Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized as follows:
conforms
yes no
1 22 8
supplier 2 25 5
3 30 10
Let A denote the event that a sample is from supplier 1, and let B denote the event that a sample from any supplier conforms to specifications. If a disk is selected at random, determine the following probabilities.
a. P(A)=0.3
b. P(B)=0.77
c. P(A ∩ B) =0.22
d. P(A U B)=0.85
Answer
[tex]P(A) = 0.30[/tex]
[tex]P(B) = 0.77[/tex]
[tex]P(A\ n\ B) = 0.22[/tex]
[tex]P(A\ u\ B) = 0.85[/tex]
Explanation:
Given
See attachment for proper data presentation
[tex]n = 100[/tex] --- Sample
A = Supplier 1
B = Conforms to specification
Solving (a): P(A)
Here, we only consider data in sample 1 row.
Here:
[tex]Yes = 22[/tex] and [tex]No = 8[/tex]
[tex]n(A) = Yes + No[/tex]
[tex]n(A) = 22 + 8[/tex]
[tex]n(A) = 30[/tex]
P(A) is then calculated as:
[tex]P(A) = \frac{n(A)}{Sample}[/tex]
[tex]P(A) = \frac{30}{100}[/tex]
[tex]P(A) = 0.30[/tex]
Solving (b): P(B)
We only consider data in the Yes column.
Here:
[tex](1) = 22[/tex] [tex](2) = 25[/tex] and [tex](3) = 30[/tex]
[tex]n(B) = (1) + (2) + (3)[/tex]
[tex]n(B) = 22 + 25 + 30[/tex]
[tex]n(B) = 77[/tex]
P(B) is then calculated as:
[tex]P(B) = \frac{n(B)}{Sample}[/tex]
[tex]P(B) = \frac{77}{100}[/tex]
[tex]P(B) = 0.77[/tex]
Solving (c): P(A n B)
Here, we only consider the similar cell in the yes column and sample 1 row.
i.e. [Supplier 1][Yes]
This is represented as: n(A n B)
[tex]n(A\ n\ B) = 22[/tex]
The probability is then calculated as:
[tex]P(A\ n\ B) = \frac{n(A\ n\ B)}{Sample}[/tex]
[tex]P(A\ n\ B) = \frac{22}{100}[/tex]
[tex]P(A\ n\ B) = 0.22[/tex]
Solving (d): P(A u B)
This is calculated as:
[tex]P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)[/tex]
This gives:
[tex]P(A\ u\ B) = \frac{30}{100} + \frac{77}{100} - \frac{22}{100}[/tex]
Take LCM
[tex]P(A\ u\ B) = \frac{30+77-22}{100}[/tex]
[tex]P(A\ u\ B) = \frac{85}{100}[/tex]
[tex]P(A\ u\ B) = 0.85[/tex]
which is greater -3/4 or -1/2 please this is big test
Answer:
-3/4 < -1/2
Step-by-step explanation:
have a good day luv! ^^
Use the following x-values (0, 1, 2, 3) to find ordered pairs for this equation: y = 2x - 3
Step-by-step explanation:
When x = 0, y = 2(0) - 3 = -3.
When x = 1, y = 2(1) - 3 = -1.
When x = 2, y = 2(2) - 3 = 1.
When x = 3, y = 2(3) - 3 = 3.
The ordered pairs are (0, -3), (1, -1), (2, 1), (3, 3).
Jason and Martin want to share 3 cookies equally. How much cookie will Jason and Martin each receive? Write an equation and express your answer as a fraction.
Answer: each will get 3/2
Step-by-step explanation:
They will each get a whole cookie with one left over that they can break in half.
4 x 4/6 is it equal to, less than, or greater than
Answer:
Greater than
Step-by-step explanation:
It becomes 8/3
Answer:m no
Step-by-step explanation:
i cant afford to get another wrong one bro
Answer:
3 & 6
Step-by-step explanation:
right angles will form perpendicular sides, and shapes 3 and 6 are the only ones with right angles
You roll two fair dice, a green one and a red one.
Required:
a. What is the probability of getting a sum of 8? (Enter your answer as a fraction.)
b. What is the probability of getting a sum of 4?
c. What is the probability of getting a sum of 8 or 4?
d. Are these outcomes mutually exclusive?
Answer:
[tex]a.\ \frac{5}{36}\\b.\ \frac{1}{12}\\c.\ \frac{2}{9}\\d.\ $Not mutually exclusive$[/tex]
Step-by-step explanation:
Given two fair dice are rolled, one green and one red.
To find:
a. Probability of getting a sum of 8.
b. Probability of getting a sum of 4.
c. Probability of getting a sum of 8 or 4.
d. Are these outcomes mutually exclusive?
Solution:
First of all, let us have a look at the output of roll of two dice.
There are a total of 36 outcomes.
{(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)}
a. Getting a sum equal to 8, we have following outcomes:
{(2, 6), (3,5), (4, 4), (5,3), (6, 2)}
5 possible outcomes for this event.
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
[tex]P($Getting 8$) = \dfrac{5}{36}[/tex]
b. Getting a sum equal to 4, we have following outcomes:
{(1, 3), (2,2), (3, 1)}
3 possible outcomes for this event.
Formula for probability of an event E can be observed as:
[tex]P($Getting 4$) = \dfrac{3}{36} = \dfrac{1}{12}[/tex]
c. Probability of getting a sum of 8 or 4?
Following possible outcomes are there:
{(2, 6), (3,5), (4, 4), (5,3), (6, 2), (1, 3), (2,2), (3, 1)}
Total 8 possible outcomes:
[tex]P($Getting 8 or 4$) = \dfrac{8}{36} = \dfrac{2}{9}[/tex]
d. Are these outcomes mutually exclusive?
These events are not mutually exclusive because they contain the similar outcome from both of the dice.
i.e. (4, 4) and (2, 2)
Plz can anyone help me?
Answer:
400x
Step-by-step explanation:
as shown in the graph from points such as (1, 400) or (2,800) the person is traveling 400 per day
-10(1 - 9x) + 6(x - 10)
Combining like terms
which graph is it?
[tex]g(x) = |x + 3| [/tex]
The probability of spinning an even number on a wheel of 4 and flipping tails is___ (Ive been checking all day and none of the answers are correct)
Answer:
i think 12
Step-by-step explanation:
Answer:
it's like a 50% probability
help pls will give you brandy
Answer:
9+2=7-4+3
9-4=5+2=7
4-9=5+2=7
4-9+5+2=7
Step-by-step explanation:
Your welcome bro
Answer:
1. A
2. C
3. B
4. B
5. A
Step-by-step explanation:
I hope this helps might be wrong if they are just delete my answer.
What is 23% of 3500
Does any one know it’s for a test lol
Answer:
805
Step-by-step explanation:
It's kinda hard to explain but first you would convert 23% to a decimal. To do that, move the decimal 2 places to the left, resulting in 0.23. Then multiply 3500 by 0.23 to get your answer.
Product A is an 8-oz. bottle of cough medication that sells for $1.36. Product B is a 16-oz. bottle of cough medication that costs $3.20. Which product has the lower unit price?
Answer:
A
Step-by-step explanation:
Hello, I have been needing help for this problem for awhile. Can someone help me please?
Answer:
x = 6
Step-by-step explanation:
[tex]x = \sqrt{10 {}^{2} - 8 {}^{2} } [/tex]
[tex]x = \sqrt{100 - 64} [/tex]
[tex]x = \sqrt{36} [/tex]
[tex]x = 6[/tex]
a in the solution to the system of equations below?
a=38 +7
4a +9 = 70
Answer:
A=45
15.25
Step-by-step explanation:
Worth a lot of points
Answer: guy Belows right
Step-by-step explanation:
The mean number of songs downloaded by a group of teens last month was 28 with a standard deviation of 3. If the number of songs that Jack downloaded wos one standard deviation below the mean, how many did
he download?
Answer:
Jack downloaded 25 songsStep-by-step explanation:
The mean = 28The standard deviation = 3One standard deviation below the mean:
28 - 3 = 25Jack downloaded 25 songs
(PLEASE HELP THIS IS DUE IN LIKE 10 MIN) What is the measure of angle P
117
130+110=240
240/101=2.37623762376x the equlatiral line by its invisible circle you get 117
Find the x- and y-intercepts of the graph of the equation.
y = 2/3x-12
Help plz
I know the y is 0,-12 but is the x intercept?
Answer:
(18,0)
Step-by-step explanation:
Set y equal to zero
0=2/3x-12
12=2/3x
x=18, the x intercept is (18,0)
Answer:
x-intercept at (18, 0)
Step-by-step explanation:
to find x-intercept, set 'y' equal to zero and solve for 'x'
0 = 2/3x - 12
12 = 2/3x
2x = 36
x = 18
HELP ASAP PLZ HELPPPP
Answer:
The angle ACX equals 51 degrees. The angle ACB equals 129 degrees.
Step-by-step explanation:
21 + 30 + y = 180
y = 129
129 + x =180
x = 51
If x=-2 substitute the value of x into the expression and simplify
Answer:
-17
Step-by-step explanation:
the expression is 6x-5
Substituting x=-2
6(-2)-5
(-12)-5=-17
Answer:
A teacher had 20 ounces of water in der
water bottle. She drank of the water.
How many ounces did she drink?
Answer:
the question is wrong
i cant answer it sorry
A teacher has 613 fliers to divide equally among 29 students. About how many fliers will each student receive?
Which choice shows the coordinates of B’ if the trapezoid is reflected across the x-axis?
A,(-7,2)
B,(2,-7)
C,(7,-2)
C,(-2,7)
Answer:
The answer is C
Step-by-step explanation:
Edgy 2021 Unit Test
80 people attended a meeting. There was x men and x women and the rest were children. How many children attended the meeting
Answer:
80 - 2x
Step-by-step explanation:
Given
Total number of people = 80 people
Total men = x men
Total women = x women
Let the number of childeren be c
x + x + c = 80
Make c the subject of the formula
c = 80 - (x+x)
c = 80 - 2x
Hence the total children attending is 80 - 2x
i will mark you as brainliest if you answer this correctly!
Answer:
1/32 yd
Step-by-step explanation
⇒ m∠A + m∠B + m∠C = 180°
⇒ 25° + 25° + m∠C = 180°
⇒ 50° + m∠C = 180°
⇒ m∠C = 180° – 50°
⇒ m∠C = 130°
Answer:
130
Step-by-step explanation:
An aerial photographer who photographs real estate properties has determined that the best photo is taken at a height of approximately 483 ft and a distance of 858 ft from the building. What is the angle of depression from the plane to the building?
Answer:
x = distance from the building = 837 ft
y = height = -483 ft (The building is DOWN from the plane.)
θ = angle of depression = to be determined
tan θ = y/x
tan θ = -0.577060932
θ = arctan (-0.577060932)
θ = -29.98756509 ° ≈ -30 ° (The building is DOWN from the plane.)
Step-by-step explanation:
Cited from Yahoo! Answers. Please don't sue me!
Given:
Opposite= 483 ft
Hypotenus= 858 ft
To find:
The angle of depression=?
Solution:
Since they are alternative inner angles, the angles of altitude and depression are equal. Within right-angle triangular, we obtain opposite=483 and hypotenus=858. So, to use a trigonometric ratio, we get[tex]\to \sin \theta =\frac{opposite}{hypotenus} \\\\ \to \sin \theta =\frac{483}{858} \\\\\to \theta = \sin^{-1} (\frac{483}{858}) \\\\\to \theta \approx 34.25^{\circ} \\\\[/tex]
An angle of dip from the plane to the building is [tex]34^{\circ}[/tex]Learn more about the angle of depression:
brainly.com/question/9817377
Solve equation q-14=12
Answer:
q=12+14
=26
Step-by-step explanation:
the answer would be 26
