The college will receive an amount of $5436.56.
What is Compound Interest?Compound interest is different from simple interest. In compound Interest, interest amount will vary each year. Interest is calculated first on the principal amount and then interest is the accumulated interest on the previous year.
Compound interest compounded continuously means interest is accumulating not within a month or year, but continuously.
If compound interest is compounded continuously, then the formula for calculating the final amount is,
A = P e^rt
where A is the final amount, P is the principal amount, r is the rate of interest and t is the time period.
Here, P = $2,000
r = 5% = 5/100 = 0.05
t = 20 years
A = 2000 × e^(0.05 × 20)
= 2000 × e^1
= 2000e
The value of e = 2.7182818..
A = 2000 × 2.7182818
= 5436.5636 ≈ 5436.56
Hence by the amount deposited by philanthropist, if the interest is compounded continuously, the college will receive $5436.56.
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Which trigonometric function would be used to find the length of this triangle's hypotenuse?
The cosine function is used to find the length of the hypotenuse of a triangle by utilizing the Pythagorean theorem.
The trigonometric function used to find the length of the hypotenuse of a triangle is the cosine function. In a right triangle, the cosine function is defined as the ratio between the length of the adjacent side to the length of the hypotenuse.
To find the length of the hypotenuse, you can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse.
For example, if the lengths of the shorter sides are 9 blocks and 5 blocks, then the length of the hypotenuse would be √(9² + 5²) = √(81 + 25) = √106 = 10.3 blocks.
Please help me thank you.
1st question - answer is #2
line P & Q = x=3, Y=5
triangle question, x = 17
In how many ways can i arrange the 6 letters a, b, c, d, e, f?
PLEASE HELP WITH THESE TWO
4. Tyler is writing a coordinate proof to show that a diagonal of a rectangle divides the rectangle into two triangles that have equal areas. He starts by assigning coordinates to a rectangle. Then he uses these coordinates to write an expression for the area of each triangle formed by the diagonal.
What is the area of one of the triangles formed by the diagonal of the rectangle?
Enter an expression in the box for the area of the triangle.
5. Amira is writing a coordinate proof to show that the area of a triangle created by joining the midpoints of an isosceles triangles is one-fourth the area of the isosceles triangle. She starts by assigning coordinates as given.
Enter your answers, in simplest form, in the boxes to complete the coordinate proof.
Point Q is the midpoint of DE , so the coordinates of point Q are (a, b).
Point R is the midpoint of FE , so the coordinates of point R are ([ ], b).
In ΔDEF , the length of the base, DF , is [ ], and the height is 2b, so its area is [ ].
In ΔQRP , the length of the base, QR , is [ ], and the height is b, so its area is ab.
Comparing the expressions for the areas proves that the area of the triangle created by joining the midpoints of an isosceles triangle is one-fourth the area of the triangle.
Thanks in advance. Please explain.
Answer:
#4) 1/2(ab); #5) 3a, 4a, 4ab, 2a
Step-by-step explanation:
#4) Take the top triangle. The height will be the difference in the y-coordinates of J and M:
b-0 = b
The base of the triangle would be the difference in the x-coordinates of J and K:
a-0 = a
The area is given by the formula A=1/2bh, where b is the base and h is the height; substituting our height and base, we have
A=1/2(b)(a) = 1/2(ab)
#5) To find the midpoint of a section, we add together the x-coordinates and divide by to, and add together the y-coordinates and divide by 2.
The endpoints of FE are (4a, 0) and (2a, 2b). This makes R:
[tex](\frac{2a+4a}{2},\frac{2b+0}{2})\\\\=(\frac{6a}{2},\frac{2b}{2})\\\\=(3a, b)[/tex]
The length of DF can be found by subtracting the x-coordinates:
4a-0 = 4a
The area is then found by multiplying 1/2 by the base and the height:
A=1/2(4a)(2b) = 1/2(8ab) = 4ab
The length of QR can be found by subtracting the x-coordinates:
3a-a = 2a
A sea turtle swims at a speed of 27 kilometers per hour. A girl swims 14 decimeters per second.
1 m = 10 dm
1000 m = 1 km
How much faster does the sea turtle swim than the girl in meters per minute?
Answer in meter per minute
~~~~~~~~~~The answer is 366 m/min~~~~~~~~~~~~~~~~~~ First, convert the turtles speed to meters per minute. 27 km/h * 1000 m/km = 27000 m/h / 60 min/h = 450 m/min Now convert the girls speed to meters per minute. 14 dm/s / 10 dm/m * 60 s/min = 84 m/min Now subtract the girl's speed from the turtle's speed. 450 m/min = 84 m/min = 366 m/min
Name two properties used to evaluate 7x1-4x1/4
Branliest offered
Decide which of the two points on the graph of the line
X=0
A. 0,7
B. -4,0
solve the system
x+3y=22
2x-y=2
Answer: The required solution is (x, y) = (4, 6).
Step-by-step explanation: We are given to solve the following system of equations :
[tex]x+3y=22~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (ii), we have
[tex]2x-y=2\\\\\Rightarrow y=2x-2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of y from equation (iii) in equation (i), we get
[tex]x+3(2x-2)=22\\\\\Rightarrow x+6x-6=22\\\\\Rightarrow 7x=22+6\\\\\Rightarrow 7x=28\\\\\Rightarrow x=\dfrac{28}{7}\\\\\Rightarrow x=4.[/tex]
From equation (i), we get
[tex]4+3y=22\\\\\Rightarrow 3y=22-4\\\\\Rightarrow 3y=18\\\\\Rightarrowy=\dfrac{18}{3}\\\\\Rightarrow y=6.[/tex]
Thus, the required solution is (x, y) = (4, 6).
What is the rate of change of the perimeter of the square at the instant the area is 49 m2?
an artist is cutting pieces of ribbon to use in a project. Each piece he cuts measures 7/8 inch. The aritst cuts off 5 pieces. How many total inches of ribbon has he cut off?
The artist has cut off a total of 4 and 3/8 inches of ribbon for his project by multiplying the length of one piece (7/8 inch) by the total number of pieces cut (5).
Explanation:The question involves a straightforward arithmetic operation of multiplication. Each piece of ribbon the artist cuts measures 7/8 inch, and he cuts off 5 pieces in total. To find the total length of ribbon cut off, we multiply the length of one piece (7/8 inch) by the number of pieces cut (5).
Calculation: \(\frac{7}{8} \text{ inch} \times 5 = \frac{35}{8} \text{ inches} = 4 \frac{3}{8} \text{ inches}\)
Therefore, the artist has cut off a total of 4 and 3/8 inches of ribbon for his project. This example demonstrates a practical application of multiplication in a real-world context, specifically within arts and crafts projects.
What is the value of x?
a. 68°
b. 62°
c. 112°
d. 124°
Rick, Maya, and Tom work in a call center. On a particular day, Rick worked 5 and ½ hours, Maya worked 6.1 hours, and Tom worked 6 hours and 30 minutes. What is the total number of minutes that they worked?
Rick, Maya, and Tom worked a total of 1086 minutes.
To calculate this:
1. Convert Rick's hours to minutes: 5 hours and ½ hour = [tex]\( 5 \times 60 + 30 = 330 \) minutes.[/tex]
2. Convert Maya's hours to minutes: 6 hours and 1/10 hour = [tex]c\( 6 \times 60 + 6 = 366 \) minutes.[/tex]
3. Convert Tom's hours to minutes: 6 hours and 30 minutes = [tex]\( 6 \times 60 + 30 = 390 \) minutes.[/tex]
Now, add up all the minutes worked:
[tex]\[ 330 + 366 + 390 = 1086 \] minutes.[/tex]
Therefore, Rick, Maya, and Tom worked a total of 1086 minutes.
- Rick worked for 5 hours and ½ hour, which is 330 minutes.
- Maya worked for 6 hours and 1/10 hour, which is 366 minutes.
- Tom worked for 6 hours and 30 minutes, which is 390 minutes.
Adding these minutes together gives a total of 1086 minutes.
complete question
Rick, Maya, and Tom work in a call center. On a particular day, Rick worked 5 and ½ hours, Maya worked 6.1 hours, and Tom worked 6 hours and 30 minutes. What is the total number of minutes that they worked?
Nine friends will equally share 12 glasses of punch how many glasses of punch will each friend get A.3/4 B.1/3 C.4/3 D.3
PLEASE ANSWER!
1. Choose the best definition for the following term: exponent
The number listed first when combining a variable and a number
The number or value being raised to a power
A letter that holds the place of some unknown value in mathematics
Shorthand that tells how many times the base is used as a factor, or how many times the base is multiplied by itself
2. Choose the best definition for the following term: variable
A letter that holds the place for some unknown value in mathematics
A process where you must look for terms that have identical variable parts and then combine their coefficients
A process where if two things are equal, one can be put in the place of the other and nothing will change
Terms that have identical variable parts
A solid right pyramid has a regular hexagonal base with an area of 7.4 units2. The pyramid has a height of 6 units.
What is the volume of the pyramid?
11.1 units3
14.8 units3
22.2 units3
44.4 units3
Answer:
Option B. 14.8 units³ is the answer.
Step-by-step explanation:
It is given in the question A solid right pyramid which has a regular hexagonal base with area = 7.4 unit²
Height of the pyramid = 6 units.
We have to calculate the volume of the pyramid.
Since volume of the pyramid = (1/3)×Area of the base × height
Volume = (1/3)×7.4×6 = 7.4 × 2 = 14.8 units³
Therefore option B. 14.8 units³ is the answer.
It should be noted that the volume of the pyramid will be 14.8 unit³.
How to calculate the volume of the pyramidFrom the information given, the solid right pyramid has a regular hexagonal base with an area of 7.4 units².
The height of the pyramid is also 6 units. Therefore, the volume of the pyramid will be:
= 1/3 × Area of the base × height
= 1/3 × 7.4 × 6
= 14.8 units³
In conclusion, the volume of the pyramid is 14.8 unit³.
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Suppose that a circular coin has an area a, a radius of r, and a diameter of
d. write a as a function of
d.
Area of the given Circle as the function of its diameter πd²/4
What is circle?A Circle is the 2D shape which is measured in the terms of its radius.
Given that Area, radius and diameter of the given Circle is a , r and d respectively.
Area of Circle (A) = π X radius²
radius = diameter/2
Therefore replacing radius by diameter we get,
A = π(d/2)²
A = πd²/4
Hence, Area as a function of d is given by A = πd²/4
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*PLEASE HELP* Compute the amount of interest earned in the following simple interest problem. Explain how you got it please
A deposit of $5,500 at 6% for 3 years
The amount of interest earned is $990 when we deposit of $5,500 at 6% for 3 years
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We have to find the amount of interest earned
The deposited amount or principal amount us 5500
Rate of interest is 6% and time is 3 years
The formula for simple interest is I=PRT
I = interest, P = principal, R = rate, T = time in years.
Let us convert 6% to decimal form
Divide 6 by 100
6%=0.06
I = 5500(0.06)(3)
I = $990
Hence, the amount of interest earned is $990 when we deposit of $5,500 at 6% for 3 years
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Simplify the expression (x^19 y^21)^4/(x^2 y^6)^2
The simplified expression is ________.
Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options: Option A: Stay with saving the same amount they've been saving each month but postpone the wedding 2 months. Option B: Increase the amount of money they save each month by $80 from what they've been saving. Which of the following is a true statement? a. Only option A will allow them to meet their goal. b. Only option B will allow them to meet their goal. c. Both options A and B will allow them to meet their goal. d. Neither option A nor option B will allow them to meet their goal
To meet their goal of saving $8,000 for their wedding, Mike and Kate need to adjust their plan. Increasing the amount they save each month by $80 (Option B) will allow them to reach their goal.
Explanation:To determine which option will allow Mike and Kate to meet their goal of saving $8,000 for their wedding, we need to analyze the information given. They saved $4,000 in the first year, which means they saved $4,000 in 12 months. To reach their goal, they need to save an additional $4,000 in 8 months.
Option A: If they stay with saving the same amount they've been saving each month, they will save the same amount each month for the remaining 8 months. Therefore, they will not reach their goal of $8,000.
Option B: If they increase the amount they save each month by $80, they will be saving $80 more each month for the remaining 8 months. This will result in them saving an additional $640 ($80 x 8 months) and reaching their goal of $8,000.
Therefore, the correct answer is Option B - Only option B will allow them to meet their goal.
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An investment is currently worth 2.125×104 dollars . Ten years ago, the investment was worth 1.25×103 dollars. How many times greater is the value of the investment today than the value of the investment ten years ago? A 0.17 B 1.7 C 17 D 170
Answer: C. 17
Step-by-step explanation:
Given : An investment is currently worth [tex]2.125\times10^4[/tex] dollars . Ten years ago, the investment was worth [tex]1.25\times10^3[/tex] dollars.
Then, the number of times the value of the investment today is greater than the value of the investment ten years ago is given by :-
[tex]\dfrac{\text{Current investment}}{\text{\text{Yen years ago investment}}}\\\\=\dfrac{2.125\times10^4}{1.25\times10^3}\\\\=\dfrac{2.125}{1.25}\times10^{4-3}\ \ [\because a^m\times a^n=a^{m+n}]\\\\=1.7\times10=17[/tex]
Hence, the value of the investment today is 17 times greater than the value of the investment ten years ago .
Help with this question !
Write all the factors of 8
A street that is 270m long is covered in snow. city workers are using a snowplow to clear the street. a tire on the snowplow has to turn 45 times in traveling the length of the street. what is the diameter of the tire?
If vx = 7.60 units and vy = -6.60 units, determine the magnitude of v⃗ .
Answer:
|v| = 10.06 units
Step-by-step explanation:
It is given that,
The x component of the vector is, [tex]v_x=7.6\ units[/tex]
The y component of the vector is, [tex]v_y=-6.6\ units[/tex]
We need to find the magnitude of vector v. The magnitude of any vector is calculated as :
[tex]|v|=\sqrt{v_x^2+v_y^2}[/tex]
[tex]|v|=\sqrt{(7.6)^2+(-6.6)^2}[/tex]
|v| = 10.06 units
So, the magnitude of vector v is 10.06 units. Hence, this is the required solution.
How many possible outcomes, including both main effects and interaction effects, are possible for a factorial design with three independent variables?
Let f(x)equals=33xminus−1, h(x)equals=startfraction 7 over x plus 5 endfraction 7 x+5 . find (hcircle◦f)(66).
How many length 6 passwords with 1 number 1 upper and 1 lower?
7(2+5v)=3v+14 can anyone help???
The solution to the equation is v = 0.
We have,
To solve the equation 7(2 + 5v) = 3v + 14, we can simplify and isolate the variable v.
Expanding the left side of the equation:
7(2 + 5v) = 14 + 35v
Now we have:
14 + 35v = 3v + 14
Next, we can combine like terms:
35v - 3v = 14 - 14
32v = 0
To solve for v, we divide both sides of the equation by 32:
v = 0/32
v = 0
Therefore,
The solution to the equation is v = 0.
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Solve for b in the formula 3 a + 2 b = c .
A. b=c-3a
B. b=c-2/3a
C. b=c-3a/2
D. b=2c/3a
The value of b from the given equation is (c-3a)/2. Therefore, option C is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 3a+2b=c.
Now, 2b=c-3a
b= (c-3a)/2
The value of b from the given equation is (c-3a)/2. Therefore, option C is the correct answer.
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Faith mixes 14 liters of 12% acid solution with a 30% acid solution, which results in an 18% acid solution. let x represent the number of liters of 30% acid solution used, and let y represent the number of liters of mixture. which system of equations can be used to find the number of liters of 30% acid solution in the mixture?