The amount that results when $2,000 is compounded at 8% annually over six years.
Answers
A=p (1+r)^t
A future value?
P present value 2000
R interest rate 0.08
T time 6 years
A=2,000×(1+0.08)^(6)
A=3,173.75
Interest earned
3,173.75−2,000=1,173.75
Related Questions
A gardener has an area 320 sq ft. its width is 4 feet less than its length. what are the dimensions of the garden?
Answers
A = 320 sq ft.
L = W + 4
W = L - 4
P = L + L + W + W
The dimensions are:
L = 20 ft
W = 16 ft
P = 72 ft
I hope this helped! :c
Answer: C
Step-by-step explanation:
Which rigid transformation would map ΔAQR to ΔAKP?
Answers
Answer:
A. Rotation around point a
Step-by-step explanation:
I hope this helps.
Increase 140g by 12.5%
Answers
add that to 140 and you get 157.5g
157.5 g is when 140g is increase by 12.5%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Initial amount = 140 g
Final amount.
= 140 + (12.5% x 140)
12.5% = 12.5/100 = 125/1000 = 0.125
= 140 + (0.125 x 140)
= 140 + 17.5
= 157.5 g
Thus,
The final quantity is 157.5 g.
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Square root of 1/121 simplified
Answers
=1/11
need to use some extra characters
The square root of the given number 121 is 11.
What is the square root?The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.
The given number is √121.
We need to find the square root of given numbers.
Here, 121=11×11
= 11²
So, √121 = √11²
= 11
Therefore, the square root is 11.
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Which type of function best models the data in the table below?
A. inverse variation
B. linear
C. logarithmic
D. quadratic
Answers
Answer: Option A inverse variation
Explanation:
when we compare the values from the given table x is increasing and y is decreasing hence we can see it is an inverse variation.
In option B difference among all consecutive values of x is 2 but in y it is not same among all consecutive terms. In linear function change in y over change in x must be same.
In option C x is increasing but y is decreasing which is violating the property of logarithmic function. In logarithmic function if x increases then y should increase.
In option D first value of x is 2 following quadratic property meaning giving square of itself in y which is 4. But not all values of y are square of x except first value. In quadratic function value of y should be square of x.
The type of function that best models the table given is: A. inverse variation.
What is Inverse Variation?Inverse variation can be described as a relationship between two variables, whereby, the product of the two variables will give a constant. It is expressed as, k = xy.
In an inverse variation, if one variable increases, the other variable decreases.
The table shows an inverse variation because as x increases, y decreases, and can be expressed as k = xy.
Therefore, the type of function that best models the table given is: A. inverse variation.
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Given that v^y = 1/ 5 root v,
Work out the value of y.
Answers
So if v^y = 1/(V^(1/5)), then v^y = V^(-1/5) because X^(-1) = 1/X
Thus you get y = -1/5 because V^y = V^(-1/5)
Hope this helps!
what are the real solutions
Answers
Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is 1 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 2
x2 - 1x + 2x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-1)
Add up the last 2 terms, pulling out common factors :
2 • (x-1)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-1)
Which is the desired factorization
A snail travels at a rate of 2.44 feet per minute. • Write a rule to describe the function. • How far will the snail travel in 7 minutes?
Answers
Expression: 2.44*7=
You can represent the measures of an angle and its complement as x° and (90 − x)°. Similarly, you can represent the measures of an angle and its supplement as x° and (180 − x)°. Use these expressions to find the measures of the angles described. The measure of an angle is equal to four times the measure of its supplement. The measure of the angle is ° and the measure of its supplement is °.
Answers
x = 720 - 4x
4x + x = 720
5x = 720
x = 720/5
x = 144
180 - x =
180 - 144 =
36
the measure of the angle is 144...the measure of its supplement is 36
To determine the size of an angle and its supplement when the angle is four times the size of its supplement, we use the equation x = 4(180 - x) and solve for x to find that the angle measures 144 degrees and its supplement measures 36 degrees.
To find the measures of an angle and its supplement when the angle is four times its supplement, we use the expressions x and 180 - x. We can set up the equation x = 4(180 - x). Then we can solve for x to find the measures of the angle and its supplement.
By expanding and rearranging the equation, we get:
x = 720 - 4x5x = 720x = 144Thus, the angle measures 144 degrees and its supplement measures 36 degrees (since 180 - 144 = 36).
Which statement is needed to complete this syllogism?
If two angles are vertical, then the angles are congruent.
If two angles are congruent, then the angles have equal measure.
Therefore, if ________________________, then the angles have equal measure.
two angles are vertical
two angles have equal measure
two angles are congruent
There is not enough information to say.
Answers
Answer:
Step-by-step explanation:
It IS "two angles are vertical".
I answered wrong on my quiz and got corrected to this answer.
△XLW≅△XDG.
What is length of line GX?
Answers
GX = WX = 5.7
hope it helps
we know that
The CPCTC states that corresponding parts of congruent triangles are congruent
so
△XLW≅△XDG.
that means
[tex]XL=XD\\LW=DG\\XW=XG[/tex]
we have
[tex]XL=6.2\ units\\LW=4.5\ units\\XW=5.7\ units[/tex]
therefore
[tex]GX=5.7\ units[/tex]
the answer is
the length of GX is [tex]5.7\ units[/tex]
An open box can hold 80 cm3. It is made from a square piece of tinplate with 3 cm squares cut from each of its 4 corners. Find the dimensions of the original piece of tinplate.
Answers
The height of the box is 3 cm.
The length & width are both (x-6) cm.
volume = length*width*height
=3*(x-6)*(x-6)
=80
x can then be obtained by solving
3(x-6)(x-6)=80
Volume of Open box which is made from square piece of tinplate=80 cm³
⇒Squares of side 3 cm is cut from 4 of it's corner.It means the square boxes are cubical.
Volume of cube=Side × Side × Side
=(Side)³
Volume of 4 cubical box having each side 3 cm
=4×3×3×3
=108 cm³
Total Volume of box=108 cm³ +80 cm³=188 cm³
Since the box is open .
Let the dimension of box be
Length= x cm
Breadth= x cm
Height = x cm
Volume of Original box=188 cm³
[tex]\rightarrow x^3=188\\\\\rightarrow x=(188)^{\frac{1}{3}}\\\\x=5.728\text{approx}[/tex]
So, Original dimension of cubical Square Box=5.73 cm(Approx)
Calculate the slope of the line that goes through the points (-15,70) and (5,10)
Answers
The slope of the line that goes through the point (-15,70) and (5,10) is - 3.
What is slope?The slope is the measure of the angle a line has with respect to the positive x-axis.
We know when two points of a line is given slope can be obtained by rise over run where the rise is the difference between the points of the y-axis and run is the difference of the points of the x-axis.
Given points are (-15,70) and (5,10) through which a line passes.
∴ Slope(m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Slope(m) = (10 - 70)/(5 + 15).
Slope(m) = -60/20.
Slope(m) = -3.
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The area of a rectangle is 14 yd2 , and the length of the rectangle is 3 yd less than twice the width. find the dimensions of the rectangle.
Answers
2x-3= length
(2x-3)(x)=14
2x^2-3x=14
2x^2-3x-14=0
(2x- 7)(x+2)=0
x=7/2 or x=-2
Since we know that negative values cannot exist in distance, we have to take 7/2 to as the correct answer.
The width would be 3.5 yards
Length= 2(3.5)-3
=4 yards
3.5 x 4 yards is the dimension of the rectangle
Hope I helped :)
The dimensions of the rectangle are 4 yd by 7/2 yd
How to determine the dimensions of the rectangle?The area is given as:
Area = 14 yd^2
Let the width be x. So, the length is:
Length = 2x - 3
The area is then calculated as:
Area = (2x - 3) * x
Expand
Area = 2x^2 - 3x
Substitute 14 for Area
2x^2 - 3x = 14
Rewrite as:
2x^2 - 3x - 14 = 0
Factorize
(2x- 7)(x+2)=0
Solve for x
x=7/2 or x=-2
Width cannot be negative.
So, we have:
x = 7/2
Substitute x = 7/2 in Length = 2x - 3
Length = 2 * 7/2 - 3
Evaluate
Length = 4
Hence, the dimensions of the rectangle are 4 yd by 7/2 yd
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In the diagram above, rectangles DEFG and WXYZ are similar. The ratio of the area of DEFG to WYXZ is 1:4. A student's work to find ZY is shown below. Describe and correct the error in finding ZY.
Answers
The area ratio should be 1:4, so if l×w = area (a) of DEFG, then L×W = Area (A) of WXYZ.
Since 4:1 is 4×1, A = 4×a or 4a
Since GF is length (l) and is 12, we can say that 12w = a
12×4 = 48 for length of ZY (L), and WX is also 48, and to find W would be: 48W = A
48W = 4a, since A=4a
Not sure what else you want by the limited information given!
Approximately how many kcal are contained in 3 ounces of 80-proof rum?
Answers
Now, we need to convert the cal into kcal. We know that:
1 cal = 1000 kcal
Therefore,
200,000 cal = 200 kcal
Find the coordinates of the midpoint of the segment whose endpoints are H(8,2) and K(6,10).
Answers
=( 7, 10 ) That's the final answer.
The coordinates of the midpoint of the segment HK are (7, 6).
The midpoint coordinates of a line segment can be found using the midpoint formula:
Midpoint =[tex]\((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\)[/tex]
Given the endpoints of the segment as H(8,2) and K(6,10), let's plug these values into the formula:
Midpoint =[tex]\((\frac{8 + 6}{2}, \frac{2 + 10}{2})\)[/tex]
Midpoint =[tex]\((\frac{14}{2}, \frac{12}{2})\)[/tex]
Midpoint =[tex]\((7, 6)\)[/tex]
The coordinates of the midpoint of the segment HK are (7, 6).
To calculate the midpoint of a line segment, you can follow these steps:
1. Identify the coordinates of the endpoints of the segment. Let's call them[tex]\( (x_1, y_1) \) and \( (x_2, y_2) \).[/tex]
2. Use the midpoint formula:[tex]\( \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).[/tex]
3. Substitute the coordinates into the formula and calculate.
In this case, the endpoints are H(8,2) and K(6,10). Plug these values into the midpoint formula:
Midpoint = [tex]\( \left( \frac{8 + 6}{2}, \frac{2 + 10}{2} \right) \).[/tex]
Simplify the equation:
Midpoint =[tex]\( \left( \frac{14}{2}, \frac{12}{2} \right) \).[/tex]
Finally, calculate the values:
Midpoint =[tex]\( (7, 6) \).[/tex]
So, the coordinates of the midpoint of the segment HK are (7, 6).
complete question
Find the coordinates of the midpoint of the segment whose endpoints are H(8,2) and K(6,10).
How many times larger is 9 x 10-4 than 3 x 10-10? A) 3 x 10^5 B) 3 x 10^6 C) 6 x 10^5 D) 6 x 10^6
Answers
Answer B.
Answer:
The correct option is B.
Step-by-step explanation:
We need to find how many times larger is [tex]9\times 10^{-4}[/tex] than [tex]3\times 10^{-10}[/tex].
Let [tex]9\times 10^{-4}[/tex] is x times larger than [tex]3\times 10^{-10}[/tex].
[tex]x\times 3\times 10^{-10}=9\times 10^{-4}[/tex]
Divide [tex]3\times 10^{-10}[/tex] on both sides.
[tex]x=\frac{9\times 10^{-4}}{3\times 10^{-10}}[/tex]
It can be written as
[tex]x=\frac{9}{3}\times \frac{10^{-4}}{10^{-10}}[/tex]
[tex]x=3\times \frac{10^{-4}}{10^{-10}}[/tex]
Using quotient property of exponent, we get
[tex]x=3\times 10^{-4-(-10)}[/tex] [tex][\because \frac{a^m}{a^n}=a^{m-n}][/tex]
[tex]x=3\times 10^{-4+10}[/tex]
[tex]x=3\times 10^{6}[/tex]
[tex]9\times 10^{-4}[/tex] is [tex]3\times 10^{6}[/tex] times larger than [tex]3\times 10^{-10}[/tex].
Therefore the correct option is B.
What is 4527 written in scientific notation?
Answers
8(10−k)=2k
solve for k
Answers
The value of k is 8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
8 (10 - k) = 2k
Multiplication over subtraction.
8 x 10 - 8k = 2k
80 - 8k = 2k
Combine like terms.
80 = 2k + 8k
80 = 10k
Divide both sides with 10
k = 8
Thus,
The value of k is 8.
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Which type of sandwich consists of two slices of bread or two halves of a roll, a spread and a filling?
Answers
The formula that describes an object's motion is given by S=ut+1/2at^2 , where S is the distance traveled, u is the initial velocity, a is the acceleration , and t is the time.
Which equation represents a in terms of the other variables?
A. a= 2S-2u/t
B. a=2S+2u/t
C. a=2S-2ut/t^2
D. a=2S+2ut/t^2
Answers
(1/2)a(t²) = S - ut Multiply both sides by 2
a(t²) = 2s - 2ut Divide both sides by t²
a= 2s/t² - 2u/t
a= (2S - 2ut)/t²
Answer is C) but there should be parentheses around the term (2S-2ut)
The sum of two consecutive odd integers is 72 write an algebraic equation to determine the two integers
Answers
if its sum is 56
means:
x+ (x+2) = 56
2x = 56 -2
x= 54/2
x= 27
27 is the first odd number and the second is 27 + 2 i.e. 29
------------------------
sum of two numbers is 72
let smaller: x
larger: 4+x
its sum:
(4+x) + x = 72
4+2x=72
x= 68/2
x= 34
smaller is 34 and the larger is 34 + 4 = 38
I AM SO CONFUSED ????
4. The following function defines a recursive sequence.
f(0) = -4
f(1) = 12
f(n) = -3•f(n -1) - 2•f(n - 2); for n > 1
Which of the following sequences is defined by this recursive function? (4 points)
a) -4, 12, -28, 60,
b) -4, -12, -28, -60,
c) -4, 12, -18, 54,
d) -4, 12, -18, -54,
Answers
=-3f(1)-2(0)
=-3*12-2*-4
=-36+8
=-28
we have f0,f1,f2,f3 is last
we know -4,12,-28, i leave it to u to find f(3)
plug in n=3 and solve
Adam wrote a check for $38 to pay his monthly gas bill, but when balancing his checkbook, he accidently recorded it as a credit rather than his debit. How will his check register compare to his monthly bank statement when he receives it?
Answers
Answer:
76 dollars more
Step-by-step explanation:
Given that Adam wrote a check for $38 to pay his monthly gas bill.
Normally cheques issued would be debited to the account maintained by the customer thus making the balance less than the previous one.
If the customer had x as balance after cheque issued the balance would be x-38
This is a debit entry
But since Adam by mistake entered as credit, he would have recorded in his books balance as x+38
Thus as a result of this
Adam check register shows x+38-(x-38)
= 76 dollars more than monthly bank statement
Bob is hiking down a 60-mile country trail. He could hike at 10 mph for the first two hours and then go the rest of the way at 30 mph or he could just go the whole way at 20 mph. How long would each of these options take? Which option is the faster?
Answers
Time taken for option two: 20mph (3 hours)
Calculate the time taken by option one, 30 mph:
60=20+30x
40/30=x
4/3 =x
1+1/3=x
It would take (option 1): 2+1+1/3= 3 1/3 hours to complete
It would take (option 2): 3 hours
Therefore, option two is faster.
Hope I helped :)
With the first option the hiking has two stages
Stage 1
Hike for
[tex]speed \: = 10mph[/tex]
for
[tex]time = 2 \: hours[/tex]
The distance covered in this stage 1 can be determined using the formula,
[tex]Speed = \frac{distance}{time \: taken} \\ \\ \\ \\10mph = \frac{distance}{2 \: h} \\ \\ \\ distane = 2 \times 10 = 20miles[/tex]
Stage 2
At this stage,the remaining distance to be covered
[tex] = 60 -20 = 40miles[/tex]
We can again calculate the time take to cover this distance using
[tex]Speed = \frac{distance}{time \: taken} \\ \\ \\ 30mph = \frac{40miles}{time \: taken} \\ \\ \\ time \: taken \: = \frac{40miles}{30mph} \\ \\ \\ \\ time \: taken \: = 1 \frac{1}{3} hours[/tex]
The total time taken for this option
[tex] = 2 \: hours \: + 1\frac{1}{3} hours = 3 \frac{1}{3} \: hours[/tex]
OPTION 2
For this option, the hiker goes 30mph throughout the whole journey for
[tex]speed = \frac{distance}{time \: taken} \\ \\ \\ \\ \\ 30mph = \frac{60}{time \: taken } \\ \\ time \: taken = \frac{60}{30} = 2 \: hours[/tex]
For the first option, it took the hiker 3⅓ hours but for the second option, it took him 2 hours.
[tex]<b>Therefore the second option is faster.</b>[/tex]
Alice and her friend want to meet for lunch at a point halfway between their homes. Alice's home can be represented by the point (-1, 2) and her friend's home by the point (3, 4). What are the coordinates of the point that represents the location where they should meet?
Answers
to find midpoint add the 2 x numbers and divide by 2
and add the 2 y numbers and divide by 2
X = -1 + 3 = 2, 2/2 =1
Y = 2 +4 = 6, 6/2 = 3
coordinate is (1,3)
The coordinates of the point that represents the location where they should meet is (1,3).
Given that,
Alice's home can be represented by the point (-1, 2).And, her friend's home by the point (3, 4).Based on the above information, the calculation is as follows:
X = -1 + 3 = 2,[tex]2\div2 =1[/tex]
Y = 2 +4 = 6, [tex]6\div2 = 3[/tex]
Therefore we can conclude that the coordinates of the point that represents the location where they should meet is (1,3).
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A football team gained 6 yards on a first down, lost 15 yards on the second down, and gained 12 yards on the third down. how many yards do they need to gain on the fourth down to have a 10 yard gain from their starting position?
Answers
then to -9 + 12 which is, 3
So then see how many something + 3 = 10
which is, 7
So 7 is your final answer
Answer:
They need to earn 7 yards on the fourth down to have a 10 yard gain from their starting position
Step-by-step explanation:
To gain a new set of downs, a football team has four downs(tries) to gain 10 net yards, in total.
Gained 6 yards on first down
Net of 6 yards gained
Needs 10-6 = 4 yards
Lost 15 yards on second down
6 - 15 = -9
In all, they have lost 9 yards, so they need
4 + 15 = 19 yards
Gained 12 yards on third down
-9 + 12 = 3 net yards(need 10)
19 - 12 = 7
They need to earn 7 yards on the fourth down to have a 10 yard gain from their starting position
What percent of 10 is 6?
Answers
4/10 40%
5/10 50%
6/10 60%
7/10 70%
To determine what percent of 10 is 6, you multiply 6/10 by 100, which equals 60%, thus 6 is 60% of 10.
Explanation:To find what percent of 10 is 6, we can use the formula for percentage which is (Part / Whole) * 100.
In this case, the 'part' is 6 and the 'whole' is 10.
So the equation to find the percentage is (6 / 10) * 100.
Calculating that out, we get 0.6 * 100, which equals to 60%.
Therefore, 6 is 60% of 10.
This is a basic concept in mathematics where you are trying to find out how one number compares to another in terms of percentage.
How much simple interest is earned on 6,000 at an interest rate of 2.25% in 4 1/2
Answers
I=prt
I interest earned?
P principle 6000
R interest rate 0.0225
T time 4 1/2 means 4 years and half
Which is 4.5 (4+1/2)
I=6,000×0.0225×4.5
I=607.5....answer
Hope it helps!