In 720 ways the letters of the word 'SEMESTER' be arranged such that at least two vowels are together.
Arrangement in probability
A number of topics like statistics and probability are closely interrelated to the topic of permutation and combination. Permutation and combination is about making arrangements and making selections on the basic of certain formulas.Given that:
In SEMESTER there are 8 letters.
Which include 3 vowels (E) and 5 consonants (S, M, T , R )
Take 3 vowels as one letter, we have 6 letters
arranged in 6[tex]p_{6}[/tex] = 6! ways E can be taken together in 1! ways
Number of words = 6! × 1!
= 6 × 5 × 4 × 3 × 2 × 1
= 720 ways
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The following graphs show the sampling distributions for two different point estimators, R and W, of the same population parameter.
Which of the following statements is true?
Pilihan jawaban
Both R and W are unbiased.
R is biased, and W is unbiased
Both R and W are biased.
R is unbiased, and W is biased.
The assessment of bias is not possible, because the sampling distributions display too much variability.
The correct statement regarding bias in either distribution is given as follows:
R is biased, and W is unbiased.
How to identify bias in each distribution?We use the graphs showing the sampling distributions for the two different point estimates to identify bias.
Then the criteria to determine that there will be bias is given as follows:
Point estimate at the center: no bias.Point estimate not at the center: bias.From the graphs given at the end of the answer, we have that:
The point estimate of estimator R is not at the center.The point estimate of estimator W is at the center.As the point estimate of estimator R is not at the center, it contains bias, and thus the fourth statement is correct.
Missing InformationThe graphs are given by the image shown at the end of the answer.
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How long will the stone be in flight?
Answer:
3 s
Step-by-step explanation:
Using this quadratic, max height will occur at t = -b/2a
t = - 48 / (2*-16) = 1.5 seconds to max height
then another 1.5 seconds to fall to the ground
for a total of 3 seconds.
Another way d = 0 when it hits the ground
0 = -16 t^2 + 48 t + 0
0 = - 16t ( t +3 ) again shows t = 3s (or 0 before it is launched)
"Let f be a function with selected values given in the table above. Which of the following statements must be true? By the Intermediate Value Theorem; there is value € in the interval (0, 3) such that f (c) = 2 By the Mean Value Theorem; there is a value € in the interval (0, 3) such that f' (c) = III: By the Extreme Value Theorem; there is a value the interval [0, 3] such that f (c) < f (2) for all € in the interval [0, 3]. None Ionly Il only L,l;and III"
Answer:
None of the above.
No assumptions can be made because we do not know if the function is continuous or differentiable on those intervals.
You have a combination lock with 3 secret digits. Find the 3 correct digits using the following clues
Answer:
987
Step-by-step explanation:
Clue 4: There is no 2, 4, 5.
Clues 1 & 2: There is no 1.
7 must be on the right.
_ _ 7
Clue 5: 9 is in the first or second place
9 _ 7 or _ 9 7
937 or 987 or 397 or 897
Try all 4 possibilities above through all 5 clues.
Only 987 works.
Answer: 987
do these 3 side lengths form a right triangle? 9m, 12m, 13m
find all x in that are mapped into the zero vector by the transformation for the given matrix a. a question content area bottom part 1 select the correct choice below and fill in the answer box within your choice. O A. There is only one vector, which is x = LLI OB. xı]+x +x) OC. x+x OD. x
This equation can be solved to find the vector x that is mapped to the zero vector - OD. x
The given matrix A is a 3x3 matrix, so the vector x is a 3-dimensional vector. To determine which vector x maps to the zero vector, 0, we can set up the equation:
Ax = 0
This equation can be solved to find the vector x that is mapped to the zero vector, 0. Solving the equation, we find that x = (0, 0, 0). Thus, the answer is OD. x = (0, 0, 0).
Matrix is a set of numbers arranged into rows and columns. It is commonly used in mathematics, science and engineering to represent a variety of data. Matrix can also be used to represent relationships between different variables.
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Mat hits a home run once every ten times at bat, and gets exactly two times at bat in every game. He wants to know the probability that he will hit at least one home run in a single game. Mat can use one of the following simulations to complete this probability. Model A - Use a random number generator to generate 500 two-digit numbers from 00 to 99. Assign "success" to the number value of 1, and count up all the random two-digit numbers that contain a 1. Model B - Use a spinner with ten different colors of equal area. Assign "success" to one of the colors. For one trial, spin the spinner twice. If the spinner lands on the color considered "success", start over. Count the trial if the spinner lands on the color considered "success" or not at all. Repeat this process for 20 trials. Model C - Use a standard six-sided die. Assign "success" to the number 1. For one trial, roll the die twice. If the die lands on 1, start over. Count the trial if the die either lands on 1 or not at all. Repeat this process for 50 trials. is the best simulation for this situation. Using this simulation, the probability that Mat will hit at least one home run in a single game is about .
Answer:Model A and 19%
Step-by-step explanation:
I saw the explanation on study island
The correct model for the probability is given as follows:
Model B.
The probability that Mat will hit at least one home run in a single game is about 0.19 = 19%.
A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.
Mat hits a home run once every ten times at bat, and gets exactly two times at bat in every game, hence the total number of outcomes is of:
10² = 100.
This is why Model B is the correct model, as it has two trials of 10 outcomes, and each trial has a 0.1 probability of success.
The probability that he hits no home runs is of:
0.9² = 0.81.
Hence the probability of hitting at least one home run is of:
1 - 0.81 = 0.19 = 19%.
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Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.)
f(x)= 1/(1-9x)
sum from n=0 to infinity [?] provided |x| < [?]
The power series representation for the given function is 1+ 9x + (9x) ^ 2 + (9x) ^ 3 + .... (9x) ^ n (where 0 ≤ n ≤ ∞).
Let u = 9x.
Return to the series above and replace each u with a 9x directly:
Where 0 n , 1 + 9x + (9x) 2 + (9x) 3 +.... (9x) n
Here, the interval of convergence is easily found. It follows that
|9x| 1 -1/9 x 1/9 because we know that geometric series must have | u | = 1
Finally, we may leverage the fact that geometric series have a sum to get the sum: S = a / (1 - u).
Here, u = 9x and a = 1
Therefore, the total is simply S = 1 /(1 - 9x).
Any sum can be calculated provided x is between -1/9 and x and less than 1/9.
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A certain forest covers an area of 2100 km2. Suppose that each year this area decreases by 4.25%. What will the area be after 10 years?
The area of the forest would decrease to 1360 km²
What is compounding in percentages?Divide the value of an investment at the end of the period by its value at the beginning of that period. Raise the result to an exponent of one divided by the number of years. Subtract one from the subsequent result. Multiply by 100 to convert the answer into a percentage.
Given here, an area of 2100 km² and each year it decreases by 4.25%
in the first year, the area of the forest becomes (2100 - 4.25/100 × 2100)
= 2010.75 km²
in the second year, the area becomes 2100 × (1-4.25/100)²
= 1925.29 km²
similarly, in the tenth year, the area becomes 2100 × ( 1- 4.25/100)¹⁰
= 1360 km²
Hence, the area of the forest reduces to 1360 km²
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mation. (See Example 5.)
30. ax² + 6x + c = 0; two real solutions
Answer:
Step-by-step explanation:
ax²+6x+c=0
disc=6²-4×a×c=36-4ac≥0,(∵ it has two real solutions.)
36-4ac≥0
36≥4ac
4ac≤36
ac≤9
The next day Tamika records the temperature of 0°F at 8:00 a.m. and 1°F
at 10:00 a.m. Assume the temperature has been rising linearly since sunrise
at 6:00 a.m.
Use point-slope form to write a linear function to model the
situation. (Hint: Solve for y, then replace y with f(x)).
The equation of line in the point slope form is y = 2x + 8
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Let temperature be denoted as x
Let the time be denoted as y
Let the initial temperature be = 0°F
Let the final temperature be = 1°F
Let the initial time be = 8 : 00 AM
Let the final time be = 10 :00 AM
And , the first point be P = P ( 0 , 8 )
The second point be Q = Q ( 1 , 10 )
Now , the slope of the equation is given as
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 10 - 8 ) / ( 1 - 0 )
Slope m = 2
Now , the equation of line is given as y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 8 = 2 ( x - 0 )
y - 8 = 2x
Adding 8 on both sides of the equation , we get
y = 2x + 8
Therefore , the value of A is y = 2x + 8
Hence , the equation is y = 2x + 8
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Solve this question
(7w^7)k³
The value of the variable 'w' for the given equation 7 ( w + 7 )³ = 7(6³) is equal to w = -1.
As given in the question,
Given equation is equal to :
7 ( w + 7 )³ = 7(6³)
Divide both the side of the equation by 7 we get,
⇒ 7 ( w + 7 )³ / 7 = 7(6³) /7
⇒( w + 7 )³ = (6³)
Take cube root both the side of the equation we get,
⇒∛( w + 7 )³ = ∛(6³)
⇒ w + 7 = 6
Now subtract 7 from both the side of the equation we get,
⇒w + 7 - 7 = 6 - 7
⇒ w = -1
Therefore, the value of the variable 'w' for the given equation is equal to w = -1.
The complete question is:
Solve this equation:
7 ( w + 7 )³ = 7(6³)
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Jason's family drinks 2 1/2 gallons of milk in 4 days. How many gallons of milk does he drink in a day?
Answer:
2.5 gallons
Step-by-step explanation:
If Jason's family drinks 2 1/2 gallons of milk in 4 days, then the amount of milk they drink per day is 2 1/2 / 4 = 5/8 gallons. Since 1 gallon is equal to 128 fluid ounces, 5/8 gallons is equal to 5/8 * 128 = 80 fluid ounces. Therefore, Jason's family drinks 80 fluid ounces of milk per day.
Note: To convert a mixed number to a decimal, we need to divide the numerator of the fraction by the denominator and add the result to the whole number. In this case, the mixed number is 2 1/2, which is equal to 2 + 1/2 = 2 + 0.5 = 2.5. This means that Jason's family drinks 2.5 gallons of milk per day.
Answer:
Step-by-step explanation:
i don't know i just need points
for which value of x does each expression make sense: square root of (x-2) / square root of (x-3)
Answer:
The expression makes sense when x > 3.------------------------------------
Given expression:[tex]\cfrac{\sqrt{x-2} }{\sqrt{x-3} }[/tex]The restrictions are:x - 2 ≥ 0, expression under square root can't be negative. x - 3 ≥ 0, same as above,x - 3 ≠ 0, denominator can't be zero.Solve each and combine:
x ≥ 2,x ≥ 3,x ≠ 3.The common interval is x > 3.
what function for 3x-5
Answer: 3
Step-by-step explanation:
Exhibit 8-1 91 In order to estimate the average time spent on the computer terminals per student at a local university data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. (SPOINTS) The standard error of the meanis a. 7.3 6..014 c..160 With a 95 probability, the margin of error is approximately 5 POINTS) b. 1.96 021 d. 164 confidence interval is approximately 5 POINTS If the sample mean is 9 hours, then the 704 10 110.96 hours 5.7.36 to 10.64 hours 780 10 10.20 hours d. 8.74 109.26 hours POINTS) 10) Two approaches to drawing a conclusion in a hypothesis testare wp-value and critical value b. one-tailed and two-tailed c. Type I and Type II d. null and alternative 5 POINTS) II) As a general guideline, the research hypothesis should be stated as the a null hypothesis b. alterative hypothesis c. tentative assumption d. hypothesis the researcher wants to disprove
in a hypothesis test, two approaches are p-value and critical value.The null hypothesis should contain the research hypothesis.
a. The standard error of the mean is 0.14.
b. With a 95% probability, the margin of error is approximately 1.96.
c. If the sample mean is 9 hours, then the 95% confidence interval is approximately 8.74 to 10.20 hours.
d. Two approaches to drawing a conclusion in a hypothesis test are p-value and critical value.
e. The research hypothesis should be given as the null hypothesis as a general rule.
The standard error of the mean is 0.14. With a 95% probability, the margin of error is approximately 1.96. For a sample mean of 9 hours, the 95% confidence interval is 8.74 to 10.20 hours. When drawing a conclusion in a hypothesis test, two approaches are p-value and critical value. The null hypothesis should contain the research hypothesis.
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PLEASE ANSWER ASAP! 50 POINTS!!!!!!!!!!!!!11
An image of a right rectangular prism is shown.
A rectangular prism with dimensions of 6.7 centimeters by 6 centimeters by 5 centimeters.
What is the surface area of the prism?
1. Write down all of the properties that each of the following binary relations satisfies from among the four properties reflexive, symmetric, antisymmetric, and transitive. Explain your answer. a. The "has a common national language with" relation on countries: (a, b) is in the relation if a and b have a common national language b. The relation on people that relates people with bachelor's degrees in computer science: (a, b) is in the relation iff both a and b have a bachelor's degree in computer science, or neither a nor b have a bachelor's degree in computer science.
Reflexive: No, two countries cannot have the same national language ,Symmetric: Yes, if one country has a common national language with another then the other must have a common national language with the former
a. The relationship between countries that "have a shared national language with"
Reflexive: No, two countries cannot have the same national language
Symmetric: Yes, if one country has a common national language with another then the other must have a common national language with the former
Antisymmetric: No, there can be multiple countries that share a common national language
Transitive: Yes, if Country A has a common national language with Country B and Country B has a common national language with Country C, then Country A has a common national language with Country C.
b. The relationship between individuals with computer science bachelor's degrees:
Reflexive: Yes, a person can have a bachelor's degree in computer science
Symmetric: Yes, if one person has a bachelor's degree in computer science, then the other must also have a bachelor's degree in computer science
Antisymmetric: Yes, if two people have a bachelor's degree in computer science then they are the same person
Transitive: No, a person who has a bachelor's degree in computer science does not necessarily have a bachelor's degree in any other subject.
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For the function f(x)=[tex]x^{2} +3x-18[/tex] solve the following. f(x)[tex]\geq 0[/tex]
3 divided by 7.14 (PLEASEE HURRRRYYY)
following is a list of variables from a study on exposure to secondhand smoke. use these to create appropriate research questions for each of the statistical techniques listed below. type the variables in exactly as listed. be sure to list the predictor first and the outcome second. variables: gender race years of education number of minutes of exposure to secondhand smoke per day currently diagnosed with asthma
On solving the question we can say that - dependent variable = Daily minutes of secondhand smoke exposure independent variables = Race, Year of Education, and Gender Currently suffering with asthma
what is independent variable?
The variable that symbolizes the amount being changed in the experiment is known as the independent variable. The variable x is frequently utilized to symbolize the equation's independent variable.
part(B):
What the difference group indicates is how the dependent and independent variables are related.
dependent variable = Daily minutes of secondhand smoke exposure
independent variables = Race, Year of Education, and Gender
Currently suffering with asthma
part(C):
Given the information,
The appropriate response is,
What is the correlation between the number of minutes of daily secondhand smoke exposure and the presence of an asthma diagnosis?
part(D):
Given the information,
The appropriate response is,
What is the correlation between the number of minutes per day of secondhand smoke exposure and the presence of an asthma diagnosis
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Suppose that you have trained a logistic regression classifier, and it outputs on a new example x a prediction hθ(x) = 0.7. This means (check all that apply):
Our estimate for P(y=0|x;θ) is 0.7.
Our estimate for P(y=1|x;θ) is 0.7.
Our estimate for P(y=0|x;θ) is 0.3.
Our estimate for P(y=1|x;θ) is 0.3.
The prediction hθ(x) = 0.7 means that the probability of the example having a value of y=1 is 0.7 (or 70%). Our estimate for P(y=0|x;θ) is 0.3. and Our estimate for P(y=1|x;θ) is 0.7.
The prediction hθ(x) = 0.7 means that the probability of the example having a value of y=1 is 0.7 (or 70%). This means that the probability of the example having a value of y=0 is 0.3 (or 30%). Therefore, our estimate for P(y=0|x;θ) is 0.3 and our estimate for P(y=1|x;θ) is 0.7.
The logistic regression classifier is a supervised learning algorithm used for binary classification. It is used to estimate the probability of an example belonging to one of two classes, typically 0 or 1. The output of the classifier, hθ(x), is a value between 0 and 1, which is interpreted as the probability of the example belonging to class 1. In the given case, the output of the classifier is hθ(x) = 0.7, which implies that the probability of the example belonging to class 1 is 0.7 (or 70%) and the probability of the example belonging to class 0 is 0.3 (or 30%). Thus, our estimate for P(y=0|x;θ) is 0.3 and our estimate for P(y=1|x;θ) is 0.7.
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the following function should swap the values contained in two integer variables, nami and num2. what, if any void swap (int nomi, int num2) int temp
Yes, there is something wrong with the function.
Here, two integer variables, num1, and num2 are taken by this function as arguments. Then it assigns the value of num1 to a newly declared integer variable, temp. It then assigns the value of temp to num2, and the value of num2 to num1, thus swapping the values of the two variables effectively.
Here, the problem with the function is that the function operates on copies of the original variables rather than the variables themselves.
The variables num1 and num2 are passed by value, which means that to swap the values of the original variables, the function should use pointers or pass the variables by reference.
For example
void swap (int* num1, int* num2) {
int temp = *num1;
*num1 = *num2;
*num2 = temp;
}
Here, the function to modify the original variables directly as the variables num1 and num2 are passed as pointers.
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Complete Question
The following function should swap the values contained in two integer variables, num1, and num2. What, if anything, is wrong with this function?
void swap(int num1, int num2)
{
int temp = num2;
num2 = num1;
num1 = temp;
}
Please help will mark Brainly
The price of the adult tickets will be $20.
The price of the child tickets will be $18
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Three adult and four children pay $132.
And, Two adult and three children pay $94.
Now,
Let The price of the adult tickets = x
The price of the child tickets = y
So, We can formulate;
Three adult and four children pay $132.
⇒ 3x + 4y = $132 ..(i)
And, Two adult and three children pay $94.
⇒ 2x + 3y = $94 ..(ii)
From (i),
⇒ 3x + 4y = $132
⇒ 3x = $132 - 4y
⇒ x = 44 - 4/3y
Substitute above value in equation (ii),
⇒ 2x + 3y = $94
⇒ 2(44 - 4/3y) + 3y = $94
⇒ 88 - 8/3y + 3y = $94
⇒ 1/3y = 94 - 88
⇒ 1/3y = 6
⇒ y = 18
And, From (ii),
⇒ 2x + 3y = $94
⇒ 2x + 3 × 18 = $94
⇒ 2x = 94 - 54
⇒ 2x = 40
⇒ x = 20
Thus, The price of the adult tickets = $20.
The price of the child tickets = $18
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Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time t, in minutes since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For each situation, decide if the slope is positive, zero, or negative.
Step-by-step explanation:
Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time t, in minutes since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For each situation, decide if the slope is positive, zero, or negative.
cruising: zero slope
descending: negative slope
ascending: positive slope
Consider function h h(x)= 2x-6/x+3 true or false?
Answer: false
Step-by-step explanation:
Im going to assume you are asking if 2x-6 is divisible by x+3
In this case, it is false.
x+3 * 2 = 2x+6
2x+6[tex]\neq[/tex]2x-6
Raul has read 4/5 of a chapter. The chapter has 25 pages. How many pages has he read so far?
Answer:
20
Step-by-step explanation
25 / 5 = 5 (each part of the chapter)
5 * 4 = 20 (the number of pages he has read
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 ​ We are interested in determining if the accident proportions differ between the two age groups. ​ Refer to Exhibit 11-7 and let p u represent the proportion under and p o the proportion over the age of 18. The null hypothesis is a. p u - p o = 0 b. p u - p o ≠0 c. p u - p o ≥ 0 d. p u - p o ≤ 0
The 95% confidence interval for the difference between the two proportions is (0.056, 0.164)
Here, we are given that from the sample information for people under 18-
n₁ = 500
x₁ = 180
⇒ p₁ = 180/ 500
p₁ = 0.36
then,
q₁ = 1 - p₁
q₁ = 0.64
Similarly, from the sample information for people over 18, we have-
n₂ = 600
x₂ = 150
⇒ p₂ = 150 / 600
p₂ = 0,25
then,
q₂ = 1 - p₂
q₂ = 1 - 0.25
q₂ = 0,75
Now, we conduct a hypothesis test as follows-
Null hypothesis (H₀) ⇒ p₁ = p₂
Alternative Hypothesis (Hₐ) ⇒ p₁ ≠ p₂
Confidence interval = 95 %
⇒ significance level (α) = 5 %
α = 0.05
and α/ 2 = 0.025
⇒ z at 95% significance level = 1.96 (from z tables)
Now, we calculate z statistic-
z(s) = (p₁ - p₂) / EED
EED = √[(p₁*q₁)n₁ + (p₂*q₂)/n₂]
EED = √[( 0.36*0.64)/500 + (0.25*0.75)/600]
EED = √[0.00046 + 0.0003125]
EED = 0.028
and (p₁ - p₂) = 0.36 - 0.25
= 0.11
Therefore,
z(s) = 0.11 / 0.028
z(s) = 3.93
we can see that z(s) > 1.96
⇒ z(s) is in the rejection region for H₀
Thus, we reject H₀. We can´t support the idea of equals means
Now, CI at 95 % = (p₁ - p₂) ± z(c) * EED
CI = (0.11 ± 1.96 * 0.028)
CI = (0.11 ± 0.054)
CI = (0.056, 0.164)
Thus, the 95% confidence interval for the difference between the two proportions is (0.056, 0.164)
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Your question was incomplete. Check for missing content below-
Q1. Let P, represent the proportion under and p, the proportion over the age of 18. The null hypothesis is:_____.
Q2. The 95% confidence interval for the difference between the two proportions is:____.
GottaGo rents portable toilets for small outdoor events. The El Paso softball league championship game is expected to draw several hundred participants, and the plan is to rent one portable toilet from GottaGo. During the event, one person will need to use the toilet every five minutes, with a standard deviation of five minutes. On average, a person uses the GottaGo toilet for two minutes, with a standard deviation of three minutes. What fraction of time (as a percent) is the GottaGo toilet occupied?
GottaGo rents portable toilets for small outdoor events. The El Paso softball league championship is expected to draw several hundred participants, and the plan is to rent one portable toilet from GottaGo. During the event, one person will need to use the toilet every five minutes, with a standard deviation of five minutes. On average, a person uses the GottaGo toilet for two minutes, with a standard deviation of three minutes. How long does a person have to wait, on average, before he or she can use the GottaGo toilet?
The average wait time before a person can use the GottaGo toilet is three minutes. This is calculated by subtracting the average usage time (two minutes) from the average time between uses (five minutes).
1. Calculate the total time the toilet is occupied by multiplying the average usage time (two minutes) by the average time between uses (five minutes). This gives a total time of 10 minutes.
2. Calculate the total time the toilet is available by subtracting the total time the toilet is occupied (10 minutes) from the total time between uses (five minutes). This gives a total time of five minutes.
3. Calculate the fraction of time the toilet is occupied by dividing the total time the toilet is occupied (10 minutes) by the total time between uses (five minutes). This gives a fraction of two-fifths (2/5).
4. Convert the fraction to a percentage by multiplying the fraction by 100. This gives a percentage of 40%. Therefore, the GottaGo toilet is occupied 40% of the time.
Time occupied = 2 minutes * 5 minutes = 10 minutes
Time available = 5 minutes - 10 minutes = 5 minutes
Fraction of time occupied = 10 minutes / 5 minutes = 2/5
Percentage of time occupied = 2/5 * 100 = 40%
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The length of a rectangle is 5 cm more than twice the width. The perimeter of the rectangle is five times the width. What are the dimensions of the rectangle?
Answer:
Wyzant
ALGEBRA WORD PROBLEM
Kieryn T. asked • 01/10/18
The length of a rectangle is 5 cm more than twice the width. The perimeter of the rectangle is 34 cm. Find the dimensions of the rectangle.
I am having trouble with this problem. I asked my parents and they didnt know what to do. I am stuck and i have looked through my notes and nothing has helped.
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Mikaila D. answered • 01/10/18
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The dimensions of the rectangle are two unknowns: The length "l" and the width "w"
The perimeter of a rectangle is found as P = 2*l + 2*w
We also know that the length is 5cm more than twice the width. l = 2*w + 5
These two equations gives us a system of linear equations.
P = 2*l + 2*w
l = 2*w + 5
We can use substitution to replace the "l" in the first equation with 2*w + 5
P = 2*(2*w + 5) + 2*w
P = 4*w + 10 + 2*w
P = 6*w + 10
We know that P = 34cm
34 = 6*w + 10
Subtract 10 from both sides
24 = 6 * w
Divide both sides by 6
4 = w
Now that we know the width, we can find the length by substituting 4 for "w" in the second equation.
l = 2*4 + 5
l = 8 + 5
l = 13