An exponential function for the amount in the account after T years if the interest of 8% is compounding annually on initial amount 1700 is: P_T = 1700(1.08)^T
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
How does compound interest works?Instead of calculating the interest on the initial amount, the compound interest repeats calculating interest on (old amount + interest to be paid).
For this case, we're specified that:
Initial amount deposited = $1700Rate of interest = 8% annual = 0.08 (converted percent to fraction).Let P be the inital amount, and r be the rate of interest compounding per unit of time (in decimal)
Let [tex]P_t[/tex] be the amount after t unit of time(same unit as the interest).
Then after 1 year, the new amount would be:
[tex]P_{t+1} = P_t + 100r \%\text{ of }P_t}\\P_{t+1}= P_t + P_t \times r\\P_{t+1} = P_t(1+r)[/tex]
Thus, we get:
[tex]P_t = P_{t-1}(1+r) = P_{t-2}(1+r)(1+r) = P_{t-2}(1+r)^2\\\\P_t = P_{t-t} (1+r)^t = P_0(1+r)^t[/tex]
where P₀ is the initial amount (as amount at t = 0 is initial amount)
Thus, we get:
[tex]P_t = P(1+r)^t[/tex]
Here, putting P = 1700, r = 0.08, and t = T, we get:
[tex]P_T = 1700(1.08)^T[/tex]
Thus, an exponential function for the amount in the account after T years if the interest of 8% is compounding annually on initial amount 1700 is: [tex]P_T = 1700(1.08)^T[/tex]
Learn more about compound interest here:
https://brainly.com/question/11897800
Determine for each number whether it is a rational or irrational number.
In order:
irrational
irrational
rational
rational
The radius of a cylindrical water tank is 6.5 ft, and its height is 12 ft. What is the volume of the tank?
Answer:
.............. just for filling 20 characters
the radius of a circle is 13 find its area un terms of pi
Answer:
530.66
Step-by-step explanation:
A = πr²
13 x 13 = 169
169 x 3.14 = 530.66
Let me know if this helps!
Use a formula to find the surface area of the cylinder. Use 3.14 for pi
Answer:
A = 376.99
Step-by-step explanation:
A=2πrh+2πr2
Just plug in and solve:
A=2πrh+2πr2
A = 376.99
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Answer:
x = 11 , y = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
The opposite sides of a parallelogram are congruent
For the figure to be a parallelogram , then
ON = LM, that is
5x - 7 = 4x + 4 ( subtract 4x from both sides )
x - 7 = 4 ( add 7 to both sides )
x = 11
and
OL = NM , that is
3y - 4 = x - 7 = 11 - 7 = 4 ( add 4 to both sides )
3y = 8 ( divide both sides by 3 )
y = [tex]\frac{8}{3}[/tex]
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Answer:
number 8 is $0
number 9 is D
Answer:
number 8 is $0
number 9 is D
Which is the equation of the parabola?
coordinate plane with a parabola facing down with vertex at negative 3 comma 0, the point negative 3 comma negative 5 and a horizontal line going through 0 comma 5
y = −one twentieth(x − 3)2
y = −one twentieth(x + 3)2
y = one twentieth(x − 3)2
y = one twentieth(x + 3)2
Answer:
y = -1/20(x + 3)²Step-by-step explanation:
Consider the parent function:
y = x²The graph of the function open up and the vertex is at the origin, the point (0, 0)
Now, if it opens down, it means it is a reflection of the parent function over x axis, hence it has a negative coefficient, the function becomes:
y = -x²The vertex is shifted to the point (-3, 0). It means the function also translated left by 3 units, the function becomes:
y = -(x + 3)²Since all the options have 1/20 as a coefficient, our function is:
y = -1/20(x + 3)²This is option B
PLEASE ANSWER QUICKLY.
I WILL GIVE THE BRAINLIEST ASAP.
Answer:
options (c) is right answer
Answer: B
Step-by-step explanation:
HELP!!!! Put the following in order from greatest to least.
Answer:
A
Step-by-step explanation:
A = 9, 7, 5, -2, -6, -8
Find the mean of 9, 1, 3, 9, 3 graphically
Answer:
The mean is 3
Step-by-step explanation:
9+ 1+ 3+ 9+ 3= 15
15/5= 3
Choose the equation that is not a linear function.
A
8x + 12 = 2y
B
y =
x
5
+ 20
C
x = 12y
D
y = (2x)x
Answer:
The answer is D
Step-by-step explanation:
D, y=(2x)x
y=2x^2
this is a parabola, not a linear equation
Which of the following translations is needed to carry AEFG onto its image AEFG'?
Answer:
Option B
Step-by-step explanation:
It's given that ΔE'F'G' is the translated image of ΔEFG.
Let the ΔEFG has been translated 'h' units on x-axis and moved by 'k' units on y-axis.
Let's choose a point E having coordinates (-5, -7)
By the rule of translation, coordinates of the image point E' will be,
E(-5, -7) → E'(-5 + h, -7 + k)
Coordinates of the image point E' → (-9, 4)
Comparing both the coordinates of E',
E'(-5 + h, -7 + k) = E'(-9, 4)
-5 + h = -9
h = -9 + 5
h = -4
-7 + k = 4
k = 4 + 7
k = 11
Therefore, rule for the translation will be,
E(-5, -7) → E'(-5 - 4, -7 + 11)
(x, y) → (x - 4, y + 11)
Option B is the answer.
What is the surface area of this Square Pyramid?
10 in
5 in
5 in.
Answer:
Base Surface Area: 25 in^2
Total surface area A = 128.07764064044 in^2
(PLEASE NOTE THIS IS BASED ON THE HEIGHT BEING 10 IN AND SIDE LENGTH A BEING 5 IN (IF THIS IS INCORRECT COMMENT AND ILL FLIP IT)
Step-by-step explanation:
How to do it
Step by step
Step-by-step explanation:
23.35......is answer.......
A circle with center O is shown. Create the equation for the circle.
Answer:
(5 - 1)^2 + (1 - 1)^2 = 4^2
Step-by-step explanation:
Circle equation: ( x - h )^2 + ( y - k )^2 = r^2
(h,K) is the coordinate of the center.
Center: (1,1)
(x,y) choose a point that could be the radius. (I choose the one on the top left side).
Point: (5,1)
Diameter: 8
Radius: 4
Plug in:
( x - h )^2 + ( y - k )^2 = r^2
(5 - 1)^2 + (1 - 1)^2 = 4^2 (or 16)
Solve to see if it's true,
(5 - 1)^2 + (1 - 1)^2 = 4^2 (or 16)
4^2 + 0^2 = 4^2
16 = 16 (This is true, therefore, the equation is correct).
Answer:(x-1)^2 + (y-1)^2=16
Step-by-step explanation:
Solve for x for 180 ° < x < 270 ° . 1/sin^2 x=4
On a map, Haven Rd and Pine Rd are parallel, and Mills Rd is a transversal. How can the
value of x be determined?
Answer:
B: Corresponding angles are congruent, so x = 43
Answer:
B: Corresponding angles are congruent, so x = 43
Step-by-step explanation:
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I'll help you, I just don't understand what the exercise is asking for x or y?
Help me find length of missing side
Answer:
x=20.26
Step-by-step explanation:
tan40°=17/x
x=17/tan40°
x=20.25981107 or 20.26
Mark hits a tennis ball into the air. He uses the equation shown to approximate the
height, h, in feet, of the ball t seconds after he hits it.
h = -1612 +886 + 4
What does the 4 represent in Mark's equation?
A.
The ball was in the air for a total of 4 seconds.
B.
The ball landed 4 feet away from where Mark hit it.
C.
The ball was 4 feet above the ground when Mark hit it.
D.
The ball reached its maximum height 4 seconds after Mark hit it.
Answer:
C. The ball was 4 feet above the ground when Mark hit it.
Step-by-step explanation:
After he hit the tennis ball into the air, the ball was 4ft above the ground.
hope this helps and is right. p.s i really need brainliest :)
if my answer is wrong then I am incredibly sorry!
A bag holds 2 red and 7 blue marbles. What is the probability of not selecting a red marble?
2/7
O a
Ob
7/2
2/9
Od
779
Figure 2 is a translation image of Figure 1. Write a rule to describe the translation.
The translation rule is (x,y) →(x+(blank),y+(blank).
Answer:
(x, y) → (x - 1, y + 2)Step-by-step explanation:
This is a translation left and up
Compare the coordinates of corresponding points:
(-2, -1) becomes (-3, 1)The difference is:
-3 - (-2) = - 1 for x and 1 - (-1) = 2 for yThe translation rule is:
(x, y) → (x - 1, y + 2)The sum of two numbers is 53 and the difference is 23. What are the numbers?
Answer: The number is 38
Step-by-step explanation:
Solve 4(b−3)=64(b−3)=6
A tree in Chau's backyard has been growing for 2.4 years. The tree is .25 meters tall.
What is the unit rate in meters per year?
Answer:
0.1042 meters per year
Step-by-step explanation:
Find the unit rate by dividing 0.25 by 2.4
0.25/2.4
= 0.1042
So, the unit rate is approximately 0.1042 meters per year
help shawty’s i’m stressin
Answer:
A dilation is a type of transformation that changes the size of the image. The scale factor, measures how much larger or smaller the image is. Each type of dilation (one that gets larger and one that gets smaller).
Step-by-step explanation:
I don't know if this'll be enough help, but it's a brief definition.
hey guys i kinda need help with this one assignment for today THANKS
Answer:
Basic physics and common sense would say that of course they'd reach the same height if placed an equal distance away. I don't really know what else to do
The farmer is not correct. She sold _% of the onions and _ % of the turnips by noon on Saturday. If she had sold 4 more pounds of onions she will have sold _% of the onions. This percentage of onions sold ___ equal to the percentage of turnips sold. *: 20 25 :: 28 :: 32 :: 35 .: 40 :: 50 :: 56 :: 80 :: is .! is not
Answer:
28 32 35 50
Step-by-step explanation:
Name two triangles that are congruent by ASA.
Answer:
correct
Step-by-step explanation:
Angle-Side-Angle (ASA) Postulate:
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
<C = <G
CA = GD
<A = <D
Triangle CAT = Triangle GDO are the two triangles that are congruent by the ASA Postulate.
which angles are complementary to eachother
Answer:
1 and 5 are complementary angles
Step-by-step explanation:
A complementary angle is either of two angles whose sum is 90, meaning two opposite angles that add up to 90 degrees.
If you look at angle 3, you see that it is a right angle which is 90 degrees already so any answer containing 3 and another angle is incorrect.
Why 1 and 5 is the correct answer:
the angles 1 and 2 are right next to 3 which is a 90-degree angle, meaning that 1 and 2 add up to 90. angle 5 is opposite of 2 which means that angle 5 and 2 are equal.
So the 1 and 5 would add up to 90, making it the right answer.
Hope this helps you :)