Consider a savings account earning annual compound interest with no additional deposits or withdrawals made after the initial deposit. The balance in the account after x years can be modeled by the function s(x) = 2.000(1.045) Which statement is the best interpretation of one of the values in this function? A) The initial balance of the account is $2,000. B) The balance in the account at the end of one year is $2,000. The initial balance of the account increases at a rate of 104.5% each year. D) The initial balance of the account decreases at a rate of 4 5% each year.
Answer:
The initial balance of the account is $2,000.
Step-by-step explanation:
I took the test on usa test prep
Answer:The initial balance of the account is $2,000.
f(x) = abx, where a = initial value, b = change factor, and x = time period.
what is the following sum
Answer:
2nd option is the correct answer
[tex] 12{b}^{2} \bigg(\sqrt[3]{2a} \bigg)[/tex]
Step-by-step explanation:
[tex]3 {b}^{2} \bigg( \sqrt[3]{54a} \bigg) + 3 \bigg( \sqrt[3]{2a {b}^{6} } \bigg) \\ \\ = 3 {b}^{2} \bigg( \sqrt[3]{27 \times 2a} \bigg) + 3 \bigg( \sqrt[3]{2a {( {b}^{2} )}^{3} } \bigg) \\ \\ = 3 {b}^{2} \bigg( \sqrt[3]{ {3}^{3} \times 2a} \bigg) + 3 \bigg({\sqrt[3]{{( {b}^{2} )}^{3}2a} } \bigg) \\ \\ = 3 {b}^{2} \times 3 \sqrt[ 3]{2a} + 3 {b}^{2} \sqrt[3]{2a} \\ \\ = 9 {b}^{2} \sqrt[ 3]{2a} + 3 {b}^{2} \sqrt[3]{2a} \\ \\ = 12{b}^{2} \bigg(\sqrt[3]{2a} \bigg)[/tex]
Answer:
second option: 12b²(∛2a)
Step-by-step explanation:
you can break [tex]\sqrt[3]{54a}[/tex] into [tex]\sqrt[3]{3^3(2a)}[/tex] which equals 3[tex]\sqrt[3]{2a}[/tex]
you can break [tex]\sqrt[3]{2ab^6}[/tex] into [tex]\sqrt[3]{2ab^3b^3}[/tex] which equals b²[tex]\sqrt[3]{2a}[/tex]
now we can simplify: (3b² · 3[tex]\sqrt[3]{2a}[/tex]) + 3b²[tex]\sqrt[3]{2a}[/tex] = 9b²[tex]\sqrt[3]{2a}[/tex] + 3b²[tex]\sqrt[3]{2a}[/tex]
this equals 12b²[tex]\sqrt[3]{2a}[/tex]
You deposit $400 in an account. The account earns $72 simple interest in 6 years. What is the annual
interest rate?
The principal was $600.
Explanation:
Find principal by using the formula , where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.
In this example I = $72, i = 4% and t = 3 years, so
Answer: 173,200
Step-by-step explanation:
This is very simple and I can help with this!!
Interest= Principal x Rate x Time
Interest = ($400)($72)(6)= 172,800+400= 173,200
If f (x) = x – 1 and g(x) = 5x – 2 , then (f/g) (x) help me plz
Answer:
[tex](f/g)x = \frac{x-1}{5x - 2}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x - 1[/tex]
[tex]g(x) = 5x - 2[/tex]
Required
(f/g)x
In functions:
[tex](f/g)x = \frac{f(x)}{g(x)}\ \ \ g(x)\ne 0[/tex]
So:
[tex](f/g)x = \frac{x - 1}{5x - 2}[/tex]
A piece of land in north county is a parallelogram with a base that is four more meters than eight times the height, h. Which of the
following represents the area of the land?
A. A(n) = 8h2 + 32
B.
A(h) = 8h2 + 4
C. A(h) = 4h2 + 8h
D.
A(n) = 8h2 + 4h
Answer:
D
Step-by-step explanation:
2 2/3 divided by 1/3?
Answer:
8
Step-by-step explanation:
i dont know set by step but m brother give me the answer he is in high school
Help pls!! I need help!!
Answer:
what u need help wt?
Step-by-step explanation:
25 divided by 12 PLEASE answer quick
24 divided by 12 equals 2,083
The division of 25 by 12 gives the quotient 2 and remainder is 1.
What is Division?One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
Given:
We have to divide 25 by 12.
The division is as follow:
12| 25 | 2
24
______
1
Thus the Quotient is 2 and remainder is 1.
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Could someone help me with this
Answer:
try to do this formula
XYZ
= X times Y times Z
Let y = x² In(x).
dy/dx the lesson is differentiate products
Answer:
dy/dx = x(1+2lnx)
Step-by-step explanation:
Given y = x² In(x).
dy/dx = Udv/dx + Vdu/dx
Let U = x², V = lnx
du/dx = 2x
dv/dx = 1/x
Substitute into the formula;
dy/dx = x²(1/x) + lnx(2x)
dy/dx = x + 2xlnx
dy/dx = x(1+2lnx)
The slope of a linear function is 1/5. For every rise of 5 units, what is the run?
Answer:
for every rise of 1 the run would be 25
can somebody help me?
write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. y=a(x-h)^2+k
vertex:(4,-1) point:(2,3)
Answer:
y = ( x − 2 ) ^ 2 + 3
y = x^2 − 4x + 7
Step-by-step explanation:
y = a ( x − h ) ^ 2 + k
where vertex is (h,k) = (4,-1)
h=4, k=-1
y = a ( x − 4 ) ^ 2 - 1
sub ( 2,3 )
3 = a (2 - 4)^2 - 1
a=1
y = 1 ( x − 2 ) ^ 2 + 3
y = ( x^2 − 4x + 4 ) + 3
y = x^2 − 4x + 7
Please help... picture is below
Answer
x=29
Step-by-step explanation:
Okay we know that the sum of all angles in a triangle is 180, so all we have to do is add them up first
(x+17)+(2x+5)=3x+22
(3x+22)+(3x-16)=6x+6
okay so we now know that 6x+6=180
subtract 6 on both sides 6x=174
then divide by 6 to get x=29
hope this helps!
help asap i will get yelled at =( this is going to give yoyu 42 points
Answer:
24+24=48
Step-by-step
24+24=48
Answer: first pic: true. second pic: is D. third pic: false. forth pic: C.
Step-by-step explanation:
find the area? need help guys!!
The probability of getting a red gumball from a gumball machine is 1/8. The probability of getting a red piece of candy from a candy machine is 1/6. If both a gumball and a piece of candy are purchased, what is the probability that both are red?
Answer: 1/48
Step-by-step explanation: equation: 1/8x1/6
you have to multiply both numerators together (1x1)=1 then you multiply the denominators together (8x6)=48. you can't simplify it so your answer is 1/48
How many notebooks do you think it would take to make a stack that is 5 feet high?
Answer:
There are total 30 books in the 5 feet high stack of books.
Step-by-step explanation:
The complete question is
Given, Each note book is 2 inches thick, How many notebooks do you think it would take to make a stack that is 5 feet high
Solution
Thickness of each book [tex]= \frac{2}{12} = \frac{1}{6}[/tex]
The total height of the book stack is [tex]5[/tex] feet.
The number of books in the stack is equal to total height of the stack divided by the thickness of one book
Number of books in five feet high stack is
[tex]\frac{5}{\frac{1}{6} } \\5 * \frac{6}{1} \\30[/tex]
Hence, there are total 30 books in the 5 feet high stack of books.
An exponential distribution is formed by the waiting times for a patient in the emergency room. The average waiting time for this distribution is 38 minutes. Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes? Round your answer to three decimal places.
Answer:
0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes
Step-by-step explanation:
To solve this question, we should understand the exponential distribution and conditional probability.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
The average waiting time for this distribution is 38 minutes.
This means that [tex]m = 38, \mu = \frac{1}{38} = 0.0263[/tex]
Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes?
Event A: Taking more than 37 minutes.
Event B: More than 37 + 41 = 78 minutes.
Probability of taking more than 37 minutes:
[tex]P(A) = P(X \leq 37) = 1 - e^{-0.0263*37} = 0.6221[/tex]
More than 37 minutes and more than 78 minutes:
The intersection is more than 78 minutes, so:
[tex]P(A \cap B) = P(X > 78) = e^{-0.0263*78} = 0.1286[/tex]
The probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1286}{0.6221} = 0.207[/tex]
0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes
what is 1235X76678 what is it
Answer:
94697330
Ur welcome
Step-by-step explanation:
Answer:
94,697,330
Explanation:
[tex]1235 x 76678 = 94697330[/tex]
What is the distance from the origin to point P graphed on the complex plane below?
Answer:
hereeeeeeeeeeee
what is the slope of (4,7) (9,7)?! please help i tried omni and it didn't give me an answer
Answer:
0
Step-by-step explanation:
Find the factors of following:
(i) 8x^2 yy
Answer:
i•8xy^2yz
Step-by-step explanation:
Remove unnecessary parentheses
Answer:
i) 8x^2 yz=2×2×2×x×x×y×z
a gain of five meters
1.A gain of five meters:5
Because gain＝+
I WILL MARK BRANLIEST IF U ARE RIGHT!!
Answer:
Perimeter=100 area=688.19
Step-by-step explanation:
There's a big formula for area of pentagon and I pretty tired, so unless you want me to show my work I wont
Ben and his housemates signed a lease for an apartment for 12 months for $563 per month of which Ben agreed to pay $215 per month. Which of the following statements best gives the reasons that Ben’s rent payment is an essential (fixed) expense?
Answer:
It is by contract the same amount every month.
Step-by-step explanation:
Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey(NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium (mg). They found in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Using these values for the mean and standard deviation for the U.S. population, find and interpret the probability that a random sample of size 50 will a mean:
Complete question :
Wright et al. [A-2] used the 1999-2000 National Health and Nutrition Examination Survey NHANES) to estimate dietary intake of 10 key nutrients. One of those nutrients was calcium in all adults 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454. Usin these values for the mean and standard deviation for the U.S. population, find the probability that a randonm sample of size 50 will have a mean: (mg). They found a) Greater than 800 mg b) Less than 700 mg. c) Between 700 and 850 mg.
Answer:
0.10935
0.3718
0.9778
0.606
Step-by-step explanation:
μ = 721 ; σ = 454 ; n = 50
P(x > 800)
Zscore = (x - μ) / σ/sqrt(n)
P(x > 800) = (800 - 721) ÷ 454/sqrt(50)
P(x > 800) = 79 / 64.205295
P(x > 800) = 1.23
P(Z > 1.23) = 0.10935
2.)
Less than 700
P(x < 700) = (700 - 721) ÷ 454/sqrt(50)
P(x < 700) = - 21/ 64.205295
P(x < 700) = - 0.327
P(Z < - 0.327) = 0.3718
Between 700 and 850
P(x < 850) = (850 - 721) ÷ 454/sqrt(50)
P(x < 850) = 129/ 64.205295
P(x < 700) = 2.01
P(Z < 2.01) = 0.9778
P(x < 850) - P(x < 700) =
P(Z < 2.01) - P(Z < - 0.327)
0.9778 - 0.3718
= 0.606
Sylvester spends a total of $1725 for Common and preferred shares. He has purchased $975 worth of preferred.
Answer:
750
Step-by-step explanation:
The sector of a circle has an area of 104pi/9 square inches and a central angle with measure 65 degrees. What is the radius of the circle in inches? Show work. a. 5.7 b. 8 c. 64 d. 104
The radius of the circle is 8 inches when the sector of a circle has an area of 104pi/9 square inches.
What is a sector of a circle?A sector is said to be a part of a circle made of the arc of the circle along with its two radii. It is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
Which is the radius of a circle?Radius of a circle is the distance from the center of the circle to any point on it's circumference.
Area of a sector = [tex]\frac{\theta}{360} \pi r^2[/tex]
[tex]\text{Given area = }\frac{104\times \pi}{9}=\frac{65}{360}\times \pi r^2\\\\\frac{104}{9}=\frac{65}{360} \times r^2\\\\r^2=\frac{37440}{585}\\\\r=8.001[/tex]
Hence, option b is correct, that is the radius of the circle is 8 inches.
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24j - 9 Factor the following expression using GCF
Answer:
See it and do it
Follow please