The value, v, of your quarters (in cents) is a function of n, the number of quarters you have.Identify the independent variablea) Draw a input-output diagram to represent this functionb. write an equation that represents this functionc. find the output when the input is 10d. identify the independent and dependent variables
Answers
Answer:
b. v = 25n
c. v = 250
d. Independent variable: n
dependent variable: v
Explanation:
Part a.
The value, v, of your quarter is a function of n, the number of quarters you have, so given a value of n, you can calculate the value of v.
If n = 1
v = 25
Because one quarter has a value of 25 cents.
If n = 2
v = 2(25) = 50
because two quartes has a value of 50 cents.
If n = 3
v = 3(25) = 75
Therefore, we can draw a diagram using the points (1, 25), (2, 50), and (3, 75) as follows
Part b.
Then, we can see that the value of your quartes is 25 times the number of quartes, so the equation that represents this function is
v = 25n
Part c.
To find the output when the input is 10, we need to replace n by 10 on the equation above
v = 25n
v = 25(10)
v = 250
So, the output is 250 cents
Part d.
The value of your quarters depends on the number of quarters you have, so the dependent variable is v, the value of your quarters and the independent variable is n, the number of quarters.
Related Questions
Hello can anyone help me with these problems please and ty
Answers
12. x= 4
13. x= 4
14. x= -1
Check the steps in the picture above
Error Analysis:
Describe and correct the error made in the reasoning:
If a/5 = b/3, then 5/a = b/3 * x
Answers
The correct expression is 5/a = 1. There is no need to introduce an additional variable "x".
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
The error in the reasoning is that it assumes that multiplying the second fraction by "x" will result in an equivalent expression to 5/a. However, this is not necessarily true.
To correct the error, we can use the property of reciprocals, which states that if a/b = c/d, then b/a = d/c. Using this property, we can rewrite the given equation as:
a/5 = b/3
5/a = 3/b (multiplying both sides by 5/a)
5/a = (b/3) * (3/b) (multiplying both sides by the reciprocal of b/3)
5/a = 1
Therefore, the correct expression is 5/a = 1. There is no need to introduce an additional variable "x".
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Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
Answers
Using the table, we can see that the loan increases by a factor of 1.058 after 1 year and by a factor of 1.058/1.045 = 1.0124 after 2 years. Thus, we have:
1.058 = (1 + r/n)^(n*1)
1.0124 = (1 + r/n)^(n*2)
Dividing the second equation by the first, we get:
1.0124/1.058 = (1 + r/n)^(n*1)
Taking the nth root of both sides, we get:
(1 + r/n) = (1.0124/1.058)^(1/n)
Solving for r, we get:
r = n * [(1.0124/1.058)^(1/n) - 1]
We don't know the value of n, but we can make an educated guess that it's either 1 or 2, since the loan is increasing by roughly 5.8% per year. If we try n = 1, we get:
r = 1 * [(1.0124/1.058)^(1/1) - 1] = -0.0427
This is clearly not the correct answer, since the interest rate cannot be negative. If we try n = 2, we get:
r = 2 * [(1.0124/1.058)^(1/2) - 1] = 0.0574
This is a reasonable answer, since it's close to the observed increase in the loan value of 5.8% per year. Therefore, the rate of interest per annum is 5.7% to 1 d.p.
(b) Using the formula for compound interest, we can find the value of the loan 10 years after it starts:
A = P * (1 + r/n)^(n*t) = 2500 * (1 + 0.0574/1)^(1*10) = £4,745.60 (to the nearest 1p
Answer:
25000
Step-by-step explanation:
x = 8 is a solution for equation 3x = 27 true or false
Answers
ANSWER
False
EXPLANATION
The guven equation is:
3x = 27
For x to be a solution of the equation, the value of x must be such that the left and right hand sides of the equation must match.
So, for x = 8:
3(8) = 27
24 = 27
As we can see, the two sides do not match, so x = 8 is not a solution.
A number is chosen at random from 1 to 50. Find the probability of selecting numbers less than 13
Answers
Answer:
6/25
Step-by-step explanation:
Less than 13, there is 12 numbers in total
Probability = favourable outcomes/ total outcomes
= 12 / 50
= 6/25 or 0.24 is the probability of selecting numbers less than 13
a) Imagine that you need to create a scale drawing of this sign. The scale drawing will
be used to create a mold that will be used to manufacture the sign. Use the grid to
make a scale drawing of this sign. Include a key to show the relationship between
the dimensions in the scale drawing and the dimensions of the actual sign. Label all
sides in the scale drawing. Show your work. (3 points)
Answers
Answer:
A=b/2
Step-by-step explanation:
you're simplifying both ends of an equation.
Answer:
A scale drawing with a 1: 0,8 scale will have sides that measure 2.24, 1.6, and 3.2.
Step-by-step explanation:
A scale drawing refers to a drawing that has been made bigger or smaller but preserves the proportions of a drawing.
How to make the scale drawing of the sign?
The first step is to decide the scale. In this case, the best scale is 1:0.8, which means the new drawing is 0.2 smaller. This scale is ideal because this sign is slightly bigger than regular signs.
Draw the sign by multiplying each side by the scale (0,8).
how much money deposited now will provide payment of Rs. 15000 at the end of each half year for 10 years, if interest is 16% compounded six-monthly
Answers
The interest is 16% compounded semi-annually, is Rs. 121,179.10.
To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.
Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)
So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:
Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.
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An investor wants to save money to purchase real estate. She buys an annuity with yearly payments that earn 5.3% interest compounded annually payments will be made at the end of each year find the total value of the annuity in 16 years if each yearly payment is 693.
Answers
The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity,
P is the yearly payment,
r is the interest rate per compounding period, and
n is the number of compounding periods.
In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.
Let's substitute these values into the formula and calculate the total value of the annuity:
FV = 693 * ((1 + 0.053)^16 - 1) / 0.053
FV = 693 * (1.053^16 - 1) / 0.053
Using a calculator, we can evaluate the expression inside the parentheses:
1.053^16 ≈ 1.9738
Substituting this value back into the formula:
FV = 693 * (1.9738 - 1) / 0.053
FV = 693 * 0.9738 / 0.053
FV ≈ 12739.62
Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.
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Find an equation of the line that satisfies the given conditions.
Through
(−3, 2) and (−2, −5)
Answers
Answer:
Step-by-step explanation:
y=mx+b, where m=slope and b=y intercept
m=(y2-y1)/(x2-x1), we have points (-3,2) and (-2,-5) so
m=(-5-2)/(-2-(-3))
m=-7/1
m=-7, now our line is
y=-7x+b, using point (-3,2) we can solve for b
2=-7(-3)+b
2=21+b
b=-19, so the completed line is
y=-7x-19
Answer:
y=−7x−19
Step-by-step explanation:
Which of these shapes have the same area?? help ;-;
Answers
Answer:
A and B because if you count they both have 16 and C has 25
what is the graph of f(x) = 5(2)^x
Answers
The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.
The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.
As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:
When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).
As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.
For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.
The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.
Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.
The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.
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Help me quick taking a test need it down before 12
Answers
I’m just filling the 20 character thing now lol
The volume of this prism is 2 1/2 cubic centimeters.
Its height is 1/3 of a centimeter.
What are possible values for its length and width?
Answers
One of the Possible values of length and width of the prism are 15 cm and 0.5 cm
What is the volume of the prism?In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.
Given here: The volume of the prism is 2¹/₂=2.5 cm³
And the height is 1/3 cm
let the length and breadth of the prism is x and y respectively.
We know the volume of the prism as
1/3 × x×y=2.5
x×y=7.5
Thus possible values of length and breadth are the factors of 7.5
out of which one of the pair whose length is 15 cm and width 0.5 cm
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Find f(-2) for f(x) = 2(4)^x
O A.1/16
O B.1/8
O C. -16
OD. - 32
Answers
Answer:
B. 1/8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
\(\displaystyle f(x) = 2(4)^x\\f(-2) \ is \ x = -2\)
Step 2: Evaluate
Substitute in x: \(\displaystyle f(-2) = 2(4)^{-2}\)Exponents: \(\displaystyle f(-2) = 2(\frac{1}{16})\)Multiply: \(\displaystyle f(-2) = \frac{1}{8}\)A direct variation includes the points (2,18) and (n,9). Find n?
Answers
The value of the n is 1
In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.
To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.
(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:
18 = k(2)
k = 18/2
k = 9
Now that we have found the value of k, we can use it to find n when y = 9:
9 = 9n
n = 1
Therefore, the value of n is 1.
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The graph shows the absolute value parent function. Which statement is true? A. (1, 1) is the x- and y-intercept of the function. B. (0, 1) is the x- and y-intercept of the function. C. The function has no intercepts. D. (0, 0) is the x- and y-intercept of the function.
Answers
Answer:(0,0) is the x and y intercept
Of the function
Step-by-step explanation:
They both meet at the origin (0,0)
The true statement is (d) (0, 0) is the x- and y-intercept of the function.
How to determine the true statement?The missing graph is added as an image
From the graph, we can see that the function passes through the point:
(x,y) = (0,0)
This means that (0, 0) is the x- and y-intercept of the function.
Hence, the true statement is (d)
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what is 0.56 ÷ 0.04 please explain in an simplified answer
Answers
Answer:
14
Step-by-step explanation:
0.56÷0.04
=(0.56×100)÷(0.04×100)
=56÷4
=14
So, the answer is 14.
Simplest form 816/10
Answers
The simplest form of 816/10 is 408/5
Please mark my answers as brainlist....
Henry correctly factored 42? + 52 - 6 as (4% - 3)(₴ + 2)
• He then claimed that the zeros of that quadratic function are located at
*=-=
and r = 2 . Did Henry correctly find the zeros of the function?
O Yes, Henry correctly found the zeros of the function.
O No, the zeros of the function are at x = 4 and =-2
• No, the zeros of the function are at z = - 5 andx = 2.
• No, the zeros of the function are at & = 4 and ≥ = -2
I attached the question and answer choices
Please help
Answers
Answer:
No, the zeros of the function are at x = 3/4 and x = –2
Step-by-step explanation:
the equation
4x² + 5x – 6 = 0
(note: since there is a coefficient of x² we need to multiply it to the last term(6))
4x² + 5x – 24 = 0
the factors are :- 8x and – 3x
4x² + 8x – 3x – 6 = 0
4x( x + 2) –3( x + 2) = 0
( 4x – 3)( x + 2) = 0
the zeros will be
4x – 3 = 0
4x = 3
\(x = \frac{3}{4} \)
x + 2 = 0
x = – 2
the zeros are x= 3/4 or –2
i hope this helps
What is the area of a triangle with side lengths 17, 18, and 19? Express your answer in simplest radical form.
Answers
The area of a triangle with side lengths 17, 18, and 19 in simplest radical form is 18√7770
How to find the area of the triangleThe area of the triangle is calculated using the formula
Area of triangle = √[s(s – a)(s – b)(s – c)]
s = perimeter o the triangle
a, b and c are the lengths of the triangle
s = a + b + c = 17 + 18 + 19 = 54
Area of triangle = √[54 * (54 – 17)(54 – 18)(54 – 19)]
Area of triangle = √[2517480]
Area of triangle = 18√7770
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Problem’s in the image
Answers
The growth rate function indicates that the number of years The Iron Man's net worth will reach the net worth of T'Challa is about 87 years
What is a growth rate?The growth rate is the rate of growth of a function with regards to the input variable.
T'Challa's net worth in the Marvel comics = 80 trillion (8 × 10¹³) Dollars
The Iron Man's net worth = 20 billion (2 × 10¹⁰) Dollars
The growth rate per annum of The Iron Man's net worth = 10% per annum
The number of years it will take to reach T'Challa can therefore, be found as follows;;
(2 × 10¹⁰) × (1 + 0.1)ˣ = (8 × 10¹³)
(1 + 0.1)ˣ = (8 × 10¹³)/(2 × 10¹⁰)
x·ln(1 + 0.1) = ln((8 × 10¹³)/(2 × 10¹⁰))
x = (ln((8 × 10¹³)/(2 × 10¹⁰)))/(ln(1 + 0.1)) ≈ 87 years
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A basketball roster is shown in the table.
A 4-column table with 7 rows titled Basketball Roster. Column 1 is labeled Player with entries Adams, Brock, Cup, Dennis, Early, Finn, Graham. Column 2 is labeled Grade with entries 11, 12, 11, 10, 12, 11, 12. Column 3 is labeled Position with entries G, F, F, G, C, F, G. Column 4 is labeled height with entries 5 foot 6, 5 foot 8, 5 foot 9, 5 foot 3, 5 foot 11, 5 foot 9, 5 foot 5.
Which variable would be classified as a continuous quantitative variable?
grade
height
player name
position
Answers
Using variable concepts, it is found that the player's height is a continuous quantitative variable.
What are continuous and discrete variables?Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, ...What are qualitative and quantitative variables?Qualitative variables: Assumes labels or ranks.Quantitative variables: Assume numerical values.In this problem:
The player name and position are qualitative variables.Grade assumes only integer values, hence it is discrete.The height is quantitative, assuming decimal values in inches, hence it is also continuous.You can learn more about continuous and discrete variables at https://brainly.com/question/16978770
Answer:
height
Step-by-step explanation:
noballz
Which is equal to –214°?
Answers
Answer:
B
Step-by-step explanation:
Convert from degrees to radians using ratio pi/180. -107pi/90 radians would be the answer. Also edg. 2020
-107pi/90 radians is equal to -214degree.
We have to determine which is equal to –214°
Convert from degrees to radians using the ratio.
How to convert a degree into a radian?
To convert the value of the angle in degree, to its equivalent radians, we need to multiply the given value by π/180.
pi/180.
-107pi/90 radians is equal to -214degree
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HELLPP Determine the constant of proportionality in the situation below.
Five bags of candy cost $15.75
Answers
Answer:
3.15
Step-by-step explanation:
15.75 divided by 5 gets you 3.15
What is the standard deviation of this data set ?Reporting 2 more decimal places than the original data. 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61
Answers
Answer:6.986
Step-by-step explanation:
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number. Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number. In this case your standard deviation is 6.986.
Answer: Standard deviation is 6.986.
Step-by-step explanation:
Given an data 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61 and have to calculate standard deviation
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number.
Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number.
In this case standard deviation is 6.986.
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a tank truck holds 33.8 kl of oil. How many gallons does it hold
Answers
human is a social being justify the statement
Answers
Step-by-step explanation:
We humans are social beings; we share mirror neurons that allow us to match each other’s emotions unconsciously and immediately. We leak emotions to each other. We anticipate and mirror each other’s movements when we’re in sympathy or agreement with one another—when we’re on the same side. And we can mirror each other’s brain activity when we’re engaged in storytelling and listening – both halves of the communication conundrum.
This view of the human state is directly contrary to the way most people think about communications. The old model has a sender, a message, a receiver, feedback and noise. It’s far too mechanistic and simple to describe adequately what’s really going on. It leaves out the communal nature of communications.
pls answer my question
Answers
Answer:
x = 23
Step-by-step explanation:
Exterior angles equals the sum of opposite interior angles.
2x+ 3 + 51 = 100
Combine like terms.
2x + 54 = 100 {Subtract 54 from both sides}
2x = 100 - 54
2x = 46 {Divide both sides by 2}
x = 46/2
x = 23
Determine the surface area and volume. Note: The base is a square.
Answers
Answer:
volume=60cm3, surface area=96cm2
Step-by-step explanation:
volume=1/3×(6×6)×5
=60cm3
surface area= 4(1/2×6×5)+(6×6)
=96cm2
Suppose S is between R and T. Use the Segment Addition Postulate to solve for each variable. Round to 3 decimal places.
RS = 7y - 2
ST = y + 7
RT = 26
Y= ?
Answers
Answer:
\(y=2.625\)
Step-by-step explanation:
With the information given, the line should look something like so:
R------------------S---------------------T
By the segment addition postulate, we know that RS+ST=RT.
Insert the given information into the equation:
\((7y-2)+(y+7)=26\)
Solve for y. SImplify the parentheses:
\(7y-2+y+7=26\)
Combine like terms:
\(7y+y-2+7=26\\\\8y+5=26\)
Subtract 5 from both sides:
\(8y+5-5=26-5\\\\8y=21\)
Isolate the variable. Divide both sides by 8:
\(\frac{8y}{8}=\frac{21}{8} \\\\ y=2.625\)
:Done