Arianna has $50 in a savings account that earns 5% annually the interest is not compounded how much will she have in a total 4 years
Answers
After four years, Arianna will have a total of $60 in her savings account.
What is Compound Interest ?
Compound interest is interest that is calculated not only on the initial principal amount, but also on the accumulated interest of previous periods. In other words, the interest earned is added to the principal amount and then the interest for the next period is calculated based on the new total amount, which includes both the principal and the previously earned interest.
For example, if you deposit $1,000 in a savings account with a 5% annual interest rate, and the interest is compounded annually, at the end of the first year, you would earn $50 in interest, and your balance would be $1,050. If you leave the money in the account and don't make any further deposits or withdrawals, in the second year, you would earn interest not only on the original $1,000, but also on the $50 in interest earned in the first year, which would be a total of $52.50 in interest. Your new balance at the end of the second year would be $1,102.50.
The power of compound interest lies in the fact that the interest earned in each period is added to the principal, so the amount of interest earned in each subsequent period increases, resulting in a larger and larger balance over time.
Since the interest is not compounded, the interest earned each year will be the same, and it can be calculated as:
Interest earned each year = Principal * Annual interest rate
So for Arianna, the interest earned each year will be:
Interest earned each year = $50 * 0.05 = $2.50
After one year, Arianna will have $50 + $2.50 = $52.50
After two years, she will have $52.50 + $2.50 = $55
After three years, she will have $55 + $2.50 = $57.50
After four years, she will have $57.50 + $2.50 = $60
Therefore, after four years, Arianna will have a total of $60 in her savings account.
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Related Questions
the insructions for a model car show a scale of 1 inch to 48 inches. How long is the actual car if the drawing is 4 inches
Answers
Answer:
192
Step-by-step explanation:
Answer:
192
Step-by-step explanation:
The ratio of inches to inches is 1:48
To get 4:x
You have to multiply, 4/1 = 4, 4 by 48.
4*1 = 4
4*48 = 192
4:192 = 1:48 * 4
derivate (cos(3x^2). (5x^3 -1)^1/3 +sin 4x^3)^4
\( \: \: \: \: find \: first \: derivative \\ ( cos(3x {}^{2} ) \times ( \sqrt[3]{5x {}^{3} - 1} ) + \sin(4x {}^{3} ) {}^{4} \)
Answers
Answer:
Step-by-step explanation:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)
Lets look at the derivative part:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)
\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)
Substituting in eq(1), we have:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)
Calculate the length between the points (2, 3)
and (5. 7)
A. 3
B. 4
C. 5
D. 6
Answers
If you count going up, down, or at an angle between each point you’ll get a distance of 4.
The x and y intercepts for the linear equation x – 2y = -8 is
Answers
Answer:
x- intercept = - 8 , y- intercept = 4
Step-by-step explanation:
to find the x- intercept let y = 0 in the equation and solve for x
x - 2(0) = - 8
x - 0 = - 8
x = - 8 ← y- intercept
to find the y- intercept let x = 0 in the equation and solve for y
0 - 2y = - 8
- 2y = - 8 ( divide both sides by - 2 )
y = 4 ← y- intercept
A farmer can cut 1/3 acre of hay every 25 minutes. What is the farmers rate, in acres per hour, for cutting hay?
Answers
Answer:
4/5
Step-by-step explanation:
e
Ahmed and Madri Jaleeni are self-employed motel operators.
They pay 100% of the PPO insurance premium of $6,510 annually.
They also have a dental plan that costs $546 annually and a vision
plan that costs $244 annually. The premiums are paid quarterly
(every 3 months). How much do they pay each quarter?
Answers
Answer:
$1825 is paid each quarter
Step-by-step explanation:
$6500 for PPO
+ 546 for Dental
+ 244 for vision
= 7300 ÷ 4 (there are 4 quarters in each year)
= $1825 each quarter
I need help with 2 + 2 please explain as much as possible
Answers
Answer:4
Step-by-step explanation:
14x4 + 8-3 - 7x4
Who can answer this for me
Answers
Answer:
it equals 33
Step-by-step explanation:
hope this helps and have a blessed day
The earth moves at about 98,000 feet per second as it resolves around the Sun. How fast is that in miles per hour?> (recall that 1 mile is 5,280.00 feet.)
Answers
Answer:
\(\frac{98000 ft}{1 second}\times \frac{? second}{1 hour}\times \frac{1 mile}{5280 ft}\)
Step-by-step explanation:
If you cancel out the same unit, one from numerator and one from denominator, you will get mile/ hour as asked. The leftover is doing your math.
You finish your work!!
I don't care about the evaluation. I do care if you can work by yourself and understand the work
Five times the product of negative four and a number
Answers
Answer:
-20x
Step-by-step explanation:
Let the number be x.
The product of -4 and this number is -4x.
5 times this is 5(-4x), which simplfiies to -20x.
-595-65
Btw they are both negative numbers
Answers
Answer:
-660
Step-by-step explanation:
-595-65=-660
What is x-²y (x³y5)³ in simplest form for all values of x and y where the expression is defined?
Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used
-18-12 4
X
7
8
9 15 16
Answers
Step-by-step explanation:
To simplify the expression x^-2y(x^3y^5)^3, we need to perform the operations inside the parentheses first, using the exponent rule that (a^m)^n = a^(mn):
x^-2y(x^3y^5)^3 = x^-2y(x^(33)y^(53)) = x^-2y(x^9y^15)
Next, we can simplify the expression by multiplying the coefficients (numbers) and adding the exponents of x and y, using the product rule that x^mx^n = x^(m+n) and (xy)^m = x^my^m:
x^-2y(x^9y^15) = (1y/x^2)(x^9*y^15) = y^(15+1)x^(9-2) = y^16x^7
Therefore, the simplified form of x^-2y(x^3y^5)^3 is y^16*x^7.
Note that this expression is defined for all values of x and y except for x=0.
Martina took a train to the bullfight. It traveled 544 km nonstop in 8.5 hours to get there. If the train moved at a steady speed, what was the rate of speed
Answers
Answer:
64 km per hour
Step-by-step explanation:
544/8.5=64
Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-ton satellite to a height of (a) 100 miles above Earth and (b) 300 miles above Earth.
Answers
Answer:
a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Step-by-step explanation:
Given the data in the question;
We know that the weight of a body varies inversely as the square of its distance from the center of the earth.
⇒F(x) = c / x²
given that; F(x) = five-ton = 5 tons
we know that the radius of earth is approximately 4000 miles
so we substitute
5 = c / (4000)²
c = 5 × ( 4000 )²
c = 8 × 10⁷
∴ Increment of work is;
Δw = [ ( 8 × 10⁷ ) / x² ] Δx
a) For 100 miles above Earth;
W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) \([\) \(-\frac{1}{x}\) \(]^{4100}_{4000\)
= (8 × 10⁷) \([\) \(-\frac{1}{4100}\) \(+\frac{1}{4000}\) \(]\)
= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]
= 487.8 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) For 300 miles above Earth.
W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) \([\) \(-\frac{1}{x}\) \(]^{4300}_{4000\)
= (8 × 10⁷) \([\) \(-\frac{1}{4300}\) \(+\frac{1}{4000}\) \(]\)
= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]
= 1395.3 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Insert a monomial such that each expression can be rewritten as the square of a sum or the square of a difference.
36-12 x+
36-12 x+
Answers
The monomial that completes the expression is x²
How to determine the monomial that completes the expression?From the question, we have the following parameters that can be used in our computation:
36 - 12x + ...
Complete the expression with a variable
So, we have
36 - 12x + y
Rewrite as
y - 12x + 36
The given terms of the expression are factors of 6
By trial and error, we make use the following representation
y - 12x + 36 = (x - 6)²
Expand the expression
y - 12x + 36 = x² - 12x + 16
Evaluate the like terms
y = x²
Hence, the monomial is x²
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ASAPPP I NEED THE ANSWER The graph of a function is given.
Is the function linear or nonlinear?
Select from the drop-down menus to correctly complete this
statement
The function is “Choose” because it “choose” have a
constant rate of change.
Answers
Answer:
Linear.
Step-by-step explanation:
The function is linear because it has a constant rate of change.
The sum of two rational numbers is______
rational.
option are
always
sometimes
never
Answers
Answer:
Another rational number
3x + 4y = -35x + 3y = 6
Answers
Step 1
Given;
\(\begin{gathered} 3x+4y=-3---(1) \\ 5x+3y=6---(2) \end{gathered}\)Required; To find the system of equations.
Step 2
\(\begin{gathered} From\text{ equation 1; } \\ 3x=-3-4y \\ x=\frac{-3-4y}{3} \end{gathered}\)\(\begin{gathered} Substitute\text{ in equation 2} \\ 5(\frac{-3-4y}{3})+3y=6 \\ 5(-3-4y)+9y=18 \\ \end{gathered}\)\(\begin{gathered} -15-20y+9y=18 \\ -11y=18+15 \\ y=\frac{33}{-11} \\ y=-3 \end{gathered}\)Step 3
Find the value of x
\(\begin{gathered} x=\frac{-3-4y}{3} \\ x=\frac{-3-4(-3)}{3} \\ x=\frac{9}{3}=3 \end{gathered}\)Answer;
\(x=3,y=-3\)If 150 vehicles passed luan
Answers
Assuming this is the question you're asking:
If 150 vehicles passed Luann, how many more minivans than cars would you expect to pass her? assume the rate continues.
Answer:
30
Step-by-step explanation:
end-of-module Assessment task 7-1 answers.
Answers
Answer: 6
Step-by-step explanation:7 -1=6
Part A: Wilson bought fruit that weighs 2 and 1 over 2 pounds. How many ounces does the fruit weigh? Show your work. (5 points) [16 ounces = 1 pound] Part B: A running tap dispenses 0.14 gallons of water every second. How many pints of water is dispensed after 50 seconds? Show your work. (5 points) [1 gallon = 4 quarts, 1 quart = 2 pints]
Answers
The weight of the fruits in ounces is 40 ounces
The pints of water dispensed after 50 seconds is 56 pints
What are the converted units?The mathematical operations that would be used to determine the answer is multiplication. Multiplication is the process of determining the product of two or more numbers. Multiplication is represented with the sign - x.
A mixed fraction is a non-integer that is made up of a whole number and a proper fraction. An example of a mixed fraction is 2 1/2.
Weight of the fruits in ounces = 2 1/2 x 16
5/2 x 16 = 40 ounces
Pints of water dispensed after 50 seconds = gallon per second x 50 x 4 x 2
0.14 x 50 x 4 x 2 = 56 pints
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Solve the equation: 10x – 11 = 7x + 22
Answers
10x - 11 = 7x + 22
10x - 7x = 22 - 11
3x = 11
x = 11/3
x = 3.66
_____
RainbowSalt2222 ☔
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Isabella sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
105 visitors purchased no costume.
41 visitors purchased exactly one costume.
8 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth.
Answers
The probability that the next person will purchase one or more costumes can be found by dividing the number of visitors who purchased one or more costumes by the total number of visitors.
The total number of visitors is 105 + 41 + 8 = 154.
The number of visitors who purchased one or more costumes is 41 + 8 = 49.
So the probability that the next person will purchase one or more costumes is 49/154, which is approximately 0.32 to the nearest hundredth.
In January, it snowed 36.45 inches. In December it snowed 19.7 inches. How many more inches did it snow in January than in December?
Answers
Determine the difference in height of snow.
\(\begin{gathered} h=36.45-19.7 \\ =16.75 \end{gathered}\)Thus, 16.75 inches more snowed in
Use the following function to complete this question:
f(x)=(x-1)^3+5
Graph the function and fill in the blanks.
If the transformation listed is not applicable write none.
Fill in the blanks in the form:
4 left
5 up
Write infinity in the form: inf
Horizontal shift:
Vertical shift:
Vertical stretch factor:
Vertical compression factor:
Axis of reflection:
Domain:
Range:
Inflection Point:
Pic is attached below
Answers
The following is deduced from the equation f(x)=(x - 1)^3 + 5
Horizontal shift: 1 left
Vertical shift: 5 down
Vertical stretch factor: 1
Vertical compression factor: 1
Axis of reflection: -x + 6
Domain: all real numbers
Range: all real numbers
Inflection Point: (1, 5)
What is vertical stretch factor?The vertical stretch factor is a term used in mathematics to describe the transformation that changes the height of a graph while leaving the horizontal axis unchanged. In other words, it's a factor by which the y-values of a function are multiplied to produce a new, stretched or compressed version of the original graph.
The stretch factor is usually represented by the symbol "k". For example, if the equation of a function is y = f(x), then the equation of its vertically stretched image would be y = k * f(x). A positive value of k stretches the graph upward, while a negative value of k compresses the graph downward. If k > 1, the graph is stretched vertically; if 0 < k < 1, the graph is compressed vertically; if k = 1, the graph remains unchanged.
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What is an approximate solution to this equation? 4/x-5=√x+3+2
A. 3.73
B. 5.81
C. 4.97
D. -0.80
Answers
The approximate solution to the equation \(\dfrac{4}{x - 5} = \sqrt{x + 3} +2\) found using
the Newton-Raphson method is option B.
B. 5.81
How can the Newton-Raphson method be used?The given function is presented as follows;
\(\dfrac{4}{x - 5} = \mathbf{ \sqrt{x + 3} +2}\)
Which gives;
\(\dfrac{4}{x - 5} -2= \sqrt{x + 3}\)
\(\left(\dfrac{14-2\cdot x}{x-5} \right)^2 = \sqrt{x+3} ^2 = x+3\)
\(\mathbf{\dfrac{4\cdot x^2 - 56 \cdot x + 196}{x^2-10\cdot x + 25}} = x + 3\)
Therefore;
\(\mathbf{\dfrac{4\cdot x^2 - 56 \cdot x + 196}{x^2-10\cdot x + 25} - (x + 3)} = 0\)
\(\dfrac{- x^3 + 11 \cdot x^2 - 51 \cdot x + 121}{x^2-10\cdot x + 25} = 0\)
x³ - 11·x² + 51·x - 121 = 0
Using the Newton Raphson method, with x₀ = 6, we have;
\(x_1 = x_0- \dfrac{x^3 - 11 \cdot x^2 + 51 \cdot x - 121}{3 \cdot x^2 - 22 \cdot x + 51}\)
Which gives;
\(x_1 = 6- \dfrac{6^3 - 11 \times 6^2 + 51 \times 6 - 121}{3 \times 6^2 - 22 \times 6 + 51} \approx \mathbf{ 5.81}\)
The correct option is B. 5.81
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State the domain and range for the following relation. Then determine whether the relation represents a function.{(8,-7)}, (9,7), (10,-7),(11,-7)}
Answers
Domain: 8, 9, 10, 11.Range: -7, 7 This relation does not represent a function because the same x-value (8, 10, 11) is associated with more than one y-value (-7, 7).
Domain: 8, 9, 10, 11
Range: -7, 7
A function is a relation between a set of inputs and a set of outputs such that each input is associated with exactly one output. This particular relation fails to meet this condition because the domain value 8 is associated with two different range values (-7 and 7). In other words, the same input (8) is associated with two different outputs, which means the relation does not represent a function. The domain of the relation is 8, 9, 10, 11 and the range is -7 and 7. Therefore, this relation does not represent a function because it violates the condition that each input must have one and only one associated output.
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How does Mathematics differ from language to language across the world
Answers
The answer is explained below.
In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a language. Linguists who don't consider math a language cite its use as a written rather than spoken form of communication.
Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. In a spoken language, there exist words, like "happiness", that defy definition.
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Find the equation of the line in slope-intercept form that passes through the following point with the given slope. Simplify your answer.
Point (3,−9)
; Slope=12
Answers
The equation of the line in slope intercept form is y = 12x - 45.
How to represent equation in slope intercept form?The equation in slope intercept form can be represented as follows:
y = mx + b
where
m = slope of the lineb = y-intercept of the lineTherefore, the slope of the line is 12 and the points it passes through is (3, -9).
Let's find the y-intercept of the line as follows:
y = 12x + b
-9 = 12(3) + b
-9 - 36 = b
b = -45
Therefore, the equation of the line is y = 12x - 45
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I NEED HELP MATH !!!!!
Answers
I think the answer is (c)