Final answer:
The total amount on a $6,500 investment at a 6% annual interest rate compounded yearly for 25 years is approximately $28,353.25, with the interest earned being about $21,853.25.
Explanation:
To calculate the total amount and the amount of interest earned on $6,500 at 6% for 25 years, we need to identify whether the interest is compounded annually, monthly, or if it's simple interest. Since the type of interest isn't specified, we'll assume it's compounded annually, which is common in savings accounts. The formula for compound interest is:
A = P(1 + r/n)nt
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount ($6,500)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time the money is invested or borrowed for, in years (25 years)
For this example, since the interest is compounded annually, n = 1. First, convert the interest rate from a percentage to a decimal by dividing by 100: 6% / 100 = 0.06. Now, plug the values into the formula:
A = $6,500(1 + 0.06/1)1*25
A = $6,500(1 + 0.06)25
A = $6,500(1.06)25
Calculating this out, A, which is the total future amount, comes out to:
A = $28,353.25 approximately
To find out the total interest earned, subtract the principal from the final amount:
Total interest = A - P
Total interest = $28,353.25 - $6,500
Total interest = $21,853.25 approximately
The total amount is about $28,353.25 and the amount of interest earned is about $21,853.25.
Which polar coordinates represent the point plotted on the graph? Select all that apply. (2 answers)
a. (-4, 90 degrees)
b. (4, 90 degrees)
c. (4, -90 degrees)
d. (-4, 270 degrees)
e. (-4, -270 degrees)
Answer: The correct options are (b) and (d).
Explanation:
It the polar form [tex]r^2=x^2+y^2[/tex], where
[tex]x=r\cos \theta,y=r\sin \theta[/tex]
The polar coordinate are in the form of [tex](r,\theta)[/tex].
From the given figure it is noticed that the value of r is 4 and [tex]\theta=\frac{\pi}{2}[/tex] or [tex]90^{\circ}[/tex] .
So the point is defined as [tex](4,90^{\circ})[/tex] and option b is correct.
The value,
[tex](r\cos \theta, r\sin \theta)=(0,4)[/tex]
Check the each option if we get the same value then that option is correct.
For option a.
[tex](r\cos \theta, r\sin \theta)=(-4\cos 90^{\circ} , -4\sin 90^{\circ})=(0,-4)[/tex]
Therefore option (a) is incorrect.
For option c.
[tex](r\cos \theta, r\sin \theta)=(4\cos (-90)^{\circ} , 4\sin (-90)^{\circ})=(0,-4)[/tex]
Therefore option (c) is incorrect.
For option d.
[tex](r\cos \theta, r\sin \theta)=(-4\cos (270)^{\circ} , -4\sin (270)^{\circ})\\(-4\cos (360-90)^{\circ} , -4\sin (360-90)^{\circ})=(0,4)[/tex]
Therefore option (d) is correct.
For option (e).
[tex](r\cos \theta, r\sin \theta)=(-4\cos (-270)^{\circ} , -4\sin (-270)^{\circ})\\(-4\cos (270)^{\circ} , 4\sin (270)^{\circ})=(0,-4)[/tex]
Therefore option (e) is incorrect.
Answer:
1. A
2. B, D
3. A, D, E
4. C
5. A
Step-by-step explanation:
3. A vacuum robot is in a room and charging at position (0, 5). Once charged, it begins moving on a northeast path at a constant speed of 1/2 foot per second along the line 4 − 3 = −15. After 60 seconds, it turns right 90° and travels in the new direction.
a. What are the coordinates of the point at which the robot made the turn?
b. Find an equation for the second line on which the robot traveled.
c. If after turning, the robot travels 80 seconds along this line, how far has it traveled from its starting position?
d. What is the equation of the line the robot needs to travel along in order to return and recharge? How long will it take the robot to get there?
Show your work
a)
The robot made the turn at the point (-20, 15).
b)
The equation of the second line on which the robot traveled is:
y = (4/3)x + 35.
c)
The distance between the starting position and the final position is 20.51 feet.
d)
The equation of the line the robot needs to travel along in order to return and recharge is y = (-3/4)x + 5.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
a.
To find the coordinates of the point at which the robot made the turn, we need to determine its position after traveling for 60 seconds along the initial northeast path.
The distance the robot covers in 60 seconds is:
distance
= speed x time
= (1/2) x 60 = 30 feet
The initial path has a slope of -3/4 (since it passes through (4, -3) and
(0, 5)), so the robot's new path after turning right will have a slope of the negative reciprocal of -3/4, which is 4/3.
We know that the robot traveled 30 feet along the initial path, so we can use the slope and distance traveled to find the endpoint of the initial path:
y = mx + b, where m is the slope and b is the y-intercept
-3 = (-3/4)(4) + b
b = 0
So the equation of the initial path is y = (-3/4)x.
The endpoint of the initial path is (-20, 15) (since the initial path passes through (0, 5) and (-20, 15)).
The robot made the turn at the point (-20, 15).
b.
Since the robot turned right, its new path will be perpendicular to the initial path.
We know the robot's position after turning (i.e., the endpoint of the initial path), so we can use this point and the slope of the new path to find the equation of the new path.
The slope of the new path is 4/3, so the equation of the new path is:
y - 15 = (4/3)(x + 20)
Simplifying this equation, we get:
y = (4/3)x + 35
The equation of the second line on which the robot traveled is:
y = (4/3)x + 35.
c.
From the last equation in part (b), we have:
9(y - 5)² = 29 - 16x² - 12x
Taking the square root of both sides and solving for y, we get:
y = 5 ± √((29 - 16x^2 - 12x)/9)
Since the robot is traveling along the new path for 80 seconds, we want to find y when t = 80.
Substituting t = 80 into the equation for y and simplifying, we get:
y = 5 + √(17/9)
So the robot's final position is approximately (20.50, 6.63).
The distance between the starting position and the final position is:
distance
= √((20.50 - 0)² + (6.63 - 5)²)
= √(421.17)
= 20.51 feet.
d.
The robot needs to travel along a path that is perpendicular to the second line on which it traveled in order to return to its starting position.
The slope of the second line is 4/3, so the slope of the path back to the starting position is -3/4 (the negative reciprocal of 4/3).
We know the robot's final position and the slope of the desired path, so we can use the point-slope form to find the equation of the path:
y - 5 = (-3/4)(x - 0)
Simplifying this equation, we get:
y = (-3/4)x + 5
So the equation of the line the robot needs to travel along in order to return and recharge is y = (-3/4)x + 5.
Setting the two equations equal to each other and solving for x, we get:
(4/3)x + 35 = (-3/4)x + 5
Multiplying both sides by 12 to eliminate fractions, we get:
16x + 420 = -9x + 60
Solving for x, we get:
x = -16.8
Substituting this value of x into either equation, we get:
y = (4/3)(-16.8) + 35
y = 13.60
So the intersection point is approximately (-16.8, 13.60).
To find how long it will take the robot to get there, we can use the distance formula between the robot's final position and the intersection point:
distance = √((-16.8 - 20.50)² + (13.60 - 6.63)²) ≈ 40.49 feet.
Since the robot travels at a constant speed of 1/2 foot per second, it will take approximately 80.98 seconds (rounded to two decimal places) for the robot to return and recharge.
Thus,
The robot made the turn at the point (-20, 15).
The equation of the second line on which the robot traveled is:
y = (4/3)x + 35.
The distance between the starting position and the final position is 20.51 feet.
The equation of the line the robot needs to travel along in order to return and recharge is y = (-3/4)x + 5.
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On two examinations, you have grades of 83 and 89. there is an optional final examination, which counts as one grade. you decide to take the final in order to get a course grade of a, meaning a final average of at least 90
If the pattern below follows the rule "Starting with four, every consecutive line has a number one more than the previous line," how many marbles must be in the seventh line?
The number of balls in 7th line would be 10.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a pattern as shown in the image.
An arithmetic sequence is of the form -a, a + d, a + 2d, a + 3d, ......,
{d} is common difference and {a} is first term.We can write the pattern as -
4, 5, 6, 7, .....
This is a arithmetic progression. We can write the nth term as -
a{n} = a + (n - 1)d
a{7} = 4 + (7 - 1) x 1
a{7} = 4 + 6
a{7} = 10
Therefore, the number of balls in 7th line would be 10.
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Two mechanics worked on a car. the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800. what was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour ?
The rates charged per hour by the first and second mechanics will be $105 and $50.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that two mechanics worked on a car, the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800.
Suppose x is the hourly rate for the first mechanic and y is the hourly rate of the second.
If the total money earned is 1800.
10x + 15 y = 1800 ---- (1)
If both have their individual rates the sum of the hourly rate is,
x+ y = 15 -------- (2)
Rearrange the equation,
x = 155- y
Substitute the value of x in equation 1 we get,
10x + 15 y = 1800
10(155-y) + 15y = 1800
1150 - 10y + 15y = 1800
5y = 250
y = 50
Substitute the value of y in equation 2 we get,
x = 155- y
x= 155 - 50
x = 105
Thus, the rates charged per hour by the first and second mechanics will be $105 and $50.
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YOOO!!!!NEEED IMMEDIATE HELP!!!!!!!!!!!!
An airplane left Miami, FL. At the same time another plane left Santiago, Chile. The two planes flew toward each other at rates of 625 mph and 575 mph. If Miami and Santiago are 4200 miles apart, how long will it take until the planes pass each other?
Write an expression for the total Surface Area (SA) of a rectangular prism whose base is a square with side of length x and height of y.
The table below shows the relative frequencies of the color of cars bought last month by males and females. Which percentage represents the car bought most often?
Options:
20%
31%
43% is wrong
57%
(I already did my other questions, this is the only one I needed help with)
PLZ help
which inequality does the graph represent
The inequality the graph represent is y > x - 2.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. An inequality is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities are used to describe relationships between quantities or to express constraints or conditions.
We are given that;
The number line
Now,
The slope of the line is 1 and the y-intercept is -2,
so we can write y = x - 2 for the equation of the line.
The line is dashed, so we know that y is not equal to x - 2.
The region above the line is shaded, so we know that y is greater than x - 2.
Therefore, by the inequality the answer will be y > x - 2.
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Find the surface area of a sphere with radius, r = 11 in.
Surface Area = ________ in^2
(Type an exact answer in terms of pi.)
I really need help with these questions:
Use basic identities to find the simplified expression-
1. (cos^2 x + sin^2 x) / (cot^2 x - csc^2 x)
2. cosine θ^2 / sine θ^2 + csc θ sin θ
Explanations would be greatly appreciated
Two lighthouses are located 40 miles from each other. A boat is spotted at an angle of 37 degrees northeast of the western lighthouse. At this point, the boat is 28 miles from the eastern lighthouse. How far is the boat from the western lighthouse?
A. 46.27 miles
B. 17.43 miles
C. Either 46.27 miles or 17.43 miles
D. There is no possible solution.
Answer:
C. Either 46.27 miles or 17.43 miles
If a person uses $700 in credit with an interest of 14%,what is that person going to owe after three billing cycles with simple interest
Write the equation in standard form using integers y=4x+5
Which is least expensive per oz rounded to the nearest cent: 20 oz for $1.79 or 2 lb 2 oz for $2.59?
A.) 20 oz
B.) 2 lb 2 oz
C.) Neither
Answer:
B.) 2 lb 2 oz
Step-by-step explanation:
$1.79 for 20 ounces gives us
1.79/20 = $0.0895 ≈ $0.09 per ounce.
1 lb = 16 oz.; this means that 2 lb = 2(16) = 32 oz.
$2.59 for 2 lb 2 oz then gives us
2.59/34 = $0.07617647059 ≈ $0.08 per ounce.
The second choice is cheaper by 1 cent.
what is the value of x, if the volume of the cone is 12piem^3
A footbridge is in the shape of an arc of a circle. the bridge is 10 ft tall and 27 ft long, horizontally. what is the radius of the circle that contains the bridge? round your answer to the nearest tenth.
The radius of the circle that includes the footbridge, given the bridge's arc length and height, is 14.1 ft.
Explanation:The problem relates to the geometry of a circle, specifically the concept of the arc length and radius. Given the arc length (L) and the height of the arc (h), we can use these to find the radius (r) of the circle using the formula r = L²/(8h) + h/2.
Here, the arc length is the horizontal length of the footbridge, which is 27 ft and the height h is the height of the bridge, 10 ft.
Substituting these values into the formula we get:
r = (27² ft)/(8*10 ft) + 10 ft/2 = 729/80 + 5 = 14.1 ft
So, to the nearest tenth of a foot, the radius of the circle that includes the footbridge is 14.1 ft.
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If f(x) = 1000(3)x and g(x) = 8x. Which statement is true? A) None are true. B) as x → ∞, f(x) < g(x). C) as x → ∞, f(x) = g(x). D) as x → ∞, f(x) > g(x).
Answer: f(x) > g(x).
If f(x) = 1000(3)x and g(x)=8x
fx=3000x
f=3000x/x
f=3000
g(x)=8x
g=8x/x
g=8
For whatever amount of X (positive), the statement f(x) > g(x) is true.
Please help asap!!!!!!!!!!!!
On a 10 item test, three students in prof. miller's advanced chemistry seminar received scores of two, five, and eight, respectively. for this distribution of test scores, standard deviation is equal to the square root of
The standard deviation for the given test scores can be calculated by finding the mean, computing the squared differences from the mean, averaging those squared differences to get the variance, and then taking the square root of that variance. The standard deviation for the scores is approximately 2.449.
The student is likely seeking assistance with the concept of standard deviation, which is a measure of dispersion or distribution around the mean in a set of data. The question at hand requires calculating the standard deviation for a small dataset consisting of three scores from a chemistry seminar. To find the standard deviation, one would first need to calculate the mean of the test scores, then find the variance by averaging the squared differences between each score and the mean, and finally, take the square root of the variance.
Step-by-step Calculation:
Calculate the mean (average) of the scores: (2 + 5 + 8) / 3 = 15 / 3 = 5.Find the squared differences from the mean: (2 - 5)² + (5 - 5)² + (8 - 5)² = 3² + 0² + 3² = 9 + 0 + 9.Calculate the variance: (9 + 0 + 9) / 3 = 18 / 3 = 6.The standard deviation is the square root of the variance: √(6) = 2.449The standard deviation of the test scores in Prof. Miller's advanced chemistry seminar is approximately 2.449.
What is the end behavior of the polynomial function? PLEASE HELP!!!
The relative locations of a swing set, a garden, and a sandbox in Gina's backyard are shown in the diagram.
What is the distance between the sandbox and garden?
Enter your answer as a decimal in the box. Round only your final answer to the nearest foot.
Let us suppose the distance between the sandbox and garden is x feet.
Apply the sine law in the given triangle, we have
[tex]\frac{x}{\sin 65^{\circ}}=\frac{36}{\sin 104^{\circ}}\\ \\ \text{On coss multiplying, we get}\\ x\sin 104^{\circ}=36\sin 65^{\circ}\\ \\ x=\frac{36\sin 65^{\circ}}{\sin 104^{\circ}}\\ \\ x\approx 33.6[/tex]
Therefore, in the nearest foot, the distance between the sandbox and garden is 34 foot.
Answer:
Hello! The correct answer is 34 ft.
Step-by-step explanation:
I am just confirming!
A cruise ship can cover 17 nautical miles in 374 minutes. How many nautical miles will it travel in 330 minutes?
The ship's speed in deep water is 0.045 nautical miles per minute. In shallow water, the ship's maximum speed typically decreases due to increased drag and turbulence.
To find the speed of the ship in very deep water:
Calculate speed = Distance / Time = 17 nmi / 374 min = 0.045 nautical miles per minute.For the ship's speed in shallow water:It depends on the water resistance; usually, in shallow water, the ship's maximum speed decreases due to increased drag and turbulence.The measure of an angle is 27°. what is the measure of a complementary angle?
The measure of a complementary angle to a 27 degree angle is 63 degrees because two angles are complementary if their measures add up to 90 degrees. This is calculated by subtracting the given angle from 90.
Explanation:The measure of an angle is given as 27°, and you are asked to find the measure of a complementary angle. In mathematics, two angles are considered complementary if their measures add up to 90 degrees. Therefore, to find the measure of a complementary angle, you subtract the given angle from 90 degrees.
So, to solve this problem, you would simply subtract 27 from 90.
The calculation would look like this:
90-27 = 63. Therefore, the measure of the complementary angle is 63°.
A fish tank contains 18 goldfish and 22 guppies. If you randomly select 2 fish, what is the probability that they are both goldfish?
Answer:
b
Step-by-step explanation:
Suppose the diameter of a circle is \color{green}{10}10 start color green, 10, end color green. what is its radius
In Miami the number of accidents increased by 20% over a four year period.how many accidents were there in 2013 if there were 5120 in 2009
4+3x-ax=9-7x+bx
PLEASE HELP
Answer:
[tex]x=\frac{5}{(10-a-b)}[/tex]
Step-by-step explanation:
4+3x-ax=9-7x+bx
take all variable terms at one side and all constant terms at one side,
3x+7x-bx-ax=9-4
10x-ax-bx=5
x(10-a-b)=5
[tex]x=\frac{5}{(10-a-b)}[/tex]
WILL GIVE BRAINLIEST OF YOU ANSWET ALL
50 points plus 49 with brainliest
Answer:
his answer is right.