Answers
Answer:
[tex]y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|}\cline{1-2} \phantom{\dfrac{1}{1}} x & y \\\cline{1-2} \phantom{\dfrac{1}{1}} -1 & 7 \\\cline{1-2} \phantom{\dfrac{1}{1}} 0 & \frac{7}{3}\\\cline{1-2} \phantom{\dfrac{1}{1}} 1 & \frac{7}{9}\\\cline{1-2} \phantom{\dfrac{1}{1}} 2 & \frac{7}{27}\\\cline{1-2} \phantom{\dfrac{1}{1}} 3 & \frac{7}{81}\\\cline{1-2}\end{array}[/tex]
Linear function: As x increases by one, y always increases by a constant value. Therefore, the first differences between y-values are the same.Quadratic function: The second differences between y-values are the same.Exponential function: The y-value either increases or decreases by a constant factor.Work out the first differences between the y-values:
[tex]7 \underset{-\frac{14}{3}}{\longrightarrow} \dfrac{7}{3} \underset{-\frac{14}{9}}{\longrightarrow} \dfrac{7}{9} \underset{-\frac{14}{27}}{\longrightarrow} \dfrac{7}{27} \underset{-\frac{14}{81}}{\longrightarrow} \dfrac{7}{81}[/tex]
As the first differences are not the same, it is not a linear function.
Work out the second differences:
[tex]-\dfrac{14}{3} \underset{+\frac{28}{9}}{\longrightarrow} -\dfrac{14}{9} \underset{+\frac{28}{27}}{\longrightarrow} -\dfrac{14}{27} \underset{+\frac{28}{81}}{\longrightarrow} -\dfrac{14}{81}[/tex]
As the second differences are not the same, it is not a quadratic function.
Work out if the second differences have a common ratio:
[tex]\implies \sf \dfrac{28}{27} \div \dfrac{28}{9}=\dfrac{1}{3}[/tex]
[tex]\implies \sf \dfrac{28}{81} \div \dfrac{28}{27}=\dfrac{1}{3}[/tex]
As the second differences have a common ratio of ¹/₃, the function is exponential with base ¹/₃.
General form of an exponential function:
[tex]y=a(b)^x[/tex]
where:
a is the y-intercept.b is the base (growth/decay factor) in decimal form.The y-intercept is the value of y when x = 0.
From inspection of the table, the y-intercept is ⁷/₃.
Therefore:
[tex]a = \dfrac{7}{3}[/tex]
[tex]b = \dfrac{1}{3}[/tex]
Substitute the found values of a and b into the formula to create an exponential function that models the given data:
[tex]\implies y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]
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Related Questions
Sofia reads 8 books over summer break. Her brother reads 3 fewer books than she reads. How many books do Sofia and her brother read in all? They read books in all.
Answers
Answer:
13
Step-by-step explanation:
8-3 is 5, so her brother read 5 books. 8+5=13 so they read 13 total books.
Round 34608 to the nearest hundred
Answers
"'s cell phone bill was $52.75 in July
In August
her bill was 60% of her July bill
How much more
did she pay in July than
she did in August?
Answer:
3460800.00
explanation:
Function yes or no whag is the domain and range?
Answers
Step-by-step explanation:
to be a function every value of x must have exactly one value of y.
in other words, if you create a vertical line and move it across the whole chart (e.g. from left to right), this line must not even once intersect the function curve more or less than once.
so, this is clearly a given here. yes, it is a function.
the domain is the interval or set of all valid x (input) values. and that starts on the right with x = 5 (included in the function indicated by the filled dot). and it goes endlessly to the left. that means -infinity (but not included as "infinity" is only a symbol but not a number).
-infinity < x <= 5
the range is the interval or set of all valid y (function result) values.
and that starts on the top with y = 2 (included). and it goes endlessly down. that means again -infinity (not included).
-infinity < y <= 2
Find a conversion factor between square feet and square yards. Write it in three forms.
Select one:
A. 1 yd^3 = (3 ft)^3 = 27 ft^3
B. 1yd^3 = (3 yd)^3 = 27 yd^3
C. 1 yd^2 = (3 ft)^2 = 9 ft2
5 D. 1ft^2 = (3 yd)^2= 9 yd^2
Answers
By dimensional analysis and the conversion factor between feet and yards, we find that a square yard is equal to a quantity of 3² square yard, that is, a quantity of 9 square feet. (Correct choice: C)
What is the conversion factor between two quantities in area units?
In accordance to dimensional analysis, area units are equal to the square of length units, that is, length unit multiplied by length unit. That is:
[A] = [L] × [L] = [L]²
Where:
L - Length unit
A - Area unit
If a yard is equal to a quantity of three feet, both length units, then a square yard is equal to a quantity of 3² square feet, that is, a quantity of 9 square feet, both area units. Therefore, we can construct the following conversion factor:
1 square yard = (3 feet)² = 9 square feet
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I don’t know how to do this -2(-5+n)=6 ?
Answers
Answer:
n = 2
Step-by-step explanation:
So all you have to do is solve:
-2(-5 + n) = 6
= 10 + -2n = 6
= -2n = -4
= n = 2
This means that n = 2.
But what if I'm wrong? So lets see if it works.
-2(-5 + 2) = 6
10 - 4 = 6
6 = 6
So n = 2 is right.
Hope this helped! :D
Answer:
n = 2Step-by-step explanation:
I don’t know how to do this -2(-5+n)=6 ?
-2*(-5+n)=6
10 -2n = 6
10 - 6 = 2n
4 = 2n
2 = n
-----------------
check
-2 ( -5 * 2) = 6
10 - 4 = 6
6 = 6
Help please .
I can’t figure out magnitude . Can anyone help me ASAP ?
Answers
Answer:
|-20| |12.3| |8| |-6| |-4| |2 3/10|
Step-by-step explanation:
Magnitude in this context means that they want you to order the values from greatest to least. These are all absolute values and that means distance from zero without regard to sign. So if you just stripped the signs and absolute value symbols off of each value, then ordered them from largest to smallest, and THEN added the signs and absolute value symbols back, you have the answer.
Answer:
From greatest to least magnitude
|-20|
|12.3|
|8|
|-6|
|-4|
[tex]\lvert {2 \frac{3}{10}}\rvert[/tex]
Step-by-step explanation:
The absolute value of a number |x| is the positive value of x. So if x is positive then it's the number itself and if x is negative it is the positive value of the number
Ex. |5| = 5 and |-5| = 5
Take the absolute values of each of the numbers first
|12.3| = 12.3
|-20| = 20
|2 3/10 | = 2 3/10 = 23/10 = 2.3
|-4| = 4
|8| = 8
|-6| = 6
Now arrange these numbers from greatest to least. The order is
20, 12.3, 8, 6, 4, 2.3
So in terms of the original numbers this corresponds to
|-20| , |12.3| , |8|, |-6| , |-4| , |2 3/10|
A certain smartphone regularly costs $849. During a clearance sale, it was marked down 30%. One day, an additional 10% was taken off already-reduced prices. Ignoring tax, what was the final price after both discounts were applied?
Answers
Answer:
$534.87
Step-by-step explanation:
($849)30%
=$254.7
subtract product from original sum $849-254.7=
$594.3
($594.3)10%=
59.43$
594.3$-59.43$=
534.87$
Which graph represents a function that has the domain (–∞, –4) ⋃ (–4, 3) ⋃ (3, ∞), has a y-intercept at (0, 3), and is increasing on the interval (0, 4)?
Answers
The y-intercept of a graph is the point, where the graph crosses the y-axis. and The graph with the given details is graph (c).
According to the statement
We have to find that the correct graph which represent the domain.
So, For this purpose, we know that the
The domain of a function is the set of all possible inputs for the function.
From the given information:
The function that has the domain (–∞, –4) ⋃ (–4, 3) ⋃ (3, ∞), has a y-intercept at (0, 3), and is increasing on the interval (0, 4).
Then
we have given a four graphs as a option which are in the image below after seeing that we know that the:
From the list of given options. graph (d) includes a y intercept of two, because it crossed the y-axis at y = 2.
So, graph (d) can not be the desired graph
And then
Graph (a) features a domain of: (–∞, –5)
So, graph (a) can't be the desired graph
And then
The domain of graph (b) is [-3,3]
So, graph (b) can't be the desired graph.
Hence, the required graph is graph (c).
So, The y-intercept of a graph is the point, where the graph crosses the y-axis. and The graph with the given details is graph (c).
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How much larger is 3/4 than 2/3
Answers
Answer:
3/4 = 0.75 2/3 = 0.6667 Now that these fractions have been converted to decimal format, we can compare the numbers to get our answer. 0.75 is greater than 0.6667 which also means that 3/4 is greater than 2/3.
Step-by-step explanation:
State the parent function and transformation. WILL GIVE BRAINLIEST
Answers
is there an image ? or just question
The parent function of the function y = 2x² - 6 is y = x². The explanation about transformation is given.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
We have the quadratic function,
y = 2x² - 6
To find the parent function:
Add
y(x) = 2x²
Divide by 2
y(x') = x²
If there is a horizontal or vertical shift, reflection around the x-axis or y-axis, or vertical stretch, the transformation may be found by comparing the equation to the parent function.
Parent Function:
y = x²
Horizontal Shift: None
Vertical Shift: Down 6 Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: Stretched
Therefore, the parent function is y = x².
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PLEASE HELP DUE SOON!
I'm so confused, help determine the 100th line segment from question below!
Answers
Answer:
20200
Step-by-step explanation:
As you're in a hurry, I can give it later? xx
Three angles are supplementary, angle one has a measure of 7x+10, angle two has a measure of 3x+4 and angle three has a measure of 3x+8.
Given that the angles are supplementary what is the measure of angle one? Round your answer to the hundredths place
Answers
The measure of the angle 1 is 95.05 degrees.
It is given in the question that:-
Measure of Angle 1 = 7x + 10
Measure of Angle 2 = 3x + 4
Measure of Angle 3 = 3x + 8
All the angles are supplementary.
We know that, the sum of all the supplementary angles is equal to 180 degrees.
Hence, we can write,
(7x + 10) + (3x + 4) + (3x + 8) = 180
(7x + 3x + 3x) + (10 + 4 + 8) = 180
13x + 22 = 180
13x = 180 - 22
13x = 158 degrees
x = 158/13 degrees
x = 12.15 degrees (rounded off to the hundredths place )
Hence,
Measure of angle 1 = 7x + 10 = 7(12.15) + 10 = 85.05 + 10 = 95.05 degrees.
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13.95 + 0.49x = 50 - 13.95 - x
Whats the value of x please i have a test today
Answers
Answer:
14.832
Step-by-step explanation:
I hope this helps good luck
what is equivalent to 10+ 4(-8q - 4)?
Answers
.25 = p ,
Solution :
equivalent to 10+ 4(-8q - 4)
Equivalent equations are systems of equations that have the same solutions. Identifying and solving equivalent equations is a valuable skill, not only in algebra class but also in everyday life. Take a look at examples of equivalent equations, how to solve them for one or more variables, and how you might use this skill outside a classroom.
Equivalent equations are systems of equations that have the same solutions. Identifying and solving equivalent equations is a valuable skill, not only in algebra class but also in everyday life. Take a look at
examples of equivalent equations
Equivalent equations are algebraic equations that have identical solutions or roots.
Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation.
Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.
The first step is to know the rules of equivalent equations:
Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation.
Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.
Raising both sides of the equation to the same odd power or taking the same odd root will produce an equivalent equation.
If both sides of an equation are non-negative, raising both sides of an equation to the same even power or taking the same even root will give an equivalent equation.
Solution :
10+ 4(-8q - 4)=0
10+ 4(-8q ) = 4
10-24 p =4
10 -4 =24 p
6 =24 p
6/24 = p
1/4 = p
.25 = p
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what is −3.6 ÷ 2 1/7
Answers
The result of the evaluation as given in the task content is; -42/25.
Fraction divisionIt follows from the task content that the result of the evaluation is required.
First, -3.6 and 2 1/7 can be converted to fractions as follows;
-3.6 = -36/10 = -18/5
2 1/7 = 15/7
Hence; −3.6 ÷ 2 1/7
= -18/5 ÷ 15/7
= -18/5 × 7/15
= -42/25.
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The record high January temperature in Austin, Texas, is 90°F. The record low
January temperature is -2°F. Find the difference between the high and low
temperatures.
Answers
Answer:
92 degrees
Step-by-step explanation:
-2 is 2 degrees from 0. the high is 90. Add them together for 92 :)
Answer:
92 degrees
Step-by-step explanation:
90 - (-2) = 92
Is a solution given?
Answers
Answer:
No, it is not given
Step-by-step explanation:
PLS HELP IM TIMED!!!
Answers
Answer:
MDS/GDS
10....../9.6
8......./7.6
4.75./4.69
4......./3.6
(I hope so)
Find the approximate side length of a square game board with an area of 200 in².
Answers
The length of the side is 10√2 cm.
To solve this problem we need to know the concepts of area of plane figures.
We know the area of a square is the square of its sides.
Now, the given data says that the area of a square game board is 200 sq.cm.
Let the side of the square be a cm.
According to question,
a × a=200
⇒ a² = 200
⇒ a = √200
∴ a = 10√2 cm
So, the length of one side of the square game board is 10√2 cm.
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g(x)=3x+1
f(x) =x^2 + 3x^2
Find g(2)•f(2)
Answers
Answer:
112
Step-by-step explanation:
Just plug in 2 into the equations and then multiply them together at the end.
g(2) = 3(2) + 1
= 6 + 1
= 7
f(2) = (2)² + 3(2)²
= 4 + 3(4)
= 4 + 12
= 16
g(2) × f(2)
7 × 16 = 112
Beinggreat78, you really are GREAT like seriously. You chose the right name
Answers
Answer:
D
Step-by-step explanation:
becasue one is shaded in so it's is going to be a mixed number and there is 15 other shaded blocks so 15/100 is 3/20 so the answer is 1 and 3/20
Answer:
D
Step-by-step explanation:
All work and the answer is provided in the attached screenshot! :)
If your expenses are more than your income, then you have a positive net cash flow . True or false?
Answers
Answer:
True it is because my expenses is more than my income
Find the amount of simple interest earned for depositing the given principle in an account. if $4200 is invested at 4.5 % for 4 months
Simple interest: $
Answers
well, keeping in mind a year has 12 months, thus 4 months is really 4/12 of a year
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$4200\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ I = (4200)(0.045)(\frac{1}{3}) \implies I=63[/tex]
w = 5x² + 3
x = -3
Work out the value of w.
Answers
Answer:
48
Step-by-step explanation:
w = 5x² + 3
x = -3
w = 5(-3)² + 3
w = 5(9) + 3
w = 45 + 3
w = 48
Estimate using compatible numbers then find quotient 62÷1178
Answers
Answer:
the answer would be 0.05
200 applicants applied to volunteer at an international tennis tournament.
14
of the applicants were successful. However, of the successful applicants, 15
couldn’t make all the training sessions and were discounted.
How many were selected to help at the tournament?
Answers
The number of volunteers who are selected for the tennis tournament is 40 as calculated by the fractions.
A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction in spoken English refers to the number of components of a particular size.
A fraction consists of a numerator and a denominator. The numerator divided by the denominator is known as a fraction.
Compound fractions, complicated fractions, and mixed numeral fractions are examples of uncommon fractions that use numerators and denominators.
There are a total of 200 applicants who volunteered at the tennis tournament.
1/4 of the volunteers were successful.
Number of successful applicants= [tex]\frac{1}{4} \times 200=50[/tex]
Now 1/5 of the successful candidates could not complete the training.
Number of unsuccessful candidates= [tex]\frac{1}{5} \times 50=10[/tex]
Number of Volunteers selected to help at the tournament= 50-10=40
Hence 40 candidates were selected to help at the tournament.
Disclaimer: The complete correct question is :
200 applicants applied to volunteer at an international tennis tournament.1/4th of the applicants were successful. However, of the successful applicants, 1/5th couldn’t make all the training sessions and were discounted. How many were selected to help at the tournament?
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A company invests $15,000 to produce a product that will sell for $56.75. Each unit costs $9.25 to produce. (Round your answers to the nearest whole number.) (a) How many units must the company sell to break even? units (b) How many units must the company sell to make a profit of $105,000? units
Answers
Answer:
x = 2,495 units
Step-by-step explanation:
16000 + 9.45x = 55.95x
by solving we find:
x = 344 units
the company must sell 344 units to break even.
b) How many units must the company sell to make a profit of $100,000?
55.95x - (16000 + 9.45x) = 100000
HELP PLEASE
The absolute value inequality 5 <= I x l — n is graphed below. What is the value of n?
Answers
Answer:
I think the answer is 7
Step-by-step explanation:
Saiqa spent a total of Rs. 280.75 on a book, a pen and a file. The pen cost Rs. 20.25 more than the file. The book cost Rs. 13.20 less than the pen. How much did she spend on the file and the pen?
Answers
The price of the file is Rs 89.18 and pen is Rs 109.43 as calculated from a linear equation .
An equation is said to be a linear equation if the maximum power of the variable is consistently 1.
Another name for it is a only one-degree equation is linear equation.There are only one or two variables in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Let us consider the cost of the file be x dollars.
Then cost of the pen = x + 20.25
And cost of the book = x + 20.25 - 13.20 = x - 7.05
The cost of all three items together is 280.75
Now we will form a linear equation in x to find the cost of each of the pen, book and file separately.
x + x + 20.25 + x - 7.05 = 280.75
or, 3x + 13.20 = 280.75
or, 3x = 267.55
or, x = 89.18
Hence the cost of the file is approximately Rs 89.18
Cost of the pen = 89.18 + 20.25 = Rs 109.43
Cost of the book = x - 7.05 = 89.18 - 7.05 = Rs 82.13
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Connor missed 12 out of his last 18 free throws. What is the experimental probability that
Connor will miss his next free-throw attempt?
Write your answer as a fraction or whole number.
Answers
The experimental probability that Connor will miss his next free-throw attempt is 2/3.
How to calculate the probability?From the information, Connor missed 12 out of his last 18 free throws.
Therefore, the probability will be:
= Number of missed throws / Total throws
= 12/18
= 2/3
Therefore, the experimental probability that Connor will miss his next free-throw attempt is 2/3.
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