Marco opened a savings account 10years ago. The account earns 5% interest,compounded annually. If the current balance is $400, how much did he deposit initially? Round your answer to the nearest cent.
Answers
Answer:
245.57
Step-by-step explanation:
[tex]P\left(1+0.05)^{10}=400 \\ \\ P=\frac{400}{(1.05)^{10}} \\ \\ P \approx 245.57[/tex]
Related Questions
consider the ellipse given by x^2+xy+2y^2=7. Find the y-coordinate(s) of all points where the ellipse has a vertical tangent line.
Answers
The ellipse given by x^2+xy+2y^2=7. The y-coordinate(s) of all points are -11.3, 11.2, -5.665, 5.585 where the ellipse has a vertical tangent line.
Define differentiation.Differentiation is the process of determining a function's derivative. Differentiating algebraic functions, trigonometric functions, and exponential functions are the three fundamental derivatives.
Given,
Ellipse given,
x²+ xy + y ² = 7
Differentiating:
dy/dx
x²+ xy + y² = 7
d/dx(x² + xy + y²) = d/dx(7)
2x + 1y + x dy/dx + 2y dy/dx = 0
dy/dx = 2x + y/ x + 2y
dy/dx = 0
2x + y = 0
x + 2y = 0
Now, we have 2 equations,
x² + xy + y² = 0
y = -2x
Solving equations by substitution method,
x² + x(-2x) + (-2x)² = 7
x² - 2x² + 4x² = 7
3x² = 7
x = ±√21/3
Using y = -2x
Points are:
( -2√21/3 , √21/3) and (2√21/3 , -√21/3)
±√21/3 = ±1.528
x² + xy + y² = 7 [-11.3, 11.2, -5.665, 5.585]}
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|y + 4| < 1
A. −5 < y < –3
B. –3 < y < 5
C. –4 < y < 1
D. 1 < y < 4
Answers
A solution to this inequality |y + 4| < 1 in as an interval is: A. −5 < y < –3.
What is an inequality?An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than or equal to (≥).Less than or equal to (≤).Greater than (>).Less than (<).Adding -1 to both sides of the inequality, we have:
|y + 4| + (-1) < 1 + (-1)
|y + 4| - 1 < 0
Evaluating the absolute value function, we have the following:
y + 4 < ±1
For the positive interval, we have:
y < -4 + 1
y < -3
For the negative interval, we have:
y < -4 - 1
y < -5
Finally, we would express the solution to this inequality as an interval as follows:
-5 < y < -3.
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Complete Question:
What is a solution to this inequality |y + 4| < 1?
A. −5 < y < –3
B. –3 < y < 5
C. –4 < y < 1
D. 1 < y < 4
15. Mohammed has $8376 in his bank account. In the next month he takes out $4595 to buy a car. He then buys some new tires for his car for $1200. The next day, he receives his salary of $2709 in his bank account. How much is in his account at the end of the month?
Answers
By doing addition and subtraction of integers, the result obtained is
Mohammed had $5290 at the end of the month
What is addition and subtraction of integers?
At first it is important to know about integers
Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.
Suppose there are many integers, and we need to find the sum total of all those integers, then the operation used in this case is called addition.
To find how big or small one integer is from the other, then the operation used is called subtraction of integers.
Here we will use addition and subtraction of integers
Bank balance of Mohammed = $8376
Amount of money taken out by Mohammed next month to buy a car = $4595
Amount of money needed to buy new tires for his car = $1200
Amount of salary received by Mohammed next day = $2709
Amount of money Mohammed had at the end of the month =
$(8376 - 4595 - 1200 + 2709)
= $5290
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What is the function rule for the line?
f (x) = 2x - 4
f(x)=-4x - 2
f(x) = 4x - 2
f (x)= -2x + 4
Answers
Answer: f (x)= -2x + 4
What is an equation of the line that passes through the points (4, -2)(4,−2) and (8, 3)(8,3)
Answers
The equation of line passing through points (4,−2) and (8, 3) is 4y - 5x + 28 = 0
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given pair of points are (4,−2) and (8, 3).
The equation of line passing through two points (x₁, y₁) and (x₂, y₂) is given as,
y = ((x - x₁) / (x₁ - x₂)) (y₁ - y₂) + y₁
Substitute the respective values to get the equation of line as,
y = ((x - 4 ) / (4 - 8)) (-2 - 3) + (-2)
y = ((x - 4 ) / 4) × 5 - 2
4(y + 2) = 5(x - 4)
4y - 5x + 28 = 0
Hence, the equation of line for the given points is 4y - 5x + 28 = 0.
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What is the y-intercept of a line that has a slope of and passes through point (8, 3)?
000
3
5
11
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Answers
The y-intercept of a line that has a slope of and passes through points (8, 3) is (0,1).
what is the slope-intercept?
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.
The slope-intercept form: y = mx + b
m - a slope
b - y-intercept
Here, we have
A slope m = 1/4.
Substitute: y = 1/4 x + b
We know that
the line passes through the point (8, 3) → x = 8, y = 3.
Put the values of x and y into the slope of the line:
1/4 · 8 + b = 3
2 + b = 3 |-2
b = 1
Hence, the y-intercept is (0, 1)
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In the first hour Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, the sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes. How many did they sell?
Answers
The number of cupcakes sold will be 4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that, in the first hour, Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, they sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes.
The number of cupcakes sold will be,
N = (1/3) + (3/8) +[(2-1/3-3/8)]+3
N = (1/3)+(3/8) + (7/24)
N = 96 / 24
N = 4
Therefore, the number of cupcakes sold will be 4.
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Aim: How can you earn money with a Savings Account?
Exit Ticket #5 Simple Interest
Find the simple interest on a $2,350 principal
deposited for 6 years at a rate of 2.77%
I =
P =
t =
I = prt
I=( )( )( )
Answers
Answer:
I = (2350)(0.0277)(6)
Step-by-step explanation:
We're told the principal, rate, and time so we just plug in.
We must convert the 2.77% to a decimal by moving the period two places to the left to get the rate 0.0277
v+8w=4v,for v
-m+5n=-2, for n
Answers
Answer:
v = 8w/3,n = (m - 2)/5.---------------------------
Given equationsv + 8w = 4v and - m + 5n = - 2Solve the first equation for vv + 8w = 4v4v - v = 8w3v = 8wv = 8w/3Solve the second equation for n- m + 5n = - 25n = m - 2n = (m - 2)/5Answer:
Value of v = (8w)/3Value of n = (m - 2)/5Step-by-step explanation:
1) v + 8w = 4v, for v?
→ v + 8w = 4v
→ 8w = 4v - v
→ 8w = 3v
→ [ v = (8w)/3 ]
Thus, value is (8w)/3.
2) -m + 5n = -2, for n?
→ -m + 5n = -2
→ 5n = -2 + m
→ 5n = m - 2
→ [ n = (m - 2)/5 ]
Thus, value is (m - 2)/5.
Graph the polygon with the given vertices and its image after a reflection in the line y = -x .
A(2, 0), B(3, 4), C(6, 4), D(5, 0)
Answers
As per the concept of transformation, the image of the polygon after a reflection in the line y = - x is has vertices at A(0,-2), B(-4,-3), C(-4,-6), D(0,-5) as shown in the diagram attached below.
Transformation:
Transformation refers the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.
Given,
Here we have the vertices A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the equation for line y = -x.
Now we have to plot the graph with the given vertices and its image after a reflection in the line y = -x .
Here reflection refers flipping of a figure.
Therefore, if a point A(x, y) is reflected about the line y = - x, the new point would be at A'(-y, -x)
For the given the polygon with vertices at A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the image of the polygon after a reflection in the line y = -x has vertices at:
A(0,-2), B(-4,-3), C(-4,-6), D(0,-5)
The image of the polygon is attached below.
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Sara sold a coin for $3, and its value increases by 2% each year after it is sold. Find the value of the coin in 8 years. Then write an exponential growth
function for this problem. After that, graph the function and state the domain and range. Finally, state what the y-intercept represents.
Answers
By using the concept of growth, it can be calculated that
Value of coin in 8 years is $3.52
[tex]3(\frac{51}{50})^x[/tex] is the required exponential function
Domain of the function is all positive real number
Range is [tex](0, \infty)[/tex]
y- intercept is 3
This means initial value of the coin is $3
What is growth?
Growth is the exponential increase in the value of the product at a certain rate over a certain period of time
Here, concept of growth has been used
Present value of the coin = $3
Rate = 2%
Time = 8 years
Future value =
[tex]3(1 + \frac{2}{100})^8\\\\3(1 + \frac{1}{50})^8 \\\\3(\frac{51}{50})^8[/tex]
= $3.52
If the time is x years, the given exponential function is
y =
[tex]3(1 + \frac{1}{50})^x\\\\3(\frac{51}{50})^x[/tex]
This is the required exponential function.
Since x represents time here, then x has to be positive
Domain of the function is all positive real number
Now
As [tex]x\rightarrow \infty[/tex], [tex]f(x) \rightarrow \infty[/tex]
As [tex]x\rightarrow -\infty[/tex], [tex]f(x) \rightarrow 0[/tex]
Range is [tex](0, \infty)[/tex]
For y- intercept, x = 0
Putting x = 0, we get y = 3
y- intercept is 3
This means initial value of the coin is $3
The graph of the function has been attached here
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I can't do math so I need someone to help me. what's the answer?
Answers
The value of TV for the similar triangles is 25
What are similar triangles?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.
Similar triangles are not the same as congruent triangles though.
triangle UXW and UTV are similar since line TV cuts lines UX and UW in the same proportion.
Let UV = p, it means also that WV = P. which means WU = 2p
so since the two triangles are similar, the ratio of their corresponding lengths are equal
meaning,
UV/UW = TV/XW
substituting their values, we have
p/2p = TV/50
by cross multiplying,
2p x TV = 50p
2TV = 50
TV = 50/2 = 25
In conclusion, the value of TV is half the value of WX = 25
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In 2012, 1,664,479 students took the SAT exam. The distribution
of scores in the verbal section of the SAT had a mean μ = 496 and a
standard deviation of o= 114.
Let X = a SAT exam verbal score section for 2012.
Then X-N (496, 114)
Find the z-scores for x1 = 325 and x2= 366.21.
Interpret each z-score.
What can you say about the x1= 325 and the x2= 366.21?
Answers
By using normal distribution of probability, it can be inferred that
For [tex]x_1 = 325[/tex], z = -1.5
This means 325 is 1.5 standard deviation below the mean.
For [tex]x_2 = 366.21[/tex], z = -1.1385
This means 366.21 is 1.1385 standard deviation below the mean.
[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.
[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.
What is normal distribution of probability?
Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-
[tex]f(x) = \frac{1}{\sigma \sqrt{2\pi}}}e^{-\frac{z^2}{2}[/tex]
where [tex]z = \frac{x - \mu}{\sigma}[/tex], [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
For [tex]x_1 = 325[/tex]
[tex]z = \frac{325 - 496}{114} = -1.5[/tex]
This means 325 is 1.5 standard deviation below the mean.
For [tex]x_2 = 366.21[/tex]
[tex]z = \frac{366.21 - 496}{114}[/tex] = -1.1385
This means 366.21 is 1.1385 standard deviation below the mean.
[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.
[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.
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Tell which number is greater 3/8,30
Answers
Answer:
30
Step-by-step explanation:
3/8 is less than 1.
30 is much greater than 1.
Answer: 30
Answer:30 is greater
Step-by-step explanation:
2x=9 what is the value of x
Answers
Answer:
The answer is x=4.5
Step-by-step explanation:
I hope this helps
What is the greatest integer solution 5 - 3m > -10
Answers
Answer:
4
Step-by-step explanation:
5-3m>-10
-5. -5
-3m>-15
/-3. /-3
m<5
so 4 is the highest integer since 4 is less than 5
Hopes this helps please mark brainliest
Put these numbers in order from smallest to largest.
Smallest
-75
-28
-3
13
103
341
619
Largest
Answers
Answer:
Step-by-step explanation:
Here by using the ascending property:
-75, -28, -3, 13, 103, 341, 619
the artist was hired to decorate 40 in 3 hours he completed 3/8 of the pots at that rate how long will it take the artist to decorate 25 clay pots?
Answers
The artist will take 5 hours to decorate 25 clay pots.
Given,
Number of pots to be decorated in 3 hours =40
Number of pots he decorated in 3 hours =[tex]\frac{3}{8}*40=3*5=15[/tex]
So, the artist took 3 hours to decorate 15 pots instead of 40 pots.
It means to decorate 1 pot he took time=[tex]\frac{Total time}{Number of pots decorated} =\frac{3}{15} =\frac{1}{15} hour[/tex]
So, to decorate 25 pots he need time,
[tex]time=\frac{1}{5}*25= 5 hours[/tex]
Thus, the artist need 5 hours to decorate 25 clay pots.
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what is the answer for -1/5x + 4 < 39
Answers
solution: [tex]x > -175[/tex]
interval notation: (-175, ∞)
explanation:
[tex]-\frac{1}{5}x + 4 < 39\\[/tex]
Subtract 4 from both sides
[tex]-\frac{1}{5}x +4-4 < 39-4\\[/tex]
Simplify
[tex]-\frac{1}{5}x < 35[/tex]
Multiply both sides by -1 (reverse the inequality)
[tex](-\frac{1}{5}x )(-1) > 35(-1)[/tex]
Simplify
[tex]\frac{1}{5}x > -35\\[/tex]
Multiply both sides by 5
[tex]5[/tex] ·[tex]\frac{1}{5}x > 5(-35)[/tex]
Simplify
[tex]x > -175[/tex]
I NEED HELP ASAP PLS!!
Answers
Answer:
7.8
Step-by-step explanation:
Switch 8 and 7, it round to 8 and end in tenths.
Answer:
7.8
Step-by-step explanation:
7.8 rounds to 8, because 8 is greater than 5, and then we end in the tenths place.
The perimeter of a triangle is 42 feet. One side of the triangle is one foot longer than the second side. The third side is five feet longer than the second side. Find the lengths of all three sides (in feet). (Enter your answers as a comma-separated list.)
Answers
Answer:
12 ft, 13 ft , 17 ft
Step-by-step explanation:
let x be the length of the second side , then
one side is x + 1
third side is x + 5
the perimeter P is the sum of the 3 sides, then
P = x + x + 1 + x + 5 ← collect like terms
P = 3x + 6
given P = 42 , then equating gives
3x + 6 = 42 ( subtract 6 from both sides )
3x = 36 ( divide both sides by 3 )
x = 12
x + 1 = 12 + 1 = 13
x + 5 = 12 + 5 = 17
the 3 sides are 12 ft, 13 ft , 17 ft
What is the unit rate of the table y = -4x + 2
Answers
The unit rate of the equation y = -4x + 2 is -4
How to determine the unit rate?From the question, we have the following equation
y = -4x + 2
The above equation is a linear equation
Linear equations are represented as
y = mx + c
Where
Unit rate = mY-intercept = cWhen the equations y = mx + c and y = -4x + 2 are compared, we have
Unit rate, m = -4
Y-intercept, c = 2
Note that all linear equations have a constant rate of change
Hence, the unit rate in the linear equation is -4
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Given: Gross sales, $170,000; sales returns and allowances, $9,000; beginning inventory, $8,000; net purchases, $18,000; ending inventory, $5,000; and operating expenses, $56,000. a. Calculate net sales. b. Calculate cost of merchandise (goods) sold. c. Calculate gross profit from sales. d. Calculate net income.
Answers
The calculation of the following income statement figures are as follows:
a) Net Sales are $161,000.b) Cost of goods sold is $21,000.c) The gross profit from sales is $140,000.d) The net income is $84,000.What is the income statement?The income statement is the first financial statement that summarizes the revenues and expenses for a business period to arrive at different profit points.
One of the profit points is the gross profit, which is the difference between the sales revenue and the cost of goods sold.
The other profit points include the operating income, income before tax, and net income.
Income StatementGross sales $170,000
Sales returns and allowances 9,000
Net Sales $161,000
Cost of goods sold:
Beginning inventory $8,000
Net purchases 18,000
Ending inventory (5,000) $21,000
Gross profit $140,000
Operating expenses (56,000)
Net Income $84,000
Thus, the calculation of the income statement figures shows a net income of $84,000.
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For the following image, find the volume:
6 in
4 in
6 ft
Answers
The required volume of the given shape is given as 432 cubic feet.
Given that,
A 3-dimensional shape with a hexagonal profile is given with dimension,
a = 6 in, H = 6 in and h = 4 in as shown in figure.
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
here,
The volume of the given shape is,
Volume = 6/2[ah] × H
Substitute the value in the above expression,
Volume = 3 [4×6] × 6
Volume = 432 cubic feet,
Thus, the required volume of the given shape is given as 432 cubic feet.
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What is the sum?
3
+
x+3x+3x+3
X
2
Answers
Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 20 years?
Answers
The amount that $100 will be able to buy in 20 years, given an inflation rate of 4% is $44.20
How to find the value of money?When given the inflation rate, know that this rate is the rate at which the value of money decreases per year.
If given a rate of 4% as inflation, then the value of a dollar would decrease by 4% a year.
In 20 years therefore, the value of $100 would be:
Value in 20 years = Value today x (1 - inflation rate) ^ number of years
= 100 x (1 - 4%) ²⁰
= $44.20
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Classify the following number: 5√2. Choose all that apply.
Answers
Answer:
Real, Irrational
Step-by-step explanation:
5sqrt2 is NOT:
Natural (1,2,3...)
Whole (0,1,2,3...)
Integer (...-3,-2,-1,0,1,2,3...)
Rational (can be written like a ratio)
Imaginary (have the number i in it.)
It IS Irrational, will have neverending decimal with no repeating pattern.
5sqrt2 = 7.0710678119...
It IS REAL and IRRATIONAL.
Help me with these 2
Answers
1) y = 3x+2, where slope is 3 and point is(3, -5).
2) y+6 = 4(x-5) is the equation for the given slope and point.
The slope of a line can be calculated from the equation of the line. The general slope of a line formula is given as,y = mx + b
The slope of a line can be calculated using two points lying on the straight line. Given the coordinates of the two points, we can apply the slope of line formula.Slope = m = tan θ = (y2 - y1)/(x2 - x1)
1) y + 5 = 3(x-1)x-x
Compare this equation to y - y₁ = m(x - x₁)
y = 3x - 3 + 5
y = 3x + 2
2) Given:
Slope = 4; point (5, -6)
y - y₁ = m(x - x₁)
y + 6 = 4(x -5 )
Option A
Hence, i) y = 3x+2, where slope is 3 and point is(3, -5) and ii) y+6 = 4(x-5) is the equation for the given slope and point.
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Consider the following table.
x y
5 0
-1 6
0 5
-3 8
4 1
Which graph corresponds to this table?
Answers
Answer:_______________________________
A school is arranging a field trip to the zoo. The school spends 654.84 dollars on passes for 32 students and 2 teachers. The school also spends 281.92 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Answers
The money was spent on a pass and lunch for each student is $28.07
How to calculate the amount?It was stated that the the school spends 654.84 dollars on passes for 32 students and 2 teachers while the school also spends 281.92 dollars on lunch for just the students.
Therefore the amount spent on pass will be:
= Total amount / Number of people
= 654.84 / 34
= 19.26
The amount spent on each student will be:
= 281.92 / 32
= 8.81
The amount spent in pass and lunch will be:
= 19.26 + 8.81
= $28.07
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