you deposit $4000 each year into an account earning 3% interest compounded annually. How much will you have in the account and 35 years?
Answers
ANSWER:
$ 241848.33
STEP-BY-STEP EXPLANATION:
Given:
P = $4000
r = 3% = 3/100 = 0.03
n = 35 years
The formula for the future value is:
[tex]\begin{gathered} FV=P\mleft(\frac{\left(1+r\right)^n-1}{r}\mright) \\ \text{ replacing} \\ FV=4000\cdot\mleft(\frac{\mleft(1+0.03\mright)^{35}-1}{0.03}\mright) \\ FV=241848.33 \end{gathered}[/tex]Therefore, after 35 years, he would have $ 241848.33 in the account.
Related Questions
what is the volume of the sphere with a radius of 2 inches ?
Answers
The volume of a sphere is
[tex]\text{volume}=\frac{4}{3}\pi^{}^{}r^3[/tex]Therefore,
[tex]\begin{gathered} \text{volume}=\frac{4}{3}\times3.14\times2^3 \\ \text{volume}=33.4933333333=33.49\text{ cubic inches} \end{gathered}[/tex]Find the inverse of the function below and sketch by hand a graph of both the function and is inverse on the same coordinate plane. Share all steps as described in the lesson to earn full credit. Images of your hand written work can be uploaded. f(x)=(x+3)^2 with the domain x \geq-3
Answers
In order to find the inverse of f(x), let's switch x by f^-1(x) and f(x) by x in the function, then we solve the resulting equation for f^-1(x).
So we have:
[tex]\begin{gathered} f(x)=(x+3)^2 \\ x=(f^{-1}(x)+3)^2 \\ \sqrt[]{x}=f^{-1}(x)+3 \\ f^{-1}(x)=-3+\sqrt[]{x} \end{gathered}[/tex](The domain of f(x) will be the range of f^-1(x), so the range of f^-1(x) is y >= -3)
In order to graph the function and its inverse, we can use some points that are solutions to each one.
For f(x), let's use (-3, 0), (-2, 1) and (-1, 4).
For f^-1(x), let's use (0, -3), (1, -2) and (4, -1).
Graphing f(x) in red and f^-1(x) in blue, we have:
Graphing it manually, we have:
Question attached!!Answer choices 1. The graph has a relative minimum 2. The graph of the quadratic function has a vertex at (0,5)3. The graph opens up 4. The graph has one x- intercept 5. The graph has a y-intercept at (5,0)6. The axis of symmetry is x=0
Answers
Consider the following table:
this table represents the following graph:
According to this graph (parabola), and remembering that an absolute minimum is also a relative minimum:
we can conclude that the correct answer is:
Answer:1. The graph has a relative minimum 2. The graph of the quadratic function has a vertex at (0,5)3. The graph opens up 6. The axis of symmetry is x=0For each line the SLOPE between the 2 points given - simplify each fraction to prove that the lines have a CONSTANT rate of change : 1) Point T : 2) Point R : 3) Point S : 4) Slope of TR : 5) Slope of RS : 6) Slope of TS : 7) Describe the SLOPE of the line : 8) Therefore the CONSTANT RATE OF CHANGE IS ...?
Answers
the point T on the line is T(-7,6)
point R = R(-3,0)
point S = S(1,-6)
the slope of TR is
[tex]\begin{gathered} m=\frac{6-0}{-7-(-3)} \\ m=-\frac{6}{4} \\ m=-\frac{3}{2} \end{gathered}[/tex]slope of RS,
m = (0 - (-6))/(-3-1)
= - 6/4
= -3/2
slope of TS
m = (-6-6)/ 1-(-7)
= -12/ 8
= -3/2
the slope of the line or the constant rate of change is m = -3/2
Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall are shown below. I will send the graph.
Answers
Given:
Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall is 42 feet and 25.5 feet.
Total cost of wallpaper was $771.12
Required:
What was the cost, in dollars, of the wallpaper per square feet.
Explanation:
We know the area of rectangle is length multiplied by breadth.
Here, we have
[tex]\begin{gathered} A\text{rea of wall =}42\times25.5 \\ =1071 \end{gathered}[/tex]Now,
The cost of wallpaper per square feet is
[tex]\begin{gathered} =\frac{771.12}{1071} \\ =0.72 \end{gathered}[/tex]Answer:
Hence, $0.72 is the answer.
Using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true:
___ / ___ = ____ / ____ = ____
Answers
The complete equality will be;
⇒ 1 / 2 = 3 / 6 = 4 / 8
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
By using the digits 1 to 9 at most one time each, fill in the boxes to make the equality true.
Now,
All the numbers from 1 to 9 are;
= 1, 2 ,3 , 4, 5, 6, 7, 8, 9
Let a proportion = 1 / 2
Hence, The equivalent ratio of 1/2 are;
= 3 / 6 and 4 / 8
Thus, The complete equality will be;
⇒ 1 / 2 = 3 / 6 = 4 / 8
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how do I solve x without measuring it, i need help with the third question please
Answers
Answer:
Explanation:
Based on the given figure, the two angles ( 54° and x) are supplementary.
So, they add up to 180°.
54 + x =180
We subtract 54 from 180 to get the value of x:
x=180-54
Calculate
x= 126°
Therefore, the value of x is 126°.
3/5 of a number is 18. What is the number
Answers
Let
x -----> the number
we have that
(3/5)x=18
solve for x
x=18*5/3
x=30
the number is 30Launch Problem The barista at Kellie's Coffee needs to make 10 12-ounce iced coffees. Each iced coffee is made with 2 ounces of oat milk, 8.2 ounces of cold brew coffee and 1.8 ounces of hazelnut flavoring. How much of each ingredient will be necessary to make the order of iced coffees? 2. How many ounces of cold brew coffee will be needed to make the order of iced coffee?
Answers
we have,
for 1 iced coffee:
2 ounces of oat milk
8.2 ounces of cold brew coffee
1.8 ounces of hazelnut.
then
answer 1:
for 10 iced coffee, we will need
2 x 10 = 20 ounces of oat milk
8.2 x 10 = 82 ounces of cold brew coffee
1.8 x 10 = 18 ounces of hazelnut flavoring
answer 2:
82 ounces of cold brew coffee are needed
Use the graph to answer the question about discontinuity refer to image
Answers
Given the graph of the function
We will check the discontinuity of the function at x = -3
So, as shown in the graph :
as the function reach to x = -3 from the right and the left , the value of the function = -1
But at x = -3 , the function does not have a value
So, there is a discontinuity at x = -3, but can be removed if f(-3) = -1
So, the answer is : option A
There is a discontinuity that can be removed by defining f(-3) = -1
For #'s 12 - 13, find the area of each figure.
Answers
Using the distance(d) formula to obtain the length AB,BC,CA.
The distance formula is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given
[tex]\begin{gathered} A\rightarrow(5,-6) \\ B\rightarrow(-5,-3) \\ C\rightarrow(5,6) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} AB=\sqrt{(-5-5)^2+(-3--6)^2}=\sqrt{(-10)^2+(-3+6)^2}=\sqrt{100+3^2}=\sqrt{109} \\ BC=\sqrt{(5--5)^2+(6--3)^2}=\sqrt{10^2+9^2}=\sqrt{100+81}=\sqrt{181} \\ CA=\sqrt{(5-5)^2+(6--6)^2}=\sqrt{0^2+12^2}=\sqrt{144}=12 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} AB=\sqrt{109}=10.44030\approx10.4 \\ BC=\sqrt{181}=13.45362\approx13.5 \\ CA=12 \end{gathered}[/tex]Using Heron's formula to solve for the area
[tex]\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]where,
[tex]\begin{gathered} a=10.4 \\ b=13.5 \\ c=12 \\ \\ s=\frac{10.4+13.5+12}{2}=17.95 \end{gathered}[/tex]Therefore, the area is
[tex]undefined[/tex]Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.Find the lateral area for the regular pyramid.L. A. =Find the total area for the regular pyramid.T. A. =
Answers
Answer
LA = 4√10
TA = 4 + 4√10
Step-by-step explanation
To find the Lateral Area (LA) of the pyramid, first, we need to calculate its slant height (s).
Considering the right triangle formed inside the pyramid, we can apply the Pythagorean theorem to find the length of s, as follows:
[tex]\begin{gathered} s^2=3^2+1^2 \\ s^2=9+1 \\ s=\sqrt{10} \end{gathered}[/tex]Now, we can calculate the lateral area as follows:
[tex]\begin{gathered} LA=\frac{1}{2}\times P\operatorname{\times}s \\ \text{ where P is the perimeter of the base of the pyramid. Substituting }P=4\times2\text{ and }s=\sqrt{10}: \\ LA=\frac{1}{2}\operatorname{\times}4\operatorname{\times}2\operatorname{\times}\sqrt{10} \\ LA=4\sqrt{10} \end{gathered}[/tex]To find the total area (TA) of the pyramid, first, we need to calculate the area of its base (B). In this case, the base is a square, then its area is:
[tex]\begin{gathered} B=b^2\text{ \lparen where b is the length of each edge\rparen} \\ B=2^2 \\ B=4 \end{gathered}[/tex]Finally, the total area is calculated as follows:
[tex]\begin{gathered} TA=B+LA \\ TA=4+4\sqrt{10} \end{gathered}[/tex]evaluate and express answer in standard form.
4.56×3.6
________
0.12
Answers
The value of the given expression in the standard form is 1.368×10².
We are given a mathematical expression. The expression consists of two arithmetic operations. First of all, two numbers are multiplied by each other, and then their result is divided by the third number. Let the mathematical expression be denoted by the variable "E". The expression is given below.
E = (4.56×3.6)/0.12
First, we will multiply the numbers in the numerator.
E = 16.416/0.12
Now we will divide the numerator by the denominator.
E = 136.8
Hence, the value of the expression is 136.8. Now we need to convert the resulting number into standard form. The standard form is given below.
E = 1.368×10²
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A rectangular certificate has an area of 35 square inches. Its perimeter is 24 inches. What arethe dimensions of the certificate?
Answers
Explanation
Given that the area of the rectangular certificate is 35 inches and its perimeter is 24 inches. Therefore, if L represents the length of the certificate and w represents its width, therefore;
[tex]\begin{gathered} lw=35---1 \\ 2(l+w)=24---2 \end{gathered}[/tex]Therefore, we can say
[tex]l=\frac{35}{w}[/tex]We will substitute the above in equation 2
[tex]\begin{gathered} 2(\frac{35}{w}+w)=24 \\ \frac{70}{w}+2w=24 \\ multiply\text{ though by w} \\ 70+2w^2=24w \\ 2w^2-24w+70=0 \\ 2(w^2-12w+35)=0 \\ w^2-7w-5w+35=0 \\ (w-7)-5(w-7)=0 \\ (w-7)(w-5)=0 \\ w=7\text{ or w=5} \end{gathered}[/tex]Since the width must be shorter than the length therefore the width will be 5 inches.
Hence;
[tex]l=\frac{35}{5}=7[/tex]Answers:
The dimensions are:
Length = 7 inches
Width = 5 inches
Circle 1 is centered at (-4, -6) and has a radius of 9 centimeters. Circle 2 is centered at (4, 2) and has a radius of 6 centimeters. What is the scale factor?Which translation rule will translate Circle 1 to Circle 2?
Answers
For this type of problem we first notice that the center of the first circle has coordinates (-4,-6) and the center of the second one has coordinates (4,2) then all point of circle 1 (x,y) are translated according to the rule (x+8,y+8).
For the scale factor, we notice that the radius of circle 1 is 9 cm and the radius of circle 2 is 6cm then the scale factor is (2/3).
Are the angles congruent If yes, how do you know?
Answers
From the given diagram, notice that DE is congruent to AB, EC is congruent to BC and the angles ABC and DEC are congruent.
Since two sides of the triangles and the included angle are congruent, we know from the SAS congruence theorem that ABC and DEC are congruent.
Therefore, the answer is: yes, the triangles ABC and DEF are congruent due to the SAS theorem.
find the missing length, assume that segments that appear to be tangent are tangent.
Answers
Since the side that measures 16 is tangent to the circle, it is perpendicular to the side that measures 12.
IT makes a right triangle.
Since it is a right triangle we can apply the Pythagorean theorem:
c^2 = a^2 + b^2
Where:
c= hypotenuse (longest side )= ?
a & b =the other 2 legs of the triangle.
Replacing:
?^2 = 12 ^2 + 16^ 2
Solve for the missing side:
?^2 = 144+256
?^2 = 400
?=√400
? = 20
How would I solve 11 I’m confused on it I’m sorry I’m a bit slow
Answers
In order to better understand the question, let's draw an image representing the situation:
We want to find the distance x of this triangle. To do so, we can use the Pythagorean theorem, which states that the length of the hypotenuse squared is equal to the sum of each leg squared.
So we have:
[tex]\begin{gathered} 110^2=55^2+x^2 \\ 12100=3025+x^2 \\ x^2=12100-3025 \\ x^2=9075^{} \\ x=95.26\text{ ft} \end{gathered}[/tex]Rounding to the nearest tenth, we have a distance of 95.3 ft.
An item has a listed price form 45. If the sale tax rate is 9?% how much is the sales tax.
Answers
In order to calculate the sales tax to 45, calculate the 9% of 45, just as follow:
(9/100)(45) = 4.05
Hence, the sales tax is $4.05
Solve the Exponential Function: [tex]x^2 * 2 - 2^x = 0[/tex]
Answers
Given the equation of the exponential function:
[tex]x^2\cdot2-2^x=0[/tex]We will solve the equation using the graph
the graph of the function is as shown in the following picture:
The solution to the equation will be the values of (x) at the point of intersection with the x-axis
As shown, there are 3 points of x-intercepts
So, the solution to the equation will be:
[tex]x=\mleft\lbrace-0.58,1,6.32\mright\rbrace[/tex]
Find the equation of a line in the form y=Mx+b MATH HW
Answers
Using y=mx+b form first we calculate the slope.
We'll use points (0,-8) and (-8,0).
[tex]\begin{gathered} m=(-8-0)\div(0--8) \\ m=-\frac{8}{8} \\ m=-1 \end{gathered}[/tex]Next we calculate our b intercept
[tex]\begin{gathered} 0=-1(-8)+b \\ b=-8 \end{gathered}[/tex]So the equation is y=-x-8
Find the probability to generate a 4 digit even number from 1, 2, 3, 5.A.1/4B.1/2C.1D.0
Answers
give the following numbers
1, 2, 3, 5
we were asked to find the probability of generating a 4 digit even number from the numbers give above
recall,
Probabily = Number of possible outcome/Total number of outcomes
Number of possible outcome is = 1
Total number of outcomes is = 4
therefore,
Probability = 1/4
so the probability of generating a 4 digit even number from 1, 2, 3, 5 is 1/4
so the correct option is A which is 1/4
I need help with my math
Answers
Given an expression
[tex]\begin{gathered} y+\frac{3}{8}\text{ = }\frac{-2}{3}\text{ } \\ \text{collect like terms} \\ y=\text{ }\frac{-2}{3}\text{ - }\frac{3}{8} \\ y\text{ = }\frac{-16-9}{24} \\ \text{LCM = 24} \\ y=\text{ }\frac{-25}{24} \\ y=\text{ -1}\frac{1}{4} \end{gathered}[/tex]Simplify the expression 3^2/ 3^1/4 to demonstrate the quotient of powers property. Show any intermittent stepsthat demonstrate how you arrived at the simplified answer.
Answers
We are given a quotinet of two power expressions to be used to demonstrate the quotient property of powers:
[tex]\frac{3^2}{3^{\frac{1}{4}}}=3^2\cdot3^{-\frac{1}{4}}=3^{(\frac{8}{4}-\frac{1}{4})}=3^{\frac{7}{4}}[/tex]ANother way of doing it is to represent 3^2 as 3 to the power 8/4 so as to have the same radical expression.
Recall that fractional exponents are associated with radicals, and in this case the power "1/4" represents the fourth root of the base "3". That is:
[tex]3^{\frac{1}{4}}=\sqrt[4]{3}[/tex]So we also write 3^2 with fourth root when we express that power "2 = 8/4":
[tex]3^2=3^{\frac{8}{4}}=\sqrt[4]{3^8}[/tex]So now, putting that quotient together we have:
[tex]\frac{\sqrt[4]{3^8}}{\sqrt[4]{3}}=\sqrt[4]{\frac{3^8}{3}}=\sqrt[4]{3^7}=3^{\frac{7}{4}}[/tex]So we see that we arrived at the same expression "3 to the power 7/4"
in both cases. One was using the subtraction of the powers as the new power for the base 3, and the other one was using the radical form of fractional powers.
2 The ratio of males to females in the class is 5 to 9. If the lunchroom has the same ratio but 45 females, how many males are in the lunchroom?
Answers
Answer:
Explanation:
From the question, we are given the ratio of males to females in the class as 5 to 9.
Total ratio = 5+9 = 14
Let the total number of student in the class be x. If there are 45 females then;
9/14 * x = 45
9x/14 = 45
Cross multiply;
9x = 14 * 45
x = 14 * 5
x = 70
Hence the total number of student in the class is 70
Get the number of male students;
Total students = Male + Female
70 = Male + 45
Male = 70-45
Male = 25
Answer:
Step-by-step explanation:
To get 45 females, you have to multiply 9 by a number. That number is 5 because 5 times 9 is 45. So what you do here is what you do with the other number, (5), so 5 times 5 is 25. That means there were 25 males in the lunchroom.
What is the area of sector GHJ, given that θ= π/3 radians? Express your answer in terms of π and as a decimal rounded to the nearest tenth.
Answers
Answer:
[tex]\text{area of sector=4.7 square }\imaginaryI\text{nches}[/tex]Step-by-step explanation:
The area of a sector when the angle is measured in radians is represented by:
[tex]\text{ area of sector= }\frac{1}{2}r^2\theta[/tex]The given theta is pi/3, and the radius is 3 inches.
[tex]\begin{gathered} \text{ area of sector=}\frac{1}{2}*3^2*\frac{\pi}{3} \\ \text{ area of sector=}\frac{3}{2}\pi \\ \text{ Convert as a decimal rounded to the nearest tenth:} \\ \text{ area of sector= 4.7 square inches} \end{gathered}[/tex]hich is the better buy? 2-quart carton of orange juice for $4.48 7-cup carton of orange juice for $3.64
Answers
According to the given data we have the following:
2-quart carton of orange juice=$4.48
7-cup carton of orange juice=$3.64
In order to find out what is the better choice to buy we would have to make the calculate the unit price.
2-quart carton of orange juice=$4.48,
Then unit price=$4.48/2
unit price=$2.24
7-cup carton of orange juice=$3.64
Then unit price=$3.64/7
unit price=$0.52
Therefore as the unit price of the 7-cup carton of orange juice is $0.52 and is lower than the unit price of $2.24 of the 2-quart carton of orange juice, hence, the better choice would be buying the 7-cup carton of orange juice.
Graph the following Y=x-4
Answers
Ok, so
We want to find the line:
[tex]y=x-4[/tex]First, remember that a line can be described with the following formula:
[tex]y=mx+b[/tex]Where "m" is its slope and b is its y-intercept.
Based in our equation, we got that m = 1 and b = - 4. So, we have a line with slope = 1, and y-intercept = -4.
To graph it, we have to take two points that lie on the line, and join them. We already know that the line has y-intercept at ( 0 , -4 ), so that's one point.
To find the other point, we could make y = 0 to find the x-intercept as follows:
[tex]\begin{gathered} y=x-4 \\ x-4=0 \\ x=4 \end{gathered}[/tex]Now, we have the x-intercept at (4 , 0) so that's other point.
We join both points:
So that's the graph for y = x-4.
Answer:
Step-by-step explanation:
1. When x is 0, y=-4, so plot the point (0,4) on the graph.
2. When y is 0, x=4, so plot the point (4,0) on the graph.
3. Draw a line between them and you're done.
7. Write an equation and solve. Round to the nearest hundredth where necessary.
19 is what percent of 40?
Answers
Answer:
47.5%
Step-by-step explanation:
-4(e+6)(b+3) (-7)-8(v-7)(2n+3)65(c+d)27(3x-1)(e-f)32(-3m+1)(2b-3) (-9)5(s+7)(t+7)36(-2v+4)(m-n) (-3)4e+7e+55-4x-8-3h-2h+6h+97-5y+2+14z+3-2z-z
Answers
By using the distribution property in the following algebraic expressions, you obtain:
6) -4(e + 6) = (-4)(e) + (-4)(6) = -4e - 24
7) (b + 3)(-7) = (b)(-7) + (3)(-7) = -7b - 21
8) (2n + 3)6 = (2n)(6) + (3)(6) = 12n + 18
9) 5(c + d) = (5)(c) + (5)(d) = 5c + 5d
10) 27(3x - 1) = (27)(3x) + (27)(-1) = 81x - 27
11) (e - f)(3) = (e)(3) + (-f)(3) = 3e - 3f
where you have taken into account, that each term inside a parenthesis must be multiplied by all terms of the other facto. Furthermore, you took into account the signs multiplcation rule (+ x + = +, - x - = +, - x + = -, + x - = -), and also you mulitiplied coefficients by coefficients for cases in which you have numbers and variables.