The monthly water bill is a function of the number of gallons used. The cost is $11.70 for 10,000 gal or less. Over 10,000 gal, the cost is $11.70 plus $1 for each 1000 gal over 10,000 with any fraction of 1000 gal charged at a fraction of $1. On what interval is the cost constant? On what interval is the cost increasing?
Answers
Answer:
Interval for constant cost = [0, 10,000] same as 0 <= x <= 10,000
Interval for increasing cost = (10,000, ∞) same as 10,000 < x < ∞
Be careful! note the use of different types of parentheses for each answer part as explained below
Step-by-step explanation:
We are only being asked for the two intervals, not the function definition itself which would have made it a little bit more work. A function has inputs and outputs. Here the input is gallons of water and output is $ cost.
Normally when asked for intervals we use a variable. Let's call it x which represents the gallons of water used
Since there is a base rate of $11.70 whether or not any water is consumed as long as it is less than or equal to 10,000 gallons we can state that over the interval 0 to 10000 (inclusive), the cost is constant
We can represent this interval in two ways
0 ≤ x ≤ 10,000
Another way of representing this interval is what we call interval notation. In interval notation the same thing can be expressed as:
[0, 10000]
Here 0 is referred to as the lower limit or bound(minimum) and the 10,000 is referred to as the upper limit or upper bound
Note the use of square brackets. This means that both upper and lower limits are included in the function. Such an interval is also called a closed interval.
After 10,000 gallons, the cost keeps increasing. There is no upper limit on the usage of water. So the lower limit is 10,000 (but does not include that number) and upper limit is infinity
We represent this interval as
10000 < x < ∞
Note that both upper and lower limits are excluded since ∞ is not realistic.
In interval notation this is represented as
(10000, ∞)
Here we are using regular brackets(parentheses) because this interval does not include lower and upper limits
This kind of interval is known as an open interval
Looks like the purpose of this question is to make sure what you understand in terms of interval notation and possibly open and closed intervals. The only relevant number there is the 10,000 gallons which represents the upper bound on the first interval. All the other numbers can be junked
Hope that is of help even if it was wordy
Related Questions
Write an equation in slope-intercept form for the line that passes through (2,4) and is parallel to the line given by y=7.
Answers
Answer:
Step-by-step explanation:
slope of y=7 is 0
As line is parallel to y=7 therefore m=0
equation of line is given by y=mx+c
m=0
therefore y=c
substituting y=4
therefore value of c=4
hence equation of line is given by y=0(x)+4
help asap please and thank you !!!!!
Answers
Answer:
Hope this helps
Step-by-step explanation:
Y = 3x - 10
So, 4x + 5y = 7
= 4x + 5(3x - 10) = 7
= 4x + 15x - 50 = 7
= 19x - 50 = 7
= 19x = 7 +50
= 19x = 57
= X = 57/19
X = 3
The points (2, -12) and (4, r) lie on a line with slope 4. Find the missing coordinate r.
Answers
Step by step: (4,r)= -10
A playground 88 ft long and 58 ft wide is to be resurfaced at a cost of $2.75 per sq ft. What will the resurfacing cost?
The resurfacing will cost $.
(Simplify your answer. Type an integer or a decimal.)
Answers
Answer: $1856
Step-by-step explanation: 88 x 58 = 5104. 5104/2.75= 1856
12. What is the value of the following expression when
a = -2 and b = -4?
5(4a3b)+ ab
A-108
B -92
C -12
D12
E 28
Answers
Answer:
1st one is b. 2nd one is A
Step-by-step explanation:
i did the quiz
What is the y-intercept of the line described by the equation below?
y = 7x+ 4
A. (0,4)
B. (0,-4)
C. (0,7)
D. (0, -7)
Answers
Answer:
A. (0, 4)
Step-by-step explanation:
y=mx+b
y=7x+4
7x<-- mx
4<-- b
b=y intercept
The value of the y-intercept of the line described by the equation is,
⇒ (0, 4)
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The equation of line is,
y = 7x + 4
Now, We know that;
The equation of line is,
y = mx + c
Where, c is y - intercept.
Hence, We get;
The value of the y-intercept of the line described by the equation is,
⇒ y = 4
⇒ (0, 4)
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ7
Refer to tool wear regression model (8.36). Suppose the indicator variables had been defined as follows: X2 = 1 if tool model M2 and 0 otherwise, X3 = 1 if tool model M3 and 0 otherwise, X4 = 1 if tool model M4 and 0 otherwise. Indicate the meaning of each of the following: (1) B3, (2) B4 - B3, (3) B. tive Predictor with More than Two Classes If a qualitative predictor variable has more than two classes, we require additional indicator variables in the regression model. Consider the regression of tool wear (Y) on tool speed (Xi) and tool model, where the latter is a qualitative variable with four classes (M1, M2, M3, M4). We therefore require three indicator variables. Let us define them as follows: X2 1 if tool model M1 0 otherwise X 3 1 if tool model M2 0 otherwise (8.35) X4 1 if tool model M3 otherwise First-Order Model. A first-order regression model is: Y = Bo + B1X11 + B2X2 + B3X3 + B4X 4 + Ei (8.36)
Answers
(1) B3 corresponds to the effect of tool model M3 on tool wear, holding all other variables constant.
(2) The difference B4 - B3 represents the effect of tool model M4 on tool wear relative to the effect of tool model M3 on tool wear, holding all other variables constant.
What is indicator variables in regression model?
An fake variable made to represent an attribute with two or more separate categories or levels is known as an indicator variable or a dummy variable. Why is it employed? All independent (X) variables are treated as numbers in regression analysis.
In this tool wear regression model, the variables X2, X3, and X4 are indicator variables that represent the tool model (M2, M3, and M4, respectively). The coefficient B3 corresponds to the effect of tool model M3 on tool wear, holding all other variables constant. The coefficient B4 corresponds to the effect of tool model M4 on tool wear, holding all other variables constant.
The difference B4 - B3 represents the effect of tool model M4 on tool wear relative to the effect of tool model M3 on tool wear, holding all other variables constant. In other words, it represents the change in tool wear that is associated with switching from tool model M3 to tool model M4, while holding the values of all other variables constant.
The overall intercept term B0 represents the expected value of tool wear when all predictor variables are equal to zero. It represents the baseline or reference level of tool wear when the predictor variables are not present or are not influencing the outcome.
To know more about indicator variables in regression model visit,
https://brainly.com/question/7781679
#SPJ4
Mr. Lai buys 2 1/4 pounds of red apples and 1 3/8 pounds of green apples. How many more pounds of red apples does he buy?
Answers
Answer:
Mr. Lai buys 2 1/4 pounds of red apples and 1 3/8 pounds of green apples. How many more pounds of red apples does he buy?
Here are the shopping times (in minutes) of ten shoppers at a local grocery store.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of shopping times in that class.
(Note that we are using a class width of 5.)
Answers
The frequency which is to filled in the table is 1, 4, 2 and 4.
Given that;
All shopping time of ten shopkeeper:
25, 29, 25, 18, 24, 28, 36, 25, 33, 37
We have to complete the frequency in the table. Frequency of something is the number of times that number is coming.
Since, Shopping time is given as ,
25, 29, 25, 18, 24, 28, 36, 25, 33, 37
And, Intervals for which frequency is given is ,
18 to 22, 23 to 27, 28 to 32, 33 to 37.
Hence, WE get;
Numbers in the range 18 to 22 = 18 therefore 1
Numbers in the range 23 to 27 = 25, 25, 24, 25 therefore 4
Numbers in the range 28 to 32 = 29, 28 therefore 2
Numbers in the range 33 to 37 = 36, 33, 37, therefore 3
Hence, the frequency which is to filled are 1, 4, 2 and 4.
Learn more about frequency visit:
brainly.com/question/254161
#SPJ1
PLEASE HELP THIS IS HARD
Answers
The Area of the shaded portion is: 72 square inches
What is the Area of the shaded region?The formula for the area of a triangle is given by the formula:
Area = ¹/₂ * base * height
Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.
Thus:
Area of larger triangle = ¹/₂ * 17 * 13 = 110.5 square inches
Area of smaller triangle = ¹/₂ * 11 * 7 = 38.5 square inches
Thus:
Area of shaded portion = 110.5 square inches - 38.5 square inches
Area of shaded portion = 72 square inches
Read more about Area of shaded portion at: https://brainly.com/question/1297097
#SPJ1
how to find the average rate of change if the function
Answers
Answer:
14
Step-by-step explanation:
Average rate of change is given as \( \frac{f(b) - f(a)}{b - a} \)
Where,
a = 4,
f(a) = f(4) = (4)² + 3(4) = 16 + 12 = 28
b = 7,
f(b) = f(7) = (7)² + 3(7) = 49 + 21 = 70
Plug in the values into the formula
Average rate of change = \( \frac{70 - 28}{7 - 4} \)
\( = \frac{42}{3} = 14 \)
At an amusement park, riders must be at least 48 inches tall to ride the Night Eagle roller coaster. Keenan has grown 1.5 inches since last summer, but he is still too short to ride. Let x represent how tall Keenan was last summer. Which inequality describes the problem?
Answers
The inequality that describes the given word problem is;
x + 1.5 < 48
How to solve Inequality word problems?Let x represent how tall Keenan was last summer. Thus;
x = Keenan's height last summer in inches
If he was x inches last summer, and has since grown an additional 1.5 inches up to date, then it means that his total height now is;
x + 1.5 inches.
The conditons state "riders must be at least 48 inches tall to ride the Night Eagle roller coaster". So it means that his height must be equal to 48 inches, or larger than 48 inches, to make him eligible to ride the roller coaster.
But since he is still too short to ride, this means the expression x+1.5 is smaller than 48 and as such the inequality of this problem is;
x + 1.5 < 48
Read more about Inequality Word Problems at; https://brainly.com/question/25275758
#SPJ1
. Ann ate 2 slices of a pizza and Teresa ate 3 slices of the pizza. The pizza had 8 slices. What is the difference in the amount of pizza that they ate written as a fraction?
Answers
Assume the average nightly payroll for a city’s downtown restaurants on the weekend is $2200 with a standard deviation of $300. The distribution has a bell-shaped curve. A manager wants to be 99% sure he has this cost covered for the next four weeks and puts away $10,000. Will he have enough? Use your z-score formula result to justify your answer. Please respond with the dollar amount and round to the nearest dollar.
Hint: Round your z-value to the hundredths place and direction of the graph will matter.
Answers
Given statement solution is :- The manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.
To determine if the manager will have enough funds to cover the nightly payroll for the next four weeks, we need to calculate the total cost for four weeks and compare it to the amount set aside.
The nightly payroll has a mean of $2200 and a standard deviation of $300. Since there are seven nights in a week, the weekly payroll can be calculated as:
Weekly Payroll = Nightly Payroll * Number of Nights in a Week
= $2200 * 7
= $15,400
To calculate the total cost for four weeks, we multiply the weekly payroll by four:
Total Cost for Four Weeks = Weekly Payroll * Number of Weeks
= $15,400 * 4
= $61,600
Now, let's calculate the z-score using the formula:
z = (X - μ) / σ
Where:
X = Total Cost for Four Weeks
μ = Mean of the distribution
σ = Standard deviation of the distribution
z = ($61,600 - $2200) / $300
z = $59,400 / $300
z ≈ 198
To determine if the manager will have enough funds to cover the payroll, we need to find the proportion of the distribution that is less than or equal to the z-score. This can be done by consulting a standard normal distribution table or using statistical software.
For a z-score of 198, the proportion in the tail of the distribution is essentially 1 (or 100%). This means that the manager is virtually guaranteed to have enough funds to cover the payroll for the next four weeks.
Since the manager has set aside $10,000, which is less than the calculated total cost of $61,600, he will indeed have enough funds to cover the payroll.
Therefore, the manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.
For such more questions on Funds Cover Payroll: Confirmed
https://brainly.com/question/32039603
#SPJ8
X over 2 minus 4 in word form
Answers
Which of these is the correct ratio of strawberries to blueberries for the fruit salad?
A. 8 strawberries: 30 blueberries
B. 8 strawberries: 8 blueberries
C. 4 strawberries: 30 blueberries
D. 32 strawberries: 30 blueberries
Answers
The ratio of the strawberries to the blueberries is 32 strawberries: 30 blueberries (option d).
What is the ratio?
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.
The ratio of strawberries to blueberries - total number of strawberries : total number of blueberries.
(8 x 4) : 30
32 : 30
To learn more about ratios, please check: https://brainly.com/question/25927869
#SPJ1
Answer: A. 8 strawberries: 30 blueberries
Step-by-step explanation:
for each situation, determine taxable income, assuming pretax accounting income is $100 million
Answers
Answer:
Temporary Differences Reported First on: The Income Statement The Tax Return Revenue Expense Revenue Expense1) $272) $273) $274) $275) $22 $276) $27 $227) $22 $27 $178) $22 $27 $12 $17Taxable Income assuming pretax accounting income is $100 million1) Pretax Income - Revenue = $100m - $27m = $73m2) Pretax Income + Expense = $100m + $27m = $127m3) Pretax Income + Revenue Return = $100m + $27m = $127m4) Pretax Income - Expense Return = $100m - $27m = $73m5) Pretax Income - Revenue + Expense = $100m - $22m + $27m = $105m6) Pretax Income + Expense + Revenue Return = $100m + $27m + $22m = $149m7) Pretax Income - Revenue + Expense - Expense Return = $100m - $22m + $27m - $17m = $88m8) Pretax Income - Revenue + Expense + Revenue Return - Expense Return = $100m - $22m + $27m + $12m- $17m = $100m
Step-by-step explanation:
First, return is added to differentiate revenue and expense from the tax return from that of the income statement.Temporary difference is defined as the difference between the tax and financial reporting bases of assets and liabilities. These differences can result in taxable or deductible amounts in future years (deferred tax assets or liabilities).For each scenario, temporal difference of revenue reported first in the income statement is deducted from the pretax accounting income while expenses are added back to the pretax accounting income.For temporal differences from the tax return, the revenue is added to the pretax accounting income while expenses are deducted.
jordan drank 36 ounces of water today , how many cups of water did he drink ?
a. 4.5 cups
b. 9 cups
c. 18 cups
d. 288 cups
answer asapppp 2 .
Answers
Answer:
jordan drinks 4.5 cup of water
Please help!
Having lots of trouble with math :)
Answers
And each side should add up to 90º
So x and y should each be 45º if I’m not mistaken, and then z is (I forgot the proper vocab term for this) right flippity across y so it should also be 45º
what answer? here, can you answer that? thankyou
Answers
It should be noted that the number of sample size based on the information will be 300.
How to explain the sampleIn order to calculate the sample size, we can use the following formula:
n = z² * p * (1-p) / E²
n = 1.96² * 0.5 * (1-0.5) / 0.05²
= 300
A questionnaire is a method of gathering data that makes use of written questions to be answered by the respondents. It is a popular method of data collection because it is relatively easy to administer and can be used to collect a wide variety of information.
In the first column, the population is the entire National Capital Region (NCR). The sample is the city of Manila. In the second column, the population is all STEM students. The sample is all academic track students. In the third column, the population is all the tablespoons of sugar in the jar. The sample is one tablespoon of sugar. In the fourth column, the population is all the vowels in the word "juice". The sample is the vowel "i".
Learn more about sample on
https://brainly.com/question/24466382
#SPJ1
Which cereal box deal has the best price per ounce $6.12 for 24 oz $9.13 for 39 oz $3.56 for 14 oz $4.95 for 18 oz
Answers
Answer:
$3.56 for 14 ozi think so
Which of the following relations is a function?
A{(3,-1), (2, 3), (3, 4), (1,7)}
B{(1, 2), (2, 3), (3, 4), (4, 5)}.
C{(3, 0), (4, -3), (6, 7), (4,4)}
D{(1, 2), (1, 3), (2, 8), (3, 9)}
Answers
Answer:
B
Step-by-step explanation:
A is not a function because the same x value is repeated twice with different y values. The same goes for C and D so the answer is C.
Answer:
B.
Step-by-step explanation:
Well a relation is a set of points and a function is a relation where every x value corresponds to only 1 y value.
So lets see which x values in these relations have only 1 y value.
A. Well a isn’t a function because the number 3 which is a x value had two y values which are -1 and 4.
B. This relation is a function because there are no similar x values.
C. This is not a function because the x value 4 has two y values which are 4 and -3.
D. This is not a function because the number 1 has 2 and 3 as y values.
Help please lol lol :))))
Answers
Answer:
is this required answer
Step-by-step explanation:
AB=3x-2
=3*8-2
=22
Answer:
\(\huge\boxed{\textbf{AB = 22}}\)
Step-by-step explanation:
Given that:
AB = 3x - 2
Put x = 8
AB = 3(8) - 2
AB = 24 - 2
AB = 22
\(\rule[225]{225}{2}\)
The graph shows a function that models the value V (in millions of dollars) of a stock portfolio as a function of time t (in months) over a 18-month period.
Answers
Answer:
Option (A)
Step-by-step explanation:
Graph attached shows a function that models the value V of a stock portfolio as a function of time.
y-values on the graph shows the value of V and x-values represent the time.
Lowest point of the curve shows the minimum value of V and highest point of the curve shows the maximum value.
Maximum value of the function → 6.93 at t = 4
Minimum value of the function → 1.05 at t = 15
Therefore, Option (A) will be the answer.
c) I use the 4 triangles to make a trapezium. What is the area of the trapezium?
Answers
Answer:
1/2=10
Step-by-step explanation:
it depends upon the area of the triwngle
need an answer quick, will give the first right answer brainliest, i need a step by step explanation please
Answers
Answer: Imma say C
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3y-9x=-6
Answers
Answer: y=3x-2
Step-by-step explanation:
3y-9x=-6
First you will need to add 9x to the other side so your equation will look like 3y=9x-6. Then you need to divide all the numbers by 3. So 3y divided by 3 and 9 divided by 3 and -6 divided by 3. Your final answer should be y=3x-2.
Answer:
This equation in slope intercept form would be y = 3x - 2
Step-by-step explanation:
The following is how to solve this equation:
3y - 9x = -6
+9x +9x
----------------------
3y = 9x - 6
divide each of the numbers by 3
So the answer is y = 3x - 2
HELP How can you test to see if a diagram made using digital tools is a construction or just a drawing based on estimation? O Digital tools cannot be used to make a construction. Construction tools are limited to only straightedge and compass. O Look to see just how accurate the diagram appears. If needed, measure the screen using a ruler and protractor. O Drag a free point to see if the construction changes. Restart your computer and see if the diagram is found in the same location.
Answers
One can be able to test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by:
Drag a free point to see if the construction changes. Restart your computer and see if the diagram is found in the same location.What is digital construction technology?Digital Construction is known to be a term that connote the act of using digital technologies to be able to make construction to be more better and with higher quality.
Note that a lot of the new technologies have been seen to have proven themselves and gives a lot of opportunities for the construction,
In the use of the digital tools, one can Construct a line or a line segment and then uses the move tool to drag some points around, and then watch to see what happens.
Therefore, One can be able to test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by:
Drag a free point to see if the construction changes. Restart your computer and see if the diagram is found in the same location.Learn more about construction tools from
https://brainly.com/question/25860017
#SPJ1
Which triangle is △ABC similar to and why?
Answers
Answer:
can we get a picture
Step-by-step explanation:
Help with evaluate and graph PLEASE HURRY
Answers
Answer:
Box 1 = -1
Box 2 = 8
Box 3 = 14