Answer: x = 23
Step-by-step explanation:
Move all terms that don't contain
x
to the right side and solve.
Hope this helps :)
identify the slope y-intercept and equation of the line given the two points, 0.4 and 2,5
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{0})\implies y=\cfrac{1}{2}x+\text{\LARGE 4}~\hfill \stackrel{y-intercept}{(0,\text{\LARGE 4})}[/tex]
let f be the function given by f(x)= lnx/x for all x>0. the derivative of f is given:
f'(x)= (1-lnx)/x^2
a) write an equation for the line tangent to the graph of f at x=e^2
b) find the x-coordinate of the critical point of f. Determine whether this point is a relative minimum, a relative maximum, or neither. justify your answer.
c) the graph of the function f has exactly one point of inflection. Find the x-coordinate of this point.
d) find thef(x)
a) To find the equation of the line tangent to the graph of f at x = e^2, we need to find the slope of the tangent line and the y-intercept. The slope of the tangent line is given by the derivative of f evaluated at x = e^2: f'(e^2) = (1 - ln(e^2))/(e^2)^2 = (1 - 2)/e^4 = -1/e^4
The y-intercept is found by plugging x = e^2 into the original function and finding the corresponding y-value: f(e^2) = ln(e^2)/e^2 = 2/e^2
We can use this information to write the equation of the tangent line in point-slope form: y - f(e^2) = -1/e^4(x - e^2)
b) To find the x-coordinate of the critical point of f, we need to find the value of x at which f'(x) = 0 or is undefined.
f'(x) = (1 - lnx)/x^2
When we set f'(x) to 0, we get 1 - lnx = 0 lnx = 1 x = e.
As a result, the critical point is at x = e.To determine whether this point is a relative minimum, a relative maximum, or neither, we need to find the second derivative of f(x) and evaluate it at x = e.
f''(x) = -(1 + lnx)/x^3
Evaluating at x = e, we get: f''(e) = -(1 + ln(e))/e^3 = -(1 + 1)/e^3 = -2/e^3
Since the second derivative is negative, the critical point is a relative maximum.
c) To find the x-coordinate of the point of inflection, we need to find the value of x at which f''(x) = 0.
f''(x) = -(1 + lnx)/x^3
Setting f''(x) = 0, we get 1 + lnx = 0 lnx = -1 x = e^-1
So the point of inflection is at x = e^-1.
d) To calculate f(x) = lnx/x, we need to substitute the value of x into the function. f(x) = lnx/x
For example, if we want to calculate f(2) f(2) = ln(2)/2 = 0.693147180559945/2 = 0.346573590279973
So f(2) = 0.346573590279973
In the us, 21% of households use a clothesline to dry their laundry. capucine would like to survey households that use a clothesline, so she plans to contact randomly selected us households until she finds ones that use one. let f be the number of households capucine contacts to reach the first household that uses a clothesline. find the mean and standard deviation of f. find the mean and standard deviation of f
answer: mean: 4.84
standard deviation: 4.24
The mean is 4.8, and the standard deviation is 4.2 if 21% of households use a clothesline to dry their laundry. Capuchin would like to survey households that use a clothesline.
It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
Let's suppose the x is the number of households to get the first that uses a clothesline
And p is the probability of a household using the clothesline
X ~ Geo (p = 0.21)
Mean = 1/p
Mean = 4.76 ≈ 4.8
Variance = q/p²
q = 1 - p
Variance = 17.9138
Standard deviation = √Variance
Standard deviation = 4.23 ≈ 4.2
Thus, the mean is 4.8, and the standard deviation is 4.2 if 21% of households use a clothesline to dry their laundry. Capuchin would like to survey households that use a clothesline.
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Please tell me the answer I have 1 more try
Answer:
4
Step-by-step explanation:
24*1/6=4
Answer:
Your answer is 4
24/6
6×4=24
(02.05 HC)
The functions f(x) = -(x + 4)2+2 and g(x) = (x - 2)2-2 have been rewritten using the completing-the-square method. Apply your knowledge of
functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning
X544
ΩΣ
For a quadratic function [tex]y=ax^2+bx+c[/tex], we know the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].
It is easy to see that for a function of the form [tex]y=a(x-h)^2+k[/tex], the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].
Therefore, the vertex of the graph of [tex]f(x)[/tex] is a maximum, and the vertex of the graph of [tex]g(x)[/tex] is a minimum.
The function f(x) = -2(x + 4)+2 is minimum point and g(x) = 2(x - 2)-2 is maximum point.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have,
f(x) = -2(x + 4)+2 and g(x) = 2(x - 2)-2
As, the equation are in the form
y = a (x-h) + k
For 1st function: f(x) = -(x + 4)²+2
f(x) = -2(x+4) + 2
So, the vertex is (4, 2) and a = -2 < 0 which is minimum point.
Now, g(x) = 2(x - 2)-2
So, the vertex is (-2, -2) and a = 2 > 0 which is maximum point.
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Solve x + 2∕5 = 1∕3 for x. Question 10 options: A) x = –1∕15 B) x = –11∕15 C) x = 1∕15 D) x = 11∕15
Step-by-Step Explanation:
[tex]x + \frac{2}{5} = \frac{1}{3} \\ = > x = \frac{1}{3} - \frac{2}{5} \\ = > x = \frac{5 - 6}{15} \\ = > x = \frac{ - 1}{15} [/tex]
Answer:
A) x = -1/15
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
Therefore , on solving the provided question we can say that inequality will be x < 2.2727272727 .
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two variables values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality.
Here,
Given :
the inequality will be
=> 3(2x – 5) < 5(2 – x)
=> 6x - 15 < 10-5x
=> 11x < 25
=> x < 2.2727272727
Thus ,
x < 2.27
Therefore , on solving the provided question we can say that inequality will be x < 2.2727272727 .
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The complete question is " Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left. "
helppppp. I needddddddddd help! Quick
Plan V: $10.00/day + $40.00/month; 100 texts (extra cost $.50 each), 100 minutes of talk roverage is $.99/minute), 100 MB of data (overage is $2.05/MB)
Plan V is a mobile phone plan that costs $10.00 per day, or $40.00 per month. The plan includes 100 texts. If the customer goes over the 100 included texts, they will be charged $0.50 for each additional text. The plan also includes 100 minutes of talk coverage, but if the customer goes over the 100 minutes, they will be charged $0.99 per additional minute. Additionally, the plan includes 100 MB of data, but if the customer goes over the 100 MB, they will be charged $2.05 per additional MB.
how many dekameters is 4500 centimeters
Answer:
4.5
Step-by-step explanation:
one decameter is equal to 1000 centimeters 4500/100= 4.5
consider the following normal-form game: 2 l c r 1 u 4, 11 3, 5 6, 12 m 2, 4 1, 8 5, 6 d 3, 10 4, 7 3, 8 a. is there a strictly dominant strategy for some player? b. are there strictly dominated strategies for some player? find them all. c. find the set of outcomes that survive the process of iterative elimination of strictly dominated strategies. is the game solvable?
The probability game is solvable, and Player 1 has a strictly dominant strategy of Left (L), while Player 2 has four strictly dominated strategies. The surviving outcomes are (L, U), (L, M), (L, D), and (L, R).
This normal-form game is solvable, with Player 1 having a strictly dominant strategy of Left (L). Player 1's left strategy is strictly dominant because it will always yield a higher payoff than any other strategy for Player 1, regardless of what Player 2 does. Player 2, on the other hand, has four strictly dominated strategies: Up (U), Middle (M), Down (D), and Right (R). These strategies are strictly dominated because they will always yield a lower payoff than any other strategy for Player 2, regardless of what Player 1 does. The set of outcomes that survive the process of iterative elimination of strictly dominated strategies is (L, U), (L, M), (L, D), and (L, R). In other words, Player 1 will always choose left, and Player 2 will choose either Up, Middle, Down, or Right.
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Janice has a 80% success rate as a free throw shooter in the season so far, in which she has attempted 15 free throws. Today she made 3 out of 5 additional free throw shots. What is the probability that she will make her next shot?
Answer: To find the probability of Janice making her next free throw, you can use the proportion of successful free throw shots out of the total number of free throw shots attempted so far.
First, we need to find the number of free throws made by Janice so far:
80% success rate * 15 free throws attempted = 12 free throws made
Then we add the number of free throws made today:
12 + 3 = 15
Then we add the number of free throws attempted today:
15 + 5 = 20
So the probability of Janice making her next free throw is:
15 free throws made / 20 free throws attempted = 75%
So, the probability that Janice will make her next free throw is 75%.
It's worth noting that this answer is based on the assumption that her success rate will remain the same and doesn't take into account any other variable or change in her performance.
Step-by-step explanation:
The height of parallelogram whose area is 35 cm2 and altitude 7 cm
please answer step by step friends.
Answer: height is 5
Step-by-step explanation:
Area of the parallelogram is altitude x height. You divide area (35) by altitude (7) to get 5
A third friend, alisha, offers to drive daisa and tymar home for spring break so that they can share the cost of gas money. when asked how fast she drives, alisha reported that the distance traveled, y, for the time, x, can be expressed as y=57x.
true or false: alisha's equation, y=57x represents a proportional relationship.
Therefore , the solution of the given problem of equation comes out to be the correct equation can be = > y/x =57.
Who or what is the equation?A mathematical equation resembles a formula connecting two assertions when the equals letter (=) is employed to denote equality. An equation in algebra is a statement of fact that demonstrates the equality of numerous mathematical variables. For example, the equation obd + 6 = 12 has an equal sign separating the numbers doc d + 6 and 12. You can mathematically expression how many syllables correspond per each side of every letter. Often, a symbol's message is its exact opposite.
Here,
Given :
Equation : y =57x for the distance travelled by alisha.
Thus,
To find the equation is correct or not.
By comparing it with distance/time = speed equation we get to know
that the equation represented by alisha is wrong.
The correct equation can be => y/x =57 .
Therefore , the solution of the given problem of equation comes out to be the correct equation can be = > y/x =57.
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Let $n$ be a positive integer greater than or equal to $3$. Let $a,b$ be integers such that $ab$ is invertible modulo $n$ and $(ab)^{-1}\equiv 2\pmod n$. Given $a b$ is invertible, what is the remainder when $(a b)^{-1}(a^{-1} b^{-1})$ is divided by $n$
We can conclude from the given problem that there are 7975/5 - 1595 different positive numbers f(a) smaller than 1992, 1991-1595 = 396 positive integers.
An integer is what?Integers can be anything from zero to a positive or negative number signified by a minus sign. A lower result is its corresponding positive number's additive reciprocal. In mathematical notation, an integer group is usually denoted by a bold Z or perhaps a bold "mathbb Z." An integer, unlike a fraction, is a positively, negative, or zero number (pronounced IN-tuh-jer). Examples of integers are the integers -5, 1, 5, 8, 97, & 3,043. Examples of non-integer numbers include 1.43, 1 3/4, 3.14, and also more. A group of integers is known as an integer.
Here,
imagine a number of zeros! be
=> f(a), where f(a) = a/5, a/25, a/125, a/625, etc.
Since
f(a) a/5 + a/25 + a/125 + a/625 +...,
=> f(a) = f(a+1) = f(a+2) = f(a+3) = f(a+4). = a/4
=>f(7975) = 1991
1992 is less than 7975/5 - 1595 different positive numbers, hence 396 positive integers are present.
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Evaluate the indefinite integral. (Use C for the constant of integration.) Integral (ln x)^30 / x dx
The outcome of the integral, in accordance with the stated statement, is (ln x)^31/31 + c.
What does integration mean?Integration is the process's polar opposite of differentiation. The integration process involves determining a function's anti derivative. Integration is the process of combining smaller, discrete data sets that cannot be represented in a numerical value and cannot be contributed individually. Calculus (Unification) is used in electrical engineering to calculate the precise length of power line needed to connect two transmission system that are miles apart from one another.
For the predicament,
[tex]\Rightarrow \int \frac{(\ln x)^{30}}{x} d x[/tex]
Consider y = lnx, differentiate with respect to x
dy = 1/xdx
Substitute these values on the integral,
[tex]\begin{aligned}& \Rightarrow \int y^{30} d y \\& \Rightarrow \frac{y^{31}}{31}+c \\& \Rightarrow \frac{(\ln x)^{31}}{31}+c\end{aligned}[/tex]
Therefore, we may say that the integral's value is (ln x)^31/31 + C.
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Solve for X, Leave in simplest radical form.
Hope it helps.
If you have any query, feel free to ask.
Evaluate the iterated integral by converting to polar coordinates
integral(upper=a, lower=0) integral(upper=0, lower= -√(a2-y2)) x2y dx dy
Integral(upper=a, lower=0) Integral(upper=0, lower=a) r2sinθ dr dθ (1/3)a3sinθ
We can evaluate this iterated integral by converting it to polar coordinates.
The first integral has an upper bound of a and a lower bound of 0. This corresponds to the radial coordinate of r, which has a lower bound of 0 and an upper bound of a. The second integral has an upper bound of 0 and a lower bound of -√(a2-y2). This corresponds to the angular coordinate of θ, which has a lower bound of -π/2 and an upper bound of π/2.
Therefore, the integral in polar coordinates is:
Integral(upper=a, lower=0) Integral(upper=0, lower=a) r2sinθ dr dθ
We can then evaluate this integral by using the formula for the area of a sector:
Area = (1/2)r2θ
Substituting in the upper and lower bounds of the integrals, we get:
(1/2)(a2)(π/2) = (1/3)a3sinθ
Therefore, the answer is (1/3)a3sinθ.
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(3x + 5.3) + (7 - 1.5x) =
Answer: 1.5x + 12.3
Step-by-step explanation:
(3x + 5.3) + (7 - 1.5x)
Since this is not multiplication, try arranging the equation so like terms are together.
3x - 1.5x + 5.3 + 7 =
Combine like terms by adding or subtracting.
3x - 1.5x + 5.3 + 7 = 1.5x + 12.3
The cost of printing a math workbook is a setup cost
plus a cost for each book printed. If 1000 books
printed cost $14 300, and 5000 books printed cost
$64 300, what is the setup cost for printing the math
workbooks?
The setup cost for printing the math workbooks, given the printed cost of the books, is $ 1, 800
How to find the setup cost ?The setup cost for printing the math workbooks is a fixed cost which means that it will not change regardless of the number of books that are printed.
Since we know that 1, 000 books are printed to be $ 14, 300 and that 5, 000 books cost $ 64, 300, we can find the cost of the books without the setup cost to be :
= Difference in cost of books / ( Difference in number of books )
= ( 64, 300 - 14, 300 ) / ( 5, 000 - 1, 000 )
= 50, 000 / 4, 000
= $ 12. 50
The setup cost is therefore :
= Cost of printing - (Number of books x cost per book )
= 14, 300 - ( 1, 000 x 12 .5)
= $ 1, 800
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at what rate is the angle between a clock's minute and hour hands changing at 10 o'clock in the evening
Answer:
Step-by-step explanation:
I guess 6%?
Solve –2(3x – 1) = 20 for x. Question 6 options: A) x = 2 B) x = –3 C) x = 5 D) x = –1
Answer:
The answer would be B) x = -3.
Step-by-step explanation:
John drives his car on two roads for a total of 6 hours. On one road, he can drive at 100 km/h and on the other, he drives at a speed of 80 km/h. If he drives a total distance of 530 km, how long does he drive on each road?
Show steps.
Answer:
53000 and 42400
Step-by-step explanation:
100*530and 80*530
Quintell is thinking about retirement and decides to sail around the world once he retires. he buys a sailboat for 125000. he borrows the money at a rate of 7.5% for five years. how much will his total interest be?
The total interest for the loan is given as follows:
46,875.
How to model the situation with simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.The interest amount is the subtraction of the balance by the principal, hence it's formula can be simplified as follows:
I(t) = Prt.
The values of the parameters for this problem are given as follows:
P = 125000, r = 0.075, t = 5.
Hence the interest amount is given as follows:
I(5) = 125000 x 0.075 x 5
I(5) = 46,875.
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you measure the distance between the finges of a diffraction pattern as follows: distance (mm): 3.27, 3.23, 3.15 you measure the distance seven additional times to obtain the following ten values: distance (mm): 3.27, 3.23, 3.15, 3.16, 3.28, 3.14, 3.16, 3.12, 3.32, 1.46 what values for the distance and uncertainty would you report using the first three measurements and the entire set of ten measurements? group of answer choices
The distance is 3.21 +/- 0.04 mm using the first three measurements, and 3.16 +/- 0.08 mm using the entire set of ten measurements.
What is deviation ?
Deviation is a measure of how much a set of values differs from a certain value, typically the mean (average) of the set. There are two types of deviation ,
The absolute deviation is the difference between each value and the mean.
The standard deviation is the square root of the average of the squared absolute deviations.
The mean distance = (3.27 + 3.23 + 3.15) / 3 = 3.21 mm
The standard deviation = sqrt(((3.27 - 3.21)^2 + (3.23 - 3.21)^2 + (3.15 - 3.21)^2) / 2) = 0.04 mm
So, using the first three measurements, we can report the distance as 3.21 +/- 0.04 mm
To report the distance and uncertainty using the entire set of ten measurements, we can calculate the mean and standard deviation of the ten measurements.
The mean distance = (3.27 + 3.23 + 3.15 + 3.16 + 3.28 + 3.14 + 3.16 + 3.12 + 3.32 + 1.46) / 10 = 3.16 mm
The standard deviation = sqrt(((3.27 - 3.16)^2 + (3.23 - 3.16)^2 + (3.15 - 3.16)^2 + (3.16 - 3.16)^2 + (3.28 - 3.16)^2 + (3.14 - 3.16)^2 + (3.16 - 3.16)^2 + (3.12 - 3.16)^2 + (3.32 - 3.16)^2 + (1.46 - 3.16)^2) / 9) = 0.08 mm.
The distance is 3.21 +/- 0.04 mm using the first three measurements, and 3.16 +/- 0.08 mm using the entire set of ten measurements.
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15. Lori is 4 years younger than Shawn. Write an expression that represents Lori's age in relation
to Shawn.
Answer:
Step-by-step explanation:
You will need to utilise algebraic expressions to create an equation to show Lori's age in relation to Shawn.
The procedure will be completely described in the sections that follow with step-by-step instructions .
Let us assume that Shawn's age is x and Lori's age is y .Younger denotes negative sign in algebric expression ( - ) .If Lori is 4 years younger than Shawn, then Lori is 4 years younger than Shawn.Therefore, an expression that represents Lori's age in relation to Shawn can be written as following : y=x-4Learn more about the expression here :
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When it was first started, the Clinton High Cooking Club had 101010 members. Each year after the club started, the number of members increased by a factor of approximately 1.21.21, point, 2.
After one year, the club had approximately 123123 members. After two years, the club had approximately 149149 members. After three years, the club had approximately 180180 members.To calculate the number of members after three years, multiply the initial number of members (101010) by the factor of 1.21.21 three times
1. To calculate the number of members after one year, multiply the initial number of members (101010) by the factor of 1.21.21:
101010 x 1.21.21 = 12312
2. To calculate the number of members after two years, multiply the initial number of members (101010) by the factor of 1.21.21 twice:
101010 x 1.21.21 x 1.21.21 = 149149
3. To calculate the number of members after three years, multiply the initial number of members (101010) by the factor of 1.21.21 three times:
101010 x 1.21.21 x 1.21.21 x 1.21.21 = 180180
After one year, the club had approximately 123123 members. After two years, the club had approximately 149149 members. After three years, the club had approximately 180180 members.
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y−3= 3/4(x+2) graph as whole numbers no fractions or decimals.
whoever answers this correctly THANK YOU ^_^
50 POINTS
Answer:
Here is a picture of it graphed
Step-by-step explanation:
in a chemistry course with two exams and a final, receiving 90-100% of the total points receives an a; 80-90% a b; 70-80% a c; 60-70% a d; and below 60% an f. a student scores an 89 / 100 on the first exam, 81/100 on the second exam, and 160/200 on the third exam. what letter grade will the student receive?
The student receives 84% overall which is between 80-90% and they will receive a letter grade of "B".
To determine the student's letter grade, you need to calculate the overall percentage of the total points possible.
A percentage is a way of expressing a number as a fraction of 100. It is often used to express a proportion or a rate, and is typically denoted by the symbol "%". To convert a number to a percentage, you multiply it by 100 and add the "%" symbol.
The first exam is out of 100 points, so the student scored 89/100 or 0.89 * 100 = 89%.
The second exam is out of 100 points, so the student scored 81/100 or 0.81 * 100 = 81%.
The final exam is out of 200 points, so the student scored 160/200 or 0.8 * 100 = 80%.
To find the overall percentage of the total points possible, you need to add the percentage scores from each exam and divide by the number of exams.
(89 + 81 + 80) / 3 = 84
Therefore,The student receives 84% overall which is between 80-90% and they will receive a letter grade of "B"
It's important to note that each institution may have different grading scales and different criteria for assigning letter grades.
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A water bottle holds 56oz. Each time Anna takes a sip she drinks 8oz.
a) Write a function to represent the scenario
b) How many sips can Anna take before she needs to refill?
c) Create a graph to represent this situation.
d) What is the domain in set notation of the function?
Answer:
Step-by-step explanation:
a) The function to represent the scenario is f(x) = 56 - 8x, where x is the number of sips Anna takes.
b) Anna can take 7 sips before she needs to refill.
c)
The graph of the function is given below:
\begin{center}
\begin{tikzpicture}
\begin{axis}[
axis lines = left,
xlabel = $x$,
ylabel = {$f(x)$},
ymin = 0,
ymax = 56,
xtick = {0,1,2,3,4,5,6,7},
ytick = {0,8,16,24,32,40,48,56}
]
\addplot[
domain=0:7,
samples=2,
color=black,
]
{56 - 8*x};
\end{axis}
\end{tikzpicture}
\end{center}
d) The domain of the function in set notation is {0,1,2,3,4,5,6,7}.
