Final answer:
To double Rahul's savings of $3,000 to $6,000 in six years through compound interest, the required annual interest rate is approximately 12.25%.
Explanation:
The student wants to determine the interest rate needed for his savings to grow from $3,000 to $6,000 over a period of six years with compound interest compounded annually. We can use the formula for compound interest: A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial sum of money), r is the annual interest rate, and n is the number of years the money is invested for.
To solve this, use the formula with A = $6,000, P = $3,000, and n = 6 years, and then solve for r:
6,000 = 3,000(1 + r)⁶
Dividing both sides by 3,000:
2 = (1 + r)⁶
Now we must take the sixth root of both sides to solve for (1 + r):
(1 + r) = √⁶(2)
Then subtract 1 from both sides to solve for r:
r = √⁶(2) - 1
Using a calculator, simply compute the sixth root of 2, subtract 1, and convert to percentage to find the required interest rate:
r = 0.122462… or 12.2462%
Therefore, the interest rate required is approximately 12.25%.
What is the common denominator of StartFraction 1 Over a EndFraction + StartFraction 1 Over b EndFraction in the complex fraction StartFraction 1 Over a EndFraction minus StartFraction 1 Over b EndFraction divided by StartFraction 1 Over a EndFraction + 1 Over b EndFraction?
a2 b2
a – b
a + b
ab
Answer:
ab
Step-by-step explanation:
Answer:
Option D : ab
Step-by-step explanation:
correct on e2020
Easy Question
Topic: Volume
Focus on question 10
Answer:
a 120 cm^3
b 70 cm^3
Step-by-step explanation:
The volume of a right rectangular prism is given by
V = l*w*h
10 a V = 12*2*5
=120 cm^3
10 b V = 2.5 *8 *3.5
=70 cm^3
Answer:
120 cm^3;70 cm^3
Step-by-step explanation:
Volume = l * w * h
That means...
a) Volume = 12cm * 2cm * 5cm = 120 cm^3
b) Volume = 2.5cm * 8cm * 3.5cm = 70 cm^3
If Jason weighs 227 and can lose 3 pounds a month what will be his weight after 7 months
Answer:
206
Step-by-step explanation:
Answer:
206 pounds
Step-by-step explanation:
what is 1+1 plus 2 divided by 35 added by 6 subtracted by 30
Answer:
-23.8857
Step-by-step explanation:
1+1+2= 4
4/35+6= 6.11429
6.11429-30= -23.8857
Lenny can choose between apple juice, orange juice, and fruit punch. She can order a small, medium, and large. If she chooses a drink at random, what is the probability she chooses a medium orange juice?
Answer:
1/9 chance
Step-by-step explanation:
3 options and 3 choices probability of picking orange juice is 1/3 chance and probability of pickinkg a medium is 1/3 chance so you multiply dem to get 1/9
Can anybody find the measure of the major arc ILK?
click on image for full picture
IL is a diameter, which is a straight line, which is equal to 180 degrees.
The arc of IL would be 180 degrees
You are told the arc of KL is 30 degrees.
The major arc of ILK would be 180 + 30 = 210 degrees.
The amount a money in the bank account can be expressed by the exponential equation A=300(1.005)^12t where A is the amount in dollars and t is the time in years. About how many years will it take for the amount in the account to be more than $900?
Answer:
It will take more than 18.35 years for the amount in the account to be more than $900
Step-by-step explanation:
The amount in the bank account can be expressed by the exponential equation :
[tex]A=300(1.005)^{12t}[/tex]
Where A is the amount in dollars
t is the time
We are supposed to find About how many years will it take for the amount in the account to be more than $900
So, [tex]300(1.005)^{12t} >900[/tex]
[tex](1.005)^{12t} > \frac{900}{300}[/tex]
[tex](1.005)^{12t} > 3[/tex]
t>18.35
Hence It will take more than 18.35 years for the amount in the account to be more than $900
Answer:
19th year
Step-by-step explanation:
19th year
Elan surveyed a random sample of 65 students at his high school. He asked them which subject is their first class on Mondays. There are 894
students in his school.
First Class Percent of Students
English
17%
Math
28%
History
40%
Science
15%
Choose two inferences that can be made from the results.
O A. Approximately 17% of all students in the city have English first on Mondays.
B. Approximately 28% of the students at Elan's school have Math first on Mondays.
C. Approximately 40% of the students at Elan's school do not have History first on Mondays.
OD. Approximately 85% of the students at Elan's school do not have Science first on Mondays.
Answer:
B and D are correct
Step-by-step explanation:
A isn't correct because the survey wasn't out of students in the city, it was out of people attending Elan's school.
B is correct because the survey said 28% of students at Elan's school have math first on mondays.
C isn't correct because the survey said the exact opposite.
D is correct because only 15% of students at Elan's school have science first on mondays
Answer:
B and D
TRUST ME
Step-by-step explanation:
Which correctly describes the consistency of the speeds of the cars in the two races? The speeds in race A are likely to be near 170 mph and the speeds in race B are likely to be near to 165 mph. The speeds in race A are likely to be near 153 mph and the speeds in race B are likely to be near to 145 mph. The speeds in race A are likely to be near 120 mph and the speeds in race B are likely to be near to 125 mph. The speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near to 153 mph.
This question is not complete.
Complete question
The box plots show the average speeds, in miles per hour, for the race cars in two different races.
Average Speeds of Cars in Race A
120.
125
130
135
140
145
150
155
160
165
170
Find attached to this question, the picture of the box plots.
Which correctly describes the consistency of the speeds of the cars in the two races?
a. The speeds in race A are likely to be near 170 mph and the speeds in race B are likely to be near to 165 mph.
b. The speeds in race A are likely to be near 153 mph and the speeds in race B are likely to be near to 145 mph.
c. The speeds in race A are likely to be near 120 mph and the speeds in race B are likely to be near to 125 mph.
d. The speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near to 153 mph.
Answer:
d. The speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near to 153 mph.
Step-by-step explanation:
For the boxplot for Race A, the following is obtained from the attached diagram
The range of speed of the race is= Highest - Lowest
170 - 120= 50
The 1st Quartile is = 142
The 2nd Quartile is = 153
The 3rd Quartile is = 165
The Inter quartile range = 3rd quartile - 1st quartile = 165-142= 23
For the boxplot for Race B
The following values is obtained from the attached image.
The range of speed of the race is
Highest speed - Lowest speed
165 - 125= 40
The 1st Quartile is = 139
The 2nd Quartile is = 145
The 3rd Quartile is 150
The Inter quartile range = 3rd quartile- 1st quartile = 150 - 139 = 11
From the values above, we can see that ,
The speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near to 153 mph.
The common ratio of a geometric series is 3 and the sum of the first 8 terms is 3280.
What is the first term of the series?
Answer:
The first term of the geometric series is 1
Step-by-step explanation:
In this question, we are tasked with calculating the first term of a geometric series, given the common ratio, and the sum of the first 8 terms.
Mathematically, the sum of terms in a geometric series can be calculated as;
S = a(r^n-1)/( r-1)
where a is the first term that we are looking for
r is the common ratio which is 3 according to the question
n is the number of terms which is 8
S is the sum of the number of terms which is 3280 according to the question
Plugging these values, we have
3280 = a(3^8 -1)/(3-1)
3280 = a( 6561-1)/2
3280 = a(6560)/2
3280 = 3280a
a = 3280/3280
a = 1
Final answer:
To find the first term of a geometric series with a common ratio of 3 and a sum of the first 8 terms being 3280, we use the sum formula for a geometric series and isolate the first term 'a'. After plugging in the values and simplifying, we find that the first term 'a' is equal to 1.
Explanation:
The student is asking about the first term of a geometric series with a known common ratio and the sum of the first 8 terms. The common ratio for this series is 3, and the sum of the first 8 terms (S8) is 3280. To find the first term (a), we'll use the following formula for the sum of the first N terms of a geometric series:
S_N = a * (1 - x^N)/(1 - x),
where 'SN' is the sum of the first N terms, 'a' is the first term, 'x' is the common ratio, and 'N' is the number of terms. In this case, x=3 and S_8=3280.
Solving for 'a' gives us:
3280 = a * (1 - 3^8)/(1 - 3)
The first term (a) can now be calculated by isolating 'a' on one side of the equation.
a = 3280 / ((1 - 3^8)/(1 - 3))
a = 3280 / (1 - 6561)/(-2)
a = 3280 / (6560/2)
a = 3280 / 3280
a = 1.
Therefore, the first term of the geometric series is 1.
The areas of the squares adjacent to two sides of a right triangle are 32units^2 and 32 units^2. Find the length, x, of the third side of the triangle.
Answer:
The length of the third side of the triangle is 8 units
Step-by-step explanation:
Here, since the two sides are adjacent a square, what this means is that the length of the square equals the length of the sides of the triangle adjacent to it.
Mathematically, the formula for the area of a square is L^2
With an area of 32 square units, the length of the side of this triangle is thus √(32) =
4√2 units
So we have two sides of the right triangle with length 4√2 units
Now we should know that this right triangle is an isosceles right triangle since the lengths of the adjacent and the opposite are equal.
Now to calculate the length of the third side which is the hypotenuse, we make use of the pythagoras’ theorem which states that the square of the longest side of a right triangle which is the hypotenuse is equal to the sum of the squares of the other two sides
Thus mathematically, the square of the hypotenuse length is 32 + 32 = 64
Let’s call the hypotenuse h for documentation purposes
h^2 = 64
h = √64
h = 8 units
Answer:
8
Step-by-step explanation:
khan is never wrong :3
A scale on a map shows that 2.5 centimeters represent 15 kilometers.
What number of actual kilometers are represented by 17.5 centimeters on the map?
Answer:
cm for centimeters, km for kilometers.
If 2.5cm → 15 km, then
17.5 cm → x km
x= (15km*17.5cm)/(2.5cm)=105 km
Step-by-step explanation:
A shoebox in the shape of a right rectangular prism has a base that measures 7 inches by 12 inches and is 5 inches high. What is the volume of the shoe box, in cubic inches?
35 a
84 b
245 c
420 d
Answer:
D. 420
Step-by-step explanation:
The volume of a right rectangular prism is given as:
V = L * W * H
where L = length
W = width
H = height
The shoebox has dimensions 7 inches by 12 inches and is 5 inches. Therefore, its volume is:
V = 7 * 12 * 5 = 420 cubic inches
The volume of the shoebox in cubic inches is 420.
A group of 5 families at Baileys Middle School sold magazine subscriptions to raise money for the school. $6.00, $7.00, $4.00, $5.00, $3.00 What was the median amount of money raised?
Answer:
The median amount of money raised is $5.00
Step-by-step explanation:
To find the median amount of money raised, we will follow the steps below:
First, arrange the data giving in ascending order. That is
$6.00, $7.00, $4.00, $5.00, $3.00
We will arrange it in ascending order, hence
$3.00, $4.00, $5.00, $6.00, $7.00
The median is the middle number, we will now proceed to take the middle number.
The middle number is $5.00
Therefore, the median amount of money raised is $5.00
The median amount of money raised by the 5 families is $5.00.
To find the median amount of money raised by the 5 families, we first need to arrange the amounts in ascending order:
$3.00$4.00$5.00$6.00$7.00The median is the middle number in a sorted, ascending or descending, list of numbers. Since there are 5 numbers, the median is the third number in this ordered list. Therefore, the median amount of money raised is $5.00.
Please help with this math
Answer:
I believe it’s C
Step-by-step explanation:
let me know if right if am mark brainliest pls
Solve this please!!!
Answer:
x = 17
Step-by-step explanation:
These angles are supplementary so (2x + 5) + (8x = 5) = 180 then you just do the algebra
Please mark Brainliest :)
Thiago and Yasmine each bought the same microwave.
Thiago used the 20% off coupon and paid $100.
Yasmine used the $20 off coupon.
How much did she pay?
Answer:
$105
Step-by-step explanation:
20% of $125 = $100
so the original price is $125
Answer:$100
Step-by-step explanation:
if they both used the 20% off coupon for the same microwave which is the same price without the coupon then with the coupon it would also be the same price
9 m
11 m
16 m
4 m
Find the area of this figure.
Answer:
Can u send picture with it pls so i can figure it out?
What are the two shapes
Step-by-step explanation:
rectangle: length times width
triangle: base times height divided by 2
parallelgram: Base times height
square: side times side
*If you get it right then follow me on roblox: Supertasticgg
and sub to Flamingo
ANd almost forgot trapezoid: base 1 + base 2 times by height then divide with 2
Somebody help me!!!
What is the area of the rectangle in the coordinate plane?
Answer:
The answer is 5 x 13. Google it bruh
Step-by-step explanation:
Need help finding the answer
Answer: x=2
Use math-way and put 3x+4/6x-2=9/9
What is a segment with its endpoints on the planes of
the bases that is perpendicular to the planes
of the bases?
Answer:
Altitude of a Cylinder
Step-by-step explanation:
Altitude of a Cylinder can be seen as a form of segment between the plane of a base to the plane of another base in which the height of the cylinder can be said to also be the length of the altitude meaning both the height and the length of the cylinder can be said to be equal which is why the axis of a cylinder is the segment which contains the centers of the two bases.
ALTITUDE OF A CYLINDER can also be seen as the distance between the bases of a cylinder which is the shortest line segment that occur between the possibly extended bases which is why ALTITUDE OF A BASE is a segment with its endpoints on the planes of
the bases that is perpendicular to the planes
of the bases.
A snack stand sold hot dogs and chips at a recent game. The hot dogs cost $2.50 and the snacks cost $0.75. After the game, they tallied 175 transactions totaling $262.50.
Represent the linear system in an augmented matrix:
ANSWER IS
[ 1 ] [ 1 ] [ 75 ]
[ 2.5 ] [ 0.75 ] [ 262.5 ]
Answer:
[1] [1] [175]
[2.5] [0.75] [262.5]
# of hotdogs sold was 75
# of chips sold was 100
Step-by-step explanation:
got it right on edge ya digg
The number of hot dogs is 75 while the number of snacks is 100.
The linear equation to solve the question will be:
h + s = 175 ........ i
2.50h + 0.75s = 262.50 ........ ii
From equation i, s = 175 - h ..... iii
Put equation iii into ii
2.50h + 0.75s = 262.50
2.50h + 0.75(175 - h) = 262.50
2.50h + 131.25 - 0.75h = 262.50
Collect like terms
2.50h - 0.75h = 262.50 - 131.25
1.75h = 131.25
h = 131.25/1.75
h = 75
The number of hot dogs is 75 while the number of snacks is 100.
Read related link on:
https://brainly.com/question/16054860
What are the solutions to the quadratic equation (5y+6)2=24?
Answer:
You chose the right answer
y = [ -6 + 2 root(6)]/5 or y = [-6 - 2 root(6)]/5
Step-by-step explanation:
from (5y + 6)^2 = 24
we can take the square root of both sides
(5y + 6) = + root(24) or (5y + 6) = -root(24)
5y + 6 = 2*root(6) or 5y + 6 = - 2 root(6)
y = [ -6 + 2 root(6)]/5 or y = [-6 - 2 root(6)]/5
Answer:
a
Step-by-step explanation:test on e
In 1906 Americans consumed an average of 26.85 gallons of whole milk per year. By 1998 the average consumption was 8.32 gallons. What is the percent decrease in consumption of whole milk?
Answer: 69.01%
Step-by-step explanation:
In 1906 Americans consumed an average of 26.85 gallons of milk per year while by 1998 the average consumption was 8.32 gallons.
To get the percent decrease in consumption of whole milk goes thus:
We first find the amount of decrease in the milk consumed. This will be:
= 26.85 - 8.32
= 18.53
Percentage decrease
= 18.53/26.85 × 100
= 0.6901 × 100
= 69.01%
8x-2y=6 and 3x+3y=-24
Answer:y= -8 -x
Step-by-step explanation:
4. A class has 12 boys and 15 girls. The teacher randomly picks one child to lead
the class in singing.
What is the probability that the teacher picks a boy?
Answer:4/9
Step-by-step explanation:
12/27 simplified is 4/9
(12 is for the boys 27 is the number of students)
Each side length is tripled. Describe the change in the area. What is the
new area?
6.4 cm
4 cm
5 cm
When Belinda asked him to what pages his book was opened, he replied that the product of the facing pages was 87,912. To what pages did Theo open his textbook?
Final answer:
To determine the page numbers, the product of two consecutive page numbers (n and n+1) was calculated to match 87,912, leading to the solution that Theo's textbook was opened to pages 296 and 297.
Explanation:
To find out to which pages Theo opened his textbook, when the product of the facing pages was 87,912, we should realize that facing pages in books have consecutive numbers. Therefore, if one page is n, the facing page would be n+1. The product of these two pages is n(n+1)= 87,912. We are solving a quadratic equation here.
Starting with an approximation, square roots of numbers near 87,912 can help identify potential page numbers. The square root of 87,912 is a bit less than 300 (since 300² = 90,000). Therefore, one of the page numbers will be just under 300, and the other just above.
Attempting a few calculations, we notice that 296² = 87,616 and 297² = 88,209. Between these two, 296 × 297 = 87,912, giving us the page numbers Theo's book is open to: 296 and 297.
What is 60% of 60 minutes?
Answer:
36 minutes
Step-by-step explanation:
60(.6)= 36
David loves his dog Thor and he wants to create a rectangular enclosure that has an area of 1600ft² for the dog to stay in while no one is home. David has a total of 120 feet of fencing available and he wants to use the wall of his garage as one of the sides of the enclosure. What are the dimensions of the enclosure?
Make a Sketch of the rectangular enclosure and label the sides using variable(s).
Write and solve an equation(s) that model this situation.
What are the dimensions of the rectangular enclosure?
Answer:
80 feet by 20 feet
Step-by-step explanation:
Area of the rectangular enclosure = 1600ft²
Area, lw=1600
w=1600/l
Perimeter, 2w+l=120 feet
Substituting w=1600/l into the perimeter
2(1600/l)+l=120
3200/l+l=120
[tex]\dfrac{3200+l^2}{l}=120\\ 3200+l^2=120l\\l^2-120l+3200=0\\l^2-40l-80l+3200=0\\l(l-40)-80(l-40)=0\\(l-40)(l-80)=0\\l-40=0\:or\:l-80=0\\l=40\:or\:l=80[/tex]
When l=40, w=1600/40=40 feet
When l=80, w=1600/80=20 feet
Since the enclosure is rectangular, the acceptable dimensions are:
Length =80 feet
Width =20 feet