Problem 5: There is a 65% chance of rain in 3 days, considering the given probabilities.
Problem 6: The invariant distribution for the probability of rain (P(R)) is 7/9 or approximately 0.778, and the invariant distribution for the probability of no rain (P(NR)) is 2/9 or approximately 0.222.
To approach this problem, we can break it down into smaller steps:
Since the chance of rain today is 50-50, the probability of no rain today is also 50-50 or 0.5.
We know that the probability of no rain in 3 days, given no rain today, is represented by 'a.' Therefore, the probability of no rain in 3 days is 0.7.
Using the principle of complements, we can find the probability of rain in 3 days, given no rain today, by subtracting the probability of no rain from 1. Therefore, the probability of rain in 3 days, given no rain today, is 1 - 0.7 = 0.3.
To calculate the final probability of rain in 3 days, we need to consider two cases: rain today and no rain today. We multiply the probability of rain today (0.5) by the probability of rain in 3 days, given rain today (1), and add it to the product of the probability of no rain today (0.5) and the probability of rain in 3 days, given no rain today (0.3).
Hence, the final probability of rain in 3 days is (0.5 * 1) + (0.5 * 0.3) = 0.65.
To find the invariant distribution, we can set up a system of equations. Let P(R) represent the probability of rain and P(NR) represent the probability of no rain. Since the probabilities should remain constant over time, we have the following equations:
P(R) = 0.5 * P(R) + 0.3 * P(NR)
P(NR) = 0.5 * P(R) + 0.7 * P(NR)
Simplifying these equations, we get:
0.5 * P(R) - 0.3 * P(NR) = 0
-0.5 * P(R) + 0.3 * P(NR) = 0
To solve this system, we can express it in matrix form as:
[0.5 -0.3] [P(R)] = [0]
Apologies for the incomplete response. Let's continue solving the system of equations for Problem 6.
We have the matrix equation:
[0.5 -0.3] [P(R)] = [0]
[-0.5 0.7] [P(NR)] = [0]
To find the invariant distribution, we need to solve this system of equations. We can rewrite the system as:
0.5P(R) - 0.3P(NR) = 0
-0.5P(R) + 0.7P(NR) = 0
To eliminate the coefficients, we can multiply the first equation by 10 and the second equation by 14:
5P(R) - 3P(NR) = 0
-7P(R) + 10P(NR) = 0
Now, we can add the equations together:
5P(R) - 3P(NR) + (-7P(R)) + 10P(NR) = 0
Simplifying, we have:
-2P(R) + 7P(NR) = 0
This equation tells us that -2 times the probability of rain plus 7 times the probability of no rain is equal to 0.
We can rewrite this equation as:
7P(NR) = 2P(R)
Now, we know that the sum of probabilities must be equal to 1, so we have the equation:
P(R) + P(NR) = 1
Substituting the relationship we found between P(R) and P(NR), we have:
P(R) + 2P(R)/7 = 1
Multiplying through by 7, we get:
7P(R) + 2P(R) = 7
Combining like terms:
9P(R) = 7
Dividing by 9, we find:
P(R) = 7/9
Similarly, we can find P(NR) using the equation P(R) + P(NR) = 1:
7/9 + P(NR) = 1
Subtracting 7/9 from both sides:
P(NR) = 2/9
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The ratio of the measure of the sides of a triangle is 9:7:3. If the perimeter of the triangle is 266 inches, find the length of the shortest side. Help me please!!
Answer:
shortest side = 42 inches
Step-by-step explanation:
9x + 7x + 3x = 266
x = 14
3x = 42
One day 1 2 tried to make a pie. Unfortunately, she only had 3, and no sugar, so she decided to use 4 to sweeten it. The pie bubbled over in the oven and looked a mess. Not one to be discouraged, she decided to remedy the situation by covering the pie with 5 . When her 6 came over, and saw what she'd done, they 7 because 8 her pie ended up 9 but the 10 still needs to be cleaned
Answer:
even though there's no options or context,most likely answers are 1.little
2.Suzzy
3. flour
4.molases
5.foil
6 aunt
7. ate
8.
9.good
10.kitchen
2 multiplied by 4 times
a. 81
b. 8,000
c. 16
20 is the base, 3 is the exponent
a. 81
b. 8,000
c. 16
Answer:
2×2×2×2=16. hope u like it
Find the area of an equilateral triangle (regular 3-gon) with 6-inch sides. Round your answer to the nearest hundredth.

Determine the value of x.
A) 4.96
B) 2.90
C) 11.62
D) 0.73
The value of x in the triangle is 11.62
How to solve for x?The complete question is in the attached image
From the image, we have the following tangent function
tan(71) = x/4
Make x the subject
x = 4 * tan(71)
Evaluate the expression
x = 11.62
Hence, the value of x is 11.62
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Answer:
11.62
Step-by-step explanation:
took the test
Scale is 1cm = 8km. Hatboro and Smithville are 24cm apart on the map, how far apart are they?
a.87 km
b.192 km
c. 216 km
d. 33 km
Answer:
B.) 192 km
Step-by-step explanation:
Since 8km is for 1 centimeter, we multiply 8 by 24 to find how many kilometers there are for 24 centimeters. 8 * 24 is 192 so B.) is your answer.
If 1 large popcorn and 4 large drinks cost $21 how much does 1 large popcorn cost?
Answer:
6-7 dollars maybe?
Step-by-step explanation:
you didn't give a picture so Im just rounding
(sorry if I'm wrong)
What is the formula for the following arithmetic sequence?
-9, -2, 5, 12, ...
an = -9 + 7( n - 1)
an = -9 + (-7)( n - 1)
an = 7 + (-9)( n - 1)
an = 9 + (-7)( n - 1)
Step-by-step explanation:
an = -9 + 7(n-1)
because you start at -9 and go up by increments of 7
o MULTIPLE CHOICE QUESTION What should the graph look like for: x <3
if you have a graphing calculator (i use a website called desmos) put in x < 3. i attached a photo of what the graph should look like. the shaded area is where the solutions are. since the shaded area ends with a dotted line, points on that dotted line are not part of the solution.
i hope this helps! sorry i couldn't give a more descriptive explanation... it's pretty much all in the picture lol. have a lovely day! <3
Answer:
getting points since this is an old question tehe
Mind lending me a hand
Answer:
54
Step-by-step explanation:
55 + 74 + 78 + z + z + 45 = 360
252 + 2z = 360
2z = 108
z = 54
Answer: 288
Step-by-step explanation:
78+74+55=207
The degree of a pentagon is 540°
so 540-207=333
so z has to be 333 but the question says +45 and that would make 333 become 378 and we need to get exactly to 333 so the answer cant be 333 but a number that 45 can be added to ,to make 333 for example 54+45=99 so 54 isnt the answer,next is 144+45 which is 189 that doesnt equall 333 so that isnt the answer either lastly is 288+45 which is 333 Thats the answer ...
2 x 5 x 10 helppppppp
Answer: 100
Step-by-step explanation:2*5 =10 then 10*10 is 100
Answer:
100
Step-by-step explanation:
so, here is how to work this problem out
2*5 = 10
10*10 = 100
The figure below is parallelogram. Find the measure of th
variable.
Answer:
D
Step-by-step explanation:
u = 4 since 2u - 1 = 8 - 1 = 7
t = 3 since 5t + 1 = 15 + 1 = 16
and 7t - 5 = 21 - 5 = 16
Hope that helps!
Need answers quick pls!!!!!!
Answer:
A. False
B. True
C. False
D. False
E. True
Step-by-step explanation:
A. The diameter would be 6 inches.
B. Circumference = Diameter × 2
C. Area = Pi * Radius^2, NOT Pi^2.
D. Same as C.
E. Area = 3.14 × 1.5 × 1.5 = 7.065
Sally measured the height of a flower growing in her garden. The flower was 3.25 inches tall. Over the next week, the flower grew h inches and measured 4.125 inches tall. How many inches did the flower grow during the week? Round to the nearest hundredth.
Answer: The flower grew 0.88 inches during the week
Step-by-step explanation:
Height of flower in the previous week = 3.25 inches
Height of flower the next week = 4.125inches
height the flower added during the week = 4.125 inches - 3.25inches
=0.875 inches
Rounding to the nearest hundredths becomes 0.88 inches
A store has a 20% off sale on pants. With this discount, the price of one pair of paints is $15.20. What was the original price of the pants?
Jacob joined a gym for a year. His total cost for the year was $410, including the monthly
Answer:
What's your question ask the full question
What is the first step in solving this equation :
2x - 7 = 19
Options :
A - Add 7 to both sides
B - Subtract 19 from both sides
C - Subtract 7 from both sides
D - Divide both sides by 2
Please help its due in 20 minutes!!
the answer is:
2x = 19 + 7
2x= 26
x= 13
2x + 5xy + 9x + 3 what is the solution to this problem?
Answer:
5xy + 11x + 3
Step-by-step explanation:
We have the expression 2x + 5xy + 9x + 3 and are asked the solution.
This is different from most standard addition problems, we have an influx of variables, since we do. We follow the like term rules, which is that we can only add the numbers that have the same variable endings, in this case, only 2x and 9x are like terms, so we add them.
2x + 9x
11x
Therefore :
5xy + 11x + 3
Simplify 28/184 by reducing to lowest form
A) 1/46
B) 1/7
C) 14/92
D) 7/46
If you graph a system of equations and they are intersect, they have no solution. True or False someone help pleaseee !!
Answer:
False
Step-by-step explanation:
If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
I hope this is correct.
Anyone able to help?
Your teacher didn't pick the most simple way to do this problem, the steps your teacher gave is confusing. Using the same concept, I am going to do this my way then I will show a different method.
3x^2+24x+9=0
x^2+8x+3=0
x^2+8x+16+3=16
(x+4)^2=13
x+4=±[tex]\sqrt13[/tex]
x=-4±[tex]\sqrt13[/tex]
This is how you are suppose to solve it with completing the square and all the steps, to fill your teacher's blank you will have to go from my answer to how your teacher want you to write it.
*Now I am going to show you a way to solve this with the quadratic formula.
I am going to use the main formula because its more clear although the even formula is easier for this question.
3x^2+24x+9=0
x=(-24±[tex]\sqrt{24^2-4*3*9}[/tex])/2*3
x=(-24±[tex]\sqrt{576-108}[/tex])/6
x=(-24±[tex]\sqrt{468}[/tex])/6
since 468 is a multiple of 36
x=(-24±6[tex]\sqrt{13[/tex])/6
x=-4±[tex]\sqrt{13}[/tex]
This bottom way is really good if you can calculate quickly, with a lot of practice this way is much better for solving quadratic equations that cannot be factored.
find the sum of series of multiple of 5 from 5 to 100 inclusive
Answer:
let me think
Step-by-step explanation:
A circular bracelet has a radius of
5cm
Answer:
ye
Step-by-step explanation:
..
om need hjbhhbb points bbbvvghhhhjjnnnnnn
Answer:
la cantidas es 45 mas 8 ya ñara poder tener ka cagdlfenjelsflahevveyjew
Suppose you write a system of equations to find out which of two video stores is cheaper to join, depending on the number of videos you will rent. You solve the system and find that it has infinitely many solutions. What would that mean in terms of the problem? A. One video store is more expensive than the other no matter how many videos are rented. B. One video store is cheaper up to a certain number of videos rented, and then the other is cheaper. C. Both video stores cost the same no matter how many videos are rented. D. The problem cannot be solved.
Simplify the following
(c) 2(а - 3) - 5[a - 2(a - 4)
Step-by-step explanation:
Let's simplify step-by-step.
2(a−3)−5a−2(a−4)
Distribute:
=(2)(a)+(2)(−3)+−5a+(−2)(a)+(−2)(−4)
=2a+−6+−5a+−2a+8
Combine Like Terms:
=2a+−6+−5a+−2a+8
=(2a+−5a+−2a)+(−6+8)
=−5a+2
If a 24oz bottle of water costs $2.35. What is the cost per ounce? Round to the nearest penny.
Answer:
10¢
Step-by-step explanation:
To find how much an ounce cost, dive 2.35 by 24.
[tex]\frac{2.35}{24} = 0.097\\[/tex]
Multiply by 100, and thus you get 9.79, or, to the nearest penny, 10 cents.
I need help on this question
9 (x - 2) = 7x + 5
Does x have a value hurry only 10 minutes left!!
Answer:
x = 11.5
Step-by-step explanation:
9 (x - 2) = 7x + 5
9x - 18 = 7x + 5
+18 +18
9x = 7x + 23
-7x - 7x
2x = 23
--- ---
2 2
x = 11.5
a^2 + b^2 + 2bc - 2ca - 2ab
Find the Slope of the line that passes through (5, -10) and (5, -4)
A. - 14/10
B. 10/14
C. 0
D. Undefined