Peter purchases a baseball card for $150 as an investment. His research tells him that the value of
the card should double every 3 years. When will the card reach a value of $ 4000?

Answers

Answer 1

Answer:

6 years

Step-by-step explanation:

Given

[tex]Initial\ Investment = 150[/tex]

[tex]Ratio = double[/tex]

Required

When will it get to 4000

This question illustrates a geometric progression and will be solved using:

[tex]T_n = ar^{n-1}[/tex]

In this case;

[tex]T_n = 4000[/tex]

[tex]r = double = 2[/tex]

[tex]a = 150[/tex]

So, we're to solve for n

[tex]4000 = 150 * 2^{n - 1}[/tex]

Divide through by 150

[tex]\frac{4000}{150} = 2^{n-1}[/tex]

[tex]26.67= 2^{n-1}[/tex]

Take Log of both sides

[tex]Log26.67= Log2^{n-1}[/tex]

Apply law of logarithm

[tex]Log26.67= ({n-1})Log2[/tex]

Take Log values

[tex]1.42602301569 = (n - 1) * 0.30102999566[/tex]

Make n - 1 the subject

[tex]n - 1 = \frac{1.42602301569}{0.30102999566}[/tex]

[tex]n - 1 = 4.73714591984[/tex]

Add 2 to both sides

[tex]n = 1 + 4.73714591984[/tex]

[tex]n = 5.73714591984[/tex]

[tex]n = 6[/tex] (Approximated)

Hence, it'll take 6 years


Related Questions

83.63 - 2.89 × (4.9 - 2.9)2 A. 72.07 B. 50.43 C. 1,046.56 D. 49.31 Please help

Answers

Answer:

A would be the anwser

Step-by-step explanation:

Answer:  A. 72.07

Step-by-step explanation: Plato

what is the answer to
10 + (-4)

Answers

Answer:

6

Step-by-step explanation:

Note the rules for signs directly next to each other:  

If there is two positive signs, the result will be positive.

If there is one positive and one negative sign, the result will be negative.

If there is two negative signs, the result will be positive.

In this case, there is a positive and a negative sign. You are, therefore, subtracting 10 with 4:

10 + (-4) = 10 - 4 = 6

6 is your answer.

~

the sqaure root of 130 falls between which consecutive numbers

Answers

11 and 12 that’s the answer

help please!
find the value of x so that the figures have the same perimeter

Answers

Answer: 7

Step-by-step explanation: For the first figure, 7 + 3 = 10, so the perimeter would be 10 + 10 + 7 + 7, which equals Perimeter = 34. For the other figure, 7 - 4 = 3, so 3 + 14 + 14 + 3 = 34, also. Hope this helps!

Phil has drawn some house plans in which the lounge room will be 9.5 m long when it is built. This length has been drawn as 19cm on the house plan. What scale did Phil use for his house plans?

Answers

Answer:

1:50 scale

Step-by-step explanation:

9.5m * 100 = 950cm

950/19 = 50

81 minus 39




And can you explain how plz?. Lol i meed it asapp

Answers

Answer:

42

Step-by-step explanation:

[tex]81-39\\\\\mathrm{Line\:up\:the\:numbers}\\\begin{matrix}\space\space&8&1\\ -&3&9\end{matrix}\\\mathrm{In\:the\:bolded\:column,\:subtract\:the\:second\:digit\:from\:the\:first}\\\begin{matrix}\space\space&8&\textbf{1}\\ -&3&\textbf{9}\end{matrix}\\\\\mathrm{The\:bottom\:number\:is\:larger\:than\:the\:upper\:number.\:\:Try\:to\:'borrow'\:a\:digit\:from\:the\:left.}\\\\\mathrm{Borrow\:}1\mathrm{\:from\:}8\mathrm{.\:\:The\:remainder\:is\:}7\\[/tex][tex]\begin{matrix}\space\space&\textbf{7}&10\\ \space\space&\textbf{\linethrough{8}}&1\\ -&\textbf{3}&9\end{matrix}\\\\\mathrm{Add\:}1\mathrm{\:ten\:to\:}1:\quad \:10+1=11\\\begin{matrix}\space\space&7&\textbf{11}\\ \space\space&\linethrough{8}&\textbf{\linethrough{1}}\\ -&3&\textbf{9}\end{matrix}\\\\\mathrm{In\:the\:bolded\:column,\:subtract\:the\:second\:digit\:from\:the\:first}:\quad \:11-9=2\\[/tex]

[tex]\frac{\begin{matrix}\space\space&7&\textbf{11}\\ \space\space&\linethrough{8}&\textbf{\linethrough{1}}\\ -&3&\textbf{9}\end{matrix}}{\begin{matrix}\space\space&\space\space&\textbf{2}\end{matrix}}\\\mathrm{In\:the\:bolded\:column,\:subtract\:the\:second\:digit\:from\:the\:first}:\quad \:7-3=4\\\\\frac{\begin{matrix}\space\space&\textbf{7}&11\\ \space\space&\textbf{\linethrough{8}}&\linethrough{1}\\ -&\textbf{3}&9\end{matrix}}{\begin{matrix}\space\space&\textbf{4}&2\end{matrix}}[/tex]

In how many ways can four people sit around a circular table? Seating arrangements are considered different only if at least one person has at least one different neighbor.

Answers

Answer:

(x-1)!

Step-by-step explanation:

lets say you want to sit x people around a table you would do x!. but since it doesn't count if you rotate the table you have to divide it by x, so the answer is x!/x = (x-1)!

The product of 7 and j is 91

Answers

Answer:

j = 13

Step-by-step explanation:

7×j = 91

j = 91 : 7

j = 13

Olga tried to solve an equation step by step.
1/4 (1/3k+9)=6
1/3k=15
k=5
Find Olga's mistake.

Answers


Answer:step 3
Step-by-step explanation:
she should have multiplied 15 x 3=45
k=45

Describe and correct the error a student made when starting to solve the equation 8 ^ (x + 3) = 2 ^ (2x - 5) 8 ^ (x + 3) = 2 ^ (2x - 5) (2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5) 2 ^ (3x + 3) = 2 ^ (2x - 5) Choose the correct answer below A. The student should have divided both sides by 2 ^ 2 to simplify the expression B. The student did not convert 8 to the correct power of 2 C. The student did not distribute 3 in * (2 ^ 3) ^ (x + 3) x + 3 D.The student should have expressed the initial rational exponent as the sum of two rational exponents ..

Answers

Answer:

C. is the correct option

C. The student did not distribute 3 in * (2 ^ 3) ^ (x + 3) x + 3

and x = - 14

Step-by-step explanation:

8 ^ (x + 3) = 2 ^ (2x - 5)

Here is how the student solved the equation

8 ^ (x + 3) = 2 ^ (2x - 5)

8 ^ (x + 3) = 2 ^ (2x - 5)

(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)

2 ^ (3x + 3) = 2 ^ (2x - 5) -----  This is where the student made the error.

The student did not distribute 3 in * (2 ^ 3) ^ (x + 3).

This is how to solve the equation

8 ^ (x + 3) = 2 ^ (2x - 5)

8 ^ (x + 3) = 2 ^ (2x - 5)

(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)

Then, we will 3 distribute in  (2 ^ 3) ^ (x + 3), so that we get

2 ^ (3x +9) = 2 ^ (2x -5)

Since the bases on both sides of the equation are equal, we can equate the powers so that we get

(3x +9) = (2x -5)

Then we will collect like terms

3x - 2x = -5 -9

∴ x = -14

This solution could be better written in this format

[tex]8^{x+3} = 2^{2x-5} \\2^{3} ^{(x+3)} = 2^{2x-5}\\2^{(3x+9)} = 2^{2x-5}\\{(3x+9)} = {2x-5} \\3x-2x= -5-9\\x = -14[/tex]

563x367
use scratch paper to help you ​

Answers

Answer: 206621

Step-by-step explanation:

563x367=206621, so 563x7=3941, 563x60=33780, and finally 563x300=168900. Add them all up, 3941 + 33780 + 168900 = 206621.

Please Mark Brainliest!

Which is an example of deductive reasoning?

Answers

Answer:

In deductive reasoning, if the given facts are true and you apply the correct logic, then the conclusion must be true.

Step-by-step explanation:

Answer:

All even numbers are divisible by 2. The number 18 is even, so it is divisible by 2.

Step-by-step explanation:

Which function is most likely graphed on the coordinate plane below? f(x) = 3x – 11 f(x) = –4x + 12 f(x) = 4x + 13 f(x) = –5x – 19

Answers

Answer:

D

Step-by-step explanation:

It's D on Enginuity

The graph of the function in the coordinate plane is f(x) = –5x – 19.

What is a Graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

As per the given diagram:

The x intercept of the line = -ve

The y intercept of the line = -ve

For f(x) = 3x - 11

x intercept = +ve

y intercept = -ve

Hence, not possible

For f(x) = -4x + 12

x intercept = +ve

y intercept = +ve

Hence, not possible

For f(x) = 4x + 13

x intercept = -ve

y intercept = +ve

Hence, not possible

For f(x) = -5x - 19

x intercept = -ve

y intercept = -ve

Hence, possible

The function plotted on the coordinate plane is f(x) = –5x – 19.

To learn more on Graphs, click:

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Sophie drove 162 miles in 3 hours. How fast did she drive in hours per mile

Answers

Answer:

54 Miles Per Hour

Step-by-step explanation:

162/3

54 mile per hour
You can divide 162 by 3 making it 54

if Kyle's terrarium had a volume of 64 ft3 ,what would the edge length be?

Answers

Answer:

4 ft

Step-by-step explanation:

Volume of a cube = [tex]x^{3}[/tex] (where x equals the side/edge length)

V = [tex]x^{3}[/tex]

64 = [tex]x^{3}[/tex]

64 divided by 3 = 4 ft

For the pair of functions, find (f o g)(x) and (gof)(x).
f(x) = -2x2, g(x) = x + 4

A. (fog)(x) = -2x^2– 8x^2; (gof)(x) = -2x^3 - 8x^2

B. (fºg)(x) = -2x^2– 16x - 32; (g = f)(x) = -2x^2+ 4

C. (fog)(x) = -2x^2 + 4; (g e f)(x) = -2x^2- 16x - 32

D. (fog)(x) = -2x^2- 32; (go 3)(x) = -2x^2 + 4

Answers

d is the correct answer i believe.❤️❤️❤️

I need help with this Algebra

Answers

Answer:

Step-by-step explanation:

f(-3) = 3(-3)^3 + 5 = 3(-27) + 5 = -81 + 5 = -76

g(4) = -4(4) - 1 = -16 - 1 = -17

Help me plz I don't know how to this I don't understand!!!

Answers

The answer is B.

In order for this chart to be true, each x and y pair must be proportional to the other ones. (in other words, each row of x and y should increase the same amount as the other ones.)

look at the first row. we can write this as 3/5 (x over y). then look at the third and fourth row. 6/10 = 3/5, and 9/15 = 3/5, so the pairs are proportional.

HELP PLS IF U DONT KNOW CEASE IT DONT ANSWER ONLY ACCEPTING VARIFIED ANSWERS !!!!!!

Answers

Answer:

31%

Step-by-step explanation:

use the formula :

P(A&B) / P(B)

meaning :

probability that a student graduates while on fin aid / student on fin aid

= 1879/6101

=1879/6101 *100

= 30.798....

= 31%

Which step can you use to solve the equation t - 8= -3?
O Add 8 to each side of the equation.
Subtract 8 from each side of the equation.
O Multiply each side of the equation by 8.
O Divide each side of the equation by 8.
Solve the equation t-8=
3.

Answers

You will need to add 8 to the other side of the equation to get t = -3 + 8


The figure below shows how Ali spends his time in a day. Calculate the number of hours Ali
spends on playing. ​

Answers

Answer:

 75°C = 5h

Step-by-step explanation :

1. Make sure your mind is fresh and that you understand each step before reading

2. 24 hours is equal to  360°C

3.  so now lets break up the hours. We can do this by choosing a simple degree that was given in the diagram. For example "Watching tv".

Tip : when choosing one of the degrees , ( i mean one of the choices like watching tv, playing and sleeping) , try choosing the simplest one , which has a simple number and a multiple of 360.

so now you want to know how many hours is 60 equal to .

= 360 ÷ 60 = 60   (this is to make sure the number is a multiple and will not be a decimal )

= 24 ÷ 6 = 4

this means Ali spend 4 hours watching tv

and by doubling that you get                    60°C = 4h

the amount of time he slept                     120°C = 8h

and you keep playing with the numbers like that

so for playing                                                

                                                                   60°C = 4h

                                             divide by 4    15°C =  1h

                                           × by 5             75°C = 5h

this means ali spends 5h playing , 8h sleeping, 4h watching tv and 7 h studding

If a triangle is an equilateral triangle, then the triangle has exactly three 60°
angles. △ABC is an equilateral triangle?

Answers

Step-by-step explanation:

In an equilateral triangle, all the three sides are equal as well as all the angles are equal. Let the angles be x.

We know that the sum of angles of a triangle is equal to 180 degrees. It means that,

x+x+x=180

3x=180

x=60°

Hence, if a triangle is an equilateral triangle, then the triangle has exactly three 60°  angles. Hence, △ABC is an equilateral triangle

What is the simplified expression for 5ab+9ab-ab? 0 12ad O 13ab 0 15ad O 16ab​

Answers

Answer:

13ab

Step-by-step explanation:

5ab+9ab = 14ab. 14ab-1ab=13ab.

Good luck

HELPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer: can i help wat is a tip

54= 4(x+5)
54= 4x+ 20
54-20=4x+ 20- 20
34= 4x
x= 8.50

please help help help

Answers

Answer:

I'm fairly sure its 4.93 grams.

Step-by-step explanation:

you take the origional water of 45.1ml and the new 52.3ml, and find the difference, which in this case is 7.2ml.

the density formula is D=M/V

D= Density

M=Mass

V=Volume

so it would be

D= 35.49/7.2

which is 4.93.

again this is just from what I remember of science class.

Answer: 4.93g/cm^3

Step-by-step explanation:

Formula for Density: D = mass / volume

We know that the mass of the unknown object is 35.49g

Mass = 35.49g

To find the volume

Initial water level: 45.1 mL

Final water level: 52.3mL

52.3cm^3 - 45.1cm^3 = 7.2cm^3

Volume = 7.2cm^3

Density = 35.49g/7.2^3

Density =

Which expression does NOT have a Greatest Common Factor?

Answers

Answer:

4x^2-9

Step-by-step explanation:

i just took the quiz

This is about greatest Common factor (G.C.F) thus Option C and Option D does not have a greatest common factor.

What is Greatest common factor?

The Greatest common factor between 2 or more numbers is simply the greatest factor that is common to all the numbers.

Option A; 2x² -18

Factors of 2 are 1, 2

Factors or 18 are; 1, 2, 3, 6, 9, 18

In this option we can see that 2 is the only common factor between all the numbers.

Thus, the GCF = 2 So this has a GCF

Option B: 3x² + 12x + 6

Factors of 3 are 1, 3

Factors of 6 are 1, 3. 6

Factors or 12 are; 1, 2, 3, 4, 6, 12

The highest common factor is 3 Thus, this has GCF.

Option C; 4x² - 9

The factors of 9 are; 1, 3, 9

The factors of 4 are; 1, 2, 4

Since there is no highest common factor here as 1 is not considered to be a highest common factor even though it is a factor.

Option D; 6x² +  2x² + 5x

The factors of 9 are; 1, 3, 9

The factors of 4 are; 1, 2, 4

Since there is no highest common factor here as 1 is not considered to be a highest common factor even though it is a factor.

To Read more about the concept at;

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12 POINTS I NEED SOMEONES HELP BEFORE THIS DAY FINISHES
A town has a population of 2000 and grows at 4% every year. Write an
equation to represent the scenario

Answers

Answer:

2000+ (2000× .04x)

Step-by-step explanation:

2000 people plus the percent that it grows, found by multiplying .04 (4%) by the original number. the x is the number of years

help i need help i can't figure this out​

Answers

Answer: A) 23

Step-by-step explanation:

3^2 + ( 6 - 2 ) ⋅ 4 -6/3

3^2 + 4 ⋅ 4 -6/3

9 + 4 ⋅ 4 -6/3

9 + 16 -6/3

25 - 6/3

75/3 -6/3 = 69/3

69/3 = 23

Answer:

23

Step-by-step explanation:

3^2 + (6 - 2) x 4 - 6/3

3^2 + 4 x 4 - 6/3

9 + 16 - 6/3

25 - 6/3

6/3 = 2

25 - 2 = 23

A farmer applies different fertilizer to his wheat crops to see which will make his plants grow the highest.
What is the independent variable?

Answers

Answer:

highest )hope this helps :)

Step-by-step explanation:

Answer:

The crop

Step-by-step explanation:

As the type of fertilizer changes it can not be the independent variable. Since nothing else (except the farmer) is referenced we can deduct that the crop is the independent variable.

When translating a number to the scientific notion (ex: 0.000157), do you count the zero to the left of the decimal point? Like would the scientific notion of 0.000157 be 1.57 x 10^-4 ? If you could explain how scientific notion works that be great. thanks

Answers

Yeah, you’re right, I like to think that when the number is a decimal and I have to put it in scientific notation the exponent next to the 10 is negative and then when the number is a whole number and I have to change it to scientific notation then the exponent next to the ten is positive.

Answer:

You do not count the zero to the left of the decimal

Step-by-step explanation:

That zero is just a placeholder as there is nothing to the left of the decimal, you could also write the number as .000157

Your answer is correct, 0.000157 is 1.57x10^-4

Scientific notation is just expressing numbers in their exponential form. The power/exponent is found by counting how many times the decimal has moved to the right or the left.

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