It takes approximately 1.083 years, or around 1 year and 1 month for an $800 investment to grow to $900 when continuously compounded with an 11% yearly interest rate.
Explanation:To calculate how long it will take for an $800 investment to grow to $900 with continuous compounding at an 11% yearly interest rate, we use the formula for continuously compounded interest, P = Pert, where P is the final amount, Pe is the original principal, r is the interest rate, and t is time in years.
Rearranging the equation to find t, we have, t = ln(P/Pe) / r.
Substitute P as $900, Pe as $800, and r as 0.11 into the formula.
Therefore, t = ln(900/800) / 0.11 = approximately 1.083 years or around 1 year and 1 month.
Learn more about Continuous Compound Interest here:
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Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true? Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent. Both plans cost the same when 22 texts are sent. Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent. Both plans cost the same when 50 texts are sent
Answer:
d
Step-by-step explanation:
took the test yahoot
p=m/1+rt solve for t
HELP? The two models shown have the same volume. Complete the equation and expression below about the volume of each figure.
Answer : The volume blue prism in Model 1 is, [tex]32in^3[/tex]
Step-by-step explanation :
As we are given that:
Volume of Model 1 = Volume of Model 2
Given:
Volume of blue prism in Model 2 = [tex]36in^3[/tex]
Volume of orange prism in Model 2 = [tex]12in^3[/tex]
Volume of orange prism in Model 1 = [tex]16in^3[/tex]
Now we have to calculate the total volume of Model 2.
Total volume of Model 2 = [tex]36in^3+12in^3[/tex] = [tex]48in^3[/tex]
Now we have to calculate the volume blue prism in Model 1.
Volume of Model 1 = Volume of Model 2
Volume of orange prism in Model 1 + Volume blue prism in Model 1 = Total volume of Model 2
[tex]16in^3[/tex] + Volume blue prism in Model 1 = [tex]48in^3[/tex]
Volume blue prism in Model 1 = [tex]48in^3-16in^3[/tex]
Volume blue prism in Model 1 = [tex]32in^3[/tex]
Thus, the volume blue prism in Model 1 is, [tex]32in^3[/tex]
What is 40 kilometers per hour in meters per hour
The average national basketball association player is over 6 feet tall. the average horse jockey is shorter than 5 1/2 feet tall. this is because height provides nba players with:
Final answer:
Height is crucial for NBA players due to its impact on their performance. Z-scores help compare player heights to the average. Taller stature offers basketball players notable advantages.
Explanation:
Height is a critical factor for NBA players as it can significantly impact their performance, especially in areas like rebounding, shot-blocking, and scoring.
Z-score calculations help determine how a player's height compares to the average, with values above the mean indicating taller heights, which are advantageous in basketball.
Being taller provides NBA players with advantages in terms of reaching high for shots, blocking opponents, and having a better field of vision on the court.
A drawer contains 12 identical white socks, 18 identical black socks and 14 identical brown socks. What is the least number of socks you must choose, without looking, to be certain that you have chosen two brown socks?
The only time you can be so certain that you have picked 2 brown socks is when there are no more white socks and black socks. This means that to be 100% sure that you have picked 2 brown socks, you must pick all 12 white socks and all 18 black socks and only then you can pick 2 brown socks without looking. Therefore the total number of socks that should be picked is:
Total number of socks = 12 white socks + 18 black socks + 2 brown socks
Total number of socks = 32 socks
A total picking of 32 socks is required to be certain without looking that 2 brown have already been chosen.
If the following system of equations was written as a matrix equation in the form AX = C, and matrix A was expressed in the form: A= {A C} {B D}, find the value of a-b +c+d. 2x+8y=7 4x-2y=9 Please help, i dont know which number would be which letters
Answer: a-b+c+d =4
Step-by-step explanation:
The given system of equation is
[tex]2x+8y=7\\4x-2y=9[/tex]
from this we have the following matrices
[tex]A_1 =\begin{bmatrix}\\2 &8 \\ \\4&2 \\\end{bmatrix}\ ,X=\begin{bmatrix}\\x\\ \\y\\\end{bmatrix}\text{and}\ C=\begin{bmatrix}\\7\\ \\9\\\end{bmatrix}[/tex]
the given matrix A =[tex]\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}[/tex]
On comparing Matrix [tex]A_1[/tex] with Matrix A
[tex]\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}=\begin{bmatrix}\\2&8 \\ \\4 &-2 \\\end{bmatrix}[/tex]
we have the following values
a=2 ,b=4,c=8,d=-2
Thus a-b+c+d =2-4+8+(-2)=4
Jonathan's Antiques purchased an old wooden sled at an auction for $210. Jonathan wants to mark up the sled 60% of the selling price. What would be the selling price of the sled?
Ethel is arranging rides so that 27 members go bowling. Some people can ride in a van that belonges to the center where they meet the rest must ride in cars if 12 can go in the van and 5 can go in each car how many cars will they need?
Answer:
Number of cars needed=3
Step-by-step explanation:
Ethel is arranging rides for 27 members.
If 12 can go in the van and 5 can go in each car.
Let c cars are needed
Then, 12+5c=27
5c=27-12
5c= 15
c= 15/5
c=3
Hence, number of cars needed equals:
3
A single batch of cookies requires two cups of sugar and three cups of flour. if more than one batch or a partial batch was made, the unit rate of sugar to flour would remain the same. match the correct amount of sugar to the correct amount of flour to keep the same unit rate of sugar and flour in a single batch. 11.5 cups of flour 4.5 cups of sugar 6.75 cups of flour 12 cups of flour 5 cups of sugar 11.25 cups of flour 7.5 cups of sugar 7.5 cups of flour 8 cups of sugar 4 cups of sugar
Answer:11.5
Step-by-step explanation: 11.5
How do you write 314,207 in word form
Two perpendicular lines intersect at the origin. If the slope of the first line is .5, what is the equation of the second line?. .
Triangle xyz has sidesxy equals 3 yz equals 4 and xz equals 5.if angle y is a right angle and yz is opposite angle x what is the tan of angle x
9.8 is 2% of what number
If you know out of 140 pounds, 60 pounds is muscle weight, what is the muscle weight of a 200 pound male?
In an inductive generalization, in order to achieve an error margin of plus or minus 3 percentage points at a confidence level of about 95 percent, whats the smallest random sample we can get away with, regardless of the size of the target population
After 5 years of earning interest at an annual rate of 3% an investment has earned $950 in interest. To the nearest whole dollar, determine the amount of the initial investment
Consider the equation ay'' + by' + cy = d, where a, b, c, and d are constants. (a) find all equilibrium, or constant, solutions of this differential equation. (enter your answers as a comma-separated list of equations.)
The constant solutions are given by [tex]\(y'' = 0\) and \(y' = 0\)[/tex].
The equilibrium solutions of the given differential equation [tex]\(ay'' + by' + cy = d\)[/tex] are found by setting the derivatives equal to zero.
1. Setting [tex]\(y'' = 0\)[/tex]: When [tex]\(y'' = 0\)[/tex], the equation becomes [tex]\(a \cdot 0 + b \cdot 0 + c \cdot y = d\)[/tex]. Solving for y, we get [tex]\(cy = d\)[/tex], and therefore, [tex]\(y = \frac{d}{c}\)[/tex].
2. Setting [tex]\(y' = 0\)[/tex]: When [tex]\(y' = 0\)[/tex], the equation becomes [tex]\(a \cdot 0 + b \cdot 0 + c \cdot y = d\)[/tex]. Again, solving for y, we obtain [tex]\(cy = d\)[/tex], and hence, [tex]\(y = \frac{d}{c}\)[/tex].
So, the constant solutions are [tex]\(y = \frac{d}{c}\)[/tex], and this is the equilibrium solution for the given differential equation.
Therefore, the constant solutions are given by [tex]\(y'' = 0\) and \(y' = 0\)[/tex].
What is the slope intercept equation of the line below
Four students did a survey to find the soda flavor sixth-grade students perefer. The table below shows the method each student used to conduct the survey:
Student. Method
Trey- asked 100 students at random from his seventh- grade class what their favorite soda flavor is
Jesse- asked 100 sixth-grade students at random what their favorite soda flavor is
Nita-asked 100 eighth-grade students at random what their favorite soda flavor is
Ruben- asked 100 third- grade students at random what their favorite soda flavor is
Which students survey is most likely not biased?
Trey
Jesse
Nita
Ruben
The price of 1 lb of potatoes is $ 1.65. if all the potatoes sold today at the store bring in $ 1220, how many kilograms of potatoes did grocery shoppers buy?
1220/1.65 = 739.39 pounds of potatoes were sold
1 pound = 0.453592 kilograms
739.39 x 0.453592 = 335.38 kilograms
Final answer:
By dividing the total sales of $1220 by the price per pound ($1.65), we find that approximately 739.39 pounds were sold, which converts to roughly 335.38 kilograms of potatoes purchased by grocery shoppers.
Explanation:
To calculate the number of kilograms of potatoes grocery shoppers bought, we need to use the given prices and total sales. Since the price of 1 lb of potatoes is $1.65, we can find the total weight of the potatoes sold by dividing the total sales amount by the price per pound:
Total weight in pounds = Total sales
= $1220
= $1220 / $1.65
= 739.39 pounds approximately
Next, we need to convert pounds to kilograms. There are approximately 2.20462 pounds in 1 kilogram. The conversion is:
Total weight in kilograms = Total weight in pounds / 2.20462
= 739.39 / 2.20462
= 335.38 kilograms approximately
Therefore, grocery shoppers bought approximately 335.38 kilograms of potatoes.
The sum of two #'s is 29. The sum of the smaller and 2 times the larger is 45. Find the #'s.
x+y=29
y=29-x
x+2y=45
x+2(29-x)=45
x+58-2x=45
-1x=-13
x=13
y=29-13=16
x+y = 13+16 = 29
x+2y= 13 + 2(16) = 13+32 = 45
so the numbers are 13 & 16
If you earn $3500 per month and you expect your earnings to increase by 2.3% per year, how much do you think you will be making in 10 years? (Express your answer rounded correctly to the nearest cent!)
Final answer:
Your expected monthly earnings in 10 years, with a 2.3% annual increase, would be $4424.10, rounded to the nearest cent.
Explanation:
To calculate your expected monthly earnings in 10 years, taking into account a 2.3% annual increase, we will use the formula for compound interest: P(1 + r)^n, where:
P is the principal amount (your current earnings)
r is the annual raise rate
n is the number of years
Your current monthly earnings are $3500. The annual raise rate is 2.3%, so r is 0.023 when expressed as a decimal. The number of years, n, is 10.
Plugging the values into the formula, we get:
Earnings in 10 years = $3500 * (1 + 0.023)^10
Calculating the result, we find that your expected monthly earnings in 10 years are:
$4424.10
Tony plans to deposit $1,000 at the end of each of the next three years. if his funds earn 5% compounded annually, how much will he have at the end of three years?
Final answer:
Tony will have a total of $3,152.50 after depositing $1,000 annually for three years in an account with 5% interest compounded annually, by calculating the future value of each deposit and summing them up.
Explanation:
When Tony deposits $1,000 at the end of each year into an account that earns 5% interest compounded annually for three years, we need to calculate the future value of an annuity. Each deposit will earn interest for a different amount of time based on when it was deposited.
The first $1,000 will earn interest for two years.
The second $1,000 will earn interest for one year.
The third $1,000 will not earn interest, as it is deposited at the end of the third year.
The formula to calculate the future value of each deposit is:
Future Value = Principal × [tex](1 + Interest rate)^{number of years}[/tex]
Calculating each separately:
First deposit: $1,000 × [tex](1 + 0.05)^2[/tex] = $1,102.50
Second deposit: $1,000 × [tex](1 + 0.05)^1[/tex] = $1,050.00
Third deposit: $1,000 × [tex](1 + 0.05)^0[/tex] = $1,000 (as it earns no interest)
Adding them together gives us the total amount Tony will have at the end of three years:
Total amount = $1,102.50 + $1,050.00 + $1,000 = $3,152.50.
Therefore, at the end of three years, Tony will have $3,152.50 in his account.
Erika worked 14 hours last week and 20 hours this week. If she earns $9 per hour, how much did she earn during these two weeks? 4 of 60
we know that
Erika earns [tex]\$9[/tex] per hour
so
By proportion
Find how much she earn during the total hours of two weeks
The total hours of two weeks is equal to
[tex]14+20=34\ hours[/tex]
[tex]\frac{9}{1} \frac{\$}{hour} =\frac{x}{34} \frac{\$}{hours} \\ \\x=34*9 \\ \\x=\$306[/tex]
therefore
the answer is
[tex]\$306[/tex]
how much larger is 1 ft in one cubic inch
A trucker had a load of grain containing 2 tons. She unloaded 1 ton 1,200 pounds at the warehouse. How much grain does she still have left on the truck?
Solve 2x2 + 26 = 0 to identify the roots.
Answer:
[tex]x=+/-i\sqrt{13}[/tex]
Step-by-step explanation:
To find the roots, factor and set equal to 0 or use the quadratic formula. This quadratic equation does not factor and must be solved using the quadratic formula.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
where a = 2, b=0, and c=26
[tex]x=\frac{0+/-\sqrt{0^2-4(2)(26)} }{2(2)} \\x=\frac{+/-\sqrt{-208)} }{4} \\x=\frac{+/-i\sqrt{16*13)} }{4}\\x=\frac{+/4i\sqrt{13} }{4}\\x=+/-i\sqrt{13}[/tex]
Answer:
Step-by-step explanation:
X=-i√13,x=i√13
91284 the nearest ten thousand
The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?