Answer:
B:<
Step-by-step explanation:
You can solve this question with fractions. The way I did it was by changing both equations into fractions like this: 6÷7=6/1x1/7=6/7 and 7÷8=7/1x1/8=7/8. Since they don't have a common denomintor and you still dont know which fraction is bigger/smaller, we are going to find a common denominator which is 56. After converting both fractions, (6/7=48/56 and 7/8=49/56) Now you can see that 7/8 is bigger than 6/7, which shows that 6÷7<7÷8.
According to an airline, flights on a certain route are on time 85% of the time. Suppose 20 flights are randomly selected and the number of on-time flights is recorded.
(a) Explain why this is a binomial experiment
(b) Find and interpret the probabdity that exadly 15 flights are on time.
(c) Find and interpret the probability that fewer than 15 flights are on time.
(d) Find and interpret the probability that at least 15 flights are on time.
(e) Find and interpret the probability that between 13 and 15 flights, inclusive, are on time.
(a) Identify the statements that explain why this is a binomial experiment. Select all that apply.
A. Each trial depends on the previous trial
B. There are three mutually exclusive possibly outcomes, arriving on-time, arriving early, and arriving late.
C. The experiment is performed unti a desired number of successes is reached
D. The trials are independent.
E. The probability of success is the same for each trial of the experiment.
F. There are two mutually exclusive outcomes, success or failure.
G. The experiment is performed a fixed number of times.
Answer:
See the answers below. Thanks!
Step-by-step explanation:
(a). Option F is the correct choice. "There are two mutually exclusive outcomes, success or failure."
(b). P(X=15) = 0.1702
(c). P(X<15) = 0.0673
(d). P(X>=15) = 1 - P(X<15) = 0.9327
(e). P(13<=X<=15) = 0.1482
Best Regards!
At what point will the graph of the equations 3x +y =7&
y=1 intersect?
=======================================================
Work Shown:
Substitute y = 1 into the first equation. Basically we replace every y with 1. From here we solve for x
3x+y = 7
3x+1 = 7
3x+1-1 = 7-1 .... subtracting 1 from both sides
3x = 6
3x/3 = 6/3 .... dividing both sides by 3
x = 2
We have x = 2 pair up with y = 1. The two equations intersect at (2,1)
As a check, plugging (x,y) = (2,1) into the first equation should lead to a true statement
3x+y = 7
3(2)+1 = 7
6+1 = 7
7 = 7 and it does lead to a true statement
The graph is shown below.
3. Students arrive at an ATM machine in a random pattern with an average inter-arrival time of 3 minutes. The length of transactions at the ATM machine is exponentially distributed with an average of 2 minutes. (a) What is the probability that a student arriving at the ATM will have to wait
Answer:
The probability that a student arriving at the ATM will have to wait is 67%.
Step-by-step explanation:
This can be solved using the queueing theory models.
We have a mean rate of arrival of:
[tex]\lambda=1/3\,min^{-1}[/tex]
We have a service rate of:
[tex]\mu=1/2\,min^{-1}[/tex]
The probability that a student arriving at the ATM will have to wait is equal to 1 minus the probability of having 0 students in the ATM (idle ATM).
Then, the probability that a student arriving at the ATM will have to wait is equal to the utilization rate of the ATM.
The last can be calculated as:
[tex]P_{n>0}=\rho=\dfrac{\lambda}{\mu}=\dfrac{1/3}{1/2}=\dfrac{2}{3}=0.67[/tex]
Then, the probability that a student arriving at the ATM will have to wait is 67%.
One solution to the problem below is 10. what is the other solution?
b^2-100=0
Answer:
the same
Step-by-step explanation:
Answer:
The two solutions can be +10 and -10
Step-by-step explanation:
b^2 - 100 = 0
b^2 = 100
Take the root of both sides
b = +- 10
b = +10 , b = -10
PLZ I NEED THIS BY THE END OF THE DAY What are at least 5 examples of math that we often do in everyday life?
Answer:
cooking ( mesurments )
gardening ( landscape )
designing ( art )
shopping for the best price ( aka money counting )
car rides ( figuring out distance and time )
sewing.
hope this helped :)
Step-by-step explanation:
Prove your work what is 1/12 of a dozen Branliest
Answer:
1/12 of a dozen is 1
Step-by-step explanation:
One dozen means 12. If you ask for 1/12 of 12, you multiply 12 and 1/12. You should get 1 as your answer.
What two numbers is the square root of 74 between?
Answer:
8 and 9
Step-by-step explanation:
√64 = 8
√81 = 9
√74 falls inbetween those 2
Compare and contrast the following piecewise
defined functions.
(-x+ 2 x<0
X+2, x<0
f(x) =
x? + 1, x>0 X + 2, x>0
g(x)=
Answer:
Both piecewise functions have a linear portion and a quadratic portion. The y-intercepts of both linear pieces are the same, 2. The quadratics are both open upward, but have different y-intercepts (one at 1, one at 2). The linear portion of the first function is decreasing, while the linear portion of the second function is increasing.
Step-by-step explanation:
Comparing and contrast of the functions are shown in below.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The given piecewise functions are;
⇒ f (x) = { - x + 2 ; x < 0
= { x² + 1 ; x > 0
Now, Comparison and contrast of the above piecewise functions are,
The similarities are;
1) Both piecewise functions are linear when x < 0.
2) Both piecewise functions are quadratic when x > 0.
3) The magnitude the slope of the linear part both function are equal.
4) The leading coefficient of the quadratic function are the same.
5) The y-intercept of the linear function are equal, therefore, the linear functions in f(x) and g(x) intersect on the y-axis.
6) The domain of the linear and quadratic functions are the same.
The contrasts (differences) in the function are;
1) The slope of the linear function of g(x) is positive and the slope of the linear function of f(x) is negative.
2) The y-intercept of the quadratic function in f(x) is +1, while the y-intercept of the quadratic function in g(x) is +2.
3) The quadratic function in f(x) and g(x) have graphs that do not intersect.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
The average amount of water in randomly selected 16-ounce bottles of water is 16.15 ounces with a standard deviation of 0.45 ounces. If a random sample of thirty-five 16-ounce bottles of water are selected, what is the probability that the mean of this sample is less than 15.99 ounces of water? Answer: (round to 4 decimal places)
Answer:
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761[/tex]
What is the probability that the mean of this sample is less than 15.99 ounces of water?
This is the pvalue of Z when X = 15.99. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15.99 - 16.15}{0.0761}[/tex]
[tex]Z = -2.1[/tex]
[tex]Z = -2.1[/tex] has a pvalue of 0.0179
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
The two figures are similar. Write a proportion to find the missing measure. Then find the value of x.
Answer:
First option is the right choice.
Step-by-step explanation:
x/95 = 15/19
x = 75
Best Regards!
Answer:
Option A
Step-by-step explanation:
Triangle ABC and DEF are similar.
Taking proportion of their sides to find the value of the unknown.
=> x/15 = 95/19
Cross Multiplying
=> 19x = 1425
Dividing both sides by 9
=> x = 75
The number of hits on a certain website during a one-minute interval follows a Poisson distribution with a mean rate of four hits per minute. What is the probability that there is at least one hit in a 30-second period (that is the probability of one or more hits)
Answer:
86.47% probability that there is at least one hit in a 30-second period
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Mean rate of four hits per minute.
This means that [tex]\mu = 4n[/tex], in which n is the number of minutes.
What is the probability that there is at least one hit in a 30-second period
30 seconds is 0.5 minutes, so [tex]\mu = 4*0.5 = 2[/tex]
Either the site doesn't get a hit during this period, or it does. The sum of the probabilities of these events is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1353 = 0.8647[/tex]
86.47% probability that there is at least one hit in a 30-second period
Please help me with this problem, I can't figure it out
Answer: 44
Step-by-step explanation:
This is a confusing problem to look at, so use PEMDAS(parenthesis, exponents, multiplication, division, addition, subtraction).
5 * (-4) + (1 - (-3)^2)^2 simplify inside the parenthesis
5 * (-4) + (1 - 9)^2
5 * (-4) + (-8)^2 simplify exponents
5 * (-4) + 64 multiply
-20 + 64 finally, addition
44
Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola
Answer:
The probability that a group of 15 randomly selected skiers will overload the gondola = (3.177 × 10⁻⁵¹)
(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)
Step-by-step explanation:
Complete Question
A ski gondola carries skiers to the top of the mountain. If the Total weight of an adult skier and the equipment is normally distributed with mean 200 lb and standard deviation 40 lb.
Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola.
Solution
For 15 people to exceed 5000 lb, each person is expected to exceed (5000/15) per skier.
Each skier is expected to exceed 333.333 lb weight.
Probability of one skier exceeding this limit = P(x > 333.333)
This becomes a normal distribution problem with mean = 200 lb, standard deviation = 40 lb
We first standardize 333.333 lbs
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (333.333 - 200)/40 = 3.33
To determine the required probability
P(x > 333.333) = P(z > 3.33)
We'll use data from the normal distribution table for these probabilities
P(x > 333.333) = P(z > 3.33) = 1 - P(z ≤ 3.33)
= 1 - 0.99957
= 0.00043
So, the probability that 15 people will now all be above this limit = (probability of one person exceeding the limit)¹⁵ = (0.00043)¹⁵
= (3.177 × 10⁻⁵¹)
(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)
Hope this Helps!!!
The commute time for people in a city has an exponential distribution with an average of 0.5 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours? Answer: (round to 3 decimal places)
Answer:
0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In this question:
[tex]m = 0.5, \mu = \frac{1}{0.5} = 2[/tex]
What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours?
[tex]P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4)[/tex]
In which
[tex]P(X \leq 1) = 1 - e^{-2} = 0.8647[/tex]
[tex]P(X \leq 0.4) = 1 - e^{-2*0.4} = 0.5507[/tex]
So
[tex]P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4) = 0.8647 - 0.5507 = 0.314[/tex]
0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours
What is the midpoint of the segment shown below?
Answer:
option a (-1,-1/2)
Step-by-step explanation:
apply mid point formula
Three solid shapes, A B and C are similar. The surface area of shape A is 9cm² The surface area of shape B is 16cm² The ratio of the volume of shape B to shape C is 27:125 Work out the ratio of the height of shape A to shape B Give your answer in its simplest form.
Answer:
9:20
Step-by-step explanation:
The ratio of the surface area of similar solid is equal to the square of the ratio of their corresponding linear measures.
If the ratio of their corresponding linear measures is a:b, the surface area ratio will be (a/b)².
Therefore, (A/B )² = 9/16
square root both sides A/B = √9/√16 A/B = 3/4 A:B = 3:4
The ratio of volume of two similar solid is the ratio cube of their corresponding linear measures.
Therefore, (B/C)³ = 27/125 cube root both sides B/C = 3/5 B:C = 3:5
To make the ratio equivalent A:B:C = 9:12:20
A:C = 9:20
Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the population of interest to the university administration.
Answer:
The population of interest is all the students at the University, to find their parking times.
Step-by-step explanation:
Sampling
This is a common statistics practice, when we want to study something from a population, we find a sample of this population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
Here, the population of interest is all New York state residents.
An administrator inconspicuously followed 250 students and carefully recorded their parking times.
Sample of 250 students at the University.
So the population of interest is all the students at the University, to find their parking times.
describe this diagram help please
Answer:
U are finding the slope. so the vertical line is ur rise(x value) and the horizontal line is ur y value. Hopefully that helped
Ethan's solution and reasoning for solving an equation are shown below: 4/2 x - 10 =30
Answer:
Step-by-step explanation:
er
Answer:
x = 20
Step-by-step explanation:
4/2x - 10 =30
Divide 4/2.
2x - 10 =30
Add 10 to both sides.
2x = 30 + 10
2x = 40
Divide 2 into both sides.
2x/2 = 40/2
x = 20
Translate to an algebraic expression.
28 more than d
Answer: d + 28
Step-by-step explanation:
Answer:
d+28
Step-by-step explanation:
it is easier to remeber that you should always flip the wording so for this on "d" would be first then add the 28
78% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below.
1. Find the mean of the binomial distribution (Round to the nearest tenth as needed.)
2. Find the variance of the binomial distribution. (Round to the nearest tenth as needed.)
3. Find the standard deviation of the binomial distribution. (Round to the nearest tenth as needed.)
4. Most samples of 6 adults would differ from the mean by no more than nothing. (Type integers or decimals rounded to the nearest tenth as needed.)
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of U.S. adults who think that political correctness is a problem in America today. This is a binomial distribution since the outcomes are two ways. The probability of success, p = 78/100 = 0.78
The probability of failure, q would be 1 - p = 1 - 0.78 = 0.22
n = 6
a) Mean = np = 6 × 0.78 = 4.68
b) Variance = npq = 6 × 0.78 × 0.22 = 1.0
c) Standard deviation = √npq = √(6 × 0.78 × 0.22) = 1.0
d) The standard deviation is used to express the spread of the data from the mean. Therefore, most samples of 6 adults would differ from the mean by no more than 1.0
20 Find the area of the rectangle given that
the perimeter is 50 cm.
3m + 2
m - 5
F 32
G 7
H 46
J 9
Answer: H - 46
Step-by-step explanation:
Primeter = 2(l + w)
50 = 2{(3m+2) + (m-5)}
25 = 3m+2 +m -5
25 = 4m -3
m = 28/4 = 7
l = 3m+2 = 23 cm
w = m-5 = 2 cm
Area = l x b
= 23 x 2 = 46 sq. cm.
how many categories are shown in the rows?
Answer:
4 categories are shown in rows.
2 categories are shown in columns.
12 14 year olds.
82 people were polled.
i dont understand, help?
The measure of two angles of a triangle are 31 and 128 degrees. Find the measure of the third angle.
Answer:
21°
Step-by-step explanation:
All angles in a triangle add up to 180°.
180 - 31 - 128
= 21
The measure of the third angle is 21°.
A perfect square number can never have the digit ….. at the units place.
a :1
b :9
c :8
please tell me the answer as soon as possible
Answer:
the answer is the last option, c :8.
Of the 3,400 widgets produced at the wacky widgets factor today, 12% are defective. How many widgets are defective? which steps would be used to find 12% of 3,400 check all that apply
Answer:
408 widgets
Step-by-step explanation:
Data provided in the question
WP = Total number of widgets produced = 3,400 widgets
DP = Defective percentage = 12%
Based on the above information, the number of widgets that are defective is
[tex]= WP \times DP[/tex]
[tex]= 3,400\ widgets \times 12\%[/tex]
= 408 widgets
We simply multiplied the total number of widgets produced by the defective percentage so that the defective widgets could come
Answer:
The answers are B,D,F
Determine whether the distribution is a probability distribution. x 0 1 2 3 4 5 P(x) StartFraction 1 Over 25 EndFraction one fifth one half three fourths StartFraction 1 Over 50 EndFraction StartFraction 1 Over 100 EndFraction Is the probability distribution a discrete distribution? Why? Choose the correct answer below. A. No comma because some of the probabilities have values greater than 1 or less than 0. B. Yes comma because the distribution is symmetric. C. Yes comma because the probabilities sum to 1 and are all between 0 and 1 comma inclusive. D. No comma because the total probability is not equal to 1. Click to select your answer and then click Check Answer.
Answer:
D. No comma because the total probability is not equal to 1.
Step-by-step explanation:
Given the distribution:
[tex]\left|\begin{array}{c|cccccc}x&0&1&2&3&4&5\\ P(x)&1/25&1/5&1/2&3/4& 1/50&1/100\end{array}\right|[/tex]
The sum of the probabilities
[tex]\sum P(x)=1/25+1/5+1/2+3/4+ 1/50+1/100\\\sum P(x) =1.52 \neq 1[/tex]
Therefore, the distribution is not a probability distribution because the total probability is not equal to 1.
The correct option is D.
In a small state, the license plate for a car begins with two letters, which may be repeated, and ends with three digits, which also may be repeated. How many license plates are possible in that state?
Answer:
676,000 possible license plate
Step-by-step explanation:
Each letter has 26 possible values (from A to Z), and each digit has 10 possible values (from 0 to 9).
So to find the number of license plates we can have, we just need to multiply the number of possible values for each letter and each digit, We have 2 letters and 3 digits, so we have:
Number of plates = 26 * 26 * 10 * 10 * 10 = 676000
We have 676,000 possible licence plates in this state.
Order the numbers from least to greatest: -5, 6, and 9.
Answer: -5, 6, and 9
Step-by-step explanation:
Step-by-step explanation:
least to greatest
-5 6 9