The expected value of the amount you would win from this game is $0.85 and the variance of the amount you win is $0.06.
Explanation:To calculate the expected value, we need to multiply each outcome with its probability and sum them up. The outcomes and corresponding probabilities are as follows:
Winning $1.10 (drawing two marbles of the same color): The probability is 4/9 (for blue) + 4/9 (for red) = 8/9Losing $1.00 (drawing two marbles of different colors): The probability is 1/9Then, the expected value is (8/9)*$1.10 + (1/9)*(-$1.00) = $0.96 - $0.11 = $0.85. So, (a) expected value of the amount you win is $0.85.
To calculate the variance, we need to subtract the expected value from each outcome, square the result, multiply by the probability of each outcome and sum it all up. Variance = (8/9)*($1.10-$0.85)^2 + (1/9)*(-$1.00-$0.85)^2 = $0.06. So, (b) the variance of the amount you win is $0.06.
Learn more about Expected Value and Variance here:https://brainly.com/question/31972753
#SPJ11
The expected value of the amount you win is approximately -$0.0667 and the variance of the amount you win is approximately $1.0888.
(a) To calculate the expected value of the amount you win, we first need to determine the probability of each outcome:
1. Probability of drawing two red marbles: [tex]\( P(\text{red-red}) = \frac{5}{10} \times \frac{4}{9} = \frac{20}{90} = \frac{2}{9} \)[/tex]
2. Probability of drawing two blue marbles: [tex]\( P(\text{blue-blue}) = \frac{5}{10} \times \frac{4}{9} = \frac{20}{90} = \frac{2}{9} \)[/tex]
3. Probability of drawing one red marble and one blue marble: [tex]\( P(\text{red-blue}) = 2 \times \frac{5}{10} \times \frac{5}{9} = \frac{50}{90} = \frac{5}{9} \)[/tex]
Now, let's calculate the expected value (\( E \)):
[tex]\[ E = (P(\text{red-red}) \times \$1.10) + (P(\text{blue-blue}) \times \$1.10) + (P(\text{red-blue}) \times -\$1.00) \]\[ E = \left(\frac{2}{9} \times \$1.10\right) + \left(\frac{2}{9} \times \$1.10\right) + \left(\frac{5}{9} \times -\$1.00\right) \]\[ E = \left(\frac{4}{9} \times \$1.10\right) + \left(\frac{5}{9} \times -\$1.00\right) \]\[ E = \$\left(\frac{4}{9} \times 1.10\right) + \$\left(\frac{5}{9} \times -1.00\right) \][/tex]
[tex]\[ E = \$\left(\frac{4.40}{9} - \frac{5.00}{9}\right) \]\[ E = \$\frac{-0.60}{9} \]\[ E = -\$0.0667 \][/tex]
So, the expected value of the amount you win is approximately -$0.0667.
(b) To calculate the variance of the amount you win, we'll use the formula for variance:
[tex]\[ \text{Var}(X) = E(X^2) - (E(X))^2 \][/tex]
We already know E(X) from part (a). Now, let's calculate E(X)²:
[tex]\[ E(X^2) = (P(\text{red-red}) \times (\$1.10)^2) + (P(\text{blue-blue}) \times (\$1.10)^2) + (P(\text{red-blue}) \times (-\$1.00)^2) \]\[ E(X^2) = \left(\frac{2}{9} \times (\$1.10)^2\right) + \left(\frac{2}{9} \times (\$1.10)^2\right) + \left(\frac{5}{9} \times (-\$1.00)^2\right) \]\[ E(X^2) = \left(\frac{4}{9} \times (\$1.21)\right) + \left(\frac{5}{9} \times \$1.00\right) \]\[ E(X^2) = \$\left(\frac{4 \times 1.21}{9} + \frac{5}{9}\right) \][/tex]
[tex]\[ E(X^2) = \$\left(\frac{4.84}{9} + \frac{5}{9}\right) \]\[ E(X^2) = \$\frac{9.84}{9} \]\[ E(X^2) = \$1.0933 \][/tex]
Now, we can calculate the variance:
[tex]\[ \text{Var}(X) = E(X^2) - (E(X))^2 \]\[ \text{Var}(X) = \$1.0933 - (-\$0.0667)^2 \]\[ \text{Var}(X) = \$1.0933 - \$0.0045 \]\[ \text{Var}(X) = \$1.0888 \][/tex]
So, the variance of the amount you win is approximately $1.0888.
Therefore, the solution is (a) Expected value: -$0.0667 and (b) Variance: $1.0888
Mark has 153 hot dogs and 171 hamburgers. He wants to put the same number of hot dogs and hamburgers on each tray. What is the greatest number of trays Mark can use to accomplish this?
Answer:
Mark will use 153 no of trays to accomplish his task.
Final answer:
Mark can use 9 trays to distribute 153 hot dogs and 171 hamburgers evenly by finding the Greatest Common Divisor (GCD) of the two numbers, which is 9.
Explanation:
Mark has 153 hot dogs and 171 hamburgers and wants to distribute them evenly across the greatest number of trays. To do this, Mark needs to find the Greatest Common Divisor (GCD) of the two numbers, which is the largest number that can evenly divide both 153 hot dogs and 171 hamburgers. The GCD of 153 and 171 is 9.
Step 1: List the factors of 153 (1, 3, 9, 17, 51, 153) and 171 (1, 3, 9, 19, 57, 171).Step 2: Identify the largest factor that appears in both lists, which is 9.Step 3: Divide the number of hot dogs and hamburgers by the GCD to find the number of items per tray. For hot dogs: 153 / 9 = 17 hot dogs per tray. For hamburgers: 171 / 9 = 19 hamburgers per tray.Therefore, Mark can use 9 trays, with 17 hot dogs and 19 hamburgers on each tray, to distribute them evenly.
A is a 7 x 7 matrix with three eigenvalues. One eigenspace is two-dimensional, and one of the other eigenspaces is three dimensional. Is it possible that A is not diagonalizable? Justify your answer
Yes, it is possible for a 7 x 7 matrix to not be diagonalizable even if it has three eigenvalues.
Explanation:Yes, it is possible for a 7 x 7 matrix to not be diagonalizable even if it has three eigenvalues. A matrix is diagonalizable if and only if it has n linearly independent eigenvectors, where n is the size of the matrix. In this case, since we have one eigenspace two-dimensional and one eigenspace three-dimensional, we have a total of 5 linearly independent eigenvectors. Since 5 is less than 7, the matrix is not diagonalizable.
Learn more about Diagonalizable matrices here:https://brainly.com/question/32357741
#SPJ12
Yes, it is possible that matrix A is not diagonalizable. For a square matrix to be diagonalizable, it must have a complete set of eigenvectors.
Explanation:Yes, it is possible that matrix A is not diagonalizable. For a square matrix to be diagonalizable, it must have a complete set of eigenvectors. In this case, we have a 7 x 7 matrix with three eigenvalues, but only two eigenspaces are given (a two-dimensional eigenspace and a three-dimensional eigenspace). Since we don't have eigenvectors for all the eigenvalues, matrix A is not guaranteed to be diagonalizable.
Learn more about diagonalizable matrix here:https://brainly.com/question/35475887
#SPJ3
Commuting. there are two routes he could take to work. Aneighbor who has lived there a long time tells him Route Awill average 5 minutes faster than Route B. The man decides to experiment. Each day he flips a coin to determine which way to go, driving each route 20 days. He finds that Route Atakes an average of 40 minutes, with stan- dard deviation 3 minutes, and Route B takes an average of 43 minutes, with standard deviation 2 minutes. His- tograms of travel times for the routes are roughly sym- metric and show no outliers. a.Find a 95% confidence interval for the difference in average commuting time for the two routes. b.Should the man believe the old-timer s claim that he can save an average of 5 minutes a day by always driving Route A
Answer:
a)We are 95% confident that the average commuting time for route A is between 1.3577 and 4.6423 minutes shorter than the average committing time for rout B.
(b) No, because the confidence internal does not contain —5, which corresponds with an average of 5 minutes shorter for route A.
Step-by-step explanation:
Given:
n_1 = 20
x_1= 40
s_1 = 3
n_2 = 20
x_2= 43
s_2 = 2
d_f = 33.1
c = 95%. 0.95
(a) Determine the t-value by looking in the row starting with degrees of freedom df = 33.1 > 32 and in the column with c = 95% in the Student's t distribution table in the appendix:
t[tex]\alpha[/tex]/2 = 2.037
The margin of error is then:
E = t[tex]\alpha[/tex]/2 *√s_1^2/n_1+s_2^2/n_2
E = 2.037 *√3^2/20+s_2^2/20
= 1.64
The endpoints of the confidence interval for u_1 — u_2 are:
(x_1 — x_2) — E = (40 — 43) — 1.6423 = —3 — 1.6423= —4.6423
(x_1 - x_2) + E = (40 — 43) + 1.6423 = —3 + 1.6423= —1.3577
a)We are 95% confident that the average commuting time for route A is between 1.3577 and 4.6423 minutes shorter than the average committing time for rout B.
(b) No, because the confidence internal does not contain —5, which corresponds with an average of 5 minutes shorter for route A.
Your friend brings 12 chocolate cupcakes and 12 vanilla cupcakes to school. Students will take turns picking a pair of cupcakes at random. What is the probability that the first student will pick 2 vanilla cupcakes?
Answer:
Answer = 11/46
Step-by-step explanation:
yo already knowww :D
Answer:
There are NO parallel sides.
Step-by-step explanation:
Look at them.
Answer: Bottom left, lamins have no parrellel sides
Step-by-step explanation: All of them have no parrellel sides. Hope this helps!
What is the formula for margin of error?
ME = StartFraction z times StartRoot s EndRoot Over StartRoot n EndRoot EndFraction
ME = StartFraction z times StartRoot s EndRoot Over n EndFraction
ME = StartFraction z times s Over StartRoot n EndRoot EndFraction
ME = StartFraction z times s Over n EndFraction
ANSWER IS:
C) ME = StartFraction z times s Over StartRoot n EndRoot EndFraction
Answer:
Margin of error = Critical value x Standard error of the sample.
Step-by-step explanation:
The margin of error can be calculated in two ways, depending on whether you have parameters from a population or statistics from a sample: Margin of error = Critical value x Standard deviation for the population. Margin of error = Critical value x Standard error of the sample.
Its C. ME= (z*s)/ sqrt n
Which of the following relationships represents a function?
A. (-3,4), (6,2), (-7,1), (2,2)
B. (-3,0), (6,3), (-7,1), (6,5)
C. (-3,4), (6,6), (-3,3), (2,2)
D. (-3,4), (6,6), (6,3), (2,2)
Answer:
A. (-3,4), (6,2), (-7,1), (2,2)
Step-by-step explanation:
Functions cannot have the x repeating. All the other answers have one of their x-values repeating, so they are not functions.
Matty jogs 9 km/hr. Compute Matty's speed in m/s.
Step-by-step explanation:
1km = 9000 m
1 min = 60 sec
So 60 min = 3600 sec
In this way Matty jogs 9000m /3600sec
Matty's speed of 9 km/hr is equivalent to 2.5 m/s when converted using the relationship where 1 km equals 1000 meters and 1 hour equals 3600 seconds.
Explanation:To compute Matty's speed in meters per second (m/s), we need to convert from kilometers per hour (km/h) to m/s. To do this, we can use the conversion rate where 1 km equals 1000 meters, and 1 hour equals 3600 seconds.
First, we convert Matty's speed to meters:
9 km/h = 9 × 1000 m/h = 9000 m/h.
Then, we convert hours to seconds:
9000 m/h × (1 h / 3600 s) = 9000 m / 3600 s = 2.5 m/s.
Therefore, Matty's speed in meters per second is 2.5 m/s.
A manufacturer wishes to estimate the proportion of dishwashers leaving the factory
that is defective. How large a sample should be tested in order to be 99% confident
that the true proportion of defective dishwashers is estimated to within a margin of
error of 3%?
1843.27
1800
1843
1844
The sample size needed with 99% confidence and 3% margin of error is 1843.
To estimate the sample size needed:
Determine the critical value for 99% confidence, which is 2.576.
Calculate the minimum sample size using the formula:
n = (Z^2 * p * q) / E^2
Substitute Z = 2.576, p = 0.5, q = 0.5, and E = 0.03.
Calculate to get the sample size, which is approximately 1843.
What is the opposite of the coordinate for point D? A) −33 B) −34 C) 33 D) 34
will mark the brainiest
The opposite of a coordinate in mathematics is obtained by changing the sign of the given number. Without the specific coordinate for point D, the opposite cannot be determined from the provided options.
The question seems to refer to the notion of opposite coordinates in a coordinate system. In mathematics, particularly in the context of a coordinate plane, the opposite of a coordinate is simply the same number with its sign changed. If the original coordinate for point D is not given in the question, it's impossible to determine the correct opposite coordinate from the options provided.
NEED HELP WITH THESE THREE QUESTIONS!!!
1.) Use the binomial probability formula to find P(x) given that n = 8, p = 0.31, and x = 4.
2.) Suppose that 5 fair coins are tossed all at once. What is the probability that all 5 of them land heads up?
3.)An unprepared student is given a 14 question multiple choice quiz on Reptiles from the Star Wars Saga. Each question has 5 possible answers of which only one is correct. What is the probability that this student answers correctly on less than 4 of these questions?
Answer:
(a) The value of P (X = 4) is 0.1465.
(b) The probability that all 5 of them land heads up is 0.0313.
(c) The probability that the student answers correctly on less than 4 of these questions is 0.6980.
Step-by-step explanation:
A Binomial distribution is the probability distribution of the number of successes, X in n independent trials with each trial having an equal probability of success, p.
The probability mass function of a Binomial distribution is:
[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...,\ 0<p<1[/tex]
(1)
The information provided is:
X = 4
n = 8
p = 0.31
Compute the value of P (X = 4) as follows:
[tex]P(X=4)={8\choose 4}0.31^{4}(1-0.31)^{8-4}\\=70\times 0.00923521\times 0.22667121\\=0.146535\\\approx 0.1465[/tex]
Thus, the value of P (X = 4) is 0.1465.
(2)
The probability of heads, on tossing a single fair coin is, p = 0.50.
It is provided that n = 5 fair coins are tossed together.
Compute the probability that all 5 of them land heads up as follows:
[tex]P(X=5)={5\choose 5}0.50^{5}(1-0.50)^{5-5}\\=1\times 0.03125\times 1\\=0.03125\\\approx 0.0313[/tex]
Thus, the probability that all 5 of them land heads up is 0.0313.
(3)
There are 5 possible answers for every multiple choice question. Only one of the five options is correct.
The probability of selecting the correct answer is, p = 0.20.
Number of multiple choice questions, n = 14.
Compute the probability that the student answers correctly on less than 4 of these questions as follows:
P (X < 4) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)
[tex]=\sum\limits^{3}_{x=0}{{14\choose x}0.20^{x}(1-0.20)^{14-x}}\\=0.0439+0.1539+0.2501+0.2501\\=0.6980[/tex]
Thus, the probability that the student answers correctly on less than 4 of these questions is 0.6980.
The final probabilities are P(4 successes) ≈ 0.146, P(5 heads) ≈ 0.03125, and P(less than 4 correct answers) ≈ 0.5972.
Solutions to Probability Questions
Let's tackle each of your probability questions step-by-step:
Question 1 To find P(x) using the binomial probability formula, given n = 8, p = 0.31, and x = 4, we use the formula:
P(x) = (ⁿCₓ) * pˣ * (1-p)ⁿ⁻ˣWhere:
(ⁿCₓ) = n! / (x! * (n-x)!)pˣ = p raised to the power of x(1-p)ⁿ⁻ˣ = (1-p) raised to the power of (n-x)Calculating:
(⁸C₄) = 8! / (4! * 4!) = 70p⁴ = 0.31⁴ ≈ 0.009235(1-p)⁸⁻⁴ = (0.69)⁴ ≈ 0.226981So, P(4) ≈ 70 * 0.009235 * 0.226981 ≈ 0.146.
Question 2 If 5 fair coins are tossed, the probability that all 5 of them land heads up is calculated as:
P(5 Heads) = (1/2)⁵ = 1/32 ≈ 0.03125.Question 3 For a student answering a multiple-choice quiz with 14 questions where each question has 5 possible answers, and we are to find the probability of correctly answering less than 4 questions, we use the binomial distribution with n = 14, p = 0.2 (since only one answer out of five is correct), and x < 4:
P(X < 4) = P(0) + P(1) + P(2) + P(3)P(x) = (¹⁴Cₓ) * (0.2)ˣ * (0.8)¹⁴⁻ˣCalculating for x = 0, 1, 2, 3 and summing the probabilities:P(0) ≈ 0.0282, P(1) ≈ 0.099, P(2) ≈ 0.209, P(3) ≈ 0.261.P(X < 4) = 0.0282 + 0.099 + 0.209 + 0.261 ≈ 0.5972.
Nathan wants to buy a sweatshirt and is trying to determine the better buy. He has a 20% coupon for the in-store purchase. The store charges $44 for the sweatshirt he wants. However, he found the same sweatshirt online for $38 and gets 15% off as a first-time buyer. There are no shipping charges. Which is the better buy? By how much? Use the Polya problem solving method to solve this problem.
Answer:
$38 + 15% off
Step-by-step explanation:
to do this, multiply each original price by the coupon percentage, (38 being .15, and 44 being .4,) and subtract the answers. when this is done and you compare, you will see that the $38 sweatshirt is less money by $2.90.
The cost of the sweatshirt both in-store and online after applying the respective discounts shows that it is better to buy the sweatshirt online, saving Nathan $2.90.
Explanation:This problem relates to the mathematics field of percentage or discount calculations. To solve this problem, we need to calculate the cost of the sweatshirt after applying the discounts both in-store and online.
First, let's calculate the amount of the 20% discount for the in-store purchase. To find the discount, we multiply the cost of the sweatshirt by the discount rate: $44 * 20% = $8.80. So the total cost for the sweatshirt in-store after the discount would be $44 - $8.80 = $35.20.
Secondly, let's calculate the online price with a 15% discount. The discount on the online price would be calculated as: $38 * 15% = $5.70. Therefore, the cost of the sweatshirt online after the discount is $38 - $5.70 = $32.30.
Based on these calculations, buying online is the better deal by $35.20 - $32.30 = $2.90.
Learn more about Discount Calculations here:
https://brainly.com/question/32761587
#SPJ2
Help fast!!! Pls!!!!!
Answer:
The height is 5 and the base is 9
Step-by-step explanation:
The area of a parallelogram is given by
A = bh
45 =x(x+4)
Distribute
45 =x^2+4x
Subtract 45 from each side
45-45 =x^2 +4x-45
0 = x^2 +4x-45
Factor
What two numbers multiply to -45 and add to 4
9+-5 = -45
9-5 =4
0=(x+9) (x-5)
Using the zero product property
0= x+9 0 = x-5
x=-9 x=5
Since length cannot be negative
x=5 is the solution
x=5
x+4 = 5+4 =9
The equations of two lines are y=4x+2 and 6x-y=4 . What is the value of x in the solution for this system of equations?
Answer: x = 3
Step-by-step explanation
This is a simultaneous equation. So to find x , we solve to ascertained the coordinate or point of intersection of the too lines.
y = 4x + 2, and 6x - y = 4
To solve , we need to rearrange first
y = 4x + 2 will be
4x - y = -2 -------------------------1
Equation 2 is in order
6x - y = 4 -------------------------- 2
Now solve the two equation for x by using any methods you are familiar with.
4x - y = -2
6x - y = 4, now subtract equation 2 from 1 in order to eliminate y,
we now have
-2x = -6, now divide through by 2
x = 3.
Hence y could be find by substitution for x in any of the equation above and now check.
4x - y = -2
4(3) - y = -2
12 - y = = -2
y = 12 + 2
y = 14.
Now let check
6x - y = 4
6(3) - 14
18 - 14
= 4.
Therefore, the value of x is 3
Subtract breaking apart 143-79
To subtract 143-79 by breaking apart, round 79 to 80, subtract it from 143 to get 63, and add 1 back for rounding to get the final answer of 64.
Explanation:The question involves breaking apart numbers to subtract 143-79. This is a technique used in math to simplify subtraction by splitting numbers into parts that are easier to work with.
Step-by-Step Explanation:First, let's round 79 to the nearest tens, which is 80.Now, subtract 80 from 143: 143 - 80 = 63.Since we rounded up 79 to 80, we subtracted one extra unit from 143. So, we need to add that 1 back to the result: 63 + 1 = 64.The final answer is 64.
Mrs. Potts is putting a fence around her rectangular garden the length of the garden is 8 yards the width of the garden is 4 yards how many feet of fencing does Mrs. Pott need
Answer:
Mrs. Potts needs 72 feet of fencing.
Step-by-step explanation:
You find the perimeter of the rectangular garden, which is 24 yards. You then convert the yards to feet. There are 3 feet in a yard. You multiply 24 by 3 to get your final answer of 72 feet.
Determine whether the following statement is true or false.
f(g(x)) = f(x) · g(x)
Answer:
False.Step-by-step explanation:
f(g(x)) = f of g of x
f(x) · g(x) = f at x times g at x, which is not the same thing.
The number of people who enter an elevator on the ground floor is a Poisson random variable with mean 10. If there are N floors above the ground floor and if each person is equally likely to get off at any one of these N floors, independently of where the others get off, compute the expected number of stops that the elevator will make before discharging all of its passengers.
Answer:
Expected no of stops=N(1-exp(-10/N)
Step-by-step explanation:
Using equation
X=∑[tex]I_{m}[/tex]
where m lies from 1 to N
solve equation below
E(X)=N(1-exp(-10/N)
Given Information:
Distribution = Poisson
Mean = 10
Required Information:
Expected number of stops = ?
Answer:
[tex]E(N) = N(1 - e^{-0.1N} )[/tex]
Explanation:
The number of people entering on the elevator is a Poisson random variable.
There are N floors and we want to find out the expected number of stops that the elevator will make before discharging all of its passengers.
Mean = μ = 10
The expected number of stops is given by
[tex]E(N) = N(1 - e^{-mN} )[/tex]
Where m is the decay rate and is given by
Decay rate = m = 1 /μ = 1/10 = 0.10
Therefore, the expected number of stops is
[tex]E(N) = N(1 - e^{-0.1N} )[/tex]
If we know the number of floor (N) then we can the corresponding expected value.
Safety regulations state that roller coasters cannot operate safely in high winds. Throughout the day, ride operators measure the wind speed at several random locations along the track to verify that the speed is below an established threshold value, allowing the ride to operate safely. The collected data is used to conduct a one-sample z -test of the null hypothesis that the mean wind speed is moderate against the alternative that the mean wind speed is too high. If the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions. Choose the correct description of a type I error and a type II error in this context.
Answer:
Type I error would be to conclude that the mean wind speed is too high and decide to shut down the ride but in actual the wind speed was moderate and it is safe to do riding.
Type II error would be to conclude that the mean wind speed is moderate and decide to go on riding but in actual the wind speed is too high and it unsafe to go on riding and should be shut down.
Step-by-step explanation:
We are given that the collected data is used to conduct a one-sample z -test of the null hypothesis that the mean wind speed is moderate against the alternative that the mean wind speed is too high.
If the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions.
So, Null Hypothesis, [tex]H_0[/tex] : The mean wind speed is moderate.
Alternate Hypothesis, [tex]H_A[/tex] : The mean wind speed is too high.
Also, it is provided that if the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions.
Now, Type I error states the Probability of rejecting null hypothesis given the fact that it was true or Probability of rejecting the true hypothesis.
So, in the given context, Type I error would be to conclude that the mean wind speed is too high and decide to shut down the ride but in actual the wind speed was moderate and it is safe to do riding.
On the other hand, Type II error states the Probability of accepting null hypothesis given the fact that it was false or Probability of accepting the false hypothesis.So, in the given context, Type II error would be to conclude that the mean wind speed is moderate and decide to go on riding but in actual the wind speed is too high and it unsafe to go on riding and should be shut down.
I need on dis plz because we’re in quarantine and I’m also dumb
Sequence B: The bacteria on a sponge multiply rapidly. This sequence describes the
growth in bacteria over time.
3, 6, 12, 24, 48, 96
the bottor in each sequence and show your work. 1
Step-by-step explanation:
The bacteria is always doubled because in the sequence we multiply the number by 2
3 x 2 = 6 x 2 = 12 x 2 = 24 x 2 = 48 x 2 = 96
(1 point) Suppose that f(x) and g(x) are given by the power series f(x)=6+7x+3x2+5x3+⋯ and g(x)=7+8x+3x2+4x3+⋯. By multiplying power series, find the first few terms of the series for the product h(x)=f(x)⋅g(x)=c0+c1x+c2x2+c3x3+⋯.
Answer:
f(x).g(x) = c0+c1x+c2x2+c3x3+⋯.
[tex]f(x).g(x) = 42 +97x +95x^{2} + 104x^{3} +77x^{4} +27x^{5} + 20x^{6}+....[/tex]
c₀ = 42 , c₁ =97 , c₂ = 95, c₃ =104, ...…...
Step-by-step explanation:
Suppose that f(x) and g(x) are given by the power series
f(x)=6+7x+3x2+5x3+⋯ and
g(x)=7+8x+3x2+4x3+⋯
By multiplying power series ,
f(x).g(x) = (6+7x+3x2+5x3+⋯).(7+8x+3x2+4x3+⋯)
= 6(7+8x+3x2+4x3+⋯)+7x(7+8x+3x2+4x3+⋯)+3x2(7+8x+3x2+4x3+⋯) + 5x3(7+8x+3x2+4x3+⋯)+......
[tex]f(x).g(x) = 42 +97x +95x^{2} + 104x^{3} +77x^{4} +27x^{5} + 20x^{6}+....[/tex]
f(x).g(x) = c0+c1x+c2x2+c3x3+⋯.is the form
[tex]f(x).g(x) = 42 +97x +95x^{2} + 104x^{3} +77x^{4} +27x^{5} + 20x^{6}+....[/tex]
c₀ = 42 , c₁ =97 , c₂ = 95, c₃ =104, ...……
In this problem, power series f(x) and g(x) are multiplied together term by term to produce the product h(x). The first few terms of the h(x) series are found by sequentially multiplying the corresponding terms of f(x) and g(x). The procedures produced the first four terms as 42, 98, 170, and 356 respectively.
Explanation:In the field of mathematics, specifically calculus, you can multiply two power series together term by term. In this case, function f(x) = 6 + 7x + 3x2 + 5x3 + ⋯ and g(x) = 7 + 8x + 3x2 + 4x3 + ⋯ are provided. When you multiply these two power series, the product h(x) = f(x) ⋅ g(x) is obtained by multiplying each corresponding term in the series of f(x) and g(x) together.
To find the first few terms we consider it like
First term, c0: f0*g0 = 6*7 =42Second term, c1: f1*g0 + g1*f0 = 7*6 + 8*7 = 98Third term, c2: f2*g0 + f1*g1 + g2*f0 = 18*3*6 + 7*8 + 21*6 = 170Fourth term, c3: f3*g0 + f2*g1 + f1*g2 + f0*g3 = 30*7 + 18*8 + 21*7 + 6*0 = 356and so on for the subsequent terms.
Learn more about Power Series Multiplication here:https://brainly.com/question/31404538
#SPJ11
In ABCD, the measure of ZD=90°, BD = 20, CB = 29, and DC = 21. What is the value
of the cosine of C to the nearest hundredth?
Answer:
0.72
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relation of interest is ...
Cos = Adjacent/Hypotenuse
Then the cosine of angle C is ...
cos(C) = CD/CB = 21/29
cos(C) ≈ 0.72
Answer:
Step-by-step explanation:
Simplify the Square root of 72a6b3c2
Jay owns some DVDs. Lamar lives next to Jay and three houses from Freda. Lamar has 2 fewer DVDs than Jay. Davina lives on the other side of Jay and has three times as many DVD's as Lamar. Bart lives in house 2 and has 4 more DVD's than Jay. If Tara had 13 more DVD's, she would have four times as many as Jay. Jay acquired all of his DVD from freda, who lives in house 6. Freda had 17 DVD before she gave "p" of them to Jay. the person in house 5 owns the most DVD's wat is the value of p?
Answer:
6
Step-by-step explanation:
Freda lives in house 6. Lamar lives 3 houses from Freda, so lives in house 3. Jay lives next to Lamar, but not in house 2, which is Bart's. So, Jay lives in house 4 and Davina lives in house 5, on the other side of Jay from Lamar.
Davina lives in house 5, so has the most DVDs.
__
Since Freda gave p DVDs to Jay, she has 17-p. Lamar has p-2, Bart has p+4, Tara has 4p-13, and Davina has the most at 3(p-2).
We want Davina to have the most DVDs, so there are some inequalities that must be true:
3(p-2) > 4p-13 ⇒ p < 7
3(p-2) > p +4 ⇒ p > 5
The only value of p satisfying both of these requirements is p = 6.
_____
Tara lives in house 1 and has 11 DVDs.
Bart lives in house 2 and has 10 DVDs.
Lamar lives in house 3 and has 4 DVDs.
Jay lives in house 4 and has 6 DVDs.
Davina lives in house 5 and has 12 DVDs. (the most)
Freda lives in house 6 and has 11 DVDs.
Using a proportion, what can you infer about the number of households in her town that have more than three children?
Answer:
About 296 households have more than three children.
Step-by-step explanation:
The complete question is:
Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,346 unique addresses in her town with numbers ranging from zero to five children. The results of 50 randomly generated households are shown below. Children in 50 Households Number of Children Number of Households 0 5 1 11 2 13 3 10 4 9 5 2 Using a proportion, what can you infer about the number of households in her town that have more than three children? About 242 households have more than three children. About 269 households have more than three children. About 296 households have more than three children. About 565 households have more than three children.
Solution:
The data provided for the number of children and number of households is:
Number of Children (X) Number of Households (f (X))
0 5
1 11
2 13
3 10
4 9
5 2
TOTAL 50
Compute the probability of households having more than three children as follows:
P (More than 3 children) = P (4 children) + P (5 children)
[tex]=\frac{9}{50}+\frac{2}{50}[/tex]
[tex]=\frac{11}{50}[/tex]
[tex]=0.22[/tex]
Let the random variable Y be defined as the number of households having more than three children.
The probability of the random variable Y is, p = 0.22.
The entire population, i.e. total number of addresses in Carmen's town with numbers ranging from zero to five children, consists of N = 1,346 households.
Compute the expected number of households having more than three children as follows:
[tex]E(Y) =N\times p[/tex]
[tex]=1346\times 0.22\\=296.12\\\approx 296[/tex]
Thus, about 296 households have more than three children.
De una cesta de manzanas se pudren 2/3 . Comemos las 4/ 5 del resto y las 25 restantes las utilizamos para hacer mermelada. ¿Cuántas manzanas había en la cesta?
Google translation
2/3 of a basket of apples rot. We eat 4/5 of the rest and use the remaining 25 to make jam. How many apples were in the basket
Answer:
375
Step-by-step explanation:
Since the basket was full, ⅔ rot so the remaining for any use will be 1-⅔=⅓
Since we only eat 4/5 of this remaining quantity, we use the 1-4/5=1/5 of ⅓ for making jam
1/5 of ⅓=1/5*⅓=1/15
If 1/15 equals 25 pieces then the full basket had
25*15/1=375 pieces
Compute the mean and standard deviation of the sampling distribution of the sample mean when you plan to take an SRS of size 49 from a population with mean 420 and standard deviation 21. Now repeat the calculations for a sample size of 576. Explain the effect of the increase on the sample mean and standard deviation.
Answer:
The mean of the sampling distribution(SRS 49) of the sample mean is 420 and the standard deviation is 3.
The mean of the sampling distribution(SRS 576) of the sample mean is 420 and the standard deviation is 0.875.
By the Central Limit Theorem, the sample size does not influence the sample mean, but it does decrease the standard deviation of the sample
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population
mean = 420, standard deviation = 21.
Sample of 49
Mean = 420, standard deviation [tex]s = \frac{21}{\sqrt{49}} = 3[/tex]
The mean of the sampling distribution of the sample mean is 420 and the standard deviation is 3.
Sample of 49
Mean = 420, standard deviation [tex]s = \frac{21}{\sqrt{576}} = 0.875[/tex]
The mean of the sampling distribution of the sample mean is 420 and the standard deviation is 0.875.
Increasing the sample size from 49 to 576 in a simple random sample from a population with a mean of 420 and a standard deviation of 21 keeps the mean of the sampling distribution the same but decreases the standard deviation.
Explanation:When taking a simple random sample (SRS) from a population where the mean (μ) is 420 and the standard deviation (σ) is 21, and using a sample size (n) of 49, the sampling distribution of the sample mean will have:
A mean (μ_x) equal to the population mean (μ), which is 420.A standard deviation (σ_x), also known as the standard error (SE), calculated using the formula σ/√n, which in this case is 21/√49 = 21/7 = 3.When the sample size increases to 576, the sampling distribution of the sample mean will still have a mean of 420, but the standard deviation will decrease because it is inversely proportional to the square root of the sample size. The new standard deviation will be 21/√576 = 21/24 = 0.875.
The effect of increasing the sample size is that while the mean of the sampling distribution remains the same, the standard deviation decreases, leading to a more narrow distribution. This indicates that there is less variability in the sample means, and they will be closer to the population mean, which is in accordance with the Central Limit Theorem.
4.7 kg = __
What equals 4.7 kg =____g
Answer:
If your asking what 4.7kg is to grams then it is 4700g
Answer:
4700 g
Step-by-step explanation:
1 kg = 1000g
Using this rule, 4.7 kg would be 4700g
4.7 x 1000 = 4700
Historically, voter turnout for political elections in Texas have been reported to be 54%. You have been assigned by a polling company to test the hypothesis that voter turnout during the most recent election was higher than 54%. You have collected a random sample of 90 registered voters from this elections and found that 54 actually voted. Assume that the true proportion of voter turnout is 0.67. Calculate the probability of a Type II error using α= 0.02.
Answer:
The probability of a Type II error is 0.3446.
Step-by-step explanation:
A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false. It is symbolized by β i.e.
β = Probability of accepting H₀ when H₀ is false
= P (Accept H₀ | H₀ is false)
In this case we need to test the hypothesis whether the voter turnout during the most recent elections in Texas was higher than 54%.
The hypothesis can be defined as:
H₀: The voter turnout during the most recent elections in Texas was 54%, i.e. p = 0.54.
Hₐ: The voter turnout during the most recent elections in Texas was higher than 54%, i.e. p > 0.54.
A type II error would be committed if we conclude that the voter turnout during the most recent elections in Texas was 54%, when in fact it was higher.
The information provided is:
X = 54
n = 90
α = 0.02
true proportion = p = 0.67
Compute the mean and standard deviation as follows:
[tex]\mu=p=0.54[/tex]
[tex]\sigma=\sqrt{\frac{0.54(1-0.54)}{90}}=0.053[/tex]
Acceptance region = P (Z < z₀.₀₂)
The value z₀.₀₂ is 0.6478.
Compute the sample proportion as follows:
[tex]z=\frac{\hat p-\mu}{\sigma}\\2.054=\frac{\hat p-0.54}{0.053}\\\hat p=0.6489[/tex]
Compute the value of β as follows:
β = P (p < 0.54 | p = 0.67)
[tex]=P(\frac{\hat p-\mu}{\sigma}<\frac{0.6489-0.67}{0.053})\\=P(Z<-0.40)\\=0.34458\\\approx 0.3446[/tex]
Thus, the probability of a Type II error is 0.3446.