Answer:
The percentage of the employee will experience a lost-time accident in both years is 0.0%
Step-by-step explanation:
Let A denote events that employees suffered lost-time accidents during the last year
Let B denote events that employees suffered lost-time accidents during the current year
P(A) = 5% = 0.05
P(B) = 4% = 0.04
P(B | A) = 15% = 0.15
(a) P (A ∩ B) = P(B | A) × P(A)
= 0.15 × 0.05
= 0.0075
= 0.0 (1 decimal place)
The probability that an employee will experience a lost- time accident in both years is 0.0
Problem 3.3.9 • (a) Starting on day 1, you buy one lottery ticket each day. Each ticket is a winner with probability 0.1. Find the PMF of K, the number of tickets you buy up to and including your fifth winning ticket. (b) L is the number of flips of a fair coin up to and including the 33rd occurrence of tails. What is the PMF of L? (c) Starting on day 1, you buy one lottery ticket each day. Each ticket is a winner with probability 0.01. Let M equal the number of tickets you buy up to and including your first winning ticket. What is the PMF of M?
Answer:
a) The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]
b)
c)
Step-by-step explanation:
a) Let p be the probability of winning each ticket be = 0.1
Then q which is the probability of failing each ticket = 1 - p = 1 - 0.1 = 0.9
Assume X represents the number of failure preceding the 5th success in x + 5 trials.
The last trial must be success whose probability is p = 0.1 and in the remaining (x + r- 1) ( x+ 4 ) trials we must have have (4) successes whose probability is given by:
[tex]\binom{x+r-1}{r-1}*p^{r-1}*q^{x} = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]
Then, the probability distribution of random variable X is
[tex]P(X=x) = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]
where;
X represents the negative binomial random variable.
K= X + 5 = number of ticket buy up to and including fifth winning ticket.
Since K =X+5 this signifies that X = K-5
as X takes value 0, 1 ,2,...
K takes value 5, 6 ,...
Therefore:
The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]
b)
Let p represent the probability of getting a tail on a flip of the coin
Thus p = 0.5 since it is a fair coin
where L = number of flips of the coin including 33rd occurrence of tails
Thus; the negative binomial distribution of L can be illustrated as:
[tex]P(X=x) = \binom{x-1}{r-1}(1-p)^{x-r}p^r[/tex]
where
X= L
r = 33 &
p = 0.5
Since we are looking at the 33rd success; L is likely to be : L = 33,34,35...
Thus; the PMF of L = [tex]P(L=l) = \binom{l-1}{33-1}(1-0.5)^{l}(0.5)^{33} \\ \\ \\ \mathbf{P(L=l) = \binom{l-1}{33-1}(0.5)^{l} }[/tex]
c)
Given that:
Let M be the random variable which represents the number of tickets need to be bought to get the first success,
also success probability is 0.01.
Therefore, M ~ Geo(0.01).
Thus, the PMF of M is given by:
[tex]P(M = m) = (1-0.01)^{m-1} * 0.01 , \ \ \ since \ \ \ (m = 1,2,3,4,....)[/tex]
[tex]P(M=m) = (0.99)^{m-1} * 0.01 , m = 1,2,3,4,....[/tex]
The strength of paper used in the manufacturing of cardboard boxes (y) is related to percentage of hardwood concentration in the original pulp (x). Under controlled conditions, a pilot plant manufactures 16 samples, each from differential batch of pulp, and measures the tensile strength. Determine if there is significance relationship between x and y.
y = 101, 117, 117, 106, 132, 147, 147, 134, 111, 123, 125, 145, 134, 145, 144, 146.9
x = 1.0, 1.5, 1.5, 1.5, 2.0, 2.0, 2.2, 2.4, 2.5, 2.5, 2.8, 2.8, 3.0, 3.0, 3.2, 3.3
Answer:
At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.
P-value = 0.003.
Step-by-step explanation:
If we perform a regression analysis relating x and y, we get the best fitting line with equation:
[tex]y=15.82x+92.9[/tex]
and a correlation coefficient r:
[tex]r=0.693[/tex]
We have to test the hypothesis, where the alternative hypothesis claims that there is a relationship between these two variables, and the null hypothesis claiming there is no relationship (meaning that the correlation is not significantly different from 0).
This can be written as:
[tex]H_0: \rho=0\\\\H_a:\rho\neq0[/tex]
where ρ is the population correlation coefficient for x and y.
The significance level is assumed to be 0.05.
The sample size is n=16.
The degrees of freedom are df=14.
[tex]df=n-2=16-2=14[/tex]
The test statistic can be calculated as:
[tex]t=\dfrac{r\sqrt{n-2}}{\sqrt{1-r^2}}=\dfrac{0.693\sqrt{14}}{\sqrt{1-(0.693)^2}}=\dfrac{2.593}{0.721}=3.597[/tex]
For a test statistic t=2.05 and 14 degrees of freedom, the P-value is calculated as:
[tex]\text{P-value}=2\cdot P(t>3.597)=0.003[/tex]
The P-value (0.003) is smaller than the significance level (0.05), so the effect is significant enough.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.
Lindsay needs to make some house repairs in four years that will cost $8,000. She has some money in an account earning 8% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs
Answer:
$5,882
Step-by-step explanation:
To calculate the money Lindsay needs today, you can use the following formula to calculate the present value:
PV=FV/(1+i)^n
PV= present value
FV= future value= $8,000
i= interest rate= 8%
n= number of periods= 4
PV= 8,000/(1+0.08)^4
PV=8,000/1.08^4
PV=8,000/1.36
PV= 5,882
According to this, Lindsay will need to have $5,882 in the account today so she will have enough to pay for the repairs in four years.
Consider the vector x: x <- c(2, 43, 27, 96, 18) Match the following outputs to the function which produces that output. Options include sort(x), order(x), rank(x) and none of these
Completed Question
Outputs to be matched to the functions are:
1,2,3,4,51,5,3,2,41, 4, 3, 5, 2 2, 18, 27, 43, 96Answer:
sort(x): 2, 18, 27, 43, 96 order(x): 1, 5, 3, 2, 4 rank(x) : 1, 4, 3, 5, 2none of these : 1, 2, 3, 4, 5Step-by-step explanation:
Given the vector x: x <- c(2, 43, 27, 96, 18)
Sort
In R, the sort(x) function is used to arrange the entries in ascending or descending order. By default, R will sort the vector in ascending order.
Therefore, the output that matches the sort function is:
sort(x): 2, 18, 27, 43, 96
Rank
The rank function returns a vector with the "rank" of each value.
x <- c(2, 43, 27, 96, 18)
2 has a rank of 143 has a rank of 427 has a rank of 396 has a rank of 518 has a rank of 2Therefore, the output of rank(x) is: 1, 4, 3, 5, 2
Order
When the function is sorted, the order function gives the previous location of each of the element of the vector.
Using the sort(x) function, we obtain: 2, 18, 27, 43, 96
In the vector: x <- c(2, 43, 27, 96, 18)
2 was in the 1st position18 was in the 5th position27 was in the 3rd position43 was in the 2nd position96 was in the 4th positionTherefore, the output of order(x) is: 1, 5, 3, 2, 4
1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5
Answer:
103
Step-by-step explanation:
[tex]\dfrac{1}{216}^{-2/3}+\dfrac{1}{256}^{-3/4}+\dfrac{1}{243}^{-1/5}= \\\\\\\sqrt[3]{216^2}+\sqrt[4]{256^3}+\sqrt[5]{243}=\\\\\\6^2+4^3+3=\\\\\\36+64+3=\\\\\\103[/tex]
Hope this helps!
What is an equivalent function to f(x)=(x-2)^3
Answer:
x^3-6x^2-4x-8
Step-by-step explanation:
First you would multiply (x-2) by itself (x-2) to get
x^2-2x-2x+4
then you would combine like terms
x^2-4x+4
Then you would multiply that by x-2
(x^2-4x+4)(x-2)
x^3-2x^2-4x^2-8x+4x-8
then you combine like terms
x^3-6x^2-4x-8
Find the value of y. -6y+14+4y=32
Answer:
So first subtract 14 from 32
That means that -6y+4y = 18
Simplify the left side 4-6=-2
-2y = 18
Divide by -2
-9 = y
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
-6y+14+4y=32
Combine like terms
-2y +14 = 32
Subtract 14 from each side
-2y +14-14 = 32-14
-2y =18
Divide each side by -2
-2y/-2 = 18/-2
y = -9
Benjamin deposits $3,000 into each of two savings
accounts. The first savings account pays 5% interest
compounded annually. The second savings account
pays 5% simple interest annually. If Benjamin makes
no other deposits or withdrawals, what will be the
difference between the interest earned by the two
savings accounts after 4 years?
Answer:
So I have never stepped foot into this. But I have experience from this. So for the first one we can use the compound intrest formula - A = P(1+r/n)^nt so if we do that we get.
A = 3000(1+0.05/1)^1*4
So then we get A is equal to 3646.52
The next one we need to calculate
A = P (1 + rt)
So now we do A = 3000(1+0.05*1)
A = 3000*1.05 = 3150. We add them together and we get 6796.52.
So we subtract 6000 from that. He earned
796.52 dollars
Fernando bought 8 pints of milk. How many fluid ounces of milk did Fernando buy? A. 16 fluid ounces B. 64 fluid ounces C. 128 fluid ounces D. 256 fluid ounces
Answer:
C.
Step-by-step explanation:
There are 16 ounces in a pint. 8 * 16 = 128
3. Set up an equation and use it to solve for x.
51°
(5x + 1)
Answer:
51 = 5x+1
x = 10
Step-by-step explanation:
The angles are vertical angles which means they are equal
51 = 5x+1
Subtract 1 from each side
51-1 = 5x+1-1
50 = 5x
Divide each side by 5
50/5 = 5x/5
10 =x
Answer:
10
Step-by-step explanation:
51 = 5x + 1
5x = 51 - 1
5x = 50
x = 10
Hope this helps!
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
The cottage inside the pen is a shape of a cylinder.
Answer:
Cylinder
As u can see the shape it's like a cylinder
A shopkeeper buys 1 dozen of pens at Rs 15 each and sells them at Rs 18
ch. Find his profit and profit percent.
Answer:
20%
Step-by-step explanation:
Cost price (C. P.) of each pen = ₹ 15
Selling price (S. P.) of each pen = ₹ 18
Profit = S. P. - C. P. = 18 - 15 = ₹3
[tex]profit \: percent \\ \\ = \frac{profit}{c.p.} \times 100 \\ \\ = \frac{3}{15} \times 100 \\ \\ = \frac{3}{3} \times 20 \\ \\ = 20\%[/tex]
Nadeen is at an arcade. She started with 18 tokens. Each game costs 3 tokens. So far, Nadeen has played 2
games.
Answer:
see below
Step-by-step explanation:
I think you are asking how many tokens she has left. She has 18 - 3 * 2 = 18 - 6 = 12 tokens left. She can play 12/3 = 4 more games.
The aspect ratio of a rectangular shape is it's length divided by it's width (L/W). If the aspect ratio of a chalkboard is 4:3 and the width is 5 in, what is the length of the chalkboard? A. 6.67 in B. 9.33 in C. 12 in D. 14 in
Answer:
A. 6.67 in
Step-by-step explanation:
length/width = 4/3 = x/5
Multiply by 5:
5(4/3) = x = 20/3 = 6 2/3
The length of the chalkboard is 6.67 inches.
what is 3 43/ 100 as a decimal number.
Answer:
3.43
Step-by-step explanation:
3 is the whole number and 43 out of 100 is a standard fraction that can simply be stated as 0.43. Hope this helps!
Answer:
3.43
Step-by-step explanation:
Used calculator.
if a propane tank has the shape of a cylindrical tank with a height of 4.2m and a radius of 1.3m how many cubic metres of propane is in the tank if it's only 50% full
Answer:
11.1 cm³
Step-by-step explanation:
V=πr²h / 2 (for half full)
V = (3.14)(1.3)²(4.2)/2
V = 11.1 cm³
PLEASE HELP!!!!!
This is edge!
A b c d
Will mark brainliest!!!!
Answer:
D. [tex] \frac{7}{12} \: of \: a \: pound[/tex]
Step-by-step explanation:
[tex]total \: candies = 2 \frac{1}{4} + \frac{2}{3} \\ \\ = \frac{9}{4} +\frac{2}{3} \\ \\ = \frac{9 \times 3 + 2 \times 4}{3 \times 4} \\ \\ = \frac{27 + 8}{12} \\ \\ = \frac{35}{12} \\ \\ share \: of \: brother = \frac{1}{5} \times \frac{35}{12} \\ \\ = \frac{7}{12} \: of \: a \: pound[/tex]
Answer:
[tex]\fbox{\begin{minipage}{10em}Option D is correct\end{minipage}}[/tex]
Step-by-step explanation:
Step 1: Let's find the total amount of candy that Loret and her sister have:
Loret has [tex]2\frac{1}{4}[/tex] pound of candy
Loret's sister has [tex]\frac{2}{3}[/tex] pound of candy
=> Total amount: [tex]A =2\frac{1}{4} + \frac{2}{3} = \frac{9}{4} + \frac{2}{3} = \frac{27}{12} + \frac{8}{12} = \frac{35}{12}[/tex] pound of candy
Step 2: Let's find the amount of candy Loret's brother could get:
If Loret's brother did the chores, he can get [tex]\frac{1}{5}[/tex] total amount of candy that Loret and her sister have.
=> The amount Loret's brother can get:
[tex]B = A*\frac{1}{5} = \frac{35}{12} * \frac{1}{5} = \frac{7}{12}[/tex] pound of candy
=> Option D is correct
Hope this helps!
:)
According to exit polls, the voting "gender gap" was 22 points in the 2016 House of Representatives election; that is, women voted for Democrats by 10 percentage points, and men voted for Republicans by 12 percentage points. Political scientists are curious to see if this gap holds- or increases- in 2018, but statisticians might be more interested in the processes behind exit polling and the rellabllity of thelr results.
When conducting exit polls, pollsters will randomly select a certain number of precincts, then attempt to get all the voters leaving the polling place to participate in their poll. If they can't get all voters, they will instead attempt to get every nth voter to participate. Many polling companies believe that Democrats are more likely to agree to an exit poll than Republicans or Independents.
Of course, not everyone votes in the morning/mid-afternoon of the election. To get an idea of the preferences of people who voted in the precinct before election day, typically by absentee ballots, companies will attempt a random telephone survey of those voters. Exit polls often wrap up and leave the field before voting stations close, so people voting in the last couple hours of the day may also be missed
(a) What type of sampling methods are used in selecting people for exit polls?
a. Simple Random Sampling
b. Cluster Sampling
c. Stratified Sampling
d. Convenience Sampling
e. Systematic Sampling
(b) Why do the polllng companles randomly select the preclncts to vislt?
a. Randomly selecting precincts to assign pollsters ensures that the companies can conclude a cause and effect relationship between the voters' beliefs and their voting pattern
b. There are too many precincts to manually select, so they are forced to randomly select them
c. Randomly selecting precincts increases the likelihood that the people polled represent the population well.
Answer:
A) cluster sampling ( b ) and systematic sampling ( e )
B ) Randomly selecting precincts increases the likelihood that the people polled represent the population well. ( c )
Step-by-step explanation:
Cluster sampling is a type of sampling plan used when there is an internally heterogeneous groups can be found inside a population that is supposed to be mutually homogeneous . while systematic sampling is a type of probability sampling that involves the selection of samples from a larger population at random but using a specific interval. to get the systematic sample the larger population is divided by the sample size.
from the information available in the report it is very evident that not all voters can be captured at once hence cluster sampling and systematic sampling would be employed .
B) the company will randomly select precinct to increase the likelihood of the sample size representing the entire population very well
Can someone help me with this I’m sorry I really just don’t know
Answer:
15
Step-by-step explanation:
Because the two triangles are similar:
[tex]\dfrac{LN}{30}=\dfrac{6}{30-18} \\\\\\\dfrac{LN}{30}=\dfrac{6}{12} \\\\\\LN=30\cdot \dfrac{1}{2}=15[/tex]
Hope this helps!
Mr. Hobbs took out a loan of $12,000 for 4 years at a simple annual
interest rate of 7%. How much interest did he pay?
Answer:
Step-by-step explanation:
I= P*r*t
I = 12000* 7% *4
Total interest paid was $3360.
Answer: $3,360
Step-by-step explanation:
A hiker starts at an elevation of 65 feet and descends 30 feet to the base camp . What is the elevation of the base camps ?
Answer:
the elevation of base camp is 35 ft
Step-by-step explanation:
Starting at 65 feet elevation, and the descending 30 feet to reach base camp, that means that base camp is at: 65 ft - 30 ft = 35 ft elevation
Answer:
35 feet
Step-by-step explanation:
65 feet- 30 feet= 35 feet is the elevation of the base
8. Mr. Azu invested an amount at rate of 12% per annum and invested another amount. GHe
580.00 more than the first at 14%. IN Mr. Azu had total accumulated amount of
GH42.358.60. how much was his total investment?
Ans:
Answer:
GH¢.37480.36
Step-by-step explanation:
Let the amount invested at 12% per annum =GH¢.x
He invested 580.00 more than the first at 14%.
Therefore:
The amount invested at 14% =GH¢.(x+580)
For each investment option:
Amount Accrued =Principal + Simple Interest
Amount Accrued at 12%
[tex]=x+x*0.12\\=1.12x[/tex]
Amount Accrued at 14%
[tex]=(x+580)+0.14(x+580)\\=x+580+0.14x+81.2\\=1.14x+661.2[/tex]
Mr. Azu had total accumulated amount of GH42,358.60
Therefore:
1.12x+1.14x+661.2=42,358.60
2.26x=42,358.60-661.2
2.26x=41697.4
x=GH¢.18450.18
Therefore:
The amount invested at 12% per annum= GH¢.18450.18
The amount invested at 14% per annum= GH¢.18450.18+580
=GH¢.19030.18
Mr Azu's Total Investment = 18450.18 +19030.18
=GH¢.37480.36
For a particular disease, the probability of having the disease in a particular population is 0.04. If someone from the population has the disease, the probability that she/he tests positive of this disease is 0.95. If this person does not have the disease, the probability that she/he tests positive is 0.01. What is the probability that a randomly selected person from the population has a positive test result
Answer:
4.76% probability that a randomly selected person from the population has a positive test result
Step-by-step explanation:
We have these following probabilities:
4% probability of having the disease.
If a person has a disease, 95% probability of a positive test.
100-4 = 96% probability a person does not have the disease.
If a person does not have the disease, 1% probability of a positive test.
What is the probability that a randomly selected person from the population has a positive test result
95% of 4% and 1% of 96%. So
p = 0.95*0.04 + 0.01*0.96 = 0.0476
4.76% probability that a randomly selected person from the population has a positive test result
how do i know when a set of ordered pairs that represents a function?
Answer:
How do you figure out if a relation is a function? You could set up the relation as a table of ordered pairs. Then, test to see if each element in the domain is matched with exactly one element in the range. If so, you have a function!
Step-by-step explanation:
Select the linear function that describes the relationship between the domain and
range in the table below.
x fx)
-15
03
1 1
The linear function that describes the table is f(x) = -2x + 3
How to find linear function?The linear function of an equation can be found as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, using the table
b = 3
using (1, 1)
1 = m + 3
m = -2
Therefore, the function that represent the table is as follows:
f(x) = -2x + 3
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Answer: f(x) = -2x + 3
Step-by-step explanation:
if log3(x+1) - log3x=2, then x = ?
Answer:
x= 1/8
Step-by-step explanation:
A lot of 1000 components contains 350 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.
a. Find P(A).b. Find P(B|A) .c. Find P(A ∩ B).d. Find P(Ac ∩ B).e. Find P(B) .f. Find P(A|B).g. Are Aand B independent? Is it reasonable to treat A and B as though they were independent? Explain.
The probabilities are:
a. P(A) = 0.35
b. P(B|A) ≈ 0.349
c. P(A ∩ B) ≈ 0.122
d. P(A^c ∩ B) ≈ 0.228
e. P(B) = 0.35
f. P(A|B) = 0.349
g. A and B are independent.
Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).
We have,
Given:
Total number of components (n) = 1000
Number of defective components (d) = 350
a.
P(A) is the probability that the first component drawn is defective:
P(A) = d/n = 350/1000 = 0.35
b.
P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:
Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.
P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349
c.
P(A ∩ B) is the probability that both the first and second components drawn are defective:
P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122
d.
P([tex]A^c[/tex] ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:
[tex]P(A^c)[/tex] is the probability that the first component drawn is not defective:
[tex]P(A^c)[/tex] = 1 - P(A) = 1 - 0.35 = 0.65
Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.
P([tex]A^c[/tex] ∩ B) = P([tex]A^c[/tex]) * P(B) = 0.65 * (350/999) ≈ 0.228
e.
P(B) is the probability that the second component drawn is defective:
P(B) = Number of defective components / Total number of components
= 350/1000
= 0.35
f.
P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:
P(A|B) = P(A ∩ B) / P(B)
= (0.35 * 0.349) / 0.35
= 0.349
g.
To determine if A and B are independent, we need to compare
P(A) * P(B) with P(A ∩ B).
P(A) * P(B) = 0.35 * 0.35 = 0.1225
P(A ∩ B) = 0.122
Since P(A) * P(B) = P(A ∩ B), A and B are independent events.
It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.
The occurrence or non-occurrence of A does not impact the probability of B.
Thus,
The probabilities are:
a. P(A) = 0.35
b. P(B|A) ≈ 0.349
c. P(A ∩ B) ≈ 0.122
d. P(A^c ∩ B) ≈ 0.228
e. P(B) = 0.35
f. P(A|B) = 0.349
g. A and B are independent.
Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).
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A, B, and C are collinear points C is the midpoint of AB AC = 5x - 6 CB = 2x Find AB
Answer:
AB = 8
Step-by-step explanation:
Since C is the midpoint, ...
AC = CB
5x -6 = 2x
3x = 6 . . . . . . . add 6-2x
x = 2
Then the length of AB is ...
AB = 2(CB) = 2(2x) = 4(2)
AB = 8
An office building loses a third of its heat between sundown and midnight and an additional half of the original amount of heat between midnight and 4 AM. If five-eighths of the remaining heat is lost between 4 AM and 5 AM, what proportion of the total heat loss occurs between 5 AM and sunrise?
Answer:
[tex]\dfrac{1}{16}[/tex]
Step-by-step explanation:
Proportion of Heat Loss Between sundown and midnight[tex]=\dfrac{1}{3}[/tex]
Proportion of Heat Loss between midnight and 4 AM [tex]=\dfrac{1}{2}[/tex]
Proportion of Total Heat Already Lost [tex]=\dfrac{1}{3}+\dfrac{1}{2} =\dfrac{5}{6}[/tex]
Proportion of Remaining Heat [tex]=1-\dfrac{5}{6}=\dfrac{1}{6}[/tex]
Between 4 AM and 5 AM, five-eighths of the remaining heat is lost.
Proportion of Heat Loss between 4 AM and 5 AM= [tex]\dfrac{5}{8}$ X \dfrac{1}{6} = \dfrac{5}{48}[/tex]
Therefore, Proportion of Remaining Heat Left [tex]=\dfrac{1}{6}- \dfrac{5}{48}=\dfrac{1}{16}[/tex]
We therefore say that:
[tex]\dfrac{1}{16}$ of the total heat loss occurs between 5 AM and sunrise.[/tex]
Mitch opened a retirement account that has an annual yield of 4.2% compounding annually. He is planning on retiring in 13 years. How much must he deposit into that account each year so that he can have a total of $1,000,000 by the time he retires?
Answer:
P = 4878
Step-by-step explanation:
So we'll use the formula
A = p(1+r/n)^ (nt)
A = 1000000
P is the unknown
R = 4.2
N = 13
T = 13
1000000= p ( 1+ 0.42/13)^ 169
1000000 = p (1.032)^169
1000000= p 205
P = 4878