The investment worth after 5 years if interest is compounded monthly is $3,579.47.
Calculation:-
FV = P (1+ r/m)^mt
= $2500 ( 1 + 7.2/12)¹²ˣ⁵
= $3,579.47.
The Future value is $3,579.47.
The total compound interest is $1,079.47.
FV - the future value of the investment, in our calculator it is the final stability
P - the preliminary stability (the fee of the funding)
r - the once-a-year interest charge (in decimal)
m - the variety of instances the interest is compounded in keeping with 12 months (compounding frequency)
t - the wide variety of years the cash is invested for 5 years
Compound interest, may be calculated with the use of the method FV = P*(1+R/N)^(N*T), wherein FV is the destiny price of the mortgage or investment, P is the initial important amount, R is the yearly interest charge, N represents the variety of times hobby is compounded in keeping with year, and T represents time in years.
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Identify the points in figure 1 that correspond to the points Q and S . Label them B and D . What is the distance between b and d
what is the distance between P and R?
Step 1
the easiest way to find the distance is by using the grid, just count the division, one division in an unit, so
between P and R, there are six units, so the distance is 6
Let f(x) = -2x^2– 7 and g(x) = 4x – 7.(fog)(x) =(gof)(x) =(fog)(1) =
Part 1.
The compositon fog is given by
[tex](f\circ g)(x)=-2(4x-7)^2-7[/tex]which gives
[tex]\begin{gathered} (f\circ g)(x)=-2(16x^2-56x+49)^{}-7 \\ (f\circ g)(x)=-32x^2+112x-98^{}-7 \\ (f\circ g)(x)=-32x^2+112x-105 \end{gathered}[/tex]Then, the answer is:
[tex](f\circ g)(x)=-32x^2+112x-105[/tex]Part 2.
The composition gof is given by
[tex](g\circ f)(x)=4(-2x^2-7)-7[/tex]Then, the answer is:
[tex](g\circ f)(x)=-8x^2-35[/tex]Part 3.
In this case, we need to substitute x=1 into the answer of Part 1, that is,
[tex]\begin{gathered} (f\circ g)(1)=-32(1)^2+112(1)-105 \\ (f\circ g)(1)=-32^{}+112-105 \end{gathered}[/tex]Therefore, the answer is:
[tex](f\circ g)(1)=-25[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
The first bar is what percent as long as the second bar?
To find the how much the first bar represents from the second bar, we need to calculate the ratio between them.
[tex]\frac{2}{5}[/tex]To convert this ratio to a percentage, we just need to convert the denominator to 100, and the numerator will be the percentual value. We can convert by multiplying both the numerator and denominator by 20.
[tex]\frac{2}{5}\times\frac{20}{20}=\frac{2\times20}{5\times20}=\frac{40}{100}=40\%[/tex]The first bar is 40% as long as the second bar.
Using long division divide y cubed + 0y squared minus 1 by y +4
Given the expression:
[tex]\frac{y^3+0y^2-1}{y+4}[/tex]Step 1:
Divide the leading term of the dividend by the leading term of the divisor. Multiply the result by the divisor and subtract the final result from the dividend as follows:
[tex]\begin{gathered} \frac{y^3}{y}=y^2 \\ \\ \\ y^2(y+4)=y^3+4y^2 \\ \\ \\ (y^3-1)-(y^3+4y^2)=-4y^2-1 \end{gathered}[/tex]Step 2: Divide the leading term of the obtained remainder by the leading term of the divisor, multiply it by the divisor, and subtract the remainder from the obtained result:
[tex]\begin{gathered} \frac{-4y^2}{y}=-4y \\ \\ \\ -4y(y+4)=-4y^2-16y \\ \\ \\ (-4y^2-1)-(-4y^2-16y)=16y-1 \end{gathered}[/tex]Step 3: Divide the leading term of the obtained remainder by the leading term of the divisor, multiply it by the divisor, and subtract the remainder from the obtained result:
[tex]\begin{gathered} \frac{16y}{y}=16 \\ \\ \\ 16(y+4)=16y+64 \\ \\ \\ (16y-1)-(16y+64)=-65 \end{gathered}[/tex]Since the degree of the remainder is less than the degree of the divisor, we would stop.
Therefore, the answer is:
[tex]\frac{y^3-1}{y+4}=y^2-4y+16+\frac{-65}{y+4}[/tex]The graph below represents compound interest over time with an initial investment of $600 at in interest rate of 6% compounded annually. Which of these statements describes the situation?-it will take less than 10 years to double the initial investment-it will take less than 20 years to triple the initial investment-it will take more than 15 years to double the investment-it will take more than 30 years to triple the initial investment
ANSWER
It will take less than 20 years to triple the investment.
EXPLANATION
We want to identify the statement that best describes the situation represented by the graph of the compound interest over time.
To do this, let us find at what point the compound amount doubles and triples.
Since the initial investment is $600, it implies that double this investment is $1200, and triple this investment is $1800.
Hence, we have to identify what happens at these points on the graph.
Notice that when y approaches $1200 on the vertical axis, x is greater than 10 and less than 15. It occurs at about x = 12 years.
Also, notice that when y approaches $1800 on the vertical axis, x is less than 20 years (also less than 30 years). It occurs at about x = 19 years.
Hence, the only correct statement that describes the situation is that it will take less than 20 years to triple the investment.
The correct answer is the second option.
2. Noelle always leaves a tip of between 10% and 15% for the stylist when she gets her hair done. This can be represented by thesystem of inequalities shown below, where y is the amount of tip and x is the cost of the hair service. Which of the following isa true statement?y > 0.12y < 0.15%O When the cost of the hair service, x, is $75 the amount of tip, y, must be between $11.25 and $15.O When the cost of the hair service, x, is $50 the amount of tip, y, must be between $5 and $7.50.When the tip, y, is $15, the cost of the hair service, x, must be between $50 and $75.aWhen the tip, y, is $10, the cost of the hair service, x, must be between $100 and $150.
Substituting with x = 75 into the inequalities, we get:
y > 0.1*75
y > 7.5
y < 0.15*75
y < 11.25
Substituting with x = 50 into the inequalities, we get:
What is the equation of a circle with center (2,-3) and radius 3?O -A. (x - 2)2 +(y +37- 3B. (x + 2)2 + (y - 3y - 9O C. (x - 2)2 +(y +3j? = 9x 2 2D. (x - 2) - (+31° - 9
The Equation of a Circle
Given a circle of radius r and centered at the point (h, k), the equation of the circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Please, note the value of the coordinates of the center appear with its signs changed.
We have to find the equation of this circle by substituting the values of r = 3 and (h, k) = (2, -3). Substituting:
[tex]\begin{gathered} (x-2)^2+(y+3)^2=3^2 \\ \text{Operating:} \\ (x-2)^2+(y+3)^2=9 \end{gathered}[/tex]Choice C.
which of the following number is rationalA
A rational number is any number that can be expressed as a ratio of two integers, in the form p/q.
We can say that root(16) is a rational number:
[tex]\sqrt[]{16}=4=\frac{4}{1}[/tex]Below, the function f(x) =3x-2 f(x)=3x-2 and the function f(x)= 3x+1f(x)=3x+1 are graphed. Compare and contrast the lines. What is similar about the equations and graphs? What is different?
You have the lines associated to the following functions:
f(x) = 3x - 2
f(x) = 3x + 1
The general equation of a line is given by:
y = mx + b
where m is the slope and b the y-intercept.
By comparing the given functions with the general form, you can notice that the slope of the lines are equal (m = 3) and the y-intercept are different, b=-2 and
b = 1.
Due to the slopes are the same you have two parallel lines.
Find the quotient. 1 5 – 2. + 3 1 55+3= 2 (Type a whole number, fraction, or mixed number.)
we have
[tex]5\frac{1}{2}\colon3[/tex]Convert mixed number to an improper fraction
5 1/2=5+1/2=11/2
substitute
(11/2):3=11/(3*2)=11/6
convert to mixed number
11/6=6/6+5/6=1+5/6=1 5/6
answer is
11/6 or 1 5/6
A circle has a diameter of 300m. What is his circumference using pi?
To find the circumference using π = 3.14, we can proceed as follows:
1. The formula to find the circumference of a circle is:
[tex]C=2\pi r\Rightarrow D=2r\Rightarrow C=D\pi[/tex]2. That is, given the diameter, we can use it directly into the answer, since twice the value of the radius is the diameter of the circle:
[tex]C=300m\cdot3.14=942m[/tex]If we find the radius as:
[tex]D=2r\Rightarrow r=\frac{D}{2}=\frac{300m}{2}=150m[/tex]And If we use the next formula:
[tex]C=2\pi r=2\cdot3.14\cdot150m=942m[/tex]As we can see, in both cases, we found that the value for the circumference is equal to 942 meters (if we use π = 3.14).
In summary, the circumference of a circle that has a diameter of 300 meters is equal to 942 meters (C = 942m) (using π = 3.14).
I need some help with this I don’t understand how I would do it can I have some help
from the graph shown in the question,
we could deduce that:
x = -3,
which means x + 3 = y,
we can also deduce that x = 4,
which means that, x - 4 = y
so, the eqaution of the graph could be
y = (x - 2) (x + 3) (x - 4)
since the graph is a cubic graph
therefore the correct option is B
The perimeter of a square is (4x - 44). What is the length of each side?
The perimeter of square is given as,
[tex](4x-44)[/tex]Let length of side is denoted as S.
The formula for the perimeter of square is,
[tex]P=4\times S[/tex]To calculate the side of square , substitute the value of perimeter in the above formula.
[tex](4x-44)=4\times S\text{.}[/tex]Solving the equation we get,
[tex]4(x-11)=4\times S\text{.}[/tex][tex](x-11)=S.[/tex]The length of the square obtained is ,
[tex]S=(x-11).[/tex]need help with hw I'm stuck
The quadratic formula is:
[tex]\begin{gathered} \frac{\text{ -}b\pm\sqrt[2]{b^2\text{ -4ac}}}{2a} \\ The\text{ }equation\text{ }is: \\ 2x^2+3x\text{ -}5=4 \\ 2x^2+3x\text{ -}5\text{ -4=0} \end{gathered}[/tex]We need to equal to zero before using the formula.
Noah's mistake was that he stated c=-5 when c= -9
[tex]\begin{gathered} \frac{\text{ -}b\pm\sqrt{b^2\text{ -4ac}}}{2a} \\ =\frac{-3\pm\sqrt{(\text{ -3\rparen}^2\text{ -4\lparen2\rparen\lparen-9\rparen}}}{2(2)} \\ =\frac{-3\pm\sqrt{9\text{ +72}}}{4} \\ =\frac{-3\pm\sqrt{81}}{4} \\ =\frac{-3\pm9}{4} \\ \\ x1=\frac{-3+9}{4} \\ =\frac{6}{4}=\frac{3}{2}=1.5 \\ \\ x2=\frac{-3-9}{4} \\ =\frac{-12}{4} \\ =\text{ -3} \end{gathered}[/tex]x = 1.5 or x = -3
Make use of structure. For rectangle ABCD, two vertices are A(-2, 3) and B(4, 6). Find the slopes of BC, CD, and DA. Explain your answer.
We are given a rectangle ABCD
A(-2, 3)
B(4, 6)
We are asked to find the slopes of sides BC, CD, and DA.
Let me first draw a rectangle to better understand the problem
Recall that the slope is given by
[tex]m=\frac{y_2−y_1}{ x_2−x_1}[/tex][tex]\text{where}(x_1,y_1)=(-2,3)\text{and}(x_2,y_2)=(4,6)[/tex]So the slope of side AB is
[tex]m_{AB}=\frac{6-3}{4-(-2)}=\frac{3}{4+2}=\frac{3}{6}=\frac{1}{2}=0.5[/tex]The sides BC and DA are perpenducluar to the side AB.
So their slopes will be
[tex]m_{BC}=m_{DA}=\frac{1}{-m_{AB}}[/tex]Substituting the value of slope of AB
[tex]m_{BC}=m_{DA}=\frac{1}{-0.5}=-2[/tex]The side CD is parallel to the side AB.
Parallel sides have equal slopes so
[tex]m_{CD}=m_{AB}=\frac{1}{2}[/tex]Therefore, the slopes of the rectangle ABCD are
[tex]\begin{gathered} m_{AB}=m_{CD}=\frac{1}{2} \\ m_{BC}=m_{DA}=-2 \end{gathered}[/tex](1a) Clare drew a dashed line as shown in the diagram. She said the thattwo resulting shapes have the same area. Do you agree? *
The area of a rectangle is given by the formula:
[tex]A=b\times h[/tex]Where b is the length of the base and h is the height of the rectangle.
The area of a triangle is given by the formula:
[tex]A=\frac{b\times h}{2}[/tex]Where b is the length of the base of the triangle and h is its height.
The resulting shape on the right is a rectangle, whose base is 2 and its height is 4, then the area of this part of the shape is:
[tex]\begin{gathered} A=b\times h \\ A=2\times4=8 \end{gathered}[/tex]The area of the triangle resulting on the left side is:
[tex]\begin{gathered} A=\frac{b\times h}{2} \\ A=\frac{4\times4}{2}=\frac{16}{2}=8 \end{gathered}[/tex]Since the area of both shapes is 8, Clare is right.
23.35 in.43 in.36 in.A.1505 in.2B.142 in.2C. 71 in.2D. 1260 in.2
TIP
This parallelogram
The area of a parallelogram =BH
The area of a parallelogram
[tex]\begin{gathered} =35\text{ in }\times36in \\ =1,260in^2 \end{gathered}[/tex]The final answer is the last option
option D
What is the first step to solving the following equation?5x – 11 = 42
Answer:
add 11 on both sides
Step-by-step explanation:
to solve this, you want x alone on one side. To achieve this, you first add 11 on both sides, so you only have the 5x alone.
Second step then is something to get only one x on the left side ;-)
(divide both sides by 5)
Answer:
the first step is to get the x term by itself on one side
Taylor wants four different pairs of sneakers, but can only afford to buy three of thepairs? How many sets of three pairs of sneakers can she possibly choose?
We have a set of four pairs of sneakers {A; B; C; D} and want to know how many sub-sets of three pairs of sneakers can be made with this.
To calculate that, we just need to have in mind that, for the first pair which Taylor will choose, there are four possibilities. After Taylor chooses the first pair, will be three possibilities for the second pair. And, for the third pair, we will have only the las two possibilities.
So, to gete the total number of sets of three pairs of sneakers that can be made, we just multiply the three correspondent possibilities for each choose: 4*3*2 = 24
Each month a shopkeeper spends 5X + 14 dollars on rent and electricity . If he spends 3X -7 dollars on rent how much does he spend on electricity? use pencil and paper for each values of X is the amount the shopkeeper spends on electricity less than 100? explain how you found the values 
The values of x is x<39.5.
Given that the shopkeeper spends on rent and electricity is = 5x+14
Spending of shopkeeper on rent = 3x-7
So shopkeeper spends on electricity = (5x+14) - (3x-7) = 2x+21
Given that amount the shopkeeper spends on electricity less than 100.
So suitable inequality,
2x+21 < 100
2x < 100-21
2x < 79
x < 39.5
All the values of x<39.5.
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solve the equations. 13x - 6y = 22x= y + 6x=y=
A 17-1b bag of Zollipops is $120.00. Connecticut 3 sales tax is 6.35% and Missouri's is 4.225%. How much more sales tax does a customer in Connecticut pay for the bag than one in Missouri?
step 1
Find out how much is the sales tax in Connecticut
we have
6.35%=6.35/100=0.0635
Multiply by $120.00
120.00*(0.0635)=$7.62
step 2
Find out how much is the sales tax in Missouri
we have
4.225%=4.225/100=0.04225
Multiply by $120.00
120.00*(0.04225)=$5.07
step 3
Find the difference
so
7.62-5.07=$2.55
therefore
the answer is $2.55If $7025 is invested at a rate of 10% compounded continuously, what will be the balance after 12 years? Round your answer to two decimal places.
p = $7025
r = 10% = 10/100 = 0.1
t = 12
[tex]A=pe^{rt}[/tex]Therefore,
[tex]\begin{gathered} A=7025\times e^{0.1\times12} \\ A=7025\times e^{1.2} \\ A=7025\times3.32011692274 \\ A=23323.8213822 \\ A=\text{ \$}23323.82 \end{gathered}[/tex]Balance after 12 years = $23,323.82
what is the maximum number of turns in the graph of this functuion f(x) x^4-x^3+3x+1
As given by the question
There are given that the function
[tex]f(x)=x^4-x^3+3x+1[/tex]Now,
By the defination, a polynomial of n degree, has a maximum turning points of:
[tex]n-1[/tex]Therefore, if you have the polynomial given in the problem, which is a polynomial of degree 4, that means (n=4).
The maximum number of turns can be obtained as following:
[tex]\begin{gathered} n-1=4-1 \\ =3 \end{gathered}[/tex]Hence, the maximum number of turns in the graph is 3.
solve the following for x 13 over8 = x over 9
ANSWER:
[tex]x=14\frac{5}{8}=14.625[/tex]STEP-BY-STEP EXPLANATION:
We have the following proportion:
[tex]\frac{13}{8}=\frac{x}{9}[/tex]We solve for x:
[tex]\begin{gathered} \frac{x}{9}=\frac{13}{8} \\ \\ x=\frac{13*9}{8} \\ \\ x=\frac{117}{8}=14\frac{5}{8}=14.625 \end{gathered}[/tex]2 4/7 divided by 2 3/5
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
Answer:
1 17/28
Step-by-step explanation:
2 4/7=18/17
2 3/5=8/5
18/17÷8/5=90/56=45/28=1 17/28
Can I please get some help on this Graph y=1
the given expression is,
y = 1
the given expression is the equation of the line,
that is passing through y = 1 and parallel to x- axis,
so, the graph will be,
Calculate the volume of the composite solid . 2 cm 3 cm 2 cm 4 cm 3 cm 4 cm 8 cm
Notice that the solid consists of an 8x4x4cm rectangular prism minus a 3x4x2cm rectangular prism (the gap shown in the image).
Therefore, the volume of the solid is
[tex]V_{solid}=(8*4*4)-(3*4*2)=128-24=104[/tex]The answer is 104cm^3Liza hired a cleaning service to clean her house. To find C, the total cost of cleaning her house, she used the following formulaC=7.5x +25What is the dependent variable of the formula
The dependent variable of the formula
[tex]C=7.5x+25[/tex]is x