Answer:
(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.
(b) The simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).
(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].
(d) The probability that only one of the three is a man is 0.375.
(e) The probability that all three are women is 0.125.
Step-by-step explanation:
We are given that three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.
(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.
(b) As we know that the gender of each person is noted by the county clerk, which means one is male and another female.
So, the simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).
Here, M is denoted for male and F for female.
(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].
Because there is 50-50 chance of selecting males or females.
(d) The probability that only one of the three is a man is given by;
The total cases in the sample space = 8
Number of cases of only one man out of three = 3
So, the required probability = [tex]\frac{3}{8}[/tex] = 0.375.
(e) The probability that all three are women is given by;
The total cases in the sample space = 8
Number of cases of all three are women = 1
So, the required probability = [tex]\frac{1}{8}[/tex] = 0.125.
PLEASE HELP!! (1/5) -50 POINTS-
Answer:
[tex]X=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]
Step-by-step explanation:
We are given the following matrix equation, from which we have to isolate X and simplify this value.
[tex]\begin{bmatrix}2&4\\ \:\:\:5&4\end{bmatrix}X\:+\:\begin{bmatrix}-8&-8\\ \:\:\:12&1\end{bmatrix}=\:\begin{bmatrix}-10&6\\ \:\:\:25&24\end{bmatrix}[/tex]
To isolate X, let us first subtract the second matrix, as demonstrated below, from either side. Further simplifying this equation we can multiply either side by the inverse of the matrix being the co - efficient of X, isolating it in the doing.
[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}[/tex] (Simplify second side of equation)
[tex]\begin{bmatrix}-10&6\\ 25&24\end{bmatrix}-\begin{bmatrix}-8&-8\\ 12&1\end{bmatrix}=\begin{bmatrix}\left(-10\right)-\left(-8\right)&6-\left(-8\right)\\ 25-12&24-1\end{bmatrix}=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] ,
[tex]\begin{bmatrix}2&4\\ 5&4\end{bmatrix}X=\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}[/tex] (Multiply either side by inverse of matrix 1)
[tex]X=\begin{bmatrix}2&4\\ 5&4\end{bmatrix}^{-1}\begin{bmatrix}-2&14\\ 13&23\end{bmatrix}=\begin{bmatrix}5&3\\ -3&2\end{bmatrix}[/tex]
Our solution is hence option c
A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 140 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month? Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents 8 15 9 8 13 6 17 15 10 9 18 12
Answer:
There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.
There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.
Step-by-step explanation:
Month No. of Mean Squared
Fatal Accidents Deviation Difference
Jan 8 -4 16
Feb 15 3 9
Mar 9 -3 9
Apr 8 -4 16
May 13 1 1
Jun 6 -6 36
Jul 17 5 25
Aug 15 3 9
Sep 10 -2 4
Oct 9 -3 9
Nov 18 6 36
Dec 12 0 0
Total 140 170
Mean = 140/12 = 12 Mean of squared deviation (Variance) = 170/12 = 14.16667
Standard deviation = square root of variance = 3.76386 = 4
The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set. It also shows how variable the data varies from the mean of approximately 12.
The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.
solve the system with elimination 4x+3y=1 -3x-6y=3
Answer:
x = 1, y = -1
Step-by-step explanation:
If we have the two equations:
[tex]4x+3y=1[/tex] and [tex]-3x - 6y = 3[/tex], we can look at which variable will be easiest to eliminate.
[tex]y[/tex] looks like it might be easy to get rid of, we just have to multiply [tex]4x+3y=1[/tex] by 2 and y is gone (as -6y + 6y = 0).
So let's multiply the equation [tex]4x+3y=1[/tex] by 2.
[tex]2(4x + 3y = 1)\\8x + 6y = 2[/tex]
Now we can add these equations
[tex]8x + 6y = 2\\-3x-6y=3\\[/tex]
------------------------
[tex]5x = 5[/tex]
Dividing both sides by 5, we get [tex]x = 1[/tex].
Now we can substitute x into an equation to find y.
[tex]4(1) + 3y = 1\\4 + 3y = 1\\3y = -3\\y = -1[/tex]
Hope this helped!
Help me please I need answers
Answer:
[tex]\huge \boxed{\mathrm{\$ \ 7,533.33}}[/tex]
Step-by-step explanation:
There are 12 months in one whole year.
In one year, the person earns $96,600 with bonus.
The person gets a bonus of $6,200 during Christmas.
96,600 - 6,200 = 90,400
The person earns $90,400 yearly.
[tex]\frac{90,400}{12}[/tex] = 7,533.3333
Each month, the person earns $7,533.33, to the nearest cent.
A blue die and a red die are thrown. B is the event that the blue comes up with a 6. E is the event that both dice come up even. Write the sizes of the sets |E ∩ B| and |B|a. |E ∩ B| = ___b. |B| = ____
Answer:
Size of |E n B| = 2
Size of |B| = 1
Step-by-step explanation:
I'll assume both die are 6 sides
Given
Blue die and Red Die
Required
Sizes of sets
- [tex]|E\ n\ B|[/tex]
- [tex]|B|[/tex]
The question stated the following;
B = Event that blue die comes up with 6
E = Event that both dice come even
So first; we'll list out the sample space of both events
[tex]B = \{6\}[/tex]
[tex]E = \{2,4,6\}[/tex]
Calculating the size of |E n B|
[tex]|E n B| = \{2,4,6\}\ n\ \{6\}[/tex]
[tex]|E n B| = \{2,4,6\}[/tex]
The size = 3 because it contains 3 possible outcomes
Calculating the size of |B|
[tex]B = \{6\}[/tex]
The size = 1 because it contains 1 possible outcome
Can I have somebody answer a few more of the questions that I need please and this one too?
Answer:
x > 22
Step-by-step explanation:
Hey there!
Well to solve,
52 - 3x < -14
we need to single out x
52 - 3x < -14
-52 to both sides
-3x < -66
Divide both sides by -3
x > 22
The < changes to > because the variable number is a - being divided.
Hope this helps :)
Answer:
x > 22
Step-by-step explanation:
First, rearrange the equation
52 - 3 × x - (-14) < 0Then, pull out the like terms:
66 - 3xNext, apply algebra to the equation by dividing each side by -3. It should now look like this: x > 22.
Therefore, the solution set of the inequality would be x > 22.
From a group of 11 people, 4 are randomly selected. What is the probability the 4 oldest people in the group were selected
The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.
Given that:
Find how many ways the 4 oldest people can be selected from the group.
Since the 4 oldest people are already determined, there is only 1 way to select them.
n = 11 (total number of people in the group) and k = 4 (number of people to be selected).To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:
Number of ways to choose k items from n items :
C(n,k) = n! / (k!(n-k)!)
Calculate the total number of ways to select 4 people from the group:
Plugging n and k value from given data:
C(11,4 )= 11! / (4!(11-4)!)
On simplifications gives:
C(11, 4) = 330.
Calculate the probability:
Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people
Plugging the given data:
Probability = 1 / 330
Probability ≈ 0.00303 or 0.303%.
Therefore, the probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.
Learn more about probabilities here:
https://brainly.com/question/23846068
#SPJ4
The angles of a quadrilateral are (3x + 2), (x-3), (2x+1), and 2(2x+5). Find x.
Answer:
3x+2+x-3+2x+1+2(2x+5)=360
10x+10=360
x=35
Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
a. (4,2,−4)
b. (0,8,15)
c. (√2,1,1)
d. (−2√3,−2,3)
Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:
[tex]\rho = \sqrt{x^{2}+y^{2}+z^{2}}[/tex]
[tex]\phi = cos^{-1}\frac{z}{\rho}[/tex]
For angle θ:
If x > 0 and y > 0: [tex]\theta = tan^{-1}\frac{y}{x}[/tex];If x < 0: [tex]\theta = \pi + tan^{-1}\frac{y}{x}[/tex];If x > 0 and y < 0: [tex]\theta = 2\pi + tan^{-1}\frac{y}{x}[/tex];Calculating:
a) (4,2,-4)
[tex]\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}[/tex] = 6
[tex]\phi = cos^{-1}(\frac{-4}{6})[/tex]
[tex]\phi = cos^{-1}(\frac{-2}{3})[/tex]
For θ, choose 1st option:
[tex]\theta = tan^{-1}(\frac{2}{4})[/tex]
[tex]\theta = tan^{-1}(\frac{1}{2})[/tex]
b) (0,8,15)
[tex]\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}[/tex] = 17
[tex]\phi = cos^{-1}(\frac{15}{17})[/tex]
[tex]\theta = tan^{-1}\frac{y}{x}[/tex]
The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = [tex]\frac{\pi}{2}[/tex]
c) (√2,1,1)
[tex]\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}[/tex] = 2
[tex]\phi = cos^{-1}(\frac{1}{2})[/tex]
[tex]\phi[/tex] = [tex]\frac{\pi}{3}[/tex]
[tex]\theta = tan^{-1}\frac{1}{\sqrt{2} }[/tex]
d) (−2√3,−2,3)
[tex]\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}[/tex] = 5
[tex]\phi = cos^{-1}(\frac{3}{5})[/tex]
Since x < 0, use 2nd option:
[tex]\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }[/tex]
[tex]\theta = \pi + \frac{\pi}{6}[/tex]
[tex]\theta = \frac{7\pi}{6}[/tex]
Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:
[tex]r=\sqrt{x^{2}+y^{2}}[/tex]
Angle θ is the same as spherical coordinate;
z = z
Calculating:
a) (4,2,-4)
[tex]r=\sqrt{4^{2}+2^{2}}[/tex] = [tex]\sqrt{20}[/tex]
[tex]\theta = tan^{-1}\frac{1}{2}[/tex]
z = -4
b) (0, 8, 15)
[tex]r=\sqrt{0^{2}+8^{2}}[/tex] = 8
[tex]\theta = \frac{\pi}{2}[/tex]
z = 15
c) (√2,1,1)
[tex]r=\sqrt{(\sqrt{2} )^{2}+1^{2}}[/tex] = [tex]\sqrt{3}[/tex]
[tex]\theta = \frac{\pi}{3}[/tex]
z = 1
d) (−2√3,−2,3)
[tex]r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}[/tex] = 4
[tex]\theta = \frac{7\pi}{6}[/tex]
z = 3
A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure:
A: The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
B: The hypothesis µ1 = µ2 would be rejected at the 10% level of significance.
C: The hypothesis µ1 = µ2 would be rejected at the 1% level of significance.
A) A and B
B) A and C
C) A only
D) A, B, and C
Answer:
C) A only
Step-by-step explanation:
In statistics, the null hypothesis is the default hypothesis and the alternative hypothesis is the research hypothesis. The alternative hypothesis usually comes in place to challenge the null hypothesis in order to determine if the test is statistically significant or not.
Similarly,
In hypothesis testing, the confidence interval consist of all reasonable value of the population mean. Values for which the null hypothesis will be rejected [tex]H_o[/tex] .
Given that:
At 95% confidence interval for the difference between the population means is (1.4, 8.7).
The level of significance = 1 - 0.95 = 0.05 = 5%
So , If the hypothesis test is based on the same samples, The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
S varies inversely as G. If S is 8 when G is 1.5, find S when G is 3. a) Write the variation. b) Find S when G is 3.
Step-by-step explanation:
a.
[tex]s \: = \frac{k}{g} [/tex]
[tex]8 = \frac{k}{1.5} [/tex]
[tex]k \: = 1.5 \times 8 = 12[/tex]
[tex]s = \frac{12}{g} [/tex]
b.
[tex]s = \frac{12}{3} [/tex]
s = 4
How many ways are there to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants
Answer:
There are 6566 ways to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants.
Step-by-step explanation:
Given:
There are 5 types of croissants:
plain croissants
cherry croissants
chocolate croissants
almond croissant
apple croissants
broccoli croissants
To find:
to choose 22 croissants with:
at least one plain croissant
at least two cherry croissants
at least three chocolate croissants
at least one almond croissant
at least two apple croissants
no more than three broccoli croissants
Solution:
First we select
At least one plain croissant to lets say we first select 1 plain croissant, 2 cherry croissants, 3 chocolate croissants, 1 almond croissant, 2 apple croissants
So
1 + 2 + 3 + 1 + 2 = 9
Total croissants = 22
So 9 croissants are already selected and 13 remaining croissants are still needed to be selected as 22-9 = 13, without selecting more than three broccoli croissants.
n = 5
r = 13
C(n + r - 1, r)
= C(5 + 13 - 1, 13)
= C(17,13)
[tex]=\frac{17! }{13!(17-13)!}[/tex]
= 355687428096000 / 6227020800 ( 24 )
= 355687428096000 / 149448499200
= 2380
C(17,13) = 2380
C(n + r - 1, r)
= C(5 + 12 - 1, 12)
= C(16,12)
[tex]=\frac{16! }{12!(16-12)!}[/tex]
= 20922789888000 / 479001600 ( 24 )
= 20922789888000 / 11496038400
= 1820
C(16,12) = 1820
C(n + r - 1, r)
= C(5 + 11 - 1, 11)
= C(15,11)
[tex]=\frac{15! }{11!(15-11)!}[/tex]
= 1307674368000 / 39916800 (24)
= 1307674368000 / 958003200
= 1307674368000 / 958003200
= 1365
C(15,11) = 1365
C(n + r - 1, r)
= C(5 + 10 - 1, 10)
= C(14,10)
[tex]=\frac{14! }{10!(14-10)!}[/tex]
= 87178291200 / 3628800 ( 24 )
= 87178291200 / 87091200
= 1001
C(14,10) = 1001
Adding them:
2380 + 1820 + 1365 + 1001 = 6566 ways
In the morning, Sophie goes to the church then goes to the school. In the afternoon she goes to school to home. The map shows the distance between school and home as 5 cm. If every 4 cm on the scale drawing equals 8 kilometers, how far apart are the school and home?
Answer:
10 km
Step-by-step explanation:
Distance = 5 cm
4 cm = 8 km
In km, how far apart is school and home?
Cross Multiply
[tex]\frac{4cm}{8km}[/tex] · [tex]\frac{5cm}{1}[/tex]
Cancel centimeters
[tex]\frac{40(km)(cm)}{4cm}[/tex]
Divide
= [tex]\frac{40km}{4}[/tex]
= 10 km
Justin is married with one child. He works 40 hours each week at a rate of $16 per hour. His wife began working part time
after their daughter was born, but still contributes about $350 to the cash inflow each month. Their monthly cash outflow
is generally about $3,000. They have a balance of $2,000 in their savings account. Justin has retirement contributions
taken out of his paycheck at work. They have renter's, car and life insurance coverage.
Based on this information, what part of their financial plan should Justin and his wife work on?
managing income
b. managing liquidity
c. protecting assets
d. retirement
a.
Please select the best answer from the choices provided
Answer:
THe answer is A
Step-by-step explanation:
given point (-6, -3) and a slope of 4, write an equation in point-slope form
Answer:
y = 4x + 21
Step-by-step explanation:
Hello!
Point-slope form is y - y1 = m(x - x1)
y1 is the y point
x1 is the x point
m is the slope
Put in what you know
y - -3 = 4(x - -6)
Subtracting a negative is the same as adding
y + 3 = 4(x + 6)
Distribute the 4
y + 3 = 4x + 24
Subtract 3 from both sides
y = 4x + 21
The answer is y = 4x + 21
Hope this helps!
The area of a rectangular garden if 6045 ft2. If the length of the garden is 93 feet, what is its width?
Answer:
65 ft
Step-by-step explanation:
The area of a rectangle is
A = lw
6045 = 93*w
Divide each side by 93
6045/93 = 93w/93
65 =w
Answer:
[tex]\huge \boxed{\mathrm{65 \ feet}}[/tex]
Step-by-step explanation:
The area of a rectangle formula is given as,
[tex]\mathrm{area = length \times width}[/tex]
The area and length are given.
[tex]6045=93 \times w[/tex]
Solve for w.
Divide both sides by 93.
[tex]65=w[/tex]
The width of the rectangular garden is 65 feet.
Multiple Choice The opposite of –4 is A. 4. B. –4. C. –(–(–4)). D. –|4|.
Answer:
a. 4
Step-by-step explanation:
-1(-4) = 4
Answer:
A 4
Step-by-step explanation:
opposite of –4 = 4
Find the product of all solutions of the equation (10x + 33) · (11x + 60) = 0
Answer:
18
Step-by-step explanation:
Using Zero Product Property, we can split this equation into two separate equations by setting each factor to 0. The equations are:
10x + 33 = 0 or 11x + 60 = 0
10x = -33 or 11x = -60
x = -33/10 or x = -60/11
Multiplying the two solutions together, we get -33/10 * -60/11 = 1980 / 110 = 18.
Which choice shows the product of 22 and 49 ?
Answer:
1078
Step-by-step explanation:
The product of 22 and 49 is 1078.
Answer:
1078 is the product
Step-by-step explanation:
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 3%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that
Answer:
The probability that none of the LED light bulbs are defective is 0.7374.
Step-by-step explanation:
The complete question is:
What is the probability that none of the LED light bulbs are defective?
Solution:
Let the random variable X represent the number of defective LED light bulbs.
The probability of a LED light bulb being defective is, P (X) = p = 0.03.
A random sample of n = 10 LED light bulbs is selected.
The event of a specific LED light bulb being defective is independent of the other bulbs.
The random variable X thus follows a Binomial distribution with parameters n = 10 and p = 0.03.
The probability mass function of X is:
[tex]P(X=x)={10\choose x}(0.03)^{x}(1-0.03)^{10-x};\ x=0,1,2,3...[/tex]
Compute the probability that none of the LED light bulbs are defective as follows:
[tex]P(X=0)={10\choose 0}(0.03)^{0}(1-0.03)^{10-0}[/tex]
[tex]=1\times 1\times 0.737424\\=0.737424\\\approx 0.7374[/tex]
Thus, the probability that none of the LED light bulbs are defective is 0.7374.
You flip two coins. What is the probability
that you flip at least one head?
Answer:
[tex]\boxed{Probability=\frac{1}{2} }[/tex]
Step-by-step explanation:
The probability of flipping at least 1 head from flipping 2 coins is:
=> Total sides of the coins = 4
=> Sides which are head = 2
=> Probability = 2/4 = 1/2
Question: The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Which equation can be used to find the length of the remaining side?
Answer:
The hypotenuse is the longest side in a triangle.
a^2=b^2+c^2.
14^2=9^2+c^2.
c^2=196-81.
c^2=115.
c=√115.
c=10.72~11cm
Help me please thank you
Answer:
x = 7
Step-by-step explanation:
The angles are alternate interior angles, so for the lines to be parallel, the angle measures must be equal.
7x - 7 = 4x + 14
3x = 21
x = 7
sorry to keep asking questions
Answer:
y = [tex]\sqrt[3]{x-5}[/tex]
Step-by-step explanation:
To find the inverse of any function you basically switch x and y.
function = y = x^3 + 5
Now we switch x and y
x = y^3 +5
Solve for y,
x - 5 = y^3
switch sides,
y^3 = x-5
y = [tex]\sqrt[3]{x-5}[/tex]
Answer:
[tex]\Large \boxed{{f^{-1}(x)=\sqrt[3]{x-5}}}[/tex]
Step-by-step explanation:
The function is given,
[tex]f(x)=x^3 +5[/tex]
The inverse of a function reverses the original function.
Replace f(x) with y.
[tex]y=x^3 +5[/tex]
Switch variables.
[tex]x=y^3 +5[/tex]
Solve for y to find the inverse.
Subtract 5 from both sides.
[tex]x-5=y^3[/tex]
Take the cube root of both sides.
[tex]\sqrt[3]{x-5} =y[/tex]
Transform the given parametric equations into rectangular form. Then identify the conic. x= -3cos(t) y= 4sin(t)
Answer:
Solution : Option D
Step-by-step explanation:
The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )
x = - 3cos(t) ⇒ x / - 3 = cos(t)
y = 4sin(t) ⇒ y / 4 = sin(t)
Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )
( x / - 3 )² = cos²(t)
+ ( y / 4 )² = sin²(t)
_____________
x² / 9 + y² / 16 = 1
Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.
I dont understand this please help Which expression represents the area of the shaded region
Answer:
I'm gonna say C
Calculate how many different sequences can be formed that use the letters of the given word. Leave your answer as a product of terms of the form C(n, r). HINT [Decide where, for example, all the s's will go, rather than what will go in each position.]
georgianna
A) C(10, 7)
B) C(2, 10)C(1, 8)C(1, 7)C(1, 6)C(1, 5)C(2, 4)C(2, 2)
C) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 1)C(3, 1)C(2, 1)C(1, 1)
D) 10 · C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
Answer: E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
Step-by-step explanation:
According to the combinations: Number of ways to choose r things out of n things = C(n,r)
Given word: "georgianna"
It is a sequence of 10 letters with 2 a's , 2 g's , 2 n's , and one of each e, o,r, i.
If we think 10 blank spaces, then in a sequence we need 2 spaces for each of g.
Number of ways = C(10,2)
Similarly,
1 space for 'e' → C(8,1)
1 space for 'o' → C(7,1)
1 space for 'r' → C(6,1)
1 space for 'i' → C(5,1)
1 space for 'a' → C(4,2)
1 space for 'n' → C(2,2)
Required number of different sequences = C(10,2) ×C(8,1)× C(7,1)× C(6,1)×C(5,1)×C(2,2).
Hence, the correct option is E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
g The intersection of events A and B is the event that occurs when: a. either A or B occurs but not both b. neither A nor B occur c. both A and B occur d. All of these choices are true. a. b. c. d.
Answer:
c. both A and B
Step-by-step explanation:
Given that there are two events A and B.
To find:
Intersection of the two sets represents which of the following events:
a. either A or B occurs but not both
b. neither A nor B occur
c. both A and B occur
d. All of these choices are true. a. b. c. d
Solution:
First of all, let us learn about the concept of intersection.
Intersection of two events means the common part in the two events.
Explanation using set theory:
Let set P contains the outcomes of roll of a dice.
P = {1, 2, 3, 4, 5, 6}
And set Q contains the set of even numbers less than 10.
Q = {2, 4, 6, 8}
Common elements are {2, 4, 6}
So, intersection of P and Q:
[tex]P \cap Q[/tex] = {2, 4, 6}
Explanation using Venn diagram:
Please refer to the image attached in the answer area.
The shaded region is the intersection of the two sets P and Q.
When we apply the above concept in events, we can clearly say from the above explanation that the intersection of two events A and B is the event that occurs when both A and B occur.
So, correct answer is:
c. both A and B
Answer:
C.
Step-by-step explanation:
In a random sample of 205 people, 149 said that they watched educational television. Find the 95% confidence interval of the true proportion of people who watched educational television. Round intermediate answers to at least five decimal places.
Answer: Given a sample of 200, we are 90% confident that the true proportion of people who watched educational TV is between 72.1% and 81.9%.
Step-by-step explanation:
[tex]\frac{154}{200} =0.77[/tex]
[tex]1-0.77=0.23[/tex]
[tex]\sqrt{\frac{(0.77)(0.23)}{200} }[/tex]=0.049
0.77±0.049< 0.819, 0.721
The weight of an object on moon is 1/6 of its weight on Earth. If an object weighs 1535 kg on Earth. How much would it weigh on the moon?
Answer:
255.8
Step-by-step explanation:
first
1/6*1535
=255.8
