The equation is separable. The solution to the initial value problem is y(t) = y(0) = -3.
A. The equation is separable. The solution to the initial value problem is y(t) = ___
To determine whether the given differential equation is separable, we need to check if it can be written in the form dy/dt = g(t) * h(y), where g(t) is a function of t only and h(y) is a function of y only.
In this case, the equation is dy/dt = 2ty + 1. We can rearrange it as:
dy = (2ty + 1) dt
Now, we can see that we have both y and t terms on the right-hand side, indicating that the equation is not yet separable.
Therefore, the correct choice is B. The equation is not separable.
Unfortunately, no solution can be provided for the initial value problem y(0) = -3 since the equation is not separable.
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Nationwide, 40% of college seniors say that if they could start their college education over, they would have selected a different major. A student researcher in the education department selected a random sample of 50 seniors at Harvard and asked them if they the same question.
a. Let X = number in 50 randomly selected seniors that would select a different major at Harvard.
Assuming the percent of seniors at Harvard that would select a different major is consistent with the national percent, would X have an approximately normal distribution? If so, what would the mean and standard deviation be?
b. If 12 of the 50 students sampled at Harvard said they would have selected a different major, would you think the percent that would have selected a different major is different at Harvard than the national average? Be sure to clearly explain your answer.
Given: Nationwide, 40% of college seniors say that if they could start their college education over, they would have selected a different major. A student researcher in the education department selected a random sample of 50 seniors at Harvard and asked them if they the same question.
a. Mean is 0.40 (40%) and Standard deviation = 0.0775.
b. we cannot conclude that the percent that would have selected a different major is different at Harvard than the national average.
a. Assuming the percent of seniors at Harvard that would select a different major is consistent with the national percentage, X (the number in 50 randomly selected seniors that would select a different major at Harvard) would have an approximately normal distribution.
The mean would be the same as the population mean, which is 0.40 (40%).
The standard deviation would be calculated using the formula given below:
Standard deviation = sqrt[(p(1-p))/n], Where, p = population proportion (0.40), n = sample size (50).
Standard deviation = sqrt[(0.40 x 0.60)/50]
Standard deviation ≈ 0.0775
b. To determine if the percent that would have selected a different major is different at Harvard than the national average, we need to perform a hypothesis test.
Hypotheses:H_0: p = 0.40 (The proportion of seniors at Harvard who would have selected a different major is the same as the national percentage.)
H_a: p ≠ 0.40 (The proportion of seniors at Harvard who would have selected a different major is different from the national percentage.)
Since the sample size (50) is greater than 30 and the population standard deviation is unknown, we can use the z-test to test the hypothesis.
The formula for the test statistic is given below:
z = (p - P)/sqrt[(P(1 - P))/n], Where, p = sample proportion, P = population proportion, n = sample size.
z = (12/50 - 0.40)/sqrt[(0.40 x 0.60)/50]
z ≈ -1.84
Using a significance level of α = 0.05 and a two-tailed test, the critical values of z are ±1.96.
Since the calculated z-value (-1.84) is less than the critical value (-1.96), we fail to reject the null hypothesis.
We do not have sufficient evidence to conclude that the proportion of seniors at Harvard who would have selected a different major is different from the national percentage.
Therefore, we cannot conclude that the percent that would have selected a different major is different at Harvard than the national average.
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help, i will give brainliest
Answer:
The answer is J
Step-by-step explanation:
If you start from Quinn's location (8,7), and move south 3 units, you get to (8,4). Then you move to the west 4 units and that gets you to (4,4).
hope this helped! :)
Help please
Lines m and n are parallel.
What is m<1?
A. 35°
B. 50°
C. 55°
D. 75
Answer: 55
Step-by-step explanation:
Since lines m and n are parallel, angle 55 would be the same for the measure of angle 1.
Part 1: Given cosine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,[infinity]). Part 2: Given θ = 495°, convert the value of θ to radians and find sec θ.
The required answer is sec θ = -√2.
Explanation:-
Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).
To determine three possible angles θ, the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.
Therefore, sec θ = 1/cos θ.To find cos 11π/4, the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.
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The point with coordinates $(6,-10)$ is the midpoint of the segment with one endpoint at $(8,0)$. Find the sum of the coordinates of the other endpoint.
Answer:
[tex](4,-20)[/tex]
Step-by-step explanation:
Let [tex]P(x,y),\,Q(u,v)[/tex] be two points then midpoint of [tex]PQ[/tex] is given by [tex](\frac{x+u}{2},\frac{y+v}{2})[/tex]
Put midpoint as [tex](6,-10)[/tex] and [tex](u,v)=(8,0)[/tex]
Therefore,
[tex](\frac{x+u}{2},\frac{y+v}{2})=(6,-10)\\\\(\frac{x+8}{2},\frac{y+0}{2})=(6,-10)\\\\\frac{x+8}{2}=6,\,\frac{y}{2}=-10\\\\x+8=12,\,y=-20\\x=12-8,\,y=-20\\x=4,\,y=-20[/tex]
So, the other point is [tex](4,-20)[/tex]
y=-3x + 4
y = 3x - 2
What solution does this system have? How do you
know? Justify (explain).
Answer:
(1,1)
Step-by-step explanation:
Since both the equations equal y, we can replace one of them with y.
y=-3x + 4
3x - 2 = -3x + 4
Add 3x to both sides.
6x - 2 = 4
Add 2 to both sides of the equation.
6x = 6
x = 1
Now that we know what x is, we can plug that value into one of the original equations.
y = 3x -2
= 3(1) - 2
= 3 - 2
= 1
Consider the system of equations 2x + 10y + 42 -1 4x + 18y + 10z 0 (a) If A is the coefficient matrix, find A-1. (b) Solve the system using A-1. (c) What does your solution indicate about the intersection of the three planes?
(a) The inverse matrix A⁻¹ is:
| -9/2 5/2 |
| 1 -1 |
(b) The solution to the system is x = -9/2 and y = 1. z is undetermined.
(c) The solution indicates that the three planes represented by the system of equations intersect at a single point and the intersection occurs along a line in the z-direction.
(a) The coefficient matrix, A, is given by:
A = | 2 10 42 |
| 4 18 10 |
We can use matrix inversion. A matrix is invertible if its determinant is non-zero. Let's calculate the determinant of matrix A:
det(A) = (2 * 18) - (10 * 4) = 36 - 40 = -4
Since the determinant is non-zero (-4 ≠ 0), the matrix A is invertible. Now, we can find the inverse of A:
A⁻¹ = (1/det(A)) * adj(A)
Where adj(A) denotes the adjugate of matrix A. To calculate the adjugate, we need to find the cofactor matrix of A and then take its transpose:
Cofactor matrix of A:
| 18 -4 |
| -10 2 |
Transpose of the cofactor matrix:
| 18 -10 |
| -4 2 |
Now, divide the transpose by the determinant:
A⁻¹ = (1/-4) * | 18 -10 |
| -4 2 |
Simplifying:
A⁻¹ = | -9/2 5/2 |
| 1 -1 |
Therefore, the inverse matrix A⁻¹ is:
| -9/2 5/2 |
| 1 -1 |
(b) We have the equation AX = B, where X is the column vector of variables (x, y, z), A is the coefficient matrix, and B is the column vector of constants.
The coefficient matrix A is:
A = | 2 10 42 |
| 4 18 10 |
The column vector B is:
B = | 1 |
| 0 |
Now, we can solve for X using A-1:
X = A⁻¹ * B
Substituting the values:
X = | -9/2 5/2 | * | 1 |
| 1 -1 | | 0 |
Multiplying the matrices:
X = | (-9/2 * 1) + (5/2 * 0) |
| (1 * 1) + (-1 * 0) |
Simplifying:
X = | -9/2 |
| 1 |
Therefore, the solution to the system is x = -9/2 and y = 1. The value of z is not determined from this calculation.
(c) x = -9/2 and y = 1 indicates that the three planes represented by the system of equations intersect at a single point. The value of z is not determined, which means that the intersection occurs along a line in the z-direction.
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The area of a circle is 4π in². What is the circumference, in inches? Express your answer in terms of π.
Answer:
C = 4π in
Step-by-step explanation:
We require to find the radius r of the circle
Given the area is 4π , then
πr² = 4π ( divide both sides by π )
r² = 4 ( take the square root of both sides )
r = [tex]\sqrt{4}[/tex] = 2
Then
C = 2πr = 2π × 2 = 4π inches
Answer:
4π in
Step-by-step explanation:
The formula for area is πr². We will work backwards from 4π. First, I will do √4 so I can find r.
√4 = 2
Now, I know that r = 2. Next, I will substitute r into the circumference formula which is 2πr.
2π(2) - I know r is 2 from my previous set.
Now, I will simplify.
2 · 2 π = 4π
Since the question is asking in terms of π, I will not simplify all the way, and leave pi as is.
9. (10 points) Find the inverse Laplace transform of 232 +7s+14 (32+2x+10) (5+1)
8. (10 points) Find the Laplace transform of f(t) = t- cos(3t) +e7+(t - 1)2.
The Laplace transform of f(t) = t - cos(3t) + [tex]e^{7t}[/tex]+ (t - 1)² is:
L{f(t)} = (1 - 2/s + 1/s²) - (s/(s² + 9)) + 1/(s - 7) + 2/s³
To find the inverse Laplace transform of the expression 232 + 7s + 14 (32 + 2x + 10) (5 + 1), we need to break it down into simpler terms and apply the inverse Laplace transform individually.
Given expression: 232 + 7s + 14 (32 + 2x + 10) (5 + 1)
Let's simplify the expression first:
232 + 7s + 14 (32 + 2x + 10) (5 + 1) = 232 + 7s + 14 ×42× 6
Simplifying further:
232 + 7s + 3528
Now we have a simple expression. To find the inverse Laplace transform, we can use the linearity property of the Laplace transform.
Inverse Laplace transform of 232 is 232 × δ(t), where δ(t) is the Dirac delta function.
Inverse Laplace transform of 7s is 7 δ'(t), where δ'(t) is the derivative of the Dirac delta function.
The inverse Laplace transform of a constant times the Dirac delta function is given by multiplying the constant with the shifted unit step function.
Inverse Laplace transform of 14 ×3528 is 14× 3528 × u(t), where u(t) is the unit step function.
Therefore, the inverse Laplace transform of the given expression is:
Inverse Laplace transform of (232 + 7s + 14 (32 + 2x + 10) (5 + 1)) = 232 ×δ(t) + 7 δ'(t) + 14×3528× u(t)
To find the Laplace transform of f(t) = t - cos(3t) + [tex]e^{7t}[/tex] + (t - 1)², we will apply the properties of Laplace transforms to each term individually.
Laplace transform of t:
The Laplace transform of t, denoted as L{t}, is given by 1/s^2.
Laplace transform of cos(3t):
The Laplace transform of cos(3t), denoted as L{cos(3t)}, is given by s/(s²+ 9).
Laplace transform of [tex]e^{7t}[/tex]:
The Laplace transform of [tex]e^{7t}[/tex], denoted as L{[tex]e^{7t}[/tex]}, is given by 1/(s - 7).
Laplace transform of (t - 1)²:
We can expand (t - 1)²to t² - 2t + 1 and then apply the linearity property of Laplace transforms.
Laplace transform of t²:
The Laplace transform of t², denoted as L{t²}, is given by 2/s³.
Laplace transform of 2t:
The Laplace transform of 2t, denoted as L{2t}, is given by 2/s².
Laplace transform of 1:
The Laplace transform of 1, denoted as L{1}, is given by 1/s.
Using the linearity property of Laplace transforms, we can add the transforms of each term.
Laplace transform of f(t):
L{t} - L{cos(3t)} + L{[tex]e^{7t}[/tex]} + L{(t - 1)²}
= 1/s² - s/(s² + 9) + 1/(s - 7) + 2/s³ - 2/s² + 1/s
= (1 - 2/s + 1/s²) - (s/(s² + 9)) + 1/(s - 7) + 2/s³
Therefore, the Laplace transform of f(t) = t - cos(3t) + [tex]e^{7t}[/tex]+ (t - 1)² is:
L{f(t)} = (1 - 2/s + 1/s²) - (s/(s² + 9)) + 1/(s - 7) + 2/s³
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PLS HELP WITH THIS ONE if a radius of a cake is 13 and the ribbon of the cake is 36 cm will the ribbon be long enough to go around the edge of the cake?
Answer:
No, the ribbon would not be long enough to go around the edge of the cake.
Circumference ≈ 81.7 cm
Step-by-step explanation:
1) Calculate the circumference of the cake
Circumference - the length around a circle
[tex]C=2\pi r[/tex] where r is the radius
Plug 13 in as the radius
[tex]C=2\pi (13)\\C=26\pi\\C= 81.7[/tex]
Therefore, the circumference of the cake is approximately 81.7 cm.
Because the ribbon is only 36 cm long, it would not be enough to go around the edge of the cake.
I hope this helps!
Anyone help pls? No links! :)
Answer:
6. D
7. F
8.A
9. B
10 C
13.Question- Write an expression using division and subtraction with a difference of 3.
answer- (12 divide 3) -1
Twelve divided by three is four. Four minus 1 is three.
12. Question- Write an expression using multiplication and addition with a sum of 16.
answer- There are many answers for this and this is one of them:
Y=4(3+1)
Y=16
or
Y=2(6+2)
Y=16
11. Question- Sam bought two CDs for $13 each. Sales tax for both CDs was $3. Write an expression to show how much Sam paid in all.
answer- Expression- (13*2)(3*2)=$32
This is the answer because Sam bought two CD's for 13, 13*2, and the sales tax was $ 3, so 3*2=6
Andrea and Tim are picking apples. Andrea picks 4 à pounds of apples. Tim picks
33 pounds of apples. How many total pounds of apples did Andrea and Tim
pick?
Answer:
37 pounds of apples.
Step-by-step explanation:
you add together the amount of apples that both people have gathered, which in this case would be 33+4 which makes 37, so your answer would be 37 apples.
Select the correct answer. Two art museums are hosting new long-term exhibits. The number of daily visitors attending each exhibit is modeled by functions v and s, where n is the number of days since the exhibits opened. Visual Arts Exhibit Sculpture Exhibit 10 50 100 120 200 210 154 147 145 143 Which statement accurately describes this situation? A. As the number of days increases, the number of daily visitors at both exhibits decreases to zero. B. As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to a higher amount than the number of daily visitors at the sculpture exhibit. C. As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to a lower amount than the number of daily visitors at the sculpture exhibit. D. As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to the same amount as the number of daily visitors at the sculpture exhibit.
Answer:
the answer is C
Step-by-step explanation:
As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to a lower amount than the number of daily visitors at the sculpture exhibit.
As the number of days increases, the number of daily visitors at the visual arts exhibit levels off to a lower amount than the number of daily visitors at the sculpture exhibit.
The correct option is C.
A function is a law that relates a dependent and an independent variable.
The function representing the Visual Arts Exhibit is
V(n) = (800/x) +120
V(10) = 80+120 = 200
V( 50) = 16+120 = 136
V(100) = 8 +120 = 128
V(120) = 6.67 + 120 = 128.67
V(200) = 4 +120 = 124
The number of visitors in the Visual Arts Exhibit is decreasing with increasing number of days.
Therefore correct option is C .
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HELP WILL MARK BRAINLIEST
Answer:
The answer is a...............
Find the area of the rectangle.
Answer:
Step-by-step explanation:
the area of the rectangle is : -7y² ( -2y^4+y²-1)
14y^6-7y^4+7y² unit
GET BRAINLESTTTTTT !!
A bag of marbles had 24 white marbles and the rest were blue. For a game, 5/6 of the white marbles were chosen, and 25 of the blue marbles were also chosen.
Use this information to answer the questions below.
If not enough information is given to answer a question, click on "Not enough information."
(a) How many of the bag's white marbles were not chosen?
(b) How many of the bag's white marbles were chosen?
(c) How many blue marbles were in the bag before the game?
Answer:
Step-by-step explanation:
We know that there are 24 white marbles in the starting.
a. How many were not chosen. => 1/6 of the white marbles.
1/6 * 24 = 4 marbles were not chosen.
b. 24 - 4 = 20 marbles were chosen
c. Not enough Info
Answer:
4,20,not enough info
Step-by-step explanation:
How can she might choose a random sample of five students from her class of 35 students?
Answer:
who?
Step-by-step explanation:
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!
Answer:
1. D
2. B
3. C
4. A
Step-by-step explanation:
just know when the sentence says "each" or "per" next to a number, there need to be an x next to it.
In other words, I kinda just winged it :P
Zeke bought 10 donuts. There were d donuts in each box. Write an expression that shows how many boxes of donuts Zeke bought.
Answer:
10/d
Step-by-step explanation:
chfhnclfsiojjcllkn
Janet's ice cream shop offers a child-size cone
with a single scoop of ice cream. Assume the
scoop of ice cream is a sphere with a volume
of 367 cubic centimeters. Find the diameter of the scoop?
Answer:
turtle biscuit believes in you
The sweater was normally $50. It was on sale for $12 off. What was the percent of discount?
Answer:
The discount was 24%.
Step-by-step explanation:
24% of 50 is 12.
Find the indicated critical z value. Find the value of z a/2 that corresponds to a confidence level of 85%. a/2 Answer:
The critical z value for a confidence level of 85% is approximately 1.44.
To understand this better, let's delve into the concept of confidence level. A confidence level is a measure of the uncertainty or margin of error associated with an estimation. In this case, we are given a confidence level of 85%, which means that we want to be 85% confident that the true population parameter falls within a specific range.
To find the critical z value, we need to determine the z value that leaves a certain percentage in the tails of the standard normal distribution. Since the confidence level is 85%, we divide this value by 2 to get a/2, which is 0.85/2 = 0.425. This value corresponds to the area under the curve in one tail of the distribution.
Using a standard normal distribution table or a statistical software, we can find the z value that corresponds to a cumulative probability of 0.425. The closest z value to this probability is approximately 1.44. Therefore, the critical z value for a confidence level of 85% is approximately 1.44.
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the same ice cream shop is running a sale on cylindrical shaped tubs of ice cream. The cylinder has a radius of 4.5 cm and a height of 18 cm. Find the volume of a tub of ice cream
Answer:
you got this
Step-by-step explanation:
I believe in you
Consider following sample: 41, 37, 48, 32, 43, 21, 29, 22, 40, 28, 22, 29, 38, 23, 24
The data points are independentely sampled from a unifrom distribution with the density function f(x) = 1/a, where 0 <= x <= a. Use the method of moments to estimate a. Use two digits after the decimal points.
The estimated value of "a" using the method of moments is 48.00.
The method of moments is a technique used to estimate the parameters of a probability distribution by equating the sample moments to their theoretical counterparts. In this case, we'll equate the sample mean to the theoretical mean of the uniform distribution.
The theoretical mean of a uniform distribution with density function f(x) = 1/a is given by (a + 0) / 2 = a / 2.
To estimate "a," we'll equate the sample mean to a / 2 and solve for "a":
Sample mean = (41 + 37 + 48 + 32 + 43 + 21 + 29 + 22 + 40 + 28 + 22 + 29 + 38 + 23 + 24) / 15
= 34.13 (rounded to two decimal places)
Setting this equal to a / 2, we have:
34.13 = a / 2
Solving for "a," we multiply both sides by 2:
a = 2 * 34.13
≈ 68.26
Rounding "a" to two decimal places:
a ≈ 68.26 ≈ 68.00
Using the method of moments, the estimated value of "a" is approximately 68.00. This suggests that the data points were sampled from a uniform distribution with a maximum value of around 68.
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Suppose you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you will receive $2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads. Continue in this fashion for a total of 10 flips of the coin, after which you receive nothing if it comes up tails. What is the mathematical expectation for this game?
Answer:
5
Step-by-step explanation:
The winnings are in G.P. : 1, 2, 4, ..... till 10 toss.
[tex]$a_n = 1 \times 2^{n-1}\ \ \ \forall \ n = 1,2,3,4,....,10$[/tex]
[tex]$a_n$[/tex] denotes the winnings on the [tex]$n^{th}$[/tex] toss.
The probability of earning amount [tex]$a_n$[/tex] on the [tex]$n^{th}$[/tex] toss is = [tex]$\left(\frac{1}{2}\right)^n$[/tex]
∴ [tex]$E(X) = \sum_{n=1}^{10} \ a_n \times \left(\frac{1}{2}\right)^n $[/tex]
[tex]$=\sum_{n=1}^{10} \ 1 \times \frac{2^{n-1}}{2^n} $[/tex]
[tex]$=\sum_{n=1}^{10} \ \frac{1}{2}$[/tex]
Sum of the 1st n terms of the A.P. is :
[tex]$=\frac{n}{2}[2a+(n-1)d] $[/tex]
[tex]$=\frac{10}{2}[2\times \frac{1}{2}+(10-1)\times 0] $[/tex]
= 5
Therefore, E(X) = 5
Hence the expected value of the game is 5
If water flows through the pipe at a rate of 2L per seconds. How much water will pass through the pipe in 1/2hour
Answer:
3600 Liters
Step-by-step explanation:
The given rate is 2L and we have to find how much water will flow in 1/2 hours at the same rate
1/2 hour is the same thing as 30 mins
multiply by 60 to convert minutes to seconds
[tex]3omin * \frac{60sec}{1min} = 1800 s[/tex]
since the rate is 2L per second we multiply 1800 by 2 and get 3600 Liters
Please help me with the question please ASAP ASAP please please ASAP please please help
* It’s NOT 24 if you get 24
Answer:
The tree is 8 foot long
hope this helps
good day mate
Answer:
8
Step-by-step explanation:
12:6 = x:4
2:1 = x:4
x=8
Please help me finish this i will give brainlest :) to the first person.
Answer: 8
Step-by-step explanation:
64 ÷[4* 27 (-5^2
-5 times -5 =25
27-25=2
4*2=8
64 divided by 8= 8
8 is your answer
A textbook store sold a combined total of 471 math and sociology textbooks in a week. The number of sociology textbooks sold was 63 less than the number of math textbooks sold. How many textbooks of each type were sold?
Answer:
The math books are 267The sociology books are 204Step-by-step explanation:
The steps are in the photo above
I hope that is useful for you :)
Please answer with explanation
a: 550-n×55
Step-by-step explanation:
because she withdraws every week 55 then the equation is that
Answer:
a. A = 550 - (n55)b. $165.00Explanation:
a. Amount of remaining dollars = $550 (the initial amount) - (numbers of weeks times $55 that she withdraws weekly)so the equation is: A = 550 - (n55)
b. using the equation in (a) we can determine the amount of money in Shirley's account after 7 weeks.A = 550 - (7×55)
A = 550 - 385
A = $165.00