given two terms in an arithmetic sequence find the recursive formula
a 19 = -101 and a36 = -220 find a 29
Answers
Using this formula, we can find a1 by plugging in a19 (the 19th term) and n=19: a19 = a1 + (19-1)(d) => -101 = a1 + 18(-119/17), Simplifying this equation, we get: a29 = -33, the value of a29 is -33.
Given two terms in an arithmetic sequence, to find the recursive formula, we need to find the common difference of the sequence first. This can be found by using the formula: common difference (d) = (a36 - a19)/(36 - 19) = (-220 - (-101))/(36 - 19) = -119/17.
Next, we can use the recursive formula for arithmetic sequences which is: an = a1 + (n-1)dwhere an represents the nth term in the sequence, a1 represents the first term, and d is the common difference that we just found.Using this formula, we can find a1 by plugging in a19 (the 19th term) and n=19: a19 = a1 + (19-1)(d) => -101 = a1 + 18(-119/17).
Simplifying this equation, we get: a1 = -101 + (18)(119/17) = 7.Next, we can use the formula again to find a29 (the 29th term) by plugging in a1 and n=29: a29 = a1 + (29-1)(d) => a29 = 7 + 28(-119/17)Simplifying this equation, we get: a29 = -33Therefore, the value of a29 is -33. Answer: a29 = -33.
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Related Questions
Identify the graph of the linear equation 2x + 2y - z=-4 in three dimensional space.
Answers
The answer is option C
The points graph must be a solution to the equation. Then, in graph C, we have three points:
(0 , -2, 0)
(-2, 0, 0)
(0, 0, 4)
Now let's try each in the equation:
\(\begin{gathered} \mleft(0,2,0\mright)\Rightarrow2\cdot0+2(-2)-0=-4 \\ -4=-4 \end{gathered}\)\(\begin{gathered} \mleft(-2,0,0\mright)\Rightarrow2\cdot(-2)+2\cdot0-0=-4 \\ -4=-4 \end{gathered}\)\(\begin{gathered} (0,0,4)\Rightarrow2\cdot0+2\cdot0-4=-4 \\ -4=-4 \end{gathered}\)
Find a Doctor, is a small startup that helps people find a physician that best meets their needs (location, insurance accepted, etc) During a "slow time for them, they have 9 staff members taking calls from customers. On average, one call arrives every 5 minutes (standard deviation of 5 minutes). Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes) Round your answer to 2 decimal places) How long does a customer spend on average waiting on hold before they can start speaking to a representative? Minutes
Answers
On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.
To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.
Given:
9 staff members taking calls.
On average, one call arrives every 5 minutes (standard deviation of 5 minutes).
Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).
To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:
"M" stands for Markovian or memoryless arrival and service times.
"c" represents the number of servers.
In our case, we have an M/M/9 queuing model since we have 9 staff members.
The average waiting time for a customer on hold is given by the following formula:
Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))
Where:
c = number of servers (staff members) = 9
μ = average service rate (1 / average service time)
λ = average arrival rate (1 / average interarrival time)
ρ = λ / (c * μ)
First, let's calculate the average arrival rate (λ):
λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute
Next, calculate the average service rate (μ):
μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute
Now, calculate ρ:
ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407
Finally, calculate the waiting time:
Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))
= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))
≈ 1.16 minutes
Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.
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Tyler’s brother works in a shoe store. The store was selling a pair of shoes for $80. They now are on sale for $50. What is the percentage of markdown on the shoes?
Answers
you can spend at most $12 on red peppers and tomatoes for salsa. red peppers cost $4 per pound and tomatoes cost $3 per pound. write and graph the inequality that represents the number of red peppers and tomatoes you can buy
Answers
Answer:
4x + 3y >/= to 12
Step-by-step explanation
The required inequality is 4x + 3y ≤ 12 which represents the number of red peppers and tomatoes.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
Red peppers and tomatoes for salsa cost no more than $12. Red peppers are $4 per pound, while tomatoes are $3 per pound.
To write the inequality, we can let x represent the number of pounds of red peppers and y represents the number of pounds of tomatoes.
The total cost of the red peppers is 4x dollars and the total cost of the tomatoes is 3y dollars.
We know that the total cost of both the red peppers and tomatoes combined is 12 dollars.
Therefore, the inequality to represent is 4x + 3y ≤ 12.
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May anyone help me with this?
Answers
Answer:
31
Step-by-step explanation:
same as my last two questions
Answers
The intervals to the given function are as follows:
Domain: (-∞,∞).Range: (-∞,∞).Rel. maximums: (1.366, -0.652).Rel. minimums: (-0.366, -5.848) and (2,-1).End behavior: As x -> -∞, f(x) -> ∞, and as x -> ∞, f(x) -> ∞.Inc. intervals: (-0.366, 1.366) U (2, ∞).Dec. intervals: (-∞, -0.366) U (1.366, 2).Domain and rangeDomain: Set of values of the input of the function, hence the values of x in the graph of the function.Range: Set of values of the output of the function, hence the values of y in the graph of the function.This function is defined(values of x) for all real values and also assumes all real values(values of y), hence both the domain and the range are of the function are given by the interval (-∞,∞).
Increasing and decresingFrom the graph, the function is classified as decreasing or increasing according to the direction of movement in the graph, as follows:
Decreasing: Right and down.Increasing: Right and up.Hence the intervals are given as follows:
Increasing: (-0.366, 1.366) U (2, ∞).Decreasing: (-∞, -0.366) U (1.366, 2).Relative maximum and relative minimumThe relative minimum is when the graph of the function changes from decreasing to increasing, hence it is at these two following points:
(-0.366, -5.848) and (2,-1).
The relative maximum is when the function changes from increasing to decreasing, hence it is at this following point:
(1.366, -0.652).
End behaviorThe end behavior of the function is given by the limits of the function when x go to infinity, looking to the left and to the right of the graph of the function, hence:
Left: Moves up, hence as x -> -∞, f(x) -> ∞.Right: Moves up, hence as x -> ∞, f(x) -> ∞.More can be learned about functions at https://brainly.com/question/28949511
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Rebecca has two part-time jobs. She earns $10 per hour working at a store. She earns $45 per lawn mowed working for a landscaper. Her goal is to earn $1,800 to pay her monthly expenses. The situation can be modeled by the formula below, where g represents the hours Rebecca works in the grocery store and m represents the number of lawns mowed. 1,800 = 10g + 45m After Rebecca learns how many hours she is scheduled to work in the grocery store, she has to figure out how many lawns she needs to mow that month. Which equation shows the formula correctly rearranged to find m given g ?
Answers
The equation to get m for a given value of g is:
(1800 - 10g)/45 = m
Which equation shows the formula correctly rearranged to find m given g?Ok, here we have the equation:
1,800 = 10g + 45m
We want to find an equation so we can find the value of m for a given value of g, then, we need to isolate m in the above equation:
First, we can subtract 10g in both sides, so we get:
1,800 - 10g = 45m
Now we can divide both sides by 45, so we get:
(1800 - 10g)/45 = m
That is the equation that we can use to find the value of m, we just need to evaluate it in the given value of g.
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Answer:
The answer is m = -2/9 g + 40
. Based on your calculation in question 1 of how many gallons of water a 10-minute shower uses and your estimate in question 3 of the number of gallons of water wasted in a day by the leaky faucet, how long does it take 1 leaky faucet to waste the water needed for 1 shower? Round to the nearest day and explain your answer.
Answers
Answer:
25 gallons of water
Step-by-step explanation:
If you look at the diagram given, it states that 2.5 gallons of water are released every minute in the shower. Multiply 2.5 gallons by 10minutes and you will get your total of 25.
2.5 gallons x 10 minutes = 25 gallons of water used in a 10 minute shower
Could some one help me please
Answers
Answer:
12
Step-by-step explanation:
15-8x Choose ALL of the statements that are TRUE. The factors are 8 and x. The coefficient is -8. The constant is -8. The terms are 15 and -8x. The coefficient is 15. The constant is 15.
Answers
Explanation:
The coefficient is the number just to the left of the variable. So that's why -8 is the coefficient for -8x. This is the variable term while 15 is the constant (it has no variable multiplied with it). The two terms are 15 and -8x since we can write 15-8x as 15+(-8x). Terms are separated by a plus sign.
Each set of ordered pairs represents a function. Write a rule that represents the function. (0, −8), (1, −7), (2, −6), (3, −5), (4, −4) A. y = x − 8 B. y = 4x − 8 C. y = −x + 8 D. None of the above
Answers
The equation of the line is y = x - 8
How to determine the rule of the ordered pairsFrom the question, we have the following parameters that can be used in our computation:
Points = (0, −8), (1, −7), (2, −6), (3, −5), (4, −4)
A linear equation can be represented as
y = mx + c
Substitute the known values in the above equation, so, we have the following representation
-8 = 0 * m + c ⇒ c = -8
-7 = 1 * m + c
In -8 = 0 * m + c, we have
c = -8
Substitute c = -8 in -7 = 1 * m + c
-7 = 1 * m - 8
Evaluate
-7 = m - 8
Evaluate the like terms
m = 1
Recall that
y = mx + c
So, we have
y = x - 8
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A shipping company uses a formula to determine the cost for shipping a package: c = 2.79 + 0.38p, where c is the cost of shipping and p is the number of pounds. What is the cost of shipping a package that weighs 8 pounds?
Answers
Using the formula they gave us:
Cost of shipping = 2.79 + 0.38(8)
Cost of shipping = 2.79 + 3.04
Cost of shipping = 5.83(currency unit)
xavier is a teacher and takes home 90 papers to grade over the weekend. he can grade at a rate of 6 papers per hour. how many papers would xavier have remaining to grade after working for 12 hours?
Answers
The number of papers xavier have remaining after working for 12 hours is 18
How many papers would xavier have remainingXavier can grade 6 papers per hour, so in 12 hours he can grade:
6 papers/hour x 12 hours = 72 papers
Therefore, after working for 12 hours, Xavier would have
90 - 72 = 18 papers remaining to grade.
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Rendell cycles 42 km at an average speed of 18 km/hr. Find the time taken, giving your
answer as a fraction of an hour in its simplest form.
Answers
Answer:
2.3333333333333333333333333333333 sec
beginning with the equations that relate e0, δg0, and k, show that δg0 is negative and k > 1 for a reaction that has a positive value of e0.
Answers
We can conclude that for a reaction with a positive value of e0:
δg0 will be negative , indicating a spontaneous reaction.
k will be less than 1 , indicating that the reaction favors the reactants over the products at equilibrium.
To show that δg0 is negative and k > 1 for a reaction that has a positive value of e0, let's start with the equations that relate e0, δg0, and k.
The relationship between e0, δg0, and k is given by the following equation:
δg0 = -RT ln(k) (Equation 1)
where:
δg0 is the standard Gibbs free energy change for the reaction.
R is the gas constant.
T is the temperature in Kelvin.
k is the equilibrium constant for the reaction.
ln(k) denotes the natural logarithm of k.
Now, let's consider the Nernst equation, which relates e0 to δg0:
δg0 = -nF e0 (Equation 2)
where:
n is the number of moles of electrons involved in the reaction.
F is Faraday's constant.
e0 is the standard cell potential or standard reduction potential.
If we combine Equation 1 and Equation 2, we get:
-nF e0 = -RT ln(k)
Rearranging the equation:
ln(k) = (nF / RT) e0
From this equation, we can observe the following:
If e0 is positive, then (-nF / RT) will be negative since all the other variables are positive constants. This implies that ln(k) will be negative.
Since ln(k) is negative, k must be less than 1 because the natural logarithm of a number less than 1 is negative.
Therefore, we can conclude that for a reaction with a positive value of e0:
δg0 will be negative (according to Equation 2), indicating a spontaneous reaction.
k will be less than 1 (according to the relationship between e0, δg0, and k), indicating that the reaction favors the reactants over the products at equilibrium.
Note: It's important to consider the sign conventions used in these equations. The standard reduction potential (e0) is typically given as a positive value for a half-reaction that involves electron gain. However, when using it in the context of Equation 2, it appears with a negative sign due to the convention of assigning signs based on electron transfer direction.
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The hire purchase for motor bike is GHC 540.00, if this is to be paid in twenty equal monthly installments, what amount is paid each monthly installments
Answers
Answer:
The monthly installment for the hire purchase of the motorbike is GHC 27.00
Step-by-step explanation:
To calculate the monthly installment for the hire purchase, we can divide the total cost by the number of months:
Monthly installment = Total cost / Number of months
In this case, the total cost is GHC 540.00 and the number of months is 20:
Monthly installment = GHC 540.00 / 20
Monthly installment = GHC 27.00
Therefore, the monthly installment for the hire purchase of the motorbike is GHC 27.00
6 cars 4 people in each car HELP I HAVE 3 minutes
Answers
Answer:
Here we have 6 cars.
And we know that there are 4 people in each car.
The question is incomplete, I assume that we want to find the total number of people in the 6 cars.
So, again, there are 6 cars, and 4 people in each one.
Then we have 6 times 4 people.
This is equal to the product between 6 and 4, which is:
6*4 = 24
There is a total of 24 people in the 6 cars.
the value of point A is less than -3. it true or false
Answers
The value of point A is less than -3: false.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
From the number line shown in the image attached below, we have the following point:
Point A = -2
In conclusion, -2 is greater than -3 based on the number line shown.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Somebody help with 1& 2
Answers
Answer:
4. (d) option is correct because -7-(-5) = -7+5 ( Because - and - makes a plus .
Hope it does aid you .
Pls mark brilliant .
2. A relationship between x and y is shown on the coordinate grid below.
100
80
60
40
20
10 20 30 40 50 60 70 80 90
What is an equation that could be used to find any y value if given an x value?
Answers
The equation that can be used to find any value of y when given a value of x is y = - 0.5x + 60
How to find the equation ?The relationship given is a linear relationship as the values are moving in one direction. The slope - intercept form can therefore be used.
First, find the slope, using the points ( 100, 10 ) and ( 60, 30) as :
= Change in y / Change in x
= ( 30 - 10 ) / ( 60 - 100)
= - 0.5
Then, we can find the y - intercept with the slope and the point ( 60, 30 ) in the slope intercept form of:
y = Slope (x ) + y - intercept
30 = - 0. 5 ( 60 ) + y - intercept
y - intercept = 30 + 30
y - intercept = 60
The equation to find y when given an x value is:
y = - 0.5x + 60
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Sean wants to practice his soccer skills for at least 2.5 hours this week write inequality to represent the number of hours Sean will spend practicing this week. Graph the solution to your inequality from part A on the number line below
Answers
Answer:
x ≥ 2.5
Step-by-step explanation:
Answer:
P > 2.5
Step-by-step explanation:
The circumference of a circle is 2π m. Find its diameter, in meters.
Answers
Answer:
The diameter is 2 meters
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
2 pi = pi *d
Divide each side by pi
2 = d
The diameter is 2 meters
Q8
The midpoint of GH is M (2,2). One endpoint is H (1,9). Find the coordinates of endpoint G.
Answers
Answer:
(3,-5)
Step-by-step explanation:
Given
\(M = (2,2)\)
\(H = (1,9)\)
Required
Determine G
This is calculated using the following midpoint formula;
\(M(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\)
Where
\((x,y) = (2,2)\) and \((x_1,y_1) = (1,9)\)
Substitute these values in the formula above
\((2,2) = (\frac{1 + x_2}{2},\frac{9 + y_2}{2})\)
Solving for \(x_2\)
\(2 =\frac{1 + x_2}{2}\)
Multiply both sides by 2
\(2 * 2 = 1 + x_2\)
\(4 = 1 + x_2\)
\(x_2 = 4 - 1\)
\(x_2 = 3\)
Solving for \(y_2\)
\(2 = \frac{9 + y_2}{2}\)
Multiply both sides by 2
\(2 * 2 = 9 + y_2\)
\(4 = 9 + y_2\)
\(y_2 = 4 - 9\)
\(y_2= -5\)
Hence, the coordinates of G is \((3,-5)\)
Let X
=
A
.
¯¯¯¯¯¯
B
C
. Evaluate X for
(a) A
=
1
,
B
=
0
,
C
=
1
, (b) A = B = C = 1 and ( c) A = B = C = 0.
Answers
The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.
To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.
(a) For A = 1, B = 0, and C = 1:
X = 1.¯¯¯¯¯¯01
To find the complement of BC, we replace B = 0 and C = 1 with their complements:
X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001
(b) For A = B = C = 1:
X = 1.¯¯¯¯¯¯11
Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:
X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111
(c) For A = B = C = 0:
X = 0.¯¯¯¯¯¯00
Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:
X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000
In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.
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Regent Stadium charges $20 for a seat in the bleachers, $30 for an end zone seat, and $40 for the excellent seats near the 50-yard line. When the stadium is full, 500 tickets were sold for a total of $14,000. The number of bleacher seats is the same as the number of end zone and 50-yard line seats combined.
Answers
Answer:
The number of bleachers seat sold = 200
The number of end zone seats sold =200
The number of excellent seats sold =100
Step-by-step explanation:
Let there are bleachers seats =x
The number of zone seats =y
The number of excellent seats =z
So, we can set up equations for given sentences as
x+y+z= 500
20 x+30 y+40 z=14000
x=y
Substitute x as y into first two equations
y+y+z=500
20 y+30 y+40 z=14000
Simplify each
2 y+z=500
50 y+40 z= 14000
Multiply 2 y +z=500 by -40 to eliminate z terms when we add them.
-80 y-40 z=-20000
Add this with 50 y +40 z=14000, which gives
-30 y=-6000
Divide both sides by -30
y=200
Now, plug in y as 200 into any of the equations to find z.
2(200)+z=500
400+z =500
Subtract both sides 400.
z=100
Now, we know x=y
So, x=200
Which of the following ratios are part of the ROI formula?
Answers
The ratios involved in the ROI formula are the net profit and the investment cost.
The ROI (Return on Investment) formula includes the following ratios:
Net Profit: The net profit represents the profit gained from an investment after deducting expenses, costs, and taxes.
Investment Cost: The investment cost refers to the total amount of money invested in a project, including initial capital, expenses, and any additional costs incurred.
The ROI formula is calculated by dividing the net profit by the investment cost and expressing it as a percentage.
ROI = (Net Profit / Investment Cost) * 100%
Therefore, the ratios involved in the ROI formula are the net profit and the investment cost.
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A city has 5 new houses for every 8 old houses. If there are 30 new houses in the city, how many old houses are there?
Answers
Answer: 48 old houses
Step-by-step explanation:
Ratio 5:8
Ratio 30:?
30/5=6
8 x 6= ...
48!!!
30:48
did this make sense??
Find the measure of
Answers
=======================================================
Explanation:
The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.
Those angles add to the other angles to form a full 360 degree circle.
Let x be the measure of angle SPT and angle TPU.
86 + 154 + 60 + x + x = 360
300 + 2x = 360
2x = 360-300
2x = 60
x = 60/2
x = 30
Each red angle is 30 degrees.
Then,
angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)
angle SPQ = (30) + (30) + (86)
angle SPQ = 146 degrees
--------------
Another approach:
Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:
360 - 214 = 146 degrees
John's library has 3 hardcover books for every 8 paperbacks. If he has 121 books in his library, how many of them are paperbacks. Will mark brainliest if correct. Pls show work.
Answers
Answer: 88
Step-by-step explanation:
1. Add 3 and 8 together
3 + 8 = 11
2. Divide 121 by 11
121/ 11 = 11
3. Multiply the amount of paperbacks in the stack of 11 books (8) by 11
11 x 8 = 88
88 Is your answer.
What operation transforms the first equation into the second? Identify any extraneous solutions and any solutions that are lost in the transformation:r2 + 3r = 7r and r + 3 = 7.
Answers
The transformation from the first equation to the second equation involved simplification by canceling out the term "3r." The solution r = 0 was an extraneous solution and lost in the transformation, while the solution r = 4 remained valid.
The operation that transforms the first equation, \(r^{2}\) + 3r = 7r, into the second equation, r + 3 = 7, is simplification or reduction.
Let's solve each equation and analyze the transformations
1. \(r^{2}\) + 3r = 7r
To solve this equation, we can rearrange it to bring all terms to one side and set it equal to zero
\(r^{2}\) + 3r - 7r = 0
\(r^{2}\) - 4r = 0
Next, we factor out the common term "r":
r(r - 4) = 0
By applying the zero product property, we have two possible solutions
r = 0 or r - 4 = 0
Therefore, the solutions to the first equation are r = 0 and r = 4.
2. r + 3 = 7
To solve this equation, we isolate the variable "r" by subtracting 3 from both sides
r = 7 - 3
r = 4
Therefore, the solution to the second equation is r = 4.
Analyzing the transformation
In the transformation from the first equation to the second equation, we simplified the left side of the equation by canceling out the term "3r" on both sides. This simplification is valid as long as the canceled term, 3r, is not equal to zero. However, we need to check if the solutions obtained in the first equation are valid in the second equation.
1. For the solution r = 0:
Substituting r = 0 into the second equation, we have 0 + 3 = 7, which is not true. Therefore, the solution r = 0 is an extraneous solution and is lost in the transformation.
2. For the solution r = 4
Substituting r = 4 into the second equation, we have 4 + 3 = 7, which is true. Therefore, the solution r = 4 is a valid solution in the transformed equation.
In summary, the transformation from the first equation to the second equation involved simplification by canceling out the term "3r." The solution r = 0 was an extraneous solution and lost in the transformation, while the solution r = 4 remained valid.
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