The mean of time between success is 0.2 minutes, rate parameter is 5 and probability that the time to succeed will be more than 55 minutes is approximately 0.000026 when Poisson random variable has a mean of 5 successes over a 125-minute period.
They can be found out by:
(A) The mean of the random variable defined by the time between successes can be found by using the fact that the Poisson distribution is memory less, which means that the time between successes follows an exponential distribution. The mean of an exponential distribution is equal to the reciprocal of the rate parameter, so:
Mean of time between successes = 1 / rate parameter = 1 / 5 = 0.2 minutes
(B) The rate parameter of the exponential distribution can be found using the fact that the mean of the exponential distribution is equal to the reciprocal of the rate parameter, as derived in part a:
rate parameter = 1 / mean of time between successes = 1 / 0.2 = 5
(C)The probability that the time to success will be more than 55 minutes can be found using the cumulative distribution function (CDF) of the exponential distribution with the rate parameter found in part b:
P(X > 55) = 1 - P(X <= 55) = 1 - F(55) = 1 - (1 - e^{(-5*55)}) = 0.000026 (rounded to 4 decimal places)
Therefore, the probability that the time to success will be more than 55 minutes is very small, approximately 0.000026.
The mean of random variable defined by time between success is 0.2 minutes, rate parameter of exponential distribution is 5 and probability that the time to succeed will be more than 55 minutes is approximately 0.000026 .
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A $2,000 investment was made 16 years ago into an account that earned quarterly
compounded interest. If the investment is currently worth $6,883.55, what is the
annual rate of interest?
Answer:
We can use the formula for compound interest to solve the problem:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, we know that P = $2,000, A = $6,883.55, n = 4 (quarterly compounding), and t = 16. We can solve for r by rearranging the formula as follows:
r = n[(A/P)^(1/nt) - 1]
Substituting the values, we get:
r = 4[(6,883.55/2,000)^(1/(4*16)) - 1] = 0.0522 or 5.22%
Therefore, the annual interest rate is approximately 5.22%
Can anyone please help with this math problem? Thanks!
Answer: Yes Sofia will have enough money
=======================================================
Explanation:
Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.
The area of the rectangle is 16*7 = 112 square meters.
The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be
sum of the exterior sides = perimeter
6+7+16+7+6+x = 54
42+x = 54
x = 54-42
x = 12
The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.
area of the trapezoid = 0.5*height*(base1+base2)
area = 0.5*5.66*(16+12)
area = 79.24 square meters
----------------
Recap so far
area of the rectangle at the bottom = 112 square metersarea of the trapezoid up top = 79.24 square metersThe total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.
Let's convert that to square decimeters.
Recall that 1 decimeter = 10 centimeters
Multiply both sides by 10
1 decimeter = 10 centimeters
10*(1 decimeter) = 10*(10 centimeters)
10 decimeters = 100 centimeters
10 decimeters = 1 meter
Then,
[tex]191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\[/tex]
The entire lawn is 19124 square decimeters.
----------------
We have one final block of calculations to determine the total price.
x = number of rolls
1 roll covers 90 square decimeters
x rolls cover 90x square decimeters
90x = 19124
x = 19124/90
x = 212.489 approximately
Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).
In short, Sofia needs 213 rolls.
1 roll costs $4.50
213 rolls will cost 213*4.50 = 958.50 dollars.
This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).
Sofia will have enough money to pay for all of the grass.
Given that sec n - tan n = ¼ , find sec n + tan n
Given, [tex]$$(\sec n - \tan n) = \frac{1}{4}[/tex], so, using Trigonometry we can obtain [tex]$$\sec n + \tan n = 0$$[/tex].
Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It involves the study of trigonometric functions such as sine, cosine, and tangent, and their applications to various fields such as engineering, physics, and navigation. Trigonometry helps in solving problems related to triangles, circles, and periodic phenomena such as waves and oscillations.
To find sec n + tan n using the given equation, we can use the following identity:
[tex]$$\sec^2 n - \tan^2 n = 1$$[/tex]
Multiplying both sides of the given equation by sec n + tan n, we get:
[tex]$$(\sec n - \tan n)(\sec n + \tan n) = \frac{1}{4}(\sec n + \tan n)$$[/tex]
Using the identity above, we can simplify the left-hand side of the equation as:
[tex]$$\sec^2 n - \tan^2 n = 1$$[/tex]
Therefore, we can substitute 1 for [tex]sec^2 n - tan^2[/tex] n in the equation above to get:
[tex]$$(\sec n - \tan n)(\sec n + \tan n) = \frac{1}{4}(\sec n + \tan n)$$[/tex]
[tex]$$1(\sec n + \tan n) = \frac{1}{4}(\sec n + \tan n)$$[/tex]
Simplifying further, we get:
[tex]\frac{3}{4} * $$(\sec n + \tan n) = 0[/tex]
Therefore, we can solve for sec n + tan n as:
[tex]$$\sec n + \tan n = \frac{0}{\frac{3}{4}}$$[/tex]
[tex]$$\sec n + \tan n = 0$$[/tex]
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how many all.number of possible.diagonal that drawing in differnt verticle of nonagon
It sounds like you want to find how many diagonals a nonagon has.
A nonagon has n = 9 sides.
The number of diagonals would be...
[tex]d = \text{number of diagonals}\\\\d = \frac{n(n-3)}{2}\\\\d = \frac{9(9-3)}{2}\\\\d = \frac{9(6)}{2}\\\\d = \frac{54}{2}\\\\d = 27\\\\[/tex]
A nonagon has 27 different diagonals.
Answer: 27Can you do Step by step because I need help
Answer:
4[tex]\sqrt{2\\}[/tex]
Step-by-step explanation:
This is a 45 45 90 Triangle meaning that x would be 4 squareroot 2
so the formula goes lets say 4= a and the other side is b
a=b and x=a[tex]\sqrt{2[/tex]
Mary runs 600m every day.
Work out how far Mary runs in one week.
Give your answer in kilometres.
Answer:
Mary runs 600 meters per day, so in one week, she runs:
600 meters/day x 7 days/week = 4200 meters/week
To convert meters to kilometers, we need to divide by 1000:
4200 meters/week ÷ 1000 meters/kilometer = 4.2 kilometers/week
Therefore, Mary runs 4.2 kilometers in one week.
Answer: 4.2 km per week
Step-by-step explanation:
You are given the following information obtained from a random sample of 6 observations. Assume the population has a normal distribution. 14 20 21 16 18 19 a. What is the point estimate of u? b. Construct an 80% confidence interval for u. Construct a 98% confidence interval for u. d. Discuss why the 80% and 98% confidence intervals are different.
A higher confidence level is associated with a wider confidence interval.
a. The point estimate of µ = (14 + 20 + 21 + 16 + 18 + 19) / 6 = 108 / 6 = 18.
b. For 80% confidence interval for µ, the confidence coefficient is 1 - α = 0.8, so α = 0.2 / 2 = 0.1. From the z-table, we can find the corresponding value of z to be 1.28. The confidence interval can be calculated as follows:
Upper Bound: µ + z*σ / √n = 18 + (1.28)(2.3) / √6 = 21.35
Lower Bound: µ - z*σ / √n = 18 - (1.28)(2.3) / √6 = 14.65
The 80% confidence interval is (14.65, 21.35). For 98% confidence interval for µ, the confidence coefficient is 1 - α = 0.98, so α = 0.01. From the z-table, we can find the corresponding value of z to be 2.33. The confidence interval can be calculated as follows:
Upper Bound: µ + z*σ / √n = 18 + (2.33)(2.3) / √6 = 23.88
Lower Bound: µ - z*σ / √n = 18 - (2.33)(2.3) / √6 = 12.12
The 98% confidence interval is (12.12, 23.88). The 80% and 98% confidence intervals are different because as we move to higher confidence levels, the z-values become larger, which in turn causes the confidence intervals to become wider. Therefore, a higher confidence level is associated with a wider confidence interval.
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Four friends all give each other presents.
The total cost of the presents is £80.52
Work out the mean cost of a present in pounds (£).
To work out the mean cost of a present in pounds (£), we need to divide the total cost of the presents (£80.52) by the number of presents (4).
The calculation will look like this:
£80.52 ÷ 4 = £20.13
Therefore, the mean cost of a present in pounds (£) is £20.13.
janelle fills two buckets with water the blue bucket holds 5 quarter of water which bucket holds more water how many cups more does it hold 1 quart= 2pints 1 pint = 2 cups
the blue bucket holds 5 x 4 = 20 cups of water.
what is a probability?
In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is represented as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.
Since 1 quart of water is equivalent to 2 pints of water and 1 pint of water is equivalent to 2 cups of water, then 1 quart of water is equivalent to 4 cups of water (2 pints x 2 cups per pint = 4 cups).
To determine which bucket holds more water, we need to know the amount of water in the other bucket. Without that information, we cannot compare the two buckets.
Assuming that Janelle filled the other bucket with water as well, we would need to know how many cups of water it holds in order to compare the two buckets.
Therefore, the blue bucket holds 5 x 4 = 20 cups of water.
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(1 point) Suppose f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x,y) comes before (z, w) if x
Increasing lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).
lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).
Suppose that f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points.
Let's discuss what are critical points and how we can determine them,A critical point is a point on the graph where the derivative changes its sign.
In other words, the derivative either changes from negative to positive or from positive to negative. A critical point is also known as a stationary point or a turning point
To determine the critical points, we need to find the derivative of the given function and set it equal to zero.The given function is[tex]f(x,y) = xy(1 - 4x - 2y).[/tex]
Let's find the partial derivative of f with respect to [tex]x:f_x(x,y) = y(1 - 4x - 2y) - 4xy = (1-2y)(1-4x)y.[/tex] (1)
Now, find the partial derivative of f with respect to y:f_y(x,y) = x(1 - 4x - 2y) - 2xy = (1-2x)(1-2y)x. (2)
To find the critical points, we need to set both partial derivatives (1) and (2) equal to zero.
(1-2y)(1-4x) = 0 and (1-2x)(1-2y) = 0.
Solving both equations separately, we have the following critical points:(1/4, 1/2), (1/4, 0), (0, 1/2), and (0, 0).
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11. twenty batteries will be put on the display. the types of batteries are: aaa, aa, c, d, and 9-volt. a. how many ways can we choose the twenty batteries? b. how many ways can we choose the twenty batteries but be sure that at least four batteries are 9-volt batteries?
a.
There are 15,504 ways to choose 20 batteries from the given types.
b.
there are 18,564 ways to choose 20 batteries such that at least four of them are 9-volt batteries.
How do we calculate?To choose 20 batteries from the given 5 types (aaa, aa, c, d, and 9-volt), we can use the combination formula and is given by:
nCr = n! / (r! * (n-r)!)
5C20 = 5! / (20! * (5-20)!) = 15,504
there are 15,504 ways to choose 20 batteries from the given types.
b. To choose 20 batteries such that at least four of them are 9-volt batteries, we employ the method:
First, we choose four 9-volt batteries out of the total number of 9-volt batteries, which is 1.
we then need to choose the remaining 16 batteries from the remaining 4 types (aaa, aa, c, and d), while making sure that we don't choose any 9-volt batteries.
Applying the combination formula, with n = 4 and r = 16:
4C16 = 4! / (16! * (4-16)!) = 18,564
Therefore, the total number of ways to choose 20 batteries such that at least four of them are 9-volt batteries is:
1 * 18,564 = 18,564
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Write the following series in sigma notation. 2 + 12 + 22 + 32 + 42
The given series in the sigma notation can be written as [tex]\sum_{n = 1} ^ 5 10n - 8[/tex].
What are arithmetic series?An arithmetic series is a set of integers where each term is made up of the common difference, a fixed amount, and the sum of the terms before it. In other words, the terms of the series may be represented as follows if the first term of an arithmetic series is a and the common difference is d:
a, a + d, a + 2d, a + 3d, ...
The given series is 2 + 12 + 22 + 32 + 42.
The total number of terms are 5.
The first term is 2, and the common difference is:
d = 12 - 2 = 10
Now, using the nth term of sequence we have:
an = 2 + (n - 1) 10
= 10n - 8
= [tex]\sum_{n = 1} ^ 5 10n - 8[/tex]
Hence, the given series in the sigma notation can be written as [tex]\sum_{n = 1} ^ 5 10n - 8[/tex].
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suppose that two people standing 2 miles apart both see the burst from a fireworks display. after a period of time, the first person standing at point a hears the burst. one second later, the second person standing at point b hears the burst. if the person at point b is due west of the person at point a and if the display is known to occur due north of the person at point a , where did the fireworks display occur?
The fireworks display occurred due north of the person at point A. This can be determined by calculating the direction and speed of sound. Assuming the speed of sound is approximately 343 meters per second, the fireworks display must have occurred approximately 0.58 seconds away from point A, which is approximately 343 meters due north of point A. This means that the fireworks display occurred somewhere between the two points.
To double-check the calculations, we can look at the two points and the direction in which the sound traveled. Point A is due north of the fireworks display, and point B is due west. This means that the sound traveled both north and west, which is consistent with the calculations.
Therefore, we can conclude that the fireworks display occurred due north of point A.
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In the morning 134 books were checked out from the library.in the afternoon 254 books were checked out and 188 books were checked out in the evening.how many books were checked out in the library that day?
Answer:
576 books.
Step-by-step explanation:
134+254+188=576 books in total.
Hopefully this helps!
c) assume that 25% of the defendants in the state are innocent. in a certain year 200 people put on trial. what is the expected value and variance of the number of cases in which juries got the right decision?
The expected value of cases in which juries got the right decision is 150, and the variance is 375.
1. Since 25% of defendants in the state are innocent, that means that 75% of the defendants are guilty.
2. This means that in the given year, 150 out of the 200 people put on trial will be guilty.
3. Thus, the expected value of cases in which juries got the right decision is 150.
4. The variance of the number of cases in which juries got the right decision is calculated by taking the expected value and subtracting it from the total number of people put on trial, which is 200.
5. The result of the calculation is 375, which is the variance of cases in which juries got the right decision.
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Pls read ss
PLS HELPP
The slopes are,
1) 7/6
2)7/2
3) -1
4) -2
5) 10/9
What is slope?
Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.
1) The given points , [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (6,8)[/tex] then,
=> slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{8-1}{6-0} = \frac{7}{6}[/tex]
2) The given points [tex](x_1,y_1) =(-1,10)[/tex] and [tex](x_2,y_2) = (-5,-4)[/tex] then,
=> Slope = [tex]\frac{-4-10}{-5+1} = \frac{-14}{-4}=\frac{7}{2}[/tex]
3) The given points [tex](x_1,y_1) =(-10,2)[/tex] and [tex](x_2,y_2) = (-3,-5)[/tex] then,
=> slope = [tex]\frac{-5-2}{-3+10} = \frac{-7}{7}=-1[/tex]
4) The given points [tex](x_1,y_1) =(-3,-4)[/tex] and [tex](x_2,y_2) = (-1,-8)[/tex] then,
=> slope = [tex]\frac{-8+4}{-1+3} = \frac{-4}{2}=-2[/tex]
5)The given points [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (-9,-9)[/tex] then,
=> slope = [tex]\frac{-9-1}{-9+0} = \frac{-10}{-9}=\frac{10}{9}[/tex]
Hence the slopes are,
1) 7/6
2)7/2
3) -1
4) -2
5) 10/9
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Function g is a transformation of the parent function f(x) = x². The graph of g is a
translation right 2 units and up 3 units of the graph of f. Write the equation for g in
the form y = ax² + bx+c.
Answer:
g(x) = x² - 4x + 7
this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. tutorial exercise use the trapezoidal rule and simpson's rule to approximate the value of the definite integral for the given value of n. round your answers to four decimal places and compare the results with the exact value of the definite integral. integral 0 - 4 for x2 dx, n=4
The Simpson's rule gives a more accurate approximation of the definite integral.
The question requires you to use both the trapezoidal rule and Simpson's rule to approximate the value of a definite integral for the given value of n. Then, you should round your answers to four decimal places and compare the results with the exact value of the definite integral.Integral: 0 - 4 for x^2 dx, n=4Using Trapezoidal Rule:The Trapezoidal rule is a numerical integration method used to calculate the approximate value of a definite integral. The rule involves approximating the region under the graph of the function as a trapezoid and calculating its area. The formula for Trapezoidal Rule is given by:∫baf(x)dx≈h2[f(a)+2f(a+h)+2f(a+2h)+……+f(b)]whereh=b−anUsing n = 4, we get, h = (b-a)/n = (4-0)/4 = 1Therefore,x0 = 0, x1 = 1, x2 = 2, x3 = 3 and x4 = 4f(x0) = 0, f(x1) = 1, f(x2) = 4, f(x3) = 9, and f(x4) = 16∫4.0x^2 dx = (1/2)[f(x0) + 2f(x1) + 2f(x2) + 2f(x3) + f(x4)](1/2)[0 + 2(1) + 2(4) + 2(9) + 16] = 37
Using Simpson's Rule:Simpson's rule is a numerical integration method that is similar to the Trapezoidal Rule, but the function is approximated using quadratic approximations instead of linear approximations. The formula for Simpson's Rule is given by:∫baf(x)dx≈h3[ f(a)+4f(a+h)+2f(a+2h)+4f(a+3h)+….+f(b)]whereh=b−an, and n is even.Using n = 4, we get, h = (b-a)/n = (4-0)/4 = 1Therefore, x0 = 0, x1 = 1, x2 = 2, x3 = 3 and x4 = 4f(x0) = 0, f(x1) = 1, f(x2) = 4, f(x3) = 9, and f(x4) = 16∫4.0x^2 dx = (1/3)[f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + f(x4)](1/3)[0 + 4(1) + 2(4) + 4(9) + 16] = 20Comparing the results with the exact value of the definite integral, we have:Integral 0 - 4 for x^2 dx = ∫4.0x^2 dx = [x^3/3]4.0 - [x^3/3]0 = 64/3 ≈ 21.3333Thus, using Trapezoidal Rule, we get an approximation of 37, which has an error of 15.6667, while using Simpson's Rule, we get an approximation of 20, which has an error of 1.3333. Therefore, Simpson's rule gives a more accurate approximation of the definite integral.
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A quadratic equation in form ax2 + bx + c = 0 cannot have:
One Imaginary solution is not possible for a quadratic equation of the form ax² + bx + c = 0.
By replacing the factorization method, the quadratic formula aids in evaluating the quadratic equations' solutions.
A quadratic equation has the general form ax² + bx + c = 0, where a, b, and c are real numbers, sometimes known as "numeric coefficient".
We can forecast the nature of the roots by determining the discriminant's value.
Three potential outcomes, each with a different impact
If b² - 4ac > 0, two separate roots that are real.
If b² - 4ac = 0, two real roots have magnitudes that are equal.
If b² - 4ac 0, there are no real roots and just imaginary ones.
Thus, the quadratic equation ax² + b x + c = 0 cannot have a single imaginary solution.
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A photograph of sides 35cm by 22cm is mounted onto a frame of external dimension 45cm by 30cm.Find the area of the border surrounding the photograph
Dimension of photograph is 35cm and 22cm.
And external dimension of photo frame is 45cm and 30cm
So, the area of the border surrounding the photograph=Area of photo frame−Area of photo.
So, The area of the border surrounding the photograph [tex]=45\times30-35\times22[/tex]
[tex]=1350-770=580cm^2[/tex]
brad is in a big dorm with 180 other students. let x be the number of other students who have the same birthday as brad. using poisson approximation, approximate the probability that (a) there is at least one student with same birthday as brad? (b) exactly one student with same birthday as brad? (c) at least two students? compare this with the exact probability. you may assume that the birthday of each of the other students is equally likely to be any one of the 365 days (no students born on leap years) and independent of each other
Using the Poisson Approximation the probability are:
a) 0.6321
b) 0.3679
c) 0.2642
The Poisson distribution is utilized to compute the likelihood of a particular amount of occurrences happening over a set period. The Poisson approximation will be used to answer the given question, and it is a form of a probability distribution that can be used to approximate the probability of particular events that occur infrequently, and it is suitable for both continuous and discrete variables.
a) The probability of having at least one student with the same birthday as Brad using the Poisson Approximation.
Let the number of other students with the same birthday as Brad be represented by x. Here, x is a discrete variable with a Poisson distribution that follows a Poisson distribution with an average of λ, which is equal to 1:
λ = average number of students having the same birthday as Brad = 1.
Using the Poisson distribution formula, the probability of having at least one student with the same birthday as Brad is given by:
P(X >= 1) = 1 - P(X = 0)
= 1 - e ^ (-λ)P(X = 0)
= (e^(-λ))(λ^0) / 0!
= e^(-λ)
= e^(-1)
= 0.3679
Therefore, the probability of having at least one student with the same birthday as Brad is:
P(X >= 1) = 1 - P(X = 0)
= 1 - 0.3679
= 0.6321
b) The probability of having exactly one student with the same birthday as Brad using Poisson Approximation
P(X = 1) = (e^(-λ))(λ^1) / 1!
= e^(-1)(1) / 1!
= e^(-1)
= 0.3679
Therefore, the probability of having exactly one student with the same birthday as Brad is:
P(X = 1)
= e^(-1)
= 0.3679
c) The probability of having at least two students with the same birthday as Brad using Poisson Approximation
P(X >= 2) = 1 - P(X < 2)
= 1 - [P(X = 0) + P(X = 1)]
= 1 - [e^(-λ)(λ^0) / 0! + e^(-λ)(λ^1) / 1!]
= 1 - [e^(-1) + e^(-1)(1) / 1!]
= 1 - [e^(-1) + e^(-1)]
= 1 - 2e^(-1)
= 0.2642
Compare the Poisson Approximation (a) Probability with the exact probability- At least one student with the same birthday as BradExact probability: 1 - (364/365)^180 = 0.4406
Poisson Approximation Probability: 0.6321
The exact probability is 0.4406, which is less than the Poisson approximation probability, which is 0.6321.
This result indicates that the Poisson approximation formula overestimates the likelihood of having at least one student with the same birthday as Brad.
(b) Exactly one student with the same birthday as BradExact probability: (364/365)^179(1/365) = 0.3775
Poisson Approximation Probability: 0.3679
The exact probability is 0.3775, which is quite similar to the Poisson approximation probability, which is 0.3679.
This result indicates that the Poisson approximation formula provides a reasonably precise estimate of the likelihood of having exactly one student with the same birthday as Brad.
(c) At least two students with the same birthday as BradExact probability: 1 - [1 + 364/365 + ... + (364!/347!)/365^34] = 0.1827
Poisson Approximation Probability: 0.2642
The exact probability is 0.1827, which is less than the Poisson approximation probability, which is 0.2642.
This result indicates that the Poisson approximation formula overestimates the likelihood of having at least two students with the same birthday as Brad.
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A triangle has an area of 42 cm. The height of the triangle is 14 centimeters. What is the length of the base of the triangle?
Each angle of a regular polygon is 1680. How
many sides has it? What is the name of this
polygon?
Answer: 2 solutions
Step-by-step explanation:
To find the angle of a regular polygon, use the formula 180(n-2)/n (where n is the amount of sides.)
Setting them equal, we get (180n-360)/n = 1680.
Multiplying by n on both sides, we get 180n-360 = 1680n.
Solving, we get 1500n = 360.
n = 0.24, which means it is not a shape, as you cannot have a shape with 0.24 sides.
The other way to look at it is to take full revolutions of 360 away from each angle, giving us 240 (the smallest remainder without it going negative). However, all the angles would be concave. If all the angles are concave, then it might connect backwards.
Subtracting 240 from 360 (to get the "exterior" angles, we get 120. Plugging it in to our equation 180(n-2)/n and solving, we get 180n-360 = 120n, and solving gives us 60n = 360, or n=6.
Since the amount of sides came together cleanly, we can classify this polygon as a normal hexagon, which has 6 sides.
5.4 ADDING A MULTIPLE OF THE ith ROW TO THE jth row. Example 6: Create a 5 by 5 matrix, E by typing: Type: Ε=[11 2-134:10-1-2-1; 8 3 2 11:10-2-3-2:1112-1]. Find det(E) by typing: Type DE =det(E)
The `det(E2) of the given matrix is equal to 366`.
Given a 5 by 5 matrix E= `[11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;2 -1 -2 1 1]`.
To find `det(E)`, we can use the following steps.
Step 1: Create a 5 by 5 matrix E1 by adding a multiple of the ith row to the jth row, given i = 3 and j = 5.
We need to add -1/3 times the 3rd row to the 5th row. It can be done by the following operation.`E1 = E` (start with the original matrix) `=> E1(5,:) = E(5,:) - E(3,:) / 3` (subtract the 3rd row of E divided by 3 from the 5th row of E)
This results in the matrix `E1 = [11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;1/3 -7/3 -7/3 7/3 4/3]
`Step 2: Create a 5 by 5 matrix E2 by adding a multiple of the ith row to the jth row, given i = 2 and j = 5.We need to add -20 times the 2nd row to the 5th row.
It can be done by the following operation.`E2 = E1` (start with the matrix from Step 1) `=> E2(5,:) = E1(5,:) - 20 * E1(2,:)` (subtract 20 times the 2nd row of E1 from the 5th row of E1)
This results in the matrix `E2 = [11 2 -1 -3 4;10 -1 -2 -1 -2;-1 2 3 2 1;1 1 1 -1 -1;0 -13 33 -13 44]
`Step 3: Find det(E2) by using the cofactor expansion along the 5th column.`det(E2) = 0 - (-13) * A1 + 33 * A2 - (-13) * A3 + 44 * A4 - 0 * A5`where A1, A2, A3, A4, and A5 are the 2 by 2 determinants of the submatrices obtained by deleting the 5th row and the ith column, for i = 1, 2, 3, 4, and 5. We can use the following notation.
A1 = det([11 -1 -3 4;10 -2 -1 -2;-1 3 2 1;]) = 324A2 = det([11 2 -3 4;10 -1 -1 -2;-1 2 2 1;]) = -54A3 = det([11 2 -1 4;10 -1 -2 -2;-1 2 3 1;]) = -142A4 = det([11 2 -1 -3;10 -1 -2 -1;-1 2 3 2;]) = 50A5 = det([11 2 -1 -3;10 -1 -2 -1;-1 2 3 2;]) = 366.
Therefore `det(E2) = 0 - (-13) * 324 + 33 * (-54) - (-13) * (-142) + 44 * 50 - 0 * 50 = 366`.
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The difference between two numbers is eight.
if the smaller number is n to the third power
what is the greater number?
The greater number is [tex]$n^3+8$[/tex]
Let x be the greater number and y be the smaller number. We know that x-y=8.
We are also given that the smaller number is n³.
So we can set up the equation:
x = y + 8
x = n³ + 8
Therefore, the greater number is [tex]$n^3+8$[/tex].
The greater number is given as n³ + 8. If the smaller number we get is represented by the n³, then by adding 8 to that value gives the greater number. The difference between the two numbers is always going to be 8, regardless of the value of n.
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Two numbers have a sum of 1022. They have a difference of 292. What are the two numbers
Answer:
The answer is 657 and 365.
Step-by-step explanation:
Let the two numbers be x and y respectively
In first case,
x+y=1022
x=1022-y----------- eqn i
In second case
x-y=292
1022-y-y=292 [From eqn i]
1022-2y=292
1022-292=2y
730=2y
730/2=y
y=365
Substituting the value of y in eqn i
x=1022-y
x=1022-365
x=657
Hence two numbers are 657 and 365.
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PLEASE HELP WITH NUMBERS 9 and 10!!!
Pythagorean theorem (triangles)
Answer:
9. 6.32
10. 4.12
Step-by-step explanation:
9. c^2 = 2^2 + 6^2 = 4 + 36 = 40
c = √40 = 6.32
10. c^2 = 1^2 + 4^2 = 17
c = √17 = 4.12
Assume that X is normally distributed with a mean of 7 and a standard deviation of 4. Determine the value for x that solves each of the following equations. (a) P(X>x) 0.5 (b) P(X>x) 0.95 (c) P(x< X<9)= 0.2 (d) P(3< X
For (a), the value for x is 11, as P(X>x) = 0.5 when the mean is 7 and the standard deviation is 4. This can be found using the standard normal table.
For (b), the value for x is 19, as P(X>x) = 0.95 when the mean is 7 and the standard deviation is 4. This can also be found using the standard normal table.
For (c), the value for x is 9, as P(x< X<9) = 0.2 when the mean is 7 and the standard deviation is 4. This is found by subtracting the z-scores of x and 9 from each other, and then finding the area of the z-score between those two numbers using the standard normal table.
For (d), the value for x is 4, as P(3< X) = 0.2 when the mean is 7 and the standard deviation is 4. This is found by subtracting the z-score of 3 from the mean and then finding the area of the z-score to the left of that number using the standard normal table.
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What is the volume of a rectangular prism that has a width of 10 cm, height of 3 cm and a depth of 7 cm
the volume of the rectangular prism with a width of 10 cm, height of 3 cm, and a depth of 7 cm is 210 cubic cm.
The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the width is 10 cm, the height is 3 cm, and the depth is 7 cm. Therefore, the volume of the rectangular prism can be calculated as follows:
Volume = Length x Width x Height
Since the length of the rectangular prism is not given, we cannot calculate the exact volume. However, we can provide a formula that can be used to calculate the volume of any rectangular prism with the given dimensions.
Formula for the volume of a rectangular prism:
Volume = Width x Height x Depth
Substituting the given values, we get:
Volume = 10 cm x 3 cm x 7 cm
Volume = 210 cubic cm
Therefore, the volume of the rectangular prism with a width of 10 cm, height of 3 cm, and a depth of 7 cm is 210 cubic cm.
It is important to note that the unit of measurement used for the dimensions should be the same for all three dimensions in order to obtain the correct volume. In this case, the unit of measurement used is centimeters (cm), and the volume is expressed in cubic centimeters (cm³).
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Complete the table for the given rule.
Rule: y=\dfrac{x}{2}y=
2
x
y, equals, start fraction, x, divided by, 2, end fraction
xxx yyy
111
2. 52. 52, point, 5
3. 53. 53, point, 5
The proportionate relationship is used to determine that:
Y=0.5 when x = 1.
Y Equals 1.25 when x = 2.5.
Y = Y = 1.75 when x = 3.5.
What does "proportional relationship" mean?
In a proportional connection, the output variable is determined by the input variable multiplied by a proportionality constant, as in the equation: y = kx.
where k is the proportionality constant.
The relationship in this issue is provided by:
y = x/2
Hence, y = 1/2 = 0.5 when x = 1.
Y = 2.5/2 = 1.25 when x = 2.5.
When x = 3.5:
y = 3.5/2 = 1.75
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