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Yasemin deposited $1000 into a savings account.
The relationship between the time, t, in years, since the account was first opened, and Yasemin's account
balance, B(t), in dollars, is modeled by the following function.
B(t) = 1000. 20.03
How many years will it take for Yasemin's account balance to reach $1500?
Round your answer, if necessary, to the nearest hundredth.

Answers

Answer 1

Answer:

The number of years it will take for Yasemin's account balance to reach $1500 is 13.52 years.

Step-by-step explanation:

Where the model of the relationship between the time, t, in years, since the account was first opened and the and the balance in Yasemin's account is presented as follows;

[tex]B(t) = 1000 \times e^{(0.03 \times t)}[/tex]

To find find out how many years it will take for Yasemin's account balance to reach $1500, we substitute B(t) = $1500 since we are told that after the years his account balance became $1500 as follows;

[tex]\$ 1500 = 1000 \times e^{(0.03 \times t)}[/tex]

We now solve for t

[tex]\$ 1500 = 1000 \times e^{(0.03 \times t)}\\\\\frac{1500 }{1000 } = e^{(0.03 \times t)}\\1.5 = e^{(0.03 \times t)}\\\\ln(1.5) = ln (e^{(0.03 \times t)})\\\\ln(1.5) = (0.03 \times t) \times ln (e)\\\\\therefore ln(1.5) = (0.03 \times t) \\\\t = \frac{ln(1.5)}{0.03 } = 13.52 \ years[/tex]

The number of years it will take for Yasemin's account balance to reach $1500 = 13.52 years.


Related Questions

What is the y coordinate of the point that divides the

directed line segment from J to k into a ratio of 2:3?

Answers

Answer:

the y coordinate is 5

Step-by-step explanation:

In the figure attached, the  directed line segment is shown.

J is located at (-3, 1) and K is located at (-8, 11)

run: x2 -x1 = -8 - (-3) = -5

rise: y2 - y1 = 11 - 1 = 10

Taking J as reference, the coordinate of the point that divides the  directed line segment from J to k into a ratio of 2:3 is:

c = 2/(2+3) = 0.4

(x1 + c*run, y1 + c*rise)

(-3 + 0.4*-5, 1+0.4*10)

(-5, 5)

3 + 2/5 + (-7 1/5) in a fraction plz

Answers

Answer

3 -4/5ths

the square root of the mass of the sun times molecular biology of a frog equals 3 -4/5ths

Answer:

-4 1/5

Step-by-step explanation:

3+2/5 = 3 2/5

3 2/5 + (-7 1/5) = -4 1/5

What are the roots of the equation x2 - 5x + 6 = 0?
A
1 and -6
B.
2 and 3
C
-1 and 6
D.
-2 and -3​

Answers

The answer is

B. -2 and 3

Step-by-step explanation :

Given the expression

x²- 5x + 6 = 0

Firstly we need to find two numbers that when multiplied will give us the constant term 6, and when added will give us the 2nd term 5

These numbers are 3 and 2

Substituting 2x +3x for 5x

x²- (2x+3x)+ 6 = 0

x²-2x-3x+6=0

(x²-2x)-(3x+6)=0

Factoring we have

x(x-2)-3(x-2)=0

x-3=0, x-2=0

x=3, x= 2

HELP ME PLS! WILL MARK BRAINLIEST!

Answers

Answer:

35

Step-by-step explanation:

The angle formed by two secants = 1/2(difference of intercepted arcs)

A = 1/2(100-30)

A = 1/2 (70)

= 35

what is the solution to the system of equations?
1) (-6,-2)
2) (-2,6)
3) (6,2)
4) (-2,-6)
i will give more points. plz help

Answers

Answer:

(-6, -2)

Step-by-step explanation:

When trying to find the solution to a system of equations on a graph, the solution is where the lines intersect.

The lines intersect at (-6, -2).  This is the solution.

The solution of the system of equations is,

⇒ (-6, -2)

We have to given that;

Graph of system of equations are shown in image.

Since, We know that;

In the graph the solution of system of equations is the intersection point of system of equations.

Hence, By definition, we get;

The solution of the system of equations is,

⇒ (-6, -2)

Therefore, Option 1 is true.

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would you rather work at restaurant A or restaurant B. Restaurant A is $ 18 a hour and has no tips and cost $8 to $28. Restaurant B is $10.50 a hour and has tips and cost $8 to $28. What restaurant would you work at

Answers

Hmmm that’s a good question

Can you help me please and show your work I will mark you Brainiest

Answers

Answer:

she would need to pay 70 Nickles to get to $3.49 and she would get 1 penny back.

What is the surface area of the triangular pyramid that can be formed from this net?

32 m

58 m

46 m

Answers

Answer:

32

Step-by-step explanation:

32

my answer is right

Answer:

ffrrv3rv4tg

Step-by-step explanation:

List the following sets A is the set of whole numbers greater than 15 but less than 25

Answers

Answer:

{a | 25>a>15}

The elements of A ={16,17,18,19,20,21,22,23,24}

Hope it will help u...

Find the next three terms of the sequence
21,19,17,15,

Answers

Answer:
15, 17, 19, 21, 23, 25, 27

Explanation: It’s adding by 2 so the next three has to be added by 2.
Final answer:

The next three terms in the sequence 21, 19, 17, 15, are found by continuing the pattern of subtracting 2 from the previous term. They are 13, 11, and 9 respectively.

Explanation:

To find the next three terms of the sequence 21, 19, 17, 15, we should first identify the pattern. Observing the sequence, we see that each term decreases by 2 from the previous term. This is called an arithmetic sequence with a common difference of -2.



Starting with the last given term (15), we subtract 2 to find the next term:

15 - 2 = 1313 - 2 = 1111 - 2 = 9



Therefore, the next three terms in the sequence are 13, 11, and 9.

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The diagonals of a trapezold are perpendicular.
O never
O always
sometimes

Answers

Answer:

If I got this wrong im sorry but I think its sometimes

What is the product? One-third times 33.99 3 11 11.33 33.11

Answers

33.99 / 3 = 11.33

Just divide all the digits by 3

hi y'all I am new to this so can y'all help me

Linear equation y=-2x+1

Answers

Answer:

That equation is in slope intercept form, the slope is equal to -2 and it has a constant of 1. Its starting point would be (0,1)

Step-by-step explanation:

I don't really understand your question, but if you need any help I would be glad to help.

Answer: . y=mx+c is one of them. y=2x−1 is in this form, therefore it is a linear equation. It has an x term, a y term and a constant.

Step-by-step explanation:

Find the difference: 1-8/13

A: 5/13

B: 12/13

Answers

It is A because 13/13 (=1) and 13/13 - 8/13 = 5/13

Hope this helped :)

Answer: 5/13

Do Keep Change Change (KCC)

Keep: 1/1

Change - into +

Change: 8/13 into -8/13

Remove

1/1 it becomes 13/13

Your new Problem: 13/13+-8/13

Add

13+-8/13=5/13

evaluate the expression xy-3x; when x=4 and y=5. Pls provide explanation. Will choose brainliest.

Answers

4*5-3*4

20-12

=8

Just plug in the numbers and solve. Remember that you multiply before you subtract.

Answer: 8

Step-by-step explanation: it was correct when I did it

I have multiple math questions to ask.. If you're bored.. Help meh!

Answers

Answer:

I might be able to help!

Step-by-step explanation:

I'm bored too.

What is the surface area of this cylinder?
Use a ~ 3.14 and round your answer to the nearest hundredth.

Answers

The surface area of the cylinder is [tex]\( 904.32 \, \text{cm}^2 \)[/tex]

The surface area (A) of a cylinder is given by the formula:

[tex]\[ A = 2\pi r^2 + 2\pi rh \][/tex]

where:

- [tex]\( r \)[/tex] is the radius of the base,

- [tex]\( h \)[/tex] is the height,

- [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14.

Given the values:

- Radius [tex](\( r \))[/tex] = 8 cm

- Height [tex](\( h \))[/tex] = 10 cm

- [tex]\( \pi \)[/tex] = 3.14

Plug these values into the formula:

[tex]\[ A = 2 \times 3.14 \times (8)^2 + 2 \times 3.14 \times 8 \times 10 \][/tex]

[tex]\[ A = 2 \times 3.14 \times 64 + 2 \times 3.14 \times 80 \][/tex]

[tex]\[ A = 401.92 + 502.4 \][/tex]

[tex]\[ A = 904.32 \, \text{cm}^2 \][/tex]

Therefore, the surface area of the cylinder is [tex]\( 904.32 \, \text{cm}^2 \)[/tex].

Final answer:

The surface area of a cylinder is calculated using the formula A = 2πr² + 2πrh, combining the areas of the top and bottom circles and the side surface.

Explanation:

To find the surface area of a cylinder, we need to add the areas of the two circular bases and the lateral surface area. The formula for the surface area of a cylinder is:

A = 2πr2 + 2πrh

where r is the radius of the circular base and h is the height of the cylinder. In this case, you can use a value of ~3.14 for π (pi) and round your answer to the nearest hundredth.

To calculate the surface area of a cylinder, you need to know the radius of the cylinder and its height. The formula for the surface area (A) of a cylinder is A = 2πr² + 2πrh, where r is the radius, and h is the height. This includes both the areas of the top and bottom circles (2πr²) and the area of the side surface (which is the circumference of the circle times the height, 2πrh). If the student provides the dimensions of the cylinder, use them to plug into this formula and calculate the surface area.

The diameter of a cart wheel is 2.1 m. Find the distance traveled when it completes 100 revolutions.
explanation pls!!

Answers

Answer

660

Step-by-step explanation:

to find the distance covered in one revolution, we need to find the circumference of the circle.

Radius of wheel is  

=  2.1 / 2

=  1.05 m

Distance traveled when 100 revolutions are completed :  

=  100 x circumference of the wheel

=  100 x 2 x (22/7) x (1.05)

=  100 x 2 x 22 x 0.15

=  660 m

Distance traveled when it completes 100 revolutions is 659.4 meter

Given that;

Diameter of a cart wheel = 2.1 m

Find:

Distance traveled when it completes 100 revolutions

Computation:

Radius of wheel = 2.1 / 2

Distance traveled when it completes 100 revolutions = [2πr]100

Distance traveled when it completes 100 revolutions = [2(3.14)(2.1 / 2)]100

Distance traveled when it completes 100 revolutions = [(3.14)(2.1)]100

Distance traveled when it completes 100 revolutions = 659.4 meter

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Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string
makes a 25° angle with the ground and when the string makes a 45° angle with the ground? Round to the nearest tenth.
14.2 feet
17.1 feet
47.6 feet
55.2 feet

Answers

By using trigonometric relations, we will see that the difference in height is 14.2 ft.

How to find the difference in height?

Here we will have two right triangles, in both, the hypotenuses are equal to 50 ft, but in one, one of the angles measures 25° and in the other, the same angle measures 45°.

The height of the kite would be given by the opposite cathetus to these angles, then we can use the relation:

sin(x) = (opposite cathetus)/(hypotenuse).

Then we can compute:

sin(25°) = h/50ft

sin(25°)*50ft = h = 21.1 ft

sin(45°) = h'/50ft

sin(45°)*50ft = 35.3 ft

The difference is:

35.36ft - 21.13ft = 14.2 ft

So the correct option is the first one.

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The approximate difference in the height of the kite when the string makes a 25° angle with the ground and when the string makes a 45° angle with the ground is 14.2 feet.

To find the approximate difference in the height of the kite when the string makes a 25° angle with the ground and when it makes a 45° angle, we can use basic trigonometry.

Step 1: Calculate the Height at 25°

When the string makes a 25° angle with the ground:

The height (h) can be calculated using the sine function:

h = L · sin(θ)

where:

- ( L ) = length of the string = 50 feet

- (θ) = angle with the ground = 25°

Calculating this:

[tex]\[ h_{25^\circ} = 50 \cdot \sin(25^\circ) \][/tex]

[tex]\[ h_{25^\circ} \approx 50 \cdot 0.4226 \approx 21.1 \text{ feet} \][/tex]

Step 2: Calculate the Height at 45°

When the string makes a 45° angle with the ground:

Using the same sine function:

h = L · sin(θ)

where:

- θ = 45°

Calculating this:
[tex]\[ h_{45^\circ} \approx 50 \cdot 0.7071 \approx 35.4 \text{ feet} \][/tex]

Step 3: Calculate the Difference in Height

Now, we find the difference in the heights:

[tex]\[ \text{Difference} = h_{45^{\circ}} - h_{25^{\circ}} \][/tex]

Difference = 35.4 - 21.1 ≈ 14.3 feet

Rounding to the nearest tenth, the approximate difference in height of the kite is 14.3 feet.

Therefore, the closest answer choice is 14.2 feet.

please help me i really need it fast!!

Answers

Answer:

They do not form a right triangle

Step-by-step explanation:

Your parents pay you an allowance each month. You spend half of it and save the other half of it in a shoebox under your bed.

What model best describes the total amount of money in your shoebox over time?
Linear
Quadratic
Exponential



Can you please tell me a explanation for the answer.

Answers

im pretty sure the answer is linear. This is because when you are earning money over time, the amount of money you have grows. and since you’re saving half of the money in a shoebox (which is what you’re looking for) the other half that you’re spending isn’t involved in the situation.

Final answer:

The total amount of money saved in the shoebox over time is best described by a linear model since a fixed amount is added each month, creating a straight line when graphed over time.

Explanation:

The model that best describes the total amount of money in a shoebox over time, assuming you consistently save half of your allowance each month, is a linear model. This is because with each month that passes, you add the same fixed amount to the total you've already saved, creating a straight line when graphed over time. A linear model is represented by the equation y = mx + b, where m is the slope (the fixed amount saved each month) and b is the y-intercept (the initial amount in the shoebox, if any).

If you were earning interest on the savings, or if the amount you saved each month changed, you might consider a quadratic or exponential model, respectively. However, without these factors, the growth of your savings is constant and linear.

❗️10 points❗️
5. simplify the expression.
pleasseee

Answers

A simplification of the expression include the following: B. [tex]2\sqrt{33} +3\sqrt{6}[/tex].

What is an exponent?

In Mathematics and Geometry, an exponent can be represented or modeled by this mathematical expression;

[tex]b^n[/tex]

Where:

the variables b and n are numbers (numerical values), letters, or an algebraic expression.n is known as a superscript or power.

In Mathematics and Euclidean Geometry, an expression is typically used for illustrating the relationship that exist between twoor more variables and numerical quantities, without an equal to sign (symbol).

Based on the information provided above, we can logically deduce the following expression;

[tex]\sqrt{6} (\sqrt{22} +3)\\\\ (\sqrt{6} \times \sqrt{22} + \sqrt{6} \times3)\\\\\sqrt{132} +3\sqrt{6}\\\\\sqrt{4 \times 33} +3\sqrt{6}\\\\2\sqrt{33} +3\sqrt{6}[/tex]

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The simplified expression is [tex]\(\sqrt{132} + 3\sqrt{6}\).[/tex] Hence, the correct answer is (a).

To simplify the expression [tex]\(\sqrt{6} (\sqrt{22} + 3)\)[/tex], you can use the distributive property, which allows you to multiply each term inside the parentheses by [tex]\(\sqrt{6}\)[/tex]. Here's how:

[tex]\(\sqrt{6} (\sqrt{22} + 3) = \sqrt{6} \cdot \sqrt{22} + \sqrt{6} \cdot 3\)[/tex]

Now, simplify each term:

1. [tex]\(\sqrt{6} \cdot \sqrt{22} = \sqrt{6 \cdot 22} = \sqrt{132}\)[/tex]

2. [tex]\(\sqrt{6} \cdot 3 = 3\sqrt{6}\)[/tex]

So, the expression simplifies to:

[tex]\(\sqrt{6} (\sqrt{22} + 3) = \sqrt{132} + 3\sqrt{6}\)[/tex]

The correct answer is (a) [tex]\(\sqrt{132} + 3\sqrt{6}\).[/tex]

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Find the vertex of the parabola.
y = 2x² + 8x + 12
a. (2,-4)
b. (-2, 4)
C
d.
(-4, 2)
(4, -2)

Answers

Answer:

Correct answer is B. (-2,4)

Step-by-step explanation:

Given: y = 2x^2 + 8x + 12

if x = 2,

Use substitution: y = 2(-2)^2 + 8(-2) + 12

                                y = 8 - 16 + 12

                                   y = -8 + 12

                                       y = 4

So, (-2, 4) would be your answer.

I hope this helps!!!

Marta’s mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the first 30 days could be modeled using the function f(x) = 33(1.3)x where x is the number of days the video has been online. About how many people had viewed the video once it had been online for 20 days?

Answers

858 days

Step-by-step explanation:

take 33*1.3*20

Answer:

its not 858 just took test and only one i got wrong

Step-by-step explanation:

How do you write an equation in vertex form. Please provide a step by step solution

Answers

Answer:

Step-by-step explanation:

Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the parabola.

The vertex of a parabola is the point at the top or bottom of the parabola.

'h' is -6, the first coordinate in the vertex.

'k' is -4, the second coordinate in the vertex.

'x' is -2, the first coordinate in the other point.

Help please?

An altitude of a triangle is a line or segment that passes through a vertex of the triangle and is _____________ to the line containing the opposite side.

Answers

I think it is an orthicenter

Answer:

Perpendicular

Step-by-step explanation:

The length of a rectangle is three times the width. The area of the rectangle is 108 sq in. What is the width of the rectangle? 6 in. 9 in. 12 in. 36 in.

Answers

The answer is 6 inches because if you do 6×18 it equals to 108 and the length is three times the size of the width

2 Points
What type of object is pictured below?
O
O A. Ray
O
B. Point
O
C. Segment
OD. Line
SUBMIT

Answers

technically this is a line segment, but since that is not an option. choose the answer “line”
The answer to this is B


What is
1 1/2-2/3?
A. 2/3
B. 5/6
C. 1 1/6
D. 1 1/3

Answers

Answer:

5/6

Step-by-step explanation:

Make common dinominator:6

1 3/6-4/6

9/6-4/6

5/6

Answer:

Step-by-step explanation:

1½ - ⅔

Convert the mixed fraction to improper fraction

³/2 - ⅔

Find the L.C.M of the denominator which is 6

9 - 4

——— = 5/6

6

Which graph shows a negative correlation?

Answers

second graph

Step-by-step explanation:

Doesn't really look like a negative correlation to me but the closest would be first one if there is a option for no correlation that'd be right too.

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