From the recursive definition, the next term of a sequence is the previous term multiplied by 3, hence it is a geometric sequence with a common ratio of 3.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
\(a_n = a_1q^{n-1}\)
In which \(a_1\) is the first term.
The recursive definition of a geometric sequence is:
\(a_{n+1} = qa_n\)
In this problem, the sequence is given by:
\(u_{n+1} = 3u_n\)
With first term \(u_1 = \frac{4}{27}\).
Hence it is a geometric sequence with a common ratio of 3.
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the number of traffic accidents per week in a small city has a poisson distribution with mean 3. what is the probability of exactly 2 accidents over the course of 2 weeks?
The probability that there will be exactly 2 accidents during the next
two weeks is 0.9828.
A Poisson distribution in statistics is a probability distribution that is used to demonstrate how frequently an event is expected to happen over a certain period of time. It is a count distribution, to put it another way. In order to comprehend separate events that happen at a steady pace throughout the course of a certain period of time, Poisson distributions are frequently utilized.
Using the Poisson distribution:
2 weeks ⇒ λ = 6.
P( X ≥ 2 ) = 1 – [ P( X = 0 ) + P( X = 1 ) ] = \(1-[\frac{6^{0}*e^{-6} }{0!} + \frac{6^{1}*e^{-6} }{1!}]\)
= 1-[0.0024+0.0148] = 0.9828
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On Wednesday morning, Smith's had 99
boxes of Sweet Smacks on the shelf. 4
out of every 11 boxes contained a prize.
How many boxes did NOT contain a
prize?
Answer:
4
Step-by-step explanation
Im sure its four. If not let me know
Students are playing a game similar to blackjack (with a standard 52 card deck)- trying to get as close to 21 points without going over. The ace is only worth 1 point and each face card is worth 10 points, the remaining cards have face value. Player A draws a eight and a nine. Player B draws a four and a jack. If Player A next draws a two, what is the probability of Player B winning the round?
2) Find x
WHERE
63 ° , 86 °
Answer:
31
Step-by-step explanation:
63+86=149
180-149=31
(180 because all angles in a triangle added together have to equal 180)
T/F: if the slope (b) of ŷ is positive, then the correlation coefficient (r) must also be positive.
True. The correlation coefficient (r) must also be positive, indicating a strong positive linear relationship between the two variables.
The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfectly negative linear relationship, a value of 1 indicates a perfectly positive linear relationship, and a value of 0 indicates no linear relationship. If the slope (b) of ŷ is positive, it means that as the independent variable increases, the dependent variable also increases.
In addition to the above explanation, it is important to note that while a positive slope (b) of ŷ indicates a positive linear relationship between two variables, it does not necessarily mean that the correlation coefficient (r) will always be positive. For example, if there is a weak positive linear relationship between two variables, the correlation coefficient (r) may still be positive but not as strong as if there was a strong positive linear relationship. Similarly, there may be situations where the correlation coefficient (r) is positive but the slope (b) of ŷ is not positive, such as in a curvilinear relationship where the relationship between the two variables is not linear.
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Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-1, -6), B(-1,7), C(1, 7), and D(1, -6). Given these coordinates, what is the length of side AB of this rectangle?
Answer:
13
A(-1, -6), B(-1,7)
7-(-6)=13
Answer:
13
Step-by-step explanation:
For breakfast, Mr. Hill bought a cup of coffee for $1.39 and a bagel for $1.85. How much change will he get back from $5.00?
Answer:
He would get $1.76 in change
Step-by-step explanation:
For the coffee, you can subtract $1.39 from $5.00
$5.00 - $1.39 = $3.61
Then for the bagel, you need to subtract 1.85 from your answer to the old equation
$3.61 - $1.85 = $1.76
So $1.76 is your answer.
There are scores between 80 and 99. there are scores greater than 99. there are scores less than 60 points
Scores range from 80 to 99, with scores exceeding 99 and scores falling below 60 points.
In the given range of scores, which spans from 80 to 99, it encompasses a range of values that are considered satisfactory and relatively high. These scores reflect a level of achievement or performance within a specific context, such as academic grading or test results. Additionally, it is important to note that there are scores that exceed 99, indicating exceptional performance or outstanding results. On the other hand, there are also scores below 60, which indicate lower levels of achievement or performance. These scores may require further attention or improvement in order to reach a more desirable outcome. The varying range of scores allows for a comprehensive evaluation of individuals or entities based on their performance, highlighting both strengths and areas that may need improvement.
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Por favor ayudadme con esto
a) The proportional relationship for the similar triangles in this problem is given as follows:
h/6 = 50/13.
b) The height of the tower is given as follows: h = 23.1 m.
What are similar triangles?Two triangles are defined as similar triangles when they share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The similar triangles for this problem are given as follows:
CAB and EDB.
Hence the proportional relationship for the side lengths is given as follows:
h/6 = 50/13.
Applying cross multiplication, the height of the tower is obtained as follows:
h = 6 x 50/13
h = 23.1 m.
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Marcus is considering adding one more dish to his menu, but he will only do so when he has
perfectly executed the recipe exactly as he will serve it in the truck 10 times. Each time he
makes the dish, there is an 80% chance that the execution is perfect.
What is the probability that Marcus has to make the new dish exactly 15 times before it goes on
the menu?
Suppose that Marcus has already perfectly executed the new recipe 5 times. There is an investor
that will meet with Marcus in 6 days, and if the new recipe is ready to be added to the menu at
the time of the meeting then he will double his investment in the food truck. If Marcus attempts
the recipe once per day until the meeting (so he has up to 6 attempts), what is the probability that
the investor will double his investment?
The probability that Marcus has to make the new dish exactly 15 times before it goes on the menu is approximately 0.053. The probability that the investor will double his investment is approximately 0.315.
To find the probability that Marcus has to make the new dish exactly 15 times before it goes on the menu, we need to calculate the probability of exactly 10 successes (perfect executions) out of the first 14 attempts and then the probability of a success on the 15th attempt. Each attempt has an 80% chance of success.
Using the binomial probability formula, the probability of exactly k successes in n attempts, with a success probability p, is given by:
\(P(X = k) = (n choose k) * (p^k) * ((1 - p)^(n - k))\)
In this case, we want to calculate\(P(X = 10) * P(X = 1) = (14 choose 10) * (0.8^10) * (0.2^4) * (0.8^1) = 0.0577 * 0.00016 ≈ 0.0092.\)
Therefore, the probability that Marcus has to make the new dish exactly 15 times before it goes on the menu is approximately 0.0092 or 0.92%.
To calculate the probability that the investor will double his investment, we need to consider the scenario where Marcus attempts the recipe once per day until the meeting. Since he has 6 days left and he has already executed the recipe 5 times successfully, he has 1 remaining attempt.
The probability of a success on the last attempt is 0.8, and the probability of failure is 0.2. Therefore, the probability that the investor will double his investment is P(X = 1) = 0.8.
Hence, the probability that the investor will double his investment is approximately 0.8 or 80%.
The binomial probability formula is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent Bernoulli trials. In this case, Marcus's attempts to execute the recipe can be modeled as a binomial distribution since each attempt has a fixed probability of success (80%) and the attempts are independent. By applying the formula, we can determine the probabilities associated with the number of successes and make informed decisions based on those probabilities.
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D=8.3m
Calculate the circumference of the circle.
Answer:
Step-by-step explanation:
C=2*3.14*r
we have the diameter d=2*r=8.3m
C=8.3*3.14=26.06 m
Three teams, A, B and C, play in a competition.
games won by A: games won by B = 3:1
games won by B: games won by C = 4:3
Team B has won 8 games.
In total, how many games have the three teams won?
Answer: In total the three teams have won
Optional working
games
Answer:
38
Step-by-step explanation:
:) hope this helps
lmk lmk i need answer asap
Answer:
5+9=9+5
Step-by-step explanation:
Because ethier way it will be 14, but idl dont take my word yet...
Answer:
The answer is C
Step-by-step explanation:
21+21=42
an airplane, flying horizontally at 200 mph at an altitude of 3 miles, passes over a radar station. what is the rate of change of the angle of elevation between the radar station and the plane 3 minutes after the plane passes over the radar station? (the angle of elevation is the angle between the horizontal and a line between the radar station and the airplane.)
The rate of change of angle of elevation between the radar station and airplane is
\(\displaystyle \frac{-10}{109} \left(\frac{rad}{min}\right)\)
The airplane is flying at the speed of 200 mph
The airplane is at an altitude of 3 miles over the radar station
The distance travelled by the airplane after 3 mins
distance = speed x time
= 200 mi/hr x 3 min
Since the speed is hour let us convert it to mins
= 200 x 3 x 1/60
= 600 / 60
= 10 miles
So , let us assume that the airplane is exactly at the top of the radar station at an altitude of 3 miles
Then the elevation angle of the between radar station and airplane can be find by
tan θ = O / A
where O is the opposite side to the angle of elevation
A is the adjacent side to the angle of elevation.
But we need the find the rate of change of angle of elevation , so let us differentiate on both side with respect to time
\(\displaystyle sec^{2}\theta\frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{A^{2}}\)
\(\displaystyle \frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{sec^{2}\theta A^{2}}\)
\(\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{sec^{2}(10)^{2}}\)
The altitude is gonna be a constant , thus the derivative of altitude will be zero whereas , the the distance travelled by airplane is changing with respect to time.
\(\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{\frac{109}{100}(10)^{2}}\)
We had found the value of sec²θ = (hyp/adj)²
\(\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \frac{rad}{hr}\)
Now , let us convert in terms of rad/min
\(\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \left(\frac{1}{60}\right)\)
\(\displaystyle \frac{d\theta}{dt} = \frac{-10}{109} \left(\frac{rad}{min}\right)\)
Therefore , the rate of change of angle of elevation is -10/109 (rad/min)
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Identify the relationship (complementary, linear pair/supplementary, or vertical) and find the measure of angle b in the image below.
Answer:
complementary
b = 45 deg
Step-by-step explanation:
Angles b and 45-deg are complementary since their measures ad to 90 deg.
45 + b = 90
b = 45
Answer:
Complementary
45°
Step-by-step explanation:
b + 45° = 90°
b = 90° - 45°
b = 45°
solve the simultaneous equation plz x
Answer:
x=4,y=3
Step-by-step explanation:
x=19-5y if we transpose equation 2 for x.
Plug that into equation 1
4(19-5y)+3y=25
76-20y+3y=25
76-25=17y
51=17y
y=3
Plug y=3 into equation 2
x+5(3)=19
x=19-15=4
We are having two equations,
4x + 3y = 25 (Equation No 1)x + 5y = 19 (Equation No 2)★ From Equation No 2 :-
>> x + 5y = 19
>> x = 19 - 5y
★ From Equation No 1 :-
Substitute here the value of x which we got above as (19 - 5y).
>> 4x + 3y = 25
>> 4 (19 - 5y) + 3y = 25
>> 4 × (19 - 5y) + 3y = 25
>> 76 - 20y + 3y = 25
>> 76 - 17y = 25
>> -17y = 25 - 76
>> -17y = -51
>> 17y = 51
>> y = 51 / 17
>> y = 3
★ Finding out value of x :-
>> x = 19 - 5y
>> x = 19 - 5(3)
>> x = 19 - 5 × (3)
>> x = 19 - 15
>> x = 4
can someone please help me with this? i don’t understand it at all
Answer: I’m pretty sure they are similar because they have the same interior degree.
Step-by-step explanation:
3/4 ft= blank inches
Please help ASAP I need this turned in! I don’t understand it!
Car A: 3x + 6
Car B: 4x+8
Step-by-step explanation:
total: 7 (x+2)
Use the given information to find n(A x B) and n(BxA) n(A)=46 and n(B)-7
To find the number of elements in the Cartesian product A x B and B x A, we need to multiply the number of elements in set A by the number of elements in set B.
Given that n(A) = 46 (the number of elements in set A) and n(B) = 7 (the number of elements in set B), we can calculate: n(A x B) = n(A) * n(B) = 46 * 7 = 322. Therefore, the number of elements in the Cartesian product A x B is 322. Similarly, to find n(B x A), we need to multiply the number of elements in set B by the number of elements in set A: n(B x A) = n(B) * n(A) = 7 * 46 = 322
Thus, the number of elements in the Cartesian product B x A is also 322.
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Peyton needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4 hours and charged her $77 for parts. The total was $497. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
Answer:
Step-by-step explanation:
the equatoin is 4x+77=497
and x is the hours spent
so solving it you subtract 77 from 497 which is 420 and 420/4 is equal to 105
Identify the roots of:y = x² - 12x + 32
Okay, here we have this:
Considering the provided function, we are going to calculate the requested roots, so we obtain the following:
\(\begin{gathered} x^2-12x+32=0 \\ x_{1,2}=\frac{-(-12)\pm\sqrt{(-12^2)-4(1)(32)}}{2(1)} \\ x_{1,2}=\frac{12\pm\sqrt{144-128}}{2} \\ x_{1,2}=\frac{12\pm\sqrt{16}}{2} \\ x_{1,2}=\frac{12\pm4}{2} \\ x_{1,2}=6\pm2 \\ x_1=6+2,x_2=6-2 \\ x_1=8,x_2=4 \end{gathered}\)Finally we obtain that the roots of the function are x=8 and x=4.
Please Help! For the table to the right, represent the relationship using words and an equation. X: 0123 Y: -3159 Write a equation.
The equation represented by the table in the right is y = 4x - 3
How to solve an equationAn equation is used to show the relationship between two or more numbers and variables.
The equation of a linear is given as:
y = mx + b
Where m is the rate of change and b is the initial value
The table have the pairs (0, -3), (1, 1), (2, 5) and (3, 9).
Using the point (0, -3) and (1, 1):
y - (-3) = [(1 - (-3))/(1 - 0)](x - 0)
y + 3 = 4x
y = 4x - 3
The equation is y = 4x - 3
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The slope of a roof is called its pitch. The parthenon, an ancient greek temple, has a roof with a rise of 3. 6 meters and a run of 12 meters. What is the pitch of the roof?.
The pitch of the roof is 0.3.
Pitch:
The pitch can be expressed numerically as a fraction. The pitch fraction represents a certain amount of vertical rise over the entire span.
Here it is given that the rise in the roof is 3.6m and a rum of 12m,
We have to find the pitch of the roof.
As is already given in the statement that the slope of a roof is called its pitch.
By this we get the slope:
Slope = 3.6/12
= 3/10
= 0.3
Therefore we get the pitch of the roof at 0.3.
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4n+3< 6n+8 -2n what is n
Answer:
\(8>3\)
Step-by-step explanation:
STEP 1: Rewrite so n is on the left side of the inequality.
\(6n+8-2n>4n+3\)
STEP 2: Subtract 2 n from 6 n .
\(4n+8>4n+3\)
STEP 3: Move all terms containing n to the left side of the inequality.
\(8>3\)
What is the value of k if one of the zeros of the quadratic polynomial K 2 x2 2x 5?
If one of the zeros in the quadratic polynomial is 4, then the value of k is 3.
What is polynomial?A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. A polynomial is a mathematical expression that only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in mathematics.
Here,
4 is a root/zero of polynomial
P(x) = (k-2) x² - 2 x - (k+5)
P(4) = 0
(k - 2) 4² - 2 * 4 - (k+5) = 0
15 k - 45 = 0
k = 3
The value of k if 4 is one of the zeros of the quadratic polynomial is 3.
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Complete question:
If one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k.
Please Help me Find NM using Secant
Answer:
NM = 15
Step-by-step explanation:
There is a property of secants and tangents to a circle where:
The square of the tangent length is equal the length of the external segment of the secant times the whole secant length.
Therefore, in our question, we have that:
\(NM^2 = ML * MK\)
The values of NM, ML and MK are:
\(NM = x + 3\)
\(ML = x - 3\)
\(MK = ML + LK = x - 3 + 16 = x + 13\)
So we have:
\((x+3)^2 = (x - 3)(x + 13)\)
\(x^2 + 6x + 9 = x^2 + 10x - 39\)
\(6x + 9 = 10x - 39\)
\(4x = 48\)
\(x = 12\)
So the length of NM is:
\(NM = x + 3 = 12 + 3 = 15\)
What is it pls tell me
this is a problem I need help with
Answer:
C) neither
Step-by-step explanation:
they add up to 190
complementary adds up to 90
supplementary adds up to 180
Answer:
supplementary
Step-by-step explanation:
sum = 180
Probability diagram question….....
The probability tree diagram is
The first roll has (0.85, 0.15).
Second Roll has (0.85, 0.85, 0.15, 0.15).
What is the probability?
The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability
Here, we have
Given: the probability of rolling a 1 on a 6-sided biased dice is 0.85
Now, the probability of not rolling 1
= 1 - 0.85
= 0.15
Hence, the First roll has (0.85, 0.15).
and, the Second Roll has (0.85, 0.85, 0.15, 0.15).
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