Answers
Answer:
rational no.
Step-by-step explanation:
4/7n-1/3
n=-1/3×7/4
n= -7/12
because it is in the form of p/q where q is not equals to 0
Related Questions
assuming that the requirements for this inference procedure have been met, what does this interval mean? there is a 99% chance that the mean price of all such road bikes is between the lower and upper bounds. there is a 99% chance that the interval contains the mean price of all such road bikes. the sample mean price will fall in this interval in 99% of samples. the prices of 99% of all used road bikes fall within this interval.
Answers
The correct interpretation of the interval would be: "There is a 99% chance that the interval contains the true population mean price of all such road bikes."
Option 1 ("There is a 99% chance that the mean price of all such road bikes is between the lower and upper bounds") is incorrect because the true population mean price is either within the interval or outside the interval. It either is or it isn't; there is no probability involved.
Option 2 ("There is a 99% chance that the interval contains the mean price of all such road bikes") is closer to the correct interpretation, but it could be interpreted as implying that the sample mean price is somehow the same as the population mean price, which is not necessarily true. The interval provides a range of plausible values for the population mean price, not a single value.
Option 3 ("The sample mean price will fall in this interval in 99% of samples") is also incorrect because it refers to the sample mean, which is a specific value that was observed in the sample, rather than the population mean, which is the parameter of interest.
Option 4 ("The prices of 99% of all used road bikes fall within this interval") is incorrect because the interval is not about the prices of individual bikes, but rather about the population mean price of all such road bikes.
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scores on a university exam are normally distributed with a mean of 78 and a standard deviation of 8. using the 68-95-99.7 rule, what percentage of students score above 86?
Answers
Approximately 32% of students scored above 86 on the university exam.
To determine the percentage of students who score above 86, we can use the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule.
According to this rule, in a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Given that the mean is 78 and the standard deviation is 8, we can calculate the z-score for 86 using the formula:
z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
z = (86 - 78) / 8 = 1
Since 86 is one standard deviation above the mean, we know that approximately 68% of students scored below 86. Therefore, the percentage of students who score above 86 can be estimated as 100% - 68% = 32%.
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The length of three sides of a triangle are 3x+1/2 ,2x+1/4 , and x +1/2 .the perimeter of the triangle is
Answers
Answer:
Step-by-step explanation:
Just add the three sides P = side1 + side2 + side3
Don't let the 'x' terms confuse you, they are just numbers times 'x'
P = 3x+1/2 + 2x+1/4 + x+1/2
= 6x + 5/4
P = 6x + 1&1/4
2. Use the rate of change from the table to determine
if the function is linear.
X
A. Yes - the function is linear
B. No - the function is not
linear
y
7
3
0
1
2.
1
3
7
3
A
B
Back
Answers
Answer:
B
Step-by-step explanation:
because 7 it can not divided into two so we simply say that the function is not a linear
if a short-day (long-night) plant flowers, you know that it received if a short-day (long-night) plant flowers, you know that it received more consecutive hours of darkness than its critical period. fewer consecutive hours of darkness than its critical period. fewer consecutive hours of light than its critical period. more consecutive hours of light than its critical period.
Answers
If a short-day (long-night) plant flowers, you know that it received more consecutive hours of darkness than its critical period.
This is because short-day plants (also known as long-night plants) require a certain period of uninterrupted darkness (usually around 12-16 hours) to trigger flowering. If the plant receives more hours of darkness than its critical period, it will flower.
If it receives fewer hours of darkness than its critical period, it will not flower. Similarly, long-day (short-night) plants require a certain period of uninterrupted light to trigger flowering. If they receive more hours of light than their critical period, they will flower, but if they receive fewer hours of light than their critical period, they will not flower.
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Television networks rely on surveys to determine how many people watch their programs. In a survey of 3,000
randomly selected households, 480 of the households watched the same game show that was airing on Saturday
night only. If there are 105 million households in the United States, about how many households watched the same
game shown?
Oa.) 14,000,000 households
Ob.) 17,000,000 households
Oc.) 16,800,000 households
Od.) 15,000,000 households
Answers
Answer:
C
Step-by-step explanation:
\(\frac{480}{3000}\) x 105,000,000 = 16,800,000
Write the slope-intercept form of the equation of a line with a slope of −58 that passes through the point (−14,6).
Answers
6 = -58(-14) + b
6 = 812 + b
b = -806
Y = -58x - 806
Answer:58x=-2
Step-by-step explanation:
A triangle has side lengths of 18 cm, 80 cm, and 81 cm. Classify it as acute, obtuse, or right.obtuserightacute
Answers
The triangle is an οbtuse triangle.
What is a triangle?Tο determine if the triangle is acute, οbtuse, οr right, we need tο check if it satisfies the Pythagοrean theοrem. Accοrding tο the Pythagοrean theοrem, in a right triangle, the sum οf the squares οf the lengths οf the legs (the shοrter sides) is equal tο the square οf the length οf the hypοtenuse (the lοngest side). Sο, if the sum οf the squares οf the twο shοrter sides is equal tο the square οf the lοngest side, then the triangle is a right triangle.
Let's calculate the squares οf the three sides:
The square οf the first side (18 cm) is 324.
The square οf the secοnd side (80 cm) is 6400.
The square οf the third side (81 cm) is 6561.
Nοw, we need tο determine if the sum οf the squares οf the twο shοrter sides is greater than οr less than the square οf the lοngest side. Sο, we have:
324 + 6400 = 6724
Since 6724 is less than 6561, the triangle dοes nοt satisfy the Pythagοrean theοrem and it is nοt a right triangle. Therefοre, the triangle is either an acute οr οbtuse triangle.
Tο determine if the triangle is acute οr οbtuse, we need tο find the largest angle οf the triangle. We can use the Law οf Cοsines tο find the largest angle οf the triangle, which is οppοsite the lοngest side. The Law οf Cοsines states that in any triangle:
\(c^2 = a^2 + b^2\) - 2ab cοs(C)
where a, b, and c are the lengths οf the sides οf the triangle, and C is the angle οppοsite the side c.
In οur case, a = 18 cm, b = 80 cm, and c = 81 cm. Sο, we have:
\(81^2 = 18^2 + 80^2 - 2(18)(80) cos(C)\)
6561 = 324 + 6400 - 2880 cοs(C)
Nοw, we can sοlve fοr cοs(C):
cοs(C) = (6400 + 324 - 6561) / (2(18)(80))
cοs(C) = -0.2216
Since cοsine is negative, the angle C is οbtuse.
Therefοre, the triangle is an οbtuse triangle.
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You want to know the classification of a triangle with side lengths 18 cm, 80 cm, and 81 cm. A triangle can be classified by looking at the measure of its largest angle. The classification of the triangle is the same as the classification of that angle: obtuse if > 90°, right if = 90°, and acute if < 90°.
Largest angleThe largest angle is always opposite the longest side. In a triangle with angles A, B, C and their opposite sides a, b, c, we can call the largest angle C. Its measure can be computed using the Law of Cosines, which tells you ...
C = arccos((a² +b² -c²) / (2ab))
C = arccos((18² + 80² - 81²) / (2×18×80)) = arccos(163/2880) ≈ 86.8°
The largest angle is less than 90°, so the triangle is an acute triangle.
Which fraction has a terminating decimal as its decimal expansion?
A. 1/3
B. 1/5
C. 1/7
D. 1/9
Answers
Answer:
B
Step-by-step explanation:
1/5=0.2
Answer:
B. 1/5
Step-by-step explanation:
A terminating decimal, true to its name, is a decimal that has an end.
So, we need to figure out which one has an end.
1/3 is a pretty famous non-terminating decimal, 0.333333333333333333333 etc, so A is not our answer
1/5 works! 1/5 is 0.2 so B is our answer
1/7 is 0.142857 etc etc so C is not our answer
1/9 is another slightly famous non-terminating decimal, 0.1111111111111111 (2/9 is 0.222 etc, 3/9 is 0.33333 etc, and it goes up to 9/9 which is 1!) so D is not our answer
Geometry question who can help so it ?
Answers
Answer:
Step-by-step explanation:
3x - 10 = x + 30
2x = 40
x = 20
You are considering purchasing a consol that promises annual payments of $4. a. If the current interest rate is 3 percent, what is the price of the consol? Instructions: Round your answer to the nearest penny (2 decimal places). The price of the consol is $ b. You are concerned that the interest rate may rise to 4 percent. Compute the percentage change in the price of the consol and the percentage change in the interest rate. Compare them. Instructions: Round your answer for dollar amounts to the nearest penny (2 decimal places ) and answers for percentages to the nearest tenth (1 decimal place) The new price of the consol would be $ The price of the consol falls by 7% and the interest rises by 7% c. Your investment horizon is one year. You purchase the consol when the interest rate is 5 percent and sell it a year later, following a rise in the interest rate to 6 percent. What is your holding period return? Instructions: Round your answer to the nearest tenth (1 decimal place) Your holding period return is %
Answers
a. The price of the consol is approximately $133.33.
b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.
c. Your holding period return is approximately -49.99%.
a. The price of the consol can be calculated using the formula for the present value of a perpetuity:
Price = Annual Payment / Interest Rate
In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:
Price = $4 / 0.03 ≈ $133.33
Therefore, the price of the consol is approximately $133.33.
b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:
New Price = Annual Payment / New Interest Rate
Substituting the values, we get:
New Price = $4 / 0.04 = $100
The percentage change in the price of the consol can be calculated using the formula:
Percentage Change = (New Price - Old Price) / Old Price * 100
Substituting the values, we have:
Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%
The percentage change in the interest rate is simply the difference between the old and new interest rates:
Percentage Change in Interest Rate = (4% - 3%) = 1%
Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.
c. The holding period return can be calculated using the formula:
Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100
The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:
Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67
Substituting the values into the holding period return formula:
Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%
Therefore, the holding period return is approximately -49.99%.
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Which form of payment can Courtney lose and NOT get back?
Answers
Answer: The form of payment that Courtney can lose and not get back would be cash.
Step-by-step explanation:
The reason why cash couldn't be returned back because it doesn't have a piece of U.S money wouldn't have a specific certified owner that they can be returned to.
Other forms of payment like credit cards, debit cards, and checks have specific bank information with the card holder's name on it so if Courtney actually lost one of those, she would be most likely to receive it back without any complicated verification process.
Therefore, Courtney would not be able to receive her cash back if she accidentally loses it. Hope this helps you with your Imagine Math homework or assignment!
-From Certified 5th Grade Honors Student
Need help with number 28. Find the specified roots of each number
Answers
Hello!
• To solve the roots ,we must factor the number, and ,count how many times its prime factors are repeated,.
,• If they are repeated at least equal to the root index, we ,can take this value out of the root,.
Let's follow these steps below:(a) the real third roots of 343Let's factorize 343 below:
\(\begin{gathered} 343\text{ | }7 \\ 49|7 \\ 7|7 \\ 1 \end{gathered}\)So, 343 can be written as 7³ = 7 * 7 * 7.
And as the index of this root is 3 we can cancel this exponent with the root, look:
\(\begin{gathered} \sqrt[3]{343}=\sqrt[3]{7^3}=7 \\ \\ \\ \end{gathered}\)(b) the real fifth roots of 1,024:I'll solve in the same way, first factorizing 1,024:
\(\begin{gathered} 1024|2 \\ 512|2 \\ 256|2 \\ 128|2 \\ 64|2 \\ 32|2 \\ 16|2 \\ 8|2 \\ 4|2 \\ 2|2 \\ 1 \end{gathered}\)So, 1,024 can be written as 2^10.
But we can write it as 2^5 * 2^5. Doing the same step, we will have:
\(\sqrt[5]{1,024}=\sqrt[5]{2^5\cdot2^5}=2\cdot2=4\)(c) the real square roots of 25:Let's factorize 25:
\(\begin{gathered} 25|5 \\ 5|5 \\ 1 \end{gathered}\)So, 25 = 5².
Look as the exponent will be canceled with the index of the root:
\(\sqrt[2]{25}=\sqrt[2]{5^2}=5\)Final Answers:• (a), 7
,• (b), 4
,• (c) ,5
one card is selected from a deck of 52 cards and placed in a second deck (also 52 cards). a card then is selected from the second deck. (a) what is the probability that the second card is an ace? (b) given that an ace was drawn from the second deck, what is the conditional probability that an ace was transferred?
Answers
The probability of drawing an ace from the second deck is 1/13. Given that an ace was drawn from the second deck, the conditional probability that an ace was transferred is 1/17.
Probability that the second card is an ace:
There are initially 4 aces in the second deck.
The total number of cards in the second deck is 52.
Therefore, the probability of drawing an ace is 4/52.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 4/52
Probability = 1/13
Conditional probability that an ace was transferred, given that an ace was drawn from the second deck:
Since an ace was drawn from the second deck, we know that the second card is one of the four aces.
There was initially one card transferred from the first deck to the second deck, so there are now 51 cards left in the second deck.
Out of these 51 cards, only 3 are aces (since one ace has already been drawn).
Conditional Probability = Number of favorable outcomes / Total number of remaining outcomes
Conditional Probability = 3/51
Conditional Probability = 1/17
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-3(3-10x) could you answer it quickly for me? please and thank you
It's distribute property.
Answers
Answer:
-9+30x
Step-by-step explanation:
-3 x 3 is -9
-3 x -10x is 30x
Answer:
-9 + 30x
Step-by-step explanation:
Like you mentioned, to solve this expression we need to use the distributive property...
We have to distribute -3 to 3 and -10x.
When multiplying negative and positive numbers it is important to know that...
-negative times negative equal positive
-negative times positive equal negative
-3 · 3 = -9
-3 · -10x = 30x
Therefore the answer is -9 + 30x
Hope this helps! Let me know if you have any further questions :D
A harried chef can't keep up with his breakfast orders and decides to automate the process with a "butter gun." The gun provides a 10 gram burst of butter spray with each hit of the trigger. He starts with a rack that holds one piece of toast 1 meter away. The demand again exceeds supply and he realizes he can use the same gun to produce more toast by placing a larger rack at a greater distance. He finds that a four-slice rack works at a distance of 2 meters. Pleased with profits he carries the idea a step further and puts a holder 3 meters away, maintaining a 10 gram spray. See figure below.a) If 1 spray entirely covers the area of a single slice at 1 meter, can it entirely cover the area of 4 slices at 2 meters? Why or why not?b) How many slices can one spray cover with a 3 meter arragnement?c) How do these changes affect the amount of butter on each piece of toastd) Our up-and-coming chef moves the fun back to 5 meters. Predict how much toast he can spray and how much better each piece gets.e) Explain how he could duplicate the original single-slice toast at 5 meters from the gun.
Answers
a) No, a single spray of 10 grams of butter would not be enough to entirely cover the area of 4 slices of toast at 2 meters. The area of 4 slices of toast is larger than the area of 1 slice of toast, meaning that it would require more butter than 10 grams to cover the entire area.
b) A single spray of 10 grams of butter would be enough to cover the area of 8 slices of toast at 3 meters.
c) These changes would affect the amount of butter on each piece of toast in that there would be more butter on each piece with a larger rack and further distance from the "butter gun".
d) At 5 meters from the gun, our up-and-coming chef would be able to spray 16 slices of toast with a single burst of 10 grams of butter. Each piece of toast would also have more butter than it would if it was sprayed at a closer distance.
e) To duplicate the original single-slice toast at 5 meters from the gun, the chef would need to reduce the amount of butter being sprayed. He could do this by simply reducing the distance between the gun and the toast rack.
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Complete question :
A harried chef can't keep up with his breakfast orders and decides to automate the process with a "butter gun." The gun provides a 10 gram burst of butter spray with each hit of the trigger. He starts with a rack that holds one piece of toast 1 meter away. The demand again exceeds supply and he realizes he can use the same gun to produce more toast by placing a larger rack at a greater distance. He finds that a four-slice rack works at a distance of 2 meters. Pleased with profits he carries the idea a step further and puts a holder 3 meters away, maintaining a 10 gram spray. See figure below.a) If 1 spray entirely covers the area of a single slice at 1 meter, can it entirely cover the area of 4 slices at 2 meters? Why or why not?b) How many slices can one spray cover with a 3 meter arragnement?c) How do these changes affect the amount of butter on each piece of toastd) Our up-and-coming chef moves the fun back to 5 meters. Predict how much toast he can spray and how much better each piece gets.e) Explain how he could duplicate the original single-slice toast at 5 meters from the gun.
Marwin pays 106.20 for 3.6 pounds lobster what is the price per pound of lobster in dollars and cents
Answers
Answer:
$29.50
Step-by-step explanation:
Divide the total (106.20) by 3.6 and you get 29.5
You can check your answer by multiplying 29.5 by 3.6 and you see it equals 106.2
Hope this helps!
Which transformations were used to create triangle A’B’C
Answers
Answer:
What transformation was performed on triangle ABC to create triangle A'B'C'?
A.rotation 90° clockwise about the origin
B.rotation 180° about the origin
C.translation 10 units right
D.reflection across the y-axis
Step-by-step explanation:reflection, across the y axis
Step-by-step explanation:
what triangle, I can't see any
what is the equation of that is perpendicular 1/2 x + 2 and passes through the point (1,3)
Answers
Answer:
y = -2x + 5
Step-by-step explanation:
In order to be perpendicular to a given line, the other line must have an opposite reciprocal slope.
\(y-3=-2(x-1)\\y-3=-2x+2\\y=-2x+5\)
An 8-kN force is applied over an area of 2 cm^2. What is the stress?
4 MPa
4 kPa
40 kPa
40 MPa
4 Pa
Answers
Answer:
Option a (4 MPa) is the right answer.
Step-by-step explanation:
The given values are:
Force,
F = 8 kN
Area,
A = 2 cm²
The stress will be:
⇒ \(\sigma = \frac{Force}{Area}\)
By substituting the given values, we get
\(=\frac{8}{2}\)
\(= 4 \ MPa\)
Find the value of z.
Answers
2z = 15
z = 7.5
Leah Deposited $7000 in an account that earns 2% interest compounded annually. How much interest will she have earned after 6 years?
Answers
Answer:
840
Step-by-step explanation:
7000×2×6 ÷ 100. since it is 2%
= 840
Here is an equation that is true for all values of x: 6(x + 3) = 6x + 18. Londyn saw this equation and says she can tell 18( x + 3) + 32 = 3(6x + 18) + 32 is also true for any value of x. How can she tell? Explain your reasoning.
Answers
We need to decide whether the given equations are always or never true for values of x .The given equations are ,
\(x - 12 = x + 1\)solve out for x,
\(\longrightarrow x -x =12+1\\ \)
\(\longrightarrow 0 =13\\ \)
This can never be true. Hence the equation is never true for any values of x.
\(x + \frac{3}{4} = x - \frac{3}{4} \)solve out for x,
\(\longrightarrow x -x =\dfrac{3}{4}+\dfrac{3}{4}\\ \)
\(\longrightarrow 0=\dfrac{3}{2}\)
This can never be true. hence the equation is never true for any values of x.
\(4(x + 3) = 8x + 12 - 4x\)solve out for x,
\(\longrightarrow 4x +12=8x+12-4x\\\)
\(\longrightarrow 4x -8x +4x =12-12\\\)
\(\longrightarrow 0=0\)
hence this equation is true for all values of x.
\(2x - 8 - x = x - 8\)solve out for x,
\(\longrightarrow 2x -x -x =8+8\\ \)
\(\longrightarrow 0=0 \)
hence the equation is true for all values of x.
\(2(x + 5) + 3x = 5(x - 5)\)solve out for x,
\(\longrightarrow 2x +10+3x =5x-25\\ \)
\(\longrightarrow 5x -5x =-25-10\\\)
\(\longrightarrow 0 =-35\)
This can never be true. hence the equation is never true for any values of x.
and we are done!
Determine the sign (+ or -) of Tan 192 degrees without using a calculator.
Answers
Answer:
Step-by-step explanation:
192 is more than 180 but less than 270. That means that Tan(192) is in the 3rd quadrant.The tangent is positive in Quad 3.Therefore the sign is +I promise, no calculator was used.
Help please it emergency if you help thank you a lot
Answers
Answer:
A
Step-by-step explanation:
That is the only rate that has the correct format.
Answer:
A. 9 miles/2 hours
Step-by-step explanation:
distance over time
what percent of flights are expected to meet the 20 minute "time to carousel"?
Answers
that it is difficult to determine an exact percentage of flights that are expected to meet the 20 minute "time to carousel" as it can vary depending on factors such as airport size, number of passengers, and baggage handling procedures. However, according to the Department of Transportation, the average wait time for baggage retrieval at major airports in the United States is around 30 minutes.
In explanation, the time it takes for baggage to reach the carousel after a flight lands is affected by several factors. These include the size of the airport, the number of passengers on the flight, the efficiency of baggage handlers, and any delays or issues that may occur during the transportation of the luggage from the plane to the carousel.
while it is difficult to provide an exact percentage of flights that meet the 20 minute "time to carousel" goal, it is clear that wait times for baggage retrieval can vary and can sometimes exceed 30 minutes. Factors such as airport size and efficiency of baggage handling can contribute to this variation.
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Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and sd = 15. what conclusion can be inferred about an individual score that corresponds to a z value of 1.0?
Answers
A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.
What is a z-value?A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:
\(Z=\frac{x\;-\;u}{\delta}\)
Where:
x is the sample mean or observed data.u is the mean.δ is the standard deviation.Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.
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Complete Question:
Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?
a.) it falls in the general region of the population
distribution
b.) it falls in the common region of the distribution
c.) it is likely to come from the healthy distribution
d.) it is unlikely to come from the healthy distribution
Determine whether the graphs of the given equations are parallel,
perpendicular, or neither.
y = 2x + 5
y = 2x - 1
Answers
Answer:
Step-by-step explanation:
Answer:
Since the graphs of the given equations have the same slope, but different y-intercepts, they are parallel.
Assume that I and y are both differentiable functions of t and are related by the equation y=cos (4:2). Find I da when = do 5- given -7 when I dt = Floo Enter the exact answer. dy dt Number
Answers
The value of dI/da can be obtained by using the chain rule, which states that dI/da = (dI/dt) / (da/dt).
Given that I_dt = Floo and y = cos(4t^2) and y_dt = -8t*sin(4t^2), we can solve for dI/da by finding da/dt when t = 5 and substituting the values in the formula.
Let's first apply the chain rule to the equation y = cos(4t^2) to find dy/dt:
dy/dt = -sin(4t^2) * d/dt (4t^2) = -8t*sin(4t^2)
Next, we can use the given value I_dt = Floo, which means that dI/dt = 1.
To find da/dt, we need to differentiate a with respect to t. However, the value of a is not given explicitly in the equation. Therefore, we need to use the given information that when t = 5, a = -7. This means that we can write the equation for a as follows:
a = 5t - 42
Taking the derivative of both sides with respect to t, we get:
da/dt = 5
Now we can substitute the values we have found into the formula for dI/da:
dI/da = (dI/dt) / (da/dt) = 1 / 5 = 1/5
Therefore, the exact value of dI/da is 1/5.
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what is the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute?
Answers
the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.
How to solve?
To solve this problem, we can use the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the expected rate of occurrence.
Let lambda be the expected rate of customer arrivals per minute. If exactly two customers arrive in the first minute, then the expected number of customers to arrive in three minutes is lambda ×3. We can use this expected value to calculate the probability of at least seven customers arriving in three minutes:
P(X ≥ 7 | X ~ ∝(λ×3))
= 1 - P(X ≤ 6 | X ~ ∝(λ×3))
= 1 - ∑[k=0 to 6] (e²(-λ3) ×(lλ3)²k / k!)
where e is the mathematical constant approximately equal to 2.71828, and k! denotes the factorial of k.
To find lambda, we can use the fact that exactly two customers arrive in the first minute. The Poisson distribution assumes that the number of events in a fixed interval of time or space follows a Poisson distribution with parameter lambda, which represents the expected rate of occurrence. Therefore, lambda is equal to the number of customers arriving per minute, which is 2.
Substituting lambda = 2 into the formula, we get:
P(X ≥ 7 | X ~ ∝(2×3))
= 1 - P(X ≤ 6 | X ~ ∝(6))
= 1 - ∑[k=0 to 6] (e²(-6) ×6²k / k!)
Using a calculator or computer software, we can evaluate this expression to get:
P(X ≥ 7 | X ~ ∝(6)) ≈ 0.081
Therefore, the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.
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