The probability that the frog will escape without being eaten by the snake is [tex]\frac{63}{146}[/tex]
What is Markov Process?
A Markov chain or Markov process is a stochastic model that depicts a series of potential occurrences where each event's likelihood is solely determined by the state it reached in the preceding event.
First, take notice that the frog has a probability of 1/2 of finally being eaten by the snake once it is on pad 5, and a probability of 1/2 of eventually emerging from the pond unharmed. Therefore, all that needs to be determined is the probability that the frog on pad 1 will make it to pad 5 without being eaten.
Consider the frog’s jumps in pairs. The frog on pad 1 will advance to pad 3 with probability [tex]\frac{9}{10} \frac{8}{10}[/tex][tex]=\frac{72}{100}[/tex] will be back at pad 1 with probability [tex]\frac{9}{10} \frac{2}{10}[/tex][tex]=\frac{18\\}{100}[/tex]
s
[tex]\frac{72}{100}[/tex] ÷ [tex](\frac{72}{100}+\frac{10}{100} )=\frac{36}{41}[/tex] and the probability that it ultimately makes it to pad 0 is [tex]\frac{10}{100}[/tex] ÷ [tex](\frac{72}{100}+\frac{10}{100} )=\frac{5}{41}[/tex].Similarly, in a pair of jumps the frog will advance from pad 3 to pad 5 with probability [tex]\frac{7}{10} \frac{6}{10} =\frac{42}{100}[/tex], will be back at pad 3 with probability [tex]\frac{7}{10} \frac{4}{10} +\frac{3}{10} \frac{8}{10} =\frac{52}{100}[/tex].
Because the frog will ultimately make it to pad 5 or pad 1 from pad 3, the probability that it ultimately makes it to pad 5 is [tex]\frac{42}{100}[/tex] ÷ [tex]( \frac{42}{100} +\frac{6}{100} )=\frac{7}{8}[/tex] and the probability that it ultimately makes it to pad 1 is [tex]\frac{6}{100}[/tex] ÷ [tex](\frac{42}{100} +\frac{6}{100} )=\frac{1}{8}[/tex]
The series of steps that must be made in pairs for the frog to get to pad 5 without being eaten is
1 → 3 → 5, 1 → 3 → 1 → 3 → 5, 1 → 3 → 1 → 3 → 1 → 3 → 5 and so on.
The sum of the respective probabilities of reaching pad 5 is then
[tex]\frac{36}{41} \frac{7}{8} +\frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{7}{8}+\frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{1}{8} \frac{36}{41} \frac{7}{8}+.....[/tex]
[tex]= \frac{63}{82} (1+\frac{9}{82} +(\frac{9}{82})^{2} +....)[/tex]
[tex]=\frac{63}{82}[/tex]÷[tex](1-\frac{9}{82} )[/tex]
[tex]= \frac{63}{73}[/tex]
Therefore the requested probability is [tex]\frac{1}{2}\frac{63}{73} = \frac{63}{146}[/tex]
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WILL GIVE 20 POINTS IF RIGHT PLEASE HELP
Given the points E(-4,k) and F(k,7) find the value of K so that the slope of EF is 2/3.
Answer:The answer is:
k
=
2
.
Given two point,
A
(
x
a
,
y
a
)
and
B
(
x
b
,
y
b
)
the slope of the line that passes from them is:
m
=
y
b
−
y
a
x
b
−
x
a
.
So:
−
2
=
6
−
2
k
−
4
⇒
−
2
(
k
−
4
)
=
4
⇒
−
2
k
+
8
=
4
⇒
−
2
k
=
−
4
⇒
k
=
2
.
Step-by-step explanation:The answer is:
k
=
2
.
Given two point,
A
(
x
a
,
y
a
)
and
B
(
x
b
,
y
b
)
the slope of the line that passes from them is:
m
=
y
b
−
y
a
x
b
−
x
a
.
So:
−
2
=
6
−
2
k
−
4
⇒
−
2
(
k
−
4
)
=
4
⇒
−
2
k
+
8
=
4
⇒
−
2
k
=
−
4
⇒
k
=
2
.
(5x + 5)°
95°
Fill in the blanks based on the diagram.
Step 1: 5x +
Step 2: 5x
Step 3: x =
In the expression 5x + 5 = 95, the value of x is 18
What is an angle ?
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
The given angle 5x + 5 is equal to 95
We need to calculate the value of x
5x + 5 = 95
5x = 95 - 5
5x = 90
x = 90/5
x = 18
Therefore, the expression 5x + 5 = 95 is solve and the value of x is 18
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The volume of the solid bounded above by the parabolic cylinder
z
=
1
−
y
2
, below by the plane
3
x
+
3
y
+
z
+
10
=
0
, and on the sides by the circular cylinder
x
2
+
y
2
−
x
=
0
. (A triple integral)
The volume of the solid bounded above by the parabolic cylinder is 191π/64.
Given:
the Parabolic cylinder z=1−y^2 and below the plane 3x+3y+z+10=0 and on the sides of circular cylinder x^2+y^2−x=0.
[tex]x^2+y^2-x=(x-\frac12)^2 +y^2-\frac14=0[/tex]
Recenter the circle with x−1/2=u and integrate the volume over the disk
u^2+y^2 = 1/4.
[tex]\int_{u^2+y^2 < \frac14} [(1-y^2)-( -2x-3y-10)][/tex]
[tex]=\int_{u^2+y^2 < \frac14} (2u+3y-y^2 +12)[/tex]
[tex]=\int_{u^2+y^2 < \frac14} (12-y^2)[/tex]
[tex]=\int_0^{2\pi}\int_0^{1/2} (12-r^2 \sin^2\theta)rdr d\theta =\frac{191\pi}{64}\\[/tex]
Therefore The volume of the solid bounded above by the parabolic cylinder is 191π/64.
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PLEASE HELP ME WILL GIVE BRAINLIEST!!!!!!
Solve this system of equations using the LINEAR COMBINATION method, then answer the questions below.
2x - y = - 4 6x + 5y = 4
• What did you get for the (x, y) solution to this system? (2.5 points)
• Explain what you did to create a pair of opposites so that you could combine the equations. (2.5 points)
Answer:( 3.5 , -2 )
Step-by-step explanation:
THE RIGHT ANSWER GETS 10 POINTS AND BRAINLIEST
An oil company fills 1 over 12 of a tank in 1 over 3 hour. At this rate, which expression can be used to determine how long it will take for the tank to fill completely? (1 point)
a
1 over 12 • 3 hours
b
1 over 3 • 12 hours
c
1 over 3 • 1 over 12 hour
d
3 • 12 hours
Answer:
B. 1 over 3 x 12 hours
Step-by-step explanation:
The oil company fills 1/12 of a tank in 1/3 an hour. So, you multiply 1/3 times 12, since 12 is a full tank. It'll take 4 hours to fill the tank at this rate.
1/12 tank: 1/3 hour
2/12 tank: 2/3 hour
3/12 tank: Full hour
3/12 is equivalent to 1/4, meaning 1/4 of the tank is filled after 1 hour. Thus, it'll take 4 hours.
Question Which of the following r-values represent the weakest linear correlation between independent (x) and dependent (y) variables? Select the correct answer below: -0.904 0 -0.312 O 0.558 0.870
The r - values that represents the weakest linear correlation is ;
-0.312 is the weakest negative correlation and 0.558 is the weakest positive correlation.
Given,
The r- values;-
- 0.904, -0.312, 0.558, 0.870
We have to find the r - values that represents the weakest linear correlation;
r- values represents correlation between two variables. The r- value lies from -1 to 1.
If r = -1 or close to -1, then it represents strong negative correlation.If -1 < r < 0 or close to -0.5, then it represents weak negative correlation.If r=0 or near to 0, then it represents no correlation.If 0 < r < 1 or close to 0.5, then it represents weak positive correlation.If r=1 or close to 1, then it represents strong positive correlation.So, here.
-0.904 is close to -1, so it represents strong negative correlation.
-0.312 is close to -0.5, so it represents weak negative correlation.
0.558 is close to 0.5, so it represents weak positive correlation
0.870 is close to 1, so it represents strong positive correlation.
Therefore,
The r - values that represents the weakest linear correlation is ;
-0.312 is the weakest negative correlation and 0.558 is the weakest positive correlation.
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Answer:
-0.312
Step-by-step explanation:
−0.312
The size of the correlation, r indicates the strength of the linear relationship between x and y. Values of r which are closer to −1 or to +1 indicate a stronger linear relationship between x and y.
describe the end behavior of each function
Answer:
f(x) = - x² + 2x - 2 :
x → - ∞
f(x) → - ∞
f(x) = x⁴ + 3x² + x - 3 :
x → ∞
f(x) → ∞
For the following right triangle, find the side length x.
24
10
x
The side length, x, of the right triangle will be 26 units.
According to the question,
We have the following information:
In a right triangle, two of the sides are 24 units and 10 units.
The complete question is that 24 units is the perpendicular and 10 units is the base of the given right triangle.
Let's denote hypotenuse with h, perpendicular with p and base with b.
We will find the hypotenuse of the triangle using the Pythagoras theorem:
[tex]h^{2} = b^{2} +p^{2}[/tex]
[tex]h^{2}= (24)^{2}+ (10)^{2}[/tex]
[tex]h^{2} = 476+100\\h^{2} = 576[/tex]
h = √576
h = 26 units
Hence, the side length, x, of the right triangle will be 26 units.
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The people at a party tried to form teams with the same number of people on each team, but when they tried to split up into teams of 2, 3, 5, or 7, exactly one person was left without a team. What is the smallest number of people (greater than $\color[rgb]{0.35,0.35,0.35}1$) who could have been at the party?
The smallest number of people when one could have been at the party is 211 people.
How to illustrate the information?This is a least common multiple question, also known as an LCM. We know this because all groups would have formed evenly if the one extra person had not arrived at the party. This means that there are 1 more people at the party than a number 2, 3, 5, or 7.
In this case, the number will be:
= (2 × 3 × 5 × 7) + 1
= 210 + 1
= 211
Applicable multiples of 7
(7 × 10) = 70 → 70 + 1 = 71 → 71/3 = 23 R2 → not possible
(7 × 20) = 140 → 140 + 1 = 141 → 141/3 = 47 → not possible
(7 × 30) = 210 → 210 +1 = 211 → 211/3 = 70 R1 → possible.
Therefore, the number of people is 211.
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[tex]A(50)=266(1/2)^{50/30}[/tex]
the answer is 83.7; rounded up to 84
i dont understand why this is the answer; can anyone explain to me what steps i have to do first? ty!! (if there's 2 people that answered, ill give brainliest to the smartest answer that helps me understand why 84's the answer)
write an equation passing through the point and parallel to the given line? (6, 10); 2x + 2y = -8
Answer:
y=-x+16
Step-by-step explanation:
let’s put this equation in slope intercept form: y=mx+b
2x+2y=-8
-2x. -2x
2y=-2x-8
/2. /2. /2
y=-x-4
We know parallel lines have the same slope as each other so let’s fill in the equation with the given point
10=-(6)-4
10=-10
We need to add 20 more to the y intercept to make this true like this
y=-x-4+20
y=-x+16
Now let’s see if it works
10=-(6)+16
10=10
It works so this is the equation
Hopes this helps please mark brainliest
Answer: y = -x +16
Step-by-step explanation:
rearrange the equation to make y the subject
2y = -2x -8
y = -x-4
equation of line parallel to the line (gradient will be the same)
y = -x +c
Substitute the x and y values into the parallel line equation
10 = -6 + c
10 + 6 = c
16 = c
Therefore, the equation of the line parallel to 2x + 2y = -8 is y = -x +16
A washing machine is priced at $450. A man buys the washing machine on HP according to the following terms: A deposit of 15% and the remaining to be paid in monthly
installment over 2 years at a simple interest rate of 10 2 % per annum. Calculate his monthly income
The monthly installment to be paid is $17.85.
Given:
A washing machine is priced at $450. A man buys the washing machine on HP according to the following terms: A deposit of 15% and the remaining to be paid in monthly installment over 2 years at a simple interest rate of 12 % per annum.
Remaining amount = 450 - 450*15/100
= 450 - 9*15/2
= 450 - 67.5
= $382.5
1 month amount = 382.5 + 382.5*0.12 / 24
= 428.4/24
= $17.85.
Therefore the monthly installment to be paid is $17.85.
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the length of line segment ab is 380. the length of line segment cd is 95% of the length of line segment ab. what is the length of line segment cd?
Answer:
361
Step-by-step explanation:
A regular polygon is shown with one of its angle measures labeled a.
5 sided regular polygon with one angle labeled a
If m∠a = (3z + 72)°, find the value of z.
z = 9
z = 12
z = 24
z = 32
Answer:
B) z = 12===========================
Sum of interior angles of a regular polygon is:
S = 180(n - 2), where n- sides of polygonFind the measure of interior angle a:
a = S/5 = 180(5 - 2)/5 = 540/5 = 108Equate the values of angle a and solve for z:
3z + 72 = 1083z = 108 - 723z = 36z = 12Correct choice is B.
Answer:
z = 12
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Interior angle of a regular polygon}\\\\$\dfrac{180^{\circ}(n-2)}{n}$\\\\where $n$ is the number of sides.\\\end{minipage}}[/tex]
Given that the regular polygon has 5 sides, then the measure of one interior angle is:
[tex]\implies \dfrac{180^{\circ}(5-2)}{5}=\dfrac{180^{\circ}(3)}{5}=\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]
If "a" is the measure of one angle, and m∠a = (3z + 72)° then:
[tex]\implies m \angle a=108^{\circ}[/tex]
[tex]\implies (3z+72)^{\circ}=108^{\circ}[/tex]
[tex]\implies 3z+72=108[/tex]
[tex]\implies 3z+72-72=108-72[/tex]
[tex]\implies 3z=36[/tex]
[tex]\implies \dfrac{3z}{3}=\dfrac{36}{3}[/tex]
[tex]\implies z=12[/tex]
A cylinder has a volume of 1 and two ninths in3 and a radius of one third in. What is the height of a cylinder? Approximate using pi equals 22 over 7.
7 twelfths inches
7 sixths inches
7 fourths inches
7 halves inches
The height of a cylinder is D. 7 halves inches
How to calculate the height?The volume of a cylinder is calculated as:
V = πr²h
r = radius = 1/3
h = height = ?
v = volume = 1 2/9
We will slot the value info the formula. This will be:
V = = πr²h
1 2/9 = 22/7 × 1/3 × 1/3 × h
1 2/9 = 22/63h
Divide through by 22 / 63
h = 1 2/9 ÷ 22/63
h = 11/9 × 63/22
h = 7/2
The correct option is D.
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Answer:
7/2 is your answer i have the same test :)))
Step-by-step explanation:
The volume of a cylinder is calculated as:
V = πr²h
r = radius = 1/3
h = height = ?
v = volume = 1 2/9
We will slot the value info the formula. This will be:
V = = πr²h
1 2/9 = 22/7 × 1/3 × 1/3 × h
1 2/9 = 22/63h
Divide through by 22 / 63
h = 1 2/9 ÷ 22/63
h = 11/9 × 63/22
h = 7/2
The correct option is D.
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Elena said the equation 8x + 16 = 2x + 16 has no solutions because 8x is greater than 2x. Do you agree with Elena? Explain your reasoning.
Answer:6x
Step-by-step explanation: Put the x's on one side and other on the other side
Answer:
The equation has a solution,
x = 0Step-by-step explanation:
Given equation,
→ 8x + 16 = 2x + 16
Now the value of x will be,
→ 8x + 16 = 2x + 16
→ 8x - 2x = 16 - 16
→ 6x = 0
→ x = 0/6
→ [ x = 0 ]
Hence, the value of x is 0.
please help me solve this
Answer:
A = ₤500
B = ₤420
C = ₤340
D = ₤260
See Image 1 attached for the plot.
Step-by-step explanation:
The bank account starts with ₤500, so that is the amount at 0 months on the chart.
After one month, ₤80 is withdrawn, and the total becomes:
[tex]500-80=420[/tex]
After two months, another ₤80 is withdrawn from the account:
[tex]420-80=340[/tex]
Finally, after 3 months, ₤80 is withdrawn again:
[tex]340-80=260[/tex]
Find the sale price when the original price is $37. 00 and the discount rate is 44%. A. $20. 72 c. $35. 37 b. $16. 28 d. $1. 63.
Answer:
$16.28
Step-by-step explanation:
44.%
Move the decimal up by two numbers to get a whole number, .44
and multiply .44 by $37
What is the slope of a line that is parallel to the line y = x + 2?
Mark this and return
The slope of a line that is parallel to the line y = x + 2 is 1.
What is slope?
A line's steepness is determined by its slope. In mathematics, the slope is determined by "rise over run" (change in y divided by change in x).
Given the equation of line: y = x + 2
We have to find the slope of a line that is parallel to the given line.
Since any line parallel to the given line y = x + 2 will have the same slope as that of a given line
The general equation of line is given as y = mx + c
where. m is the slope of the line and c is y-intercept.
Thus for given equation of line y = x + 2
Comparing , we get
slope is m=1
Thus, any line with slope 1 is parallel to the given line y = x + 2
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8th grade math! (Picture attatched)
The equations that represent the left side, right side, top side and bottom side are y = 3x+2, y = 3x-10, y = 5 and y = -1 respectively
How to write the equation that represents each side of the figure?The slope-intercept form of the equation of a line is y =mx+c,
where m is the slope and c is the y-intercept
slope(m) = y2-y1 / x2-x1
Left side
The line moves from point 1 (-1, -1) to point 2 (1,5)
x1 = -1, y1 = -1 and x2 = 1, y2 = 5
Slope(m) = 5-(-1) / 1-(-1) = 6/2 = 3
Using the equation of a line for 2 points:
y-y1 = m(x-x1)
y-(-1) = 3(x-(-1))
y+1 = 3(x+1)
y+1 = 3x+3
y = 3x+2
Right side
The line moves from point 1 (3, -1) to point 2 (5,5)
Slope(m) = 5-(-1) / 5-3 = 6/2 = 3
y-(-1) = 3(x-3)
y+1 = 3x -9
y = 3x-10
Top side
y = 5
Bottom side
y = -1
Therefore, equation for the left side : y = 3x+2, equation for the right side: y = 3x-10, equation for the top side: y = 5 and equation for the bottom side: y = -1
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Determine whether each expression is equivalent to
(3+) t+3
9.27t
3².27t
Equivalent
O
Not Equivalent
K
3t² + 3t
Answer: The answer is 81m + 27t
Step-by-step explanation:
Answer: (3t)^t+3 and 3^t^2 x 27^t are both equivalent to the expression while 9^t x 27^t is not equivalent.
Step-by-step explanation:
Suppose you have a nickel, two dimes, and a quarter. One of the dimes was minted in 1976, and the other one was minted in 1992. a. Assuming you choose at least one coin, how many different sets of coins can you form? b. Assuming you choose at least one coin, how many different sums of money can you produce? c. Explain why the answers in part a and part b are not the same.
As per the concept of counting problem, the reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.
Counting Problems
Basically, counting refers the process of finding the number of elements of a finite set of objects.
Given,
Suppose you have a nickel, two dimes, and a quarter. One of the dimes was minted in 1976, and the other one was minted in 1992.
While we looking into the given problem,
For A) states that, If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins. Let us label the dime as D, the penny as P, the quarter minted in 1976 as Q1 and the quarter minted in 1992 as Q2.
Here in this process if you choose one coin, you could choose either D, P, Q1, or Q2. This gives us 4 possible sets.
And If you choose two coins, you choose the following sets of coins: DP, DQ1, DQ2, PQ1, PQ2, Q1Q2. This gives us 6 possible sets.
Then If you choose three coins, you could the following sets of coins: DPQ1, DPQ2, DQ1Q2, PQ1Q2. This gives us 4 possible sets.
So, If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible set.
So, the total number of different sets of coins you can form is 4 + 6 + 4 + 1 = 15 different sets of coins can be formed.
Similarly, for b) If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins.
Then If you choose one coin you could choose either D, P, Q1, or Q2. However, since Q1 and Q2 give us the same sum, they are effectively the same set. This gives us 3 possible sums.
So, If you choose two coins, you could choose the following sets of coins : DP, DQ, PQ, Q1Q2.And this gives us 4 possible sums
Then If you choose three coins, you could choose the following sets of coins: DPQ, DQ1Q2, PQ1Q2. And this gives us 3 possible sums
Then If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible sum.
So, the total number of different sums of coins you can form is 3 + 4 + 3 + 1 = 11 different sums of money can be produced.
Finally, c) The reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.
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29n=−6
I need answer now
What is the percent of increase from 5 to 8
Answer: 60%
Step-by-step explanation:
(5 × p) / 100 = 3
((5 × p) / 100) × 100 = 3 × 100
5p = 300
5p / 5 = 300 / 5
p = 60
Percent Increase = 60
Determine how many solutions there are to the equation
8x+4=4(2x+1)
Answer: 0
Step-by-step explanation:
8x-4=4(2x+1)
8x-4=8x+4
0= 8
This isn't true as 0 can't equal to 8 so there are 0 solutions
is 23/25 greater than or less than9/10
23/25 is greater than 9/10
23/25=92/100
9/10=90/10
92>90
Lenny works a basic week of 32 hours. His basic rate of pay is $1,750. During a certain week he worked 9 hours overtime for which he was paid triple time. What was Lenny's total wage?
Lenny's total wage is $7000
In this question, Lenny works a basic week of 32 hours. His basic rate of pay is $1,750. During a certain week he worked 9 hours overtime for which he was paid triple time.
32 hours of work = $1750
In a certain week, we work 9 hours as over time
For this overtime which he was paid triple time.
1750 * 3 = $5250
So, Lenny's total wage would be,
$1,750 + $5250 = $7000
Therefore, Lenny's total wage is $7000
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f(x) = -x² +9
Find f(-5)
Answer:
f(-5) = -16
Step-by-step explanation:
f(-5) = - [tex](-5)^{2}[/tex] + 9
-(25) + 9
-25+9
-16
Given: line m represented by
Y= 3/4x + 2
Match each of the following equations to the term that accurately described its relationship to line m.
Answer:
Neither, Perpendicular, Parallel, Neither
Step-by-step explanation:
Parallel lines have the same slope.
Perpendicular lines have slopes that are negative reciprocals.
$15 a share. A month later, it was
selling at $27 a share. What is
the percent increase?
Answer: 0.555555556
Step-by-step explanation:
15/27=0.555555556
Checking work by plugging it in: 27x0.555555556=15
======================================================
Work Shown:
a = old value = 15
b = new value = 27
c = change in values
c = b-a
c = 27-15
c = 12
The positive c value tells us that we have an increase.
Then divide over the starting value a = 15
c/a = 12/15 = 0.80
Move the decimal point two spots to the right to go from 0.80 to 80%
Or multiply 0.80 with 100% to get 0.80*100% = 80%
We have a percent increase of 80%
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Check:
80% of 15 = 0.80*15 = 12
If the stock increases by 80%, then it has increased by $12 to go from $15 a share to 15+12 = 27 dollars a share. This confirms the answer.
A slight shortcut would be to say 1.80*15 = 27
The multiplier 1.80 represents an increase of 80% since 100% + 80% = 1 + 0.80 = 1.80