peter put $8,000 into a savings account that pays 6% interest, compounded continuously. what will he have after 5 years?

Answers

Answer 1

So, continuous compound formula is:
[tex] Pe^{rt} [/tex]
P is Principal Amount
r is Rate
t is Time
P is 8000
r is 6%
t is 5
Therefore, you get $10,798.86.

Related Questions

In a right triangle, the measure of one acute angle is 13°. What is the measure of the other acute angle?
32°
77°
90°
167°

Answers

77° is your answer.

-JJ

The sum of the angles in a triangle is always 180 degrees. In a right triangle, one angle is 90 degrees, and given that one acute angle is 13 degrees, the measure of the other acute angle is 180 - 90 - 13, which equals 77 degrees.

In the context of Euclidean geometry, we have a well-established theorem which stipulates that the sum of the angles in any triangle equals 180 degrees. Since we are dealing with a right triangle, we know that one of its angles measures 90 degrees. The question states that one acute angle measures 13 degrees. To find the measurement of the other acute angle, we subtract the known angles from 180 degrees.

180 degrees (sum of all angles in a triangle) - 90 degrees (right angle) - 13 degrees (given acute angle) = 77 degrees.

Therefore, the measure of the other acute angle is 77 degrees.

Joylin receives a 50 gift card for the local movie theater for her birthday. She uses the card to purchase tickets and snacks for her family.if joylin spends $6more on tickets than she does on snacks, how much does joylin spend on tickets.

Answers

Let amount spent on snacks be x
amount spent on tickets be x+6

So, x+(x+6) = 50
2x = 44
x = 22 (44/2)
so, (x+6) = 22+6 = 28

Final answer is $28

Answer:

Step-by-step explanation:

edge 2020

What is the sun made of (by mass)?
a. 50 percent hydrogen, 25 percent helium, 25 percent other elements
b. 70 percent hydrogen, 28 percent helium, 2 percent other elements
c. 90 percent dark matter, 10 percent ordinary matter
d. 100 percent hydrogen and helium?

Answers

B. 70 percent hydrogen, 28 percent helium, 2 percent other elements

Anyone know the answer?

Answers

3. Both are supplementary to angle BCE
4. Angle 2 = Angle 1

Find the solution of this system of equations. Separate the x- and y- values with a comma. x+4y=1 and x-y=1

Answers

Equation 1: x+4y=1
Equation 2: x-y=1

solve equation 2 for x: x=1-y
substitute 1-y into equation 1: (1-y) +4y=1
solve for y: 1-y+4y=1
1+3y=1
3y=0
y=0
Substitute y=0 into equation 2: x-(0)=1
x=1
Solution: (1,0)

A lady bought plates and bowls, 24 items in all. The price of each bowl was 60 cents; the price of each plate was 75 cents. The cost of the whole purchase was $15. How many plates did the lady buy?

Answers

plate bowl total
.60 .75 1.35
8.4(14) 7.5(10) 15.9
7.8(13) 8.25(11) 16.05
9.6(16) 6(8) 15.6
9(15) 6.75(9) 15.75
13.8(23) .75 14.55
13.2(22) 1.5(2) 14.7
12.6(21) 2.25(3) 14.85
12(20) 3(4) 15

answer: 4

aina, Kareem, and David have a total of $92 in their wallets. Kareem has $7 less than Raina. David has 3 times what Kareem has. How much do they have in their wallets?

Answers

Answer: Kareem has $17, David has $51, Raina has $24

-----

Step 1:
Solve this by using a system of equations. Start by changing what you're given from words into equations. Put variables in for the peoples' names. Let's say Raina = R, Kareem = K, and David = D. You will have 3 equations:
1) Raina, Kareem, and David have a total of $92 in their wallets.
R + K + D (sum of all three) = 92 (total)

2) Kareem has $7 less than Raina
K = R - 7 (seven less than Raina)

3) David has 3 times what Kareem has.
D = 3K (three times Kareem)

-----

Step 2:
You can solve for the values of R, K, and D using substitution. Let's put the first equation, R + K + D = 92, all in terms of one variable, so we can solve for that variable. Since both equations 2 and 3 have K in relation to one of the other variables, I will be putting equation 1 in terms of K! Do this by substitution some equation of K in for variables R and D in the first equation.

From equation 2, we know that K = R - 7. Add 7 to both sides, making R = K + 7.
From equation 3, we know that D = 3K. This is already in perfect form to substitute.

Now substitute both R = K + 7 and D = 3K into the first equation. Simplify and solve for K:
R + K + D = 92
(K + 7) + K + (3K) = 92
5K + 7 = 92
5K = 85
K = 17

Kareem has $17 in his wallet.

-----

Step 3:
Now that you know K = 17, plug that into equation 3, D = 3K, and solve for how much David has:
D = 3K
D = 3(17)
D = 51

David has $51 in his wallet.

-----

Step 4:
Finally, plug K = 17 into equation 2, K = R - 7, to find how much Raina has:
K = R - 7
17 = R - 7
R = 24

Raina has $24 in her wallet.

Final answer:

Kareem has $17, Raina has $24 ($17 + $7) and David has $51 (3 x $17).

Explanation:

Let's represent the amount of money that Kareem has in his wallet as 'K'. Since Kareem has $7 less than Raina, we can represent Raina's amount of money as 'K + 7'. David has 3 times what Kareem has, so we can represent David's amount of money as '3K'.

According to the problem, the sum of all three amounts is $92. So we can set up the equation: K + (K + 7) + 3K = 92.

Combining like terms, we get 5K + 7 = 92. Subtracting 7 from both sides, we have 5K = 85. Dividing both sides by 5, we find that K = 17. Therefore, Kareem has $17, Raina has $24 ($17 + $7) and David has $51 (3 x $17).

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A truck tire has a diameter of 4 feet and is revolving at a rate of 45 rpm. at t = 0, a certain point is at height 0. what is the height of the point above the ground after 15 seconds?

Answers

45 rpm=2π rad*45/60=1.5π rad/sec
radius=1.5 ft
axle at 2 ft and up and down from there:
thus
y=2-1.5cos(1.5πt)
to make y=0 at 0
at 15 sec
y=2-1.5cos(15*1.5π)
y=2-0
y=2 ft

How to solve x in a trapezoid

Answers

For Volume is V=(base1 + base2)h and then divide by two

At the zoo on Monday, 65 percent of the people in attendance were children. If 520 children were in attendance, how many people in total were visiting the zoo on Monday?

Answers

800 people because when you try to find the number of people, x, you do cross multiply. So it will be 520/x = 65/100, next you multiply 520 by 100, then divide that by 65 to get 800 people

Answer:

800+

Step-by-step explanation:

You are considering two investment opportunities. For investment A there is a 25% chance that you lose $20,000, a 50% chance that you break even, and a 25% chance that you make $80,000. For investment B there is a 30% chance that you lose $50,000, a 50% chance that you break even, and a 20% chance that you make $180,000. Based on the expected value of each, which investment should you make?

Answers

The answer is investment B.

Solution:
For investment A - the expected value of the investment is
($20,000) * 25% = ($5,000)
$80,000 * 25% = $20,000
$15,000

For investment B - the expected value of the investment is
($50,000) * 30% = ($15,000)
$180,000 * 20% = $36,000
$21,000

So you can gain more by $6,000 if you choose investment B.

Answer:

For investment A - $15,000

For investment B - $21,000

So you can gain more by $6,000 if you choose investment B.

Step-by-step explanation:

A 12' by 20' rectangular garden is to have a walkway of uniform width added around its entire perimeter. if the area of the walkway is 68 square feet, find the width of the walkway.

Answers

I believe you will have to times 12’ by 20’ then divide 68 by it I hope this helps

A restaurant offers 88 appetizers and 99 main courses. in how many ways can a person order a two-course meal

Answers

Number of ways = 88 x 99 = 8712

Answer: 8712

A right rectangular prism has base dimensions of 3 inches by 12 inches and a height of 5 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches and a height of 5 inches. Are the volumes the same?

Answers

Volume of right rectangular prism = Length x Width x Height
Using the given dimensions, we can write:

Volume of right rectangular prism = 3 x 12 x 5 = 180 cubic inches

Volume of oblique rectangular prism = Base Area x Height
Base Area = 4 x 9 = 36 square inches

So, Volume of oblique rectangular prism = 36 x 5 = 180 cubic inches

Thus, we can conclude that the two volumes are the same.

A right triangle has legs that measure 7cm and 3cm. What is the length of the Hypotenuse?

Answers

7² + 3² = c²
49 + 9 = c²
58 = c²
c = √58

Answer:

square root of 58

Step-by-step explanation:

If its wrong e2020 says its right

A skier leaves an 8-foot-tall ramp with an initial vertical velocity of 28 feet per second. the function h = −16t^2 28t 8 represents the height h (in feet) of the skier after t seconds. the skier has a perfect landing. how many points does the skier earn? 1 point per foot in the air, 5 points per second in the air, and a perfect landing is 25 points.

Answers

The skier earns 35.875 points.

We can find the height in the air by using -b/2a:
-28/2(-16) = -28/-32 = 0.875

This will give the skier 0.875 points.

To find the amount of time in the air, we solve the related equation:
0=-16t²+28t+8

We will first factor out the GCF, -4:
0=-4(4t²-7t-2)

Now we will factor the trinomial in parentheses using grouping. We want factors of 4(-2)=-8 that sum to -7; -8(1) = -8 and -8+1=-7. This is how we will "split up" bx:
0=-4(4t²-8t+1t-2)

Now we will group the first two and last two terms:
0=-4[(4t²-8t)+(1t-2)]

We will factor out the GCF of each group:
0=-4[4t(t-2)+1(t-2)]

This gives us the factored form:
0=-4(4t+1)(t-2)

Using the zero product property, we know that either t-2=0 or 4t+1=0:
t-2=0
t-2+2=0+2
t=2

4t+1=0
4t+1-1=0-1
4t=-1
4t/4 = -1/4
t=-1/4

Negative time makes no sense, so t=2. This gives the skier 5(2) = 10 points.

Counting the perfect landing, we have 25+10+0.875 = 35.875 points.

Final answer:

The skier earns approximately 27 points.

Explanation:

To find the total points earned by the skier, we need to calculate the time it takes for the skier to reach the ground. In this case, the height function h = -16t^2 + 28t + 8 represents the height of the skier after t seconds. To find the time it takes for the skier to reach the ground, we need to find the value of t when h = 0.

Setting h = 0, we get:

-16t^2 + 28t + 8 = 0

Using the quadratic formula, t = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = -16, b = 28, and c = 8:

t = (-28 ± sqrt(28^2 - 4(-16)(8))) / (2(-16))

Simplifying the equation, we get:

t = (-28 ± sqrt(672)) / -32

t = (-28 ± 26) / -32

Since the skier has a perfect landing, we can disregard the negative value and take the positive value of t:

t = (-28 + 26) / -32

t = -2 / -32

t = 1/16

This means the skier takes 1/16 seconds to reach the ground. To calculate the total points earned, we need to find the total time the skier is in the air. Since the skier starts with an initial vertical velocity of 28 ft/s, we can use this velocity to find the time it takes to reach the ground:

t = h / v

t = 8 / 28

t = 2/7 seconds

Therefore, the skier is in the air for 2/7 seconds. To find the total points earned:

Points = (h * 1) + (t * 5) + 25

Points = (8 * 1) + ((2/7) * 5) + 25

Points = 8 + (10/7) + 25

Points = 189/7

So, the skier earns approximately 27 points.

Find the value of each variable. If your answer is not an integer, express it in simplest radical form. Please explain how you got the answer! I can't figure it out.

Answers

For y we have:
sine (60) = y / 14
Clearing y we have:
y = 14 * sine (60)
Rewriting:
y = 14 * (root (3) / 2)
y = 7 * root (3)

For x we have:
cosine (60) = x / 14
Clearing x we have:
x = 14 * cosine (60)
x = 14 * (1/2)
x = 7

Answer:
the value of each variable is:
y = 7 * root (3)
x = 7

In the given right triangle, x and y are 7 and 7√3 respectively.

What is the sine of an angle?

Sine of an angle = [tex]\frac{OPPOSITE SIDE}{HYPOTENUSE}[/tex]

From the diagram, we can see that y is the opposite side to angle B while x is the adjacent side while 14 is the hypotenuse.

Sin α = opposite side/ hypotenuse

Sin 60° = y/14(given)

y = 14sin60

y=7√3

Cos α = adjecent side / hypotenuse

Cos60° = x/14(given)

x = 14cos60

x= 7

So, for the given right triangle x and y are 7 and 7√3 respectively.

Therefore, In the given right triangle, x and y are 7 and 7√3 respectively.

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Tabby Soft believes that it will need new equipment in 5 years. The equipment will cost $26,000. What lump sum should be invested today at 6%, compounded semiannually, to yield $26,000? a. $22,558.87 c. $22,390.94 b. $23,948.47 d. $19,346.44

Answers

The following compounding formula applies:
A = P (1+R/2)^2t

Where, A = Amount after 5 years = $26,000; P = Amount invested now; R = Annual rate of earning = 6% = 0.06; t = time = 5 years.

Substituting;
26000 = P(1+0.06/2)^2*5 = P(1.3439)

Therefore, P = 26000/1.3439 = $19,346.44

The correct answer is d.

Answer:

Step-by-step explanation just put D

The length of a rectangle is twice the width. the area is 256 squared. find the length and the width.

Answers

The solution is quite simple.
First, draw a rectangle. Label two opposite sides as "w", representing the width. Label the other two sides as "2w", since the length is twice the width.
Next, write an equation. In this case, the equation would be 256=2w*w.
Simplify the equation to 2w^2=256. Divide both sides by two to get w^2=128. The width would be the square root of 128. The length would be twice that, so it would be the square root of 256. That would be 16, so the length is 16.

sigma notation 2+ (-8)+32+(-128)+...

Answers

here u go hope this helps

Whst is the remainder when f(x)=x^3+3x^2-10x-4 is diveded by x-3

Answers

The polynomial remainder theorem allows us to calculate the remainder when a polynomial is divided by a linear polynomial:
The remainder of f(x) divided by (x-k) equals f(k).

Thus
f(x)=x^3+3x^2-10x-4 divided by x-3
gives a remainder of
f(3)=27+3(9)-10(3)-4=27+27-30-4=20
Therefore the remainder required is 20.

The remainder when the polynomial [tex]f(x)=x^3+3x^2-10x-4[/tex] is divided by x-3 is found using the Remainder Theorem and is 20.

The remainder when a polynomial f(x) is divided by a linear divisor such as x - 3 can be found using the Remainder Theorem, which states that the remainder is simply f(3). To find the remainder for [tex]f(x)=x^3+3x^2-10x-4[/tex], we substitute x = 3 into the polynomial.

Calculate f(3):

[tex]f(3) = (3)^3 + 3*(3)^2 - 10*(3) - 4[/tex]

f(3) = 27 + 27 - 30 - 4

f(3) = 54 - 34

f(3) = 20

Therefore, the remainder when f(x) is divided by x - 3 is 20.

What is the volume of the cone to the nearest tenth?

1,244.1 m^3

829.4 m^3

552.9 m^3

1,520.5 m^3

Answers

The formula for the volume of a cone is
V = (1/3)π*r^2*h
Of course, the radius is half the diameter, so is 11 m. Substituting the given values, you have
V = (1/3)π(11 m)^2*(12 m)
V = 484π m^3
V ≈ 1520.5 m^3

The volume of the cone to the nearest tenth is ...
1520.5 m³

In the school election, votes were cast for sam, mary, and bill in the ratio of 4:3:2. if a total of 2178 votes were cast, how many votes did mary receive?

Answers

2178÷(4+3+2)=242
Sam's votes=242×4=968
Mary's=242×3=726
Bill's=242×2=484

Mary received 726 votes.

Find the quotient of -36x^3-6x^2+12x/-6x

Answers

Answer:
6x² + x - 2

Explanation:
To find the quotient of a polynomial expression divided by a monomial, divide each term by the monomial.

[tex]\frac{-36x^3-6x^2 + 12x}{-6x}[/tex] becomes [tex]\frac{-36x^3}{-6x} + \frac{(-6x^2)}{(-6x)} + \frac{12x}{(-6x)}[/tex]

-36x³ / (-6x) = 6x²

(-6x²) / (-6x) = 1x = x

12x / -6x = -2

Place each of these terms together into an polynomial expression once more and the quotient is: 6x² + x - 2

40 POINTS!

Find the exact value by using a half-angle identity.

⬇️⬇️⬇️

Answers

[tex]\cos\dfrac{5\pi}{12}=\cos\left(\dfrac{6\pi}{12}-\dfrac{\pi}{12}\right)=\cos\left(\dfrac{\pi}{2}-\dfrac{\pi}{12}\right)=(*)[/tex]

[tex]Use: \cos(\alpha-\beta)=\cos\alpha \cos\beta+\sin\alpha \cos\beta[/tex]

[tex](*)=\cos\dfrac{\pi}{2} \cos\dfrac{\pi}{12}+\sin\dfrac{\pi}{2} \sin\dfrac{\pi}{12}\\\\=0\cdot\cos\dfrac{\pi}{12}+1\cdot\sin\dfrac{\pi}{12}=\sin\dfrac{\pi}{12}[/tex]

[tex]\dfrac{\pi}{12}=\dfrac{\dfrac{\pi}{6}}{2}[/tex]

[tex]The\ half-angle\ identity\ \sin^2\dfrac{\alpha}{2}=\dfrac{1}{2}\left(1-\cos\alpha\right)[/tex]

[tex]Using\ the\ above\ formulas,\ we\ get:\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}\left(1-\cos\dfrac{\pi}{6}\right)\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}\left(1-\dfrac{\sqrt3}{2}\right)\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}-\dfrac{\sqrt3}{4}[/tex]

[tex]Since\ 0 \ \textless \ \dfrac{\pi}{12} \ \textless \ \pi,\ then\ \sin\dfrac{\pi}{12}\ is\ a\ positive\ number.\\\\ Therefore,\ we\ have:\\\\\sin\dfrac{\pi}{12}=\sqrt{\dfrac{1}{2}-\dfrac{\sqrt3}{4}}=\sqrt{\dfrac{2-\sqrt3}{4}}=\dfrac{\sqrt{2-\sqrt3}}{2}[/tex]

[tex]Answer:\ \boxed{\cos\dfrac{5\pi}{12}=\dfrac{\sqrt{2-\sqrt3}}{2}}[/tex]

I agree with him because it's correct and makes sense!

The function g(x)=(x-2^2. The function f(x)=g(x) +3

The function f(x) is shifted horizontally how many places to where ?

The function f(x) is shifted vertically how many places where ?

Answers

the parent function is:
y = x ^ 2
Applying the following function transformation we have:
Horizontal translations:
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right.
We have then:
g (x) = (x-2) ^ 2
Then, we have the following function transformation:
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
We have then that the original function is:
g (x) = (x-2) ^ 2
Applying the transformation we have
f (x) = g (x) +3
f (x) = (x-2) ^ 2 + 3
Answer:
the function f(x) moves horizontally 2 units rigth.
The function f (x) is shifted vertically 3 units up.

Answer:

The function f(x) moves horizontally 2 units right.

The function f (x) is shifted vertically 3 units up.

Step-by-step explanation:

The diameter of a circle has endpoints (-3, 2) and (3, -2) which is closest to the length of the diameter of the circle?

Answers

D=√((x2-x1)²+(y2-y1)²)

D=√((x2-x1)²+(y2-y1)²) = √(3-(-3))²+(-2-2)²) = √(6² + 4²)=√(36+16)=√52
D=2√13≈7.21

[tex]\text{Diameter = } \sqrt{(2+ 2)^2+ (-3-3)^2 } = \sqrt{16 + 36} = \sqrt{52} = 7.21 \text{ units}[/tex]

Answer: Diameter = 7.21 units

A boat traveled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average of (v+3) miles per hour. if the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?

Answers

Trip upstream took 90v−390v−3 hours and trip downstream took 90v+390v+3 hours. Also given that the difference in times was 1212 hours --> 90v−3−90v+3=1290v−3−90v+3=12;

90v−3−90v+3=1290v−3−90v+3=12 --> 90(v+3)−90(v−3)v2−9=1290(v+3)−90(v−3)v2−9=12 --> 90∗6v2−9=1290∗6v2−9=12 --> v2=90∗6∗2+9v2=90∗6∗2+9 --> v2=9∗(10∗6∗2+1)v2=9∗(10∗6∗2+1) --> v2=9∗121v2=9∗121 --> v=3∗11=33v=3∗11=33;

Trip downstream took 90v+3=9033+3=2.590v+3=9033+3=2.5 hours.

PLS HELP ME ASAP WITH C!! (SKETCH A LINE THAT REPRESENTS THE DIFF SHAPES)

- ALSO INDICATE WHICH LINE IS WHAT FUNCTION

THANK YOU!!

(Random answers gets moderated!)

Answers

Since the cross section is of uniform width (front to back), the fill rate (rate of change of depth vertically) is inversely proportional to the horizontal (side-to-side) dimension.

a) The horizontal width is narrow near the bottom, so the fill rate will be relatively fast until the depth where the width changes. Then the fill rate will slow to perhaps 1/3 of what it was.

b) The horizontal width is a linearly decreasing function of depth, so the fill rate will be increasing on a hyperbolic curve--increasingly fast as the depth increases.

c) This is the reverse of case (a). The fill rate is initially slow, then jumps dramatically when the depth reaches the point where the horizontal width suddenly narrows.

It is not clear whether you are supposed to graph fill rate as a function of depth or as a function of time. The desriptions are for fill rate. If you want to graph versus time, these descriptions apply to the slope of the curve, not its level.

From a carton containing 50kg of sugar 24 half-kilogram packets were taken . How many kilograms of sugar remained?

Answers

24 half-kg packets = 24 x 1/2 = 12kg

Sugar remained = 50 - 12 = 38 kg

Answer: 38 kg

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