Answer:
The events are independent.Their conditional probability is equal to the probability of an event .
2) The probability that there is line spoilage given that there is transformer spoilage=0.08
- Transformer spoilage but not line spoilage=0.046
Transformer spoilage given that there is no line spoilage = 0.05
- Neither transformer spoilage nor there is no line spoilage =0.03
v- Either transformer spoilage or there is no line spoilage = 0.97
Step-by-step explanation:
Let A be an event that the spoilage is due to transformers so
P(A) = 5% = 5/100 or 0.05
Let B be an event that the spoilage is due to line so
P(B) = 8% = 8/100 or 0.08
Let C be an event that the spoilage is due to both then
P(C) = 3% = 3/100 or 0.03
1) Independence
For events to be independent their joint probability is given by
P(A) = P(A∩B)/ P (B) By Law of independence
P(A∩B)= P(A/B)P(B)
P(A∩B) = 5/100 *8/100=40/10000= 4/1000
P(A) = 5/100
P(A/B) =P(A∩B)/ P (B)
= 4/1000/8/100= 1/20
P(A)= P(A/B)
5/100 is equal to 1/20
The events are independent.Their conditional probability is equal to the probability of an event
2) The probability that there is line spoilage given that there is transformer spoilage
P(B/A)= P(A∩B)/ P (A) = 4/1000/5/100= 4/50= 2/25=0.08
Which is again equal to probability of event B.
- Transformer spoilage but not line spoilage
P(A∩1-B)= 5/100*92/100= 460/10000=0.046
Transformer spoilage given that there is no line spoilage
P(A/1-B) =P(A∩1-B)/ P (1-B)
= 5/100*92/100/92/100= 5/100 = 0.05
- Neither transformer spoilage nor there is no line spoilage
1-P(A) +P(1-B)= 1-(5/100+92/100)= 3/100= 0.03
v- Either transformer spoilage or there is no line spoilage
P(A)+P(1-B)= 5/100+92/100= 97/100= 0.97
Simplify the expression. 1/2 (-sin2x - cos 2x)
Answer:
1/2 (-sin2x - cos 2x)
Step-by-step explanation:
Distribute 1/2 to every term in the parentheses
A couple wants to install hardwood into their bedroom. The wood is bought in 0.5×5 square foot pieces. They have 422 square feet of floor on which to install the hardwood. How many 0.5×5 sections must be purchased?
124 sections
25 sections
169 sections
84 sections
Answer:
169 sections
Step-by-step explanation:
A couple wants to install hardwood into their bedroom. The wood is bought in 0.5×5 square foot pieces
The area of the 0.5×5 square foot pieces
Area= 0.5*5.
Area= 2.5 square feet
They have 422 square feet of floor on which to install the hardwood.
Number of sections to be purchased
= 422/2.5
= 168.8 sections
Approximately= 169 sections
Find the standard form of the equation of the ellipse with the given characteristics. Center: (1, 2); vertex: (−7, 2); minor axis of length 12
Answer:
(x-1)²/64 + (y-2)²/ 144= 1
Step-by-step explanation:
Given that
The standard form for an ellipse is
(x-h)/a² + ( y-k)/b²=1
So
h, k
is the centre of the ellipse, and
a is the distance from the centre to the vertices and c is the distance from the centre to the foci.
b is the minor axis.
So b² + c²= a²
In this example
a= -7-1= -8
Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n 2 if heads comes up first on the nth toss. If we play this game repeatedly, how much money do you expect to win or lose per game over the long run
Answer:
In the long run, ou expect to lose $4 per game
Step-by-step explanation:
Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n^2 if heads comes up first on the nth toss.
Assuming X be the toss on which the first head appears.
then the geometric distribution of X is:
X [tex]\sim[/tex] geom(p = 1/2)
the probability function P can be computed as:
[tex]P (X = n) = p(1-p)^{n-1}[/tex]
where
n = 1,2,3 ...
If I agree to pay you $n^2 if heads comes up first on the nth toss.
this implies that , you need to be paid [tex]\sum \limits ^{n}_{i=1} n^2 P(X=n)[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = E(X^2)[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =Var (X) + [E(X)]^2[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+(\dfrac{1}{p})^2[/tex] ∵ X [tex]\sim[/tex] geom(p = 1/2)
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p}{p^2}+\dfrac{1}{p^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{1-p+1}{p^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-p}{p^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) = \dfrac{2-\dfrac{1}{2}}{(\dfrac{1}{2})^2}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{4-1}{2} }{{\dfrac{1}{4}}}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ \dfrac{3}{2} }{{\dfrac{1}{4}}}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =\dfrac{ 1.5}{{0.25}}[/tex]
[tex]\sum \limits ^{n}_{i=1} n^2 P(X=n) =6[/tex]
Given that during the game play, You pay me $10 , the calculated expected loss = $10 - $6
= $4
∴
In the long run, you expect to lose $4 per game
Can someone come Plzzz help??
Answer:
The probability of HHH=1/8.
Sample space=(HHH,HHT,HTH,HTT,TTT,TTH,THT,THH).
A man has 12 different colored shirts and 20 different ties in his closet. How many shirts and tie combinations can he select to take on a trip if he only takes 3 shirts and 5 ties?
We hat does (-9) mean
Answer:
(-9) still means -9 it doesn't really mean anything thou....but if u have another number besides it then it means to multiply like maybe 2(-9)then it will be -18...... but if it is just (-9) then it doesn't mean anything.....
In class, there are 9 boys and 13 girls. If half of the class has a cold, how many girls must have a cold?
Answer: a or c one of those
Step-by-step explanation:
If the volume of a cube is increased by a factor of 10, by what factor does the surface area per unit volume change
Answer:
(1/10)∛100 ≈ 0.4642
Step-by-step explanation:
For a cube of volume V, the edge length is ...
s = ∛V
and the area is ...
A = 6s² = 6V^(2/3)
Then the ratio of area to volume is ...
r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)
If the value of V is increased by a factor of 10, the ratio of area to volume is now ...
r2 = 6(10V)^(-1/3)
The factor by which the ratio changed is ...
r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100
The surface area per unit volume changes by a factor of (∛100)/10.
___
Example
For a cube of side length 2, the volume is 2³ = 8 and the surface area is 6·2² = 24. The ratio of surface area to volume is 24/8 = 3.
Multiplying the edge length by ∛10, we now have a volume of (2∛10)³ = 80, and a surface area of 6(2∛10)² = 24(10^(2/3)). The ratio of surface area to volume is ... 24(10^(2/3))/80 = 0.3∛100.
The ratio of area to volume changed by a factor of (0.3∛100)/3 = (∛100)/10, as above.
Beverly has a backyard that is square. One of the sides is 10 feet long. What is the area of her back yard?
Answer: all of the sides are 10ft long
Step-by-step explanation:
Clark and Lana take a 30-year home mortgage of $128,000 at 7.8%, compounded monthly. They make their regular monthly payments for 5 years, then decide to pay $1300 per month.
A) Find their regular monthly payment.
B) Find the unpaid balance when they begin paying the $1400.
C) How many payments of $1400 will it take to pay off the loan?
D) How much interest will they save by paying the loan using the number of payments from part (c)?
Answer:
Step-by-step explanation:
From the given information:
The present value of the house = 128000
interest rate compounded monthly r = 7.8% = 0.078
number of months in a year n= 12
duration of time t = 30 years
To find their regular monthly payment, we have:
[tex]PV = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{r}{n})^{-nt}}{\dfrac{r}{n}} \end {bmatrix}[/tex]
[tex]128000 = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{0.078}{12})^{- 12*30}}{\dfrac{0.078}{12}} \end {bmatrix}[/tex]
128000 = 138.914 P
P = 128000/138.914
P = $921.433
∴ Their regular monthly payment P = $921.433
To find the unpaid balance when they begin paying the $1400.
when they begin the payment ,
t = 30 year - 5years
t= 25 years
[tex]PV= 921.433 \begin {bmatrix} \dfrac{1 - (1 - \dfrac{0.078}{12})^{25*30}}{\dfrac{0.078}{12}} \end {bmatrix}[/tex]
PV = $121718.2714
C) In order to estimate how many payments of $1400 it will take to pay off the loan, we have:
[tex]121718.2714 = \begin {bmatrix} \dfrac{1300 (1 - \dfrac{12.078}{12}))^{-nt}}{\dfrac{0.078}{12}} \end {bmatrix}[/tex]
[tex]121718.2714 = 200000 \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}[/tex]
[tex]\dfrac{121718.2714}{200000 } = \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}[/tex]
[tex]0.60859 = \begin {bmatrix} (1 - \dfrac{12}{12.078}))^{nt} \end {bmatrix}[/tex]
[tex]0.60859 = (0.006458)^{nt}[/tex]
[tex]nt = \dfrac{0.60859}{0.006458}[/tex]
nt = 94.238 payments is required to pay off the loan.
How much interest will they save by paying the loan using the number of payments from part (c)?
The total amount of interest payed on $921.433 = 921.433 × 30(12) years
= 331715.88
The total amount paid using 921.433 and 1300 = (921.433 × 60 )+( 1300 + 94.238)
= 177795.38
The amount of interest saved = 331715.88 - 177795.38
The amount of interest saved = $153920.5
PRECALC HELP WILL GIVE BRAINLIEST
Answer:
(d, left, right) ⇒ (d, di, -di)
Step-by-step explanation:
In the complex plane, successive left turns make this your sequence of facing directions: 1, i, -1, -i, 1. Effectively, your facing direction is multiplied by i.
Successive right turns make this your sequence of facing directions: 1, -i, -1, i, 1. Effectively, your facing direction is multiplied by -i.
Your table can be filled as follows:
(initial d, left turn, right turn)
(-1, -i, i)
(1, i, -i)
(i, -1, 1)
(-i, 1, -1)
(d, di, -di)
Evaluate f(x) = 6x - 2 for x = 3 Group of answer choices 7 16 10 61
Cassius drives his boat upstream for 45 minutes. It takes him 30 minutes to return downstream. His speed going upstream is 3 miles per hour slower than his speed going downstream. Find his upstream and downstream speed
Answer:
Upstream speed= 6 mile per hour
Downstream speed= 9 miles per hour
Step-by-step explanation:
Distance traveled during upstream
= x miles
Distance traveled during downstream
= y
Time traveling upstream
= 45 minutes.
Time traveling downstream
= 30 minutes
Speed traveling upstream
= a miles/hour
Speed traveling downstream
= b miles/hour
But
b = a+3
Distance= speed*time
X=45a
a= x/45
Y= 30(a+3)
Y= 30a +90
a= (y-90)/30
Equating both a
X/45= (y-90)/30
30x= 45(y-90)
X= 1.5y-135
But x= y
Y= 1.5y-135
135= 0.5y
270 miles = y
Y= x= 270 miles
X= 45a
270/45= a
6 mile/hour = a
b = a+3
b= 6+3
b = 9 miles/hour
the cell that contains 28 joins female and cat. Explain the context of the joint frequency cell.
animals vs gender
Dog Cat Total
Male 32 8. 40
Female. 11. 28. 39
Total. 43. 36. 79
A. 28 of the cats in the distribution are female
B. In the distribution of cats, 8 are female
C. 28 of the dogs in the distribution are female
D. 28 animals in the distribution are female cats and dogs
The correct answer is A. 28 of the cats in the distribution are female
Explanation:
The table presented shows the number of female/male dogs and cats, as well as the total of animals in each category. Moreover, in this, the columns show the type of animal (dog or cat), while the rows show its gender (female/male). Also, these categories intersect to show the frequency. For example, number 32, which is the intersection of the categories Dog and Male shows there are 32 male dogs. In this context, if the number 28 joints the categories female and cat, this means 28 of the total animals are female cats and out of the total cats 28 are female. This makes option A the correct answer.
Answer: two-ways tables quiz
1. 38.0%
2. 54.4%
3. 28.5%
4. 21.3%
5. 71.5%
6. 21.8%
7. Twenty-eight of the cats in the distribution are female.
8. 74.4%
9. 49.4%
10. 62.0%
Step-by-step explanation:
Judah worked at the bakery for 14 hours last week. He spent $12 of his earnings on a cake for his father’s birthday. If he was left with $86 after buying the cake, what is Judah’s hourly wage?
Answer:
Judah's hourly wage is $7/hr.
Step-by-step explanation:
x = (86 + 12)/14
x = 98/14
x = 7
Answer:
$7 per hour
Step-by-step explanation:
$86+ 12( the money he spent on the birthday cake)=$98
$98 divided by 14=7
Round to the nearest dollar $7,563.27
Answer:
$7,563
Step-by-step explanation:
We will round to the nearest whole number to round to the nearest dollar
$7,563.27
since we have 27 cents ( .27), that is less than 50 cents, we leave it alone
$7,563.00 or $7,563
Answer:
$7,563
Step-by-step explanation:
Rounding to the nearest dollar is just like rounding to the nearest whole number.
The number we are given is:
$7,563.27
To round to the nearest dollar, look to the tenths place. If it is less than or equal to 4, round down. If it is greater than or equal to 5, round up.
The tenths place has a 2. Therefore, we leave the number as is.
$7, 563
$7,563 rounded to the nearest dollar is $7,563.00
can some one please help me with this.
3 1⁄8 − 1 7⁄8 =
Answer:
1 2/8
Step-by-step explanation:
3 1/8 = 25/8
25/8 - 15/8 = 10/8 = 1 2/8
Tyra bought 4.5 pounds of strawberries. They cost $2.60 a pound. How much did
she spend?
Below is the table of values of a function. Write the output when the input is n. input 3 8 72 ñ
output 6 11 12 []
Answer:
n + 3
Step-by-step explanation:
6 is 3 + 3, 11 is 8 + 3 and 12 is 9 + 3 so the output seems to be the input plus 3. Therefore, when the input is n, the output is n + 3.
Answer:
output = n+3
Step-by-step explanation:
When the input changes by 5 units (from 3 to 8), the output changes by 5 unis (from 6 to 11). So the rate of change of the output with respect to the input is 1. However, each output is 3 more than the input, so ...
for input n
output = n+3
The table below gives the numbers of protons, electrons, and neutrons in four atoms. Atom Number of protons Number of electrons Number of neutrons 1 39 39 52 2 40 40 50 3 39 39 54 4 40 40 51 Based on the information that is given, which atom in the table has the highest mass? 1 2 3 4
Answer:
3
Step-by-step explanation:
As per table, the mass is:
1 | 39 + 39 + 52 = 1302 | 40 + 40 + 50 = 1303 | 39 + 39 + 54 = 1324 | 40 + 40 + 51 = 131So the atom 3 has the highest mas of 132
Answer choice 3 is correct
Answer:
3
Step-by-step explanation:
Add protons and neutrons.
10 degrees above 0?
If x = 9, then x is between
15 and 20
02 and 3
80 and 90
0 4 and 5
What are the Division Properties of Zero?
You cannot divide any number by zero since it is meaningless to say that we are dividing a number or object in zero groups or in 0 size parts
i enter the bedroom. there are 34 people. i kill 30 people. how many people are there in bedroom
Answer:
35
Step-by-step explanation:
Even if you killed 30 people, 34 people remained in the room (30 dead and 4 alive).
You must add a person which is YOU.
Answer:
there are 35 people in the bedroom.
Step-by-step explanation:
2) the quotient of 14 and 7
Answer:
The quotient of 7 and 14 is 2..
What proportion of these candy bars have more than 300 calories per serving? (Round your answer to two decimal places.)
Answer: 0.12
Step-by-step explanation:
There are 65 candy bars. Out of that;
2 candy bars have 300 to 350 calories
1 candy bar has 350 to 400 calories
4 candy bars have 400 to 450 calories
1 candy bar has 450 to 500 calories
The total proportion out of 65 candy bars that have over 300 calories is;
= ( 2 + 1 + 4 + 1) / 65
= 8/65
= 0.12
Find the surface area of the rectangular prism
2mi 2mi
4mi
Answer:
the SA is 40
Step-by-step explanation:
the formula for SA of a rectangular prism is 2(lw + lh + wh)
so it would be: 2(2x2+2x2+4x2)
can i get brainliest please? i only need two more
The 100th term of 50, 80, 110 is??
Can you please help me with this I’ll give a brain list
Answer: opposite
Step-by-step explanation:
Answer:
opposite
Step-by-step explanation:
the opposite of -4 is 4.
the absolute value of -4 is 4.
the reciprocal of -4 is -1/4.