Using the future value formula, it is found that the value of the account after the tenth deposit is of $26,361.59.
What is the future value formula?The future value formula is given by:
[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]
In which:
P is the payment.n is the number of payments.r is the interest rate.For this problem, the parameters are given as follows:
P = 2000, r = 0.06, n = 10.
Hence the value of the account will be of:
[tex]V(10) = 2000\left[\frac{(1 + 0.06)^{10} - 1}{0.06}\right][/tex]
V(10) = $26,361.59.
What is the missing information?The complete problem is:
"Suppose that there is an account that pays 6% interest that is compounded annually. At the beginning of each year, $2,000 is deposited into the account (starting with $2,000 for the first year).
What will be the value of the account after the tenth deposit if no withdrawals or additional deposits are made?"
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Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of s and t. Please use * for multiplication between all factors.)[tex]z = x^{7}y^{7}, x = s cos(t), y = s sin(t)[/tex]
Applying the Chain Rule, the derivatives are given as follows:
[tex]\frac{\partial z}{\partial s} = 7(s\cos{t})^6(s\sin(t))^6(y\cos{t} + x\sin{t})[/tex][tex]\frac{\partial z}{\partial t} = 7s(s\cos{t})^6(s\sin{t})^6(-y\sin{t} + x\cos{t})[/tex]What is the derivative of Z as a function of s?
The function Z is defined as follows:
z = x^7y^7.
The variables x and y are functions of variables s and t, as follows:
x = s cos(t).y = s sin(t).Hence the derivative of z as a function of s is given as follows:
∂z/∂s = (dz/dx)(dx/ds) + (dz/dy)(dy/ds).
Hence, applying the derivative rules for the exponents, and for the exponents, we have that:
[tex]\frac{\partial z}{\partial s} = 7x^6y^7\cos{(t)} + 7y^6x^7\sin{(t)} = 7x^6y^6(y\cos{t} + x\sin{t})[/tex]
Replacing the values of x and y, we have that:
[tex]\frac{\partial z}{\partial s} = 7(s\cos{t})^6(s\sin(t))^6(y\cos{t} + x\sin{t})[/tex]
What is the derivative of Z as a function of t?We follow the same logic as above, only that now the inside derivatives, that is, the derivatives of x and y, are as function of t and not of s, hence:
∂z/∂t = (dz/dx)(dx/dt) + (dz/dy)(dy/dt).
Then:
[tex]\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7sx^6y^6(-y\sin{t} + x\cos{t})[/tex]
Then, replacing x and y as functions of s and t, we have that:
[tex]\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7s(s\cos{t})^6(s\sin{t})^6(-y\sin{t} + x\cos{t})[/tex]
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The cost of 8 shirts is $72 find the cost of 12 shirts
Answer: $108
Step-by-step explation:
Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?
2(25) + c
25c + 3
3(c) + 25
3(c + 25)
The final expression that represent the total owed is 3c + 25
How to represent mathematical expression?He owed 3 months cable at a price of c dollars for each month, plus a one-time equipment fee of $25,
Therefore, the situation can be expressed as follows:
For a single month he pays c dollars
Hence, 3 month will be 3 × c.
Recall he also needs to pay a one time fees of 25 dollar.
Therefore, the final expression that represent the total owed is as follows:
total owed = 3c + 25
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A baker sells muffins in boxes that contain exactly 9 muffins each. Can the baker place 576 muffins in boxes with none left over. Explain
The baker can put all the 576 muffins in the box that contains exactly 9 muffins with none left over.
Can the baker put all the muffins in the box with none left over?In order to determine if the baker can put all the 576 muffins in the box that contains exactly 9 muffins with none left over, divide 576 by 9. If 9 perfectly divides 576, then there would be no remainder.
Division is the process in mathematics that is used to group a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other operations in mathematics are addition, subtraction and multiplication.
Number of boxes needed = number of muffins / capacity of each box
576 / 9 = 64
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 line m || line n m<4 = 72°
what is the measure of angle 1?
Answer:
angle 1 = 108°
Step-by-step explanation:
You want the measure of angle 1, given the measure of angle 4 is 72° in the diagram.
Linear pairAngles 1 and 4 are a linear pair, so are supplementary:
angle 1 + angle 4 = 180°
angle 1 + 72° = 180°
angle 1 = 108° . . . . . . . subtract 72°
You put some money in a bank account one year ago. You have not done anything with it since. The bank takes out a low balance fee of $0.25 each month. After 8 months, you had $28 in the account. Choose the equation that best shows the money in your bank account over time. CLEAR CHECK Balance=−0.25⋅Months Balance−28=−0.25(Months−8) Balance−8=−0.25(Months−28) Balance−28=−0.25(Months+8)
Answer:
Step-by-step explanation:
A cashier has 35 bills, all of which are $10 or $20 bills. The total value of the money is $520. How many of each type of bill does the cashier have?
After solving some mathematical operations we can conclude that the cashier has 16 bills of $10 and 18 bills of $20.
What do we mean by mathematical operations?A mathematical function called an operation, also known as an "operand" or "argument," transforms zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The operations that are most frequently studied are unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, and binary operations (i.e., operations of arity 2), such as addition and multiplication.An operation of arity zero also referred to as a nullary operation, is a constant.The mixed product is an illustration of an operation of arity 3, also referred to as a ternary operation.So, the total value of money by 35 bills is $0, and $20 is $520.
Now, we know that: 20 × 18 = 360Similarly, we know that: 10 × 16 = 160Sum of 360 and 160: 360 + 160 = $520So, 185 bills of $20 and 16 bills of $10.Therefore, after solving some mathematical operations we can conclude that the cashier has 16 bills of $10 and 18 bills of $20.
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Please answer I give Brainliest
Answer:
The value of x is 3 cm
Step-by-step explanation:
x is 3 cm because we can take 3/2 and make it easier for us and turn it into 1 and 1/2. As you can see 6, is 1 and 1/2 of 4, so all we have to do is find out what x equals by finding out what is 1 and 1/2 of 2. 2 is already 1, so we take half of 2 and add it and we get our answer 3 cm.
If Gabriella has 3 more nickels than dimes and they have a combined value of 90 cents, how many of each coin does she have?
Correct dimes
nickels
If Gabriella has 3 more nickels than dimes and they have a combined value of 90 cents, The number of coin she have is; 4 nickels and 7 dimes.
Nickels and dimesx = number of nickels that Gabriella has
x +3 =number of dimes that Gabriella
Hence,
0.05x + 0.10 ( x + 3 ) = 0.9
Solving for x
Multiply both sides of the equation by 100 so as to eliminate two decimal places
5x + 10x + 30 = 90
Collect like terms
15x = 60
Divide both side by 15x
x = 60/15
x = 4 nickels
So,
x + 3 where x = 4
4 + 3 =7 dimes
Therefore she has 4 nickels and 7 dimes.
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What is the slope of the line on the graph?
need answer asap pls help
Answer:
-2/6
Step-by-step explanation:
go down the y axis 2 times (-2) and over 6
y=-2/6x+4
what are the domain and range of the function?
The domain and range are the set of all real numbers, so:
Domain: x ∈ R
Range: x ∈ R
Thus, the correct option is the second one
What are the domain and range of the function?
For any function y = f(x), we define the domain as the set of the possible values of x (the ones on the horizontal axis) and the range is the set of the possible values of y (vertical axis).
In this case, we have a linear equation (you can see that the lines extend to the bottom left and the top right)
So both domain and range are the sets of all real numbers.
Thus, the correct option is the second one.
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A hat costs $10.95 and a T-shirt costs $14.20. How much change will you receive if you pay for both items with a $50 bill?
Pls give a good explanation
Answer: $24.85
Step-by-step explanation:
10.95+14.20= 25.15
25.15+24.85= 50
Answer:
24.35
Step-by-step explanation:
Add 10.95 to 14.20:
10.95+14.20=25.15
Then subtract the answer 25.15 from 50
50-25.15=24.35
What is 581/14 in partial quotients?
The quotient of 581 and 14 has a value of 40.07
How to evaluate the expression using partial quotients?The quotient expression is given as
581/14
Next, we express 581 as the sum of a multiple of 14 and another number
Say 581 = 280 + 280 + 1
So, we have the following equation
581/14 = (280 + 280 + 1)/14
Expand the bracket
So, we have the following equation
581/14 = 280/14 + 280/14 + 1/14
Evaluate the quotients
581/14 = 20 + 20 + 0.07
Evaluate the sum
581/14 = 40.07
Hence, the value of the quotient expression is 40.07
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Help pls!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
it should be 180
9 1/4 to 9
20 stays the same
Please help with number 8 step by step
Answer:
It is a function because circles are functions
Step-by-step explanation:
the formula for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h,k) = center
r=radius
radius is 4 because diameter is 8
Center is (2,1)
plug it into the equation:
[tex](x-2)^2+(y-1)^2=16[/tex]
[tex] \rm \int_0^1 \frac{ {x}^{3} - {x}^{2} - 1 }{ {x}^{2} - x - 1 }dx \\ [/tex]
Simplify the integrand.
[tex]\displaystyle \frac{x^3-x^2-1}{x^2-x-1} = x + \frac{x-1}{x^2-x-1}[/tex]
Expand into partial fractions, recalling that [tex]\phi[/tex] and [tex]-\frac1\phi[/tex] are roots to the quadratic in the denominator.
[tex]\dfrac{x-1}{(x - \phi) \left(x + \frac1\phi\right)} = \dfrac1{1+\phi^2} \left(\dfrac1{x-\phi} + \dfrac{\phi^2}{x + \dfrac1\phi}\right)[/tex]
Then the integral is
[tex]\displaystyle I = \int_0^1 \frac{x^3-x^2-1}{x^2-x-1} \, dx \\\\ ~~~~ = \int_0^1 x \, dx + \frac1{1+\phi^2} \int_0^1 \left(\frac1{x-\phi} + \frac{\phi^2}{x+\frac1\phi}\right) \, dx \\\\ ~~~~ = \frac12 + \frac{1}{1+\phi^2} \left(\ln|1-\phi| + \phi^2 \ln\left|1 + \frac1\phi\right| - \ln|-\phi| - \phi^2 \ln\left|\frac1\phi\right|\right)[/tex]
and this reduces significantly, when we recall that [tex]\phi = 1 + \frac1\phi[/tex], to
[tex]\displaystyle I = \boxed{\frac12 + \frac{2\phi}{1 + \phi^2} \ln(\phi)}[/tex]
write 7298 to nearest thousand?
Answer:
Rounds down to 7000.
Step-by-step explanation:
It takes 4 cups of sugar to make 6 batches of cookies. How many cups of sugar is needed for 15 batches of cookies?
Answer:
10 cups
Step-by-step explanation:
6 divided by 4 is 1.5 and if you take 15 divided by 1.5 it'd be 10
Answer:
10 cups of sugar
Step-by-step explanation:
you can easily make it into a ratio.... ( the amountof sugar needed to make 15 batches of cookies is x)
x/15 = 4/6
when you multiply you get 6x = 4 × 15
6x = 60, then you divide by 6
giving you x=10
Translate the phrase into an Algebraic expression The sum of 6 and b
The translation of the phrase into an algebraic expression which is the sum of 6 and b is 6+b.
What is an algebraic expression?It should be noted that an algebraic expression is used in Mathematics to show the relationship between the terms that are given. The concept of utilizing letters or alphabets to convey numbers without defining their exact values is known as algebraic expressions.
We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
In this case, we want to translate the phrase into an algebraic expression. The phrase is the sum of 6 and b. This will simply be:
= 6 + b
Therefore, the expression is 6+b.
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Clancy has 423 cups of yogurt to share with his friends at a party. Each guest will receive 1 serving of yogurt which is 34 of a cup.
Write a multiplication equation to determine the number of people, p, who can be invited to the party.
Answer: Around 141 guests can be invited
Explanation: 423 divided by 3/4 is 141, and 141 x 3/4 is 423
Find all points on the x-axis that are 12 units from the point (3,-6)
The points on the x-axis that are 12 units away from the point (3,-6) is found to be 3 ± [tex]6\sqrt{3}[/tex].
What is the circle equation?r² = (x - h)² + (y - k)²is the standard equation for a circle, where (h,k) are the coordinates of the circle's center and r is the radius.
We must locate all points on the x-axis that are 12 units away from the starting point (3,-6).
Let these points be (x,0)
All points 12 units away from the point (3,-6) form a circle with a radius of 12 and a center at (3,-6). The formula would be as follows:
r² = (x - h)² + (y - k)²
12² = (x-3)² + (0+6)²
144 = (x-3)² + 36
(x-3)² = 108
x-3 = ± [tex]\sqrt{108}[/tex]
x = ± [tex]\sqrt{108}+3[/tex]
x = 3 ± [tex]6\sqrt{3}[/tex]
Therefore, the points on the x-axis 12 units away from point (3,-6) is calculated as 3 ± [tex]6\sqrt{3}[/tex].
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shade the portion of this figure that represents 14/4
14/4 = ?
There are 4x5 = 20 squares
Then 14/4 = 3 + 2/4
also 14/4 = 70/20 = 7/2
Take 14 squares, from figure
Now graph portion shade
Multiply using the associative property.
Enter your answer by filling in the boxes.
(7×5) x2=
(7×5) x2=7x
(7 × 5) x 2 =
X
x 2)
Answer this problem
The answer of (7 ×5) ×2 using associative property is 70.
What is associative property?
(a ×b) ×c = a ×(b ×c) and (a+b)+c = a+(b+c)
Addition and multiplication are supported by the associative property but not division and subtraction.
Using associative property ,
(7 ×5) ×2 = 7×(5 ×2)
(7 ×5) ×2 = 7×10
(7 ×5) ×2 = 70
Therefore, the answer of (7 ×5) ×2 using associative property is 70.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
B) The blue square on the right contains the yellow square + the green square on the left
Step-by-step explanation:
hope this helps ;)
Find the slope from the given table. Simplify your answer. Hint: Make Time (x) and Distance (y). Does it matter which two points you use? Type yes or no.
m = 15/8 and yes it dep
Here, we want to find the slope from the given table
Mathematically, that could be calculated using the formula;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ we\text{ can select any two points} \\ \\ \text{let us select the first and the last;} \\ \\ m\text{ = }\frac{17-2}{9-1}\text{ = }\frac{15}{8}\text{ } \end{gathered}[/tex]Now, we want to find out if it differs if we use any other random two points
Let us select the 1st and the 3rd point
Mathematically, the slope here would be;
[tex]m\text{ = }\frac{12-2}{6-1}\text{ = }\frac{10}{5}\text{ = 2}[/tex]From these, we can see that the value of the slope obtained depends on the two points that are selected
Which of the following are the coordinates of point F' , the image of point F, after a rotation of 90° about (1 point)
the origin?
Answer:
(3, 0)
Step-by-step explanation:
I assume this means a clockwise rotation.
let's think this through logically :
the last option (0, 3) cannot be right, because that is F before the rotation. to go back to the original position requires a full rotation of 360° (remember, a circle has 360°, and that means to travel one complete time around the circle).
(0, -3) cannot be right, because this is just mirrored down, and would represent a turn of 180° (a half-circle).
for the other options imagine you use a math compass, put the pin on the origin, and the writing arm on F. and the you draw a circle through F.
(3, 0) is the result of the clockwise (right) turn of 90°, (-3, 0) would be the result of a counterclockwise (left) turn of 90°.
so, if my assumption above is incorrect, please pick (-3, 0) for the counterclockwise solution.
El volumen de un cubo que tiene como arista 14 cm es?
1000 cm3
2.744 cm3
216 cm3
The volume of the cube is 2744 cm³.
QuadrilateralsThere are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a square all angles are 90° and all sides present the same value.
A square is a 2D figure, when the square is associated a 3D figure, the figure is called a cube. The cube presents 6 faces with length (l) , height (h) and width (w) equal. Thus, the cube presents congruent edges.
The volume is given from the formula V=a³, where a is a congruent edge.
The question gives:
edge=14 cmTherefore,
V=a³
V=14³
V=14*14*14
V=2744 cm³
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A train travels along a straight piece of track between 2 stations
A and B. The train starts from rest at A and accelerates at
1.25m/s² until it reaches a speed of 20m/s. Find the distance
from A to B.
Answer:
v=20m/s ,u= 0m/s( from rest) a=1.25m/s Distance s=?
V²= UT +2as
make s subject
2as=v²-u²
S= v²-u²/2a
S =20²-0²/2*1.25
S=400/2.5
S= 160m
Miguel reads that the average low temperature today is −8.5°F and that the average high temperature is 10.2º F.
Miguel plots the points on the number line to determine the temperature change between these two readings.
What is the temperature change?
The change in temperature between the two readings as measured by Miguel is 18.7°F .
In the question ,
the temperature readings on the Miguel is
Average low temperature = -8.5°F
Average high temperature = 10.2°F
the change in the temperature , is given by the difference between the two reading .
which means
Change in temperature = Average high temperature - Average low temperature .
Substituting the values of average high and average low reading of the temperature from above ,
we get ,
Change in temperature = 10.2 -(-8.5)
= 10.2 + 8.5
= 18.7
the temperature change is 18.7°F .
Therefore , the temperature change is 18.7°F .
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Convert 67/9 into a mixed number.
The answer for this is 7 4/9