A water bottle holds 120oz. Each time Anna takes a sip she drinks 10oz.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 of the function?
Answers
From the situation described, we have that:
a) The linear function is: f(s) = 120 - 12s.
b) She can take 10 sips before she needs to refill.
c) The graph is given at the end of the answer.
d) The domain is: 0 ≤ s ≤ 10.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the parameters are given as follows:
m = -12, b = 120.
Hence the function is:
f(s) = 120 - 12s.
She can take sips until f(s) = 0, hence:
120 - 12s = 0
12s = 120
s = 10.
She can take 10 sips before she needs to refill, and hence the domain(set that contains the input values for the function) is 0 ≤ s ≤ 10.
The graph is given at the end of the answer.
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Related Questions
In a circle of radius 6 miles, the length of the arc that subtends a central angle of 1 radians is
Answers
We get the length of the arc that subtends a central angle of 1 radians as 6 miles with radius as 6 miles also.
We are being asked to solve for the length of the arc of a circle.
For this, we are given that:
A radius of around 6 miles.
And a central angle that is subtended by the arc which is equal to 1 radians.
In order to solve for this, we need to use the length of the arc formula.
The formula is:
s = r θ
Where r = is the radius
and
θ = is the subtended central angle given in radians
Now, by substituting the values in the formula, we get that:
s = 6 mi (1 rad) = 6 miles
Therefore, we get the length of the arc that subtends a central angle of 1 radians as 6 miles with radius as 6 miles also.
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I need help pls and thank u What is 5.3=z-2.7?
Answers
Answer: z=8
Step-by-step explanation:
5.3=z-2.7
5.3+2.7=z-2.7+2.7 ==> remove the 2.7 in 'z-2.7' to single out the variable z.
z=5.3+2.7
z=8
z = 8 ✅
Step-by-step explanation:Step 1:
Add 2.7 to both sides
5.3 = z - 2.7
5.3 + 2.7 = z - 2.7 + 2.7
⬆️ ⬆️
Step 2:
Simplify
5.3 + 2.7 = z - 2.7 + 2.7
( = 8 ) ⬇️ ( = 0 )
⬇️ ⬇️
8 = z
Do the following sets of data represent a function? Justify your answer.
1. (1,4), (2, 4), (3, 5), (2, 2)
2. (10, 5), (12, 5), (7, 12), (12, 2)
3. (0, 0), (5, 4), (4, 5), (1, 0)
Answers
1. No, the set of data does not represent a function.
A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.
We are given with (1,4), (2, 4), (3, 5), (2, 2)
This is because every output of this data does not have unique input.
4 and 2 have the same input i.e. 2.
2. Yes, the set of the data represents a function.
We are given with (10, 5), (12, 5), (7, 12), (12, 2)
It is a function as every input has a single output.
So, (10, 12, 07) are the elements of the domain and (2, 5, 7, 12) is the range of the function.
3. Yes, it is a function as every input of this data represents the single and unique output.
We are given with (0, 0), (5, 4), (4, 5), (1, 0)
It has its unique elements and domain (0,1,4,5) and range is from (0, 1, 2, 3, 4, 5).
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Find the perimeter of the equilateral triangle.
9x16
8-3x
The perimeter is
Answers
The perimeter of the equilateral triangle will be 27x - 48.
How to calculate the perimeter?It should be noted that the perimeter of an equilateral triangle is the addition of all its sides or multiplying by three since they're equal.
Therefore, the perimeter of the equilateral triangle will be:
= 3(9x - 16)
= 27x - 48
Therefore, the perimeter of the equilateral triangle will be 27x - 48.
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Find the perimeter of the equilateral triangle.
9x - 16
Tell whether the angles are complementary or supplementary. Then find the value of x.
Answers
Step-by-step explanation:
SUPPLEMENTARY because they are on a staright line and add up to 180°
[tex]76 + (2x + 4) = 180 \\ 2x + 76 + 4 = 180 \\ 2x = 180 - 76 - 4 \\ 2x = 100 \\ \frac{2x}{2} = \frac{100}{2} \\ x = 50[/tex]
x=50°
2^n * 3 * 5^m
Write 8A as a product of powers of its prime factors
Answers
8A = [tex]2^{n + 3} * 3 * 5^{m}[/tex] is a product of powers of its prime factors of Polynomials.
What is Polynomials ?
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video.Given - [tex]2^{n} * 3 * 5^{m}[/tex]
The numbers 2, 3 and 5 are already prime numbers.
Multiplying 8 on both sides
8 × A = [tex]2^{n} * 3 * 5^{m} * 8[/tex]
Expressing 8 as the product of prime numbers
8A = [tex]2^{n} * 3 * 5^{m} * 2 * 2 * 2[/tex]
8A = [tex]8A = 2^{n} * 3 * 5^{m} * 2^{3}[/tex] (When the base is same, the power is added)
Adding the power of base 2, we add n and 3
8A = [tex]2^{n + 3} * 3 * 5^{m}[/tex]
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100 points + first decent answer gets brainliest
The mean of a distribution of selected theme park admission prices is $59 with a standard deviation of $3.99. The mean cost of a distribution of a specific home stereo system sold at many different stores is $1,499 with a standard deviation of $4.
Which distribution has the lower standard deviation?
Which distribution is more spread out? Explain.
Answers
Answer:
See explanation
Step-by-step explanation:
Selected theme park admission prices has the lower standard deviation.
Specific home stereo system's distribution is more spread out since the ratio between the standard deviation and the mean is greater compared to that of selected theme park admission prices.
specific home stereo system: 3.99/59=0.0676.
selected theme park admission prices: 4/1499=0.002668
0.0676>0.002668
Answer:
The theme park ahs the lower standard deviation
Please help me
"The verticles of ABC are A(-4,5,)B(-2,4), and C(-3,2). If ABC is reflected across the line y = - 2 to produce the image ABC, find the coordinates of the vertex C.
The coordinates of C' after a reflection across the line y = -2 are ___
Answers
The coordinates of C' after a reflection across the line y = -2 are (3, -2).
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.
Given that the verticles of ABC are A(-4,5,)B(-2,4), and C(-3,2). If ABC is reflected across the line y = - 2 to produce the image ABC, then we need to find the coordinates of the vertex C.
Let (x, y) represent the coordinate of the point C
x-coordinate value:
The line y = -2 is parallel to the x-axis, therefore the x-value will remain the same following a reflection across the x-axis.
Taking the point C' as the image of the corresponding point C(-3,2), we need that the x-coordinate of the point C' is also 3
x = 3
y-coordinate value:
The difference between the coordinate of the pre-image and the reflecting line is same as difference between the reflecting line and the coordinates of the image.
Therefore, the coordinates of the point C' is (x, y) = (3, -2)
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What is
1
4
+
9
10
y
−
3
5
y
+
7
8
written in simplest form
Answers
A data set had values ranging from 117 to 139. A new data point of 30 was
added to the data set. Would this point affect the mean or the median more? How
(increase/decrease) and why? (2 points)
Answers
Answer:
This point would affect the mean more because the median is less sensitive to outliers.
Step-by-step explanation:
Hope this helps!
0.789x10^5
is this correct scientific notation
Answers
The correct scientific notation of [0.789×(10⁵)] is 78900.
As per the question statement, we are provided with a multiplication of a decimal number and an exponential number.
We are required to determine its correct scientific notation.
A decimal number, say 0.059, can be expressed as a multiplication of a decimal number and an exponential number, such as [5.9×(10)⁻²].
But in our case, after performing the multiplication of the given values, we get, [tex][0.789*10^{5}]=(\frac{789}{1000}*100000)=(789*100)=78900[/tex]
And 78900 is not a decimal value. Hence, the correct scientific notation of [0.789×(10⁵)] is 78900.
[Note: Here, we need to know the procedure to convert a decimal into a fraction, using which we converted 0.789 into [tex]\frac{789}{1000}[/tex]. First, we will need to eliminate the decimal point and consider the digits in the same order as a complete number which will be our numerator. Secondly, we will use (10ⁿ) as the denominator, where "n" is the number of digits to the right side of the decimal point in the original decimal number. Thus, 0.789 can be written as [tex]\frac{789}{1000}[/tex], as there are three digits to the right of the decimal point in 0.789]
Scientific Notation: It is a method of expressing numbers that are too large or too small to be conveniently written in decimal form.Exponential Number: Any number which is in the form of (aⁿ), is known as an exponential number.To learn more about Scientific Notations, click on the link below.
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Find the perimeter of the regular polygon ?
Answers
The perimeter of the regular polygon is 232
How to find the perimeter of the regular polygon?The side lengths of the regular polygon are given as
4/3x - 1/3 and x + 7
The sides of regular polygon are equal
So, we have:
4/3x - 1/3 = x + 7
Multiply both sides by 3
4x - 1 = 3x + 21
Collect like terms
4x - 3x = 1 + 21
Evaluate the like terms
x = 22
Substitute x = 22 in x + 7
Side = 22 + 7
Side = 29
The perimeter of the regular polygon is calculated as:
Perimeter = Number of sides x Side length
So, we have
Perimeter = 8 * 29
Evaluate
Perimeter = 232
Hence, the perimeter of the regular polygon is 232
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what is the arctan (-1)?
B. [tex]-\frac{\pi }{4}[/tex]
Answers
Answer:
Option B. is correct.
Step-by-step explanation:
arctan(y) = tan - 1(y) = x+ kπ
for k = {...,-2,-1,0,1,2,...}
➫ e.g tan(45°) = 1
➫ and that would mean the arctangent of 1 is 45 degrees(We represent this in π/? form)
arctan(1) = tan-1(1) = 45° = -π/4
Hope this helps!
Write 4,000,000 in scientific notation
Answers
4 × 10 then put a 6 by the 10 as an exponent.
A sun in a distant galaxy has an estimated Mass of 1.55272 x 10³1 kg and the earth has a mass of
5.972 x 1024
kg, how many earths would it take to equal the mass of the sun? Write your answer in
scientific notation.
It would take
earths to equal the mass of the sun
Answers
A sun in a distant galaxy has an estimated Mass of 1.55272 x [tex]10^{31}[/tex] kg and the earth has a mass of 5.972 x [tex]10^{24}[/tex] kg,26x[tex]10^{5}[/tex] earths would it take to equal the mass of the sun.
A sun in a distant galaxy has an estimated Mass of 1.55272 x [tex]10^{31}[/tex]kg
earth has a mass of 5.972 x [tex]10^{24}[/tex]kg
Let x number of earths equal the mass of the sun
x (5.972 x [tex]10^{24}[/tex]) = 1.55272 x [tex]10^{31}[/tex]
x= 1.55272 x [tex]10^{31}[/tex] / 5.972 x [tex]10^{24}[/tex]
x= 26x[tex]10^{5}[/tex]
The wavelength of light emitted by a far-off galaxy extends and is "redshifted" toward the infrared region of the electromagnetic spectrum as it moves away from us. This means that by the time the light from a very distant galaxy that emits mostly visible or ultraviolet light reaches Earth, it will appear as infrared light.
Webb's ability to detect infrared light and the cosmos' expansion, which extends light to redder wavelengths, make it a good tool for identifying galaxies that originated at the beginning of the Universe's existence.
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need help with 36.01 x 0.06
Answers
Answer: 2.1606
Step-by-step explanation:
36.01 x 0.06 =
3601/100 x 6/100=
3601 x 6/(100 x 100)=
21606/10000=2.1606
What is the solution set of the quadratic inequality 4(x + 2)²(less than equal to)0
Answers
Answer:
{-2}
Step-by-step explanation:
You want the solution set for the inequality 4(x +2)² ≤ 0.
SolutionThe expression on the left cannot be negative, but it can be zero when ...
x +2 = 0 ⇒ x = -2
The only solution to this inequality is x = -2.
Expressed as a set of solutions, we have ...
x ∈ {-2}
Please help !
What is the coefficient in the term 4w?
4
w
0
1
Answers
Answer:
4
Step-by-step explanation:
the coefficient is usually a constant factor for a variable.
so, the answer here is 4.
Zan needs 28 centimeters of ribbon for each bow she makes. What is the greatest number of bows Zan can make with 9 feet of ribbon?
Answers
Answer:
3
Step-by-step explanation:
i think its 3 because 28 divided by 9 is 3
Data was collected on salaries of compliance specialists in corporate accounting firms. The salaries ranged from $58,000 to $238,000
If these values are grouped into six class intervals, indicate the class boundaries.
What class interval width was chosen?
What are the six class midpoints?
Answers
The class boundaries are:
1 58000 but less than 88,000
2 88,000 but less than 118,000
3 118,000 but less than 148,000
4 148,000 but less than 178,000
5 178,000 but less than 208,000
6 208,000 but less than 238,000
The class interval width for the distribution that we have here is given as $30000.
The six midpoints and the class boundaries are:
73000103,000133,000163000193000223000How to solve for the class boundary238,000 - 58,000= 180000
180000 / 6 = 30000
Class Boundaries1 58000 but less than 88,000
2 88,000 but less than 118,000
3 118,000 but less than 148,000
4 148,000 but less than 178,000
5 178,000 but less than 208,000
6 208,000 but less than 238,000
What is the class interval width?238,000 - 58,000= 180000
180000 / 6 = 30000
width = 30000
The six class midpoints58000 + 88000 / 2 = 7300088000 + 118000 / 2 = 103,000118000 + 148000 / 2 = 133,000148000 + 178000 / 2 = 163000178000 + 208000 / 2 = 193000208000 + 238000 / 2 = 223000Read more on class intervals here;
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Evaluate the expression ab, for a = 4 and b = 7.
Answers
Answer:
28
Step-by-step explanation:
4 x 7 = 28
The following table shows the estimated number of millionaire households (households with a net worth of at least $1 million, not including primary residence) in a certain country for selected years.
Year Millionaire Households
2015 9,200,000
2016 9,350,000
2017 9,620,000
2018 9,970,000
If the percentage increase between 2017 and 2018 continued for 2018 and 2019, how many millionaire households would there be in 2019? Round to the nearest ten thousand.
Answers
If the percentage increase between 2017 and 2018 continued for 2018 and 2019, there would be 10332908 millionaire households in 2019
How many millionaire households would there be in 2019? Round to the nearest ten thousand?The given parameters are:
Year Millionaire Households
2015 9,200,000
2016 9,350,000
2017 9,620,000
2018 9,970,000
From the question, we have
The percentage increase between 2017 and 2018 continued for 2018 and 2019
The percentage increase between 2017 and 2018 is calculated as
Percentage = (2018 - 2017)/2017 * 100%
So, we have
Percentage = (9,970,000 - 9,620,000)/9,620,000 * 100%
Evaluate
Percentage = 3.64%
The number of millionaire households in 2019 is calculated as
2019 = 2018 * (1 + percentage)
So, we have
Households = 9,970,000 * (1 + 3.64%)
Evaluate
Households = 10332908
Hence, if the percentage increase between 2017 and 2018 continued for 2018 and 2019, there would be 10332908 millionaire households in 2019
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The graph of f(x) is shown.
How many horizontal tangent lines does f(x) have?
0
1
2
3
4
Answers
Check the picture below.
Can you guys help me solve this?
Answers
Answer:
Step-by-step explanation:
97
Answer:
$97 per/tire
Step-by-step explanation:
Long division[tex]Borrow\:8\\4 \cdot 9 = 36\\= 38 - 36\\= 2\\4 \cdot 7 = 28\\28 - 28 = 0\\\\= 97\:\mathrm{R0}[/tex]
Can anyone help me with this
Answers
Answer:
B. SAS
Step-by-step explanation:
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Just need these answers for an assignment help would be nice
Answers
Answer:
below
Step-by-step explanation:
25)-ab
=-(-1/2)(3/4)
=3/8
26)b÷c
=(3/4)×1/-6
=3/-24
=-1/8
27)c÷a
=-6÷-1/2
=6×2/1
=12
in the grid below what is the distance between point a and b. round to the nearest tenth
Answers
find the area of the circle
Answers
The circle has an area of 28.26 ft².
It is assumed that the circle's radius is 3 feet.
The circle's area must be determined.
What is radius of a circle ?
A line segment from a circle's center to its perimeter is known as the radius.
As per the question ;
Radius of circle , r = 3 ft
Area of the circle is given by ;
A = πr²
A = π × 3²
A = 9π
or
A = 9 × 3.14
or
A = 28.26 ft²
Thus , the area of the circle will be 28.26 ft².
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(a) Write the next whole number after 222three in the base-three system.
Answers
Answer:
1000
Step-by-step explanation:
You want the next number after 222 in base 3.
Counting sequenceIn any useful number base, the counting at any given integer position is ...
0, 1, 2, 3, ..., (base -1), 0 and add 1 to the next number position
For base 3, this is ...
0, 1, 2, 10
When the digit in the next higher position is also (base -1), then it gets incremented to 0 and the carry is propagated to the left.
In base 10, the equivalent is ...
999 +1 = 99(9+1) = 99(10) = 9(9+1)0 = 9(10)0 = (9+1)00 = 1000
In base 3, your incremented value is ...
222 +1 = 22(2+1) = 22(10) = 2(2+1)0 = 2(10)0 = (2+1)00 = 1000
The next whole base 3 number after 222 is 1000.
A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each column and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular. How many columns are in the tile floor before the change in layout?
Answers
The number of columns is in the title floor before the change in layout is 10
Given that A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each columns and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular asked to find the number of columns in the tile floor before the change in layout.
Let's assume the number of rows is x
The number of columns will be [tex]\frac{70}{x}[/tex]
After the changing, the rows can be x+4
The number of columns will be [tex]\frac{70}{x}[/tex]-2
The equation will be (x+4)([tex]\frac{70}{x}[/tex]-2)=70
⇒[tex]x^{2} +4x-140=0[/tex]
⇒x=10
Therefore,The number of columns is in the title floor before the change in layout is 10
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