The equation needed to calculate the compound interest is [tex]A = P(1 +\frac{r}{n} )^{nt}[/tex]
The value of the account after ten years is $9347.62 .
If the account is left alone for 20 years, the amount of interest earned is $6942.76
How to calculate compound interest?The compound interest formula is represented as follows;
[tex]A = P(1 +\frac{r}{n} )^{nt}[/tex]
where
A = amountP = principalr = raten = compounded months, years etc.t = time in yearsTherefore,
where
r = 3.7% = 3.7 / 100 = 0.037
n = 1
t = 10
P = $6500
Hence,
[tex]A = 6500(1+\frac{0.037}{1} )^{1(10)}[/tex]
[tex]A = 6500(1.037)^{10}[/tex]
[tex]A = 6500(1.43809495884)[/tex]
A = 9347.61723247
A = $9347.62
The value of the account after ten years is $9347.62
Interest = 9347.62 - 6500 = 2847.62 dollars
When it is 20 years.
r = 3.7% = 3.7 / 100 = 0.037
n = 1
t = 20
P = $6500
Hence,
[tex]A = 6500(1+\frac{0.037}{1} )^{1(20)}[/tex]
[tex]A = 6500(2.06811711064)[/tex]
A = 13442.7612192
A = $13442.76
Interest = 13442.76 - 6500 = 6942.76 dollars
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Simplify.
(7sqrt(2))(3sqrt(3))
A sqrt(14) * sqrt(9)
B. 10sqrt(5)
C. 21sqrt(6)
D. 10sqrt(6)
E. 63
Answer:
21sqrt(6)
Step-by-step explanation:
Hope it helps......
pls help the question is here (12points) DUE TO DAY
Answer:
[tex]\bf Area= 90\;in[/tex]
Step-by-step explanation:
Area of ABCD = L * W
[tex]\bf 6\times 12[/tex]
[tex]\bf 72 \;in^2[/tex]
Area of EFGC:- L * W
[tex]\bf 6 \times 3[/tex]
[tex]\bf 18\; in^2[/tex]
Now, the area of the combind rectangles:-
ABCD + EFGC
[tex]\bf 72+18[/tex]
[tex]\boxed{\bf 90\; in}[/tex]
-2/3(x+12)+2/3x= -5/4x +2
show your work thanks! :)
Answer:
Step-by-step explanation:
PLEASE ANSWER FAST! NO LINKS!
Answer:
the first one
Step-by-step explanation:
absolute value is a number's distance from zero, so distance from zero can not possibly be negative. Therefore, |4x-2|=-6 has no solution.
Answer:
It would be the first one because there is no value of x that makes the equation be true since an absolute value can never be negative.
Step-by-step explanation:
Hope this helps:)....if don't help then sorry for wasting your time and may God bless you:)
∣x−7∣<9 what is the answer
Answer:
x < 16
Step-by-step explanation:
∣x−7∣ < 9
x < 9 + 7
x < 16
Answer:
7x < 9
Step-by-step explanation:
because the absolute value of -7 is 7 and 7 + x = 7x.
Find the area please!!!
Answer:
32.24
Step-by-step explanation:
To get the height, use Pythagoras theorem on the smaller triangle
8^2=2^2+x^2
x^2=64-4
x=√60=2√15.
then for the base use P.T for the bigger triangle
10^2=y^2+√60^2
y^2=100-60
y=√40=2√10
1/2×(2√10+2)×2√15
=32.24
Which is f(5) for the function –2x2 2x – 3? –107 –63 –43 –37
Answer:
- 43
Step-by-step explanation:
f ( x ) = - 2x² + 2x - 3
To find : f ( 5 )
f ( 5 ) = f ( x )
Here,
x = 5
f ( 5 ) = - 2x² + 2x - 3
= - 2 ( 5 )² + 2 ( 5 ) - 3
= - 2 ( 25 ) + 10 - 3
= - 50 + 7
f ( 5 ) = - 43
Answer:
-43
Step-by-step explanation:
oon edge
mark me brain
Which deal is better $1.95 for 5 kg or $0.96 for 2 kg
Answer:
$1.95 for 5kg
Step-by-step explanation:
0.96 x2 is 1.92 and not even 5kg so if you get 5kg worth of the 0.96$ per kg then it will be more expensive.
So $1.95 for 5kg is the better deal.
Please help me asap with my grade 11 trigonometry math! I'll give brainliest, please help, thank you. *URGENT*
Answer:
Around 295m
Step-by-step explanation:
Answer:
295.44 m to the neaest hundredth
Step-by-step explanation:
A line drawn from the kite perpendicular to the ground forms 2 right triangles. Let this line be x m.
Also let y be the distance from Allison to the bottom of the line.
Consider 'Alison' triangle
cos 70 = y/150
y = 51.303 m
sin 70 = x/150
x = 150 sin 70 = 140.954 m
Consider 'Marcs' triangle
tan 30 = x / (AM - y)
tan 30 = 140.954 / (AM - 51.303)
AM - 51.303 = 140.954/tan 30
AM = 140.954/tan 30 + 51.303
AM = 295.442 m
Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x 1 out of a larger piece of paper. which expression can be used to find the perimeter of the rectangle and what is the perimeter if x = 4? (5x−2) (3x 1); 31 centimeters (5x−2) (3x 1); 36 centimeters 2(5x−2) 2(3x 1); 62 centimeters 2(5x−2) 2(3x 1); 70 centimeters
The expression that can be used to find the perimeter of the rectangle is 62 centimeters 2(5x−2)+2(3x+1).
What is the perimeter of the rectangle?The perimeter of the rectangle is equal to the 2 times sum of the length and width of the rectangle.
Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper.
The expression that can be used to find the perimeter of the rectangle is given by;
[tex]\rm Perimeter \ of \ rectangle = 2 (length +width)\\\\\rm Perimeter \ of \ rectangle = 2 (5x-2+3x+1)\\\\ \rm Perimeter \ of \ rectangle = 2 (7x-1)\\\\ \rm Perimeter \ of \ rectangle = 16x-2\\\\When , x\ =\ 4\\\\ \rm Perimeter \ of \ rectangle = 14x-2\ = 16(4)-2\ =\ 64-2\ =\ 62\\[/tex]
Hence, the expression that can be used to find the perimeter of the rectangle is 62 centimeters 2(5x−2)+2(3x+1).
To know more about the perimeter of the rectangle click the link given below.
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The quadratic functions f(x) and g(x) are described as follows: f(x) = −4x2 5 x g(x) 0 0 1 1 2 5 3 1 4 0 which of the following statements best compares the maximum value of the two functions? the maximum value is the same for both functions. f(x) has a greater maximum value than g(x). g(x) has a greater maximum value than f(x). the maximum values cannot be determined.
Then the maximum value of both the quadratic functions is the same. Then the correct option is A.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
The quadratic functions f(x) and g(x) are described as follows:
f(x) = −4x² + 5
x g(x)
0 0
1 1
2 5
3 1
4 0
The value of x for which f(x) will be maximum
[tex]\begin{aligned} \dfrac{d}{dx} \ f(x) = 0\\\\\dfrac{d}{dx} \ (-4x^2 + 5) = 0\\\\-8x =0\\\\x = 0 \end{aligned}[/tex]
Then the maximum value of f(x) will be
f(x) = −4(0)² + 5
f(x) = 5
Then the maximum value of both the functions is the same.
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
Answer:
The maximum values is the same for both functions.
Step-by-step explanation:
I took the test on flvs and got it right. And it should be correct too on other places like flvs. Hope this helps.
(please don't report me for advertisement of other websites. I believe how I have put it doesn't break that rule.)
How many sets of three consecutive integers are there whose sum is between 51 and 60?
Answer:
4 sets
Step-by-step explanation:
16 + 17 + 18 = 51
17 + 18 + 19 = 54
18 + 19 + 20 = 57
19 + 20 +21 = 60
A landscaping company uses a mixture of 20 pounds of grass seed and 356 pounds of fertilizer when reseeding a customer's lawn.
How many pounds of fertilizer will the company need for each pound of grass seed?
O A. 20
O B. 5. 6
O C. 16. 0
D. 17. 8
Answer:
D
Step-by-step explanation:
for 20 pounds of grass seed, we need 356 pounds of fertilizer
20 pounds of grass seed : 356 pounds of fertilizer
divide both sides by 20 to get 1 pound of grass seed on one side, as we want to figure out the corresponding amount of fertilizer for 1 pound of grass seed
20 pounds of grass seed/20 : 356 pounds of fertilizer/20
1 pound of grass seed: 17.8 pounds of fertilizer
What is the volume of a right rectangular prism with a length of 4.8 meters, a width of 23 meters, and a height of 0.9 meters?
A.4.968 m
B.9.936 m
C.11.94 m
D.34 86 m
Answer:
Volume of prism = Area of base× height
= l×b×h
=4.8×23×0.9
= 99.36 m³
All options are incorrect : )
Answer:
The answer is B
Step-by-step explanation:
Im 3 weeks late lol sorry. I took the quiz.
HELP NEEDED NOW/ASAP PLS NO LINKS AND NO JOCKING.
AND PLS SHOW UR WORK IF POSSIBLE
evaluate (-3 1/3)^2
[tex]\\ \rm\Rrightarrow (-3\dfrac{1}{3})^2[/tex]
[tex]\\ \rm\Rrightarrow (\dfrac{-10}{3})^2[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{(-10)^2}{3^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{100}{9}[/tex]
[tex]\\ \rm\Rrightarrow 11\dfrac{1}{9}[/tex]
Answer:
100/9 (or) 11 1/9
Step-by-step explanation:
Q) (-3 1/3)² = ?
→ (-3 1/3)²
→ (-10/3)²
→ 100/9
→ [ 11 1/9 ]
Hence, the solution is 11 1/9.
the graphs of the functions f(x)=|x-3| + 1 and G(x)=2x + 1 are drawn. which statement about these functions is true?
A: The solution to f(x)=g(x) is 3
B: The solution to f(x)=g(x) is 1
C: The graphs intersect when Y=1
D: The graphs intersect when X=3
The only true statement that compares the two functions is:
B: The solution to f(x)=g(x) is 1
Which statements are correct?Here we have the functions:
f(x) = |x - 3| + 1
g(x) = 2x + 1
First, let's find the solution for:
f(x) = g(x)
|x - 3| + 1 = 2x + 1
|x - 3| = 2x
Notice that we have two options, x = 3:
|3 - 3| = 2*3
0 = 6 (x = 3 is not a solution)
And x = 1:
|1 - 3| = 2*1
2 = 2 (x = 1 is a solution).
Now to get the y-value where the graphs intersect, we just evaluate one of the functions in the solution we found above;
f(1) = |1 - 3| + 1 = 2 + 1 = 3
The graphs intersect when y = 3.
Then we conclude that the only true statement is:
B: The solution to f(x)=g(x) is 1
If you want to learn more about systems of equations, you can read:
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The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table below. stopping distance of a car vs. speed stopping distance, d (in feet) speed, s (in miles per hour) 20 17.89 40 25.30 60 30.98 80 35.78 100 40.00 which equation best represents the data in the table? s = 4 startroot d endroot s = 0.37 d 20 s = 13.7log(d) s = startfraction 1 over 25 endfraction d squared
Answer:
The answer is (A.)
Step-by-step explanation:
Answer: A on edge 22
Step-by-step explanation:
Here is a cube.
Area = 4x(squared)
The area of a face of the cube is 4x(squared).
Write an expression for the total surface area of the cube. Write your answer as simply as possible.
Answer:
Step-by-step explanation:
A cube has 6 faces. Area of one face is 4x². To find the total suface area of cube, multiply 4x² by 6
Area of cube = 6 * 4x²
= 24x²
Sal recorded the number of crackers in each snack-sized package he opened. a number line goes from 5 to 15. the whiskers range from 7 to 15, and the box ranges from 7 to 10. a line divides the box at 9. which statement must be true according to the box plot? the data is symmetric, and the lowest number of crackers in a package was 7. the data is symmetric, and the lowest number of crackers in a package was 8. the data is skewed, and the lowest number of crackers in a package was 7. the data is skewed, and the lowest number of crackers in a package was 8.
The statement must be true according to the box plot if the data is skewed, and the lowest number of crackers in a package was 7. Option C is correct.
What is a number line?A number line is drawn with numbers equally spaced or sections running the length of it.
A number line should be drawn horizontally and can be extended in any direction indefinitely.
The number line shows the number of crackers lies between 7 and 13. Which is numerically as 7,8,9,10,11,12,13.The number of the digit on the number line skewed is 7.
Hence statement must be true according to the box plot if the data is skewed, and the lowest number of crackers in a package was 7. Option C is correct.
To learn more about the number line refer to the link;
https://brainly.com/question/13189025
Answer:
the answer is C
Step-by-step explanation:
Because im js swag
Find the volume of the cylinder.
Either enter an exact answer in terms of pi or use 3.14 for pi
Volume of cylinder,=πr²h
(22÷7)×5²×3
3.14×25×3
235.5
Answer :
235.5 units³
Need help math problem
Answer:
Question 16: 44 inches
Question 18: 10, 24, 26
Step-by-step explanation:
Question 16:
Pythagoras Theorem: c^2 = a^2 + b^2, where c is the hypotenuse and the longest side.
125^2 = 117^2 + b^2
15,625 = 13,689 + b^2
15,625 - 13689 = b^2
1936 = b^2
√1936 = b
44 = b
Question 18:
Pythagoras Theorem: c^2 = a^2 + b^2, where c is the hypotenuse and the longest side. You have to try all the possibilities. The ones that match are the lengths.
The answers are 10, 24, 26
c^2 = a^2 + b^2
26^2 = 10^2 + 24^2
676 = 100 + 576
676 = 676
PLEASE HELP I WILL GIVE BRAINLIEST IF CORRECT
I belive the correct answer would be A because if M and N are the signatures it would make sense to add them. Multiply the signatures by the days, and you have your self an equation. So because we added the first two... Nikkis's petition is still the same so we would have to add hers to M again leaving you with the equation of A.
Hope this helps :)
NEED HELP PLEASE!!!!
The expressions are equivalent.
[tex] \sqrt{ \frac{2x}{9} } = \frac{ \sqrt{2x} }{ \sqrt{9} } = \frac{ \sqrt{2x} }{3} = \frac{1}{3} \sqrt{2x} \\ [/tex]
3sqrt x =x-4
[tex]3 \sqrt{x} = x - 4[/tex]
solve for x
Answer:
x = 16
Step-by-step explanation:
3√x = x - 4
Raise the equation to the second power.
(3√x)² = (x - 4)²
9x = x² - 8x + 16
Rewrite the equation with the values on the left.
-x² + 17x - 16 = 0
x² - 17x + 16 = 0
Factor.
(x - 16)(x - 1) = 0
Set each part equal to 0.
x - 16 = 0
x = 16
x - 1 = 0
x = 1
Your solutions are 16 and 1, but it doesn't end there. Both of these may not satisfy the original equation, so plug them back in.
3√x = x - 4
3√16 = 16 - 4
3(4) = 12
12 = 2
16 is a solution.
3√x = x - 4
3√1 = 1 - 4
3(1) = -3
3 ≠ -3
1 is NOT a solution.
Find the mean
X. 10 20 30 40 50 60
F. 4 5 6 2 3 5
Answer:
Mean:To find the mean, you must add all the given numbers in your data then divide the sum of that by the many numbers you added together.X.
10, 20, 30, 40, 50, 60
Add them:
10 + 20 + 30 + 40 + 50 + 60
= 210
Then divide that sum by the many numbers there are, and there are 6 numbers in which we added.
210 ÷ 6
= 35, the mean for this is 35.
F.
4, 5, 6, 2, 3, 5
Add them:
4 + 5 + 6 + 2 + 3 + 5
= 25
Then divide that sum by the many numbers there are, and there are 6 numbers in which we added.
25 ÷ 6
= 4.1666..., the mean for this is 4.17.
A solid wooden post in the shape of a right rectangular prism measuring 10 cm by 12
cm by 30 cm is drilled with a cylindrical hole of radius 2 cm. Find the volume of the
post after the hole has been drilled. Round your answer to the nearest tenth if
necessary?
The volume of the post = volume of rectangular prism - volume of cylindrical hole = 3,223.0 cm³.
What is the Volume of a Rectangular Prism?Volume = (l)(w)(h)
What is the Volume of a Cylinder?Volume = πr²h
Volume of the post = volume of rectangular prism - volume of cylindrical hole
= (l)(w)(h) - πr²h
= (10)(12)(30) - π(2²)(30)
Volume of the post = 3,223.0 cm³
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Trevor has an investment worth $6,774.50. he made his only deposit in it 22 years ago. given that the investment yields 2.7% simple interest annually, how big was the initial deposit? a. $2,524.50 b. $4,024.03 c. $4,250.00 d. $11,404.88 please select the best answer from the choices provided a b c d
Answer:
c. 4,250.00
Step-by-step explanation:
The initial deposit amount is $4,250.00.
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that,
The worth of an investment is $6774.50
The time period is 22 years.
The rate of interest is 2.7%.
Now, Based on the above information, the calculation is as follows:
We know that;
SI = P x r x t
SI = P x 2.7% x 22
SI = 0.594P
Now,
Investment worth = P + SI
= P + 0.594P
= 1.594P
So, we get;
1.594P = 6774.50
P = $4,250
Therefore, we can conclude that the initial deposit amount is,
⇒ $4,250.00
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PLEASE HELP!!
it’s multiple choice but i never get any of the answers.
differentiate y=x^(e^x)
We are given the function to differentiate:
[tex]{\quad \qquad \sf \rightarrow y=x^{e^x}}[/tex]
Do take natural log on both sides, then we will be having
[tex]{:\implies \quad \sf ln(y)=ln(x^{e^{x}})}[/tex]
[tex]{:\implies \quad \sf ln(y)=e^{x}ln(x)\quad \qquad \{\because ln(a^b)=bln(a)\}}[/tex]
Now, differentiate both sides by using so called chain rule and the product rule
[tex]{:\implies \quad \sf \dfrac{1}{y}\dfrac{dy}{dx}=e^{x}ln(x)+\dfrac{e^x}{x}}[/tex]
[tex]{:\implies \quad \boxed{\bf{\dfrac{dy}{dx}=x^{e^x}\bigg\{\dfrac{e^x}{x}+ln(x)e^{x}\bigg\}}}}[/tex]
Hence, Option B) is correct
Product rule of differentiation:
[tex]{\boxed{\bf{\dfrac{d}{dx}(uv)=u\dfrac{dv}{dx}+v\dfrac{du}{dx}}}}[/tex]Where, u and v are functions of x
If a1= 5 and an = 2an-1 + 5 then find the value of a4.
Answer:
a₄ = 75
Step-by-step explanation:
using the recursive formula and a₁ = 5 , then
a₂ = 2a₁ + 5 = 2(5) + 5 = 10 + 5 = 15
a₃ = 2a₂ + 5 = 2(15) + 5 = 30 + 5 = 35
a₄ = 2a₃ + 5 = 2(35) + 5 = 70 + 5 = 75
Answer:
[tex]a_4=75[/tex]
Step-by-step explanation:
Given:
[tex]a_1=5[/tex][tex]a_n=2(a_{n-1})+5[/tex][tex]\implies a_2=2(a_1)+5=2(5)+5=15[/tex]
[tex]\implies a_3=2(a_2)+5=2(15)+5=35[/tex]
[tex]\implies a_4=2(a_3)+5=2(35)+5=75[/tex]
find the slope of the line through the given points 4,2 and 6,4
Answer:
2/2 = 1
Step-by-step explanation:
Slope intercept equation:
y2 - y1 / x2 - x1 = slope