A person places $3090 in an investment account earning an annual rate of 3%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 11 years.

The notation of the limit as a definite integral is given as follows:

[tex]\lim_{n \rightarrow \infty} \sum_{k = 1}^{n} \sqrt{k} \times n^{-\frac{3}{2}} = \int_0^{n^{-\frac{1}{2}}} \sqrt{x} dx[/tex]

The limit for this problem is defined as follows:

[tex]\lim_{n \rightarrow \infty} \sum_{k = 1}^{n} \sqrt{k} \times n^{-\frac{3}{2}}[/tex]

This is a limit of a Riemann sum, hence it can be written as a definite integral according to the rule presented as follows:

[tex]\int_a^b f(x) dx = \lim_{n \rightarrow \infty} \sum_{i = 1}^{n} f(a + \Delta_x i) \Delta_x[/tex]

As the second term is only a factor of n, the Delta is given as follows:

[tex]\Delta_x = n^{-\frac{3}{2}}[/tex]

As the a term does not appear in the function, the value of the coefficient a is given as follows:

a = 0.

The parent function dependent on k is given as follows:

[tex]f(x) = \sqrt{x}[/tex]

The parameter b is obtained as follows:

[tex]\Delta_x = \frac{b - a}{n}[/tex]

[tex]n^{-\frac{3}{2}} = \frac{b}{n}[/tex]

[tex]b = n^{-\frac{1}{2}}[/tex]

(the parameter n is not given).

Hence the definite integral is obtained as follows:

[tex]\int_0^{n^{-\frac{1}{2}}} \sqrt{x} dx[/tex]

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Answer: 10

Step-by-step explanation:

it says round to nearest 10 your answer was 9.8 so round to 10.

hope this helps :)

Answer:

Step-by-step explanation:

Identify the input values. Identify the output values. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

There are infinite many triangles that can be formed with the angle measures 20, 100, and 60 degrees

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

Angles = 20, 100, and 60 degrees

The above parameters are angles

When only angles are given, the triangle can have as many side lengths as possible

This means that there are infinite many triangles

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Answer:

u=37

Step-by-step explanation:

u+41= u+4 + u (sum of 2 interior angles is equal to exterior angle)

u+41= 2u+4

2u-u= 41-4

u=37

Answer:

true

Step-by-step explanation:

Answer:

Step-by-step explanation:

the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14.

Answer: 9.85 inches

Step-by-step explanation:

Each point on the graph represents the total rainfall in one month in this desert. For instance, the 2 points on top of 1.0 inches indicates that there were two months in the year where rainfall was 1.0 inches.

The total rainfall in this desert was therefore:

= 0.4 + 0.5 + 0.5+ 0.6 + 0.85 + 0.85 + 0.95 + 1.0 + 1.0 + 1.05 + 1.05 + 1.1

= 9.85 inches

Answer:

77

Step-by-step explanation:

solution

Perimeter of a rectangle (P) = 36 m

length (l) = (x+1) m

breadth (b) = (x+5) m

Area (A)= ?

We know that ;

P = 2(l+b)

or,36 = 2(x+1+x+5)

or,36 = 2 (2x+6)

or, 18 = 2x+6

or,18 - 6 = 2x

or, 12 = 2x

x = 6

length (l) = (x+1) = 6+1 = 7 m

breadth (b) = (x+5) = 6+5 = 11 m

Now;

Area (A) = l × b

= 7 × 11

= 77 square m

Answer:

77 m^2.

Step-by-step explanation:

Perimeter = 2 * (length + breadth)

36 = 2(x + 1 + x + 5)

36 = 2(2x + 6)

36 = 4x + 12

4x = 24

x = 6

So  breadth =  6 +1 = 7 and

length = 6 + 5 = 11 m.

Area = length * breadth = 7 * 11

= 77 m^2

Answer:1 0 (

Answer:

12870 ways

Step-by-step explanation:

10c2*13c3

10!/(10-2)!2! *13!/(13-3)!3!

[(10*9*8!)/8!*2*1] *[(13*12*11*10!)/10!*3*2*1]

45*286

12870 ways

Answer:

12,983.04

Step-by-step explanation:

[tex]1)\ A_1 = R^2 * Pi = (\frac{56}{2})^2 * 3.14 = 28^2 * 3.14 = 784 * 3.14 = 2,461.76\\[/tex]

[tex]2)\ 2,461.76 * 4 = 9,847.04\ (There\ are\ four\ semi\ circles)[/tex]

[tex]3)\ A_2 = 56^2 = 3,136[/tex]

[tex]4)\ A = A_1 + A_2 = 3136 + 9,847.04 = 12,983.04[/tex]

Answer:

Step-by-step explanation:

x²-8x+16+y²+2y+1=16+1-13
(x-4)²+(y+1)²=2²

general form of a circle's equation is
(x-h)^2 + (y-k)^2 = r^2
Where (h,k) is the center and r= radius
By comparing with A,
(4,-1) is center and radius= 2.

The center of the circle is (-4,2) and the radius is 2

The equation is given as:

x^2 + y^2 - 8x + 2y + 13 = 0

Rewrite as:

x^2 - 8x + y^2  + 2y + 13 = 0

Subtract 12 from both sides

x^2 - 8x + y^2  + 2y = -13

Group each variable

[x^2 - 8x] + [y^2  + 2y] = -13

-------------------------------------------------------------------

Take the coefficient of x and y

-8 and 2

Divide by 2

-4 and 1

Square both numbers

16 and 1

-------------------------------------------------------------------

Next, we add 16 and 1 to both sides of the equation

[x^2 - 8x + 16] + [y^2  + 2y + 1] = -13 + 16 + 1

Express as perfect squares and evaluate the sum

(x - 4)^2 + (y + 1)^2 = 4

Express 4 as 2^2

(x - 4)^2 + (y + 1)^2 = 2^2

A circle is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where:

Center = (a,b)

Radius = r

This means that the center of the circle is (-4,2) and the radius is 2

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Answer:

3.2 mph

Step-by-step explanation:

If it takes her 3 hours to walk 9.6 miles, we need to divide 9.6 by 3.

To do so, we can remove the decimal point in 9.6, to give us 96.

Then, we can divide 96 by 3 to get 32.

Add the decimal back to 32.

Doing so would give us 3.2, and our answer.

We can check this answer by multiplying 3.2 by 3, which gives us 9.6, telling us our answer is correct.

Answer:

Discrete

Step-by-step explanation:

Discrete means it has ends, and continuous means it continues on forever.

Answer:

I'm pretty sure the answer is A

Answer:

Answer is A

Step-by-step explanation:

B- The area is LxW meaning it is 3x9= 27 sq cm

C- Area LxW meaning 4x8= 32.

A- I only see 6 but this would mean that the width is 7. 7x6= 42 sq cm.

There you go: Formula is : LxW or multiplying the two numbers.< Hope it helps!

Answer:

the answer would be 30 for positive and -30 for negative

The effect that a decrease in the price of milk and input to ice cream would have on the market for ice cream is that there will be more production and demand in the market.

This is referred to as a place where buyers and sellers can meet to facilitate the exchange or transaction of goods and services.

A decrease in the price of milk and input to ice cream means that production costs would fall, which will cause the suppliers to produce more thereby shifting the supply curve to the right with the demand for the goods being increased which is therefore the effect on the market.

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Answer:

a c

Step-by-step explanation:

Answer:

graph should show an open circle on -2 with shading to the right

Step-by-step explanation:

-6n + 5 < 11

-6n < 6

n > -1

solutions consist of all number greater than -1

Answer: 28%

Step-by-step explanation: First, we need to find how much she runs in total on Tuesday and Wednesday. So, we add 3 + 4 to get 7. With that, we need to determine how much 7 is from 25. So, it'd look like this:

7 * 100 / 25

700 / 25

=28

Therefore, she's done 28% of her goal (within the 2 days) I hope this helped!

Answer:

I think the other person who answered the question is right

Step-by-step explanation:

Answer:

40 + 5 = 45

45 ÷ 9 = 5

Therefore, he will have 5 boxes of rocks.

==========================================================

Explanation:

Add up the percentage values:

25+20+6+6+6 = 63

This means 63% of the trip was driven by anyone but Dan. That must mean 100-63 = 37% of the trip is how much Dan drove.

Apply this percentage to the 20 hour duration

37% of 20 = 0.37*20 = 7.4 hours represents how long Dan drove.

extra notes:

All the table show the linear relationship, but none of the table show the proportional relationship.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

A). x → y

0 → 3

3 → 6

6 → 9

To show the linear relationship:

We have to find the constant first difference.

That means,

6-3 = 3

And 9 - 6 = 3

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/3 = 0,

3/6 = 1/2,

6/9 = 2/3.

The values of this table do not show the proportional relationship.

B). x → y

0 → 4

2 → 6

4 → 8

To show the linear relationship:

We have to find the constant first difference.

That means,

6-4 = 2

And 8 - 6 = 2

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/4 = 4,

2/6 = 1/3,

4/8 = 1/2.

The values of this table do not show the proportional relationship.

C). x → y

0 → 0

6 → 3

12 → 6

To show the linear relationship:

We have to find the constant first difference.

That means,

3-0 = 3

And 6 - 3 = 3

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/0 = undefined,

6/3 = 2,

12/6 = 2.

The values of this table do not show the proportional relationship.

D). x → y

0 → 3

5 → 5

10 → 7

To show the linear relationship:

We have to find the constant first difference.

That means,

5 - 3 = 2

And 7 - 5= 2

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/3 = 0,

5/5 = 1,

10/7 = 10/7.

The values of this table do not show the proportional relationship.

Therefore, none of the table show the proportional relationship.

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Answer:

Step-by-step explanation:

Its A

Answer:

c=200+0.4Yd find determine equlibirum level investment is =400

Answer:im pretty sure its D

Step-by-step explanation:it goes through the origin