A fresh food distributor receives orders from 100 customers daily. Assume that the quantities ordered by customers, in kg, are independent continuous random variables uniformly distributed over the interval (0, 9). Assuming that the distributor only has the capacity to ship 477 kg of products daily, calculate the probability that all orders are fulfilled on a day chosen at random. Indicate the result to at least four decimal places.
Answers
The probability that all orders are fulfilled on a day chosen at random is approximately 1. Answer: 1.0000 (rounded off to at least four decimal places).
The quantities ordered by customers are independent continuous random variables, and they are uniformly distributed over the interval (0, 9).
The fresh food distributor only has the capacity to ship 477 kg of products daily, and the distributor receives orders from 100 customers daily.
The probability that all orders are fulfilled on a day chosen at random is given by;P(all orders fulfilled) = P(X1 + X2 + ... + X100 < 477)
where X is the quantity ordered by each customer. Since X is a continuous random variable, we can use the probability density function of a uniform distribution to calculate the probability density function of X as;f(x) = 1/9, 0 < x < 9
Hence, the probability that all orders are fulfilled on a day chosen at random is given by;
P(all orders fulfilled) = P(X1 + X2 + ... + X100 < 477)= P[(X1/9) + (X2/9) + ... + (X100/9) < (477/9)]= P[U < (53 + 1/3)], where U ~ Uniform(0, 1)
Now, using the central limit theorem, we can approximate the distribution of U by a normal distribution with mean μ = 1/2 and variance σ^2 = 1/12 such that;Z = (U - μ) / σ ~ N(0, 1)
Hence, P[U < (53 + 1/3)] = P[Z < (53 + 1/3 - μ) / σ]= P[Z < (53 + 1/3 - 1/2) / sqrt(1/12)]≈ P[Z < 9.6067]≈ 1
Thus, the probability that all orders are fulfilled on a day chosen at random is approximately 1. Answer: 1.0000 (rounded off to at least four decimal places).
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Related Questions
vaccinations are intended to prevent illness. suppose a flu vaccine is determined to be effective for 57% of patients administered the shot. a random sample of 65 people will be selected from the population. (a) what is the population proportion of success in the above scenario? .57 correct: your answer is correct. (b) calculate the mean of the sampling distribution of the sample proportion of people for whom the shot was effective. (c) calculate the standard deviation of the sampling distribution of the sample proportion of people for whom the shot was effective. (round your answer to three decimal places.)
Answers
(a) The population proportion of success in this scenario is 0.57 or 57%.
(b) To calculate the mean of the sampling distribution of the sample proportion, we use the formula: mean = population proportion = 0.57. Therefore, the mean of the sampling distribution is 0.57.
(c) To calculate the standard deviation of the sampling distribution of the sample proportion, we use the formula: standard deviation = sqrt((population proportion * (1 - population proportion)) / sample size). Plugging in the values, we get: standard deviation = sqrt((0.57 * 0.43) / 65) = 0.079
Therefore, the standard deviation of the sampling distribution of the sample proportion of people for whom the shot was effective is 0.079 (rounded to three decimal places).
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solve for y
7y+16=3y
Answers
Answer:7y7=3y-16
Step-by-step explanation:
Solve for
Subtract from both sides
Answer: -4
Step-by-step explanation: Tell me if it's correct. :)
3Kim eats 3 pounds of rice in one week, which is of the total rice in the full rice bag. Howmany pounds of rice are in the full rice bag
Answers
Step 1: Calculate the percentage accuracy for both Round 1 and Round 2
For Round 1, the percentage accuracy will be
\(\begin{gathered} \text{percentage accuracy=}\frac{Number\text{ of targetS }}{Number\text{ of throws}}\times100\text{ \%} \\ \text{percentage accuracy=}\frac{9}{12}\times100\text{ \%} \\ \text{percentage accuracy= }\frac{900}{12}\text{ \%} \\ \text{Percentage accuracy=75 \%} \end{gathered}\)For round 1, the percentage accuracy is 75%
For Round 2,the percentage accuracy will be
\(\begin{gathered} \text{Percentage accuracy=}\frac{\text{Number of targets}}{Number\text{ of throws}}\times100\text{ \%} \\ \text{percentage accuracy=}\frac{16}{20}\times100\text{ \%} \\ \text{percentage accuracy=}\frac{1600}{20}\text{ \%} \\ \text{percentage accuracy=80 \%} \end{gathered}\)For Round 2, the percentage accuracy is 80%
Therefore, with the calculation above we can conclude that on the comparison,
Sasha threw more accurately in Round 2 because she hit the target on a higher percentage of her throws.
Hence,
The correct answer is OPTION D
Answer:
Sasha threw more accurately in Round 2 because she hit the target on a higher percentage of her throws.
Step-by-step explanation:
if an angle bisector in a triangle is its altitude, prove that the triangle is isosceles
Answers
Prove that a triangle AC is isosceles, if: (i) altitude AD bisects angle ∠ BAC, or (ii) bisector of angle BAC is perpendicular to base BC. Solution In ΔABC, let the altitude AD bisects ∠BAC. Then we have to prove that the ΔABC is isosceles.
GIVING BRAINLIEST. LOTS OF POINTS. Describe a real-life situation that can be modeled by the equation 11x + 5 = 8x + 23
Answers
Answer:
See below.
Step-by-step explanation:
Jane and John are each hiking a trail in the city. Jane is on her bike, and John is jogging.
At noon, Jane is at the 5 mile mark and rides at 11 miles per hour.
Also at noon, John is at the 23 mile mark and jogs at 8 miles per hour.
x is the number of hours after noon.
Will Jane catch John? After how many hours?
please help (15 points +brainliest)
Answers
Answer: The range values would be 9.5, 13.5, 4.5, 6, 6.3.
Step-by-step explanation: You can do 2 things here, plug in the domain values (for example -3,-1, etc.) into the equation of the function, solve for that and you would get the range for the given domain, or you can input this equation in a calculator, and see what the y values are, for the given x values.
Marilyn selects a piece of candy at random from a
jar that contains four peppermint, five cherry, three
butterscotch, and two lemon candies. What is the
probability that the candy she selects is not a cherry
candy?
(WILL MARK BRAINLIEST)
Answers
Answer: 9/14
Step-by-step explanation: 4+3+2/4+5+3+2 = 9/14
Please help I need the answers asap
Answers
To get rid of a fraction in an equation, you need to multiply both sides of the equation by the reciprocal of the fraction.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
To get rid of a fraction in an equation, you need to multiply both sides of the equation by the reciprocal of the fraction.
For example, if you have the equation:
1/3x = 4
To get rid of the fraction 1/3, you can multiply both sides of the equation by its reciprocal, which is 3/1 (or just 3):
(3/1) * (1/3)x = (3/1) * 4
Simplifying, we get:
x = 12
So the solution to the original equation is x = 12.
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−2+(−7)? help me what is the answer please help.
Answers
Answer:
-9
Step-by-step explanation:
-2 + (-7) = -2 - 7-2 - 7 = -9I hope this helps!
Answer:
-9
Step-by-step explanation:
Please make me Brainliest
Do you know anything about functions
Answers
1)
Take into account that the equation of a line can be written as follow:
y = mx + b
where m is the slope and b the y-intercept.
the slope can be calculated as follow:
m=(y2 -y1)/(x2 - x1)
where (x1,y1) and (x2,y2)
For the given graph, consider the points (0,3) and (4,4)
Compute the Taylor polynomial T5(x) and use the Error Bound to find the maximum possible size of the error. f(x) cos(x), a = 0, x = 0.1
Answers
The Taylor polynomial T₅(x) is 0.99500416 and by use the Error Bound the maximum possible size of the error is 49943.1 × 10⁻⁷.
What is Taylor Series?
The Taylor series or Taylor expansion of a function in mathematics is the infinite sum of terms represented in terms of the function's derivatives at one particular point. The function and the sum of its Taylor series are roughly equivalent for the majority of typical functions at this point.
Taylor series or Taylor expansion:
Infinity ∑ (n = 0) fⁿ(a)/n! (x - a)ⁿ
Where,
n! = factorial of n
a = real or complex number
fⁿ(a) = nth derivative of function f evaluated at the point a.
As given function is,
f(x) = cosx, a = 0, x = 0.1
Taylor polynomial of degree 'n' for f(x) center a,
Tₙ(x) = f(a) + f'(a)(x - a) + f''(a)/2 (x - a)² + f'''(a)/3 (x - a)³ + ......+ fⁿ⁻¹(a)/(n - 1)! (x - a)ⁿ⁻¹ + fⁿ(a)/n! (x - a)ⁿ
Evaluate values as follows:
f(x) = cosx ⇒ f(0) = 1
f'(x) = -sinx ⇒ f'(0) = 0
f''(x) = -cosx ⇒ f''(0) = -1
f'''(x) = sinx ⇒ f'''(0) = 0
f⁴(x) = cosx ⇒ f⁴(0) = 1
f⁵(x) = -sinx ⇒ f⁵(0) = 0
Substitute obtained values in Taylor series,
T₅(x) = 1 + (0) (x - 0) + (-1)/2 (x - 0)² + 0 + 1/24(x - 0)⁴ + 0
T₅(x) = 1 -1/2x² + 1/24x⁴
At x = 0.1
T₅(0.1) = 1 -1/2(0.1)² + 1/24(0.1)⁴
T₅(0.1) = 1 - 0.005 + 4.16 × 10⁻⁶
T₅(0.1) = 0.99500416
Hence, the Taylor polynomial T₅(x) is 0.99500416.
Evaluate the maximum possible size of the error:
cos(0.1) = 0.99999847
T₅(0.1) = 0.99500416
Icos(0.1) - T₅(0.1)I = 0.99999847 - 0.99500416
Icos(0.1) - T₅(0.1)I = 0.00499431
Icos(0.1) - T₅(0.1)I = 49943.1 × 10⁻⁷.
Hence, the Error Bound the maximum possible size of the error is 49943.1 × 10⁻⁷.
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Austin mowed 7 lawns in 4 hours at the rate how long will it take him to mow 21 lawns
Answers
7 lawns / 4 hours = 1.75 hours per lawn.
1.75 hours per lawn x 21 lawns = 36.75 hours total ( 36 hours and 45 minutes)
Please help..... ASAP lots of points (just two questions)
Answers
Answer:
1. 3 3/4 in
2. 4 1/4
Step-by-step explanation:
look at graph
if a cup has a diameter of 8 centimeters and a height of 12 centimeters , how much juice will the cup hold.
Answers
The amount of juice the cup can hold given that the cup has diameter of 8 centimeters and a height of 12 centimeters is 602.88 cm³
How do i know the amount of juice the cup can hold?To know the amount of juice the cup can hold, we shall obtain the volume of the cup.
We shall use the formula for obtaining volume of cylinder to obtain the volume of the cup. Details below:
Diameter of cup = 8 cmRadius of cup (r) = diameter / 2 = 8 / 2 = 4 cmHeight of cup (h) = 12 cmVolume of cup (V) =?Volume = πr²h
Volume = 3.14 × 4² × 12
Volume = 3.14 × 16 × 12
Volume = 602.88 cm³
Thus, we can conclude from the above calculation that the amount of juice the cup can hold is 602.88 cm³
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What is x? 4^x= 1/64
Answers
Answer: x= -3
Step-by-step explanation:
You would use the formulas b^x=y <----> log∨b(y)=x
b=4
x=?
y=1/64
Plug in:
log(∨4)(1/64)= x
then you use...
log(y)/log(b)=x
log(1/64)/log(4)
plug into calculator and you would get -3 for x
hope that helps :)
there are two important properties of probabilities. 1) individual probabilities will always have values between and . 2) the sum of the probabilities of all individual outcomes must equal to .
Answers
1.) Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.
2.) The sum of probabilities of all possible outcomes is equal to 1.
1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.
A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.
Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.
2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.
Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.
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A student’s performance in Test 1 and Test 2 for all the 6 subjects has to be compared graphically for the current academic year. Which form of graph would be appropriate in this case? *
Bar Graph
Histogram
Double Bar Graph
Answers
Answer:
Double Bar Graph
Step-by-step explanation:
A double bar graph would be suitable to show the performance of test 1 and 2 in all 6 subjects
Kenton compared gas mileage for three cars. Car A—340 miles for 17 gallons Car B—361 miles for 19 gallons Car C—450 miles for 18 gallons Which car has the best rate of miles per gallon?
Answers
The car has the best rate of miles per gallon is A. Car A has the best rate at 32 miles per gallon.
What is the ratio ?
ratio can be defined as the given value divided by total value.
It should be noted that Car A has 512 miles for 16 gallons. The miles per gallon will be:
= 512 / 16
= 32 mile per gallon
It should be noted that Car B has 360 miles for 20 gallons. The miles per gallon will be:
= 360 / 20
= 18 miles per gallon
It should be noted that Car C has 486 miles for 18 gallons. The miles per gallon will be:
= 486 / 18
= 27 miler per gallon
Therefore, the car has the best rate of miles per gallon is Car A has the best rate at 32 miles per gallon.
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What is the integrated rate law for a 1st order reaction?
Answers
Expiation: the half-life of a first-order reaction is independent of concentration, and this equation has the form y=mx + b so a plot of the natural log of [A] as a function of time yields a straight line
Source: khanacadamey.org
Hope this helps!
Please write word answer that I can use I will mark brainliest
Answers
Answer: Kevin drew an obtuse scalene triangle.
A student committee is organizing a school dance as a fundraiser. The function f ( x ) = 5 x − 320 represents the total amount of funds raised based on the number of tickets sold, x , minus the cost of decorations
Answers
I assume you want this explained
Answer and explanation:
If the function f ( x ) = 5 x − 320 represents the total amount of funds raised based on the number of tickets sold, x , minus the cost of decorations then x number of tickets is an independent variable here that will determine the total amount of funds raised y(dependent variable)
The y intercept is -320 and the slope is 5
If for example the number of tickets sold = 100 tickets
Total amount of funds using the function :
f(100)= 5×100-320
=500-320
= $180
Answer:
The slope of the function is 5, and it represents the price of each ticket .
Step-by-step explanation:
Is - 7/8 or - 1/15 larger
Answers
Answer:
-1/15 because it is closer to zero on the negative half of a number line.
Answer:-1/15
Step-by-step explanation:When it comes to negatives sign the smaller number with the negative sign is always the greater number
Which equation represents a line that is parallel to
the line y = - 4x +5?
(A) y=-4x +3
(B) y=-x+3
(C) y=-=x+5
(D) y = 4x + 5
Answers
Answer:
A. y = -4x + 3
Step-by-step explanation:
Parallel lines have the same slope, but will have a different y-intercept.
In the equation y = -4x + 5, -4 is the slope.
This means a line that is parallel to this one will also have a slope of -4.
So, this means that A is the correct answer, because it has a slope of -4.
y = -4x + 3 denotes a line that is parallel to y = - 4x +5. Parallel lines are two lines in the same plane that are equal in length and never intersect.
How can a line that is parallel to a line be found?By comparing the slopes of two lines, we can determine whether they are parallel. When two lines have the same slope but different y-intercepts, they are said to be parallel.The lines are not parallel if the slopes differ. axes that are parallel We can use their equations to compare the slopes of two lines to see if they are parallel. If the slopes are the same but the y-intercepts are different, the lines are parallel. If the slopes differ, the lines are not parallel. m is the slope in the generic linear equation y = mx + b.Therefore,
Points of axis interception y = -4x + 5
-4x + 5 : m = -4
Same as,
y = -4x + 3
Simplifying the above equation, then we get
-4x + 3 : m = -4
Hence, y = -4x + 3 denotes a line that is parallel to y = - 4x +5.
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12_15=-3 what will be in the blanck addition,subtracting,multiply,divide.
Answers
Answer:
Subtraction
Step-by-step explanation:
Hello!
We can check by using each operation in the blank space.
If we go through the options:
Multiplying will give us 12 * 15 = 180Adding will give us 12 + 15 = 27Dividing will give us 12/15 = 0.8Subtracting will give us 12 - 15 = -3The correct option is subtracting.
PLEASE I NEED HELP!!
Answers
because 22.75 times 4 is 91
Answer:
by 91 dollars
Step-by-step explanation:
22.75
4
----------
91 0 0
what is the distance between (12,12) (-12,-12)
Answers
Answer:
\(24\sqrt{2}\) or 33.94112
Step-by-step explanation:
Use the distance formula to determine the distance between the two points.
\(d = \sqrt{(x_{2} -x_{1})^{2} + (y_{2} - x_{1})^{2} }\)
d = distance
\((x_{1}, y_{1})\) = coordinates of the first point
\((x_{2}, y_{2})\) = coordinates of the second point
Evaluate |-15| + |-6|.
Answers
Answer:
21
Step-by-step explanation:
The absolute value of an expression is its distance from 0.
For example, take the number -5:
<-------|------------------|------------->
-5 0
It is 5 units to the left of zero, so its absolute value is 5, NOT -5 because distance is always positive, no matter the direction.
To evaluate the given expression, first find each absolute value:
\(|-15| = 15, \, \, \, \, \, \, |-6| = 6\)
Then, simplify:
\(|-15| + |-6| \\ =15 + 6 \\= 21\)
So, the evaluated expression is 21.
How do you find the horizontal and vertical asymptote of a curve?
Answers
Answer: search it up
Step-by-step explanation:
Question 6 of 10
The product of two rational numbers:
A is a rational number.
B. cannot be determined without more information.
O c. is an irrational number.
D. is undefined.
Answers
Answer:
A. is a rational number.
Step-by-step explanation:
You want to know whether a product of rational numbers is rational.
ProductYou know that the product of fractions is ...
\(\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{ac}{bd}\)
where a, b, c, d are integers.
A rational number can always be expressed as the ratio of two integers. The product of any two integers is an integer, so the product of any two rational numbers is rational.
Solve for m 3/5m > -12 help I’ll give 30 points
Answers
Answer:
m > -20
Step-by-step explanation:
Multiply the 5 on both sides. Now you have 3m > -60. Divide both sides by 3. Now you have m > -20.
Voila