[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$8000\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &4 \end{cases} \\\\\\ 8000=Pe^{0.06\cdot 4}\implies 8000=Pe^{0.24}\implies \cfrac{8000}{e^{0.24}}=P\implies 6293.02\approx P[/tex]
"You've fallen into my trap!" Justin shouts, laughing like
the madman he is. The mouse he captured stares back at
him indifferently as it munches on a piece of cheese at the
bottom of a box whose base measures 12 cm by 12 cm.
Move the points on the grid below to draw the base of
the box in which the mouse is trapped.
Answer:
18 units by 18 units
makes sure the square add up to 18 going across and 18 going down.
Step-by-step explanation:
Suppose you know the volume of a pyramid with a rectangular base is 200 cubic units. How could you find a set of dimensions for the pyramid?
Write in point-slope form the equation of the line that passes through the point (- 1, 6) and has a slope of -2
Answer:
y= -2x+4
Step-by-step explanation:
Calculate the monthly payment for a 5-year car loan of $23,570 at 10.43% interest, compounded monthly. a. $247.44 b. $337.56 c. $433.88 d. $505.79
The monthly payment for a 5-year car loan of $23,570 at 10.43% interest, compounded monthly will be $660
It is given that the monthly payment for a 5-year car loan of $23,570 at 10.43% interest, is compounded monthly.
It is required to find the monthly payment.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A=P(1+ \frac{r}{n})^n^t[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have P = $23,570
r = 10.43% = 10.43/100 = 0.1043
n = 12
t = 5 years
Putting all the values in the formula, we get:
[tex]\rm A=23,570(1+\frac{0.1043}{12})^1^2^\times^5[/tex]
[tex]\rm A = 23,570\times1.680\\\rm A = 39597.6[/tex]
The monthly payment will be:
=[tex]\rm \frac{A}{t(in \ months)}[/tex]
[tex]\rm = \frac{39597.6}{60} \\\rm = 659.96\\\rm \approx 660[/tex]
Thus, the monthly payment for a 5-year car loan of $23,570 at 10.43% interest, compounded monthly will be $660.
Learn more about the compound interest:
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Answer:
D. 505.79
Step-by-step explanation:
edge 2022
write the equation that models each linear relationship
Note: I will be writing these in slope-intercept form.
[6] y = 2x + 4
Since the line is going from bottom left to top right, we know the slope of the line is positive.
-> The b, or y-intercept, is 4 because the line hits the y-axis at 4.
-> The slope can be found with change in y over change in x,
[tex]\frac{14-4}{5-0} =\frac{10}{5} =2[/tex]
-> The final equation is y = 2x + 4
[7] y = -3x - 5
Because the line is going from top left to bottom right, we know the slope of the line will be negative.
-> The b, or y-intercept, is -5 because the line hits the y-axis at -5.
-> The slope can be found with change in y over change in x,
[tex]\frac{4--5}{-3-0}=\frac{4+5}{-3-0}=\frac{9}{-3}=-3[/tex]
-> The final equation is y = -3x - 5
The formula for an area of a triangle is :____.
Answer:
Area of a triangle
Step-by-step explanation:
A= [tex]\frac{1}{2}[/tex]bh
A: area
b: base
h: height
hope this helps..
A theater has 15 seats in the front row. The number of seats in each row follows an arithmetic series with 72 seats in the last row. The theater has a total of 870 seats. How many rows does the theater have? By how many seats does each row increase? Please show all work.
Step-by-step explanation:
Given:
Theater has 15 seats
Last Row has 72 seats.
Theater has a total of 870 seats.
Unknown: Number of rows
Number of seats in each row.
Equations: Since we know the total number of seats the Theater has we can use the sum of arithmetic series
[tex]s = \frac{a _{1} + a _{n} }{2} n[/tex]
Where a1 is the first row of seats
s is total number of seats
an is last row of seats
n is number of rows.
[tex]870 = \frac{15 + 72}{2} (n)[/tex]
[tex]870 = \frac{87}{2} n[/tex]
[tex]2(870) = 87n[/tex]
[tex]20 = n[/tex]
So we have 20 rows.
To find how many seats does each row increase, we use this formula,
[tex]a _{n} = a + (n - 1)d[/tex]
Let use the 20th row as an example,
[tex]a _{20} = 15 + (19)d[/tex]
[tex]72 = 15 + (19)d[/tex]
[tex]57 = 19d[/tex]
[tex]3 = d[/tex]
So the common difference is 3.
So the seats of each row increase by 3.
BRE
What is the scale factor of this dilation?
A'
9
6
B'
15
10
[Not drawn to scale]
O
WN
O
O 3
OO
5
Answer:
2nd option
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{A'C'}{AC}[/tex] = [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}[/tex] = 1 [tex]\frac{1}{2}[/tex]
Solve the equation on the
interval [0, 27).
4(sin x)2 - 2 = 0
X
.
7
[?] []? []T
x =
4) 4 4 4
Write your answer in increasing order. Enter the
number that belongs in the green box.
Enter
Answer:
see explanation
Step-by-step explanation:
note that (sinx)² = sin²x
4sin²x - 2 = 0 ( add 2 to both sides )
4sin²x = 2 ( divide both sides by 4 )
sin²x = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] ( take square root of both sides )
sinx = ± [tex]\sqrt{\frac{1}{2} }[/tex] = ± [tex]\frac{1}{\sqrt{2} }[/tex]
sinx = [tex]\frac{1}{\sqrt{2} }[/tex] ( sinx > 0 , then x is in 1st/2nd quadrants )
x = [tex]\frac{\pi }{4}[/tex] , π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{3\pi }{4}[/tex]
sinx = - [tex]\frac{1}{\sqrt{2} }[/tex] ( sinx < 0 , then x is in 3rd/4th quadrants )
x = π + [tex]\frac{\pi }{4}[/tex] = [tex]\frac{5\pi }{4}[/tex] , 2π - [tex]\frac{\pi }{4}[/tex] = [tex]\frac{7\pi }{4}[/tex]
solutions are
[tex]\frac{\pi }{4}[/tex] , [tex]\frac{3\pi }{4}[/tex] , [tex]\frac{5\pi }{4}[/tex] , [tex]\frac{7\pi }{4}[/tex] in the interval [ 0, 2π )
f (x)=6xº + 2x² +
+ x
O The function is an even function.
O The function is an odd function.
O The function is neither even nor odd.
Foreign Policy: Imperialism For82622
JAVA
Write a program that repeatedly reads in integers until a negative integer is read. The program also keeps track of the largest integer that has been read so far and outputs the largest integer at the end.
Ex: If the input is:
2 77 17 4 -1
the output is:
77
Assume a user will enter at least one non-negative integer.
The program is an illustration of loops
What are loops?Loops are program statements that are used to execute repeated statements
The java programThe program, written in Java where comments are used to explain each line is as follows:
import java.util.*;
public class Main{
public static void main(String[] args) {
Scanner input = new Scanner(System.in);
int num;
//Get input from the user
num = input.nextInt();
//Initialize the largest to the first input
int maxn = num;
//This loop is repeated until a negative input is recorded
while (num >=0){
//If the current input is greater than the previous largest
if (num>maxn){
//Set largest to the current input
maxn = num; }
//Get another input from the user
num = input.nextInt();
}
//Print the largest
System.out.print("Largest: "+maxn);
}
}
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Write an equation of the line in slope- intercept form.
A. Y= -4/5x - 3
B. Y = -4/5x + 3
C. Y= -5/4x - 3
D. Y= -5/4x + 3
Answer:
A
Step-by-step explanation:
becuase the 3 is negtive and the 4/5 so it A
Answer:
[tex]a)\ y=-\frac{4}{5}x -3[/tex]
Step-by-step explanation:
Slope (m) form: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{-3-1}{0-(-5)} \\\\m=\frac{-4}{0+5} \\\\m=-\frac{4}{5}[/tex]
[tex]y=mx+b\\y=-\frac{4}{5}x +b[/tex]
(-5, 1)
[tex]y=-\frac{4}{5}x +b\\1=-\frac{4}{5}(-5) +b\\1=4+b\\-4-4\\-3=b[/tex]
[tex]y=-\frac{4}{5}x -3[/tex]
Check your answer:
[tex]y=-\frac{4}{5}x -3 \\1=-\frac{4}{5}(-5) -3\\1=4-3\\1=1[/tex]
This statement is true
Hope this helps!
find the length of the diameter of circle 0
Answer:
Diameter = 19.33
Step-by-step explanation:
Imaging a radius line from O to the endpoints of the 7. call this line R.
Label the part of the vertical line from O to the 90 degree intersection y.
Now you have a right triangle.
Using the Pythagorean theorem:
R² = 7² + y²
also
y = R - 3
substitute for y:
R² = 49 + (R-3)²
R² = 49 + R² - 6R + 9
simplify:
0 = 58 - 6R
6R = 58
R = 9.6667
Diameter = 2(9.6667) = 19.33
You pick a card at random. Without putting the first card back, you pick a second card at random. 5 6 7 What is the probability of picking an even number and then picking an even number?
Answer:
The probability of picking a 7 as the first card is 4 out of 52 or 1/13. The probability of picking a 5 as the second card is 4 out of 51. For both to happen, we multiply and get about .00603318
Thanks!
person above me is correct
Step-by-step explanation:
An engineer is tasked with doubling the length and width of a city park. The engineer draws the park on a coordinate plane and labels it ABCD. Find the area of the park before and after the expansion. A coordinate plane with Square A B C D plotted. Point A is at zero comma three. Point B is at thee comma three. Point C is at three comma zero, Point D is at zero comma zero. A photo of a park with a caption that says, dimensions of park are being doubled. What is the area of the park before the expansion?
The vertex coordinates of the park the engineer draws, A(0, 3), B(3, 3),
C(3, 0), D(0, 0) give the area of the park before expansion as 9 unit².
How can the area of the park be found?
The shape of the park = A square
The vertices of the park = ABCD
The coordinates of the point are; A(0, 3), B(3, 3), C(3, 0), D(0, 0)
The length of side AB = 3 - 0 = 3
Length of side BC = 3 - 0 = 3
Length of side CD = 3 - 0 = 3
Length of side AD = 3 - 0 = 3
Therefore, the park is a square with side length, s = 3 units
The area of a square, A = Side × Side = s²
The area of the park before expansion, A = 3 unit × 3 unit = 9 unit²
Learn more about finding the area of geometric shapes here:
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There is a bag filled with 5 blue, 2 red and 3 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?
Answer:
7/25
Step-by-step explanation:
working out above.
To find the probability = Times BB RR and GG
then at the end add them all together.
Angle KLM and angle MLN are a linear pair.
A horizontal line has points K, L, N. A line extends from point L up and to the right to point M.
Ray LR is to be added to the diagram so that it is opposite ray LM. Which is true about angle RLN that would be formed?
Angles RLN and MLK would be vertical angles.
Angles RLN and MLN would be vertical angles.
Angles RLN and KLM would be a linear pair.
Angles RLN and KLN would be a linear pair.
Answer: Angles RLN and MLK would be vertical angles.
Step-by-step explanation:
A horizontal line has points K, L, N. A line extends from point L up and to the right to point M: Angles RLN and MLN would be vertical angles.
Based on the given information, if a horizontal line contains points K, L, and N, and a line extends from point L up and to the right to point M, then angle KLM and angle MLN are a linear pair.
Now, if Ray LR is added to the diagram opposite to Ray LM, the resulting angle RLN would be formed.
Vertical angles are formed when two lines intersect. They are opposite angles and have equal measures. Looking at the diagram, angles RLN and KLN do not share a common vertex, so they cannot be vertical angles.
Similarly, angles RLN and KLM do not share a common side or form a straight line, so they cannot be a linear pair.
Therefore, the correct statement is: Angles RLN and MLN would be vertical angles.
To know more about Angles
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#SPJ4
Could Y'all Please Help Me! I'll Give you Good Points!
Answer:
I would say its D
Step-by-step explanation:
10:9:10 is the original ratio
It gets turned into 1:1:2, making it very distorted
4. Courtney wants to sell her grandfather's antique 1932 Ford. She begins to set her price by looking at ads and finds these prices: $24,600, $19,000, $33,000, $15,000, and 20,000. What is the mean price?
Answer:
$22,320
Step-by-step explanation:
1. Understanding
Mean is the average of a given set
2. Solving
We have to find the average of all of these numbers.
How do I find the average?
I add all of the numbers and divide by the number of numbers I added. Example:
(x + x + x + x)/4 or,
(x+x)/2 and examples in numbers:
(3+4)/2 or,
(9+4+8+5+7)/5
See what I mean? Dividing by the number of numbers I have.
Ok, now we know that, we can solve!
Here is the equation for this problem:
(24,600+19,000+33,000+15,000+20,000)/5 (We have 5 numbers)
We have to do Parentheses First
(24,600+19,000+33,000+15,000+20,000)/5 --> 111,600/5
111,600/5 = 22,320
22,320 is the average number of all of the numbers, which is the mean
Hope this helps :)
-jp524
Graph g(x)=5|x -6|+2g(x)=5∣x−6∣+2g, left parenthesis, x, right parenthesis, equals, 5, vertical bar, x, minus, 6, vertical bar, plus, 2.
The graph of the absolute value function can be seen at the end of the answer. There we see a translated and dilated parent function.
How to graph the absolute value function?Here we want to graph:
g(x) = 5*|x - 6| + 2
First, remember that the minimum of the absolute value part |f(x)| is 0, so the minimum of the above function is 2, and that happens when x = 6. That will be the vertex of our function.
From that point, we will have two lines, one that goes to the right with a slope of 5, and the other that goes to the left with slope of -5 (the coefficient that multiplies the absolute value part of the function).
The graph of the function can be seen below.
If you want to learn more about absolute value functions, you can read:
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Answer:6,2 & 7,7
Step-by-step explanation:
what is f in this equation?
0.32=1/f
Step-by-step explanation:
0.32=1/f
1/0.32=f
f=3.125
please help, will give brainlist to first answer
Answer:
3 .62 lt
4 4300 g
5 1.78 mt
6 .0031 g
7 500 lt
8 .083 g
Please show work on answer
Answer:
x = 14
Step-by-step explanation:
x + 96 + 5x = 180
6x + 96 = 180
6x = 84
x = 14
Answer:
[tex]\huge\boxed{\sf x = 14}[/tex]
Step-by-step explanation:
x + 96 + 5x = 180 (Angles on a straight line)
Combine like terms
x + 5x + 96 = 180
6x + 96 = 180
Subtract 96 to both sides
6x = 180 - 96
6x = 84
Divide both sides by 6
x = 84 / 6
x = 14
[tex]\rule[225]{225}{2}[/tex]
What is the solution of log (2 t 4) = log (14 minus 3 t)?.
The solution the equation [tex]\rm log(2t+4)=log(14-3t)[/tex] is t = 2.
What is logarithmic properties?
Considering that the logarithm function is injective then the log is removing from the both sides and solving the equation for the value of t.
Given
The equation is;
[tex]\rm log(2t+4)=log(14-3t)[/tex]
The solution of the equation is;
[tex]\rm log(2t+4)=log(14-3t)\\\\2t+4=14-3t\\\\2t+3t=14-4\\\\5t=10\\\\t=\dfrac{10}{5}\\\\t=2[/tex]
Hence, the solution the equation [tex]\rm log(2t+4)=log(14-3t)[/tex] [tex]\rm log(2t+4)=log(14-3t)[/tex] is t = 2.
To know more about logarithmic properties click the link given below.
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Find the ending balance
if $2,000 was deposited
at 4% annual interest
compounded
semi-annually for 6 years.
The ending balance would be $2,536.48
Answer:
the person above has the answer:>
A bag contains 20 balls.
The ratio of red to blue to yellow balls is 1:2:2.
Find how many red, blue and yellow balls there are.
Answer: red=4 blue=8 yellow=8
4:8:8
Step-by-step explanation: 1+2+2=5
20÷5=4 4×1=4 2×4=8 2×4=8
I can't find the answer could you please help me?
Answer: 10.5
Step-by-step explanation:
A triangle prism is 21 yards long and has a triangular face with a base of 12 yards and a height of 8 yards the other two sides of a triangle are each 10 yards what is the surface area of the triangular prism
first find perimeter and area of base
then, find tsa of triangular prism
as done in the solution above!
Factorise 4x² + 2y² + x²y² + 8
Answer:
[tex]4x² + 2y² + x²y² + 8 \\arranging \: them \\ 4 {x}^{2} + {x}^{2} {y}^{2} + 2 {y}^{2} + 8 \\ {x}^{2} (4 + {y}^{2} ) + 2(y^{2} + 4) \\ ({x}^{2} + 2)(y^{2} + 4)[/tex]
Answer:
(4 + y^2) ( x^2 + 2)
Step-by-step explanation:
irst rearrange the terms
4x^2 + x^2 y^2 + 2y^2 + 8
then factorise
x2 ( 4 + y^2) + 2 ( y^2 + 4)
group like terms together and insert the remaining terms into a bracket
(4 + y^2) ( x^2 + 2)
Instructions: Find the length of the missing side.
Please help explain how I do this!! I will give you a Brainliest!!!!
Answer:
side AB = [tex]9\sqrt{2}[/tex]
hypotenuse CB = 18
Step-by-step explanation:
with a 45-45-90 triangle, we know that the two legs (AC and AB in this picture) are the same length, so if AC is [tex]9\sqrt{2}[/tex] , then AB would have to be the same so therefore it would also be [tex]9\sqrt{2}[/tex]. We also know that the length of the hypotenuse (CB) is the length of the leg times [tex]\sqrt{2}[/tex]. So, it would be [tex](9\sqrt{2} ) *\sqrt{2}[/tex], which is the same as saying [tex]9*(\sqrt{2}) * (\sqrt{2} )[/tex]. Doing [tex](\sqrt{2}) * (\sqrt{2} )[/tex] would cancel out the square roots, leaving you with just 2, so you get 9*2, which is 18.