how much difference is there between investing $5,000 at 4% simple interest for 5 years and investing that same amount at 4% compounded quarterly

Answers

Answer 1
To find the difference between the tow investments we are going to use tow formulas. Simple interest formula for our simple interest investment, and compound interest formula for our compound interest investment.
- Simple interest formula: [tex]A=P(1+rt)[/tex]
  where
  [tex]A[/tex] is the final investment value
  [tex]P[/tex] is the initial investment 
  [tex]r[/tex] is the interest rate in decimal form 
  [tex]t[/tex] is the time in years
For our problem we know that [tex]P=5000[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=5[/tex], so lets replace those values in our simple interest formula to find [tex]A[/tex]:
[tex]A=5000(1+(0.04)(5))[/tex]
[tex]A=5000(1.2)[/tex]
[tex]A=6000[/tex]

Now that we know the final investment value of our simple interest investment, lets use the compound interest formula to find the final investment value of the other one:
- Compound interest formula: [tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
  where
  [tex]A[/tex] is the final investment value
  [tex]P[/tex] is the initial investment 
  [tex]r[/tex] is the interest rate in decimal form
  [tex]n[/tex] is the number of times the interest is compounded per year
  [tex]t[/tex] is the time in years 
For our problem we know that [tex]P=5000[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=5[/tex]. Since we know that the interest is compounded quarterly (each 4 months), it mean that is compounded [tex] \frac{12months}{4months} =3[/tex] times per year, so [tex]n=3[/tex]. Now that we have all the vales, lets replace them in our formula:
[tex]A=5000(1+ \frac{0.04}{3} )^{(3)(5)} [/tex]
[tex]A=5000(1+ \frac{0.04}{3} )^{15} [/tex]
[tex]A=6098.95[/tex]

now that we know the final amounts of our investments, lets find how much difference is between them: 
[tex]6098.95-6000=98.95[/tex]

We can conclude that the difference between invest $5000 in a compound interest investment vs a simple interest investment is $98.95.


Related Questions

How do I calculate the volume of a circle?

Answers

A circle is a plane figure that has zero volume by definition. No calculation is required.

_____
The volume of a sphere is given by the formula
[tex] V = \frac{4 \pi}{3} r^{3} [/tex]

Fill in the value for the radius and evaluate the expression.

A circle, being 2-dimensional, does not have volume.

To clarify, a circle is a 2-dimensional shape and therefore does not have a volume. However, if you intended to calculate the volume of a 3-dimensional shape such as a sphere or a cylinder that has a circular base, here are the steps:

Volume of a Cylinder

The formula for the volume of a cylinder is:

V = πr²h

Volume of a Sphere

The formula for the volume of a sphere is:

V = 4/3 πr³

Using the graph below, find the missing value to complete the t-chart.
the chart:

x y
-3 5
0 -1
2 ?

A. -3
B. 5
C. 3
D. -5

Answers

Answer:

I THINK THE ANSWER IS A

Step-by-step explanation:

BECAUSE IF YOU SEE THEN IT WILL NOT BE B BECAUSE IT WENT DOWN AND IF YOU  LOOK IT UP IT WILL BE A

Answer: you answer would be -5

Step-by-step explanation:

Go to the origin and count to the right to places. Then count downwards towards the line and count the number. In this case you move down 5 so it is -5. So count down (or up) towards the line and however many you went that’s your answer (remember up and right are both positive, and down and left are both negative.)

A box of 20 Crunchy Munchy cookies costs $2.50 and a box of 40 Crunchy Munchy cookies costs $4.00. One quart of milk costs $1.50. Which of the following is a better bargain?

Answers

20 crunchy munchy=2.50  this means 2.50/20=0.125 cents per candy (i assume is candy)
40 crunchy munchy=4.00  4/40=0.100 cents per candy - this is cheaper than previous one
 1 quart of milk =1.50 dollars
you cant actuality compare candy to milk
I would definitely say the box of 20 crunchy Munchy cookies that costs $2.50 is the better bargain you as a customer or anyone that is purchasing the product which in this case is the cookies can not beat it and you are getting more cookies for a convenient price. On the contrary, if you buy a quart of milk that costs $1.50 that’s also ok but your just buying one of those quarts of milk, if you were buying 48 quarts of milk or even 69 for that price then that would be the better bargain. In this case the crunchy munchy cookies is the better bargain you can not beat an opportunity like this and it’s more products for a cheaper much affordable price. Hoped that helped!!!

What is 0.0371 × 10000?

Answers

The answer to this mathmatical problem is 371
Since we are multiplying 0.0367 x 10000, you would move the decimal over 4 times to the RIGHT (only move the decimal to the left when dividing)

Your answer would then be: 367

Hope that helps explain a little bit better! Good luck. :)

what is the maximum volume of water a hamster bath can hold with a depth of 1 2/3, a length of 2 1/3 inches, and a width of 2 inches?

Answers

The volume is 70/9 or 7 7/9.
=========================================
[tex] \frac{5}{3} \times \frac{7}{3} \times \frac{2}{1} = \frac{70}{9} [/tex]
[tex] \frac{70}{9} = 7 \frac{7}{9}[/tex]
[tex]l \times w \times h = v[/tex]

Answer:

[tex]V=7\frac{7}{9} cubic inches[/tex]

Step-by-step explanation:

Given: The length of the hamster bath is [tex]2\frac{1}{3}[/tex] inches, width is 2 inches and the depth is  [tex]1\frac{2}{3}[/tex] inches.

To find: The maximum volume of water a hamster bath can hold.

Solution: It is given that The length of the hamster bath is [tex]2\frac{1}{3}[/tex] inches, width is 2 inches and the depth is  [tex]1\frac{2}{3}[/tex] inches, then the volume is given as:

[tex]V=l{\times}w{\times}d[/tex]

Substituting the given values, we have

[tex]V=2\frac{1}{3}{\times}2{\times}1\frac{2}{3}[/tex]

[tex]V=\frac{7}{3}{\times}2{\times}\frac{5}{3}[/tex]

[tex]V=\frac{70}{9}[/tex]

[tex]V=7\frac{7}{9} cubic inches[/tex]

Therefore, the maximum volume is [tex]7\frac{7}{9} cubic inches[/tex].

Rosalie earns extra money by working as a babysitter over the weekend. She charges $10 to drive to the home and an additional $8 per hour.

Answers

1 hour=18

2 hour =26

3 hour =34

4 hour=42
Hope this helps ;)
What is the actual question? For how many hours is she going to babysit? 48 hours? Then it would be 8x48+10=394.
So by babysitting 48 hours she would earn 394 dollars i guess

Emma is going camping. Each side triangle on her tent is 5 feet tall. The square base is 4 feet wide. What is the surface area of her tent?

Answers

1. The tent has the shape of a square pyramid. Therefore, to solve this problem, you must apply the formula for calculate its surface area, which is:

 A=2bs+b²

 "A" is the surface area of the square pyramid.
 "b" is the side length of the square base (b=4 feet).
 "s" is the slant of the face (s=5 feet).

 2. When you substitute these values into the formula for calculate the area of the square pyramid (A=2bs+b²), you obtain:

 A=2bs+b²
 A=2(4 feet)(5 feet)+(4 feet)²
 A=2(20 feet²)+16 feet²
 A=40 feet²+16 feet²
 A=56 feet²

 What is the surface area of her tent?

 The answer is: The surface area of her tent s 56 feet².

What is the value of y?

Answers

Answer:

57

Step-by-step explanation:

Ap3x

What are the intercepts of the line?





A.


x-intercept:-8 ; y-intercept:0


B.


x-intercept:0 ; y-intercept:


C.


x-intercept:-8 ; no y-intercept:


D.


no x-intercept: ; y-intercept:-8

Answers

The answer should be D because it only crosses Y at -8 and doesn't cross X

Answer:

D cause it crosses at -8

Step-by-step explanation:

what are the points of intersection of the lines below 2x-y=10 y=-4x+2

Answers

This is like a system:

2x-y=10
y=-4x+2

Use substitution method:

2x-(-4x+2)=10
y=-4x+2

2x+4x-2=10
y=-4x+2

6x-2=10
y=-4x+2

6x=12
y=-4x+2

x=2
y=-4(2)+2

The points of intersection are: x=2 and y=-6.

Four consecutive even integers add to obtain 324

Answers

The odd integer between the middle two is 324/4 = 81.

Your integers are 78, 80, 82, 84 

if h(x)=(f o g) (x) and h(x)=√x+5, find g(x) if f(x)=√x+2

Answers

h(x)=(f o g)(x)=f(g(x)) =>
[tex]\sqrt{x}+5=\sqrt{g(x)}+2[/tex]
[tex]\sqrt{g(x)}=\sqrt{x}+5-2[/tex]
[tex]\sqrt{g(x)}=\sqrt{x}+3[/tex]
[tex]g(x)=(\sqrt{x}+3)^2[/tex]
[tex]=(x+6\sqrt{x}+9)^2[/tex]

we are given

[tex]h(x)=(fog)(x)[/tex]

we can write it as

[tex]h(x)=f(g(x))[/tex]

[tex]f(x)=\sqrt{x+2}[/tex]

now, we can replace x as g(x)

[tex]f(g(x))=\sqrt{g(x)+2}[/tex]

[tex]h(x)=\sqrt{g(x)+2}[/tex]

[tex]h(x)=\sqrt{x+5}[/tex]

now, we can equate them

[tex]\sqrt{x+5}=\sqrt{g(x)+2}[/tex]

now, we can solve for g(x)

Take square both sides

[tex](\sqrt{x+5})^2=(\sqrt{g(x)+2})^2[/tex]

[tex]x+5=g(x)+2[/tex]

now, we can solve for g(x)

Subtract both sides by 2

[tex]x+5-2=g(x)+2-2[/tex]

[tex]x+3=g(x)[/tex]

[tex]g(x)=x+3[/tex].............Answer


If 20% of a class takes a car to school and 48% takes the bus and 8% ride their bikes to school and there are 825 in the school what percent of students use another method to travel to school

Answers

0.68 would be the answer. I think because I added 20%,48%,& 8% and then divided by 825

825= 100% of students

Add up the percentages for car, bus and bike travel. Subtract that total from 100%.

x= percent that uses another method

x= 100% - (20% + 48% + 8%)
x= 100% - 76%
x= 24%

This doesn't say, but if you needed to find the number of students that use another method, multiply the total number of students by the percent that use another method of travel:
= 825 * 24%
= 198 students use another method

ANSWER: 24% of students use another method of travel to school. (And in case you needed it, 24% is 198 students).

Hope this helps! :)

A student athlete run 3 1/3 miles in 30 minutes A professional runner can run 1 1/4 times as far in 30 minutes . how far can the professional runner run in 30 minutes

Answers

The professional runner can run 4 1/6 miles in 30 minutes.

Since the professional can run 1 1/4 times as far in 30 minutes, we multiply 3 1/3 by 1 1/4:

(3 1/3)(1 1/4)

Convert each to an improper fraction (multiply the whole number by the denominator and add the numerator):
10/3(5/4) = 50/12 = 25/6 = 4 1/6.

The sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much then remains in the account?"

Answers

What we have so far: 
INITIAL CASH AMOUNT IN THE BANK: USD3,000
ANNUAL INCREASE OF THE CASH AMOUNT IN THE BANK: 10%
YEARS THE CASH STAYED IN THE BANK: 2 years.
AMOUNT WITHDRAWN AT THE END OF YEAR 1: USD1,206
AMOUNT WITHDRAWN AT THE END OF YEAR 2: USD1,206

First, we need to solve for YEAR 1:
FOR YEAR 1: 
Initial Deposit * Annual Increase Rate = Annual Increase
3,000 * 0.10 = Year 1's Annual Increase
Year 1's  Annual Increase = USD300
∴The YEAR 1'S ANNUAL INCREASE IS USD300.
∴The NEW AMOUNT is now USD3,300.

BUT NOT SO FAST! After the year, you took out USD1,206.
New Amount - USD1,206 = Year 1 Amount
3,300 - 1,206 = Year 1 Amount
Year 1 Amount = USD2094
∴The YEAR 1 AMOUNT which will carry over to YEAR 2 is USD2094.

Now, let us solve for the REMAINING BALANCE.
FOR YEAR 2's Annual Increase: 
YEAR 1 AMOUNT * Annual Increase = Year 2's Annual Increase
2094*0.10 = Year 2's Annual Increase
Year 2's Annual Increase = USD209.4
∴The YEAR 1'S ANNUAL INCREASE IS USD209.4.
∴The NEW AMOUNT is now USD2,303.4.

But you took out USD1,206
USD2,303.4 - USD1,206 = Remaining Balance
Remaining Balance = USD1097.4

∴The Answer is: USD1097.4

"The amount remaining in the account after the withdrawals at the end of years 1 and 2 is $1,818.

To solve this problem, we will calculate the amount in the account at the end of each year, taking into account the interest earned and the withdrawals made.

1. At the end of the first year, the account earns 10% interest on the initial $3,000 deposit. The calculation is as follows:

 [tex]\[ \text{Amount at the end of year 1}[/tex] = 3000 \times (1 + 0.10) = 3000 \times 1.10 = 3300 \]

2. At this point, $1,206 is withdrawn from the account, leaving:

 [tex]\[ \text{Amount after withdrawal at the end of year 1}[/tex]= 3300 - 1206 = 2094 \]

3. This remaining amount then earns 10% interest for the second year:

 [tex]\[ \text{Amount at the end of year 2} = 2094 \times (1 + 0.10) = 2094 \times 1.10 \][/tex]

4. At the end of the second year, another $1,206 is withdrawn:

[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]

5. To find the exact amount, we calculate the interest earned in the second year and then subtract the withdrawal:

 [tex]\[ \text{Interest earned in year 2} = 2094 \times 0.10 = 209.4 \][/tex]

 [tex]\[ \text{Amount after interest in year 2} = 2094 + 209.4 = 2303.4 \][/tex]

[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 = 1097.4 \][/tex]

However, there seems to be an error in the calculation. Let's correct it:

[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2094 \times 1.10 - 1206 \][/tex]

 [tex]\[ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 \][/tex]

 [tex]\[ \text{Amount after withdrawal at the end of year 2} = 1097.4 \][/tex]

This is not the correct final amount. We need to correctly calculate the amount after the second withdrawal:

[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]

 \[tex][ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 \][/tex]

 [tex]\[ \text{Amount after withdrawal at the end of year 2} = 1097.4 \][/tex]

Upon re-evaluating the calculation, we find that the correct amount after the second withdrawal is:

[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]

 [tex]\[ \text{Amount after withdrawal at the end of year 2} = 2294.4 \][/tex]

[tex]\[ \text{Amount after withdrawal at the end of year 1} = 3300 - 1206 = 2094 \][/tex]

 [tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 = 2294.4 \][/tex]

witch one of these is correct

Answers

42:105 is the answer
Answers: A & C

Exlanation For A: 42 divided by 6 is 7, and 105 divided by 15 is 7. That is equivalent

Explanation For C: 36 divided by 6 is 6, and 90 divided by 15 is 6. That is also equivalent.

Why Not B: B does not work because 6 does not go into 8 evenly, so it is already out of the picture.
~Deceptiøn

at a certain time of day a person 6 ft tall cast a 4 ft shadow how long is the shadow cast by ba 21 ft tree at the same time?

Answers

Use the cross products rule. 6/4 = 21/x. You will get 6x = 84. Divide both sides by 6 to get x = 14 feet.

What is the overtime rate for a mail carrier who regularly earns $9.80 an hour?

Answers

Assuming that the mail carrier earns 1.5x usual for overtime like Normal workers it should be $14.7

The overtime rate for a mail carrier earning $9.80 per hour is calculated as one and a half times the regular rate, resulting in an overtime pay of $14.70 per hour.

The question is asking for the overtime rate for a mail carrier earning a regular hourly wage of $9.80. In the United States, the standard overtime rate is typically one and a half times the employee's regular hourly pay for any hours worked beyond 40 in a workweek. Therefore, to calculate the overtime rate for a mail carrier earning $9.80 per hour, the following calculation is performed:

Regular hourly wage times 1.5 = Overtime rate

$9.80 times 1.5 = $14.70 per hour

on a map, each centimeter represents 45 kilometers. two towns are 135 kilometers apart. what is the distance between the towns on the map

Answers

1 cm = 45 km
x cm = 135 km

135/45 = 3 cm

distance between the towns on the map is 3 cm.

i hope this helps :)

0.5cm=1.5m. 36m tall. Find the scale factor.

Answers

To answer this I would set this up as a proportion.  I would write 0.5 cm/1.5 m. Make this equal to x/36 m.  x would be the scale measurement needed for the real height of 36 m.  You can solve this proportion by using cross products to get 1.5x = 18 and solve for x.  18/1.5=12 cm. Or you can determine how many groups of 1.5 it would take to get to 36 (36/1.5 = 24).  Then multiply 0.5 by 24 to get 12 cm.

Final answer:

To find the model height for an object that is 36 m tall using the given scale of 0.5 cm equals 1.5 m, we establish a proportion, which yields a model height of 12 cm, representing the scale factor as 1 cm : 3 m.

Explanation:

The question asks to find the scale factor given that 0.5 cm on a model equals 1.5 m in real life, and an object's real-life height is 36 meters. First, understand that the scale factor is the ratio of the model's size to the actual size. For this scenario, the given scale is 0.5 cm = 1.5 m. To find the model height for an object that is 36 m tall, we use this scale.

Set up a proportion based on the given scale: 0.5 cm/1.5 m = x cm/36 m. Simplifying the ratio to its smallest form, we get 1 cm = 3 m. Therefore, using cross multiplication, we find the height of the model as x = 0.5 cm * (36 m / 1.5 m).

Calculating gives x = 12 cm. Hence, the scale factor, when considering the model's size to the actual size, is represented as 1 cm : 3 m, and the actual model height is 12 cm for the 36 m tall object.

Janice used a 16-inch dowel and a 21-inch dowel to build a kite what is the perimeter of her kite

Answers

16x2=32
21x2=42
32+42=54

the perimeter is 54

Which equation represents the line that passes through (–6, 7) and (–3, 6)? y = –x + 9 y = –x + 5 y = –3x – 11y y = –3x + 25

Answers

Step [tex]1[/tex]

Find the slope of the line

we know that

the formula to calculate the slope between two points is equal to

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

Let

[tex]A(-6,7)\\B(-3,6)[/tex]

substitute the values

[tex]m=\frac{(6-7)}{(-3+6)}[/tex]

[tex]m=\frac{(-1)}{(3)}[/tex]

[tex]m=-1/3[/tex]

Step [tex]2[/tex]

with the slope m and the point [tex]A(-6,7)[/tex] find the equation of the line

we know that

the equation of the line in the point-slope form is equal to

[tex]y-y1=m*(x-x1)[/tex]

substitute the values

[tex]y-7=(-1/3)*(x+6)[/tex]

[tex]y=(-1/3)x-2+7[/tex]

[tex]y=(-1/3)x+5[/tex]

therefore

the answer is

[tex]y=(-1/3)x+5[/tex]

Which triangle is it ?

Answers

The answer is: The first triangle. The reasons are shown below:

 1. All the triangles are rigth triangles, because they have an angle of 90°. So, let's calculate the others angles of the first one:

 Tan(α)^-1= opposite leg/adjacent leg

 Opposite leg=5
 Adjacent leg=5√3

 Tan(α)^-1= 5/5√3
 Tan(α)^-1=30°

 2. Let's calculate the other angle:

 Tan(α)^-1= opposite leg/adjacent leg

 Now, the opposite leg will be 5√3 and the adjacent leg will be 5. Then:

 Tan(α)^-1= 5√3/5
 Tan(α)^-1=60°

 As you can see, the angles of first triangle are: 30°,60° and 90°. 

The function f is such that f(x)=4x-1 find f^-1(x)

Answers

Let y=4x-1
The inverse is basically expressing x in terms of y.
y=4x-1  =>
y+1=4x
x=(y+1)/4
Since the inverse is still a function of x, we only have to interchange x and y
inverse of f(x) = f^-1(x) = (x+1)/4 

Tom  and Arnold both leave the internet cafe at the same time, but in opposite directions. If Tom travels 9mph and Arnold travels 16mph, how long until they are 200 miles apart?

Answers

x = hours walking
9x + 16x = 200
25x = 200
x = 8 hours
Hello There! ;)

Work:
First, we create our equation right so its...
9x + 16x = 200
25x = 200

Then, we can just divide 25/200
Which is 8

Answer:
x= 8 h or hours.

Hoping this helps you!
-Arianna

a population of 140000 grows 4% per year for 16 years. How much will the population be after 16 years?

Answers

At the end of the Year 1 the population will be = 110,000 + 4% of 110,000 =P1At the end of the Year 2 the population will be=P1+ 4% of P1= 110,000 + 4% of 110,000 + 4% of (110,000 + 4% of 110,000) =  110,000 +  4% of (110,000+ 110,000 + 4% of 110,000) =  110,000 + 2*4% of 110,000 + (4%)2  of 110,000= P2At the end of the Year 3 the population will be= P2+ 4% of P2= 110,000 +2* 4% of 110,000 + (4%)2 of 110,000 + 4% of [ 110,000 +2* 4% of 110,000 + (4%)2 of 110,000] = 110,000 +2* 4% of 110,000 + (4%)2 of 110,000 + 4% of 110,000 + 2* (4%)2 of 110,000 + (4%)3 of 110,000 =110,000 +3* 4% of 110,000 +3* (4%)2 of 110,000 + (4%)3 of 110,000 =P3At the end of the Year 4 the population will be= P3+ 4% of P3=110,000 +3* 4% of 110,000 +3* (4%)2 of 110,000 + (4%)3 of 110,000 +4% of [110,000 +3* 4% of 110,000 +3* (4%)2 of 110,000 + (4%)3 of 110,000] =110,000 +4* 4% of 110,000 + 6*(4%)2 of 110,000+4* (4%)3 of 110,000+ (4%)4 of 110,000 Now if we substitute n for 110,000 and r for 4% yearly rate of increase, we can rewrite,Before Year 1, at Year 0, the population, P0= n = n(1+r)0At the end of the Year 1 the population , P1= n+rn= x(1+r)1At the end of the Year 2 the population , P2= n+2rn+r2n =n(1+2r+r2)=n(1+r)2At the end of the Year 3 the population , P3= n+3rn+2r2n+r3n=n(1+3r+3r2+r3)=x(1+r)3At the end of the Year 4 the population , P4= n+4rn+6r2n+4r3n+r4n=n(1+r)4.
.
.
.
.
.
At the end of the Year n the population , Px=n+nrx+(x-1)r2n+(x-2)r3n+...........+(x-x+2)r(x-1)x+(x-x+1)rxn=n(1+r)x.....At the end of the Year 16 the population , P16= n+16rn+15r2n+14r3n+.............+3r14n+2r15n+r16n=n(1+r)16 Thus under given condition of rate of growth, the Population P(x) at xth year will be P(x)=n(1+r)x Therefore, a population of 110,000 growing at 4% per year, in 16 years will be= 110,000(1+4/100)16= 110,000(1.04)16=206027.93702999115428132473599427≈206028

I hope this is helpful. I found the solution on the internet. Hope you have a good day and bye.

What is the order of 5x10^4 , 7x10^-5 , 3x10^-9 , 8x10^4 from least to greatest?

Answers

Answer:

[tex]3\times10^{-9},7\times 10^{-5},5\times 10^4,8\times10^4[/tex]

Step-by-step explanation:

We want to order ; [tex]5\times 10^4,7\times 10^{-5},3\times10^{-9},8\times10^4[/tex] from least to greatest.

Observe that all these numbers are in standard form.

We can order them based on the exponents.

[tex]-9<\:-5<\:4[/tex]

Since two numbers have the same exponent of 4, we need to use the multiplier to order the last two(5<8).

From least to greatest we have;

[tex]3\times10^{-9}\:<\:7\times 10^{-5}\:<\:5\times 10^4\:<\:8\times10^4[/tex]

The numbers in ascending order from least to greatest are 3x10²-9, 7x10²-5, 5x10²4, 8x10²4

To order the numbers from least to greatest, to compare the values of the numbers without the powers of 10 first and then consider the powers of 10.

Given numbers:

5x10²

7x10²-5

3x10²-9

8x10²4

Step 1: Compare the numbers without the powers of 10:

The numbers without the powers of 10 are: 5, 7, 3, and 8.

Step 2: Arrange the numbers in ascending order based on their values:

3, 5, 7, 8

Step 3: Now, consider the powers of 10:

The powers of 10 are: 10²4, 10²-5, 10²-9, and 10²4.

Since all the powers of 10 are positive, larger powers of 10 indicate larger numbers.

Step 4: Combine the results from Steps 2 and 3 to get the final order:

3x10²-9, 7x10²-5, 5x10²4, 8x10²4

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the longest side of an acute isosceles triangle is 8 centimeters . rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

Answers

Answer: greater than 5.7 cm

Explanation:

1) The acute angle is restricted to an upper bound of to 90°, i.e. the greatest value of an acute angle must be less than 90°.

2) the smaller the acute angle the longer the two congruent sides of the isosceles triangle, the greater the acute angle the shorter the two congruent sides.

3) Find the lower bound of the two congruent sides by using the upper bound of the acute angle.

4) when the angle is 90°, you can use the Pytagorean theorem

c^2 = a^2 + b^2

c = 8 cm, a = b

c^2 = 2a^2

8^2 = 2a^2

2a^2 = 64

a^2 = 64/2

a^2 = 32

a = √32

a = 5.7 cm

5.7 cm is the lower bound of the length of the two small sides, therefore, the length of the two small sides has to be greater than 5.7 cm

Answer:5.7 cm

Step-by-step explanation:

Just took the test.

Dr. Silas studies a culture of bacteria under a microscope. The function b(t)=50(1.4)^t represents the number of bacteria t hours after Dr. Silas begins her study.

a) What is the y-intercept of the function? What does this mean in the context of the problem?
b) Is this exponential growth or decay? How do you know?
c) How many bacteria would there be 5 hours after Dr. Silas began her study?

Please show all your work!

Answers

a) Remember that the y-intercept of a exponential function [tex]f(x)=a^{x} [/tex] is [tex]f(0)[/tex], so the only thing to do to find the y-intercept in our functions is evaluate it at t=0:
[tex]b(t)=50(1.4) ^{t} [/tex]
[tex]b(0)=50(1.4)^{0} [/tex]
[tex]b(0)=50(1)[/tex]
[tex]b(0)=50[/tex]
We can conclude that the y-intercept of our function is (0,50), and it represents the initial bacteria population in the sample.

b) To find if the function is growing or decaying, we are going to convert its decimal part to a fraction. Then, we will compare the numerator and the denominator of the fraction. If the numerator is grater than the denominator, the function is growing; if the opposite is true, the function is decaying.
Remember that to convert a decimal into a fraction we are going to add the denominator 1 to our decimal and then we'll multiply both of them by a power of ten for each number after the decimal point:
[tex] \frac{1.4}{1} . \frac{10}{10} = \frac{14}{10} = \frac{7}{5} [/tex]
Now we can rewrite our exponential function:
[tex]b(t)=50( \frac{7}{5})^{t} [/tex]
Since the numerator is grater than the denominator, it is growing faster than the denominator; therefore the function is growing.

c) The only thing we need to do here is evaluate the function at t=5:
[tex]b(t)=50(1.4)^{t} [/tex]
[tex]b(5)=50(1.4)^{5} [/tex]
[tex]b(5)=50(5.37824)[/tex]
[tex]b(5)=268.912[/tex]

We can conclude that after 5 hours Dr. Silas began her study will be 268.9 bacteria in the sample.
Final answer:

The function relates to a bacteria count that starts at 50, grows exponentially due to the base of the exponent being greater than 1, and is projected to reach approximately 192 bacteria after 5 hours.

Explanation:

a) The y-intercept of the function is the value of the function when t = 0. For the function  [tex]b(t)=50(1.4)^t[/tex], if you substitute 0 for t, you get  [tex]50(1.4)^0[/tex] which simplifies to 50. Consequently, the y-intercept is 50 which in context, means the study started with 50 bacteria.

b) This function represents exponential growth. We know this because the base of the exponent (1.4) is greater than 1. If the base had been less than 1, it would represent exponential decay.

c) To determine the number of bacteria 5 hours into the study, we need to substitute 5 for t in the formula.

Hence, [tex]b(5)=50(1.4)^5 = approximately 192.2.[/tex] The number of bacteria cannot be in fractions, thus we consider this as approximately 192.

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The rule of thumb in filmmaking is that you must shoot at least 3 minutes of film for every minute in a movies “final cut”. A 30 minute roll of film cost $250. How much will film cost to make a 90 minute movie?
Please explain how to do this problem! I can’t figure it out!

Answers

You add 250 to the price for every 30 minutes, so it would cost $750 for 90 minutes of film.
However, since you have to shoot three minutes for every one minute in the final cut, you would multiply that by 3. So I think it would be 2,250
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