P(x < 1) = 0.082085.
The given parameters are μ and x. The mean and variance of the Poisson distribution are μ and σ^2 = μ.The probability that the random variable X takes on the value x is given by P(x).P(x=1) when μ = 3.5
Here, x = 1 and μ = 3.5Plug in the given values in the Poisson distribution,
P(x = 1) = ((e^-3.5) (3.5^1))/1!P(x = 1) = ((0.0301974) (3.5))/1!P(x = 1) = 0.105691(1)P(x = 1) = 0.105691
Thus, P(x=1) = 0.105691.P(x ≤ 9)when μ = 6. The given parameters are μ and x. The mean and variance of the Poisson distribution are μ and σ^2 = μ.
P(x ≤ 9) when μ = 6. Here, x ≤ 9 and μ = 6
Using the Poisson formula:
P(x ≤ 9) = Σ P(x = i) for i = 0 to 9.P(x ≤ 9) = Σ P(x = i) for i = 0 to 9.P(x ≤ 9) = Σ ((e^-6)(6^i))/i! for i = 0 to 9P(x ≤ 9) = 0.091578So,
P(x ≤ 9) = 0.091578P(x > 2) when μ = 3.The mean and variance of the Poisson distribution are μ and σ^2 = μ.P(x > 2) when μ = 3:Here, x > 2 and μ = 3
Using the Poisson formula:
P(x > 2) = Σ P(x = i) for i = 3 to infinityP(x > 2) = Σ ((e^-3) (3^i))/i! for i = 3 to infinityP(x > 2) = 1 - P(x ≤ 2)P(x > 2) = 1 - ((e^-3)(3^0))/0! + ((e^-3) (3^1))/1! + ((e^-3) (3^2))/2!P(x > 2) = 1 - ((0.04978706836)(1))/1 + ((0.04978706836)(3))/1 + ((0.04978706836)(9))/2P(x > 2) = 1 - (0.04978706836 + 0.1493612051 + 0.2240418077)P(x > 2) = 0.5768099198So, P(x > 2) = 0.5768099198.P(x < 1) when μ = 2.5.
The given parameters are μ and x. The mean and variance of the Poisson distribution are μ and σ^2 = μ.P(x < 1) when μ = 2.5:Here, x < 1 and μ = 2.5
Using the Poisson formula:
P(x < 1) = P(x = 0)P(x < 1) = ((e^-2.5) (2.5^0))/0!P(x < 1) = 0.082085P(x < 1) = 0.082085Thus, P(x < 1) = 0.082085.
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Given that X is a random variable having a Poisson distribution, the probability mass function of X is [tex]P(x)=((e^{-\mu})(\mu^{x}))/x![/tex],
x=0,1,2,…
Here, μ is the mean or the expected value of the distribution.
a) P(x=1) when μ=3.5 is 0.1288 (approx.)
b) P(x≤9) when μ=6 is 0.99988 (approx.)
c) P(x>2) when μ=3 is 0.5766 (approx.)
d) P(x<1) when μ=2.5 is 0.0821 (approx.).
Compute the following:
a) P(x=1) when μ=3.5
Calculate probability for random variable by using the probability mass function of X as follows:
[tex]P(x=1)=((e^{-3.5})(3.5^{1}))/1![/tex]
=0.1288 (approx.)
b) P(x≤9) when μ=6
Calculate, [tex]P(x\leq9)= \sum P(x=k)[/tex] from
k=0 to
[tex]9= \sum ((e^{-6})(6^{k}))/k![/tex] from
k=0 to
9=0.99988 (approx.)
c) P(x>2) when μ=3
We are given μ=3. Then,
P(x>2)= 1- P(x≤2)
= 1- (P(x=0)+P(x=1)+P(x=2))
[tex]= 1- (((e^{-3})(3^{0}))/0!+((e^{-3})(3^{1}))/1!+((e^{-3})(3^{2}))/2!)[/tex]
= 0.5766 (approx.)
d) P(x<1) when μ=2.5
Then, P(x<1)=
P(x=0)
[tex]= ((e^{-2.5})(2.5^0))/0![/tex]
= 0.0821 (approx.)
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Find an equation of the sphere that passes through the point (7.3.-1) and has center (5, 8, 5).
The equation of the sphere passing through the point (7, 3, -1) with center (5, 8, 5) is:
(x - 5)^2 + (y - 8)^2 + (z - 5)^2 = 65.
To find the equation of the sphere passing through the point (7, 3, -1) with center (5, 8, 5), we can use the general equation for a sphere in three-dimensional space. The equation of a sphere with center (h, k, l) and radius r is given by:
(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2.
Using the given center (5, 8, 5), we have:
(x - 5)^2 + (y - 8)^2 + (z - 5)^2 = r^2.
Since the sphere passes through the point (7, 3, -1), we can substitute these values into the equation:
(7 - 5)^2 + (3 - 8)^2 + (-1 - 5)^2 = r^2.
Simplifying the equation gives us:
4 + 25 + 36 = r^2.
65 = r^2.
Therefore, the equation of the sphere passing through the point (7, 3, -1) with center (5, 8, 5) is:
(x - 5)^2 + (y - 8)^2 + (z - 5)^2 = 65.
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The volume of a cylinder can be determined using the formula V=πr2h, where r and h represent the radius and height of the cylinder, respectively. A volume of paint expressed as (8x3 + 31x2 + 32x)π and a volume of paint expressed as (10x3 + 17x2)π are poured into a paint can in the shape of a cylinder. Determine possible expressions for the radius of the can and the depth of the paint in the can.
Answer:
Possible expressions for the radius of the can and the depth of the paint in the can are [tex]r = \sqrt{9\cdot x^{2}+24\cdot x+16}[/tex] and [tex]h = 2\cdot x[/tex], respectively.
Step-by-step explanation:
Let be the initial volumes of the initial cans represented by these expressions:
[tex]V_{1} = (8\cdot x^{3}+31\cdot x^{2}+32\cdot x)\cdot \pi[/tex] (1)
[tex]V_{2} = (10\cdot x^{3}+17\cdot x^{2})\cdot \pi[/tex] (2)
The resulting volume of the paint can is the sum of the two functions:
[tex]V_{3} = (18\cdot x^{3}+48\cdot x^{2}+32\cdot x)\cdot \pi[/tex] (3)
Then, we proceed to factor the polynomial:
[tex]V_{3} = 2\cdot (9\cdot x^{2}+24\cdot x +16)\cdot x \cdot \pi[/tex]
[tex]V_{3} = \pi\cdot (9\cdot x^{2}+24\cdot x + 16)\cdot (2\cdot x)[/tex] (3b)
By direct comparison with the volume formula for the cylinder we have the following expressions:
[tex]r^{2} = 9\cdot x^{2}+24\cdot x + 16[/tex]
[tex]r = \sqrt{9\cdot x^{2}+24\cdot x+16}[/tex]
[tex]h = 2\cdot x[/tex]
Possible expressions for the radius of the can and the depth of the paint in the can are [tex]r = \sqrt{9\cdot x^{2}+24\cdot x+16}[/tex] and [tex]h = 2\cdot x[/tex], respectively.
A test for divisibility by 11 is to see if the digits taken in order and alternately added and subtracted produce a number which is divisible by 11. Consider 5-digit numbers of the form "abcde'. Show that "abcde' will be divisible by 11 if and only if a - b+c-d+e is divisible by 11.
An test for divisibility that a 5-digit number "abcde" will be divisible by 11 if and only if "a - b + c - d + e" is divisible by 11.
To show that a 5-digit number "abcde" is divisible by 11 if and only if "a - b + c - d + e" is divisible by 11, the concept of modular arithmetic.
The 5-digit number "abcde" as a sum of its digits multiplied by their respective place values:
"abcde" = a × 10000 + b × 1000 + c × 100 + d × 10 + e
Then express "a - b + c - d + e" in terms of the digits:
a - b + c - d + e = a × (10,000 mod 11) - b × (1,000 mod 11) + c × (100 mod 11) - d × (10 mod 11) + e
examine the patterns of the modulos:
10,000 mod 11 = 1
1,000 mod 11 = 10
100 mod 11 = 1
10 mod 11 = 10
Substituting these values back into the expression,
a - b + c - d + e = a × 1 - b ×10 + c × 1 - d × 10 + e
Simplifying further:
a - b + c - d + e = a - b + c - d + e
observe that the expression "a - b + c - d + e" is equivalent to the original 5-digit number "abcde." This means that if "abcde" is divisible by 11, then "a - b + c - d + e" will also be divisible by 11.
Conversely, if "a - b + c - d + e" is divisible by 11, it implies that the expression and the 5-digit number "abcde" have the same remainder when divided by 11. Since they are equivalent, "abcde" must also be divisible by 11.
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Please help AND SHOW WORK!!!!
3x^(3)-6x^(2)+15x-30
Answer:
(x - 2)(3x^2 + 5)
Step-by-step explanation:
All four terms here have 3 as a factor. Factor out 3:
3x^(3)-6x^(2)+15x-30 => 3(x^3 - 2x^2 + 5x - 10)
The last two terms can be rewritten as 5(x - 2). The first two terms can be rewritten as 3x^2(x - 2). So (x - 2) is a factor of 3(x^3 - 2x^2 + 5x - 10). We get:
3x^2(x - 2) + 5(x - 2) = (x - 2)(3x^2 + 5)
kelly deposits $3,000 at a rate of 5.2ompounded quarterly. with no additional deposits or withdrawals, what is the account balance after 10 years?
The account balance after 10 years will be approximately $5,259.99.
The balance in Kelly's account after 10 years can be determined using the formula for compound interest which is given as:
A = [tex]P(1 + r/n)^{nt}[/tex]
Where, A is the balance after time t, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
Using this formula and substituting the given values, we get:
A = [tex]3000(1 + 0.052/4)^{4 \times 10}[/tex]
= [tex]3000(1.0125)^{40}[/tex] ≈ $5,259.99
Therefore, the account balance after 10 years will be approximately $5,259.99.
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describe the vertical asymptotes) and holes) for the graph of y=x-6/x^2 5x 6
Given the function `y = (x-6) / (x^2 + 5x + 6)`, let's identify the vertical asymptotes and holes: Factoring the denominator, we get`(x^2 + 5x + 6) = (x+2)(x+3)`So, `y = (x-6) / (x+2)(x+3)`
The vertical asymptotes of the function are the roots of the denominator. Thus, the vertical asymptotes of the function are `x = -2` and `x = -3`.Now, we'll look for the holes in the function. A hole is a point where the function is undefined but can be simplified by canceling common factors.
In the given function, we notice that the numerator `(x-6)` and the denominator `(x+2)(x+3)` have a common factor of `(x-6)`. Thus, there is a hole at `x = 6`.We can cancel `(x-6)` from both numerator and denominator to obtain the simplified function `y = 1 / (x+3)`.Therefore, the vertical asymptotes are `x = -2` and `x = -3`, and there is a hole at `x = 6`.
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A sample of two items is selected without replacement from a batch. Describe the ordered sample space for the following batch:
(a)The batch contains 3 defective items and 10 good times.Hint: suppose we denote defective item by ‘d’ and good item as ‘g’, so one possible outcome could be "dg".
(b)The batch contains the items {a, b, c, d}.
For both scenarios, a sample is selected without replacement from a batch of items. In the first scenario, the batch contains 3 defective items ('d') and 10 good items ('g'). The ordered sample space consists of all possible ordered pairs of items: {dd, dg, gd, gg}. In the second scenario, the batch contains the items {a, b, c, d}. The ordered sample space also consists of all possible ordered pairs of items: {aa, ab, ac, ad, ba, bb, bc, bd, ca, cb, cc, cd, da, db, dc, dd}.
In the first scenario, the ordered sample space is derived by considering all possible combinations of the two items selected from the batch. Since the selection is done without replacement, the first item can be either defective ('d') or good ('g'). For each case, the second item can also be defective or good, depending on what was chosen as the first item. Therefore, the ordered sample space consists of four possibilities: dd, dg, gd, and gg.
In the second scenario, the batch consists of four distinct items: a, b, c, and d. Again, the ordered sample space is obtained by considering all possible combinations of the two items selected without replacement. Since there are four items, there are 16 possible combinations. Each combination is represented by an ordered pair of the selected items, such as aa, ab, ac, and so on.
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HELPPPO !% PT PLZZZZZZZZZZZZZZZZZZZZZ
Answer:
6/12, 2/4,
Step-by-step explanation:
6/12 because half of 12 is 6.
2/4 because half of 4 is 2.
Both can equal 1/2.
If the true means of the k populations are equal in an ANOVA model, then MSTR/MSE should be: a. more than 1.00 b. close to 1.00 c. close to 0.00 d. close to -1.00 e. a negative value between 0 and - 1 f. not enough information to make a decision
The correct answer is b. close to 1.00. Ratio close to 1.00 indicates that the between-group variation is similar to the within-group variation.
In an ANOVA (Analysis of Variance) model, MSTR refers to the mean square treatment (or between-group variation), while MSE refers to the mean square error (or within-group variation).
If the true means of the k populations are equal, it means that the between-group variation is similar to the within-group variation, and there is no significant difference between the group means.
In this scenario, we would expect the MSTR/MSE ratio to be close to 1.00 (answer b). A ratio close to 1.00 indicates that the between-group variation is similar to the within-group variation, supporting the assumption that the true means of the populations are equal.
Therefore, the correct answer is b. close to 1.00.
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Assume that a sample is used to estimate a population proportion μ. Find the margin of error M.E. that corresponds to a sample of size 10 with a mean of 33.7 and a standard deviation of 13.3 at a confidence level of 95%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = _________ Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
The margin of error for a 95% confidence level is 8.2.
How to find the margin of error?The margin of error (ME) is determined using the formula:
ME= z ∗ σ/√n
where:
z is the z-score for the desired confidence level
σ is the population standard deviation
n is the sample size
For a 95% confidence level, the z-score is 1.96. Thus, we have:
z = 1.96
σ = 13.3
n = 10
Substituting these values into the formula, we have:
ME = 1.96 ∗ 13.3/√10
ME = 8.2
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Hi can you guys please answer this! I’ll mark you as brainless
Answer:
0.42846931021
Step-by-step explanation:
Marissa bought 7 bottles of soda for a party. Each bottle was 2-liters. How many gallons of soda did she buy?
Answer
3.7 or approximately 4 gallons
Step-by-step explanation:
7x2=14 total liters.
3.78 liters=1 gallon
14/3.78= 3.7 gallons
Sort each expense as either a fixed expense or a variable expense.
monthly rent
ixed Expense
Variable Expense
car payment
movies
savings for new guitar
snacks
video games
Answer:
fixed - monthly rent, car payment, savings for new guitar
variable - movies, video games, snacks
Step-by-step explanation:
Fixed costs are costs that do not vary with output.
the amount of rent paid is fixed.
Variable costs are costs that vary with production
the amount paid at the movies depend on the number of movies watched
(4, 4 3 ) (i) find polar coordinates (r, ) of the point, where r > 0 and 0 ≤ < 2. (r, ) = (ii) find polar coordinates (r, ) of the point, where r < 0 and 0 ≤ < 2.
(i) The polar coordinates (r, θ) of the point (4, 3) are (5, arctan(3/4)). (ii) For a point with negative radius, the concept of polar coordinates is not applicable as polar coordinates are defined for points in the positive radial direction.
(i) To find the polar coordinates (r, θ) of the point (4, 3), we can use the formulas:
r = √(x² + y²) and θ = arctan(y/x).
Given that x = 4 and y = 3, we can calculate the values:
r = √(4² + 3²) = 5
θ = arctan(3/4)
Therefore, the polar coordinates of the point (4, 3) are (5, arctan(3/4)).
(ii) For a point with negative radius, the concept of polar coordinates is not applicable. In polar coordinates, the radius (r) is always defined as a positive value. Negative values of r would imply a direction opposite to the positive radial direction. However, the convention of polar coordinates focuses on the positive radial direction, so negative radius values are not considered.
In conclusion, polar coordinates are not defined for points with negative radius values, and therefore, the concept of polar coordinates does not apply to find the polar coordinates of a point with r < 0.
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I finally started watching my hero academia, its really good but i HATEEE the season long competition thing!! its annoying! same with naruto, u watch an episode thinking ur gonna at least finish the round he is in but nOOOOoOOO
Answer:
same
Step-by-step explanation:
use the inner product u, v = 2u1v1 u2v2 in r2 and the gram-schmidt orthonormalization process to transform {(2, 1), (−2, −5)} into an orthonormal basis.
The orthonormal basis for (2, 1), (2, 5) is therefore u1, u2 = (2/5, 1/5), (2/5, -1/5) because u2 = v2_orth/||v2_orth|| = (2/5, -1/5).
In R2, the internal result of the two vectors u and v is as follows: The Gram-Schmidt procedure can be used to request the transformation of (2, 1), (2, 5) into an orthonormal premise. u, v = 2u1v1 + u2v2. An orthonormal premise is made by changing over a bunch of directly free vectors utilizing the Gram-Schmidt process. Our set's principal vector, v1 = (2, 1), should serve as our starting point.
We standardize v1 to obtain our first orthonormal premise vector: We must locate the second vector in our set, v2 = (-2, -5), and we can orthogonalize v2 by deducting its projection from u1: u1 = v1/||v1|| = (2/5, 1/5) proj_u1(v2) = (v2 u1)u1 = (- 8/5, - 4/5)v2_orth = v2 - proj_u1(v2) = (6, - 21/5)Our second orthonormal premise vector is acquired by normalizing v2_orth: The orthonormal reason for (2, 1), (2, 5) is subsequently u1, u2 = (2/5, 1/5), (2/5, - 1/5) in light of the fact that u2 = v2_orth/||v2_orth|| = (2/5, - 1/5).
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Pew research reported in 2013 that 15% of American adults do not use the internet or e-mail. They report a margin of error of 2.3 percentage points. The meaning of that margin of error is: A) If they repeatedly sampled from the population, and constructed a confidence interval for each estimate, about 2.3% of those intervals would capture the proportion of American adults who don't use the internet or e-mail. B) They estimate that 2.3% of those surveyed answered incorrectly. C) There is a 2.3% probability that their estimate is incorrect. D) They are pretty sure that the poll result differs from the actual percentage of American adults who don't use the internet or e-mail by 2.3% or less.
Answer:
B) They estimate that 2.3% of those surveyed answered incorrectly
Step-by-step explanation:
hope it helps you dude
Ice rental: $150 Skate rental: $3
Write a problem that can be solved using an equation then solve the problem
Answer:
Ice rental at the local skating rink is $150 for 2h. Skate rental is $3 per person. The Grade 8 class went skating. All students rented skates. The total cost was $231. How many students went skating?
slope of (9,3) (19,-17) using slope formula
The number of calories of a food item varies directly with the size of the portion. If a 2-inch slice of a certain delicacy contains 170 calories, how many calories are in a 3-inch slice?
Answer:
A 3-inch slice of the food item contains 255 calories.
Step-by-step explanation:
Set calories per inch slice as variable x.
2x = 170
x = 85 cal
Since each inch slice of the food item contains 85 calories, a 3-inch slice would contain:
3x = 3(85) = 255 cal
what is 25/x 15/30 can you please help
Answer:
x = 50.... 25/50 = 15/30 or 1/2 = 1/2
Step-by-step explanation:
25/x = 15/30
consider the cross multiply
25 * 30 = 15 * x
750 = 15x
divide both sides with 15 to make the co-efficient of x, 1.
x = 50
Answer:
5×15/6
5×5/2
25/2
12.2 is your answer ☺️☺️☺️. If I'm right so,
Please mark me as brainliest. thanks!!!
Determine the area of a circle whose radius is 15 feet. Use pie=3.14
Answer:
Down below
Step-by-step explanation:
[tex]A=\pi r^2\\A=3.14*(15)^2\\A=3.14*225\\A=706.5[/tex]
Given the set S = (Q n [13, 16]) U (1,5) U (5, 7) U20 + ()" u{zo-1-8"} n ηε N Answer the following questions. Mark all items that apply. 1. Which of these points are in the interior of S?
The interior of S consists of all the points in S that are not in the boundary of S. These points are:
The rational numbers strictly between 13 and 16
The rational numbers strictly between 1 and 5
The rational numbers strictly between 5 and 7
The natural numbers strictly between 1 and 18, excluding 20
The set S consists of the rational numbers between 13 and 16 (inclusive), the open interval between 1 and 5, the open interval between 5 and 7, the singleton set {20}, and the set of natural numbers between 0 and 18.
To find the interior of S, we need to find all the points in S that have a neighborhood entirely contained in S. In other words, we need to find all the points in S that are not on the boundary of S.
The boundary of S includes the endpoints of the closed interval [13, 16] and the endpoints of the open intervals (1, 5) and (5, 7), as well as the points 20, 0, and 18.
Therefore, the interior of S consists of all the points in S that are not in the boundary of S. These points are:
The rational numbers strictly between 13 and 16
The rational numbers strictly between 1 and 5
The rational numbers strictly between 5 and 7
The natural numbers strictly between 1 and 18, excluding 20
Note that the point 20 is not in the interior of S because it is on the boundary of S. Similarly, the points 0 and 18 are not in the interior of S because they are in the boundary of S.
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Let X be a normal random variable with a mean of 0.33 and a standard deviation of 2.69.
a)Calculate the corresponding standardized value (z) for the point x = 4.1. Give your answer to 2 decimal places.
z =
b)The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable is:
less than or equal to z
equal to z
greater than or equal to z
a) the corresponding standardized value (z) for x = 4.1 is approximately 1.39.
b) The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable is less than or equal to z.
a) To calculate the standardized value (z) for the point x = 4.1, we can use the formula:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
In this case, x = 4.1, μ = 0.33, and σ = 2.69. Plugging these values into the formula:
z = (4.1 - 0.33) / 2.69
z ≈ 1.39
So, the corresponding standardized value (z) for x = 4.1 is approximately 1.39.
b) The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable is less than or equal to z.
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The lifetimes of Triple X TV Tubes are approximately normally distributed with mean 13.2 years and standard deviation 3.5 years. Consider the distribution of sample means for all samples of 100 Triple X TV tubes.
Part A
What is the standard error, to two decimal places, of the sample means? Give your answer to two decimal places in the form x.xx
Standard error: ?
Part B
And what is the mean of the sample means? Give your answer to one decimal place in the form xx.x or x.x as appropriate
Mean of sample means: ?
In Part A: Standard error = 3.5 / √100 = 3.5 / 10 = 0.35 years and in Part B: the mean of the sample means is 13.2 years.
Part A: The standard error of the sample means can be calculated using the formula: standard deviation / square root of the sample size. In this case, the standard deviation is 3.5 years and the sample size is 100. So, the standard error is given by:
Standard error = 3.5 / √100 = 3.5 / 10 = 0.35 years
Part B: The mean of the sample means is equal to the population mean, which is 13.2 years. When we take multiple samples from a population, the mean of those sample means is expected to be equal to the population mean. In this case, the mean of the sample means is 13.2 years. The standard error of the sample means is 0.35 years, indicating the average deviation of the sample means from the population mean. The mean of the sample means is 13.2 years.
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2) On a map, the scale is 1 inch represents 150 miles. If the map distance is 3 inches, find the actual distance.
Answer:
150*3= 450 miles
Hope this helped :)
Find the compound interest paid at the end of 11 years and 33 months when a sum of ₹20000 is invested at a rate of 6% per annum compounded annually?
DONT ADD LINKS PLEASE ANSWER CORRECTLY AND FAST, PLEASE I WILL MARK YOU BRAINLIEST FOR CORRECT ANSWER
Answer:
The total would be 36,600.
Step-by-step explanation:
First you will convert 33 months into years which is 2 years and 10 months.
You will then add the 2 years and the 11 years together which gets you 13 so now you have a total of 13 years and 10 months. (this information will be used later)
Now we will start by multiplying the 20000 by 16% and we should get a total of 1200. That means the interest is 1200 per year so lets first take our 13 years and multiply it by the 1200 (13x1200). You should have 15600 as an answer (save this number for later) since we have 10 months were going to take that 1200 and divide it into 12 month meaning the monthly interest should be 100 per month since we have 10 months we will multiply 100 by 10 and get 1000. Now lets bring back that 15600 and add the additional 1000 to it, our answer should be 16,600, and then we add the original 20000 to the 16600 and your final answer should be 36600.
Ajar contains 5 red and 3 purple jelly beans. How many ways can 4 jelly beans be picked so that at least 2 are red? 11 15 10 6
There are 10 ways to pick 4 jelly beans from a jar containing 5 red and 3 purple jelly beans, ensuring at least 2 are red.
To calculate the number of ways, we consider the cases where we choose exactly 2 red jelly beans, 3 red jelly beans, or all 4 red jelly beans.
Case 1: Choosing 2 red jelly beans - There are 5 red jelly beans to choose from, and we need to select 2. This can be done in [tex]5C2 = 10[/tex] ways.
Case 2: Choosing 3 red jelly beans - There are 5 red jelly beans to choose from, and we need to select 3. This can be done in [tex]5C3 = 10[/tex] ways.
Case 3: Choosing all 4 red jelly beans - There are 5 red jelly beans, and we need to select 4. This can be done in [tex]5C4 = 5[/tex] ways.
Adding up the possibilities from all three cases, we get 10 + 10 + 5 = 25 ways. However, we need to subtract the case where we select all 4 purple jelly beans, which is only 1 way. Therefore, the final number of ways is 25 - 1 = 24 ways.
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Consider the function h(z) = 1 4iz + 2 defined on the extended complex plane. (a) Write h as a composition of the linear function g(z) and reciprocal function f(z) (b) Determine the image of the line y = 2 under w=h(z). (c) Determine the image of the circle |z - i| = 1/2 under w = h(z).
The function h(z) = 1 4iz + 2 defined on the extended complex plane,
(a) The function h(z) = 1/(4iz + 2) can be expressed as a composition of the linear function g(z) and reciprocal function f(z).
(b) The image of the line y = 2 under w = h(z) is the point z = -3/(8i).
(c) The image of the circle |z - i| = 1/2 under w = h(z) is the two points z = i + √7/2 and z = i - √7/2.
(a) To express the function h(z) = 1/(4iz + 2) as a composition of a linear function g(z) and reciprocal function f(z), we can rewrite h(z) as follows:
h(z) = 1/(4iz + 2)
= 1/(4i(g(z)) + 2)
= 1/f(g(z))
Here, g(z) represents the linear function and f(z) represents the reciprocal function. To determine g(z), we set g(z) = 4iz + 2.
Therefore, the composition of the linear function g(z) and the reciprocal function f(z) is:
h(z) = 1/f(g(z)) = 1/(4iz + 2)
(b) To find the image of the line y = 2 under w = h(z), we substitute y = 2 into the function h(z) and solve for z.
y = 2
1/(4iz + 2) = 2
To simplify the equation, we multiply both sides by (4iz + 2):
1 = 2(4iz + 2)
1 = 8iz + 4
8iz = -3
z = -3/(8i)
Therefore, the image of the line y = 2 under w = h(z) is the point z = -3/(8i).
(c) To determine the image of the circle |z - i| = 1/2 under w = h(z), we substitute z - i = 1/2 into the function h(z) and solve for w.
|z - i| = 1/2
|z - i|² = (1/2)²
(z - i)(z - i*) = 1/4
z² - iz - iz + i² = 1/4
z² - 2iz + 1 = 1/4
z² - 2iz + 3/4 = 0
Now we solve this quadratic equation using the quadratic formula:
z = (-(-2i) ± √((-2i)² - 4(1)(3/4))) / (2(1))
z = (2i ± √(-4i² - 3)) / 2
z = (2i ± √(4 + 3)) / 2
z = (2i ± √7) / 2
z = i ± √7/2
So, the image of the circle |z - i| = 1/2 under w = h(z) is the two points z = i + √7/2 and z = i - √7/2.
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sum of -10°C,24°C,-12°C,8°C,-1°C
Answer:
9°C
Step-by-step explanation:
Group the terms and get [tex]24+8-1-10-12[/tex]
Then simplify to get [tex]32-23[/tex]
Subtract and you get 9
So the answer is 9°C.
Hope this helps!