Benjamin invested $66,000 in an account paying an interest rate of 63%
compounded annually. Christian invested $66,000 in an account paying an interest
rate of 5% compounded continuously. After 19 years, how much more money would
Benjamin have in his account than Christian, to the nearest dollar?

It will take approximately 4687.9 years for an investment principal of $1500 to reach $1000000 at an interest rate of 14.2% per year

Simple interest is a type of interest calculated only on the principal amount of a loan or deposit, without taking into account the compound interest earned on that principal. It is calculated by multiplying the principal amount, the interest rate and the time period.

The formula of simple interest is given as;

A = P(1 + rt)

where;

In this problem, we have to find the rate first.

The investment doubles after 7 years.

A = p(1 + rt)

2 = 1(1 + r * 7)

2 = (1 + 7r)

2 = 1 + 7r

7r = 2 - 1

7r = 1

r = 1 / 7

r = 0.142

r = 14.2%

The rate is 14.2 %

Now, we can proceed to determine how many years it will take to reach a value of 1000000

Using simple interest formula again;

A = P(1 + rt)

100000 = 1500(1 + 0.142 * t)

1000000 = 1500(1 + 0.142t)

t = 4687.8 years

It will take approximately 4687.8 years

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Answer:

D.

Step-by-step explanation:

They are parallel would be the best explanation. AB and PQ are in a sense the same segment but PQ is AB translated.

The conditions (b),(e) and (f) comes under one quadrilateral and conditions (a),(c) and (d) comes under many quadrilaterals.

What is a quadrilateral?

A  quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. Quadrilaterals always have a total internal angle of 360 degrees.

Given,

condition A : a rectangle with four right angles

condition B : a square with one side measuring 5 inches

condition C : a rhombus with one angle measuring 43°

condition D : a parallelogram with one angle measuring 32°

condition E : a parallelogram with one angle measuring 48° and adjacent sides measuring 6 inches and 8 inches

condition F : a rectangle with adjacent sides measuring 4 inches and 3 inches.

Now we are asked to match the above conditions to one quadrilateral and many quadrilaterals groups according to the number of quadrilaterals that can be constructed using the given condition.

Condition A : Many Quadrilaterals

All the rectangles have four right angles in them. So many rectangles of different lengths can be formed.

Condition B : One Quadrilateral

The defining factor that make a square unique is the length of its side. All the sides of the square also has equal length. So only one square of 5 inches side can be made.

Condition C: Many Quadrilaterals

For a rhombus the opposite angles are equal and the sum of angles should be 360°. Even though the angles are fixed, this rhombus can have any side length.

Condition D: Many Quadrilaterals

As discussed for rhombus, even though the angles of the parallelogram is fixed, there can be many sides lengths.

Condition E: One Quadrilateral

In this case, side length as well as the angle of the parallelogram is given. So there can be only one parallelogram.

Condition F:One Quadrilateral

The side lengths are what make a rectangle one of its kind. So one one rectangle can be formed with lengths 4 inches and 3 inches.

Therefore conditions (b),(e) and (f) comes under one quadrilateral and conditions (a),(c) and (d) comes under many quadrilaterals.

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Answer:

41.5 g

Step-by-step explanation:

This is correct! mark me brainliest!

Answer:

8.3 x 5 = 41.5

Step-by-step explanation:

standard algorithm- 3 x 5=15 1 on top 5 stays on bottom

5 x 8 = 40

40+1 = 41

415

then add decimal dot after one number

hope this helps :P

Answer:

48+23(6)½

Step-by-step explanation:

A = l × w

A =[(8-(6)^½) × (9+4(6)^½)]

A =8(9+4(6)^½) + [-(6)^½(9+4(6)^½]

A =(72 + 32(6)^½ - 9(6)^½ - 24)

A =(72 - 24 + 32(6)^½ - 9(6)^½)

A =(48 + 23(6)^½)

Answer:

all will be 45* angles except the 90* one because a triangle always has 180* angle if you add them all up

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of Triangles.

1.) Sin x = 20/36 , hence x° = 33.74

2.) Sin n = 35/51, hence n° = 43.33

3.) Cos z = 18/21 , hence z° = 31.00

4.) Tan w = 15/6 , hence w° = 0.04

Answer:

t = 9.7 seconds

Step-by-step explanation:

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation as :

[tex]y=-16x^2+147x+80[/tex]

We need to find the time that the rocket will hit the ground, to the nearest 100th of second.

When the rocket hit the ground, So,

[tex]-16x^2+147x+80=0\\\\x=-0.515\ s\ and\ 9.70\ s[/tex]

Neglecting negative tim,

t = 9.7 s

Hence, it will hit the ground at 9.7 seconds.

Answer:The average rate of the function from x = 2 to x = 4 is 6.

Step-by-step explanation:

10.  This system has one solution with coordinates (1, -2)

11. This system has one solution with coordinates (0,-3)

12. This system has one solution with coordinates(-1, -2)

13. This system has no solution.

14. This system has no solution.

16.   This system has one solution with coordinates (0,-4)

According to question:-

10. y = x - 3 ------- 1

y = -5x + 3 ------- 2

substitute 1 in 2,

x - 3 = -5x + 3

x = 1

y = 1 - 3 = -2

y = -2

The co-ordinates is (1,-2)

11. y = -3

substitute in y = x-3

-3 = x - 3

x = 0

The co-ordinates is (0,-3)

12. y = 4x + 2 --------- 1

y = -2x - 4 ------------2

Substitute 1 in 2,

4x + 2 = -2x - 4

6x = -6

x = -1

substitute x = -1 in 2

y = -2

The co-ordinates is (-1, -2)

13. y = x - 6 -----1

y = x+ 2 -------2

It has no solution, so there is no co-ordinates.

14. x + y = 4

3x + 3y = 12

It has no solution, so there is no co-ordinates.

16. 2x + 3y = 12 ------1

2x - y = 4 --------2

from 2 we rewrite the equation as y = 2x-4

Sub in eq 1

2x + 3(2x-4) = 12

2x + 6x - 12 = 12

8x = 24

x = 3

y = 2

The co-ordinates is (3,2)

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Answer:

52 bags and 2 extra

Step-by-step explanation:

Simply divide the no. of rolls by no. of rolls per bag

Answer:

12 bags

Step-by-step explanation:

158 rolls ÷ 13 rolls/bag = 12.15 bags

You will have 12 full bags plus about 2 extra rolls left over, which you can try to sell separately or as a "pack" of 2.  Or, you can sell one overstuffed bag with 2 extra rolls in it (for a total of 15 rolls) for a little extra on the price.

Answer:

2) 127 degrees

3)360 degrees

Step-by-step explanation:

2)

Since angle 1 and angle 2 add up to 180 degrees

180-53(angle 2)=angle 1

=127

angle 1 and angle eight are alternate exterior angles, so they are congruent

3)

angle 4= 127

angle 3= 53

angle 5= 127

angle 6= 53

add it all up

360 degrees

Answer:

? whats the number your multiplying by

Step-by-step explanation:

Answer:

-12.5

Step-by-step explanation:

Hope it helps

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Answer:

b

Step-by-step explanation:

because 1/5 divide by six is 0.03333333333

Answer:

(3,2) and (-2,7)

Step-by-step explanation:

Look for the intercepts of both graphs.

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Answer:

103 degrees

Step-by-step explanation:

These two angles are supplementary (add up to 180 degrees)

knowing this information

a + 77 =180

subtract 77 from both sides

a = 103

Answer:

I think it is 103

Step-by-step explanation:

Answer:

i think its 358

Step-by-step explanation:

Answer:

part a: 840 if she withdrew the first month down to 730 and the rate it decreases is 110 then it is 840

part b: 110every month she withdraws 55 dollars because 55 plus 55 is 110

so every 2 months she would have withdrawn 110 dollars

Step-by-step explanation:

The projected Population in 2020 is given by 4146.

Compounding is the method through which interest is added to both the principle balance already in place and the interest that has previously been paid. Thus, compounding may be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."

Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has previously accrued over the course of prior periods are used to compute compound interest.

Number of years to compound is 10 years from 2010 to 2020.

The population deplition is 0.6 % = next year population is 99.4% of present.

So population after 10 years = 4403 * [tex].994\x^{10}[/tex] = 4145.84 =4146

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A) The frequencies and the relative frequencies of the observations are as follows,

Value __frequency (F)__Relative frequency (x)

0_____ 7 _______ 7/60 = 0.1167

1 _____ 12_ _____ 12/60 = 0.200

2 _____ 12_______ 12/60 = 0.200

3 _____ 14 _______ 14/60 = 0.2333

4 _____ 6 _______ 6/60 = 0.1000

5 _____ 3________ 3/60 = 0.0500

6 _____ 3 _______ 3/60 = 0.0500

7 _____ 1 _______  1/60 = 0.0167

8 _____ 1 ________ 1/60 = 0.0167

B)  What proportion of batches in the sample have at most five nonconforming transducers?

X =  0.1167 +0.200 +0.200 +0.2333 +0.100

= 0.85

Relative frequency

A relative frequency is the ratio of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes.

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Answer:

To obtain the g function, move f upward by 5 units and to the left by 3 units.

Step-by-step explanation:

from khanacademy

The experimental probability is 30% higher than the predicted probability.

What is meant by experimental probability?

Experimental Probability: what actually occurs when the experiment is carried out. For example, the probability of getting a head if you flip a coin is ½, since only 2 things could happen (a head or a tail) and each one has an equal chance of occurring.

The spinner has 10 sections and a 10% chance of landing on the section representing rain. Therefore, the probability of rain predicted by the spinner is 0.1 or 10%.

From the simulation, the results are 3, 6, 1, 8, and 3. Out of these 5 spins, 2 of them landed on the section representing rain (1, 3). Therefore, the experimental probability of rain from the simulation is 2/5 or 40%.

The difference between the experimental probability from the simulation and the prediction is the difference between the two percentages, which is:

(experimental probability) - (predicted probability) = 40% - 10% = 30%

Hence, the experimental probability is 30% higher than the predicted probability.

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Answer: 105x²y

Step-by-step explanation:

The answer is that space contains at least four points that are not coplanar or not all coplanar.

Axioms are statements or propositions taken to be established, accepted, or self-evident truths. In other words, a statement or mathematical statement that serves as a starting point from which other statements are logically derived. This is formulated in Hypothesis 1 as follows:

A plane contains at least three points that are not all on a straight line. Space contains at least four points that are not all in one plane. "

Simply put,

"There is at least one plane for every three points. There is exactly one plane for every three non-collinear points."

"There are at least 3 points in the plane that are not co-linear. There are at least 4 points in space that are not co-planar."

Not collinear:

Not all lined up.

Not coplanar:

do not occupy the same area or rectilinear plane

An axiom of Euclidean geometry states that there are at least four points in space that are not in the same plane.

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Answer:

3920 - 36x ≤ 500

Step-by-step explanation:

Calista worked all summer to save for spending money while she is away for college. She goes off to college with $3920 in her savings account. She wants to have at least $500 left in her account at the end of her 36-week school year. Write an inequality to represent this situation.

Let the amount of money spent in 36 weeks = x

At least = Less than or equal to = ≤

$3920 - 36x ≤ $500

Hence, the inequality to represent this situation is written as:

3920 - 36x ≤ 500

Answer:

Yes

Step-by-step explanation:

y = x has the inverse x = y

Answer:

145

Step-by-step explanation:

m<4 and m<3 would equal 90 so subtract 55 from 90 and you get 35 for m<3 so you subtract 35 from 180 and you get 145