
3) Probability that at least 8 have used their phones to access the Internet is;
P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)
Using binomial probability calculator, we have;
P(X ≥ 8) = 0.00001
4) Probability that no more than 5 have used their phones to access the Internet is;
P(X ≤ 5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
P(X ≤ 5) = 0.99862
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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
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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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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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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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
Can someone help me figure this out, i’ve been stuck on this question for an hour.
According to the given statement the function representing the points relation is f(x) = 32(3x - 1)
What are the different kinds of functions?An statement, rule, or law in mathematics that establishes the link between an independent variable and a predictor variables (the dependent variable). Equations may be found all around arithmetic, and they are essential for building physical connections in the sciences. A mappings between A and B will only be a function if every member in set A only has end and only 1 photo in set B. Where A & B even be two separate sets.
Briefing:Depicts a few points within the graph of the linear function f given a table.
x = -2, 1, 5, 10
f(x) = -224, 64, 448, 928
From option first,
f(x) = 32(3x - 1)
Put x = -2
= 32(-2x3-1)
= 32x(-7) = -224
Consequently, f(x) = 32 is the function used to express the points connection (3x - 1)
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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:
what are all of the equivalent ratios to 4.5
Answer:
The two equivalent ratios of 4:5 are 8:10 and 12:15.
Step-by-step explanation:
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
what is the coefficient of -2 and -3
Answer:
The coefficient of -2 and -3 is -6.
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)
Multiply the following 2 polynomials
(9 + 2x)(9 - 2x)
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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Which graph represents function?
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
3. Select all that apply. Which of the following are equal to 600?
A. 400 increased by 50%
B. 500 increased by 25%
C. 300 increased by 75%
D. 800 decreased by 25%
The answer's are A and D!
Let me know if I'm right please!
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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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
please help solve! cannot find answer and i’m trying to work on math
Answer: 19/21>8/9
Step-by-step explanation:
common denominator is 63
19*3=57 so thats 57/63
8*7=56 so thats 56/63
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.
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?
Write the equation of the given line in slope-intercept form.
Answer:
SO... y=3x+0b
Or... y = -3x+0b
Step-by-step explanation: