what is the total amount you would have to pay back on a $4500 loan at 5% for 3 years?

The solution to the recurrence relation is \(\(T(n) = 1 + 5(n-1) = 5n - 4\)\).

To solve the given recurrence relation \(\(T(n) = T(n-1) + 5\)\) with the initial condition \(\(T(1) = 1\)\) using the substitution method, we can proceed as follows:

Step 1: Start with the assumption that the solution can be expressed as a function of \(\(n\)\), that is, \(\(T(n) = f(n)\)\).

Step 2: Substitute \(\(T(n-1)\) with \(f(n-1)\)\) in the recurrence relation:

\(\[f(n) = f(n-1) + 5.\]\)

Step 3: Repeat the substitution process until reaching the base case. We have:

\(\[f(n) = f(n-2) + 5 + 5 = f(n-2) + 10,\]\[f(n) = f(n-3) + 5 + 5 + 5 = f(n-3) + 15,\]\)

and so on.

Step 4: Continue this pattern until reaching \(\(T(1)\)\):

\(\[f(n) = f(n - (n-1)) + 5(n-1) = f(1) + 5(n-1).\]\)

Step 5: Substitute \(\(f(1)\)\) with the given initial condition \(\(T(1) = 1\)\):

\(\[f(n) = 1 + 5(n-1).\]\)

Therefore, the solution to the recurrence relation is \(\(T(n) = 1 + 5(n-1) = 5n - 4\)\).

To check the solution, we can substitute it back into the recurrence relation:

\(\[T(n) = T(n-1) + 5 = 5(n-1) - 4 + 5 = 5n - 9.\]\)

We can see that the solution satisfies the original recurrence relation.

Thus, \(\(T(n) = 5n - 4\)\) is the solution to the given recurrence relation, and it is confirmed by plugging it back into the recurrence relation.

For more questions on recurrence relation:

https://brainly.com/question/4082048

#SPJ8

Answer: There are no solutions.

Step-by-step explanation: So the way you do this is by subtracting 9p from both sides, which gets you:

8 = -7

Since 8 is not equal to -7, there is no solution to this equation.

Answer:

There is no answer

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

8+9p=9p−7

8+9p=9p+−7

9p+8=9p−7

Step 2: Subtract 9p from both sides.

9p+8−9p=9p−7−9p

8=−7

Step 3: Subtract 8 from both sides.

8−8=−7−8

0=−15

Answer:

There are no solutions.

Answer:

a

Step-by-step explanation:

Answer:

9/5 es mayor que 4/5 Realmente espero que esto te ayude

Answer:

This makes no sense

Step-by-step explanation:

The angle between the ropes is 53°.

We are given that a barge is being towed by two tugboats using ropes. The force vectors of the two tugboats are represented by F1 and F2. A vector is an entity that has both a magnitude and a direction. The vectors are F1 = 11000i + 5000j and F2 = 14500i + -8000j. We need to find the angle between the ropes. The best method is to find the dot product. Let the angle between the ropes be θ. We can say that cos(θ) = F1.F2/(|F1|*|F2|) = (11000*14500 + 5000*-8000)/[√[(11000)² + (5000)²] * √[(14500)² + (-8000)²]] = (11*14.5 + 5*-8)/[√[(11)² + (5)²] * √[(14.5)² + (-8)²]] = 119.5/[√146*√274.25] = 119.5/200.1 = 0.597. So, the value of θ is 53°.

To learn more about angles, visit :

https://brainly.com/question/28451077

#SPJ9

In this case the given expression when x=-7 and y=4 is:

The expressions that are equivalent to the expression y + y + y + 3z are 3y + 3z and 3(y + z)

From the question, we have the following parameters that can be used in our computation:

y + y + y + 3z

To start with, expressions that are equivalent are expressions that have equal values when evaluated

Using the above as a guide, we have the following:

Evaluate the like terms in y + y + y + 3z

So, we have the following representation

y + y + y + 3z = 3y + 3z

Factor out 3 from the expression

So, we have the following representation

y + y + y + 3z = 3(y + z)

Hence, the equivalent expressions of y + y + y + 3z are 3y + 3z and 3(y + z)

Read more about equivalent expressions at

https://brainly.com/question/15775046

#SPJ1

Answer:

Step 1: Put the numbers in order.

1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.

Step 2: Find the median.

1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.

Step 3: Place parentheses around the numbers above and below the median.

Not necessary statistically, but it makes Q1 and Q3 easier to spot.

(1, 2, 5, 6, 7), 9, (12, 15, 18, 19, 27).

Step 4: Find Q1 and Q3

Think of Q1 as a median in the lower half of the data and think of Q3 as a median for the upper half of data.

(1, 2, 5, 6, 7), 9, ( 12, 15, 18, 19, 27). Q1 = 5 and Q3 = 18.

Step 5: Subtract Q1 from Q3 to find the interquartile range.

18 – 5 = 13.

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

3*50=150. 150/5=30 pounds

An equation for this statement "The sum of seven times a number and 16 is 163," is 7n + 16 = 163.

The solution is 21.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The sum of seven times a number and 16 is 163," we can logically deduce the following algebraic equation;

7n + 16 = 163

7n = 163 - 16

7n = 147

n = 147/7

n = 21.

Read more on equation here: brainly.com/question/18912929

#SPJ4

Answer:

your answer is d i do beleive i hope i helped:) and also please mark me brainlest

Step-by-step explanation:

Answer:

D is wrong And so is A i just did the test

Step-by-step explanation:

I'm sure its either B or C

Answer:

Step-by-step explanation:

ChecK THE Picture attached for both the answers.

Hope it helps ❤️

Answer:

Step-by-step explanation:

hello : here is an solution

Answer:

Please take a picture and ask it again, it had failed to access it.

Answer:

  $11.40

Step-by-step explanation:

You want to know the mom's total spending if she bought ...

using a $0.50 discount coupon.

The total bill is the sum of the costs of the items, less the amount of the discount coupon:

  $4.25 +2×2.25 +3.15 -0.50 = $11.40

She spent $11.40 at the coffee shop.

<95141404393>

Answer:

11.40

Step-by-step explanation:

Your welcome!

Answer:

$ 6.52

Step-by-step explanation:

marked price =16.85

discount 20%=3.37

net payable .=.13.48

Amount paid==$ 20

payable .=====13.48

balance to receive=$ 6.52  

The required value of x is 7.

In the given statement is:

m/HGS = 3x + 5,

m/SGF=21x +3, and m/HGF = 176º.

and, to find the value of 'x'

The two angles, ∠HGS & ∠SGF, when combined, will result in ∠HGF

m ∠HGS = 3x + 5

m ∠SGF = 21x + 3

m ∠HGF = 176°

Set the equation:

m ∠SGF + m ∠HGS = m ∠HGF

Plug in the corresponding terms to the corresponding variables:

21x + 3 + 3x + 5 = 176°

24x + 8 = 176°

24x = 176° - 8

24x = 168°

x = 168°/24

x = 7

Hence, The required value of x is 7.

Learn more about Variables at:

https://brainly.com/question/24357656

#SPJ1

Answer:

F

Step-by-step explanation: c=0.10m+30

Plzz give me brainliest

To construct a 4x2 matrix D such that AD=I2, we can use the following matrix: D = [0 0 1 0; 0 0 0 1]. It is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C.

Constructing a matrix D such that AD=I2

Let A = -1 be a 1x1 matrix. We want to construct a 4x2 matrix D such that their product AD is equal to the 2x2 identity matrix I2. We can use the following matrix for D:

D = [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

To verify that AD=I2, we can compute the matrix product:

AD = [-1 0 0 0; 0 -1 0 0] [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

= [0 0 -1 0; 0 0 0 -1]

= -I2

Note that D only uses 1 and 0 as entries.

Now, it is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C. To see why, we can use the definition of matrix multiplication. Let C be a general 4x2 matrix:

C = [c11 c12; c21 c22; c31 c32; c41 c42]

Then, we can compute CA as:

CA = [-1 0; 0 -1] [c11 c12; c21 c22; c31 c32; c41 c42]

= [-c11 -c12; -c21 -c22; -c31 -c32; -c41 -c42]

Since CA is a 4x2 matrix and 4 is a scalar, it is not possible for CA to be equal to 4. Similarly, since the entries of C are only 0 or 1, it is not possible for CA to be equal to 14.

Therefore, there is no matrix C that satisfies the equations CA=4 or CA=14.

To know more about matrix here:

https://brainly.com/question/28180105#

#SPJ11

Answer:

B

Step-by-step explanation:

The 2 triangles are similar but not congruent

The probability of selecting the red marble on the fourth draw is 1/10.

We have,

The probability of selecting the red marble on the first draw is 1/10, as there is only one red marble among ten total marbles in the bag.

If the red marble is not selected on the first draw, it is set aside and not put back into the bag for the subsequent draws.

Thus, on the second draw, there are 9 marbles left in the bag, only one of which is red.

So the probability of selecting the red marble on the second draw is 1/9.

Similarly, if the red marble is not selected on the first and second draws, it is set aside and not put back into the bag for the subsequent draws.

Thus, on the third draw, there are 8 marbles left in the bag, only one of which is red. So the probability of selecting the red marble on the third draw is 1/8.

Finally, if the red marble is not selected on the first three draws, it is set aside and not put back into the bag for the subsequent draws.

Thus, on the fourth draw, there are 7 marbles left in the bag, only one of which is red.

So the probability of selecting the red marble on the fourth draw is 1/7.

Since each draw is independent, we can multiply the probabilities of each individual event to find the probability of selecting the red marble on the fourth draw:

P(selecting red on fourth draw) = P(not red on 1st, 2nd, and 3rd draws) x P(selecting red on 4th draw)

= (9/10) x (8/9) x (7/8) x (1/7)

= 1/10

Therefore,

The probability of selecting the red marble on the fourth draw is 1/10.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

learn more about binomial here:

https://brainly.com/question/31049218

#SPJ4

Answer: this is not a reasonable answer because 20 – 5 – 2 = 13

Step-by-step explanation:

   Let us see how much he will have actually have left.

       $20 - $5.10 - $1.90 = $13

➜ Our answer appears to be "this is not a reasonable answer because 20 – 5 – 2 = 13"

➜ This option rounded $5.10 to $5 and $1.90 to $2, which helps give a reasonable answer.

Answer:

x ≥ 1

Step-by-step explanation:

3 + 4x ≥ 7

3 - 3 + 4x ≥ 7 - 3

4x ≥ 4

4x / 4 ≥ 4 / 4

x ≥ 1

The probability that a  randomly selected point within the circle falls in the red square is approximately 64%.

To find the probability that a randomly selected point within the circle falls in the square, we need to compare the areas of the square and that of  the circle.

Area of the square is  8 x 8 = 64Units²

The area of the  circle can be found using the formula for the area of a circle.

A = πr²

⇒ π x (4 √2 )² = 32π units²

The  probability is then given by the ratio of the area of the square to the area of the circle

Probability = Area of  Square / Area of Circle

= 64 / (32 π)

= 2 / π

≈ 0.6366

Rounded to the nearest hundredth, the  the probability that a randomly selected  point within the circle falls in the red square is about 0.64 or 64%.

Learn more about probability at:

https://brainly.com/question/24756209

#SPJ1