The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)
The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80
This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%
We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.
The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)
=========================================
In summary, we have these answers
confidence level = 90%margin of error = 5% = 0.05confidence interval = (0.70, 0.80)interpretation = We're 90% confident that the average exam score is between 0.70 and 0.80A random sample of size results in a sample mean of and a sample standard deviation of . An independent sample of size results in a sample mean of and sample standard deviation of . Does this constitute sufficient evidence to conclude that the population means differ at the level of significance?
Answer:
A typical example would be when a statistician wishes to estimate the ... by the standard deviation ó) is known, then the standard error of the sample mean is given by the formula: ... The central limit theorem is a significant result which depends on sample size. ... So, the sample mean X/n has maximum variance 0.25/ n.
Step-by-step explanation:
Solve 2x+2y=6 and 3x-2y=11
Answer:
x = 17/5
y = -2/5
Step-by-step explanation:
2x + 2y = 6
3x - 2y = 11
sum both equations results
5x + 0 = 17
x = 17/5
2x + 2y = 6
2*17/5 + 2y = 6
34/5 + 2y = 6
2y = 6 - 34/5
2y = 30/5 - 34/5
2y = -4/5
y = (-4/5)/2
y = -2/5
verify:
3x - 2y = 11
3*17/5 - 2*-2/5 = 11
51/5 + 4/5 = 55/5
51 + 4 = 55
PLEASE ANSWER ASAP!!!
Equation in the picture
Solve for r in the equation in the picture. You must use the LCD (Least Common Denominator) to simplify. You can also use cross products to solve.
Must show work
A. r = 19
B. r = 21
C. r = 25
D. r = 30
any unrelated answer will be reported
Answer:
r = 19
Step-by-step explanation:
( r-5) /2 = ( r+2) /3
The least common denominator is 6
3/3 *( r-5) /2 = ( r+2) /3 * 2/2
3( r-5) /6 = 2( r+2) /6
Since the denominators are the same, the numerators are the same
3( r-5) = 2(r+2)
Distribute
3r -15 = 2r+4
Subtract 2r from each side
3r-2r -15 = 2r+4-2r
r-15 =4
Add 15 to each side
r-15+15 = 4+15
r = 19
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
Need Help
Please Show Work
Answer:
-36
Step-by-step explanation:
3*12=36
she is going down (negative) so, it is -36
not sure if this is what you are asking for, if not try this
0-12-12-12=-36
A charity organization is holding a food drive with a goal to collect at least 1,000 cans of
food by the end of the month. It currently has 565 cans from donations and is having an
event where 87 guests will attend and bring cans. Which solution set represents the
number of cans each guest must bring to meet the goal?
+
OA
++
0
1
2
3
4
5
6
7
8
9
10
---
+
OB. 4
+
0
1
2
3
4
5
6
7
8
9
10
OC.
+
1
2
3
5
6
7
8
9
10
OD. +
+
++
-
6
+
7.
+
0
1
2
3
4
5
8
9
10
Answer:
Each guest must bring 5 cans.
Step-by-step explanation:
1000-565=435
435/87=5
Please Solve
F/Z=T for Z
Answer:
F /T = Z
Step-by-step explanation:
F/Z=T
Multiply each side by Z
F/Z *Z=T*Z
F = ZT
Divide each side by T
F /T = ZT/T
F /T = Z
Answer:
[tex]\boxed{\red{ z = \frac{f}{t} }}[/tex]
Step-by-step explanation:
[tex] \frac{f}{z} = t \\ \frac{f}{z} = \frac{t}{1} \\ zt = f \\ \frac{zt}{t} = \frac{f}{t} \\ z = \frac{f}{t} [/tex]
Given the number of trials and the probability of success, determine the probability indicated: a. n = 15, p = 0.4, find P(4 successes) b. n = 12, p = 0.2, find P(2 failures) c. n = 20, p = 0.05, find P(at least 3 successes)
Answer:
A)0.126775 B)0.000004325376 C) 0.07548
Step-by-step explanation:
Given the following :
A.) a. n = 15, p = 0.4, find P(4 successes)
a = number of trials p=probability of success
P(4 successes) = P(x = 4)
USING:
nCx * p^x * (1-p)^(n-x)
15C4 * 0.4^4 * (1-0.4)^(15-4)
1365 * 0.0256 * 0.00362797056
= 0.126775
B)
b. n = 12, p = 0.2, find P(2 failures),
P(2 failures) = P(12 - 2) = p(10 success)
USING:
nCx * p^x * (1-p)^(n-x)
12C10 * 0.2^10 * (1-0.2)^(12-10)
66 * 0.0000001024 * 0.64
= 0.000004325376
C) n = 20, p = 0.05, find P(at least 3 successes)
P(X≥ 3) = p(3) + p(4) + p(5) +.... p(20)
To avoid complicated calculations, we can use the online binomial probability distribution calculator :
P(X≥ 3) = 0.07548
There are 30 colored marbles inside a bag. Six marbles are yellow, 9 are red, 7 are white, and 8 are blue. One is drawn at random. Which color is most likely to be chosen? A. white B. red C. blue D. yellow Include ALL work please!
Answer:
red
Step-by-step explanation:
Since the bag contains more red marbles than any other color, you are most likely to pick a red marble
Identifying the Property of Equality
Quick
Check
Identify the correct property of equality to solve each equation.
3+x= 27
X/6 = 5
Answer:
a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication
Step-by-step explanation:
a) This expression can be solved by using the Compatibility of Equality with Addition, that is:
1) [tex]3+x = 27[/tex] Given
2) [tex]x+3 = 27[/tex] Commutative property
3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition
4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property
5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction
6) [tex]x=24[/tex] Modulative property/Subtraction/Result.
b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:
1) [tex]\frac{x}{6} = 5[/tex] Given
2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division
3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication
4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property
5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse
6) [tex]x = 30[/tex] Modulative property/Result
Answer:
3 + x = 27
✔ subtraction property of equality with 3
x over 6 = 5
✔ multiplication property of equality with 6
-8 + (-15)
Evaluate this expression
Answer:
-23
Step-by-step explanation:
-8+(-15) means that you are subtracting 15 from -8. So you end up with -8-15=-23.
If the sample size is increased and the standard deviation and confidence level stay the same, then the margin of error will also be increased.
a. True
b. False
False!
The answer is: False.
Whomever stated the answer is "true" is wrong.
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
When you enter the Texas Turnpike, they give you a ticket showing the time and place of your entry. When you exit, you turn in this ticket and they use it to figure your toll. Because they know the distance between toll stations, they can also use it to check your average speed against the turnpike limit of 65 mph. On your trip, heavy snow limits your speed to 40 mph for the first 120 mi. At what average speed can you drive for the remaining 300 mi without having your ticket prove that you broke the speed limit?
Answer:
87 mph
Step-by-step explanation:
Total distance needed is 120 mi + 300 mi and that is 420 mi.
Driving at 65 mph means that it would take
420 / 65 hours to reach his destination.
6.46 hours .
at the first phase, he drove at 40 mph for 120 mi, this means that it took him
120 / 40 hours to complete the journey.
3 hours.
the total time needed for the whole journey is 6.46 hours, and he already spent 3 hours in the first phase. To keep up with the 6.46 hours required, in the second phase, he has to drive at a speed of
6.46 - 3 hours = 3.46 hours.
300 mi / 3.46 hours => 86.71 mph approximately 87 mph
Therefore, he needs to drive at not more than 87 mph to keep up with the journey while not breaking his speed limit
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
Find the domain and the range of the relation.
Find the domain of the relation. Select the correct choice below and fill in the answer box to
complete your choice.
O A. The domain is _
(Type your answer in interval notation.)
B. The domain is {_}
(Type an integer or a fraction. Use a comma to separate answers as needed.)
Find the range of the relation. Select the correct choice below and fill in the answer box to
complete your choice.
O A. The range is _
(Type an integer or a fraction. Use a comma to separate answers as needed.)
OB. The range is {_}
Answer:
1) the domain is all real numbers
2) the range is
[tex]y \geqslant 3[/tex]
can anyone show me this in verbal form?
Answer:
2 * (x + 2) = 50
Step-by-step explanation:
Let's call the unknown number x. "A number and 2" means that we need to add the numbers, therefore it would be x + 2. "Twice" means 2 times a quantity so "twice a number and 2" would be 2 * (x + 2). "Is" denotes that we need to use the "=" sign and because 50 comes after "is", we know that 50 goes on the right side of the "=" so the final answer is 2 * (x + 2) = 50.
Ava placed the point of her pencil on the origin of a regular coordinate plane. She marked a point after moving her pencil 4 units to the left and 7 units up. Which ordered pair identifies where Ava marked her point?
[tex] \Large{ \boxed{ \bold{ \color{lightgreen}{Solution:}}}}[/tex]
So, Let's solve this question by using cartesian plane.
Here, Origin is shown by (0, 0)Ava moves 4 units left from origin. On the left side of origin, negative x axis begins. So, she reached (-4, 0) now.Then, from that point she moved 7 units upwards. On the upper side, there is positive y axis. So, Finally she will reach point (-4, 7).(-4, 7) is the coordinate of point which is 4 units left from y axis and 7 units up from x axis.It lies on the second quadrant.Well, What is cartesian plane?
A - A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
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Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation 5 v plus 7 f equals 28.70, where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies?
Answer:
(7 x 2.85) + 5v = 28.70. 19.95 + 5v = 28.70. 5v = 28.70 - 19.95. 5v = 8.75. v = 8.75/5. v = 1.75. A pint of veggies costs $1.75.
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
Help me please please please please
Answer:
1.
d. (-14) + (-8)
2.
a. (-14) + 8
Step-by-step explanation:
(-14) - 8 is equal to (-14) + (-8) because we still add two negative values so the result wouldn't change.
(-14) - (-8) is equal to (-14) + 8 because there's two negative sign in front of 8 and two negative values multiplied makes a positive result.
Answer:
1. D
2. A
Step-by-step explanation:
1. It asks you what expression has the same value as (-14)-8. All you need to do is find other equations that have the same value as that. So the equation is -14-8. IF a negative is outside a parenthesis with a positive number inside like -(+5), it is going to be -5. If it's both negative: -(-5), it will be +5. If it is both positive: +(+5), it is going to be +5.
IMPORTANT!
- and + = -
- and - = +
+ and + = +
What we are looking for: -14-8
So choice A is (-14)+8 which is simplified to -14+8. So, this one isn't right.
Choice B: 14-(-8)= 14+8. So, it's incorrect.
Choice C: 14+(-8)= 14-8. Again, it's not -14-8 so it's not right.
Choice D: (-14)+(-8)= -14-8. This equation matches the one we are looking for! So it's correct!
2. Same thing as number 1. Let's simplify the equation it wants us to find first.
(-14)-(-8)= -14+8
So -14+8 is what we are looking for.
Choice A: (-14)+8= -14+8. It matches! So it is correct. Let's look at the other options anyway.
Choice B: 14-(-8)= 14+8. Nope. Not right.
Choice C: 14+(-8)= 14-8 because - always beats +. So, this one is also incorrect.
Choice D: (-14)+(-8)= -14-8. Oops, this is also wrong. So choice A is the right answer.
Keep in mind, when you start getting questions like this with numbers inside the parenthesis as well, you want to remember the same rules for positive and negative, but also multiply the numbers together:
(When there is a number outside and inside a parentheses, multiply them.)
2(5)=10, CORRECT! 2+(5) is not 2 times 5. It's whatever is closest to the parentheses, in this case being the positive sign. So + and 5 is just 5!
IMPORTANT!
-2(-5)= - and - is positive, so positive (2 times 5). Positive 10.
-2(+5)= - and + is negative, so negative (2 times 5). Negative 10.
+2(+5)= + and + is positive, so positive (2 times 5). Positive 10.
Look at the figure below. which ratio represents tan 0?
A -5/4, B -4/5, C -3/4, D 3/5.
The required value of the tanФ is given as -3/4. C option is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.
here,
Tan(180 - Ф) = -tanФ = perpendicular / base
From figure, perpendicular= 12 and base = 16
-tanФ = 12 / 16
tanФ = -3/4
Thus, the required value of the tanФ is given as -3/4. C option is correct.
Learn more about trigonometry equations here:
brainly.com/question/22624805
#SPJ5
Find the value of the expression: −mb −m^2 for m=3.48 and b=96.52
Answer:
The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.
Step-by-step explanation:
Let be [tex]f(m, b) = m\cdot b - m^{2}[/tex], if [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex], the value of the expression:
[tex]f(3.48,96.52) = (3.48)\cdot (96.52)-3.48^{2}[/tex]
[tex]f(3.48,96.52) = 323.779[/tex]
The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.
Is the square root of 65 a rational number
Answer:
No
Step-by-step explanation:
The square root of 65 is irrational.
It is not a rational number because 65 is not a perfect square.
The square root of 65 is 8.06225775...
The square root of 65 is not a rational number.
65 is not a perfect square which means it's impossible to
find a whole number times itself to give us 65.
On a calculator if you type in the square root of 65,
you will get an infinite decimal number.
The decimal values never end and never have same repeated pattern.
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:
Find the length of GV¯¯¯¯¯¯¯¯ A. 43.92 B. 33.1 C. 41.45 D. 68.87
Answer:
The answer is option AStep-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find GV
To find GV we use cosine
cos∅ = adjacent / hypotenuse
From the question
GV is the adjacent
GC is the hypotenuse
So we have
[tex] \cos(37) = \frac{GV}{GC} [/tex]GC = 55°
GV[tex] \cos(37) = \frac{GV}{55} [/tex]GV = 55 cos 37
GV = 43.92495
We have the final answer as
GV = 43.92Hope this helps you
Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.1. Compute the values below.
(a) P(E ∪ F) =
(b) P(Ec) =
(c) P(Fc ) =
(d) P(Ec ∩ F) =
Answer:
(a) P(E∪F)= 0.8
(b) P(Ec)= 0.4
(c) P(Fc)= 0.7
(d) P(Ec∩F)= 0.8
Step-by-step explanation:
(a) It is called a union of two events A and B, and A ∪ B (read as "A union B") is designated to the event formed by all the elements of A and all of B. The event A∪B occurs when they do A or B or both.
If the events are not mutually exclusive, the union of A and B is the sum of the probabilities of the events together, from which the probability of the intersection of the events will be subtracted:
P(A∪B) = P(A) + P(B) - P(A∩B)
In this case:
P(E∪F)= P(E) + P(F) - P(E∩F)
Being P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.1
P(E∪F)= 0.6 + 0.3 - 0.1
P(E∪F)= 0.8
(b) The complement of an event A is defined as the set that contains all the elements of the sample space that do not belong to A. The Complementary Rule establishes that the sum of the probabilities of an event and its complement must be equal to 1. So, if P (A) is the probability that an event A occurs, then the probability that A does NOT occur is P (Ac) = 1- P (A)
In this case: P(Ec)= 1 - P(E)
Then: P(Ec)= 1 - 0.6
P(Ec)= 0.4
(c) In this case: P(Fc)= 1 - P(F)
Then: P(Fc)= 1 - 0.3
P(Fc)= 0.7
(d) The intersection of two events A and B, designated as A ∩ B (read as "A intersection B") is the event formed by the elements that belong simultaneously to A and B. The event A ∩ B occurs when A and B do at once.
As mentioned, the complementary rule states that the sum of the probabilities of an event and its complement must equal 1. Then:
P(Ec intersection F) + P(E intersection F) = P(F)
P(Ec intersection F) + 0.1 = 0.3
P(Ec intersection F)= 0.2
Being:
P(Ec∪F)= P(Ec) + P(F) - P(Ec∩F)
you get:
P(Ec∩F)= P(Ec) + P(F) - P(Ec∪F)
So:
P(Ec∩F)= 0.4 + 0.3 - 0.2
P(Ec∩F)= 0.8
10-
What is the equation of the line that is perpendicular to
the given line and passes through the point (2, 6)?
8-
(2,6)
-6
O x = 2
4
O x = 6
-2
-10 -3 -6 -22
2
4
B
8
10
X
O y = 2
O y = 6
(-34)
(814)
8
WO
Answer:
x = 2
Step-by-step explanation:
This blue line seems to be horizontal, and so a line perpendicular would have to be vertical. The only vertical line that passes through (2, 6) would be x = 2.
The equation of the line perpendicular to the given line and passes through the point (2, 6) is x = 2.
What is the Equation of line in Slope Intercept form?Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.
Given is a line that passes through the points (-8, -4) and (8, -4).
This line is parallel to the X axis.
A line parallel to X axis has the equation y = b.
The y coordinate is -4 throughout the line.
So equation of the line is y = -4.
A line perpendicular to the given line will be parallel to Y axis.
Parallel lines to Y axis has the equation of the form x = a.
Line passes through the point (2, 6).
x coordinate will be 2 throughout.
So the equation of the perpendicular line is x = 2.
Hence the required equation is x = 2.
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Solve for W.
W/9 = g
Answer:
W = 9 * g
Step-by-step explanation:
W/9 = g
W = 9 * g
The expression W/9 = g can be written as W = 9g after cross multiplication.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
W/9 = g
To solve for W
Make subject as W:
W = 9g
By cross multiplication.
Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.
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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%.
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