Answer:
a. Relative rate of growth = 0.2
b. Initial population: 920
c. 2501
Explanation:
If we have an exponential function of the form
[tex]y=A_0e^{kt}[/tex]Then
A0 = inital amount
k = relative rate of growth
t = time
Now in our case we have
[tex]n(t)=920e^{0.2t}[/tex]Therefore,
Inital population = 920
Relative rate of growth = 0.2
Now at t = 5, the above formula gives
[tex]n(5)=920e^{0.2*5}[/tex]
which evaluates to give
[tex]n(5)=2500.8[/tex]which rounded to the nearest whole number is
[tex]\boxed{n(5)=2501.}[/tex]Find the volume of this cylinder. Use 3 for A.5 ftV = 7r2h=12 ftV V [?]ft
We're going to find the volume of the cylinder using the following equation:
[tex]V=\pi\cdot r^2\cdot h[/tex]Since the radius measures 5 ft, the height measures 12 ft and the problem tells us that we should take pi as 3, we could replace:
[tex]\begin{gathered} V\approx3\cdot(5ft)^2\cdot12ft \\ V\approx3\cdot25ft^2\cdot12ft \\ V\approx900ft^3 \end{gathered}[/tex]Therefore, the volume is approximately 900ft3.
I need help with getting to the answer to number 6
We have the following pair of functions:
[tex]\begin{gathered} f(x)=x^3+6x \\ g(x)=\sqrt{8x} \end{gathered}[/tex]And we need to find (fog)(2). In order to do this we can start by calculating the composite function (fog)(x)=f(g(x)). Its expression is given by taking the equation of f(x) and replacing x with the expression of g(x). Then we get:
[tex]\begin{gathered} (f\circ g)(x)=f(g(x))=g(x)^3+6g(x)=(\sqrt{8x})^3+6\sqrt{8x} \\ (f\circ g)(x)=(\sqrt{8x})^3+6\sqrt{8x} \end{gathered}[/tex]We need to find (fog)(2) so we just need to take x=2 in the equation above:
[tex]\begin{gathered} (f\circ g)(2)=(\sqrt{8\cdot2})^3+6\sqrt{8\cdot2} \\ (f\circ g)(2)=(\sqrt{16})^3+6\cdot\sqrt{16} \\ (f\circ g)(2)=4^3+6\cdot4 \\ (f\circ g)(2)=64+24 \\ (f\circ g)(2)=88 \end{gathered}[/tex]AnswerThen the answer is 88.
392196 divided by 87(using king division)
Answer: The result of 392,196 divided by 87 is 4,508
Use the number line diagram below to answer the following questions.1.What is the length of each segment on the number line?
Given from the number line that the total number of segments between 0 and 1 is 12 segments.
1) Therefore, the length of each segment on the number line is
[tex]\frac{1-0}{12}=\frac{1}{12}[/tex]Hence, the answer is
[tex]\frac{1}{12}[/tex]2) There are 8 segments between 0 and K.
Therefore, point K represents
[tex]\frac{1}{12}\times8=\frac{8}{12}=\frac{2}{3}[/tex]Hence, the answer is
[tex]\frac{2}{3}[/tex]3) The opposite of K is
[tex]-\frac{2}{3}\text{ since it falls on the negative side of the number line.}[/tex]Hence, the answer is
[tex]-\frac{2}{3}[/tex]please help me with this pleasethe direction is write the equations in slope interception form
In this case, we'll have to carry out several steps to find the solution.
Step 01:
7.
Data
point 1 ( -4 , -2) x1 = -4 y1 = -2
point 2 ( 3 , 3 ) x2 = 3 y2 = 3
Step 02:
Slope formula
m = (y2 - y1) / (x2 - x1)
[tex]m\text{ = }\frac{(3-(-2))}{(3-(-4))}=\text{ }\frac{3+2}{3+4}=\frac{5}{7}[/tex]Slope-intercept form of the line
y = mx + b
intercept (0 , 1 )
b = 1
m = 5 / 7
y = 5/7 x + 1
The answer is:
y = 5/7 x + 1
What is the perimeter and the area of the following trapezoid. Round to the nearest whole number if needed
First, we need to find the length of the bottom base.
The next right triangle is formed inside the trapezoid:
From definition:
[tex]\cos (angle)=\frac{\text{adjacent side}}{hypotenuse}[/tex]Substituting with data from the picture:
[tex]\begin{gathered} \cos (60)=\frac{x}{22} \\ \frac{1}{2}\cdot22=x \\ 11=x \end{gathered}[/tex]Since there are two congruent angles, then the opposite sides are also congruent, that is, there are two sides with lengths equal to 22.
Then, the length of the bottom base is 11 + 25 + 11 = 47.
The perimeter of the figure is obtained by adding the length of all its sides. In this case, the perimeter is 47 + 22 + 25 + 22 = 116
The area of a trapezoid is computed as follows:
[tex]A=\frac{a+b}{2}\cdot h[/tex]Where a and b are the bases and h is the height
The height of the shape can be calculated with the help of the previous right triangle, as follows:
[tex]\begin{gathered} \sin (angle)=\frac{\text{opposite side}}{hypotenuse} \\ \sin (60)=\frac{h}{22} \\ \frac{\sqrt[]{3}}{2}\cdot22=h \\ 11\cdot\sqrt[]{3}=h \end{gathered}[/tex]Substituting into area's formula:
[tex]\begin{gathered} A=\frac{25+47}{2}\cdot11\cdot\sqrt[]{3} \\ A=36\cdot11\cdot\sqrt[]{3} \\ A=396\cdot\sqrt[]{3}\approx686 \end{gathered}[/tex]a1 = -20 ; an = 0.5a n - 1? what are the first five terms
The first five terms are:
-20, -10, -5, -2.5, and -1.25
Explanation:Given that:
[tex]\begin{gathered} a_1=-20 \\ a_n=0.5a_{n-1} \end{gathered}[/tex]For n = 2
[tex]\begin{gathered} a_2=0.5a_1 \\ =0.5\times20 \\ =-10 \end{gathered}[/tex]For n = 3
[tex]\begin{gathered} a_3=0.5a_2 \\ =0.5\times10 \\ =-5 \end{gathered}[/tex]For n = 4
[tex]\begin{gathered} a_4=0.5a_3 \\ =0.5\times5 \\ =-2.5 \end{gathered}[/tex]For n = 5
[tex]\begin{gathered} a_5=0.5a_4 \\ =0.5\times2.5 \\ =-1.25 \end{gathered}[/tex]Therefore, the first five terms are:
-20, -10, -5, -2.5, and -1.25
Precalc and i need help withb. Sec(18pie)c. Sin(7pie/6) tan(8pie/3)d. Tan(pie/12)
In b we need to find:
[tex]\sec 18\pi[/tex]It's important to recal that the secant is equal to:
[tex]\sec 18\pi=\frac{1}{\cos18\pi}[/tex]Another important property that will be useful is:
[tex]\cos x=\cos (x+2\pi m)[/tex]Where m is any integer. Let's see if we can write 18*pi using this. We can take x=0 so we have:
[tex]\begin{gathered} 18\pi=x+2\pi m=2\pi m \\ 18\pi=2\pi m \end{gathered}[/tex]If we divide both sides by 2*pi:
[tex]\begin{gathered} \frac{18\pi}{2\pi}=\frac{2\pi m}{2\pi} \\ 9=m \end{gathered}[/tex]Since m is an integer then we can assure that:
[tex]\cos 18\pi=\cos (0+2\pi\cdot9)=\cos 0=1[/tex]Then the secant is given by:
[tex]\sec 18\pi=\frac{1}{\cos18\pi}=\frac{1}{\cos 0}=1[/tex]So the answer to b is 1.
In c we need to find:
[tex]\sin (\frac{7\pi}{6})\tan (\frac{8\pi}{3})[/tex]Here we can use the following properties in order to write those angles as angles of the first quadrant:
[tex]\begin{gathered} \sin (x)=-\sin (x-\pi) \\ \tan (x)=\tan (x-m\pi)\text{ with }m\text{ being an integer} \end{gathered}[/tex]So we have:
[tex]\begin{gathered} \sin (\frac{7\pi}{6})=-\sin (\frac{7\pi}{6}-\pi)=-\sin (\frac{\pi}{6}) \\ \tan (\frac{8\pi}{3})=\tan (\frac{8\pi}{3}-3\pi)=\tan (-\frac{1}{3}\pi) \end{gathered}[/tex]If we convert these two angles from radians to degrees by multiplying 360° and dividing by 2*pi we have:
[tex]\begin{gathered} \frac{\pi}{6}\cdot\frac{360^{\circ}}{2\pi}=30^{\circ} \\ -\frac{1}{3}\pi\cdot\frac{360^{\circ}}{2\pi}=-60^{\circ} \end{gathered}[/tex]And remeber that:
[tex]\tan x=-\tan (-x)[/tex]So we get:
[tex]\begin{gathered} \sin (\frac{7\pi}{6})=-\sin (\frac{\pi}{6})=-\sin (30^{\circ}) \\ \tan (\frac{8\pi}{3})=\tan (-\frac{\pi}{3})=-\tan (\frac{\pi}{3})=-\tan (60^{\circ}) \end{gathered}[/tex]Then we can use a table of values:
Then:
[tex]\sin (\frac{7\pi}{6})\tan (\frac{8\pi}{3})=\sin (30^{\circ})\cdot\tan (60^{\circ})=\frac{1}{2}\cdot\sqrt[]{3}=\frac{\sqrt[]{3}}{2}[/tex]So the answer to c is (√3)/2.
In d we need to find:
[tex]\tan (\frac{\pi}{12})[/tex]In order to do this using the table we can use the following:
[tex]\begin{gathered} \tan x=\frac{\sin x}{\cos x} \\ \sin 2x=2\sin x\cos x \\ \cos 2x=\cos ^2x-\sin ^2x \\ \cos ^2x+\sin ^2x=1 \end{gathered}[/tex]So from the first one we have:
[tex]\tan (\frac{\pi}{12})=\frac{\sin (\frac{\pi}{12})}{\cos (\frac{\pi}{12})}[/tex]We convert pi/12 into degrees:
[tex]\frac{\pi}{12}\cdot\frac{360^{\circ}}{2\pi}=15^{\circ}[/tex]So we need to find the sine and cosine of 15°. We use the second equation:
[tex]\begin{gathered} \sin 30^{\circ}=\frac{1}{2}=\sin (2\cdot15^{\circ})=2\sin 15^{\circ}\cos 15^{\circ} \\ \sin 15^{\circ}\cos 15^{\circ}=\frac{1}{4} \end{gathered}[/tex]Then we use the third:
[tex]\begin{gathered} \cos (30^{\circ})=\frac{\sqrt[]{3}}{2}=\cos (2\cdot15^{\circ})=\cos ^215^{\circ}-\sin ^215^{\circ} \\ \frac{\sqrt[]{3}}{2}=\cos ^215^{\circ}-\sin ^215^{\circ} \end{gathered}[/tex]And from the fourth equation we get:
[tex]\begin{gathered} \cos ^215^{\circ}+\sin ^215^{\circ}=1 \\ \sin ^215^{\circ}=1-\cos ^215^{\circ} \end{gathered}[/tex]We can use this in the previous equation:
[tex]\begin{gathered} \frac{\sqrt[]{3}}{2}=\cos ^215^{\circ}-\sin ^215^{\circ}=\cos ^215^{\circ}-(1-\cos ^215^{\circ}) \\ \frac{\sqrt[]{3}}{2}=2\cos ^215^{\circ}-1 \\ \cos 15^{\circ}=\sqrt{\frac{1+\frac{\sqrt[]{3}}{2}}{2}} \\ \cos 15^{\circ}=\sqrt{\frac{1}{2}+\frac{\sqrt[]{3}}{4}} \end{gathered}[/tex]So we found the cosine. For the sine we use the expression with the sine and cosine multiplying:
[tex]\begin{gathered} \sin 15^{\circ}\cos 15^{\circ}=\frac{1}{4} \\ \sin 15^{\circ}\cdot\sqrt[]{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}=\frac{1}{4} \\ \sin 15^{\circ}=\frac{1}{4\cdot\sqrt[]{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}} \end{gathered}[/tex]Then the tangent is:
[tex]\tan (15^{\circ})=\frac{\sin(15^{\circ})}{\cos(15^{\circ})}=\frac{1}{4\cdot\sqrt[]{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}}\cdot\frac{1}{\sqrt[]{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}}=\frac{1}{4}\cdot\frac{1}{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}[/tex][tex]\tan (15^{\circ})=\frac{1}{4}\cdot\frac{1}{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}=\frac{1}{2+\sqrt[]{3}}[/tex]Then the answer to d is:
[tex]\frac{1}{2+\sqrt[]{3}}[/tex]A.) 0, 1, 2, 3, 4B.) 0, 2, 4, 7, 8C.) 1, 2, 3, 4, 5D.) 1, 3, 5, 7, 9
Answer
1, 2, 3, 4, 5
Explanation
Given the following data
a(0) = 0
a(i + 1) = a(i) + 1
Find a(0) to a(5)
Step 1: find a(i) when i = 0
a(0 + 1) = a(0) + 1
Where a(0) = 0
a(1) = 0 + 1
a(1) = 1
Find a(2) when i = 1
a(i + 1) = a(1) + 1
a(1) = 1
a(1 + 1) = 1 + 1
a(2) = 2
find a(3) when i = 2
a(2 + 1) = a(2) + 1
a(3) = 2 + 1
a(3) = 3
Find a(4) when i = 3
a(3 + 1) = a(3) + 1
a(4) = 3 + 1
a(4) = 4
Find a(5) when i= 4
a(4+1) = a(4) + 1
a(5) = 4 + 1
a(5) = 5
Therefore,
a(1) = 1
a(2) = 2
a(3) = 4
a(4) = 4
a(5) = 5
The answer is 1, 2, 3, 4, 5
Find the measure of each labeled angle as well as the values of x, y, and z.
Notice that the angle labelled as 3y and the angle with a measure of 72° are supplementary angles. Then:
[tex]3y+72=180[/tex]Substract 72 from both sides of the equation:
[tex]\begin{gathered} 3y+72-72=180-72 \\ \Rightarrow3y=108 \end{gathered}[/tex]The angle labelled as x and the angle labelled as 3y are corresponding angles. Then, they have the same measure:
[tex]x=3y[/tex]Since 3y=108, then:
[tex]x=108[/tex]On the equation 3y=108, divide both sides by 3 to find the value of y:
[tex]\begin{gathered} \frac{3y}{3}=\frac{108}{3} \\ \Rightarrow y=36 \end{gathered}[/tex]Finally, notice that the angle labelled as 3z+18 and the angle labelled as x are corresponding angles. Then, they have the same measure:
[tex]3z+18=x[/tex]Substitute x=108 and isolate z to find its value:
[tex]\begin{gathered} \Rightarrow3z+18=108 \\ \Rightarrow3z=108-18 \\ \Rightarrow3z=90 \\ \Rightarrow z=\frac{90}{3} \\ \Rightarrow z=30 \end{gathered}[/tex]Therefore, the measure of the angles labelled as 3z+18, x and 3y is 108°. The values of x, y and z are:
[tex]\begin{gathered} x=108 \\ y=36 \\ z=30 \end{gathered}[/tex]108010 -8 -62IC-Find the slope of the line.Slope = m =Enter your answer as an integer or as a reduced fraction in the form A/B.Question Help: Video Message
The slope formula is givenb by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]To get the slope from the graph, we will pick out two points lying on the line:
Point 1: (x, y) = (-6, 10)
Point 2: (x, y) = (0, -8)
We will then proceed to use these points to calculate the slope, we have:
[tex]\begin{gathered} m=\frac{-8-10}{0--6}=-\frac{18}{6} \\ m=-3 \end{gathered}[/tex]The slope (m) = -3
I need to know the steps to solve this equation using the quadratic formula.
Given a quadratic equation with the following form
[tex]ax^2+bx+c=0[/tex]By the quadratic formula, the solutions are given by the following expression
[tex]x_{\pm}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In our problem we have the following equation
[tex]4x^2-7x+3=0[/tex]Therefore, our coefficients are
[tex]\begin{gathered} a=4 \\ b=-7 \\ c=3 \end{gathered}[/tex]Plugging those values into the quadratic formula, we have
[tex]x_{\pm}=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(3)}}{2(4)}[/tex]Solving this equation, we have
[tex]\begin{gathered} x_{\operatorname{\pm}}=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(3)}}{2(4)} \\ =\frac{7\pm\sqrt{49-48}}{8} \\ =\frac{7\pm1}{8} \\ \implies\begin{cases}x_+={1} \\ x_-={\frac{3}{4}}=0.75\end{cases} \end{gathered}[/tex]The sum of two numbers is 60. The greater number is 6 more than the smaller number which equation can be used to solve for the smaller number
x ----> is the smaller number
x+6 ----> is the greater number
the equation is
[tex]x+(x+6)=60[/tex]Use the linear regression model ^ Y=-13.5x+857.78 to predict the y-value for x=31
We will predict the value for x = 31 as follows:
[tex]y=-13.5(31)+857.78\Rightarrow y=439.28[/tex]So, the predicted y-value for x = 31 is y = 439.28.
The area of a soccer field is ( 24x^2 + 100x + 100) m^2. The width of the field is (4x + 10)m. What is the length?Please help, need right away.Be sure to show work. NEED HELP BEEN ON THIS PROBLEM FOR 2 DAYS
hello
to solve this question, we have to understand that a soccer field is rectangular in shape and we can find this length from factoring the area
formula of area of a rectangle
[tex]\begin{gathered} A=L\times W \\ A=\text{area} \\ L=\text{length} \\ W=\text{width} \end{gathered}[/tex][tex]\begin{gathered} A=24x^2+100x+100 \\ W=4x+10 \\ L=\text{ ?} \end{gathered}[/tex]we can proceed to solve this by dividing the polynomial or simply checking it from the options
from the options given,
we have option A
3x + 10
let's multiply both the L and W to see if it gives us the answer
[tex](4x+10)\times(3x+10)=12x^2+70x+100_{}[/tex]option A is incorrect
let's test for option B
L= 6x + 10
[tex]\begin{gathered} A=L\times W \\ (6x+10)\times(4x+10)=24x^2+100x+100_{} \end{gathered}[/tex]option B is correct
let's test for option C
L= 6x + 1
[tex]\begin{gathered} A=L\times W \\ (6x+1)\times(4x+10)=24x^2+70x+10 \end{gathered}[/tex]option C is also incorrect and so it'll be for option D
from the calculations above, only option B corresponds with the value of length for the soccer field
how many weeks does it take to empty the lake?
The rate of emptying the lake is -1/8.
The rate of filling the lake is 1/15
Let t be the time in weeks to empty the lake,
Now, add the given rate to get the total rate of emptying of -1/t.
[tex]\begin{gathered} \frac{-1}{8}+\frac{1}{15}=-\frac{1}{t} \\ \frac{-15+8}{120}=-\frac{1}{t} \\ -7\times t=-120 \\ t=\frac{120}{7} \end{gathered}[/tex]Thus,
[tex]t=17\frac{1}{7}[/tex]Therefore, it will take 17 weeks and 1 day to empty the lake.
Pamela is 15 years younger than Jiri. The sum of their ages is 29 . What is Jiri's age?
To determine the age of jiri:
Let P represent Pamela age
Let J represent Jiri age
p + j = 29 (their ages added together is 29)
p = j - 15 (Pam is 15 years younger (less) than Jiri)
We have a value for Pam, so plug it in:
j -15 + j = 29
2j - 15 = 29
Add 15 to both sides:
2j = 44
Divide by 2:
j = 22
Now find Pamela's age:
p = 22 - 15
p = 7
check:
7 + 22 = 29
29 = 29
Therefore the age of Jiri is 22 years
How can you represent Pattered from every day life by using tables,expressions and graphs
For example, we can look at the variations of temperature by the time of the day.
We can write it in a two column table, where we can write the hour in one column and the temperature in the other column.
This will show us a relationship between them that is oscillating.
We can graph this and have something like:
Then, we can adjust a function to that, like a trigonometrical function that can model this relation between temperature and hour of the day. There you wil have an expression for this pattern.
12. Write a paragraph proof.Given: AB = CD, BC = DAProve: AABC = ACDA
Answer:
Triangles ABC and CDA share the side AC, therefore they have three congruent sides. Since AB is congruent to CD and BC is congruent to DA then by the SSS criteria we get that triangles ABC and CDA are congruent.
Part CCreate two tables that represent proportional relationships betweentwo quantities. Explain or show proof that the table representsproportional relationships.
Given:
It is required to create a table that represents a proportional relationship between two quantities.
Let the first table: represents the relation between the money saved every month and the number of months
Let the number of months = x, And the total saving = y
Assume we save $2 per month
so, we will have the following table:
The function f(x)=2,500(1.012)^x represents the amount, in dollars, in a savings account after x years. Which statement is true? A. The account earns 0.12% interest per year. B. The account earns 0.012% interest per year. C. The initial amount in the account was $2.500. D. The amount in the account increases by $2,500 each year,
Answer:
C. The initial amount in the account was $2,500.
Explanation:
The function that represents the amount, in dollars, in a savings account after x years is given as:
[tex]f\mleft(x\mright)=2,500\mleft(1.012\mright)^x[/tex]When x=0 (Initially)
[tex]\begin{gathered} f\mleft(0\mright)=2,500\mleft(1.012\mright)^0 \\ =2,500\times1 \\ =\$2,500 \end{gathered}[/tex]Therefore, the initial amount in the account was $2,500.
A litter of kittens consists of one gray female, two gray males, two black females and one black male. You randomly pick one kitten, what is the probability it is black?
Total number of kittens = 6
Gray kittens= 1 female+2 males = 3
Black kittens= 2 female+ 1 male =3
Probability of picking one black kitten = black kittens/ total kittens = 3/6 =1/2
Which sequence describes Ahmed's expected hourly wages, in dollars, starting with his current wage?
Since Ahmed will start with $7.50 per hour
Then the sequence must start with 7.50
Then the answer should be A or B or C
Since his hourly rate will increase by $0.25 per hour
Then the number in the sequence should be increased
Then the answer is B or C because A is decreasing
We have to add 0.25 to the first rate to get the second rate
[tex]\begin{gathered} 7.50+0.25=7.75 \\ 7.75+0.25=8.00 \\ 8.00+0.25=8.25 \\ 8.25+0.25=8.50 \end{gathered}[/tex]Then the correct answer is
$7.50, $7.75, $8.00, $8.25, $8.50
The answer is B
Which of the following is irrational?A.24.3B./2D. /25C.7
a) 24.3 is a rational number
[tex]\frac{243}{10}[/tex]b)
[tex]\begin{gathered} \sqrt{2}=1.41421 \\ \sqrt{2}\text{ is irrational} \end{gathered}[/tex]c) 7 is a rational number
d)
[tex]\begin{gathered} \sqrt{25}=5 \\ \sqrt[]{25}\text{ is rational} \end{gathered}[/tex]Answer: Letter B
fing the length of the missing side
The area is given as
[tex]x^2-6x+9[/tex]We can either divide the area by the side given and get the other side
OR
We can simply factorize the area and hence determine the two factors that were multiplied together. Note that one factor has already been given (that is x-3).
To factorize the polynomial;
[tex]\begin{gathered} x^2-6x+9 \\ =(x-3)(x-3) \end{gathered}[/tex]This means the other side is also (x - 3)
how do I solve a liner model ?
The values that are represented by the dots are close to the horizontal line, so they are a non-random pattern, because they follow the horizontal line without going to far from it
Since these points are all around the horizontal line, they also represent a linear model
So the answer for hte first box is "non-random" and the answer for the second box is "linear"
Pablo deposited $600 in an account earning 2% interest compounded annually.To the nearest cent, how much interest will he earn in 3 years?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
The given information is:
- The initial amount is $600
- The interest rate is 2% (compounded annually)
The given formula is:
[tex]B=p(1+r)^t[/tex]Where B is the balance (final amount), p is the principal (starting amount), r is the interest rate as a decimal, and t is the time in years.
By replacing the known values we obtain the balance after 3 years:
[tex]\begin{gathered} B=600*(1+0.02)^3 \\ B=600(1.02)^3 \\ B=600*1.06 \\ B=636.72 \end{gathered}[/tex]The answer is $636.72
How much interest in dollars is earned in 5 years on $8,200 deposited in an account paying 6% interest compounded semiannually round to the nearest cent
Using compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount
P = Principal = 8200
r = Interest rate = 6% = 0.06
n = Number of times interest is compounded per year = 2
t = time = 5
so:
[tex]\begin{gathered} A=8200(1+\frac{0.06}{2})^{2\cdot5} \\ A=11020.11 \end{gathered}[/tex]Therefore, the interest is the amount minus the amount invested:
[tex]\begin{gathered} I=A-P \\ I=11020.11-8200 \\ I=2820.11 \end{gathered}[/tex]Answer:
$2820.11
Which is the measure of an interior angle of a regular decagon?30°36°144°150°
SOLUTION:
We are to find the measure of an interior angle of a regular decagon.
A decagon is a plane figure with ten straight sides and angles.
To find the sum of interior angles in a decagon;
(n - 2) x 180 (where n = 10)
(10 - 2) x 180
= 8 x 180
= 1440 degrees
The measure of an interior angle of a regular decagon is;
1440 / 10
144 degrees
Length of carrier A is about how many football fields ?
Given:
The total length of carriers A and B, T=4198 feet.
The difference in lengths of the carriers is, D=10 feet.
The length of football field, L=100 yards.
Let a be the length of carrier A and b be the length of carrier B. It is given that carrier A is longer than carrier B.
Hence, the expression for the difference in lengths of the carriers can be written as,
[tex]\begin{gathered} D=a-b \\ 10\text{ =a-b ----(1)} \end{gathered}[/tex]The total length of carriers A and B can be written as,
[tex]\begin{gathered} T=a+b \\ 4198=a+b\text{ ----(2)} \end{gathered}[/tex]Add equations (1) and (2) to find the value of a.
[tex]\begin{gathered} 2a=10+4198 \\ 2a=4208 \\ a=\frac{4208}{2} \\ a=2104\text{ f}eet \end{gathered}[/tex]We know, 1 yard=3 feet.
So, 1 feet=(1/3) yard
The length of carrier A in yards is,
[tex]a=2104\text{ f}eet\times\frac{\frac{1}{3}\text{yard}}{\text{ 1 fe}et}=\frac{2104}{3}\text{yards}[/tex]We know, the length of a football field is l=100 yards
Now, the ratio between a and l can be found as
[tex]\frac{a}{l}=\frac{\frac{2104}{3}\text{ yards}}{100\text{ yards}}\cong7.0[/tex]Hence, we can write
[tex]a=7.0\times l[/tex]Since l is the length of a football field, the length of carrier A is about 7.0 football fields.