Answer:
0.24
Step-by-step explanation:
Answer:
0.24kg
Step-by-step explanation:
The answer is 0.24 kg since
1 gram equals 0.001 kg
1g = 0.001kg
Suppose that $10,083 is invested at an interest rate of 6.8% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Answer:
a) The exponential function is [tex]A(t) = 10083(1.068)^t[/tex]
b)
The balance after 1 year is of $10,768.644
The balance after 2 years is of $11,500.91
The balance after 5 years is of $14,010.25.
The balance after 10 years is of $19,467.15
c)
The doubling time is of 10.54 years.
Step-by-step explanation:
Continuously compounded interest:
The amount of money earning after t years, with interest compounded continuously, is given by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the amount of the initial investment and r is the growth rate, as a decimal.
a) Find the exponential function that describes the amount in the account after time t, in years.
Suppose that $10,083 is invested at an interest rate of 6.8% per year
This means, respectively, that [tex]A(0) = 10083, r = 0.068[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 10083(1+0.068)^t[/tex]
[tex]A(t) = 10083(1.068)^t[/tex]
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
After 1 year:
[tex]A(1) = 10083(1.068)^{1} = 10,768.644[/tex]
The balance after 1 year is of $10,768.644
After 2 years:
[tex]A(2) = 10083(1.068)^{2} = 11,500.91[/tex]
The balance after 2 years is of $11,500.91.
After 5 years:
[tex]A(5) = 10083(1.068)^{5} = 14,010.25[/tex]
The balance after 5 years is of $14,010.25.
After 10 years:
[tex]A(10) = 10083(1.068)^{10} = 19,467.15[/tex]
The balance after 10 years is of $19,467.15.
c) What is the doubling time?
This is t for which [tex]A(t) = 2A(0)[/tex]. So
[tex]A(t) = A(0)(1.068)^t[/tex]
[tex](1.068)^t = 2[/tex]
[tex]\log{(1.068)^t} = \log{2}[/tex]
[tex]t\log{1.068} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.068}}[/tex]
[tex]t = 10.54[/tex]
The doubling time is of 10.54 years.
Please help!!! These are the options
From the table Riley is moving forward on the interval [0,
A.4.5 B. 1.5 C.3 D.6.
It takes Riley A.3 B.4.5 C.6 D.1.5 seconds to swing forward,back and then return to her standing position. Riley reaches a maximum distance of A.6.75 B.38.9 C.1.5 D.55 inches of her starting position.
Answer:
From the table, Riley is moving forward on the interval [0,1.5].
I takes Riley 6 seconds to swing forward, back, and then return to her starting position.
Riley reaches a maximum distance of 38.9 inches from her starting position.
Step-by-step explanation:
PLATO/Edmentum
The blanks in the given statements can be filled as [0,1.5], 3 seconds, and 55 inches, respectively.
What is a table?Mathematical tables are collections of numbers that display the outcomes of calculations made using various inputs.
Given that in the table the position of Riley with respect to time. Also, If her position is ahead of its initial position it is positive, while if she is behind her initial position it is negative.
Now as per the table, the statements can be completed as,
Riley is moving forward on the interval [0, 1.5]It takes Riley 3 seconds to swing forward, back, and then return to her starting position.Riley reaches a maximum distance 55 of Inches from her starting position.Hence, the blanks in the given statements can be filled as [0,1.5], 3 seconds, and 55 inches, respectively.
Learn more about Table here:
https://brainly.com/question/10670417
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A red die and a blue die are rolled. You win or lose money depending on the sum of the values of the two dice. If the sum is 6 or 10, you win $4. If the sum is 5, 9, or 12, you win $1. If the sum is any other value (2, 3, 4, 7, 8, or 11), you lose $2. Let X be a random variable that corresponds to your net winnings in dollars. What is the expected value of X
Answer:
The expected value of X is $0.0833.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
For each dice, there are 6 possible outcomes(values from 1 to 6). So for 2 dices, there are [tex]6^2 = 36[/tex] desired outcomes.
Desired outcomes:
Sum 5: (1,4), (2,3), (3,2), (4,1).
Sum 6: (1,5),(2,4),(3,3),(4,2),(5,1)
Sum of 9: (3,6), (4,5), (5,4), (6,3)
Sum of 10: (4,6), (5,5), (6,4)
Sum of 12: (6,6)
Probabilities:
5 + 3 = 8 outcomes in which the sum is 6 or 10, that is, 8/36 probability of winning $4.
4 + 4 + 1 = 9 outcomes in which the 5, 9, or 12, that is, 9/36 probability of winning $1.
36 - (8 + 9) = 36 - 17 = 19 remaining outcomes, that is, 19/36 probability of losing $2.
What is the expected value of X?
Multiplication of each outcome by its probability. So
[tex]E(X) = \frac{8}{36}*4 + \frac{9}{36}*1 - \frac{19}{36}*2 = \frac{8*4 + 9*1 - 19*2}{36} = \frac{32 + 9 - 38}{36} = \frac{3}{36} = 0.0833[/tex]
The expected value of X is $0.0833.
Please help I’ll mark you as brainliest if correct!
Answer:
The wright answer is 16.33 inches
PLSSSS HELP ME ALOT OF CREDITS AND BRAINLIST IF YOU HELP ME!!!!!
G. A. B. O
By probability in the chart, it goes from most to least that is grapes, apples, bananas and oranges
Find the accumulated value of an investment of $14,000 at 10% compounded semiannually for 11 year
Given:
Principal = $14000
Rate of interest = 10% compounded semiannually.
Time = 11 years.
To find:
The accumulated value of the given investment.
Solution:
Formula for amount or accumulated value after compound interest is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is the principal values, r is the rate of interest in decimal, n is the number of times interest compounded in an year and t is the number of years.
Compounded semiannually means interest compounded 2 times in an years.
Putting [tex]P=14000,r=0.10,n=2,t=11[/tex] in the above formula, we get
[tex]A=14000\left(1+\dfrac{0.10}{2}\right)^{2(11)}[/tex]
[tex]A=14000\left(1+0.05\right)^{22}[/tex]
[tex]A=14000\left(1.05\right)^{22}[/tex]
[tex]A\approx 40953.65[/tex]
Therefore, the accumulated value of the given investment is $40953.65.
Answer:
A = $41,867.06
A = P + I where
P (principal) = $14,000.00
I (interest) = $27,867.06
Step-by-step explanation:
Given: Investment = $14,000 Annual Rate: 10% compounded semiannually = 11 year
To find: The accumulated value of an investment
Formula: [tex]A = P(1 + \frac{r}{n}) ^n^t[/tex]
Solution: First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 14,000.00(1 + 0.1/12)(12)(11)
A = 14,000.00(1 + 0.008333333)(132)
A = $41,867.06
Henceforth:
The total amount accrued, principal plus interest, with compound interest on a principal of $14,000.00 at a rate of 10% per year compounded 12 times per year over 11 years is $41,867.06.
Prove that sin^4x + cos^4x= sinxcosx
Answer:
(the relation you wrote is not correct, there may be something missing, so I will simplify the initial expression)
Here we have the equation:
[tex]sin^4(x) + cos^4(x)[/tex]
We can rewrite this as:
[tex](sin^2(x))^2 + (cos^2(x))^2[/tex]
Now we can add and subtract cos^2(x)*sin^2(x) to get:
[tex](sin^2(x))^2 + (cos^2(x))^2 + 2*cos^2(x)*sin^2(x) - 2*cos^2(x)*sin^2(x)[/tex]
We can complete squares to get:
[tex](cos^2(x) + sin^2(x))^2 - 2*cos(x)^2*sin(x)^2[/tex]
and we know that:
cos^2(x) + sin^2(x) = 1
then:
[tex]1 - 2*sin(x)^2*cos(x)^2[/tex]
This is the closest expression to what you wrote.
We also know that:
sin(x)*cos(x) = (1/2)*sin(2*x)
If we replace that, we get:
[tex]1 - \frac{sin^2(2*x)}{2}[/tex]
Then the simplification is:
[tex]cos^4(x) + sin^4(x) = 1 - \frac{sin^2(2*x)}{2}[/tex]
When 1 is added to one-half of number x, the result is 3. What is the value of x?
A) 1
B) 3
C) 4
D) 6
E) 8
And why?
Answer:
C) 4
Step-by-step explanation:
1 + x/2 = 3
x/2 = 2
x = 4
The value of x is 4.
Start with 4. Half of 4 is 2. Add 1. You get 3. 4 makes the problem work, so 4 is the answer.
Answer: C) 4
find the surface area .NO FILES #2
Answer:
486
Step-by-step explanation:
The solid is a cube. The faces of a cube are 6 congruent squares.
side = 9 ft
surface area = 6 * side²
SA = 6 * (9 ft)²
SA = 486 ft²
Anyone know the answer?
Answer:
12.4
Step-by-step explanation:
Wayne Gretsky scored a Poisson mean six number of points per game. sixty percent of these were goals and forty percent were assists (each is worth one point). Suppose he is paid a bonus of 3K for a goal and 1K for an assist. (a) Find the mean and standard deviation for the total revenue he earns per game. (b) What is the probability that he has four goals and two assists in one game
Answer:
a) The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.
b) 0.05 = 5% probability that he has four goals and two assists in one game
Step-by-step explanation:
In hockey, a point is counted for each goal or assist of the player.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval. The standard deviation is the square root of the mean.
(a) Find the mean and standard deviation for the total revenue he earns per game.
60% of six are goals, which means that 60% of the time he earned 3K.
40% of six are goals, which means that 40% of the time he earned 1K.
The mean is:
[tex]\mu = 6*0.6*3 + 6*0.4*1 = 13.2[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{\mu} = \sqrt{13.2} = 3.63[/tex]
The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.
(b) What is the probability that he has four goals and two assists in one game
Goals and assists are independent of each other, which means that we find the probability P(A) of scoring four goals, the probability P(B) of getting two assists, and multiply them.
Probability of four goals:
60% of 6 are goals, which means that:
[tex]\mu = 6*0.6 = 3.6[/tex]
The probability of scoring four goals is:
[tex]P(A) = P(X = 4) = \frac{e^{-3.6}*(3.6)^{4}}{(4)!} = 0.19122[/tex]
Probability of two assists:
40% of 2 are assists, which means that:
[tex]\mu = 6*0.4 = 2.4[/tex]
The probability of getting two assists is:
[tex]P(B) = P(X = 2) = \frac{e^{-2.4}*(2.4)^{2}}{(2)!} = 0.26127[/tex]
Probability of four goals and two assists:
[tex]P(A \cap B) = P(A)*P(B) = 0.19122*0.26127 = 0.05[/tex]
0.05 = 5% probability that he has four goals and two assists in one game
What is the volume of the square pyramid, in cubic inches?
Can you answer this? 99^9 × 66 it kinda hard for me
Answer:
60292138333920306000
Step-by-step explanation:
Please take a look at the picture. :)
Answer:
3÷1/6
Step-by-step explanation:
here is your answer. If it helps don't forget to like and Mark me
Mark had 3 times as many quarters as nickels. He had $1.60 in all. How many nickels and how many quarters did Mark have? x represents . 3x represents .
Answer:
x represents nickels = 2
3x represents number of quarters = 6
Step-by-step explanation:
x represents nickels
3x represents number of quarters
We'll multiply each of those times the value of the coin they represent, and make that equal to the total amount of money Mark has to get the value of x
x(0.05) + 3x(0.25) = 1.60
0.05x + 0.75x = 1.60
0.80x = 1.60
x = 2 = number of nickels
So 3x = 6 = number of quarters
Checking the math:
2(0.05) + 6(0.25)= 0.10 + 1.50 = 1.60
PLZZZ Help I need to hurry I got all the other questions right except this one. I dont understand it.
One of the terms in the summation is _______.
I think its B because i did this in class before and it looks familiar. (branliest will be appreciated as well) Thanks
One of the terms in the summation is(1,3)
Can someone help me with this question if two figures are similar but not congruent, how are they alike, and how are they different?
Which equation shows how to find the
angle measure of the part of the circle
without the arrow?
The diameter of a circle is 14cm. Which TWO statements are correct?
A
Answer:
(a) and (e)
Step-by-step explanation:
Given
[tex]d = 14cm[/tex]
Required
Select the true statements
First, is a statement about the area.
The area is calculated as:
[tex]Area= \pi*\frac{d^2}{4}[/tex]
So, we have:
[tex]Area= 3.14*\frac{14^2}{4}[/tex]
[tex]Area= 3.14*49[/tex]
(a) is true
Next, is a statement about the circumference.
This is calculated as:
[tex]C = \pi d[/tex]
So, we have:
[tex]C = 3.14 * 14[/tex]
(e) is true
In your own words, state what you know about piecewise-defined function. Use complete sentences.
Answer:
A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1 <x ≤ 9.
write a real world problem that could be represented by 1/5 x 5 = 1
Answer:
Each person received 1/5 of a pizza. There were 5 people in total. How much pizza was there originally before the split?
Find the volume of a cone with a base diameter of 8 in and a height of 6 in. Write the exact volume in terms of pi, and be sure to include the correct unit in your answer.
Volume of a cone = pi x r^2 x h/3
Volume = pi x 4^2 x 6/3
Volume = 32pi cubic inches ( in.^3)
The slope of the line whose equation is 2x + 5y + 1 = 0 is
0-2/5
05/2
0-1/5
Answer:
0-2/5
I think this is it ;-;
Ms. Marcus saws an 8-foot board into 2 pieces. One piece is 3.625 feet long. What is the length of the other piece?
Answer:
4.375
Step-by-step explanation:
Taking off the length, we know you need to subtract. We can write out the answer as 8-3.625 which is 4.375.
By the way can you follow me on Brainly?
Thanks!
Identify whether the following equation has a unique solution, no solution, or infinitely many solutions. 3 + 5= 8
Answer:
to me it's a simple solution
Step-by-step explanation:
One number is equal to the square of another. Find the numbers if both are positive and their sum is 306.
Answer: 17 or -18
Step-by-step explanation:
x^2+x=306
x^2+x-306=0
(x-17)(x+18)=0
x-17=0
x=17
x+18=0
x=-18
..i think this is the right answer
does anyone know this
Answer: 761 yd
split the figure into different pieces to make it easier
(23 x 7) + (40 x 15)
161 + 600
761
hope this helped :)
Answer:
761 yd ^3
Step-by-step explanation:
is 1 5/6 a rational number or a iraarational
Answer: rational number
Step-by-step explanation:
Mixed numbers are all rational numbers because they can be expressed as a fraction. To be a rational number, a number must be able to be written
If cosx=-3/7, find the value for cos4x
Answer:
cos ( 4 x ) = - 479 / 2401
Step-by-step explanation:
:D
rachel has 4 notebooks.Her mother gives her n notebooks.she wants to use the same number of notebooks in each of her 7 classes. which expression shows the number of notebooks rachel will use for each class?
A.n+4/7
B.4÷7/n
C.4n+7
D.4+n+7
Answer:
i think its b
Step-by-step explanation:
