The amount of time shoppers wait in line can be described by a continuous random variable, x, that is uniformly distributed from 2 to 10 minutes. What is the probability that a randomly chosen shopper will wait in line for exactly 6 minutes? Round to 2 decimal places.
Suppose the continuous random variable, X, is uniformly distributed between 4 and 14. What is the probability that X is either between 5 and 7, or between 8 and 12? Round to 2 decimal places.
Answers
For a continuous random variable like X, the probability of waiting exactly 6 minutes (or any specific time) is always 0, as there are infinitely many possible values within the distribution.
For the second part of your question, since X is uniformly distributed between 4 and 14, the probability of X being between two specific ranges can be calculated by finding the lengths of those ranges divided by the length of the overall distribution.
For the range of 5 to 7, the length is (7 - 5) = 2.
For the range of 8 to 12, the length is (12 - 8) = 4.
The total length of the distribution is (14 - 4) = 10.
So the probability of X being in either range is (2 + 4) / 10 = 6 / 10 = 0.6, or 60% when rounded to 2 decimal places.
For the first question, since the continuous random variable x is uniformly distributed from 2 to 10 minutes, the probability that a randomly chosen shopper will wait in line for exactly 6 minutes is:
P(x = 6) = 1/(10-2) = 1/8 = 0.125
Therefore, the probability that a randomly chosen shopper will wait in line for exactly 6 minutes is 0.125.
For the second question, we need to find the probability that X is either between 5 and 7, or between 8 and 12. Since X is uniformly distributed between 4 and 14, we can find the probabilities of each interval separately and then add them up.
P(5 ≤ X ≤ 7) = (7-5)/(14-4) = 2/10 = 0.2
P(8 ≤ X ≤ 12) = (12-8)/(14-4) = 4/10 = 0.4
Therefore, the probability that X is either between 5 and 7, or between 8 and 12 is:
P(5 ≤ X ≤ 7 or 8 ≤ X ≤ 12) = P(5 ≤ X ≤ 7) + P(8 ≤ X ≤ 12) = 0.2 + 0.4 = 0.6
Therefore, the probability that X is either between 5 and 7, or between 8 and 12 is 0.6.
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Related Questions
If x = 4, what is the value of 4x + 3?
Answers
Answer:
19
Step-by-step explanation:
4(4)+3=19
Put the following in order LEAST to GREATEST:
54%, 2/5, .45
a) 54%, 2/5, .45
b) 2/5, .45, 54%
c) 54%, .45, 2/5
d) .45, 2/5, 54%
Answers
Answer:
b) 2/5, .45, 54%
below are graphs of functions over the interval (-4,4). find the following for each function: The domain, the zeros ( the value of x where the value of the function is 0) and the intervals where the interval is positive and intervals where it is negative
Answers
From the graph, we get that:
The domain is (-4,4).The function has no zeros.The function is positive in the interval (-4, 0].The function is negative in the interval (0,4).------------------------------------
The domain of a function is the set that contains all the possible input values. In a graph, it is the values of the x-axis, that is, the horizontal axis.In this question, the values of x are in the interval of (-4,4) thus, the domain is (-4,4).The zeros are the values of x for which y = 0, that is, the values of x where the function crosses the horizontal axis. In this question, the function does not cross the horizontal axis, thus, it has no zeros.The function is positive when the graph is above the horizontal axis. In this question, it is in the interval (-4,0].The function is negative when the graph is below the horizontal axis. In this question, it is in the interval (0,4).A similar problem is given at https://brainly.com/question/24493729
Answer: No Zeros
Domain: -4<=x<=4
Positive: -4<=x<=0
Negative: 0<x<=4
Step-by-step explanation: The other person had a good explanation but the problem needed a different format.
A ball is dropped from the top of a
building. The expression 4.9x2 gives the distance in meters the ball
has fallen after x seconds. Write and simplify an expression that gives the
distance in meters the ball has fallen after x2 seconds. after x3 seconds.
Answers
Clear question is;
A ball is dropped from the top of a
building. The expression 4.9x² gives the distance in meters the ball
has fallen after x seconds. Write and simplify an expression that gives the
distance in meters the ball has fallen after x² seconds. after x³ seconds.
Answer:
A) Distance = 4.9x⁴
B) Distance = 4.9x^(6)
Step-by-step explanation:
We are given the expression 4.9x² which is the distance in meters the ball
has fallen after x seconds.
Thus,
A) after x² seconds, we have;
Distance = 4.9(x²)²
Distance = 4.9 * (x²) * (x²)
When we have to multiply 2 same numbers with the same power, the powers add up. Thus, we now have;
Distance = 4.9x⁴
B) after x³ seconds, we have;
Distance = 4.9(x³)²
Distance = 4.9 * (x³) * (x³)
When we have to multiply 2 same numbers with the same power, the powers add up. Thus, we now have;
Distance = 4.9x^(6)
I have 39 test to do and it takes me approximately 5 minutes to do one. How long will it take me to do all of them?
Answers
Answer:
3 hrs and 15 minutes :)
Step-by-step explanation:
We can solve this by multiplying :)
39 x 5 = 195 minutes
195/60 = 3 hrs and 15 minutes :)
Have an amazing day!!
Please rate and mark brainliest!!
Answer: 195 minutes or 3 hours and 15 mintues
Step-by-step explanation:
We will multiply the number of tests by the amount of time it takes to do each test.
39 total tests * 5 minutes = 195 minutes
195 minutes or 3 hours and 15 mintues
One of the familiar weather patterns in Jordan are derived from what is the Red Sea trough, seen both in the spring and the fall. a. What is this phenomenon and how does it occur? b. How does it manifest itself in terms of weather? c. What challenges does it pose in terms of weather forecasting? d. What hazards does it present?
Answers
a. The Red Sea trough refers to a dip in the upper-level height originating over the eastern Mediterranean moving southeastward, and deepening over the Red Sea.
b. This weather phenomenon manifests itself as it causes a sudden drop in temperatures, thunderstorms, and dust storms.
c. The Red Sea trough presents a challenge to weather forecasting as it is hard to predict when the trough will develop.
d. The Red Sea trough presents several hazards as causes heavy rainfall, strong winds, and a sudden drop in temperatures.
The Red Sea trough is one of the familiar weather patterns in Jordan. It is seen both in spring and fall.
a. The Red Sea trough is a dip in the upper-level height that originates over the eastern Mediterranean, advances southeastward, and deepens over the Red Sea. During the fall and spring seasons, this trough becomes more profound and generates a shallow low-pressure system over the Levant region, resulting in a northwesterly to northeasterly wind.
b. This weather phenomenon manifests itself in terms of weather in several ways. They are as follows:
It causes a sudden drop in temperatures and a strong wind that blows from the north or northeast.It also brings clouds, rain, and thunderstorms to Jordan. In addition, it causes dust storms and sandstorms, which often reduce visibility and disrupt travel and other activities.c. The Red Sea trough presents a significant challenge to weather forecasting. It is difficult to predict when the trough will develop and the magnitude of its impacts on weather. The weather forecasters struggle to estimate the movement of the trough, its depth, and intensity, and the amount of rain and wind it will produce. As a result, the meteorological department often issues warnings and alerts, but the severity and impact of the weather are not always accurately forecasted.
d. The Red Sea trough presents several hazards. They are as follows:
It causes heavy rainfall that results in flash floods, landslides, and inundation. The strong winds associated with the trough lead to damage to infrastructure and cause power outages, transportation disruption, and difficulties for outdoor activities. It also causes a sudden drop in temperatures that can result in hypothermia and other weather-related illnesses. The dust and sandstorms reduce visibility and air quality, which causes respiratory problems.Learn more about Pressure system:
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A combination of 3 erasers and 5 pencils cost $7.55. A combination of 6 erasers and 12 pencils cost $17.40. How much is each pencil?
Answers
Answer:
9.85
Step-by-step explanation:
I subtract 17.40 and 7.55 to get 9.85 they just wanted to know how much the pencil cost not erasers.
The cost of each pencil is $1.15.
What is a system of equation?A system of equations is used when there are two variables, and you are given two pieces of information about how those variables are related.
Given that, A combination of 3 erasers and 5 pencils cost $7.55. A combination of 6 erasers and 12 pencils cost $17.40.
Let e represents eraser and p represents a pencil.
Establishing the equations,
3e+5p = 7.55
6e+12p = 17.40
Solving by elimination, we get,
p = 1.15
Hence, The cost of each pencil is $1.15.
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Write the quadratic function f(x) = x2 + 8x + 3 in vertex form.
Answers
Choose the best estimate for the weight of a cantaloupe. Responses A 2 decigrams2 decigrams B 2 kilograms2 kilograms C 2 grams2 grams D 2 milligrams
Answers
The best estimate for the weight of a cantaloupe is 2 kilograms (B).
A decigram is 1/10th of a gram, which would be too small of weight for a cantaloupe. 2 grams (C) is also too small for a cantaloupe as it would only be the weight of a few small seeds. 2 milligrams (D) is an extremely small weight, only suitable for a single grain of salt or a tiny insect.
Therefore, 2 kilograms (B) is the most reasonable estimate for the weight of a cantaloupe as it falls within the typical range of cantaloupe weights.
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Complete Question:
Choose the best estimate for the weight of a cantaloupe. Responses
A 2 decigrams
B 2 kilograms
C 2 grams
D 2 milligrams
The simplified slope of item number 1 is:
a. 1
b. -1
c. 3/2
d. 1/2
Answers
The slope of the line passing through (1, 4) and (3, 2) is -1. Therefore, the simplified slope of item number 1 is -1,so the correct option is (b).
What is slope?The slope of a line, which measures how steep it is, is calculated by dividing the change in the y-axis (vertical direction) by the change in the x-axis (horizontal direction) between any two points on the line.
Now, we shall solve the question by two-point formula method:-
1. (1, 4) and (3,2)
Slope = (y2 - y1) / (x2 - x1) = (2 - 4) / (3 - 1) = -2/2 = -1
2. (2,5) and (4,-7)
Slope = (y2 - y1) / (x2 - x1) = (-7 - 5) / (4 - 2) = -12/2 = -6
Therefore, the slope of the line passing through (2,5) and (4,-7) is -6.
3. (-5, 3) and (2,7)
Slope = (y2 - y1) / (x2 - x1) = (7 - 3) / (2 - (-5)) = 4/7
Therefore, the slope of the line passing through (-5, 3) and (2,7) is 4/7.
4. (3,-4) and (-2, 8)
Slope = (y2 - y1) / (x2 - x1) = (8 - (-4)) / (-2 - 3) = 12/(-5) = -2.4
Therefore, the slope of the line passing through (3,-4) and (-2, 8) is -2.4.
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what is the range of the discrete function shown below?
Answers
The Range of the function is { 10,11,12,13} ,Option D is the correct answer.
What is a Function ?A function is a mathematical statement which creates a relationship between a dependent variable and an independent variable.
It always comes with a defined Domain and Range.
Domain is the possible input value to the function.
Range is the set of values that can be obtained from the function
The discrete function given is
G(x) = { (9,10) (10,11) (11,12) (12,13) }
All the possible input value is the x value and all the possible output value is y.
Therefore the Range of the function is { 10,11,12,13}
Option D is the correct answer.
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HELP DUE SOON!!!Elise says, "If you subtract 14 from my number and multiply the difference by - 4, the result is
- 100." What is Elise's number?
Elise's number is
Answers
Answer:
39
Step-by-step explanation:
If you subtract 14 from my number and multiply the difference by -4, you should get -100.
You need to setup the equation that is being given to you.
Subtract 14 from my number.
x - 14
Multiply the difference by -4
(x-14) * -4
You should get -100.
(x-14) * -4 = -100
Solve for x
(Elise's number is X, the missing number).
\(-4(x-14) = -100\\-4x+56 = -100\\-4x=-156\\x=39\)
Elise's number is 39.
1. Circle the following scenarios that are DEPENDENT events.
a) Flipping a coin three times.
b) Taking two pieces of candy out of a bag.
c) Picking four students to volunteer to read.
d) Hitting a red light three days in a row.
e) Spinning a wheel and getting a prize twice.
f) Getting four hearts in a row from a deck of cards.
Answers
Hitting a red light three days in a row
Using the polynomial remainder theoremP(x) = x^2-9x^3-5x^2-4x+5 divided by x + 3
Answers
The given polynomial is
x^2 - 9x^3 - 5x^2 - 4x + 5
By simplifying it, it becomes
- 9x^3 + x^2 - 5x^2 - 4x + 5
- 9x^3 - 4x^2 - 4x + 5
We want to divide it by x + 3. To use the remainder theorem, we would substitute x = - 3 into the polynomial to find the remainder, r. We have
r = p(- 3) = -9(-3)^3 - 4(-3)^2 - 4(-3) + 5
243 - 36 + 12 + 5
r = 224
Thus, the remainder when P(x) = x^2-9x^3-5x^2-4x+5 is divided by x + 3 is 224
P(-3) = 224
-
1. Let the distribution of X be the normal distribution N (μ, σ2) and let Y = aX + b. Prove that Y is distributed as N (aμ + b, a2σ2).
2. Let X and Y be two independent random variables with E|X| < [infinity], E|Y| < [infinity] and E|XY| < [infinity]. Prove that E[XY] = E[X]E[Y].
Answers
1 Y is distributed as N(aμ + b, a^2σ^2), as desired.
2 We have shown that under these conditions, E[XY] = E[X]E[Y].
To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.
First, let's find the mean of Y:
E(Y) = E(aX + b) = aE(X) + b = aμ + b
Next, let's find the variance of Y:
Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2
Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.
We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:
E[XY] = ∫∫ xy f(x,y) dxdy
where f(x,y) is the joint probability density function of X and Y.
Then, we can use the fact that X and Y are independent to simplify the expression:
E[XY] = ∫∫ xy f(x) f(y) dxdy
= ∫ x f(x) dx ∫ y f(y) dy
= E[X]E[Y]
where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.
Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].
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Jade can travel 42 miles in 4 hours. Please calculate Jade's rate of speed. (round to 2 decimal places)
Answers
Answer:
10.50 Miles per hour
Step-by-step explanation:
42/4 = 10.50 easy
Several people show up at a local hospital with the symptoms of food poisoning. They are all interviewed about what they have recently eaten, and a common source of exposure is found: a nearby restaurant. Samples are taken from foods at the restaurant to be tested for pathogens causing the outbreak of illness. This scenario describes
Answers
This scenario describes a foodborne illness outbreak investigation, where several individuals with similar symptoms of food poisoning have been identified and traced back to a nearby restaurant.
In this situation, the local hospital has encountered multiple cases of individuals exhibiting symptoms consistent with food poisoning. Through interviews, it is discovered that all of them have recently dined at a nearby restaurant, indicating a potential common source of exposure. To further investigate and identify the cause of the illness outbreak, samples from the restaurant's food are collected.
These samples will undergo laboratory testing to check for the presence of pathogens, such as bacteria or viruses, that may be responsible for the foodborne illness. By analyzing the test results, health authorities can pinpoint the specific pathogen and take appropriate measures to prevent further spread and ensure the safety of the community.
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if the total elapsed time in clock hours for corrective maintenance is 1200 hours and there are 60 maintenance actions completed in mean time to repair (MTTR)
Answers
The mean time to repair (MTTR) is 20 hours.
What is MTTR?
MTTR (mean time to respond) is the average time it takes to recover from a product or system failure from the time when you are first alerted to that failure.Mean time to repair (MTTR) is the average time taken to repair an item.Mean time to repair = Total hours spent on corrective maintenance / Number of maintenance actions completed
Mean time to repair = 1,200/60
Mean time to repair = 20 hours
Therefore, the mean time to repair is 20 hours.
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Jack and Jill order a delicious pizza. Jack ate 1/2 of the pizza. Jill ate some pizza, too.
1/6 of the pizza was left. How much pizza did Jill eat?
Answers
Using fractional operation, since Jack ate ¹/₂ of the delicious pizza with ¹/₆ left, Jill ate ¹/₃ of it.
What is a fractional operation?The fractional operations involve mathematical operations using fractions, which are parts or portions of the whole value or quantity.
Some of the mathematical operations include addition, subtraction, multiplication, and division.
The fraction ate by Jack = ¹/₂
The fraction of the pizza left over after Jack and Jill have eaten = ¹/₆
The fraction or portion that Jill ate = ¹/₃ [1 - (¹/₂ + ¹/₆)]
Thus, we can conclude that Jill ate ¹/₃ of the delicious pizza.
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Which window with the following dimensions is too small to allow a 48-inch piece of glass to fit through it?
28 x 45 inches
36 x 27 inches
40 x 40 inches
40 × 42 inches
Answers
The dimensions 36 x 27 inches are too small to allow a 48-inch piece of glass to fit through it.
What is meant by dimensions?An object's dimension is a topological measure of the size of its covering properties. It is the number of coordinates required to specify a point on the object.A dimension is a measurement that includes things like length, width, and height. When you talk about an object's or place's dimensions, you're referring to its size and proportions. Dimensions are the powers to which basic units or quantities are raised in order to represent a specific physical quantity. <br> e.g., : In the gravitational constant formula, the length, mass, and time dimensions are 3, -1, and -2, respectively. The dimensional formula is defined as the physical quantity expressed in terms of its basic unit with proper dimensions. Dimensional force, for example. F = [M L T-2] It's because the Force unit is Newton, or kg*m/s2.To learn more about dimensions, refer to:
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Thank u to da person who is willing to help me will get this Brainliest! :3
Answers
3x - 6 + 5x + 4
8x - 2
2) 4-2x - 14 - 3
-14 - 2x
Answer:
1) x=0.25, or 1/4, 2) 6.5
Step-by-step explanation:
1)
3(x-2) + 5x+4
3x - 6 + 5x + 4
8x - 6 + 4
8x + 2
/2 /2
x= 0.25
2)
4 - 2(x+7) - 3
4 - 2x - 14 + 3
4 - 2x - 17
-2x - 13
/-2 /-2
x = 6.5
Plz help me with this math problem
Answers
Answer:
leg 1 is on 6 see look at the dot thats on x and leg 1 on y is 1 so 6/1 then for number 2 9/5
14.875/1.5 step by step
Answers
Answer:
9.916...
Step-by-step explanation: (The "6" is repeating)
Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
This gives us a mixed number-fraction: 9 and 11/12.
If we then turn this into a simplified fraction, then it becomes 119/12. Turn that into a decimal by dividing the numerator by the denominator.
This gives us our answer of 9.916...!!! Hope that helps!
Distribute: 2x ( 3 + 8x) *
Answers
Answer:16x^2+6x
Step-by-step explanation:
What is the value of b on the number line below? A number line from 0 to 1 showing fourths. There is a dot labeled b that is halfway between one half and three fourths.
Answers
Answer:
B is 5/8
Step-by-step explanation:
Note: 4/8 = 1/2 and 6/8 = 3/4
you take a random of twenty ksu students and find that 16 of them have jobs. what is the probability that you would find exactly 16 out of twenty have jobs if the .50 conjectured by the professor was correct? what is the probability that you would find 16 or more have jobs? what will you say to the professor?
Answers
The probability of exactly 16 students having jobs in the sample is 0.204 and the probability of 16 or more students having jobs in the sample is 0.334.
Let X be the number of KSU students with jobs in a random sample of 20 students. Since each student in the sample can be either employed or not employed, X follows a binomial distribution with parameters n = 20 (the sample size) and p = 0.50 (the probability of a student having a job).
To find the probability of exactly 16 students having jobs in the sample, we can use the binomial probability mass function
P(X = 16) = (20 choose 16) * 0.5^16 * 0.5^(20-16) = 0.204
To find the probability of 16 or more students having jobs in the sample, we can use the cumulative distribution function
P(X ≥ 16) = 1 - P(X < 16) = 1 - ∑(i=0 to 15) (20 choose i) * 0.5^i * 0.5^(20-i) = 0.334
Based on the sample data, it appears that the proportion of KSU students with jobs is higher than the professor's conjectured value of 0.50. However, we cannot conclusively reject the professor's conjecture based on a single sample of 20 students.
We would need to conduct a hypothesis test with appropriate statistical significance level to determine if the difference between the sample proportion and the conjectured value is statistically significant or not.
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Identify next three numbers in this sequence: 3, 12, 6, 24, 18, … 27, 13.5, 22.5 72, 66, 264 72, 36, 144 27, 21, 30
Answers
Answer:
its 72, 36, 144
Step-by-step explanation:
yes it is!!!
Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.
Answers
Answer:
x = 16
y = 8√3
Step-by-step explanation:
This is a special right triangle with angle measures of 30° 60° 90° and side lengths x, x√3, and 2x
The side length that sees angle measure of 30° is equal to x
and the side length that sees 60° is equal to x√3 and the side length that sees 90° is equal to 2x
(order of operations mc) simplify: the sum of 5.5 and 4.3 all divided by the quantity 4 end quantity times the quantity 2 minus 6 end quantity squared plus 5. 44.2 −4.8 −14.6 −34.2
Answers
The simplified value of the expression is 51.45. To simplify the expression, we need to follow the order of operations, which is also known as PEMDAS.
This stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
1. Start by evaluating the expression inside the parentheses: 2 - 6 = -4.
2. Next, square the result: \((-4)^2\)= 16.
3. Then, add 5 to the result: 16 + 5 = 21.
4. Now, we can divide the sum of 5.5 and 4.3 by 4: (5.5 + 4.3)/4 = 9.8/4 = 2.45.
5. Finally, multiply the result from step 4 by the result from step 3: 2.45 * 21 = 51.45.
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The given expression: (5.5 + 4.3) / (4 * (2 - 6)^2) + 5, is simplified using the BODMAS rule, which states that mathematical operations should be performed in the order of Brackets, Orders or Indices, Division and Multiplication, and Addition and Subtraction. Following this rule, the simplified answer to the expression is (9.8 / 64) + 5.
Explanation:In Mathematics, one of the fundamental principles we operate on is the order of operations, also known as
BODMAS/BIDMAS
(Brackets, Orders or Indices, Division and Multiplication, and Addition and Subtraction). Using this principle, the given expression: (5.5 + 4.3) / (4 * (2 - 6)^2) + 5, can be simplified step by step as follows:
Work on the expressions in brackets first: (5.5 + 4.3) becomes 9.8, and (2 - 6) becomes -4. Next, square the result of the operation in the bracket, which was -4: This becomes 16. Now work on the multiplication: 4 * 16, which is 64. Then divide 9.8 by 64. Finally, add 5 to the result of the division.
So, the simplified answer to the expression is (9.8 / 64) + 5.
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Araceli recorded the height (in centimeters) of a pea plant over a 10-day
period for a science experiment. Which equation is the best model of the
data?
30 pints please help
Answers
Answer:B. y=0.5x+0.3
Step-by-step explanation:a. p. e. x.
The slope of the points is closer to 0.5 thus y = 0.5x + 1.2 will be the best approximation thus option (B) is correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
As per the given points,
Let's take two-point (1,1) and (2,1.5)
The slope associated with the above points will be as,
(1.5 - 1)/(2 - 1) = 0.5
Thus, the line will be y = 0.5x + 0.3
Hence "The slope of the points is closer to 0.5 thus y = 0.5x + 1.2 will be the best approximation".
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