Amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).
As given in the question,
Amount invested by Nathan is principal 'P' = $3,500
Interest rate 'r' = 3.5% compounded quarterly
Number of compounding periods per year for given quarterly 'n' = 4
Time period 't'= 19 years
Amount of money in the account after 19 years when no deposits or withdrawals are done.
Let 'A' be the amount.
Formula used:
[tex]A = P \times ( 1+ \frac{r}{n} )^{nt}[/tex]
Substitute the value in the formula we get,
A = 3500 × [ 1 + (0.035/4) ]⁽⁴⁾⁽¹⁹⁾
= 3500 × [ 1 + 0.00875]⁽⁴⁾⁽¹⁹⁾
= 3500 × [ 1.00875]⁷⁶
= 6,786.06 (approximately)
= $6800 (nearest hundred dollars)
Therefore, amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).
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11. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the triangles
Make A the subject of the formula
what are the factors of 28?
Answer:
1, 2, 4, 7, 14 and 28
Step-by-step explanation:
1 x 28 = 28
2 x 14 = 28
4 x 7 = 28
Answer:
1, 2, 4, 7, 14 and 28
Step-by-step explanation:
Someone please help me out on this ( this is due tonight )
Answer the 2 question in the photo!
Answer:
1. 190 degrees
2.
For the red triangle
-2,4, -4,2 -2,1
For the blue triangle
-2,-5 -5,-5 -7,-4
I don't know if this is correct but I hope this helps :)
Emma recorded the weight of her kitten in ounces on certain days for 24 days. The data are shown in the scatter plot
Answer:
what are the instructions
Step-by-step explanation:
please repost with instructions
Given (x – 1)^2 = 50, select the values of x.
x = –49
x = 51
x = 1+5√2
x = 1-5√2
Answer:
[tex]x=1+5\sqrt{2}, 1-5\sqrt{2}[/tex]
Step-by-step explanation:
[tex](x-1)^2=50 \\ \\ x-1=\pm 5\sqrt{2} \\ \\ x=1 \pm 5\sqrt{2}[/tex]
Convert to vertex form. State the vertex. f(x)=-3x^2+12x-7
The vertex form of the quadratic equation is f(x) = -3(x - 2)² + 5. The coordinates of the vertex are (2, 5).
We are given a quadratic function. The equation of the quadratic function is f(x) = -3x² + 12x - 7. We need to convert the equation to vertex form. We can convert a quadratic equation to its standard vertex form by "completing the square" method. The calculations are done below.
f(x) = -3x² + 12x - 7
f(x) = -3(x² - 4x) - 7
f(x) = -3(x² - 4x + 2² - 2²) - 7
f(x) = -3(x² - 4x + 2²) - 7 + 3*2²
f(x) = -3(x - 2)² - 7 + 12
f(x) = -3(x - 2)² + 5
The coordinates of the vertex are (2, 5).
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The perimeter of a rectangle i 202020 centimeter. The length i 666 centimeter. What i the area of the rectangle?
quare centimeter
The area of the rectangle is, 24 square centimeter.
What is area?
Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Let, the perimeter of the rectangle is 20 centimeter.
The length is 6 centimeter.
Suppose the width of the rectangle is y.
So,
Perimeter = 2(6) + 2(y)
20 = 12 + 2y
8 = 2y
y = 4
Hence, the width of the rectangle is 4 centimeter.
Since,
Area of rectangle = length x width
A = 6 x 4
A = 24
Therefore, the area of the rectangle is, 24 square centimeter.
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(r, 3), (5, 9), m=2 what is the answer
The value of the unknown variable in the ordered pair is 8
How to determine the value of the unknown variable in the ordered pair?From the question, we have the following ordered pairs that can be used in our computation:
(r, 3), (5, 9)
Also, we have
m = 2
The meaning of the above notations are
Ordered pairs (x, y) = (r, 3), (5, 9)
Slope, m = 2
The slope of points is calculated using the following slope equation
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (r, 3), (5, 9) and m = 2
Substitute the known values in the above equation, so, we have the following representation
(9 - 3)/(r - 5) = 2
Evaluate the difference
This gives
6/(r - 5) = 2
Divide both sides by 2
So, we have
3/(r - 5) = 1
Cross multiply
r - 5 = 3
So, we have
r = 3 + 5
Evaluate the sum
r = 8
Hence, the value of r is 8
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Possible question
What is the value of r using the following points and slope
(r, 3), (5, 9), m=2
Multiply. 3√2 ⋅ 2√8 ⋅ 3√. 6√ Enter your answer, in simplest radical form, in the box.
Answer:
the answer i think it is 432
Find the quotient 2 divided by 3/7
[tex]2\div \cfrac{3}{7}\implies \cfrac{2}{1}\div \cfrac{3}{7}\implies \cfrac{2}{1}\cdot \cfrac{7}{3}\implies \cfrac{14}{3}\implies 4\frac{2}{3}[/tex]
The quotient for the expression is 4.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
2 ÷ [tex]\frac{3}{7}[/tex]
= 2 / (3/7)
= (2 x 7) / 3
= 14/3
Now,
3 ) 14 ( 4
12
2
Remainder = 2
Quotient = 4
Thus,
The quotient is 4.
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1024,-256,64,-16, 3rd term
The next term of the given geometric series is the fifth term which is; a₅ = 4
What is the nth term of the geometric series?We are given the geometric series as;
1024, -256, 64, -16,.....
The formula to find the nth term of a geometric series is;
aₙ = ar^(n - 1)
where;
a is first term
r is common ratio
n is position of term
Thus, from the given series, we have that;
a = 1024
r = -256/1024
r = -1/4
Thus, the formula for the nth term of the series is;
aₙ = 1024(-¹/₄)^(n - 1)
Next term is the fifth term and so we have;
a₅ = 1024(-¹/₄)^(5 - 1)
a₅ = 1024(-¹/₄)^(4)
a₅ = 4
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These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?
Give your answer as a ratio, reduced to
simplest terms.
?
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer
Answer:
There are 10 marbles, 2 are yellow
The probability would be 2:10 but in simplest form 1:5
The probability of picking both the same = 1:5 x 1:5 = 1:25
Step-by-step explanation:
9 A rectangle and a square have the same area. The length
of the rectangle is 70 feet more than two times its width. The
length of a side of the square is 30 feet. Set up an equation to
find the dimensions of the rectangle. What are the dimensions
of the rectangle? Include units of measurement.
Answer:
Step-by-step explanation: If the square is 30 ft on one side the other side must be too. So 30x30 = 900. Now, we know the rectangle must also be 900 in area. So, the width must be 10feet and the length must be 90ft because 10x90 is also 900. How I got the length? I did 10x2+70.
i need help with my math work
Answer: I believe y=1x+0 (or y=x)
Step-by-step explanation: if you copy the slope and make the line go through (2,2), you get this line.
I need Help pleaseeeeeeeeeeeeeeee
Answer:
D
Step-by-step explanation:
500 user in a day that mean in 2 days you get 1000 user cause the double of 500 is 1000
I need help please!!
Answer:
9/14 (9 over 14)
Step-by-step explanation:
3³× (3⁴} ⁰.⁵ simplified
Thank you
Step-by-step explanation:
so, it is
3³ × (3⁴)^(0.5) ?
remember, when multiplying exponents of the same base, we add the exponents : e.g.
a⁵ × a³ = a⁸
when we have exponents in exponents we multiply the exponents : e.g.
(a³)⁴ = a¹²
now, also remember the priorities of mathematical operations :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
now, let's look at our expression again :
3³ × (3⁴)^(0.5)
since we only want to simplify and not to calculate, we leave (3⁴) alone, because the only thing we could do would be to actually calculate 3⁴.
so,
(3⁴)^(0.5) = 3^(4×0.5) = 3²
and then,
3³ × 3² = 3^(3+2) = 3⁵
so, the simplified expression is 3⁵.
which is 243 ...
there is a line that includes the point (2,10) and has a slope of 8. what is its equation in slope intercept form?
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{10})\hspace{10em} \stackrel{slope}{m} ~=~ 8 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ 8}(x-\stackrel{x_1}{2}) \\\\\\ y-10=8x-16\implies {\Large \begin{array}{llll} y=8x-6 \end{array}}[/tex]
7.78, 7.8, 6.969, 7.7081 order these numbers from least to greatest
The graph of a sinusoidal function has a minimum point at (0,2)(0,2)left parenthesis, 0, comma, 2, right parenthesis and then has a maximum point at (3\pi,6)(3π,6)left parenthesis, 3, pi, comma, 6, right parenthesis.
Write the formula of the function, where xxx is entered in radians.
The (0, 2) and (3•π, 6) minimum and maximum points on the graph of the sinusoidal function indicates that the function is as follows
[tex]y = 2\cdot sin\left(\dfrac{1}{3} \times \left(x - \dfrac{3\times \pi}{2} \right)\right) + 4[/tex]
What is a sinusoidal function?A sinusoidal function is a function based on the trigonometric function of sine.
The points on the graph of the sinusoidal function are;
Minimum point of the function; (3•π, 6)
Maximum point of the function; (0, 2)
The general form of the equation of a sinusoidal function is presented as follows;
The sinusoidal function equation is; y = a×sin(b×(x - h)) + k
The amplitude, a, is half the distance between the maximum and minimum points, therefore;
a = (6 - 2)÷2 = 2
a = 2
From the information in the question, when x = 0, y = 2
Plugging in the values of x = 0, y = 2in the equation, y = a×sin(b×(x - h)) + k, produces;
2 = 2×sin(b×(0 - h)) + k
The point (0, 2) is a minimum point, therefore; sin(b×(0 - h)) = -1
2 = 2×sin(b×(0 - h)) + k = 2×(-1) + k = -2 + k
k = 2 + 2 = 4
At the minimum point the value of sine is -1, which indicates that the value of the argument, (b•(0 - h)) = -π/2
Therefore; -b•h = -π/2
h = π/(2·b)
At the maximum point, (b×(x - h)) = π/2
Therefore; (b×(3×π - π/(2×b))) = π/2
b = 1/3
Therefore;
h = π/(2×b) = 3×π/2
y = 2×sin((1/3)×(x - 3×π/2)) + 4
The function is; y = 2×sin((1/3)×(x - 3×π/2)) + 4
The formula of the function for the graph is therefore; y = 2×sin((1/3)×(x - 3×π/2)) + 4
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Find the amount (future value) of ordinary annuity $1000 a year for 10 years at 10%/year compounded annually.
a.
$15,500
b.
$15,937
c.
$16,456
d.
$16,845
The future value of ordinary annuity $1000 a year for 10 years at 10% year compounded annually is $15937.
The value of a sum of money that will be paid on a specified date in the future is known as its future value. Since each payment is made at the end of a period, the formula for the future value of an ordinary annuity refers to the value on a specified future date of a series of periodic payments.
Given,
R=$1000, n=10, i=10%=10/100=0.1
The formula to calculate the future value is
FV=R[(1+i)^n-1]/i
[tex]FV=R(\frac{(1+i)^{n} -1}{i})[/tex]
[tex]FV=1000(\frac{(1+0.1)^{10} -1}{0.1})[/tex]
[tex]FV=1000(\frac{(1.1)^{10} -1}{0.1})[/tex]
[tex]FV=1000(\frac{1.593742}{0.1})[/tex]
[tex]FV=1000\times15.9374[/tex]
[tex]FV=15937.4[/tex]
Future Value approximately equal to $15937.
Therefore, the future value of the ordinary annuity $100 a year for 10 years at 10% compounded annually is $15937, Option c is the correct answer.
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Can someone pleaseeee solve this for me?
Answer:26
Step-by-step explanation:
The Florida Fish and Wildlife Conservation Commission is conducting a study on wildlife patterns and behaviors in a specific area of the Florida Everglades. A stationary camera is placed where the area being observed can be filmed and recorded for 96 hours. Researchers found that the footage revealed that the Cape Sable Seaside Sparrows were observed in the area once every 6 hours and the Florida Leafwing Butterfly was observed in the area once every 9 hours.
How many hours of footage would the observers need to review to see the Cape Sable seaside sparrow and the Florida leafwing butterfly in the area at the same time?
Number of Hours:
Answer:
18 hours of footage.
Step-by-step explanation:
This is a LCM problem. The least common multiple of 6 and 9 is 18. The minimum amount of hours needed to see the sparrow and butterfly at the same time is 18.
In the given figure, the reflex angle DOB measures 3.5y and AOD measures Y. Find the measures of the non reflex DOB in degrees.
The measure of non reflex angle DOB in degrees is 140°
Calculating the measure of an angleFrom the given information, we are to determine the measure of the non reflex angle DOB
From the given information,
m reflex ∠ DOB = 3.5y
and
m ∠ AOD = y
First, we will determine the value of y
From Linear pair theorem, we can write that
3.5y + y = 180°
4.5y = 180°
y = 180°/4.5
y = 40°
Also,
y + m ∠ DOB = 180° (Linear pair theorem)
Thus,
40° + m ∠ DOB = 180°
m ∠ DOB = 180° - 40°
m ∠ DOB = 140°
Hence, the measure of ∠ DOB is 140°
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Grace and her dad are planning to attend the state fair. An adult ticket is $15. The price of an adult ticket is one half the price of a student ticket plus $8. Write an equation to determine how much grace will pay for a student ticket.
1/2 x + 8 = 15 Grace will pay for a student ticket
the question requests the cost of a "student ticket." Because we don't know, let's assume the student ticket price is "x" dollars.
Because we know from the question that "the price of an adult ticket is half the price of a student ticket plus $8.00," we can represent the adult ticket price as follows:
1/2 x + 8
If we also get "An adult ticket costs $15.00" from the question, we can write the equation as:
1/2 x + 8 = 15
Grace will pay for a student ticket
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log((4x)/(8))=log(x-5)
The given logarithmic equation solved for x is x = 10
Solving Logarithmic equationsFrom the question, we are to solve the given logarithmic equation.
The given logarithmic equation is
log((4x)/(8)) = log(x - 5)
To solve the given logarithmic equation, we will determine the value of the unknown variable.
The unknown variable in the equation is x.
From one of the rules of logarithm, we have that
If logₓY = logₓZ
Then,
Y = Z
Thus,
From log((4x)/(8)) = log(x - 5)
We can write that
(4x)/(8) = (x - 5)
Now, solve for x
(4x)/(8) = (x - 5)
Multiply both sides by 8
8 × (4x)/(8) = (x - 5) × 8
4x = 8x - 40
Subtract 8x from both sides of the equation
4x - 8x = 8x - 8x - 40
-4x = -40
Multiply both sides by -1
-1 × -4x = -1 × -40
4x =40
Divide both sides by 4
4x/4 = 40/4
x = 10
Hence, the solution of the equation is x = 10
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find the missing side of the right triangle.
Answer:
8
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + (4√3)^2 = c^2
16 + 48 = c^2
64 = c^2
√64 = c
8 = c
Write an equation for the trend line shown on the scatter plot.
An equation for the trend line shown on the scatter plot is y = 5x + 15.
How to find an equation for the trend line?In order to determine a linear equation for the trend line (line of best fit) that models the data points described in the scatter plot above, we would have to calculate the slope of this line.
By critically observing the scatter plot, we can reasonably and logically deduce the following points through which the trend line passes through:
Points (x, y) = (2, 25)
Points (x, y) = (6, 45)
Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (45 - 25)/(6 - 2)
Slope, m = 20/4
Slope, m = 5.
At point (2, 25), a linear equation for the trend line can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x represents the length of trip (in days).y represents the weight (lbs).Substituting the given parameters into the formula, we have;
y - y₁ = m(x - x₁)
y - 25 = 5(x - 2)
y - 25 = 5x - 10
y = 5x - 10 + 25
y = 5x + 15.
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Last year, Dan opened an investment account with $7800. At the end of the year, the amount in the account had increased by 29.5%. How much is this increase
In dollars? How much money was in his account at the end of last year?
Answer:
10,101
Step-by-step explanation:
Percent (%) means 'out of one hundred'
29.5%= 29.5/100 'out of one hundred'
----------------------------------------------------------------------
How to increase the number 7,800
by 29.5% of it's value?
1.) Calculate the new value of the number increased by the percentage of it's initial value
The new value=
7,800+ The value of the percentage increase=
7,800 + (29.5% x 7,800) =
7,800 + 29.5% x 7,800=
(1 + 29.5%) x 7,800=
(100% + 29.5%) x 7,800=
129.5% x 7,800
129.5 ÷ 100 x 7,800=
129.5 x 7,800 ÷ 100=
1,010,100 ÷ 100=
10,101
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I hope this was helpful!