Find the slope.

Bonus: Write the equation of the line.

Answer:

As a logarithm, the money had been in the account for [tex]t = \frac{\ln{2}}{0.08}[/tex] years.

Step-by-step explanation:

The amount of money in the account after t years is given by:

[tex]A(t) = Pe^{rt}[/tex]

In which P is the initial amount deposited and r is the interest rate, as a decimal.

Michelle deposited $1,600 into an account that is compounded continuously with an annual interest rate of 8%.

This means that [tex]P = 1600, r = 0.08[/tex]

After t years, there was $3,200 in the account. How many years had the money been in the account?

This is t for which [tex]P(t) = 3200[/tex]. So

[tex]A(t) = Pe^{rt}[/tex]

[tex]3200 = 1600e^{0.08t}[/tex]

[tex]e^{0.08t} = \frac{3200}{1600}[/tex]

[tex]e^{0.08t} = 2[/tex]

[tex]\ln{e^{0.08t}} = \ln{2}[/tex]

[tex]0.08t = \ln{2}[/tex]

[tex]t = \frac{\ln{2}}{0.08}[/tex]

[tex]t = 8.67[/tex]

As a logarithm, the money had been in the account for [tex]t = \frac{\ln{2}}{0.08}[/tex] years.

The value of time t is [tex]\frac{ln(2)}{0.08}[/tex].

Given: P=1600

r=8%=0.08

t = ?

A=3200

Using the given compound interest formula we get:

[tex]A=Pe^{rt}\\3200=1600e^{0.08t}\\2=e^{0.08t}\\[/tex]

Take ln on both sides,

[tex]ln(2)=ln(e^{0.08t})\\ln(2)=0.08t\\t=\frac{ln(2)}{0.08}[/tex]

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Answer:

It's 3 1/6 :) I hope it helps

Answer:

24 m

Step-by-step explanation:

it is 24metre ok......

The greatest circumference is 25.12 meters.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

A circle with a radius of 4 meters.

Circumference.

= 2πr

= 2 x 3.14 x 4

= 25.12 meters

A circle with a diameter of 7 meters

Radius =  7/2 meters

Circumference.

= 2πr

= 2 x 3.14 x 7/2

= 21.98 meters.

A circle with a circumference of 24 meters

Circumference = 24 meters

A circle with a circumference of 5 pi

Circumference = 5π

= 5 x 3.14

= 15.7 meters

Thus,

The greatest circumference is 25.12 meters.

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Answer:

$15.02

Step-by-step explanation:

Given data

Total cost= $16

tax= 6.5%

let the actual cost of the slippers be x

6.5/100*x+ x= 16

0.065x+x= 16

1.065x= 16

divide both sides by 1.065

x= 16/1.065

x= 15.02

Hence the actual cost of the slippers is $15.02

Answer:

josh

rabeesh

ronger

roger

roge

robert

Step-by-step explanation:

The dilation of an image with a scale factor less than 1 will have the angle proportional to the preimage, and the side lengths have been smaller. Thus, option B) is correct.

The dilation factor has been the scale factor that has been used for the enlargement or reduction of the image. The images with a dilation factor of more than 1 enlarge, while the images with a dilation factor less than 1 shrinks.

The angle of the image with a scale factor less than 1 has been proportional as with shrinking, the angles have been reduced proportionally with the scale factor.

The reduction in scale factor from 1 will shrink the image. The shrinked image will be consist of a smaller size. So there has been a reduction in the side length of the image.

So, with the image with dilation of scale factor less than 1, the angles are proportional while the side length is smaller. Thus option B) is correct.

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9514 1404 393

Answer:

  $43.75

Step-by-step explanation:

The amount of the markup is ...

  $25 × 0.75 = $18.75

The final cost to the customer is ...

  selling price = purchase price + markup

  = $25.00 + 18.75 = $43.75

They charge customers $43.75 for a videogame.

Answer:

Step-by-step explanation:

(84/100)^4(16/100)

(0.84)^4(0.16)^1

Answer:

Answer:

(2x−1)(2x−1)(2x−1)(2x−1)

Step-by-step explanation:

Factor 16x4−32x3+24x2−8x+1

16x4−32x3+24x2−8x+1

=(2x−1)(2x−1)(2x−1)(2x−1)

For question 1 and 2, you should keep in mind that the sum of all angles in a triangle is 180°. 1. If the measure of one angle of a triangle is 90 degrees, you can assume that the sum of the other two triangles should be 90 degrees. Because

180 - 90 = 90

The sum of the three angles of any triangle is equal to 180 degrees.

Angle 2=127 because 180-53=127.

Angle 3=23 because 180-30-127=53

Angle 1=37 because 90-53=37

Angle 4=90

Angle 1+4=127

The measure of ∠1 is 125° .

Next x+64=110. The reason why you can do this is because ∠R is going to be an opposite interior angle. Subtract 64 from the left and right sides. x=46

Answer:

AP EX

Step-by-step explanation:

Answer:

There are infinite solutions because they are the same equation

2D + 1G = 12

and

4D + 2G = 24 (divide by 2) 2D + G = 12

2D + 1G = 12 is the same as 2D + 1G = 12

Answer:

1. Construct the perpendicular bisector of one side of triangle.

2. Construct the perpendicular bisector of another side.

3. Where they cross is the center of the Circumscribed circle.

4. Place compass on the center point, adjust its length to reach any corner of the triangle, and draw your Circumscribed circle!

There are four steps for constructing a circle that is circumscribed about a triangle.

A triangle is a three-sided polygon with three angles. The total of the triangle's angles is 180 degrees.

The steps for constructing a circle that is circumscribed about a triangle are as follows;

1. Draw the perpendicular bisector of one of the triangle's sides.

2. Create another side's perpendicular bisector.

3. The intersection is the circumscribed circle's center.

4. Place the compass on the center point, change the length of the compass to reach any corner of the triangle, and draw your circumscribed circle.

Hence, the above steps help to construct a circle that is circumscribed about a triangle.

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Answer:

Part A

The expression in terms of 't' representing the number of radians Josh has swept since the ride started is 3·t rad

Part B

The time to complete one revolution is (2·π/3) minutes

Part C.

The function 'f' that determines Josh's height above the ground (in feet) in terms of 't' is, f(t) = 44·sin(3·t + π/2) + 50

Step-by-step explanation:

The radius of the Ferris wheel = 44 foot

The height of the Ferris wheel above the ground = 50 feet

The direction of rotation of the Ferris wheel = CCW

The angular speed of the Ferris wheel, ω = 3 radians per minute

The position from which Josh boards the Ferris wheel = 3-O'Clock

The number of minutes since the ride started started = t

Part A

The expression in terms of 't' to represent the number of radians Josh has swept since the ride started = ω × t = 3 × t rad = 3·t rad

Part B

One complete revolution = 2·π radians

The time to complete one revolution = 2·π/ω = 2·π/(3 rad/minute) = (2·π/3) minutes =  [tex]0.\overline{6}[/tex]·π minutes ≈ 2.0943951 minutes

Part C.

The height, 'h', of the Ferris wheel is given by the following sinusoidal relation

f(t) = A·sin(B·t + C) + D

Where;

A = The amplitude = The radius of the Ferris wheel = 44 ft.

The period, T = (2·π/3) minute

B = 2·π/T = 3

t = The time in minutes

D = The Ferris wheel's height above ground = 50 ft.

C = The horizontal shift = π/2 (Josh boards the Ferris wheel at t = 3-O'Clock which is the midline, a rotation of π/2 from the lowermost end of the Ferris wheel)

Therefore the function that determines Josh's height above the ground (in feet) in terms of 't' is presented as follows;

f(t) = 44·sin(3·t + π/2) + 50

Answer:

I believe it's A and D.

If I helped you're welcome. If I didn't I'm sorry.

Answer:

A and D

Step-by-step explanation:

im not too good on fractions but hopefully its right

Answer:

yes c is correct ... go on keep going

BEST OF LUCK

Answer:

P 145.55

Step-by-step explanation:

435.30 - 289.75 = 145 .55

Answer:

to convert an improper fraction to a mixed fraction, follow these steps:

-divide the numerator by the denominator.

-write down the whole number answer.

-then write down any remainder above the denominator.

Step-by-step explanation:

Answer:

Divide the numerator by the denominator. The quotient is the whole number, and the remainder is the other fraction.

Example: 46/17

46/17= 2 r 12

2 is the whole number, and 12/17 is the fraction next to it.

Answer:

(x/8) - 13 > -6

Step-by-step explanation:

If you want to take it further, add 13 to both sides to make it x/8 > 7. Then divide both sides by 8 to get x by itself. you are left with x > 7/8

Random tip to remember: when dividing by negatives, remember to switch the inequality signs (this is just for future reference)

Answer:

please put a picture so i can awnser

Step-by-step explanation:

Answer:

where is the picture ?

Step-by-step explanation:

Answer: 1/15

Step-by-step explanation:

An hour is 60 minutes.  Thus, simply do 60/4 to get 15, and that the fraction is 1/15.

Hope it helps <3 :)

Answer:

1/15

Step-by-step explanation:

1 hour = 60 minutes

[tex]\frac{4}{60}=\frac{1}{15}[/tex]

Answer:

18: Safe volume: s <= 115. Unsafe: s > 115.

19: 2-a, 1-b, 3-c, 4-d

20a: Justin is incorrect. 12 is a solution. 12 >= 12 is a true statement.

20b: f > 12

Step-by-step explanation:

Answer:

5.7

Step-by-step explanation:

Im not so sure if this is the correct answer but i hope if helps! <3

Answer:

x is equal to 11...........

90°-35°= 55°

Mark as brainlist

Answer:

Step-by-step explanation:

two integers mean numbers that do not have decimals. Whole numbers

to figure out between what two integers get a calculator

which is 4.123 (to three decimal places)

thus it falls between 4 and 5. since it is above 4 and below 5 and there are no integers in between possible.

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The solution is Option C.

The number of ways 3 positions can be filled by the 12 students is given by combinations where ¹²C₃ = ( 12 x 11 x 10 ) / 3 x 2 x 1

What are Combinations?

The number of ways of selecting r objects from n unlike objects is:

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the equation be represented as A

Now , the value of A is

The total number of students n = 12 students

The number of positions in the council x = 3 positions

So , the number of ways the 3 positions can be filled by 12 students is calculated by combinations

where n = 12 and x = 3

ⁿCₓ = n! / ( ( n - x )! x! )

Substituting the values in the equation , we get

¹²C₃ = ( 12! / ( 12 - 3 )! 3! )

On simplifying the equation , we get

¹²C₃ = ( 12! / 9! 3! )

And ,

¹²C₃ = ( 12 x 11 x 10 x 9! / 9! 3! )

¹²C₃ = ( 12 x 11 x 10 ) / 3!

¹²C₃ = ( 12 x 11 x 10 / 3 x 2 x 1 )

¹²C₃ = 220 ways

Hence , the number of ways the 3 positions can be filled by the 12 students is 220 ways

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