In this team activity, we were given a weather forecasting problem in which we had to determine the stochastic matrix and calculate the probabilities of different weather conditions for a given day.
To solve the problem, we first needed to determine the stochastic matrix M, which is a matrix that represents the probabilities of transitioning from one state to another. In this case, the three possible states are good, indifferent, and bad weather. Using the given probabilities, we constructed the following stochastic matrix:
M = [[0.7, 0.2, 0.1], [0.6, 0.3, 0.1], [0.4, 0.4, 0.2]]
For the second question, we used the stochastic matrix to calculate the probabilities of bad weather tomorrow, given that there is a 20% chance of good weather and an 80% chance of indifferent weather today. We first calculated the probability vector for today as [0.2, 0.8, 0], and then multiplied it by the stochastic matrix to get the probability vector for tomorrow. The resulting probability vector was [0.14, 0.36, 0.5], so the chance of bad weather tomorrow is 50%.
For the third question, we used the stochastic matrix to calculate the probability of good weather on Wednesday, given that the predicted weather for Monday is 50% indifferent and 50% bad. We first calculated the probability vector for Monday as [0, 0.5, 0.5], and then multiplied it by the stochastic matrix twice to get the probability vector for Wednesday. The resulting probability vector was [0.46, 0.31, 0.23], so the chance of good weather on Wednesday is 46%.
For the final question, we needed to find the steady-state vector, which is a vector that represents the long-term probabilities of being in each state. We calculated the steady-state vector by solving the equation Mv = v, where v is the steady-state vector. The resulting steady-state vector was [0.5, 0.3, 0.2], so in the long run, the chance of bad weather on a given day is 20%.
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Anyone pls help on this
4 When a ball bounces, the heights of consecutive bounces form
a geometric sequence. The height of the first bounce is
121 centimeters and the height of the third bounce is
64 centimeters. To the nearest centimeter, what is the height of the
fifth bounce?
Answer:
34 cm
Step-by-step explanation:
The nth term of a geometric progression Tₙ = arⁿ⁻¹ where a = first term, and r = common ratio.
Given that our first term, T₁ = ar¹⁻¹ = a = 121 cm and our third term T₃ = ar³⁻¹ = ar² = 64 cm
Then, T₃/T₁ = ar²/a = r²
r² = T₃/T₁
r² = 64 cm/121 cm
r = √64/121
r = 8/11
So, the height of our fifth bounce T₅ = ar⁵⁻¹
= ar⁴
= 121 cm × (8/11)⁴
= 121 × 4096/14641
= 4096/121 cm
= 33.9 cm
≅ 34 cm to the nearest cm
Using a geometric sequence, it is found that the height of the fifth bounce is of 33.85 cm.
In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio r.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1r^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem:
The height of the first bounce is of 121 cm, hence [tex]a_1 = 121[/tex].The height of the third bounce is of 64 cm, hence [tex]a_3 = 64[/tex], and this is used to find r.[tex]a_n = a_1r^{n-1}[/tex]
[tex]64 = 121r^{2}[/tex]
[tex]r^2 = \sqrt{\frac{64}{121}}[/tex]
[tex]r = \frac{8}{11}[/tex]
Hence:
[tex]a_n = 121\left(\frac{8}{11}\right)^{n-1}[/tex]
The height of the fifth bounce is of [tex]a_5[/tex], hence:
[tex]a_5 = 121\left(\frac{8}{11}\right)^{4} = 33.85[/tex]
The height of the fifth bounce is of 33.85 cm.
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I NEED HELP NOW ITS 100 points!!!!!
You are going to paint 3 rooms in your house. Two of the rooms measure 12 ft. by 15 ft. and the third is 15 ft. by 20 ft. The ceilings are 9 ft. high. You are going to paint the 2 rooms the same size the same color. The third room will be a different color. You will paint the ceilings in all three rooms with ceiling white paint. This ceiling paint costs $39.99 per gallon and will cover 250 square ft.. The paint for the two rooms will be tan and costs $27.95 per gallon and covers 320 sq. ft. The paint for the third room will be waterfall blue and will cost $32.50 per gallon and covers 288 sq.ft. How much will it cost to paint these three rooms if the store has a 20% off your entire purchase and sales tax is 7.35%?? *
40 points
Answer:
im sorry i dont know
Step-by-step explanation:
Please find X ASAP. You’ll find it on the picture
Answer:
51°
Step-by-step explanation:
so lets all know that the sum of a trapezoid is 360°
so lets find x
360-83-115-111=51
so your answer is 51°
Hope this helped :)
You have $10 saved. Each week you receive $5 more. Fill in the table to show how much you will have each week. You keep filling out the table to see how much you will have at the end of 6 weeks.
Answer:
90
Step-by-step explanation:
You have 10 dollars saved and each week you recieve 5,multiply 10 x 5 and then multiple 15x6 and there you go
is a(t) = 1200(1 + .03)t a decay function?
Answer:
Step-by-step explanation:
No, it is an exponential growth function because 1.03>1. An exponential decay function would have a rate less than 1.
PLEASE ANSWERRRRRRRRRRRRRRRRRRRRRRRRR
Sara and 3 of her friends went to lunch one day. Each person paid for her own lunch, but they agreed to split the tip. If the tip amount was 15% of the total, and the 4 lunches totaled $60, what was the portion of each person’s tip amount?
Answer:
Step-by-step equation:
15% of 60 is nine.
Percentage is equivalent to the portion of a quantity present in the whole. The portion of each person’s tip amount shared by Sara and 3 of her friends is $2.65.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
To convert percentage into a fraction it is divided by 100.
Given that,
The amount of tip is 15% of the total amount A.
The total amount of 4 lunches = $60.
As per the question, the total amount can be written as,
15% of A = A - 60
=> 15 / 100 × A = A - 60
=> A - (3 / 20) × A = 60
=> A - (3 / 20) × A = 60
=> (17 / 20) × A = 60
=> A = (60 × 20) / 17
=> A = 70.58
Now, the total amount of tip is,
15% of 70.58
(15 / 100) × 70.58 = 10.58
The tip shared by each friend = 10.58 ÷ 4
= 2.65
Hence, the portion of each person’s tip amount is $2.65.
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A rectangle with length 3 1/2 ft and width 2 1/4 ft what is the area
Answer:
Step-by-step explanation:
Hope this helps
click link
Answer: 5 2/6
Step-by-step explanation:
can someone explain how to do this
Answer:
مرحبًا ، سأكون سعيدًا لمساعدتك في حبك في العمل ، وأريد المزيد من التفاصيل ، وسأبذل قصارى جهدي لإرضائك
Step-by-step explanation:
Answer:
I recommend using GeoGebra to graph the coordinates
Step-by-step explanation:
I use that whenever someone asks if certain coordinates make a shape
Here's the link:
http://contentstore.ple.platoweb.com/content/GeoGebra.v5.0/GeoGebra_Activity.html
find the distance of each the following lines from the origin.
(a),4x_3y=10
b,x_5y+2=0
c,3x+y_7=0
Answer:
Step-by-step explanation:
3x+y−7=0 and x+2y+9=0
write in the form y=mx+c
i.e.y=−3x+7,y=
2
−x
−
2
9
∴m
1
=−3 and m
2
∓−
2
1
tan(A−B)=
∣
∣
∣
∣
∣
1+tanAtanB
tanA−tanB
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
1+(−3)(−y
2
)
−3−(−y
2
)
∣
∣
∣
∣
∣
=
∣
∣
∣
∣
∣
5/2
−5/2
∣
∣
∣
∣
∣
=1
∴ Angle b/w then is tan
−1
(1)=45
∘
=
4
π
Problem situation:
Janelle is at the movie theater and has $20
to spend.
She spends $8 on a ticket and wants to buy some snacks. Each snack costs $4.99.
How many snacks, x, can Janelle buy?
Inequality that represents this situation:
20 > 8 + 4.99x
Drag each number to show if it is a solution to both the inequality and the problem
situation, to the inequality only, or if it is not a solution.
Answer:
Rewrite so x is on the left side of the inequality.
8 + 4.99x < 20
Move all terms not containing x to the right side of the inequality.
4.99x < 12
Divide each term by 4.99 and simplify.
x < 2.405
The result can be shown in multiple forms.
Inequality Form:
x < 2.405
Interval Notation:
( −∞ , 2.405 )
Step-by-step explanation:
Answer:
Both:
1
2
Inequality Only:
-4
3/4
2.3
Neither:
2.5
The equation y+6=3(x-9) is written in point-slope form. What is the equation written in slope-intercept form?
o y = 1/2x-3
Oy=}x+9
yafe- ར ་
y=3x+3
Please helppppp!!!!!!
Answer:
$7.44
Step-by-step explanation:
4.96/8= .62 per ounce
.62 x 12 = $7.44
Which set of numbers could represent the lengths of the sides of a right triangle?
12, 18, 22
8. 15. 17
10. 15.20
7.9.11
Answer:
8, 15, 17
Step-by-step explanation:
The 2nd option. You know this by using this math formula: a^2 + b^2 = c^2. That is the formula to find a right triangle. So if you square 8 and 15 you get 64 and 225, and if you add them together you get 289, which is 17^2. Hope this helps! :)
PLS HELPP I WILL GIVE BRAINLIEST
Help me with this please!!!
this question answer is 4.25
I will mark brain list to the person who got it correct
Answer:
-6
djdhhdhdxbxvsbsbvsshhsdh
-6 hehdbnfjenend
Step-by-step explanation:
hfea ehsusbshidbd
Plz plz, help I don't understand 24 points !!! Will mark brainiest for correct answers only quick!!!
The measure of angle 1 is (10x+8) and the measure of angle 3 is (12x-10)
What is the measure of angle 2 in degrees?
9
98
82
16
Answer:
The answer is C. 82 degrees!
Step-by-step explanation:
Hope this helped! Have a fantastic rest of ur day/ night! :)))
For part (a), determine whether the triangles are congruent by SSS or SAS. If not congruent, write “not congruent.” If congruent, write a congruency statement for part (b).
The congruency rules is as follows;
4)a) The triangles are congruent by SSS Congruency Postulate
b) Triangle PQR is congruent to Triangle PQS
5a) The triangles are not congruent
b) Triangle VWZ is not congruent to Triangle YXZ
6a) The triangles are congruent by SAS Congruency Postulate
b) ΔACB is congruent to ΔDBC by SAS Congruency Postulate
7) The triangles are not congruent
b) ΔKLJ is not congruent to ΔMNL
How to Identify Congruent Triangles?There are different congruency postulates or theorems as it pertains to congruent triangles and they are;
AAS theorem which denotes Angle-Angle-Side Theorem
HL theorem which denotes Hypotenuse-Leg Theorem
SSS Postulate which denotes Side-Side-Side Postulate
ASA postulate which denotes Angle-Side-Angle Postulate
SAS Postulate which denotes Side-Angle-Side Postulate
5) We can see that we are given two sides of one triangle that are congruent to two sides of another triangle. However, the third side is also congruent by reflexive property of congruency and as such we now have three sides congruent by SSS Congruency Postulate.
5) We can see that we are given two sides of one triangle that are congruent to two sides of another triangle. Now, the angle where the transverse lines intersect is not given but we can see that they are opposite angles by definition of opposite angles. Thus, the triangles are congruent by SSA Congruency Theorem because it has a non-included angle but SSA Congruency is not valid and so this is not congruent.
6) We can see that one side is given to be congruent. However, by reflexive property of congruence, we see that BC is congruent to itself and also the included right angle being congruent to each other. Thus, this is congruent by SAS Congruency postulate.
7) The triangles are not congruent because we are not given any third congruent side nor the angles and we can't use the given data to prove congruency.
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write : what’s the algebraic expression for the difference of 9 and x
Answer:
9-x
Step-by-step explanation:
ez dub
Answer:
9-x
Step-by-step explanation:
the difference of (tells you to subtract) 9 and x (9-x)
hope this helps have a blessed
Ellen Greenberg loves to make and fly kites. Ellen is planning to open a shop that
sells custom-made kites. She asks for your advice to help her set financial goals.
Ellen estimates that after expenses, she can make a $15 profit on each kite she
sells. If her annual income goal is $15,400, how many kites will she have to sell?
Answer:
She must sell 1026.66666667 kites
Step-by-step explanation:
15,400/15
The number of kites that Ellen needs to sell to complete her annual goal is 1027.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that Ellen can make a $15 profit on each kite she sells. Also, Ellen's annual income goal is to have $15,400. Therefore, the number of kites that Ellen needs to sell is,
Number of kites that Ellen will sell = Annual income goal/Profit on each kite
Number of kites that Ellen will sell = $15,400 / $15
= 1026.6667
Since Ellen can not sell half kites, therefore, she needs to sell 1027 kites to complete her annual income goal.
Hence, the number of kites that Ellen needs to sell to complete her annual goal is 1027.
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4(5.8 - 9x) + 8.2 + 22x
Answer:
157 - 70x
—————————
5
Step-by-step explanation:
Answer:
31.4 - 14x
Step-by-step explanation:
4(5.8 - 9x) = 23.2 - 36x
23.2 - 36x + 8.2 + 22x
23.2 + 8.2 - 36x + 22x
only add/subtract LIKE terms
31.4 - 14x
Hey, guys I need help :D
Answer:
D
Step-by-step explanation:
Dilating BC to B'C' by a factor of 1/2 makes each side of the triangle halved. Originally BC is 16, so when it's halved, it becomes 8
We know when triangle are similar and are changed only by a scale factor, the angle will not change. Angle A' = 28 degrees
i really need help wit this pleasee help and show work pleasee
Answer:
4000π cm^2
Step-by-step explanation:
first we change the 1.6m to cm:
1.6m = 160cm
Now we can use the formula:
V = πr^2h
where π is just π, r is the radius (not the diameter) and h is the height
V = π * 5^2 * 160 = 4000π cm
Answer:
Step-by-step explanation:
[tex]\text{They give you the equation for the volume.}\\ \\ V=\pi r^2h\\ \\ \text{You simply need to plug in the values given to you for r and h.}\\ \\ r=10/2=5cm,\ h=1.6m(100cm/m)=160cm\\ \\
V=\pi 5^2(160)\\ \\ V=160(25)\pi\\ \\ V=4000\pi cm^3\\ \\ V\approx 12566.37 cm^3[/tex]
Can somebody help me out ? Please
Answer:
52 sq mm
Step-by-step explanation:
you can break it into a long rectangle in the middle with dimensions of 2(6+8) or 2(14) = 28 sq mm
the triangle on the bottom has a base of (8-4) x height of 3, which gives 6 sq mm (you have to divide by 2)
the upper left rectangle is 6 x 3 = 18 sq mm
add: 28 + 6 + 18 = 52
How is a "series" different than a "sequence"?
Answer:
See below
Step-by-step explanation:
A series is the terms added together and a sequence is the list of terms. When you add the terms of a sequence, then you have formed a series.
Help please ASAP
Brainiest answer to whoever is correct
hey hons, i'd love some help here if you could take a look and see if you could help i'd be grateful! <33333
Step-by-step explanation:
A function is a rule that relates how one quantity depends on other quantities
Ginger the cat weighed 25lbs! The vet put Ginger on a diet and by the end of the month, Ginger weighed 20lbs. What percentage of her weight did Ginger loose? She lost of her weight.
Answer:
20%
Step-by-step explanation:
25 divided by 5 is 5 and in fractions 1/5 is 20 therefore 20% for every 5 pounds so if you lose 5 pounds you lost 20% of her weight.
Answer:
ana totta
Step-by-step explanation: