Answers
8. For brevity, let U = unemployed, E = employed, M = male, F = female. We're given that
P(M) = P(F) = 50/100 = 1/2
P(U) = 60/100 = 3/5
P(M | U) = 2/3
P(E) = 40/100 = 2/5
P(F | E) = 3/4
8a. This follows immediately from the given information. Specifically,
P(E) = 1 - P(U) = 1 - 3/5 = 2/5
8b. By definition of conditional probability,
P(A | B) = P(A and B) / P(B) ⇒ P(A and B) = P(A | B) P(B)
It follows that
P(M and U) = P(M | U) P(U) = 2/3 • 3/5 = 2/5
8c. Using Bayes' rule/the definition of conditional probability,
P(U | F) = P(U and F) / P(F) = P(F | U) P(U) / P(F)
Since F and M are mutually exclusive,
P(F | U) = 1 - P(M | U)
and so
P(U | F) = (1 - 2/3) • 3/5 / [(1 - 2/3) • 3/5 + 3/4 • 2/5] = 2/5
8d. Here we assume gender and employment status are independent, so for instance
P(F and E) = P(F) P(E)
We then have by the inclusion/exclusion principle that
P(F or U) = P(F) + P(U) - P(F and U) = P(F) + P(U) - P(F) P(U)
We also have by the law of total probability
P(F) = P(F and U) + P(F and E)
so
P(F or U) = P(F and U) + P(F and E) + P(U) - P(F) P(U)
By the assumed independence,
P(F or U) = P(F) P(U) + P(F) P(E) + P(U) - P(F) P(U)
P(F or U) = P(F) P(E) + P(U)
P(F or U) = 1/2 • 2/5 + 3/5 = 4/5
9.
a. This is mostly a matter of counting the ways a given type of stamp can fall out.
[tex]P(A) = \dfrac{\dbinom{20}3}{\dbinom{24}3} = \dfrac{285}{506}[/tex]
since there are 20 non-green stamps.
[tex]P(B) = \dfrac{\dbinom21 \dbinom{22}2}{\dbinom{24}3} = \dfrac{21}{92}[/tex]
since there are 2 red and unused stamps, 1 of which we want; the other 2 stamps come from the remaining 22 non-red-and-unused stamps.
[tex]P(A \cap B) = \dfrac{\dbinom21 \dbinom{18}2}{\dbinom{24}3} = \dfrac{153}{1012}[/tex]
since exactly 1 of the stamps must be red and unused, and the other 2 stamps that fall out can be neither green nor red and unused.
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B) = \dfrac{162}{253}[/tex]
which follows from the inclusion/exclusion principle.
b. There is a total of 10 used stamps, so the probability of at least 1 going missing is
[tex]P(C) = \dfrac{\dbinom{10}1\dbinom{14}2 + \dbinom{10}2\dbinom{14}1 + \dbinom{10}3}{\dbinom{24}3} = \dfrac{415}{506}[/tex]
By definition of conditional probability,
[tex]P(C \mid A) = \dfrac{P(C \cap A)}{P(A)}[/tex]
However, there are no used green stamps; any used stamp that goes missing must be red, blue or yellow. So the event A ∩ C is really just the event C, and
[tex]P(C \mid A) = P(C) = \dfrac{415}{506}[/tex]
c. A and C are independent if and only if
[tex]P(A \cap C) = P(A) P(C)[/tex]
We know
[tex]P(C \cap A) = P(C)[/tex]
so if A and C are independent, then
[tex]P(C) = P(A) P(C)[/tex]
but this would imply P(A) = 1, which is clearly not the case as we found in 9.a. So A and C are not independent.
Related Questions
Determine the total length of the major and minor axes for the ellipse 25x^2+y^2=25
Will give brainliest
Answers
Answer:
Step by step Solution :-
25X^2 + Y^2 = 25
A) Finding X value :-
1. Subtract Y^2 from both sides:
25X^2 = 25 - Y^2
2. Divide both sides by 25 :
( 25X^2 ) ÷ 25 = ( 25 - Y^2 ) ÷ 25
3. Dividing by 25 undo the multiplication by 25 :
X^2 = ( 25 - Y^2 ) ÷ 2
4. Divide ( 25 - Y^2 ) by 25 :
X^2 = ( - Y^2 ÷ 25 ) + 1
5. Take Square Root for both sides of equation ( before & after (=) ) :
X = √ ( 25 - Y^2 ) ÷ 5
X = - √ ( 25 - Y^2 ) ÷ 5
------------
Now that we knew what X value is, we'll figure out Y value too!
B) Finding Y value ( Finding Square Root ):-
Y^2 = 5√ ( 1 - X^2 )
1. Finding Square Root :
25X^2 + Y^2 = 25
2. Subtract 25X^2 value from both sides :
Y^2 = 25 - 25X^2
3. Take square root for both sides of equation :
Y = 5√ ( 1 - X^2 )
Y = - 5√ ( 1 - X^2 )
Gifts are packaged in cylinders.
Each cylinder is 12 cm high with a diameter of 8 cm.
Calculate the volume of each cylinder.
Use 3 as a value for at
Give your answer using the correct units.
Answers
Answer:
Step-by-step explanation:
V = [tex]\pi r^{2} h[/tex]
V = (3.14)(16)(12)
V = 50.24 cm³
An item on sale costs 60% of the original price. If the original price was $30, what is the sale price?
si
Х 5 ?
Answers
Answer: $18
Step-by-step explanation:
60% of original cost means 40% is taken off
40% = 0.4
30 x 0.4 = 12 so that is how much will be taken off
30-12= 18
$18
I don’t understand how to do this! Could you help me step by step, please?
Answers
Answer: x=12
Step-by-step explanation: Combine Multiplied terms into a single fraction: 3 = 18 - 5/4 x 3 = 18 - -5/4x
Find common denominator: 3= 18+ -5/4x 3= 4 x 18/4 + -5x/4
Combine fractions with common denominator: 3= 4 x 18/4 + -5x/4 3=4 x 18/- 5x/4
Mr. Alden Richards is planning to build a gazeboo whose base is a regular octadecagon. At what angle should he cut the lumber to frame the base.
Answers
Answer: Set your blade tilt to 67.5 degrees.
Help what is the product?
Answers
Answer:
(6 18)
Step-by-step explanation:
[tex](4 \: 2) \times \binom{ - 2 \: \: \: \: \: \: \: \:5 }{7 \: \: \: \: \: \: - 1} \\ \\ (4 \times - 2 + 2 \times 7 \: \: \: 4 \times 5 + 2 \times - 1) \\ \\ ( - 8 + 14 \: \: \: \: \: \: 20 - 2) \\ \\ (6 \: \: \: 18)[/tex]
i need help solving for x. with pythagorean theorem.
Answers
Answer:
[tex]14 \sqrt{3} [/tex]
Step-by-step explanation:
Here you use the 30-60-90 triangle
Note that the side length opposite of the 60 degree triangle is root of 3 times greater than the side opposite of the 30 degree angle.
Here, x is the opposite of 60 degree angle.
7 times root of 4 is opposite of the 30 degree angle,
So we have
So this means
[tex]7 \sqrt{4} \times( \sqrt{3} ) = x[/tex]
Note that
[tex]7 \times \sqrt{4} = 7 \times 2 = 14[/tex]
So we have
[tex]14 \sqrt{3} = x[/tex]
Dan needs to make a total of 25 deliveries this week So far he has completed 19 of them. What percentage of his total deliveries has Dan completed?
Answers
Answer:
76 percent.
Step-by-step explanation:
76% of deliver Dan completed
Explanation:
19/25
19 out of 25
Hope it helps, Let me know if you have any other questions!
Have a nice rest do your day :)
10
10
U
U
g(x)
f(x)
8
10
-2
10-8
2
-108
--2
2
4
-8
- 10
If g(x) = f(x + k), what is the value of k?
Answers
Answer: -6
Step-by-step explanation:
The graph of g is the graph of f translated left 6 units.
the sum of two integers is - 120 if one of them is 82 find the other
Answers
Answer:
38
Step-by-step explanation:
Here,
Let one of the unknown integer be x whereas the other one be 82 (according to question)
Now,
X+82=120
Or, x=120-82
Or, x=38
Therefore the value of the unknown integer is 38.
If two angles are complementary in a right triangle, then explain how you can find the
value of x if sin 440 = cos x using 2-3 sentences. In the last sentence, give the value of x.
Answers
Answer:
46°
Step-by-step explanation:
Points of note
two angles are complementary in a right trianglesin 44° = cos x°Solving
The first thing to understand is "complementary" means that the two angles add up to 90°Therefore, 44 + x = 90x = 46°Answer:
46°
Step-by-step explanation:
Complementary angles
Two angles whose measures sum to 90°
In a right triangle, the angle opposite the hypotenuse is always 90°.
The interior angles of a triangle sum to 180°, therefore the other two angles are complementary angles since their sum is always 90°.
So we can label one angle as [tex]x[/tex] and the other as [tex](90-x)[/tex].
The side opposite angle [tex]x[/tex] is the side adjacent to angle [tex](90-x)[/tex].
Therefore, using trig ratios, we can say that [tex]\sin(x) = \cos(90-x)[/tex]
So, if [tex]x=44[/tex] then:
[tex]\implies \sin(44) = \cos(90-44)=\cos(46)[/tex]
find the equation of line that passes through the point (4,-5) and the slope 5/4
Answers
Answer:
[tex]\boxed{\sf{y=\dfrac{5}{4}x-10 }}[/tex]
Step-by-step explanation:
To find the equation of line, you have to use a slope and slope-intercept formula.
Slope formula:
[tex]\Longrightarrow:\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
Slope-intercept formula:
[tex]\Longrightarrow:\sf{y=mx+b}[/tex]
M represents the slope.B represents the y-intercept.So, the slope is 5/4.The y-intercept is -10.Rewrite the problem down.
y=5/4x-10
So, the correct answer is y=5/4x-10.I hope this helps you! Let me know if my answer is wrong or not.
Are constant functions periodic? The reason I ask this is because a function is periodic if it has a period but in a constant function the period could be infinitely small.
Answers
Answer:
A function f:R→R is periodic if there exists some number t>0 such that
f(x)=f(x+t)
A constant function is periodic since you can take t=1,t=2, etc. (Hint: Hover over the tag "periodic-functions". What do you see?)
The fundamental period of f is the smallest of such t's. Since t cannot be 0, you are looking for the minimum of (0,∞), which does not exist.
Step-by-step explanation:
Simplify the expression with nested parentheses.
430+ 26+6−33
Answers
Answer:
using bodmas.
6-33=-27.
430+26=456.
456-27=429
A point on a pre-image is currently located at (1, -3). The pre-image is translated 3
units right and 6 units up.
What are the NEW coordinates for the point after the translation? Use graph paper
to sketch the translation if needed.
(3, 4)
(3,4
(4,3)
)
(7.0)
0
(-2.2)
Answers
Answer:
(4,3)
Step-by-step explanation:
Since its a positive translation you add 3 to 1 because you are going to the right. You coordinates of that step then becomes (4,-3). Then you need to translate up 6 units. Because the y is -3 you add 3 to make 0, then 3 more (3+3=6) to get positive 3. You then end up with the coordinates (4,3)
On a given planet the weight of an object varies directly with the mass of an object. Suppose that an object whose mass is 3kg weighs 21N. Find the weight of an object whose mass is 7kg
Answers
Rearrange to get gravity
Gravity = weight/mass
Using 3kg, 21N
Gravity = 21/3 = 7
On this particular planet the gravity is measure at 7 m/s
Therefore:
Weight = 7kg*7= 49N
A rectangle has an area of 20 cm^2. What will the area be if the rectangle tripled in size?
Answers
Answer:
180 cm^2
Step-by-step explanation:
For similar figures the ratio of areas is the square of the ratio of linear dimensions.
We take "tripled in size" to mean that the linear dimensions of the larger rectangle are 3 times those of the smaller rectangle. That means the area of the larger rectangle will be 3² = 9 times the area of the smaller one.
Area = (3²)(20 cm²) = 180 cm² . . . . area after tripled in size
Given f(x) = x2 + 1 and g(x) = |x + 31| which value of x is a
solution to the equation f(x) = g(x)?
Answers
Answer:
the answer is 30..........
cumulated Depreciation and Fees Earned would be sorted to which respective columns in completing a work
eet?
ect one:
. a. Balance Sheet and Statement of Owner's Equity-Credit; and Income Statement-Credit.
b. Balance Sheet and Statement of Owner's Equity-Debit; and Income Statement-Debit.
c. Income Statement-Debit and Income Statement-Credit.
d. Balance Sheet and Statement of Owner's Equity-Debit; and Balance Sheet and Statement of Owner's Equity-
Credit.
e. Balance Sheet and Statement of Owner's Equity-Debit; and Income Statement-Credit.
Answers
Accumulated Depreciation and Fees Earned would be sorted into Balance Sheet and Statement of Owner's Equity-Debit; and Income Statement-Credit.
What is an accumulated depreciation?Accumulated depreciation is the accumulation of an asset's depreciation through a specific point in its lifetime. It is a contra asset account, which means that its proper balance is a credit that decreases the asset's overall value.
A corporation debits depreciation expenditures and credits accumulated depreciation when accounting for depreciation in the general ledger.
On the balance sheet, accumulated depreciation is recorded and shown underneath the line for associated capitalized assets.
Therefore, we can conclude that Accumulated Depreciation and Fees Earned would be sorted into the Balance Sheet.
Learn more about accumulated depreciation here:
https://brainly.com/question/9041582
A social security number contains nine digits, such as 224-10-7135. How many different social security numbers can be formed?
Answers
Answer:
420 million
Step-by-step explanation:
There are up to 420 million numbers that were assinged.
Find the area of the triangle with the following coordinates. A (-5,9) B (1,-7) C (8,4)
Answers
QUESTION : > FIND THE ARE OF THE TRIANGLE WITH THE FOLLOWING COORDINATES.
A. (-5,9)
B . (1,-7)
C . (8,4)
ANSWER :> A.
(-5,9).
HOPE IT HELPS
THANK ME LATER.
#CARY ON LEARNINGevaluate the equation: F( 2 ) =
Answers
Answer:
3
Step-by-step explanation:
it's basically asking what is the y value that corresponded to x = 2
that value is 3.
If your net pay, after a $142.00 automatic withdrawal, is $2,665.00, what percent of your net pay was withdrawn?
Answers
Answer:
Net pay = $142 + $2665 = $2807
Percent withdrawn = (withdrawal ÷ net pay) × 100%
= (142 ÷ 2807) × 100%
= 5.058781617...%
= 5.1% (nearest tenth)
Test help picture below problem 19 21
Answers
Step-by-step explanation:
PROBLEM 19
(side 1)² + (side 2)² = (hypo)²
56² + (side 2)² = 61²
3136 + (side 2)² = 3721
(side 2)² = 3721 - 3136
(side 2)² = 585
side 2 = root 585
side 2 = 24.1867732449
side 2 = 24.2cm
E. Parallelogram
reason
opposite sides are parallel
MARK ME AS BRAINLIST. What is 1- 87+23
What is 5- 700÷7
Answers
Step-by-step explanation:
[tex]1 - 87 + 23 \\ = - 86 + 23 \\ = - 63 \\ \\ \\ \\ 5 - 700 \div 7 \\ = 5 - 100 \ \\ = - 95[/tex]
hope it helps ..
GIVING BRAINLIEST
What is the measure of angle x?
40 degrees
80 degrees
130 degrees
140 degrees
Answers
Answer:
140 degrees
Step-by-step explanation:
Since alternate angles are equal, corresponding angles are equal, a pair of interior angles on the same side of the transversal are supplementary, and angles on a straight line add up to 180 degrees, 40 + x must equal 180 degrees.
To find angle x in this instance, you would need to subtract 40 degrees from 180 degrees.
[tex]180-40=140[/tex]
Therefore, the answer is 140 degrees.
Answer:
my test said 140
Step-by-step explanation:
Manuel wants to rent a boat and spend at most 34. The boat costs 8 per hour, and Manuel has a discount coupon for 6 off. What are the possible numbers of hours Manuel could rent the boat?
Answers
5 hours
6 times 5 is 30, and if hes not wanting to go over, then it'd be 5 hours for $30
PLEASE HELP FOR EACH OF THE FIGURES, WRITE AN ABSOLUTE VALUE EQUATION
Answers
The solution set 0 and 8 are the true values of the absolute value equation
The absolute value equation that has the a solution set of 0 and 6 is |x - 3| = 3
How to determine the absolute value equation?From the figure, the solution sets of the absolute value equation are given as:
x = {0, 6}
Calculate the mean of the solution set
Mean = 0.5 * (0 + 6)
Mean = 3
Calculate the difference of the solution set divided by 2
Difference = (6 - 0)/2
Difference = 3
The absolute value equation is the represented as:
|x - Mean| = Difference
Substitute known values
|x - 3| = 3
Hence, the absolute value equation that has the a solution set of 0 and 6 is |x - 3| = 3
Read more about absolute value equation at:
brainly.com/question/2166748
Answer:
|x-3|=3
Step-by-step explanation:
A student recorded the distance and height of a basketball when shooting a free throw.
Distance feet X 0 2 6 9 12 13 15
Height (feet) Y 4 8.4 12.1 14.2 13.2 10.5 9.8
(a) Write the quadratic regression equation mal models the data Letx=distance in feet and let y= height in feet Round all numbers to the nearest hundredth
(b) Use the equation to estimate the height of basketball when shot from 20 feet. Show your work.
Answers
Answer:
a) [tex]y = 0.118x^{2} +2.112x+4.215\\[/tex]
b)height = 896.2 feet
Step-by-step explanation:
for b, substitute 20 in place of x in the first equation.
In a circle, a central angle of 2 radians intercepts an arc of 6 centimeters.
Find the length of the radius in centimeters.
Answers
Answer:
3 cm
Step-by-step explanation:
To solve this problem, we can use the Arc Length Formula. This states that s = r · [tex]\bf \theta[/tex], where s = arc length, r = radius, and [tex]\theta[/tex] is the measure of the central angle (in radians).
From the problem, we are given that s = 6 cm, [tex]\theta[/tex] = 2, and we need to solve for r. Substituting these values into the equation gives us the following:
6 = r · 2
Solving the equation gives us r = 3 cm. Hope this helps!
