The function for the amount after {t} years can be written as -
[tex]$710(1 + 0.45/12nt)^{nt}[/tex]
What is compound interest?Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
where -
[A] = final amount
[P] = initial principal balance
[r] = interest rate
[n] = number of times interest applied per time period
[t] = number of time periods elapse
Given is that $710 is invested in an account earning 3.7% interest (APR), compounded monthly.
We can write -
A = 710(1 + 0.37/12)¹²⁽¹⁾
A = 710(1 + 0.037/12)¹²
A = 710(1 + 0.031)¹²
A = 710(1.031)¹²
A = 710 x 1.45
A = 1029.5
Let the annual growth rate be R. Then, we can write the function for annual growth rate after {t} years as -
1029.5 = [tex]$ 710(1 + R/1)^{t}[/tex]
1029.5 = [tex]$710(1+R)^{t}[/tex]
1.45 = [tex]$(1 + R)^{t}[/tex]
1.45 = 1 + tR + ..... {Binomial expansion}
Neglecting the binomial series from the third term as the value of the terms become negligible -
1.45 = 1 + tR
R = 0.45/t
Function for the amount after t years can be written as -
[tex]$710(1 + 0.45/12nt)^{nt}[/tex]= A
Therefore, the function for the amount after {t} years can be written as -
[tex]$710(1 + 0.45/12nt)^{nt}[/tex]
To solve more questions on compound interest, visit the link below -
brainly.com/question/14295570
#SPJ1
What is the greatest common factor of 24,40,32 A.1 B.2 C.4 D.8
Answer:
D. 8
Step-by-step explanation:
8*3=24
8*5=40
8*4=32
Tickets to a concert are $35 each. In addition to the cost for the tickets ordered, there is a $15 processing charge per order
An expression that represents the total cost of an order of n number of tickets: 35n + 15
Let n be the number of tickets to a concert.
Let C be the cost for the tickets
Given that the tickets to a concert are $35 each.
So, by unitary method the cost of n number of tickets would be,
n × 35
And the cost for the tickets would be,
C = 35n
In addition to the cost for the tickets ordered, there is a $15 processing charge per order.
So, the cost for the tickets would be,
C = 35n + 15
This is the required expression.
Learn more about the expression here:
https://brainly.com/question/30091997
#SPJ4
The complete question is:
Tickets to a concert are $35 each. In addition to the cost for the tickets ordered, there is a $15 processing charge per order.
Write an expression that represents the total cost of an order of n number of tickets.
Reflect shape A in the line y = -x. (See picture)
Answer:
See picture below
Step-by-step explanation:
FIND THE SUM OF ALL NATURAL NUMBERS FROM 1 TO 100 (ARITHMETIC PROGRESSION)
Answer:
According to arithmetic progression, natural numbers can be written down as 1, 2, 3, 4, 5, 6, 7, and 8 to 100. Basically, the sum of the first 100 natural numbers is equal to 5050.
Luke and Seth each need to buy the same amount of fencing for their gardens. While Seth's garden is square in shape, Luke's garden is rectangular with the length 3 feet longer than Seth's. Luke's width is half of the length of his own garden.
How much fencing did each buy? Need this asap please and thank you.
option
40. 5 feet
81 feet
72 feet
36 feet
Fencing that Luke and Seth did each buy is 72 feet
Using the information given, you can set up and solve the system of equations. Let x be the length of Seth's garden.
Seth's garden is square, so it has four times the perimeter.
The perimeter of Luke's garden is a rectangle of length x + 3 feet and width x/2 feet, so 2(x + 3) + 2(x/2).
We also know that Luke and Seth should buy the same amount of fences. So:
4x = 2(x + 3) + 2(x/2)
Solving this equation for x gives x = 6 feet.
So Seth's yardage is 6 feet and Luke's yardage is 9 feet.
So the fence required for Seth's garden is 46 = 24 feet
and the fence required for Luke's garden is 2(9) + 2(9/2) = 29 + 2*4.5 = 36 + 9 = 45 It's feet.
So the total fencing required is 24 + 45 = 72 feet.
Learn more about length and width here: https://brainly.com/question/24571594
#SPJ4
(6b+ 2) - (4b + 3)
Help pls I don’t know how to do this
Answer:
2b - 1
Step-by-step explanation:
To solve this problem, we will need to open the parentheses. To do this, we will put an imaginary 1 in front of both sets of parentheses to open them using the distributive property, this gives us:
1(6b + 2) - 1(4b + 3)
We will open the first set of parentheses with no problem, but in the second set, we have -1, so we need to make every positive number negative and every negative number positive, giving us:
6b + 2 - 4b - 3
Then, we group our like terms:
6b - 4b + 2 - 3
Then, we subtract, giving us:
2b - 1
So the most simplified version is 2b - 1.
Hope this helped!
Answer:
Step-by-step explanation:
You begin by distributing the negative so -4b -3
then you will multiply (6b+2) by (-4b -3)
24b^2 - 18b - 8b - 6
answer = 24b^2 - 26b - 6
What is the SHAPE of the 22nd figure?
The color of the 15th figure is green.
The shape of the 40th figure star.
The shape of the 22nd figure triangle.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
We have,
The pattern of shapes we get is:
circle - Triangle - Square - Star
The pattern of color we get is:
Purple - Red - Green
Now,
The color of the 15th figure.
= 15 is a multiple of 3
= 5 x 3
So,
Green will be the color of the 15th figure
Now,
The shape of the 40th figure.
= 40 is a multiple of 4
= 10 x 4
So,
Star will be the shape of the 40th figure.
Now,
The shape of the 22nd figure.
= 22 ÷ 4
We get 2 as the remainder.
So,
Triangle will be the shape of the 22nd figure.
Thus,
The 15th figure color is green.
The 40th figure is a star.
The 22nd figure is a triangle.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
C. It will
make 18 more parts.
5
Which number line shows the solution set to 1< -49 - 13/9 x <55/3?
The inequality is x 26 and asks for the values of x where the perimeter of the rectangle is smaller than 112.
The definition of inequalityIn mathematics, a link between two terms or values that isn't comparable is referred to as an inequality. As a result, imbalance leads to inequality. A mathematical inequality is a relationship between two non-equal expression . Egality is distinct from inequality. The not common basic is frequently used to denote that two values aren't actually equal (). Various inequalities are used to contrast the values, no matter how small or large. Many simple inequalities can be resolved by switching the two aspects until the variables are the only thing remaining. But a number of things encourage inequality: Values that are negative are divided or added along either side.
Here,
given
A rectangle's perimeter is determined by its length, width, and height.
rectangle's perimeter is calculated as length + length + width + width.
(x +4) + (x+4) + x + x < 112
x + 4 + x + 4 + x + x < 112
4x + 8 < 112
4x < 104
x < 26
In order to find the x value that occur when the rectangle's boundary is less than 112, the inequality is x 26.
To know more about inequality visit :-
brainly.com/question/28823603
#SPJ1
which equation represents a line perpendicular to the given line x-4y=7
The equation of the line perpendicular to x - 4y = 7 can be written as:
y = 4*x + b
Where b could be any real number.
Which equation represents a line perpendicular to x - 4y = 7?Two lines are perpendicular if the product between the slopes of the lines is equal to -1.
Where a general line in the slope-intercept form is written as:
y =a*x +b
And the given line is:
x - 4y = 7
Writing this in the slope-intercept form we will get:
-4y = -x - 7
y = (-1/4)*x + 7/4
So the slope is -1/4, then the slope of our line must be such that:
a*(-1/4) = -1
a = -4*-1 = 4
a =4
So the line perpendicular to the given one is:
y = 4*x + b
Where b can be any real number.
Learn more about perpendicular lines at:
https://brainly.com/question/1202004
#SPJ1
Factor the expression completely.
x^4-17x^2+72
Answer:
It's neither:
x =√ 9.000 = 3.00000 or :
x =√ 9.000 = -3.00000 or :
x =√ 8.000 = 2.82843 or :
x =√ 8.000 = -2.82843
Four solutions
Answer:
x^4 - 17x^2 + 72 = (x^2 - 9)(x^2 - 8)
Step-by-step explanation:
First, we need to find two numbers that multiply to give us 72 and whose sum is -17. We can see that 8 and 9 multiply to give us 72, and their sum is 8 + 9 = 17. Since we want the sum to be negative, we need to change one of the signs. So we write -(8 + 9) = -17.
Next, we write the expression as the product of two binomials. We factor out the common factor x^2 from the first two terms: x^4 - 17x^2 + 72 = x^2(x^2 - 17) + 72
Now, we complete the square in the first binomial. To do this, we need to add and subtract (17/2)^2 = (8.5)^2 = 72.25 inside the bracket:
x^2(x^2 - 17) + 72 = x^2(x^2 - 17 + 72.25 - 72.25) + 72 = x^2(x^2 - 17 + 72.25) - 72.25 + 72
Now we can rewrite the square of a binomial :
x^2(x^2 - 17 + 72.25) = x^2((x-8.5)^2)
Finally, we can combine the two binomials
x^2((x-8.5)^2) + 72 = (x^2(x-8.5)^2) + 8(9)
So the expression x^4 - 17x^2 + 72 factors completely as (x^2 - 9)(x^2 - 8)
Hope this helps!
Using the five digits 7, 7, 8, 8, and 8 once each, how many positive five-digit integers can be formed?
Answer:
There are 5 choices for the first digit, 5 choices for the second digit, 4 choices for the third digit, 3 choices for the fourth digit, and 2 choices for the fifth digit.
What are the 3 types of translations in math?
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1). Determine the scale factor used.
1
1/2
3
1/3
If Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1) then the scale factor used is 1/3
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1).
A(−3, −3)---->A(−3/3, −3/3)---->A′(−1, −1)
B(3, 3)---->B(3/3, 3/3)---->B′(1, 1)
C(0, 1)---->C(0/3, 1/3)---->B′(0, 1/3)
Hence, the scale factor used is 1/3.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
How do you write 5 more than a number?
x+5 is the way we can write 5 more than a number.
In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra.
Using the knowledge provided above, we must translate the mathematical statement provided in the question into an algebraic expression. Let's say that number is "x". The result of adding 5 to the provided number is a number that is 5 greater than this number. Thus, a number that is 5 more than x is equal to x+5. As a result, "5 more than a number" is represented by the algebraic expression "x+5".
To learn more about number here:
https://brainly.com/question/17429689
#SPJ4
In altitude BH and angle bisector AL intersect at point M. Given m∠HML = 100° and m∠MLC = 110°. Find angles of △ABC
The angles of triangle ABC are 60 degrees when altitude BH and bisector AL intersect at point M.
What is equilateral triangle?
An equilateral triangle in geometry is a triangle with equal-length sides on all three sides.
Given that:
[tex]\angle HML = 100 \\\\\angle MLC = 110[/tex]
Since, BH is the altitude [tex]\angle MHC= 90[/tex].
The total angle of a quadrilateral is 360, hence:
100 + 110 + 90 + C = 360
C = 60 degrees.
Now consider triangle BHC:
The sum of angle of a triangle is 180, hence:
90 + 60 + B = 180
B = 30
Since the half angle B = 30, the entire [tex]\angle ABC = 60[/tex].
Consider triangle ABC:
Using sum of triangles, we have:
[tex]\angle A + \angle B + \angle C = 180\\\\\angle A + 60 + 60 = 180 \\\\\angle A = 60[/tex]
Hence the measure of angles of triangle ABC is 60 degrees.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ4
Colin invests £3300 into his bank account. He receives 3% per year compound interest. How much will Colin have after 4 years? Give your answer to the nearest penny where appropriate
Answer:
Below
Step-by-step explanation:
3% = .03 in decimal 4 (yearly) periods
The effective interest and deposit amount after 3 years compounded yearly will be
3300 (1 +.03)^4 = £ 3714.18
HELP ASAP PLSS 50 POINTS!!!
Answer:
Missing part is ∠BAC and ∠DPFStep-by-step explanation:
ASA requires that both triangles have two angles and the included side to be congruent.
We have one side and an adjacent angle and need the second angle adjacent to the marked side to be congruent as well
It is the ∠BAC of ΔABC and ∠DPF of ΔPDF or simply ∠A and ∠P.
please help kinda confused!!
The equation of the line in fully simplified intersect is y = mx + b
What is general equation of the line?The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis.The equation of a line is y = mx + c , where m is the slope of the line and c is a constant.We have the x-intercept (3,0) and y-intercept (0,3) on the graph.Slope of these line through these points will be ;m = (y2-y1) / (x2-x1)m= (3-0) / (0-3)m= 3/-3m= -1Also , we will get the value of c = 3 .The equation of line after putting the value of m and c will be ,y = -x + 3Thus, the equation of line is y = -x + 3To learn more about general equation of the line refers to:
brainly.com/question/18439547
#SPJ1
Is x-intercept a number or a point?
The point at a graph where the graph cuts the x-axis is known as the x-intercept. Therefore, the x-intercept is a point.
A graph is made up of four quadrants in which two are positive and two are negative quadrant.
There are two types of axis which are x-axis and y-axis two negative and two positive.
The y-intercept is the point where the graph cuts the y-axis .Graph Theory is the study of graphs which comes under discrete mathematics.
It is defined as a mathematical structure that connects a group of points to express a specific function.
To learn more about graphs
brainly.com/question/17267403
#SPJ4
Find the point(s) on the surface at which the tangent plane is horizontal.
z = xy + 1 x + 1 y
The point(s) on the surface at which the tangent plane is horizontal are (0, 0, 1).
To find the point(s) on the surface at which the tangent plane is horizontal, we need to find the points at which the partial derivatives of z with respect to x and y are both equal to 0. This means we need to solve the system of equations:
∂z/∂x = 0 ∂z/∂y = 0Solving this system of equations yields x = 0, y = 0, and z = 1. Therefore, the point(s) on the surface at which the tangent plane is horizontal is (0, 0, 1).
To understand why solving the system of equations yields the points for which the tangent plane is horizontal, it is important to understand what the partial derivatives represent. The partial derivative of z with respect to x is the rate of change of z with respect to x, and similarly for y.
When the partial derivatives are both equal to 0, it means that the rate of change of z with respect to x and y is 0, which implies that the tangent plane is horizontal.
Learn more about tangent planes here:
https://brainly.com/question/17192497
#SPJ4
Which of the following points is a solution to the system of equations shown?
y - x = -1
x + y = -5
`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.
[tex]\quad \qquad \huge \bf \dag \: Answer \: \dag[/tex]
`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.
[tex] \underline{ \large \rm Solution} : [/tex]
[tex]\rm Given : [/tex]
Two equations are -
y - x = -1 (i)x + y = -5 (ii)[tex] \rm Procedure : [/tex]
Considering the equations as (i) and (ii) respectively
From equation (i) -
y = x - 1put this value of y in equation (ii) -
x + y = -5x + x - 1 = -52x = -5 + 12x = -4 x = -2Next thing to do would be to put value of x we got in equation (i) to get y
y - x = -1y - (-2) = -1 y + 3 = -1 y = -1 - 3 y = -4Values asked are :
[tex] \rightarrow \rm y = - 4[/tex]
[tex] \rightarrow \rm x= - 2[/tex]
`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.
[tex] \large \bf hope \: \: it \: \: helps \: - dabI [/tex]
`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.
F(x)=\begin{cases}-2 & \text{ for }\hspace{10px} -6< x <-1\phantom{\frac{1}{1}} \\ -x-3 & \text{ for }\hspace{10px} -1< x <5\phantom{\frac{1}{1}}\end{cases} f(x)={ −2 −x−3 for −6
f(7) = 14 is calculated. Each function is given a domain and a codomain, or scope.
what is function ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
We note that x=7 is on 1<x< 9 so we use the second piece. Replace x with 7 and
evaluate to find f(7):
f(7)=2(7)
f(7)=14
so f( 7 ) = 14
f(7) = 14 is calculated. Each function is given a domain and a codomain, or scope.
To know more about function visit :-
https://brainly.com/question/28193995
#SPJ1
Find the values of x and y
The values of x and y, given the angles in the diagram, can be found to be :
x = 11y = 17How to find the value of x and y ?The angles given above are called vertical angles and they are such that the two corresponding angles are equal to each other.
This means that ( 8 x + 7 ) ° is equal to ( 9 x - 4 )° and 5 y° is equal to ( 7y - 34 )°.
The value of x is :
8 x + 7 = 9 x - 4
9x - 8x = 7 + 4
x = 11
The value of y is :
5 y = 7y - 34
7y - 5y = 34
2 y = 34
y = 34 / 2
y = 17
Find out more on the value of x and y at https://brainly.com/question/30091286
#SPJ1
Are 2 sides of an isosceles triangle?
Yes, the lengths of the two sides of an isosceles triangle are equal.
An isosceles triangle is a type of triangle that has two sides that are equal in length. The other side of the triangle can be either longer or shorter than the two equal sides. The two equal sides are called the legs, and the other side is called the base. The angles opposite the two equal sides are also equal in measure. Because of this, the two equal sides create an angle bisector that divides the base into two equal parts. This angle bisector forms two angles of equal measure as well. Thus, the two equal sides of an isosceles triangle are a defining feature of the shape.
Learn more about isosceles triangle here
https://brainly.com/question/2456591
#SPJ4
Ben wants to buy a binder and some penicals from the school store.binders coast 2.25 each of the pencials coast 0.75 each.how much will it coasg ben to buy 1 binder and P penicals
The total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Cost of a binder = 2.25
Cost of a pencil = 0.75
We have to find the total cost for Ben to buy 1 binder and P pencils.
Cost of 1 binder = 2.25
Cost of P pencils = 0.75 × P = 0.75 P
Total cost of 1 binder and P pencils = 2.25 + 0.75 P
Hence the total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.
To learn more about Multiplication, click on the link :
https://brainly.com/question/29558206
#SPJ1
HEEELLP me PLEASE!!!
Answer:
T=(I/p)/r
Step-by-step explanation:
I = Prt is the same thing as: I = P*r*t
We want the answer to be as:
T = ???
The only thing you need to do is the get T to one side.
1. [tex]I = P*r*t[/tex]
2. [tex]I/p=r*t[/tex]
3. [tex](I/p)/r=t[/tex]
4. [tex]t=(I/p)/r[/tex]
Can you help me with this
Step-by-step explanation:
to find the equation of any line we have to first find the slope. the slope formula is:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
our slope here would be 8/13
now we input the points in the equation
y = mx + b
then we find b to be -3(7/13)
so the final equation would be:
[tex]y = \frac{8x}{13} - 3( \frac{7}{13} )[/tex]
a. Complete the table to show the length of the field for each given width.
Width (feet) Length (feet) 0 50 100 150 200 250 300
b. Define the function (w) to represent the length of the field as
The length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that a table for showing the relation between length and width of a field;
Width (w) Length (l)
0 50
100 150
200 250
300 350
We see, that, width is 50 less than the length.
Therefore, the function (w) to represent the length of the field will be =
w = l-50
Hence, the length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)
For more references on functions, click;
https://brainly.com/question/21145944
#SPJ1
..Solve multi step problems
Help me.....
Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards
What is MultiplicationMultiplication is a mathematical operation that involves multiplying two or more numbers together. It is one of the four basic operations in mathematics, along with addition, subtraction, and division.
In this problem, we may require the use of some mathematical operators to find the solution to the problem.
1.
He currently has 216 cards, but he needs 15 sets of cards.
1 set of card = 72 cards
Let's calculate the number of sets he currently has.
1 set of card = 72 cards
x set = 216 cards
cross multiply both sides and solve for x.
x * 72 = 216 * 1
x = 216 / 72
x = 3 sets
He currently has 3 sets of cards.
Since he wants 15 sets of cards, we will need 12 more set of cards.
The number of cards can be calculated by multiplying 12 by 72
Number of cards = 12 * 72 = 864
He needs 864 more cards.
2.
1 set of card = $27
1 set = 72 cards
But she's bringing $9 to join, we can calculate the ratio of cards she will get.
1 / 27 = x / 9
x = 9 / 27
x = 1/3
She will get 1/3 of the cards bought which will be
72 * 1/3 = 24 cards
She will get 24 cards
Learn more on multiplication here;
https://brainly.com/question/4721701
#SPJ1
Please help me plssss
Explanation
Check the picture below.