The Phillips family bought 8 bags of cookies. Each bag had 17 cookies. They have since eaten 29 of the cookies. How many cookies do they have left?
Answer:107
Step-by-step explanation:8*17-29=107 so our answer is 107
A jury of 6 persons was selected from a group of 20 potential jurors, of whom 8 were african american and 12 were white. the jury was supposedly randomly selected, but it contained only 1 african american member. a) do you have any reason to doubt the randomness of the selection
Yes, there is reason to doubt the randomness of the jury selection based on the information provided.
Given data:
Out of the 20 potential jurors, 8 were African American and 12 were white. The probability of randomly selecting an African American juror from the pool of potential jurors would ideally be 8/20, which simplifies to 2/5 or 40%. However, the actual jury selected had only 1 African American member out of 6 jurors, which is significantly lower than the expected 40% if the selection were truly random.
This deviation from the expected probability raises questions about the randomness of the selection process. The observed outcome appears to be disproportionately skewed against the representation of African American jurors. While random variations can occur, the extent of the deviation in this case warrants further investigation into the jury selection process to determine if there were any biases or factors influencing the outcome.
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a) express ∂z/∂u and ∂z/∂v as functions of u & v by using the chain rule and by expressing z directly in terms of u & v before differentiating.
b) evaluate ∂z/∂u and ∂z/∂v at the given (u,v)
z = tan^-1
(x/y) x = ucosv
y= usinv
(u,v) = (1.3, pi/6)
a) To express ∂z/∂u and ∂z/∂v as functions of u and v, we first need to express z directly in terms of u and v. We are given that:
z = tan^-1(x/y)
And that:
x = ucosv
y = usinv
Substituting these expressions for x and y into the equation for z, we get:
z = tan^-1((ucosv)/(usinv))
z = tan^-1(cotv)
Now we can use the chain rule to find ∂z/∂u and ∂z/∂v:
∂z/∂u = ∂z/∂cotv * ∂cotv/∂u
∂z/∂v = ∂z/∂cotv * ∂cotv/∂v
To find ∂cotv/∂u and ∂cotv/∂v, we use the quotient rule:
∂cotv/∂u = -cosv/u^2
∂cotv/∂v = -csc^2v
Substituting these into the chain rule expressions, we get:
∂z/∂u = (-cosv/u^2) * (1/(1+cot^2v))
∂z/∂v = (-csc^2v) * (1/(1+cot^2v))
Simplifying these expressions using trig identities, we get:
∂z/∂u = (-cosv/u^2) * (1/(1+(cosv/usinv)^2))
∂z/∂v = (-1/sinv^2) * (1/(1+(cosv/usinv)^2))
b) To evaluate ∂z/∂u and ∂z/∂v at (u,v) = (1.3, pi/6), we simply plug in these values into the expressions we derived in part (a):
∂z/∂u = (-cos(pi/6)/(1.3)^2) * (1/(1+(cos(pi/6)/(1.3*sin(pi/6)))^2))
∂z/∂v = (-1/sin(pi/6)^2) * (1/(1+(cos(pi/6)/(1.3*sin(pi/6)))^2))
Simplifying these expressions using trig functions, we get:
∂z/∂u = (-sqrt(3)/1.69^2) * (1/(1+(sqrt(3)/1.3)^2))
∂z/∂v = (-4) * (1/(1+(sqrt(3)/1.3)^2))
Plugging in the values and evaluating, we get:
∂z/∂u ≈ -0.5167
∂z/∂v ≈ -1.5045
To answer this question, we'll first express z directly in terms of u and v, and then apply the chain rule to find the partial derivatives ∂z/∂u and ∂z/∂v.
Given:
z = tan^(-1)(x/y)
x = u*cos(v)
y = u*sin(v)
First, let's express z in terms of u and v:
z = tan^(-1)((u*cos(v))/(u*sin(v)))
Now, we can simplify the expression:
z = tan^(-1)(cot(v))
Next, we'll find the partial derivatives using the chain rule:
a) ∂z/∂u:
Since z doesn't have a direct dependence on u, we have:
∂z/∂u = 0
b) ∂z/∂v:
∂z/∂v = -csc^2(v)
Now let's evaluate the partial derivatives at the given point (u,v) = (1.3, π/6):
∂z/∂u(1.3, π/6) = 0
∂z/∂v(1.3, π/6) = -csc^2(π/6) = -4
So, the partial derivatives at the given point are:
∂z/∂u = 0 and ∂z/∂v = -4.
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Lawrence bought his condominium for
$100,900. During the past 2 years, its
value increased 8%. What is the current
value of Lawrence's condominium?
Answer: $108,972
Step-by-step explanation:
To find the current value of Lawrence's condominium, we need to calculate the 8% increase in value over the past 2 years.
First, find the increase in value:
$100,900 * 0.08 = $8,072
Next, add this increase to the original price:
$100,900 + $8,072 = $108,972
So, the current value of Lawrence's condominium is $108,972.
Select allá transformations that Will map a pentágon onto itself
There are several transformations that can be applied to a pentagon in order to map it onto itself. One such transformation is a rotation of 72 degrees, which can be performed by rotating the pentagon about its center point by 72 degrees clockwise. This will result in the pentagon appearing exactly as it did before the rotation, but in a different orientation.
Another transformation that will map a pentagon onto itself is a reflection along one of its symmetry lines. A pentagon has five symmetry lines, which are lines that divide the shape into two congruent halves. Reflecting the pentagon along any of these lines will result in the same shape being produced, but in a mirror image orientation.
Finally, a translation can also be used to map a pentagon onto itself. This involves moving the pentagon a certain distance in a particular direction, such as shifting it 2 units to the right or 3 units upwards. As long as the distance and direction of the translation are such that the pentagon ends up exactly where it started, it will be a valid transformation.
Overall, there are several transformations that can be applied to a pentagon in order to map it onto itself, including rotations, reflections, and translations.
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Please answer all three question
1. To the nearest tenth how many miles is alshleys house from Bridget house
2. To the nearest tenth how many miles is Ashley’s house from carlys house
3. Whose house does Ashley live the closet to and by how many miles
Please answer
The nearest tenth how many miles is alshleys house from Bridget house is AB = √[(xB-xA)² + (yB-yA)²]
The nearest tenth how many miles is Ashley’s house from carlys house is AC = √[(xC-xA)² + (yC-yA)²]
The distances from Ashley's house to both Bridget's house and Carly's house, we can compare them and see which one is shorter.
To find the distance between Ashley's house and Bridget's house, we need to know the coordinates of both locations. Let's say Ashley's house is located at point A, and Bridget's house is located at point B. We can use the distance formula to find the distance between A and B:
distance AB = √[(xB-xA)² + (yB-yA)²]
Here, xA and yA represent the coordinates of Ashley's house, and xB and yB represent the coordinates of Bridget's house. The formula calculates the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates of the two points.
To find the distance between Ashley's house and Carly's house, we again need to know the coordinates of both locations. Let's say Ashley's house is located at point A, and Carly's house is located at point C. We can use the same distance formula as before:
distance AC = √[(xC-xA)² + (yC-yA)²]
Here, xC and yC represent the coordinates of Carly's house. Plug in the values and calculate the distance to the nearest tenth of a mile.
To determine whose house Ashley lives closest to, we need to calculate the distances from Ashley's house to both Bridget's house and Carly's house. Whichever house has the shorter distance will be the closer one.
To find the difference between the two distances, we can subtract the smaller distance from the larger distance.
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Find The Area Of This Shape.
Answer:
34.65 mi²
Step-by-step explanation:
Area of parallelogramam = b · h
b = 6.3 mi
h = 5.5 mi
Let's solve
6.3 · 5.5 = 34.65 mi²
So, the area of the shape is 34.65 mi²
Quadrilateral ABCD is dilated about the origin into quadrilateral EFGH so that point G is located at (16,8).
Which rule represents the dilation?
Select one:
(x, y) → (18x, 18y)
(x, y) → (x+8, y+4)
(x, y) → (12x, 12y)
(x, y) → (2x, 2y)
The dilation is (x, y) → (2x, 2y). So, the correct answer is D).
Let the coordinates of point C be (x, y). Then, the distance from the origin to point C is given by the distance formula
OC = √(x² + y²)
The corresponding side lengths are
CG = 16 - x
CD = √((x - 0)² + (y - 0)²)
The scale factor is the ratio of corresponding side lengths
CG/CD = 2
Therefore,
16 - x = 2*√(x² + y²)
Solving for y, we get
y = √(13x² - 64x + 256)
If we assume that point G corresponds to point C, then the center of dilation is the origin and the rule that represents the dilation is
(x, y) → (2x, 2y)
Therefore, the answer is
(x, y) → (2x, 2y)
So, the correct answer is D).
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--The given question is incomplete, the complete question is given
" Quadrilateral ABCD is dilated about the origin into quadrilateral EFGH so that point G is located at (16,8). scale factor is 2.
Which rule represents the dilation?
Select one
(x, y) → (18x, 18y)
(x, y) → (x+8, y+4)
(x, y) → (12x, 12y)
(x, y) → (2x, 2y) "--
help pls!
Use unit multipliers to convert 123 pounds per mile to ounces per centimeter.
There are 5,280 feet in 1 mile. There are 16 ounces in 1 pound. There are approximately 2.54 cm in 1 inch.
Enter your answer as a decimal rounded to the nearest hundredth. Just enter the number.
The conversion is given as follows:
123 pounds per mile = 0.01 ounces per cm.
How to obtain the conversion?The conversion is obtained applying the proportions in the context of the problem.
There are 16 ounces in 1 pound, hence the number of ounces in 123 pounds is given as follows:
123 x 16 = 1968 ounces.
There are 5,280 feet in 1 mile, 12 inches in one feet and 2.54 cm in one inch, hence the number of cm is given as follows:
5280 x 12 x 2.54 = 160934.4 cm.
Hence the rate is given as follows:
1968/160934.4 = 0.01 ounces per cm.
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12 16 10 find d surface area of d solid
Clare made $160 babysitting last summer. She put the money in a saving account that pays 3% interest per year. If Clare doesn't touch the money in her account, she can find the amount she'll have the next year by multiplying her current amount by 1.03.
Write an expression for the amount of money Clare would have after 30 years if she never withdraws money from the account.
Evaluating an exponential function A(x) = 160*(1.03)ˣ we can see that in 30 years she will have:
$388.36
How much money will eh have in 30 years?We know that the initial investment is 160, and the rate per year is 3%.
Then after x years, the value is given by the exponential function.
A(x) = 160*(1.03)ˣ
The amount of money in the account after 30 years is what we get if we evaluate the equation in x = 30, then we will get:
A(30) = 160*(1.03)³⁰
A(30) = 388.36
In 30 years she will have a total amount of 388.36 dollars.
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Chris bought 5 tacos and 2 burritos for $13. 25.
Brett bought 3 tacos and 2 burritos for $10. 75.
The price of one taco is $
The price of one burrito is $
Answer:
Let's start by assigning some variables to the unknowns:
Let's call the price of one taco "t".
Let's call the price of one burrito "b".
With these variables, we can write two equations based on the information given in the problem:
5t + 2b = 13.25 (equation 1)
3t + 2b = 10.75 (equation 2)
We now have two equations and two variables. We can use algebra to solve for t and b. One way to do this is to eliminate b by subtracting equation 2 from equation 1:
(5t + 2b) - (3t + 2b) = 13.25 - 10.75
Simplifying this equation, we get:
2t = 2.5
Dividing both sides by 2, we get:
t = 1.25
So the price of one taco is $1.25.
Now that we know the price of one taco, we can substitute this value into one of the equations to solve for b. Let's use equation 1:
5t + 2b = 13.25
Substituting t = 1.25, we get:
5(1.25) + 2b = 13.25
Simplifying this equation, we get:
6.25 + 2b = 13.25
Subtracting 6.25 from both sides, we get:
2b = 7
Dividing both sides by 2, we get:
b = 3.5
So the price of one burrito is $3.5.
Therefore, the price of one taco is $1.25 and the price of one burrito is $3.5.
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It is asking for the perimeter and area
The perimeter and area of the shape is 18cm² and 12cm respectively.
What is perimeter and area of shape?The perimeter of a shape is the total measurement of all the edges of a shape. Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
The perimeter of the shape = 4+4+5+5 = 8 +10
= 18cm.
The area of the shape is = b×h
the base = 4cm and height is 3cm
A = 4× 3
= 12cm²
therefore the perimeter and the area of the shape is 18cm² and 12cm² respectively.
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A binomial experiment has the given number of trials n and the given success probability p.
n=10, p=0. 2
(a) Determine the probability P (2 or fewer). Round the answer to at least three decimal places.
P(2 or fewer)
The probability P(2 or fewer) is 0.678.
To find the probability of 2 or fewer successes in a binomial experiment with 10 trials and a success probability of 0.2, we can use the binomial probability formula:
P(2 or fewer) = P(0) + P(1) + P(2)
where P(0), P(1), and P(2) represent the probabilities of getting 0, 1, or 2 successes, respectively.
P(0) = (10 choose 0) * 0.2^0 * 0.8^10 = 0.1074
P(1) = (10 choose 1) * 0.2^1 * 0.8^9 = 0.2684
P(2) = (10 choose 2) * 0.2^2 * 0.8^8 = 0.3020
Therefore,
P(2 or fewer) = 0.1074 + 0.2684 + 0.3020 = 0.6778
Rounded to at least three decimal places, the probability P(2 or fewer) is 0.678.
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Tony is playing a games there is 1/8 chance the spinner will land on red and 3/8 chance that the spinner will land on yellow what is the probabilty chance the the spinner will not land on red then land on red
The probability of the spinner not landing on red and then landing on red is 7/64.
What is the probability that none is red?
The probability chance that the spinner will not land on red then land on red is calculated as follows;
The probability of the spinner not landing on red is 1 - 1/8 = 7/8.
To find the probability that the spinner will not land on red and then land on red, we multiply the probabilities:
(7/8) x (1/8) = 7/64
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what is the length of the hypotenuse of the triangle when x=2? round your answer to the nearest tenth
Answer:
17.1
Step-by-step explanation:
Solve for f(-2).
f(x) = -3x + 3
4
f(-2) = [?]
Answer:
f(-2) = 9
Step-by-step explanation:
f(x) = -3x + 3 Solve for f(-2)
f(-2) = -3(-2) + 3
f(-2) = 6 + 3
f(-2) = 9
How did new leaders gain power in both Germany and Japan after World War I?John threw the Javelin 106 feet in his last track meet. The average throw was 130 ft. The standard deviation was 8 feet. How many standard deviations below the mean did John throw?
John threw the javelin 3 standard deviations below the mean
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
The z score shows by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
Given that John threw 106 feet. The average throw was 130 ft. The standard deviation was 8 feet. Hence:
z = (106 - 130) / 8
z = -3
John threw 3 standard deviations below the mean
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how long is the red ribbon if the blue ribbon is 10 inches?
Consider a population that grows according to the recursive rule Pn=Pn−1+50
, with initial population P0=30
To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.
We are given a population growth model with a recursive rule and an initial population. Let's break down the information and find the population at any given term n.
Recursive rule: Pₙ = Pₙ₋₁ + 50
Initial population: P₀ = 30
Now let's find the population at any term n, using the recursive rule:
Step 1: Determine the base case, which is the initial population.
P₀ = 30
Step 2: Apply the recursive rule to find the next few terms.
P₁ = P₀ + 50 = 30 + 50 = 80
P₂ = P₁ + 50 = 80 + 50 = 130
P₃ = P₂ + 50 = 130 + 50 = 180
Step 3: To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.
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what percentage of 2 hours is 48 minutes
Answer:
40%
Step-by-step explanation:
[tex] \frac{48}{120} \times 100 = 40[/tex]
Answer:
40%
Step-by-step explanation:
To find out what percentage of 2 hours is 48 minutes, we need to first convert both values to the same unit of time, such as minutes.
2 hours is equal to 120 minutes (2 x 60).
So, the fraction of 2 hours that is represented by 48 minutes is:
48/120
Simplifying this fraction by dividing both the numerator and denominator by 12, we get:
4/10
Multiplying the numerator and denominator by 10 to convert this fraction into a percentage, we get:
40%
Therefore, 48 minutes is 40% of 2 hours.
Tickets for the school basketball game cost $4 each. Spencer plans to
make a table relating the number of people (x) to the money made from
ticket sales (y).
What is the most appropriate domain for Spencer's table?
A.
all integers
B.
all rational numbers
C.
all real numbers
D
all whole numbers
The most appropriate domain for Spencer's table would be D. all whole numbers.
To explain this, let's first understand the terms involved. In this context, the domain refers to the set of possible input values (x) for the function, which in this case, represents the number of people attending the school basketball game.
Option A, all integers, includes negative numbers, which are not suitable as you cannot have a negative number of people. Option B, all rational numbers, comprises fractions, which are also not applicable because you cannot have a fraction of a person attending the game. Option C, all real numbers, consists of all numbers including irrational numbers like π, which are not relevant in this context as well.
Option D, all whole numbers, represents the most suitable domain as it includes all non-negative integers (0, 1, 2, 3, ...). This set accurately represents the possible number of people attending the game, since you can have zero or a whole number of people attending but not negative or fractional values.
Therefore, Spencer should use whole numbers as the domain for his table to relate the number of people (x) to the money made from ticket sales (y).
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Pls answer this asap
Answer:
(C) Neither
Step-by-step explanation:
You want to know if the function values in the table represent an even function, and odd function, or neither.
SymmetryAn Even function is symmetrical about the y-axis:
f(-x) = f(x)
An Odd function is symmetrical about the origin:
f(-x) = -f(x)
ApplicationThe attached graph of the given points shows the function has no symmetry at all.
The table represents neither an even nor odd function.
Answer:
Neither
Step-by-step explanation:
In an even function, f(x) = f(-x).
Look at x = 2 and x = -2.
f(2) = -4; f(-2) = 2
Since f(2) ≠ f(-2), the function is not even.
In an odd function, f(x) = -f(-x).
Look at f(2) and f(-2).
f(2) = -4; f(-2) = 2
Since f(2) ≠ -f(-2), the function is not odd.
Answer: C Neither
A football player is practicing making field goals from the 30-yard line. if the probability of his kicking a field goal is 0.75, what is the probability he will kick at least 12 field goals in the next 15 tries
This is a binomial probability problem, where the number of trials (n) is 15, the probability of success (p) is 0.75, and we want to find the probability of at least 12 successes.
We can use the binomial probability formula to calculate this:
P(X >= 12) = 1 - P(X < 12)
P(X < 12) = sum[k=0 to 11] (n choose k) * p^k * (1-p)^(n-k)
where n choose k is the binomial coefficient, which represents the number of ways to choose k items out of n.
Using a calculator or statistical software, we can calculate:
P(X < 12) = sum[k=0 to 11] (15 choose k) * 0.75^k * 0.25^(15-k) = 0.0278 (rounded to four decimal places)
Therefore,
P(X >= 12) = 1 - P(X < 12) = 1 - 0.0278 = 0.9722
So the probability that the football player will kick at least 12 field goals in the next 15 tries is approximately 0.9722, or about 97.22%
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The opposite of z is greater than 5 what are two possible options for z
Possible options for z could be:
1) z = -6
2) z = -7
These are two possible options for z that satisfy the given inequality.
Given that the opposite of z is greater than 5, we can write this as an inequality:
-z > 5
To find the possible options for z, we can follow these steps:
Step 1: Multiply both sides of the inequality by -1 to solve for z. Remember to flip the inequality sign when multiplying by a negative number:
z < -5
Step 2: Choose two values for z that satisfy the inequality z < -5.
Possible options for z could be:
1) z = -6
2) z = -7
These are two possible options for z that satisfy the given inequality.
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The diameter of a circle is 2 kilometers. What is the circle's circumference? d=2 km Use 3. 14 for . Kilometers?
The circumference of the circle is 6.28 kilometers if the diameter of the circle is 2 kilometers and assuming the value of π is 3.14 kilometers.
The diameter of the circle = 2 kilometers
The circumference of a circle is calculated by using the formula,
C = π *d
where,
C = circumference of a circle
d = diameter of the circle
π = Constant value = 3. 14 Km
Substituting the above-given values into the equation, we get:
C = π*d
C = 3.14 x 2 km
C = 6.28 km
Therefore, we can conclude that the circumference of the circle is 6.28 kilometers.
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Prove that if G is a cyclic group of order m and d | m, then G must have a subgroup of
order d
Since G is a cyclic group of order m, there exists an element g in G such that the subgroup generated by g contains all elements of G. We denote this subgroup by <g>. The order of <g> is equal to the order of g, which is a divisor of m. Hence, there exists an integer k such that m = kg.
Now, consider the element [tex]g^{(k/d)[/tex]. Since ([tex]g^k[/tex]) generates G and d is a divisor of k, ([tex]g^k/d[/tex]) is an element of <g>. Therefore, the subgroup generated by [tex]g^{(k/d)[/tex] is a subgroup of <g> with order d.
To show that this subgroup has order d, suppose that there exists an integer r such that [tex](g^{(k/d)})^r[/tex] = [tex]g^{(kr/d)[/tex] = e, where e is the identity element of G. This means that kr/d is an integer multiple of k, which implies that r is a multiple of d. Thus, the order of [tex]g^{(k/d)[/tex] is d, and the subgroup generated by [tex]g^{(k/d)[/tex] has order d.
Therefore, we have shown that if G is a cyclic group of order m and d | m, then G must have a subgroup of order d, which is generated by an element of the form [tex]g^{(k/d)[/tex], where g is a generator of G and m = kg.
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- (1 point) If ao = 2, aj = 4, and Ak+1 = 10ak-1 +9ak for all k > 1, use methods of linear algebra to determine the formula for ak. Ak = ak+1 ? What is lim kak
the formula for ak, we can set up a system of linear equations using the given values for ao, aj, and Ak+1.
Let x = ak-1 and y = ak. Then we have:
2 = a0 = x
4 = a1 = y
Ak+1 = 10ak-1 + 9ak
Substituting x and y, we get:
Ak+1 = 10(2) + 9(4) = 56
So we have the system of equations:
x = 2
y = 4
y = 10x + 9y
Rewriting the third equation, we get:
-10x + y = 0
Adding the first two equations, we get:
x + y = 6
Solving this system of equations, we get:
x = 2
y = 4
Therefore, ak = 4 for all k > 0.
To find lim kak, we can use the formula for ak:
lim kak = lim 4 = 4
So the limit of ak as k approaches infinity is 4.
To find the formula for a_k using linear algebra, we can first form a system of linear equations using the given recurrence relation:
a_(k+1) = 10a_(k-1) + 9a_k
Since we know a_0 = 2 and a_1 = 4, we can start by finding a_2:
a_2 = 10a_0 + 9a_1 = 10(2) + 9(4) = 20 + 36 = 56
Next, we can find a_3 using a_1 and a_2:
a_3 = 10a_1 + 9a_2 = 10(4) + 9(56) = 40 + 504 = 544
Now, we can represent this system of linear equations in matrix form:
[ [ 1 0 ] [ a_0 ] [ 2 ]
[ 0 1 ] * [ a_1 ] = [ 4 ]
[ 10 9 ] * [ a_2 ] = [ 56 ]
[ 10 9 ] * [ a_3 ] = [ 544 ] ]
We can then use methods of linear algebra such as Gaussian elimination, Cramer's rule, or matrix inversion to solve the system and find a_k.
However, this particular system does not provide a direct formula for a_k. Moreover, as the given information doesn't suggest a converging series, we cannot determine the limit as k approaches infinity (lim k→∞ a_k).
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Identify the name of the shape. prove with the explanation.
Assume base is 2.a b c
a = 5
b = 4
c= 0
Therefore, the equation for graph C is Y = a ^b + c
Y = 5 ^4 + 0
What is a graph?A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Graphs are a popular tool for graphically illuminating data relationships. A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.
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