If $2,500 is invested at 12% annual interest, which is compounded continuously, what is the account balance after 3 years, assuming no additional deposits or withdrawals are made?

Answer:

The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.

The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.

So, the impulse on the ball is -80 kg m/s.

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

The cuboid in question has a surface area of 202 square units.

We must sum together the areas of all six faces to determine a cuboid's surface area.

The dimensions of the given cuboid are:

length (l) = 9 units

width (w) = 5 units

height (h) = 4 units

The area of each face is given by:

Top and bottom faces:\(lw = 9 * 5 = 45\) square units each

Front and back faces: \(lh = 9 *4 = 36\) square units each

Left and right faces: \(wh = 5 * 4 = 20\) square units each

Therefore, the total surface area of the cuboid is:

\(2(lw + lh + wh) = 2(45 + 36 + 20)\\ = 2(101) \\= 202 \ square \ units\)

Hence, the surface area of the given cuboid is 202 square units.

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Based on the sample response given, the statements included in the explanation on the horizontal line test are:

The horizontal line test is used to not only find out if a graph has an inverse function, but also if that inverse is also a function itself.

To pass the horizontal line test, the function has to be one-to-one which means that a horizontal line can intersect the graphed function at one point in all places. If this happens, then there is an inverse and the inverse itself is a function.

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Answer:

$97.50

Step-by-step explanation:

30%/100%×$75=$22.50

$22.50+$75=$97.50

Answer:

24+21

Step-by-step explanation:

24+21

Hope you got your answer

Answer: 4(20+9)+4(6) thats the first one

4(20)+4(9)+4( 6) thats the second one

80+36+24=140 that is the third

Step-by-step explanation:

Answer:

4(20+9)+4(6)

4(20)+4(9)+4( 6)

Step-by-step explanation:

The value of f-¹(x) for the function f(x) = (x + 2)/x is y = 2/(x-1).

The inverse of a function f is denoted by f-¹ and it exists only when f is both one-one and onto function. An inverse function in mathematics is function which "reverses" the another function.

For example, If function f which is applied to input a gives result b and then applying inverse of the function g to b, it gives result a and vice versa.

It can be written as:

f(a) = b if and only if g(b) = a or, f⁻¹ (b) = a

In order to calculate the inverse of function f(x) = (x + 2)/x just simply swap the x and y, and solve the resulting equation for the x.

So, we have f(x) = (x + 2)/x, swap the variable x by y, we get

f(x) = (y + 2)/y ............(1)

Now, solving the above equation x = y+2/y for y.

⇒y = 2/(x-1)

∴ The value of f-¹(x) for the function f(x) = (x + 2)/x is y = 2/(x-1).

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Answer:

7854

Step-by-step explanation:

Answer:

Step-by-step explanation:

nnnnnn

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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Answer: 64%

Step-by-step explanation:

Given: Size of photo = 7-by-5-inch

Area of photo = 7 x 5 = 35 sq. inches   [ Area = Length x width]

Required size = 4.2 inches by 3 inches

Area of required size = 4.2 x 3 =12.6 sq. inches

Area reduced =Area of photo  - Area of required size = 35-12.6 =22.4 sq. inches

Percentage of the photo need to be reduced to in order for it to fit in the allotted space

\(=\dfrac{22.4}{35}\times100=64\%\)

Percentage of the photo need to be reduced to in order for it to fit in the allotted space = 64%

H

Answer:

X times .7 = y.

Step-by-step explanation:

I know what question you are reffering to, don’t worry. <33

The relation that is a function is relation (b)

The ordered pairs in the option represent the given parameters

For a relation (i.e. the ordered pairs) to be a function, the following must be true:

Each y value on the ordered pair must have exactly one x value

i.e. no x value must point to the different y value

Having said that the relation that is a function is relation (b)

Hence, the the relation that is a function is relation (b)2

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

Step-by-step explanation:

731² - 631² is the difference of squares.

731² - 631² = (731+631)(731-631) = 1362×100

therefore, 731² - 631² is divisible by 100

Answer:

Step-by-step explanation:

Answer:

65/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(5 \times 1 \frac{5}{8} \)

\( = 5 \times \frac{13}{8} \)

\( = \frac{65}{8} \)

\( = 8 \frac{1}{8} (ans)\)

E

Step-by-step explanation:

cause it the best estimate of a value of an unknown parameter and E describes it best

Answer: -4

Step-by-step explanation: The points are (2,4) and (4,-4) using the slope formula, (y2-y1)/(x2-x1) youd get -4 as your slope. Hope this helps!!

Answer:

14.94

Step-by-step explanation:

25/30 = 83.333

.30x83 = 24.9

.60 x 24.9 = 14.94

Answer:50

Step-by-step explanation:

30% to 60% is times 2

So 25 ×2=50

The line that would appear parallel to HG and would go through point D, is DC.

When describing parallel lines, we describe two lines in the same plane that are equally spaced apart and never cross each other. Both horizontal and vertical shapes are possible.

The only line that would go through point D and would be parallel to line HG, would therefore be Line DC. This is because this line is equally spaced from line HG and would never cross it.

In conclusion, line DC would be parallel to line HG.

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Answer:

y=11x

Step-by-step explanation:

we use formula y2-y1/x2-x1 with 2 of the order pairs

22-11/2-1

11/1

11 is the slope

We find y intercept by finding when x is equal to zero and we subtract 11 until we find the 0 x unit since it goes down 11 every time

When x is zero y is zero so we write it like this

Y=11x

Hopes this helps please mark brainliest

Answer:

We can use the formula for compound interest to find the future value (FV) of Natalie's investment:

FV = P * (1 + r/n)^(n*t)

Where:

P is the principal amount (the initial investment), which is $2,000 in this case

r is the annual interest rate as a decimal, which is 11% or 0.11

n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly

t is the number of years, which is 20

Substituting the values into the formula, we get:

FV =

2

,

000

∗

(

1

+

0.11

/

12

)

(

12

∗

20

)

�

�

=

2,000 * (1.00917)^240

FV = $18,255.74

Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.

Answer:

$17,870

Step-by-step explanation:

You must use the formula for compound interest.

A = P(1 + r/n)^nt

I suggest you look it up at some point so that you can do these more easily in the future!

There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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Answer:

option D: BC = EF

Step-by-step explanation:

as according to SAS their corresponding sides should also be same if the angles between them is congruent

Using the arrangements formula, it is found that the number of different arrangements that can be made using all of the letters of TOPIC is given by:

c. 120

The number of possible arrangements of n elements is given by the factorial of n, that is:

\(A_n = n!\)

In this problem, the word TOPIC has 5 non-repeating letters, hence the number of arrangements is given by:

\(A_5 = 5! = 120\).

Which means that option C is correct.

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Answer:

all of them

Step-by-step explanation:

I did this same exact test

Answer:

I don't really know what the question is but..

Step-by-step explanation:

Since total of 92 people in the trip including student and chaperon, add groups of 23 to become 92 or use this equation

(20+3)xy=92

23y=92

y=92/23

y=4

therefore,

20x4=80 (students)

3x4=12 (chaperons)

Answer:

15 chaperones

Step-by-step explanation:

1. Okay, First you're going to see how many times 20 can feet into 92. Which is 4.5 times. However, you cannot cut someone in half. So the answer would actually be 5. Then. Just do 5*3, because remember, there are THREE chaperones for every 20 students.