9 Continuously compounded interest: word problems 82J
Learn with an example
Gigi opened a savings account and deposited $600.00 as principal. The account earns 3%
interest, compounded continuously. What is the balance after 2 years?
Use the formula A = Pe", where A is the balance (final amount), P is the principal (starting
amount), e is the base of natural logarithms (~2.718 28), r is the interest rate expressed as
a decimal, and t is the time in years.
Round your answer to the nearest cent.
$
Submit

Answer:

Step-by-step explanation:

it would be great if u had the image, but at least I can give some advice: use the method of rise over run to find the slope. use 2 points and count the number of squares "rising" and turn right and count the number of squares "running". left and down if it's going downward.

for the y intercept, find the x that equals 0. your coodinate should look like this: (0, *insert y*)

+5 degree.

Formula for Length Change due to Thermal Expansion: The formula for calculating the change in length of a substance due to thermal expansion is ΔL=αLΔT Δ L = α L Δ T where L is the original length of the substance and ΔT is the change in temperature of the substance either in degrees Celsius or in Kelvin.

For comparision of temperature -

Subtract the final temperature from the starting temperature to find the difference. So if something starts at 50 degrees Celsius and finishes at 75 degrees C, then the change in temperature is 75 degrees C – 50 degrees C = 25 degrees C.

Given data

temperature of tuesday = 55 degree

temperature of saturday = 60 degree

Difference between temperature  = 60 -55 = 5 degree.

Hence, 5 degree more colder was Tuesday then Saturday.

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Answer:

Step-by-step explanation:

go pathways gives all the answers

The  average for a student with 64 on attendance, 82 on the first paper, 61 on the second paper, 72 on test 1, 64 on test 2, 93 on test 3, and 82 on the final exam is 77.31% and the average for a student with the above scores on the papers, tests, and final exam, but with a score of only 29 on attendance is 73.23%.

a. Average:

Average: 82(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33

Average=5.74+5.49+10.08+8.96+13.02+27.06÷0.91

Average=70.35÷0.91

Average=77.31%

b. Average

Average= 29(0.07)+ 61(0.09)+ 72(0.14) +64(0.14) + 93(0.14)+ 82(0.33)÷0.07+0.09+3(0.14)+0.33

Average=2.03+5.49+10.08+8.96+13.02+27.06÷0.91

Average=66.64÷0.91

Average=73.23%

Therefore the average for both a and b is 77.31% and 73.23%.

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The limit dimensions of the part are 3.135 inches and 3.155 inches

The given parameters are

The limit dimensions of the part are calculated as

Limit = Thickness +/- Tolerance

So, we have

Limit = 3.145 inches +/- 0.010 inches

Expand the above expression

So, we have

Limit = (3.145 inches - 0.010 inches, 3.145 inches + 0.010 inches)

Evaluate the sum

Limit = (3.135 inches, 3.155 inches)

Hence, the limit dimensions of the part are 3.135 inches and 3.155 inches

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Answer:

x=29 angle a=63 Ang b=46 and c=71

Step-by-step explanation:

2x+5+x+17+3x-16=180 (sum of angles in triangles)

value of x is 29 substitute it in angle a b c

a=2*29+5

=63

b=29+17 = 46

c=3*29-16 = 71

Answer: x=18 ==> C

Step-by-step explanation:

19+15+11=14+15+?

19+11=14+?

30=14+?

?=16

?+11+x=19+15+11

x+?=19+15

x+16=34

x=18 ==> C

Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 6.

A bisector divides a segment or angle into two equal halves.

Given the data in the question;

Since XZ is a perpendicular bisector of segment WY,

Segment WX is equal to Segment XY

Segment WX = Segment XY

Plug in the given values and solve for k.

3k + 17 = 7k - 7

Collect like terms

3k - 7k = -7 - 17

-4k = -24

Divide both sides by the coefficient of k

-4k/-4 = -24/-4

k = 6

Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 6.

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Answer:

x=26, y=90

Step-by-step explanation:

This is what I did,

I knew that y = 90 because it is a Right Angle. I subtracted 90 - 64 and that got me = y 26

Therefore, the price elasticity of demand by percentage change method is -0.025.

Given the price of a first commodity (p₁) = 6 rs

the price of a second commodity (p₂) = 10 rs

Expenditure on first commodity (s₁) = 120

Expenditure on second commodity (s₂) = 180

We need to find the quantity as

120 = 6 * Q₁.              180 = 10 * Q₂

Q₁ = 120 / 6                 Q₂ = 180 / 10

Q₁ = 20                         Q₂ = 18

price elasticity of demand by percentage change method as

Eₐ = P / Q * ΔQ /ΔP

ΔQ = Q₂ - Q₁ = 18 -20 = -2

ΔP = p₂ - p₁ = 10 - 6 = 4

Eₐ = 6 / 120 * -2 / 4

Eₐ = - 0.025

Therefore, the price elasticity of demand by percentage change method is -0.025.

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The given system has zero solutions.

Lines that never cross one other are said to be parallel. Hence, a pair of parallel lines must have the same slope but distinct intercepts. (On the other hand, identical lines have same intercept).

In the general equation of a line, y = mx + b, m represents the slope of the line.

The general equations of parallel lines would be of the form:

(1) y = mx + b

(2) y = mx + c

where b and c are any constants.

Now, we observe that the given equations are of the above form with m=2, b=2 and c=0, therefore, they are parallel lines. Since, parallel lines never intersect each other, they have no solution.

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The first company shipping charge is 5 $

the second company shipping charge is 2 $

let the size of the box be 'x'

Given the first company charged as below

20$ for medium-sized and an extra 1$ for one pound

=  20x + 1

The second company charged as below

$5 for the same size of the box, plus an additional $4 per pound

= 5x + 4

The price of the two shipping options will be same.

20x + 1 = 5x + 4

20x - 5x = 4- 1

15x = 3

x= 3 / 15

x = 1/5

x = 0.2

∴ 20x+1 = 20 * 0.2 +1 = 5

   5x + 4 = 5 * 0.2 + 1 = 2

Therefore, The first company's shipping fee is $5, whereas the second company's fee is $2.

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The unit tangent vector for the parametrized curve is [tex]\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}[/tex].

In this question we know a three-dimension parametrized curve, of which we must derive its unit tangent vector in accordance with the following formula:

[tex]\vec T(t) = \frac{\vec R'(t)}{\|\vec R'(t)\|}[/tex]

Where:

First, determine the first derivative of the parametrized curve:

[tex]\vec R'(t) = -\sin t \,\hat{i} + \cos t \,\hat{j} + \cos t \,\hat{k}[/tex]

Second, derive the magnitude of the parametrized curve:

[tex]\|\vec R'(t)\|[/tex] = √[(- sin t)² + (cos t)² + (cos t)²]

[tex]\|\vec R'(t)\|[/tex] = √(1 + cos² t)

Third, substitute every term in the unit tangent curve formula:

[tex]\vec T(t) = - \frac{\sin t}{\sqrt{1 + \cos ^{2} t}}\,\hat{i} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{j} + \frac{\cos t}{\sqrt{1 + \cos ^{2} t}}\,\hat{k}[/tex]

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14912 years ago, the tree that was used to kill the support pole died which is one-sixth of the carbon-14 of a modern, living tree.

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

One-sixth of a modern, living tree's carbon-14 is present in an ancient structure.

Assume that the half-life of carbon-14 is 5770 years

As per the given condition, the expression would be

[tex]A(t) = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}\\A(t) = (0.167)A_o}[/tex]

[tex](0.167)A_o} = A_o}\dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]

[tex](0.167) = \dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]

Take the logarithms of both sides to get:

[tex]log(0.167) =log \dfrac{1}{2} ^{(\frac{t}{5770} )}[/tex]

Using logₐ(xⁿ) = n logₐx.

⇒ log 0.167= (t/5770) log (0.5)

⇒ log 0.167/ log (0.5)= (t/5770)

⇒ 3 = (t/5770)

⇒ t = 3 × 5770

⇒ t = 14912

Hence, 14912 years ago, the tree that was used to kill the support pole died.

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Answer:

See work below.

30 sold for full price and 68 sold for a discount.

Step-by-step explanation:

The length of the pen is 2√3 feet

The formula for calculating the area of a rectangle is expressed according to the formula below:

Area of a right triangle = 1/2 * base * height

A = 1/2 bh

Given the following parameters

Area = 20 square feet

If the height is five times the length, then;

h = 5b

Substitute

A = 1/2 bh

A = 1/2(b)5b

30 = 1/2(5b²)

60 =5b²

b² = 12

b = 2√3

Hence the length of the pen is 2√3 feet

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The height of the box that has a volume of 1250 cubic cm with a length of 20cm and a width of 5cm will be 12.5cm.

It should be noted that the formula for the volume will be:

= Length × Width × Height

Therefore the height will be:

Volume = LWH

where

L = length = 20cm

W = width = 5cm

H = height = unknown

1250 = (20 × 5 × H)

1250 = 100H

Height = 1250/100

Height = 12.5 cm

Therefore, the height is 12.5cm.

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Answer:

31x+0.5

Step-by-step explanation:

In this problem, we must combine like terms to simplify the expression. We can begin by writing out the expression:

13x + 5 + 17x - 4.5 + x

Now that we have rewritten the expression, we can combine like terms to simplify the expression. This would look like:

13x + 17x + x = 31x

5 - 4.5 = 0.5

The answer would be “31x + 0.5” when simplified.

The image of triangle DEF after the dilation with a scale factor of -1/2  is given at the end of the answer.

Transformations in the graph of a function involve operations in the vertices of the image, such as addition, subtraction, division or multiplication.

The transformation used in this problem is a dilation, in which the coordinates of the vertices of the original figure are multiplied by the scale factor.

For this problem, the vertices of the triangle are given as follows:

D(3,6), E(3,2) and F(5,4).

The dilation has a scale factor of -0.5 = -1/2, hence the coordinates of the image are given as follows:

The dilated triangle is given by the graph at the end of this answer.

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Answer:

–24x – 24 = x3 + 8x2

Step-by-step explanation:

-24x-24=x^3+8x^2

x^3+8x^2+24=-24x-24+24

x^3+8x^2+24=-24x

x^3+8x^2+24+24x=-24x+24x

x^3+8x^2+24x+24=0

Answer: x=-2

Step-by-step explanation:

[tex]-24x-24=x^3+8x^2\\-24x-24+24=x^3+8x^2+24\\-24x=x^3+8x^2+24\\-24x+24x=x^3+8x^2+24+24x\\0=x^3+8x^2+24x+24\\x^3+8x^2+24x+24=0\\x^3+8x^2+12x+12x+24=0\\(x)(x^2+8x+12)+(12)(x+2)=0\\(x)(x^2+2x+6x+12)+(12)(x+2)=0\\(x)((x)(x+2)+6(x+2))+(12)(x+2)=0\\(x+2)((x)(x+6)+12)=0\\ (x+2)(x^2+6x+12)=0\\x+2=0\\x+2-2=0+(-2)\\x=-2\\x^2+6x+12=0\\D=(-6)^2-(4)(1)(12)\\D=36-48\\D=-12\\Hence,\\The\ equation\ has\ no\ valid \ roots\\Thus,\\x=-2[/tex]

The distribution is a probability distribution, and the reasons are

The probability distribution is given as:

X     0   1    2

P(X) 0 1/3 2/3

From the above table of probability distribution, we can see that each probability value is between 0 and 1 (inclusive)

Also, the sum of probabilities is 1

i.e. 0 + 1/3 + 2/3 = 1

Hence, the distribution is a probability distribution, and the reasons are

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The turning point of the function f(x) = |x-2| + 3 will be (3, 2).

Here,

We have to find the turning point of the graph of function,

f(x) = |x−2|+3

What is an absolute function?

The non-negative value of real number without regard to its sign is known as its absolute value.

Now,

The absolute function is;

f(x) = |x+3| -2.

Since, When we plot the graph of the absolute function f(x) = |x+3| -2,

it will give two straight lines which is shown in the graph.

Clearly, The graph of the function changes its position at the coordinate

(3, 2).

Therefore, The absolute function having its turning point at the coordinate ( 3, 2).

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Answer:

i don't know how to attach the file

Answer:

8 pizzas

Step-by-step explanation:

Answer:

7.5 : 3.5

Step-by-step explanation:

ratio of time spent studying in math to studying for English is ;

time spent studying in math. / time spent in studying English

[tex] \frac{7.5}{3.5} [/tex]

= 7.5 : 3.5

Answer:

1/8

Step-by-step explanation:

When worked out, all numbers are equal to 1.8 except 1/8. (1/8 is equal to .125)

1/8) 1 divided by 8 is .125

18/10) 18 divided by 10 is 1.8

1.8) 1.8=1.8

1 4/5) 4 divided by 5 is .8, and when you add the 1 it ends up as 1.8

Answer:

Step-by-step explanation:

According to the graph, point A has a negative value, between - 1 and zero.

All the expressions could result in negative value apart from the sum of the squares, which is never negative.

Correct choice is C.

Answer:

2445

Step-by-step explanation:

it would have 2445 more costumers

Answer:

2445

Step-by-step explanation:

Subtract.

14301 - 11856 = 2445 more people on weekdays