an initial deposit of $200 is made into an account that pays 4.2% annual interest. What is a model to represent the balance in the account after x years?
The model to represent the balance in an account from an initial deposit of $200 at an annual interest of 4.2% is given by the formula A = 200(1.042)^x. Here A is the amount accrued after x years.
Explanation:The subject of the given problem is related to exponential growth as it involves the growth of a principal amount in a bank account accruing annual interest. The model to represent the balance in the account after x years can be described by the formula A = P(1 + r/n)^(nt). Where, A represents the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, t is the time the money is invested for in years.
In this case, P = $200, r = 4.2/100 = 0.042 (converted percentage to decimal), n = 1 (since it is compounded annually), and t = x (number of years). Substituting these values into the formula, we obtain the model: A = 200 (1 + 0.042) ^ (1*x) simplified to, A = 200(1.042)^x. Which is used to represent the balance in the account after x years.
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What is the interval for the number of people who are likely to want this restaurant in their city?
At bonnie's bagels, you can choose from five different types of bagels, four different spreads, and four different toppings. how many different bagel combinations are possible?
The next stop on the road trip is the zoo! jacob goes to find his favorite animal, the giraffe. jacob wonders how tall the tallest giraffe at the zoo is. if jacob is 5 feet 6 inches and his shadow at the time is 3 feet long, find the height of the giraffe whose shadow is 5 feet 9 inches at the same time.
The height of the giraffe whose shadow is 5 feet 9 inches at the same time will be 10 feet and 6.5 inches.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
The next stop on the road trip is the zoo.
Jacob goes to find his favorite animal, the giraffe.
Jacob wonders how tall the tallest giraffe at the zoo is.
If Jacob is 5 feet 6 inches and his shadow at the time is 3 feet long.
Then the height of the giraffe whose shadow is 5 feet 9 inches at the same time will be
Let x be the hieght of the giraffe. Then we have
The ratio will remain constant.
x / 5.75 = 5.5 / 3
x = 10.54
x = 10 feet 6.5 inches
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Rearrange the formula to calculate the diameter of a circle.
how do we find the volume ?
The volume of figure is 877.876 yd³
1. Volume of Cone
= 1/3πr²h
= 1/3 x 3.14 x 2 x 2 x 4
= 16.746
2. Volume of cylinder
= 3.14 x 2 x 2 x 8
= 100.48
3. Volume of Hemisphere
= 2/3πr³
= 7.065
4. Volume of cylinder
= 3.14 x 1.5 x 1.5 x 9
= 63.585
5. Volume of prism
= 1/2 x ( 6 x 6) x 12
= 216
6. Volume of Cuboidal prism
= l w h
= 6 x 6 x 12
= 432
7. Volume of pyramid
= 1/3 x 3 x 2
= 2
8. Volume of cuboidal prism
= 10 x 2 x 2
= 40
So, the volume of figure is
= 16.746 + 100.48 + 7.065 + 63.585 + 216 + 432 + 2 + 40
= 877.876 yd³
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a drainage pipe 66 in. tall measures 25.12 in. around.
Using the formula for the volume of a cylinder, what is the volume of the drainage pipe rounded to the nearest hundredth of a cubic inch?
(Pi = 3.14)
A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = −16t2 + 32t + 6. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
The ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.
To find the time at which the ball reaches its maximum height, we can first determine the vertex of the quadratic function [tex]\( h(t) = -16t^2 + 32t + 6 \),[/tex] where t represents time in seconds and h represents height in feet.
The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is given by the formula:
[tex]\[ t_{\text{max}} = \frac{-b}{2a} \][/tex]
For the function [tex]\( h(t) = -16t^2 + 32t + 6 \)[/tex], we have a = -16 and b = 32 . Plugging these values into the formula:
[tex]\[ t_{\text{max}} = \frac{-32}{2(-16)} \]\[ t_{\text{max}} = \frac{-32}{-32} = 1 \][/tex]
So, the ball reaches its maximum height at t = 1 second.
To find the maximum height, we substitute t = 1 into the function h(t) :
[tex]\[ h(1) = -16(1)^2 + 32(1) + 6 \]\[ h(1) = -16 + 32 + 6 \]\[ h(1) = 22 \][/tex]
Therefore, the ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.
What is the value of x? x = 2 x = 3 x = 4 x = 6
Answer:
The answer is 3
Step-by-step explanation:
The value of x is 3.
The correct option is B.
Use one of your formulas from the figure we can write
x(x+21) = (x+1)(x+1+14)
Now, solving for x we get
x² + 21x = (x+1)(x+15)
x² + 21x = x² + 15x + x + 15
x² + 21x= x² + 16x+ 15
21x = 16x+ 15
21x - 16x = 15
5x= 15
x= 15/5
x= 3
Thus, the value x is 3.
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The total price of an article is $7.02, including tax. If the tax rate is 8%, what is the retail price of the article?
The solution is: The retail price is $6.50.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Here, we have,
given that,
The total price of an article is $7.02, including tax.
If the tax rate is 8%
Lets price of article = x
Tax is 8% of article = 0.08x
so, we get,
x+0.08x=7.02
1.08x=7.02
x=7.02/1.08
x=6.5
The retail price is $6.50.
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10PTS!!!!!! UGRENT WILL MARK BRAINLYEST, THANK AND 5 STARS!!
Find the volume of the tank below.
could't inbed the image but it a cylindar 5m tall and has a radius of 2m
96 m3
78 m3
54 m3
63 m3
Box a is by 2 lb lighter than box b and 5 times lighter than box
c. boxes a and c together are 4 times heavier than box
b. find the weight of each box.
Answer:
Box A: 4
Box B: 6
Box C: 20
Step-by-step explanation:
Because 4+2 = 6
4 x 5 = 20
Which measure is of an angle that is coterminal with a 425 degree angle
A. 425 degree-(1,000n)degree, for any integer n
B.425 degree-(840n)degree, for any integer n
C. 425 degree+(960n)degree, for any integer n
D. 425 degree+(1,440n)degree, for any integer n
We know that co terminal angles are those angles which have a difference equal to a multiple of 360 degrees. For example co terminal angle of 45 degrees is 76 degrees because their difference is equal to 720 degrees, which is a multiple of 360.
We have been given an angle 425 degrees.
From the given choices, we need to check if angles being added or subtracted to 425 degrees are multiples of 360 or not.
Let us check each of the options one by one.
(A) The angle being subtracted is [tex]1000n[/tex]. Therefore, we have [tex]\frac{1000n}{360}=2.77n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(B)
The angle being subtracted is [tex]840n[/tex]. Therefore, we have [tex]\frac{840n}{360}=2.33n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(C)
The angle being added is [tex]960n[/tex]. Therefore, we have [tex]\frac{960n}{360}=2.67n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(D)
The angle being added is [tex]1440n[/tex]. Therefore, we have [tex]\frac{1440n}{360}=4n[/tex], which is an integer for all values of n. Therefore, angle given in this option is indeed a co terminate angle to 425 degrees.
Hence, correct answer is option (D).
He shorter leg of a 30°-60°-90° triangle is 6. what is the length of the hypotenuse?
The combined cost of one advance ticket and one same-day ticket to a show was $50. it is known that 17 advance tickets were sold and 48 same-day tickets were sold, for total receipts of $1842. what was the price of each kind of ticket?
Given:
CDKM is a parallelogram,
DA
⊥
CK
, DK – CD = 7
CA = 6, AK = 15
Find: CD and DK
In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
The quadrilateral CDKM is a parallelogram. In this parallelogram, the side DA is perpendicular to the side CK.
The difference of the side DK and CD is,
[tex]DK - CD = 7\\DK=7+CD[/tex]
The length of the line segment CA and AK is 6 units and 15 units respectively.Then by the Pythagoras theorem,
[tex](AD)^2=(CD)^2-(AC)^2\\(AD)^2=(CD)^2-(6)^2[/tex] ....1
Again by using the Pythagoras theorem
[tex](AD)^2=(Dk)^2-(AK)^2\\(AD)^2=(DK)^2-(15)^2[/tex]
Put the value of (AD)², from equation 1 in the above equation as,
[tex](CD)^2-6^2=(DK)^2-(15)^2\\(CD)^2-36=(DK)^2-225[/tex]
Put the value of DK in the above equation as,
[tex](CD)^2-36=(7+CD)^2-225\\(7+CD)^2-(CD)^2=225-36\\(CD)^2+14CD+49-(CD)^2=189\\CD=10[/tex]
Hence, the value of DK is,
[tex]DK=7+10DK=17[/tex]
Hence, In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.
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If line segment ab is defined by the endpoints a(4,2) and b(8,6) , write an equation of a line that is the perpendicualr bisector line segment ab
An equation of a line that is the perpendicular bisector line segment AB is y=-x+10.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, line segment AB is defined by the endpoints A(4,2) and B(8,6).
Midpoint of line AB is (x, y) =[(x₂+x₁)/2, (y₂+y₁)/2]
= [(8+4)/2, (6+2)/2]
= (6, 4)
Slope of line AB is (y₂-y₁)/(x₂-x₁)
= (6-2)/(8-4)
= 4/4
= 1
The slope of a line perpendicular to given line is m1=-1/m2
So, the slope of a line is -1
Now, substitute m=-1 and (x, y)=(6, 4) in y=mx+c, we get
4=-1(6)+c
c=10
Substitute m=-1 and c=10 in y=mx+c, we get
y=-x+10
Therefore, an equation of a line that is the perpendicular bisector line segment AB is y=-x+10.
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Guys I need help with this question, I have some marked but i have no idea which ones are the correct ones to begin with...
Alexandra rented a costume for $39 per day.
She knows there was a deposit for the costume, but she cannot remember the amount of the deposit.
If she rented the costume for 3 days and paid a total of $167, the deposit must have been $____
Answer:
$50
Step-by-step explanation:
because I know :p
Have a good day!
A hang glider is soaring over a 100-acre area that consists of thick forest and open fields. In the diagram below, the forested area is shaded in green and the open field is the white space. Upon landing, the hang glider realizes she has dropped her keys.
What is the probability that her keys have landed within the forest?
The blacked out middle section of the pyramid is 20 acres
A 0.2
B 0.6
C 0.8
D 1.0
The probability that her keys have landed within the forest will be C. 0.8.
How to calculate probability?From the information given, the blacked out middle section of the pyramid is 20 acres. Therefore, the probability will be:
= 20/100 = 0.2
Now, the probability that her keys have landed within the forest will be:
= 1 - 0.2
= 0.8
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The central angle of a circle is equal in measure to one radian when the corresponding arc length is equal to which of the following? A) The radius of the circle B) Any chord of the circle C) The diameter of the circle D) One-half the circumference of the circle
Find g(x), where g(x) is the translation 9 units up of f(x)=x2. write your answer in the form m(x+a)2+b, where m, a, and b are integers.
Answer:
(x+9)^2
Step-by-step explanation:
How many zeros does the function f(x) = 4x^11 − 20x^7 + 2x^3 − 15x + 14 have?
I'm between 3 & 11.
Express each product in the simplest form. 3wx\6x * 3wx\9w
Anyone know the answer?
In how many different ways can someone arrange 6 books on a shelf
Need help please ASAP!!
How many combinations with 3 numbers 0-6?
The mathematics department of a college has 1414 male professors, 99 female professors, 99 male teaching assistants, and 1111 female teaching assistants. if a person is selected at random from the group, find the probability that the selected person is a professor or a male.
I think the answer is Probability is (1513+99)/(1414+99+1111+99)=1612/2723
Suppose that on a particular computer, it takes the merge sort algorithm a total of 60 seconds to sort an array with 60,000 values. approximately how long will it take the algorithm to sort an array with 120,000 values? round to the nearest second.