The formula can also be written as: a(n) = 25(1.025)ⁿ where 1.025 is the factor by which the initial amount is multiplied after each year of interest.
What is function?In mathematics, a function is a rule that assigns each input (or element of the domain) a unique output (or element of the range). It is a mathematical object that takes an input and produces an output based on a specified rule or set of rules. A function can be represented in different ways, such as by an equation, a graph, or a table of values. The most common notation for a function is f(x), where x is the input and f(x) is the corresponding output. Functions are used to describe relationships between quantities in various fields of mathematics and science, such as in calculus, linear algebra, statistics, physics, and engineering. They are also used in modeling real-world situations and solving problems in many areas, including finance, economics, and computer science.
Here,
The formula for calculating the amount of money in Anna's savings account with an initial deposit of $25 and 2.5% annual interest rate, compounded annually, is:
a(n) = 25(1 + 0.025)ⁿ
where t is the number of years since the account was opened.
This is the formula for calculating the future value of a present sum using compound interest formula.
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Complete question:
anna uses $25 to open a savings account. The function a(t) models the amount of money, a in her account, where t is the number of years since the account was opened. create a function that models the situation if her account earns 2.5% interest per year.
how do you do this mathematics?
Answer:
What Mathematics
Step-by-step explanation:
If the diameter of a circle is
30
30 centimeters, what is the radius of the circle?
Answer:
15 centimeters
Step-by-step explanation:
radius is half of the circles diameter
If the graph of a polynomial function P(x) has -intercepts at x = - 4, x = 0, x * 1 point
= 5, which of the following must be true for P(x)?
• (x + 5) is a factor of the polynomial.
• (x-4) is a factor of the polynomial.
•' The degree of the polynomial is 3.
• The degree of the polynomial is greater than or equal to 3.
(x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
What is a functiοn ?Functiοn can be define in which it relates an input tο οutput.
If the graph οf a pοlynοmial functiοn P(x) has x-intercepts at x = -4, x = 0, and x = 5, then we knοw that the factοrs οf P(x) are (x + 4), x, and (x - 5). This is because a pοlynοmial has x-intercepts where the value οf P(x) is equal tο zerο, and this οccurs when each factοr is equal tο zerο.
Therefοre, we can cοnclude that (x + 4) and (x - 5) are factοrs οf the pοlynοmial P(x), but x is nοt necessarily a factοr. This is because x is a linear factοr with a zerο intercept, but it cοuld be cancelled οut by anοther factοr in the pοlynοmial.
Thus, the cοrrect statement is:
(x + 5) is nοt necessarily a factοr οf the pοlynοmial.
(x-4) is a factοr οf the pοlynοmial.
The degree οf the pοlynοmial is 3 οr greater since the pοlynοmial has three x-intercepts. Hοwever, we cannοt determine the exact degree οf the pοlynοmial withοut additiοnal infοrmatiοn.
Therefοre, (x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
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What is the value of x in (x+3)^2=49 show your work
Answer:
x = 4,-10Step-by-step explanation:
(x+3)^2=49
x+3=√(49)
x+3=√(7^2)
x+3=7
x+3-3=7-3
x=4x+3=-√(49)
x+3=-7
x+3-3=-7-3
x=-10x = 4,-10
For a given recipe 8 cups of flour are mixed with 12 cups of sugar how many cups of flour should be used if 27 cups of sugar are use
Therefore, if we are using 27 cups of sugar, we also need 18 cups of wheat.
What does an arithmetic ratio mean?An ordered combination of integers a and b, rendered as a / b, is a ratio if b is not equal to 0. A percentage is an expression that sets two numbers at the same value. For instance, you could put the percentage as follows: 1: 3 if it's 1 male and 3 girls. (for every one boy there are 3 girls)
If 8 cups of flour are mixed with 12 cups of sugar, then the ratio of flour to sugar is:
8 : 12
Simplifying this ratio by dividing both numbers by 4, we get:
2 : 3
This means that for every 2 cups of flour, we need 3 cups of sugar.
If we are using 27 cups of sugar, we can set up a proportion to find out how much flour we need:
2/3 = x/27
Multiplying both sides by 27:
2 × 27 / 3 = x
Simplifying:
x = 18
Therefore, we need 18 cups of flour if we are using 27 cups of sugar.
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Danny is opening a savings account with an initial deposit of 45$. He saves $3 per day
The equation of the line is slope intercept form is y = 3x + 45.
What is a graph?
The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, Danny is opening a savings account with an initial deposit of $45 and he saves $3 per day.
Let y be the total amount he saves and x is the no. of days.
As he starts with $45 deposit it'll be added as a constant.
∴ The equation of the required line is y = 3x + 45.
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Can someone help me!!!!!
Answer:
c
Step-by-step explanation:
because I did it in my book ️
9. If the figure below is made of cubes with 2 cm side lengths, what is its volume? 14 cu. cm. 42 cu. cm. 144 cu.cm 280 cu. cm.
is this correct??
Total volume of shape is =144cu.cm
Formula for Cube VolumeBy knowing the length of the cube's edges, we can quickly determine its volume (V). Assume that "a" is the cube's edge length. The product of length, height, and breadth will then be the V. The cube's volume formula is as follows:
Cube Volume = Length× Width× Height
Volume equals= a× a× a =a³
where "a" denotes the cube's side or edges' length.
GivenLength of each cube = 2cm
Volume of each cube=a³
=2³
=8cm³
Total number of cubes=18
Total volume of shape=18×8
=144 cu.cm
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June is driving from Brookline, Massachusetts, to Brooklyn, New York. The cities are 200 miles apart. Pretend June lives in a world in which she encounters no traffic jams and can drive at a constant speed of 50 mph the entire way. The distance June has traveled, c, is a function of her driving time, t Write a formula that describes this function.
This function's definition is given by the formula [tex]c = 50t + 200[/tex].
What pace is it moving at?Consider how many individuals and gadgets will be utilizing the network at once as well as how it will be utilized before choosing the "optimal" speed for your home. As a general rule, anything that can connect many devices simultaneously and is above 200 Mbps is regarded as "fast" internet.
What would you define speed as?Speed, which is a scalar number, is the "speed at which an item is moving." The pace at which an item travels a distance may be referred of as its speed. A fast-moving item travels at a great velocity and completes a significant distance in a brief period of time.
[tex]y = mx + b[/tex]
Where [tex]y,x[/tex] are variables, m is the rate of change and [tex]b[/tex] is the y intercept.
Let [tex]c[/tex] represent the distance June has traveled after time [tex]t[/tex].
Since the cities are [tex]200[/tex]miles apart, hence [tex]b = 200[/tex]. Also the speed is [tex]50[/tex]mph, hence [tex]m = 50[/tex]:
[tex]c = 50t + 200[/tex]
The formula that describes this function is [tex]c = 50t + 200[/tex]
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Your take home pay is $3,210 and your federal witholding tax rate is 16%. What was your gross pay? show the math
Answer:
To find your gross pay, we can use the following formula:
Gross Pay = Take Home Pay / (1 - Federal Withholding Tax Rate)
Plugging in the given values, we get:
Gross Pay = 3,210 / (1 - 0.16)
Simplifying the denominator, we get:
Gross Pay = 3,210 / 0.84
Calculating the division, we get:
Gross Pay = 3,821.43
Therefore, your gross pay was $3,821.43.
Can someone help me, please?
In a land far away, green goo varies jointly with blue goo and red goo. There are pounds of green goo when pounds of blue goo and pounds of red goo are present. Therefore, there will be blank pounds of green goo when pounds of blue goo and pounds of red goo are present.
So, when 14 pounds of blue goo as well as 16 pounds of red goo are present, there are 2688 pounds of green goo.
Explain about the direct variation?Simply generate ratios from a table of values to see whether it reflects a direct variation. A direct variation exists if every one of the ratios are the same.Any time one quantity directly affects the other, such as when one quantity rises in relation to the other and vice versa, there is a direct variation between the two variables. When one of the variables is still a constant multiple of another one, there is a link between the two variables.Let the green goo be G.
Let the blue goo be B.
Let the red goo be R.
G ∝ B*R
G = k*B*R (k is the constant of proportionality)
Put the values:
G = 288 = k*B*R
288 = k*8*3
288 = k*24,
k = 288/24 = 12
Now, for the second case:
G = k*B*R
Put the value of k.
G = 12*14*16 = 2688.
So, when 14 pounds of blue goo as well as 16 pounds of red goo are present, there are 2688 pounds of green goo.
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Answer:
Step-by-step explanation:
ut it A
Decomposing numbers to add make a new 10 adding.
29+14
29 + 14 = 44 by decomposing numbers to add and make a new 10.
Describe Decomposition of numbers?Decomposition of numbers involves breaking a number down into its constituent parts or smaller numbers that add up to the original number. This can be done in different ways depending on the purpose and context of the problem.
For example, one common way of decomposing a number is by place value. In this case, the number is broken down into its digits, which represent different powers of ten. For instance, the number 562 can be decomposed into 500 + 60 + 2.
Another way of decomposing numbers is by factoring. In this case, the number is expressed as a product of its factors. For example, the number 12 can be decomposed as 2 x 2 x 3.
Decomposing numbers is a useful skill in many areas of mathematics, including arithmetic, algebra, and geometry. It is often used to simplify problems, make computations easier, and facilitate further analysis.
To decompose 29 to make a new 10, we can break it into 9 and 20. Then, to decompose 14 to make a new 10, we can break it into 6 and 8.
So, we have:
29 + 14 = (9 + 20) + (6 + 8)
Now, we can regroup the numbers to make a new 10:
= (9 + 1) + (20 + 6) + 8
= 10 + 26 + 8
= 44
Therefore, 29 + 14 = 44 by decomposing numbers to add and make a new 10.
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Anna has one dollar she buy some candy for $.83 which shows how much change and I should get
Answer:
Anna should receive $0.17 (17 cents) in change
Step-by-step explanation:
Anna has $1, she spends $.83 on candy
To find how much change she will get, we must subtract
1 - 0.83
$0.17
Answer:$0.17
Step-by-step explanation:
A dollar is 100 cents just subtract 83 from 100 to get 17.
What is 17 + 8 x (2.7 ÷ 6) - 3
using
P
E
M
D
A
S
Answer:
17.6
Step-by-step explanation:
2.7÷6= 0.45
0.45×8= 3.6
17+3.6 - 3=17.6
Question 4
What are the coordinates of point C on the directed segment
from A(-8,4) to B(10,-2) that partitions the segment such that
AC:CB is 2:1?
We may conclude after answering the presented question that Therefore, the coordinates of point C are (-6, 0).
what are coordinate ?In mathematics, a coordinate is a number or combination of numbers that represents the location of a point or object in space. Coordinates are frequently used to define a point or object's position in a certain coordinate system, such as the Cartesian or polar coordinate systems. In the Cartesian coordinate system, a point is found by its distance from the origin along the x-axis and its distance from the origin along the y-axis. These distances are represented by two integers, the x-coordinate and the y-coordinate. The point's location in the plane is specified by the two coordinates.
Using the distance formula, we can find the distances AC and CB:
[tex]AC = \sqrt((x - (-8))^2 + (y - 4)^2)\\CB = \sqrt((10 - x)^2 + (-2 - y)^2)\\[/tex]
Since AC:CB = 2:1, we have:
[tex]AC/CB = 2/1\sqrt((x - (-8))^2 + (y - 4)^2) / \sqrt((10 - x)^2 + (-2 - y)^2) = 2/1\\(x - (-8))^2 + (y - 4)^2 / ((10 - x)^2 + (-2 - y)^2) = 4\\(x - (-8))^2 + (y - 4)^2 = 4((10 - x)^2 + (-2 - y)^2)\\5x^2 + 5y^2 - 116x + 20y + 340 = 0\\(x - (-8))^2 + (y - 4)^2 = r^2\\(x - (-8))^2 + (y - 4)^2 / ((10 - x)^2 + (-2 - y)^2) = 4\\[/tex]
where r is the radius of the circle.
Solving this system of equations, we get:
x = -6
y = 0
Therefore, the coordinates of point C are (-6, 0).
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in which place is the first digit of the quotient: 3,587 ÷ 18
Answer: The quotient is 199.277777778, the answer is the hundreds place
Step-by-step explanation:
199.277777778, the 1 in 199 is in the hundreds place :)
100 POINTS + BRAINLIEST!!
Answer:
Taking radius of a semicircle to be 3cm calculate the area using (1/2πr²) and add the area of rectangle calculated by use of formula L×w
Therefore Area=π(1/2×3²)+(12×6)
=76.5π
Answer:
82.27
Step-by-step explanation:
Please see the diagram attached to this solution for measurements
Area of the figure = Area of semi circle + area of rectangle
As per the figure
[tex]l_{rectangle} = 9\\w_{rectangle} = 6\\r_{semi-circle} = 3[/tex]
therefore,
[tex]Area = \dfrac{\pi r^{2}}{2} + l\cdot w[/tex]
substitute values of l, w and r, we get
[tex]Area = 82.27 cm^2[/tex]
Hopefully this answer helped you!!!
an athlete ran 200m race in 25 seconds. how fast did he run in meters per second
Answer:
To calculate the speed of the athlete in meters per second (m/s), we can use the formula:
Speed = Distance / Time
Here, the distance is 200 meters and the time is 25 seconds. Substituting these values into the formula, we get:
Speed = 200 meters / 25 seconds
Simplifying, we get:
Speed = 8 meters/second
Therefore, the athlete ran at a speed of 8 meters per second.
Lyla invests $2,500 into a savings account
which earns 5% per year. In 15 years, how
much will Lyla's investment be worth if interest
is compounded semiannually (twice a year)?
Round to the nearest dollar.
Answer:
We can use the formula for compound interest to find the future value of Lyla's investment:
A = P(1 + r/n)^(nt)
where A is the future value, P is the principal (initial investment), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years.
Substituting the given values, we get:
A = $2,500(1 + 0.05/2)^(2*15)
Simplifying, we get:
A = $2,500(1.025)^30
Using a calculator, we get:
A ≈ $5,016.35
Therefore, Lyla's investment will be worth approximately $5,016.35 in 15 years if interest is compounded semiannually. Rounded to the nearest dollar, the answer is $5,016.
At summer camp, 40 students are divided in two groups for swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking.
Outcome Frequency
Swimming 12
Hiking 28
Compare the probabilities and determine which statement is true.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 28 over 40.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40.
The theoretical probability of swimming, P(swimming), is 12 over 28, but the experimental probability is one half.
The theoretical probability of swimming, P(swimming), is 28 over 40, but the experimental probability is one half.
Answer:
Step-by-step explanation:
The theoretical probability of an event is the number of favorable outcomes over the total number of possible outcomes. In this case, the total number of possible outcomes is 2, since each camper can either swim or hike. The number of favorable outcomes for swimming is also 2 (heads on a coin flip). Therefore, the theoretical probability of swimming is 2/2 or 1/2.
The experimental probability of an event is the number of times the event occurred in the experiment divided by the total number of trials. In this case, there were 12 students who chose to swim out of 40 total students. Therefore, the experimental probability of swimming is 12/40 or 3/10.
Comparing the two probabilities, we see that the theoretical probability of swimming is 1/2 while the experimental probability of swimming is 3/10. Therefore, the statement "The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40" is true.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40. (option b)
The theoretical probability of an event is calculated based on the assumption of equal likelihood for all possible outcomes. In this case, since each student flips a fair coin, there are two equally likely outcomes: heads (swimming) and tails (hiking). Therefore, the theoretical probability of swimming (P(swimming)) is 1/2, and the theoretical probability of hiking is also 1/2.
However, the experimental probability is determined by the actual outcomes observed in the experiment. According to the data provided, out of the 40 students, 12 students got heads (swimming) and 28 students got tails (hiking). To find the experimental probability of swimming, we divide the number of students who swam by the total number of students:
12/40 = 0.3.
The theoretical probability of swimming, P(swimming), is one half (0.5), but the experimental probability is 28 over 40 (0.7).
The theoretical probability of swimming, P(swimming), is one half (0.5), but the experimental probability is 12 over 40 (0.3).
The theoretical probability of swimming, P(swimming), is 12 over 28 (~0.4286), but the experimental probability is one half (0.5).
The theoretical probability of swimming, P(swimming), is 28 over 40 (0.7), but the experimental probability is one half (0.5).
Out of these options, the correct one is the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40. (option b).
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The ratio of boys to girls in a class is 4:5 a)What fraction of the class are boys b) what a fraction of the class are boys!
the fraction of the class that are boys is 4/9. And the fraction of the class that are girls is 5/9.
What is ratio?
A ratio is a comparison of two or more quantities that are related in some way. It expresses the relationship between these quantities in terms of the number of times one quantity contains another. Ratios are usually expressed as a fraction, where the numerator represents the first quantity and the denominator represents the second quantity. For example, the ratio of boys to girls in a class of 40 students may be expressed as 2:3 or 2/3, meaning there are 2 boys for every 3 girls. Ratios can also be expressed in other forms, such as percentages or decimals. Ratios are commonly used in mathematics, science, engineering, and everyday life to compare quantities and make predictions or decisions.
A fraction is a number that represents a part of a whole or a ratio of two quantities. It consists of two numbers, a numerator and a denominator, separated by a line. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or in the comparison. Fractions are used in many areas, such as mathematics, science, engineering, cooking, and everyday life. They can be added, subtracted, multiplied, and divided, and can be converted to decimals or percentages.
a) The total ratio of boys to girls in the class is 4+5 = 9. Therefore, the fraction of the class that are boys is 4/9.
b) The question is unclear as it seems to be asking for the same answer as in part (a). If you meant to ask for the fraction of the class that are girls, you can use the same approach: the fraction of the class that are girls is 5/9.
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a toy rocket is shot vertically into the air from a 9-foot-tall launching pad with an initial velocity of 144 feet per second. Suppose the height of the rocket in feet t seconds after being modeled by the function h(t)=-16² gthg. where v is the initial velocity of the rocket and he is the initial height of the rocket. How long will it take for the rocket to reach its maximum The rocker will reach its maximum height in second(s) launched can be height what s
Answer:
9 is answer you fool......
answer: Click THANKS if you like my answer. have a good day sir/maam #keep safe
First, we need to find the maximum height that the rocket will reach. To do that, we need to find the vertex of the parabolic function h(t) = -16t^2 + 144t + 9. We can use the formula for the vertex of a parabola, which is given by the formula t = -b/2a, where a = -16 and b = 144.
t = -b/2a = -144/(2*(-16)) = 4.5
So the rocket will reach its maximum height after 4.5 seconds.
To find the maximum height, we need to substitute t = 4.5 into the function h(t):
h(4.5) = -16(4.5)^2 + 144(4.5) + 9 = 324
So the maximum height that the rocket will reach is 324 feet.
Therefore, the rocket will reach its maximum height of 324 feet after 4.5 seconds.
Step-by-step explanation:
hope its help<:
PLEASE HELP ASAP DUE IN A HOUR
Answer:
51
Step-by-step explanation:
3x+4y^2
3(5)+4(3)^2
3(5)+4(9)
15+36
51
Answer: 51
Step-by-step explanation:
100 Points!!! Algebra question, multiple choice. Only looking for an answer to #8. Find the maximum value of f(x,y)=3x+y for the feasible region. Photo attached. Thank you!
Answer:
+4
Step-by-step explanation:
F(x,y) = 3x+y and y <= -2x+ 4 sub in for 'y'
= 3x + (-2x+4)
= x + 4
If you look at the graph for y <= - 2x+4 ( see below)
you will see that the domain (x values ) can only go from 0 to 4 and the max value is +4 ( rememeber too that y is restricted to >= 0 as is x )
what is the angle measurement of 1
I'm sorry, but your question is not clear. Did you mean "What is the angle measurement of a unit circle when radius equals 1?" If so, the answer is that the angle measurement is 360 degrees or 2π radians.
Solve the radical equation √2-√36 - 2x = 6. Check for extraneous solutions.
The solution is |
The extraneous solution is
Enter the real solution first followed by the extarneous solution separated
by a comma.
For example, if real solution is 10 and the extraneous solution is 2.
Enter as 10,2.
Answer:
We have the equation:
√2 - √36 - 2x = 6
Simplifying the radicals we get:
√2 - 6 - 2x = 6
Adding 6 to both sides we get:
√2 - 2x = 12
Subtracting √2 from both sides we get:
-2x = 12 - √2
Dividing by -2 we get:
x = (6 - (1/√2))
Therefore, the real solution is:
x = (6 - (1/√2))
To check for extraneous solutions, we need to substitute this value of x back into the original equation and check if it satisfies the equation.
√2 - √36 - 2(6 - (1/√2)) = 6
Simplifying this we get:
-6 = 6
This is not true, so the solution x = (6 - (1/√2)) is extraneous.
Therefore, there is no real solution to the equation.
As shown in the figure below, Kaitlin is standing 93 feet from the base of a leaning tree. The tree is growing at an angle of
88° with respect to the ground. The angle of elevation from where Kaitlin is standing to the top of the tree is 35°. Find the
length, x, of the tree. Round your answer to the nearest tenth of a foot.
35°
-93 ft-
H
88°
feet
X
5
Answer:The measure of Ф = 75.7° :)
Step-by-step explanation:the measure of Ф = 75.7°,We will use the rule sin to find the measure of Ф
At first we will find the angle opposite to the side of length 31
∵ 180° - 73° = 107°
hope this helps:)(:
find the value of x and y
Answer:
Try using the Symbolab calculator.
Step-by-step explanation:
Thats what I usually use and it works
There is a park near Raphael’s home. To find its area, Raphael took the measurements shown. Select all the true statements about the area of the park.
(a)The park can be decomposed into two parallelograms.
(b)The formula A = bh can be used to find the area of each piece of the park.
(c)The park can be decomposed into a parallelogram, a triangle, and a trapezoid.
(d)The area of the park is 126 m2.
(e)The area of the park is 96 m2.
Answer:
A, C, and D
Step-by-step explanation:
If you split the shape right along the bottom of the first part, you get two parallelograms. If you split it like you split it the first time and then split it along the side of the bottom parallelogram you get a triangle, a parallelogram, and a trapezoid. Then, because the area of a parallelogram is A=bh, you can substitute the numbers in. 5*12=60 and 6*11=66. However, this is not all, remember to add the area together! 60+66=126 so D is also true.
Hope this helps!