Answers
x is approximately equal to 1.893 when solving the equation [tex]3^{(x+1)} = 8^x[/tex].
To solve for x in the equation [tex]3^{(x+1)} = 8^x[/tex], we can rewrite 8 as [tex]2^3[/tex] since 8 is equal to 2 raised to the power of 3. The equation becomes:
[tex]3^{(x+1)} = (2^3)^x[/tex]
Now, we can simplify further:
[tex]3^{(x+1)} = 2^{(3x)[/tex]
Taking the logarithm of both sides can help us solve for x. Let's take the natural logarithm (ln) of both sides:
[tex]ln(3^{(x+1)}) = ln(2^{(3x)})[/tex]
Using the logarithmic property [tex]ln(a^b) = b \times ln(a)[/tex], we have:
(x+1) × ln(3) = 3x × ln(2)
Expanding further:
x × ln(3) + ln(3) = 3x × ln(2)
Next, we isolate the terms with x on one side and the constant terms on the other side:
x × ln(3) - 3x × ln(2) = -ln(3)
Factoring out x:
x × (ln(3) - 3 × ln(2)) = -ln(3)
Now, we can solve for x by dividing both sides of the equation by (ln(3) - 3 × ln(2)):
x = -ln(3) / (ln(3) - 3 × ln(2))
Using a calculator to evaluate the expression, we find:
x ≈ 1.893
Therefore, x is approximately equal to 1.893 when solving the equation [tex]3^{(x+1)} = 8^x.[/tex]
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Related Questions
On the main floor of the Kodak hall at Eastman theater the number of seats per row increases at a constant rate Steven counts 31 seats in row three and 37 seats in row six how many seats are there in route 20
Answers
Answer:
67
Step-by-step explanation:
no
Which point is a reflection of (12, −8) across the y-axis on a coordinate plane? A (8, 12) B (−8, 12) C (−12, −8) D (12, 8)
Answers
Answer:
option A
Step-by-step explanation:
thats the answer!!!
Matt bought 7 shirts for a total of $38. Tee shirts cost $5 and long sleeve shirts cost $6. How many of each type of shirt did he buy? HELP PLZ 100 POINTS
Answers
Answer:
tee shirt:4
sleeve shirt:3
Step-by-step explanation:
we are given two conditions
Matt bought 7 shirts for a total of $38Tee shirts cost 5 dollars and long sleeve shirts cost 6 dollarswe want to figure out how many each type of shirt he bought
let tee and sleeve shirts be t and s respectively
according to the first condition
[tex] \displaystyle t + s = 7[/tex]
according to the second condition
[tex] \displaystyle5t + 6s = 38[/tex]
therefore
our system of linear equation is
[tex] \displaystyle\begin{cases}t + s = 7 \\ 5t + 6s = 38 \end{cases}[/tex]
so
now we need our algebra skills to figure out t and s
to do so we can use substitution method
cancel s from both sides of the first equation:
[tex] \displaystyle t = 7 - s \: \cdots \: i[/tex]
now substitute the value of i equation to the second equation:
[tex] \displaystyle 5(7 - s) + 6s = 38[/tex]
distribute:
[tex] \displaystyle 35 - 5s+ 6s = 38[/tex]
collect like terms:
[tex] \displaystyle s + 35 = 38[/tex]
cancel 35 to both sides:
[tex] \displaystyle \therefore s = 3[/tex]
now substitute the value of s to the i equation:
[tex] \displaystyle t = 7 - 3 \\ \therefore \: t = 4[/tex]
hence,
he bought tee shirt 4 and sleeve shirt 3
Kathy bought a total of 60 cupcakes. Supreme cupcakes cost $12 each and regular cupcakes cost $3 each. She spent a total of $90. Which system of equations will determine the number of supreme (s) and regular (r) cupcakes that Kathy purchased?
Answers
Answer:
s + r = 60 and 12s + 3r = 90
Step-by-step explanation:
I just took the quiz and it said this is correct
ANSWER NO LINKS!!!! OKAY
Answers
Answer:
50
Step-by-step explanation:
180-(65+65)
Answer:
<C = 50
Step-by-step explanation:
<c = x
x + 65 + 65 = 180
x + 130 = 180
x = 50
HELP ASAP!!
Rewrite the function by completing the square
f(x) = x^2 - 6x - 60
f(x) = (x+ ___)^2 + ___
Answers
Answer:
-3 for the first box and -69 for the second one.
Step-by-step explanation:
Select all the TRUE sentences!!!
Answers
Answer:
The last two.
Step-by-step explanation:
Answer:
A and C
Step-by-step explanation:
Use inverse matrix to solve the following systems of equations: - 3', 2X, - 4X2 = -3 3X1 +5X2 = 1 9.) 3X1 - 2X2-4 = 0 -4X1 + 3X2 + 5 = 0
Answers
Using the inverse matrix, the solution to the system of equations is X₁ = -7/25 and X₂ = -2/25.
To solve the system of equations using the inverse matrix, we can represent the equations in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
The system of equations can be written as:
Equation 1: -3X₁ + 2X₂ = -3
Equation 2: 3X₁ + 5X₂ = 1
Equation 3: 3X₁ - 2X₂ = 4
Equation 4: -4X₁ + 3X₂ = -5
Rewriting the equations in matrix form, we have:
[tex]\left[\begin{array}{ccc}-3&2\\3 &5\\3 &-2\\-4 &3\end{array}\right] \left[\begin{array}{ccc}X1\\X2\end{array}\right]=\left[\begin{array}{ccc}-3\\1\\4\\-5\end{array}\right][/tex]
To find the solution, we need to calculate the inverse of the coefficient matrix A. Let's call it A^(-1).
[tex]A^{-1}=\left[\begin{array}{ccc}\frac{-11}{25}&\frac{2}{25}\\\frac{3}{25}&\frac{3}{25}\\\end{array}\right][/tex]
Now, we can solve for X by multiplying A^(-1) with B:
[tex]\left[\begin{array}{ccc}X1\\X2\end{array}\right]=\left[\begin{array}{ccc}\frac{-11}{25}&\frac{2}{25}\\\frac{3}{25}&\frac{3}{25}\\\end{array}\right]\left[\begin{array}{ccc}-3\\1\\4\\-5\end{array}\right][/tex]
Performing the matrix multiplication and Simplifying the results, we have:
X₁ = -7/25
X₂ = -2/25
Therefore, the solution to the system of equations is X₁ = -7/25 and X₂ = -2/25.
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4 cards are drawn from a deck of shuffled cards without
replacement.
Find the probability that:
a) All are kings
b) All are red cards
Answers
a) The probability of drawing all kings from a shuffled deck of cards without replacement is approximately 0.0000014, or 1.4 in 1 million.
b) The probability of drawing all red cards from a shuffled deck without replacement is approximately 0.000000103, or 1.03 in 10 million.
a) Probability of drawing all kings:
To calculate the probability of drawing all kings, we need to determine the total number of possible outcomes and the number of favorable outcomes. Let's break it down step by step:
Step 1: Total number of possible outcomes
In a standard deck of 52 playing cards, there are four kings. When we draw one card, there are 52 cards to choose from. For the second draw, only 51 cards remain, and so on. Therefore, the total number of possible outcomes for drawing four cards without replacement is:
52 × 51 × 50 × 49 = 649,740
Step 2: Number of favorable outcomes
Since we want all four cards to be kings, there are only four kings in the deck. When we draw the first card, there is a 4/52 chance of it being a king. For the second card, the probability reduces to 3/51 since there are three kings remaining out of 51 cards. Similarly, for the third and fourth cards, the probabilities become 2/50 and 1/49, respectively. Therefore, the number of favorable outcomes is:
(4/52) × (3/51) × (2/50) × (1/49) = 1/270,725
Step 3: Calculating the probability
Finally, we can calculate the probability of drawing all kings by dividing the number of favorable outcomes by the total number of possible outcomes:
P(all kings) = (1/270,725) / (649,740) ≈ 0.0000014
b) Probability of drawing all red cards:
Similarly, let's calculate the probability of drawing all red cards from the deck. We follow the same steps:
Step 1: Total number of possible outcomes
When we draw the first card, there are 26 red cards in a deck of 52. For the second draw, there are 25 red cards remaining out of 51, and so on. Hence, the total number of possible outcomes for drawing four cards without replacement is:
26 × 25 × 24 × 23 = 358,800
Step 2: Number of favorable outcomes
Since we want all four cards to be red, there are 26 red cards in the deck. The probability of drawing a red card for the first draw is 26/52. For the second draw, the probability becomes 25/51, for the third draw it is 24/50, and for the fourth draw, it is 23/49. Thus, the number of favorable outcomes is:
(26/52) × (25/51) × (24/50) × (23/49) ≈ 0.037
Step 3: Calculating the probability
The probability of drawing all red cards is the ratio of the number of favorable outcomes to the total number of possible outcomes:
P(all red cards) = (0.037) / (358,800) ≈ 0.000000103
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Which is NOT an equation?
a
x + 14 = 32
b
3 + x
c
10 – 2x = 10 + 5x
d
12 = 0.5x – 3
Answers
Answer:
B because it does not contain an = sign
S5=7+7x^(5)+7x5^(2)+7x5^(3)+7x5^(4)
Answers
Answer:7
+
7
(
5
)
+
7
5
(
2
)
+
7
5
(
3
)
+
7
5
(
4
)
Step-by-step explanation:
Answer: 5473+7x^5
Step-by-step explanation:
Try Photo Math! Gives step by step explanations!
Hope this helps!!
two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 6t, 1 30t, 1 126t . find the points at which their paths intersect. (if an answer does not exist, enter dne.)
Answers
Two particles are traveling along space curves defined by the equations r₁(t) = (t, t², t³) and r₂(t) = (1/6t, 1/30t, 1/126t). We need to find the points at which their paths intersect.
To find the points of intersection, we need to solve the system of equations formed by equating the components of the two space curves.
Comparing the x-components, we have:
t = 1/(6t) => t² = 1/6 => t = ±√(1/6).
Comparing the y-components, we have:
t² = 1/(30t) => t³ = 1/30 => t = ±∛(1/30).
Comparing the z-components, we have:
t³ = 1/(126t) => t⁴ = 1/126 => t = ±∜(1/126).
Combining all the solutions, we have four possible values for t: √(1/6), -√(1/6), ∛(1/30), and -∛(1/30). However, we need to check if these values are valid for all components of the curves.
By substituting these values of t into the equations, we find that only the value t = √(1/6) yields valid points of intersection: (√(1/6), 1/6, 1/√6) and (-√(1/6), 1/6, -1/√6).
Therefore, the points at which the paths of the particles intersect are (√(1/6), 1/6, 1/√6) and (-√(1/6), 1/6, -1/√6).
Please note that the other values of t do not yield valid points of intersection, so they are not considered as solutions in this case.
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A square dance floor has a perimeter of 120 yards.
What is the length of a diagonal of the dance floor?
O 38.3 yd
O 30 yd
O 60 yd
O 42.4 yd
Answers
You intend to conduct a goodness-of-fit test for a multinomial distribution with 5 categories. You collect data from 55 subjects. What are the degrees of freedom for the xa distribution for this test?
Answers
For the goodness-of-fit test with data collected from 55 subjects, the degrees of freedom for the chi-square distribution will be 4.
In a goodness-of-fit test, the degrees of freedom for the chi-square distribution determine the critical values and the interpretation of the test statistic. For a multinomial distribution with k categories, the degrees of freedom are calculated as (k - 1).
In this specific case, we have a multinomial distribution with 5 categories. Therefore, the degrees of freedom for the chi-square distribution will be (5 - 1) = 4.
Having 4 degrees of freedom means that the chi-square test statistic will be evaluated against the chi-square distribution with 4 degrees of freedom to determine the p-value and assess the significance of the test. The critical values at the chosen significance level will also depend on these degrees of freedom.
In summary, when conducting a goodness-of-fit test for a multinomial distribution with 5 categories and collecting data from 55 subjects, the chi-square test will have 4 degrees of freedom. These degrees of freedom play a crucial role in determining the validity and interpretation of the test results.
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Follow the process of completing the square to solve x2 - 10x + 8 = 0. What is the value of the constant that will be isolated on the right side of the equation in step 3? -8 -12 -32
Answers
Answer:
25
Step-by-step explanation:
Given the expression x^2 - 10x + 8 = 0.
According to completing the square method
Subtract 8 from both sides
x^2 - 10x + 8 - 8 = 0 - 8
x^2 - 10x = -8
Complete the square
Add the square of half of coefficient of x to both sides
Coefficient of x = -10
Half of Coefficient of x = -10/2
Half of Coefficient of x = -5
Square of Half of Coefficient of x = (-5)^2
Square of Half of Coefficient of x = 25
Add (-5)^2 to both sides
x^2 - 10x + (-5)^2 = -8 + (-5)^2
(x-5)^2 = -8 + 25
(x-5)^2 = 17
Hence the required constant that was added is 25
Tad and his buddies drove to the orange bowl to see their favorite football team win the national championship because of heavy traffic they only avsraged 50 mph however on the return trip they averaged 75 mph if the total round trip took 12 hours how long did it take tad and his buddies to drive to the orange bowl
Answers
Answer:
7.2
Step-by-step explanation:
Answer:
Step-by-step explanation:
Distance "D" = rate × time
or d = r × t.
Tad and his buddies drove to the orange bowl(while going) -50mph
Tad and his buddies while returning from a trip -75mph
Total round trip = 12 hours
Distance while going = 50 x t
Distance while returning = 75 (12 - t)
50t = 75(12 -t)
50t = 900 -75t
50t + 75t = 900
125t = 900
t = 900/125
t= 7.2
The total number of hours it takes Tad and his buddies to drive to the orange bowl is 7.2 hours.
Find the value of the variables in the simplest form
Answers
Answer:
y = 2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
y² = ([tex]\sqrt{2}[/tex] )² + ([tex]\sqrt{2}[/tex] )² = 2 + 2 = 4 ( take the square root of both sides )
y = [tex]\sqrt{4}[/tex] = 2
Peterkin park has a square fountain with a walkway aroind it. The fountain measures 12 feet on each side. The walkway is 3 1/2 feet wide.Find the area of the walkway
Answers
Answer: 829.44 ft²
Step-by-step explanation:
Correction - The walkway is 31.2 feet wide.
To solve this, first find the area of the fountain:
Area of a square = Length * Width
= 12 * 12
= 144 ft²
The find the area of the walkway including the fountain:
= 31.2 * 31.2
= 973.44 ft²
To find the area of the walkway alone, subtract the area of the square from the area of the rectangle:
= 973.44 - 144
= 829.44 ft²
Can you please help me with this question I keep getting the wrong answer
Answers
Answer:
14
Step-by-step explanation:
BRAINLIEST AND 50 POINTS UP FOR GRABS: PLEASE LEAVE DETAILED ANSWERS
Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(3, −6), Q(0, 9), and R(−3, 0). Triangle P'Q'R' has vertices P'(1, −2), Q'(0, 3), and R'(−1, 0).
Plot triangles PQR and P'Q'R' on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R'? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P''Q''R'' congruent? Explain your answer. (2 points)
Answers
Answer:
Triangle P' Q' R' is half the size of the original triangle.
-The scale factor is probably 1/3.
Part B: P'(1, −2), Q'(0, 3), and R'(−1, 0).
Part C: No, the triangles are not congruent. If the second triangle didn't have a dilation, and instead have a reflection of the first triangle, then it would be congruent.
Step-by-step explanation:
:)
what is the equation of a line that is parallel to the line 2x 5y = 10 and passes through the point (–5, 1)? check all that apply.
A. y = −x − 1
B. 2x 5y = −5
C. y = −x − 3
D. 2x 5y = −15 y
E. − 1= −(x 5)
Answers
The equation of a line that is parallel to the line 2x - 5y = 10 and passes through the point (-5, 1) is B. 2x - 5y = -5.
To find the equation of a line that is parallel to the line 2x - 5y = 10, we need to determine the slope of the given line first. The equation is in the form of Ax + By = C, where A = 2, B = -5, and C = 10.
To find the slope, we can rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope.
2x - 5y = 10
-5y = -2x + 10
y = (2/5)x - 2
From this equation, we can see that the slope of the given line is 2/5.
A line that is parallel to this line will have the same slope. Therefore, the equation of the parallel line can be determined using the point-slope form (y - y1 = m(x - x1)), where (x1, y1) represents the coordinates of the given point (-5, 1).
Using the slope of 2/5 and the point (-5, 1), we can now check the options to see which ones satisfy the conditions:
A. y = -x - 1: This equation has a slope of -1, not 2/5. It is not parallel to the given line.
B. 2x - 5y = -5: This equation has the same slope of 2/5 and passes through the point (-5, 1). It satisfies the conditions and is parallel to the given line.
C. y = -x - 3: This equation has a slope of -1, not 2/5. It is not parallel to the given line.
D. 2x - 5y = -15y: This equation has a slope of 2/20, which simplifies to 1/10. It is not parallel to the given line.
E. -1 = -(x - 5): This equation does not represent a line. It is not a valid option.
Therefore, the equation of a line that is parallel to the line 2x - 5y = 10 and passes through the point (-5, 1) is B. 2x - 5y = -5.
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Laura is the fund-raising manager for a Local charity. She is Ordering caps for an upcoming charity walk. the company that makes the caps charges six dollars per cap plus a $25 shipping fee Laura has a budget of $1000 what is the greatest number of cats so she can buy
Answers
Answer:
162 caps.
Step-by-step explanation:
Let x be the number of caps.
We have been given that cost of one cap is $6, so cost of x caps will be equal to 6x.
We are also told that the company charges an amount of $25 for shipping, so total cost of buying x caps will be equal to the cost of x caps plus shipping charges ().
Since Laura has a budget of $1,000, so cost of x caps will be less than or equal to 1,000. We can represent this information in an equation as:
Now let us solve for x.
Let us divide both sides of our inequality by 6.
Sydney is building a doghouse. The house will be 3 and one-half feet tall. How
many inches tall will the house be?
Answers
Answer:
42 inches
Step-by-step explanation:
1 FT=12 inches
One half FT=6 inches
12×3=36
36+6=42
Answer:
42 inches
Step-by-step explanation:
The question is basically asking you to convert 3 1/2 ft into inches. Since there are 12 inches in a feet you have to multiply 3 1/2 by 12. It easier to do it when you turn 3 1/2 into a decimal, which would be 3.5. So then, you multiply 3.5 by 12, to get 42 inches.
12 inches = 1 feet
3 1/2 = 3.5
3.5 x 12 = 42
The house will be 42 inches tall.
find the slope of the two points: 4,-3 and 8,-3
Answers
Answer:
0 slope
Step-by-step explanation:
flat horizantal line
no increase in y-value
The table shows the transactions for one week for Tasha and Jamal Who was the greater account balance at the end of the week How Much greater?
______ has the greater balance at the end of the week. This balance is $_______ greater than the other balance
Answers
Answer:
Tasha has the greater balance at the end of the week.This balance is $381
The account balance is the remaining amount after the deduction of withdrawals from the deposits.
Tasha has the greater balance at the end of the week. This balance is $1 greater than the other balance.
What is account balance?It is the remaining amount after the deduction of withdrawals from the deposits.
We have,
Tasha:
Initial deposits = $250
Withdrawals = $20
Deposits = $65
Debit card purchases = $46
Balance = $250 - $20 + $65 - $46 = $249
Jamal:
Initial deposits = $200
Withdrawals = $60
Deposits = $135
Debit card purchases = $27
Balance = $200 - $60 + $135 - $27 = $248
We see that Tasha has a greater balance than Jamal and Tasha's balance is greater than Jamal's by $1.
Thus,
Tasha has the greater balance at the end of the week. This balance is $1 greater than the other balance.
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What will the answer be?
Answers
Answer:
hi!
Step-by-step explanation:
what percent of 272 is 34?
Answers
Problem 6. Miss Ang buys a dozen of eggs (12 eggs in an egg tray) from HS Farm every day, starting at Day 1. For each egg produced by HS Farm, there is a 0.001 chance that it is spoiled.
(a) Find the probability of that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg. Write your answer (applying to (b) and (c) as well) up to 3 decimal point.
(b) Let N be the first day (counted from Day 1) that Miss Ang bought a tray of eggs containing at least one spoiled. Find the expected value of N.
(c) Suppose Day 1 is Sunday. Compute the probability that Day N is also Sunday.
Answers
a) The probability that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg=0.016
b) The expected value of N=86.6
c) The probability that Day N is also Sunday=1/7.
Explanation:
a)
For 1 day, 1 tray must contain no spoiled eggs: 0.999^12,
1 tray must have at least 1 spoiled egg: 1 - 0.999^12,
and the probability that Miss Ang has 2 trays, each containing at least 1 spoiled egg in one day:
(1 - 0.999^12) * (1 - (0.999^12 + 11 * 0.001 * 0.999^11)) = 0.00245
For 7 days, the probability that Miss Ang has at most 2 trays, each containing at least 1 spoiled egg:
= 0.00245 * C(7,0) * 1^0 * (1 - 1)^7 + 0.00245 * C(7,1) * 1^1 * (1 - 1)^6 + 0.00245 * C(7,2) * 1^2 * (1 - 1)^5
= 0.01622 ≈ 0.016
b)
Let X be the number of trays that Miss Ang has to buy to get the first tray containing at least 1 spoiled egg. Then X follows a geometric distribution with parameter
p = 1 - 0.999^12 and
E(X) = 1/p = 1/0.011543 ≈ 86.6 (rounded to the nearest 0.1).
c)
Since Miss Ang buys one tray of eggs a day, the probability that Day N is Sunday is 1/7. Therefore, the probability that Day N is Sunday given that it is the first day that Miss Ang bought a tray of eggs containing at least one spoiled is also 1/7.
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a) The probability of that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg:
P(X ≤ 2) = 0.2966763801
b) The expected value of N = 83.8059327318 days
c) The probability that Day N is also Sunday= 0.1406909760
(a)
For each egg produced by HS Farm, there is a 0.001 chance that it is spoiled. Therefore, the probability that an egg is not spoiled is
1-0.001 = 0.999.
Since Miss Ang buys one dozen eggs every day, the probability that all 12 eggs in a tray are not spoiled is
(0.999)¹² = 0.98806738389.
Therefore, the probability that there is at least one spoiled egg in a tray is
1 - 0.98806738389 = 0.01193261611.
The probability that Miss Ang buys at most 2 trays of eggs with each having at least one spoiled egg in one week (7 days) can be found using the Poisson distribution with a mean of λ = 1.19574793916.
Therefore,
P(X ≤ 2) = 0.2966763801
(b)
Let N be the first day that Miss Ang bought a tray of eggs containing at least one spoiled.
Since Miss Ang buys one tray of eggs every day, the probability that N = n is the probability that the tray she buys on day n has at least one spoiled egg, and all the trays she buys on days 1, 2, ..., n - 1 have no spoiled eggs.
This probability is given by
[tex]P(N = n) = (0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]
The expected value of N can then be found by taking the sum of nP(N = n) over all possible values of n.
This gives
[tex]E(N) = Σn=1∞nP(N = n)[/tex]
[tex]= Σn=1∞(0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]
n= 83.8059327318 days.
(c)
Suppose Day 1 is Sunday. Since Miss Ang buys one tray of eggs every day, Day N is also Sunday if and only if N ≡ 1 (mod 7).
Using the same method as in part (b), we get
[tex]P(N ≡ 1 (mod 7)) = Σk=0∞P(N = 7k + 1)[/tex]
=[tex]Σk=0∞(0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]
= 0.1406909760
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If the probability of surviving the zombie apocalypse for 1 year is 20% a. what are the odds of surviving (explain)? (1 pt) b. What are the odds of not surviving (explain)? (1 pt) c. If I bet $25 on you to survive, and you do, how much would you pay based on the odds? (1 pt)
Answers
a) The odds of surviving is 1/4
b) The odds of not surviving is 4.
c) You would receive a payout of $6.25 if you bet $25 on surviving and you successfully survive the zombie apocalypse.
a) The odds of surviving the zombie apocalypse can be calculated by taking the probability of survival (20%) and dividing it by the probability of not surviving
100% - 20% = 80%
So the odds of surviving would be,
20%/80% = 1/4
This means that for every one chance of surviving, there are four chances of not surviving.
b) The odds of not surviving the zombie apocalypse can be calculated by taking the probability of not surviving (80%) and dividing it by the probability of survival (20%).
So the odds of not surviving would be
80%/20% = 4/1
This means that for every four chances of not surviving, there is one chance of surviving.
c) If you bet $25 on surviving and you do survive, based on the odds of 1/4, you would win the bet. The payout can be calculated by multiplying the bet amount by the odds of surviving.
So the payout would be
$25 * 1/4 = $6.25
Therefore, based on the odds, you would receive a payout of $6.25 if you bet $25 on surviving and you successfully survive the zombie apocalypse.
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