The function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings is C(x) = 9.99 + 1.25x
The domain is x >= 0 and the range is c(x) >= 9.99
Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.The given parameters are:
One topping = 9.99
Additional topping = 1.25 each
We have x to represent the number of toppings
This means that
C(x) = One topping + Additional topping * x
So, we have
C(x) = 9.99 + 1.25x
How to find the domain and range?We have
C(x) = 9.99 + 1.25x
The smallest number of topping is 0
So, the domain is x >= 0
Substitute 0 for x in C(x) = 9.99 + 1.25x
C(0) = 9.99 + 1.25(0)
This gives
C(0) = 9.99
So, the range is c(x) >= 9.99
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Answer:
C(x) = 8.74 + 1.25x
Domain: 1 ≤ x ≤ 10
Range: [9.99, 21.24]
Step-by-step explanation:
a) We need to find the function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.
We know that a pizza with one topping is $9.99 and that you can add additional toppings for 1.25 each.
So the equation is C(x) = 9.99 + 1.25x right?
Not really... Since $9.99 is the price of a pizza and 1 topping, we need to subtract 1 from x otherwise we would be paying for a pizza with 2 toppings when we had ordered a pizza with 1!
So the new equation is:
C(x) = 9.99 +1.25(x - 1)
or, C(x) = 9.99 + 1.25x - 1.25
or, C(x) = 1.25x + 8.74
b) We need to find the Domain of C(x).
We know that the pizzeria's menu lists 10 different toppings and that a pizza has at least one topping.
So we can choose up to 10 different toppings. And we need at least 1 topping.
∴ Domain is 1 ≤ x ≤ 10.
b) We need to find the Range of C(x).
We know that the domain of C(x) is 1 ≤ x ≤ 10, and that a pizza with 1 topping is $9.99.
Since we already know the minimum (9.99) all we have to do is find the maximum. We can do that by plugging in 10 into C(x) since it is the maximum of our domain.
C(10) = 1.25(10) + 8.74
or, C(10) = 12.50 + 8.74
or, C(10) = 21.24
∴ Range of C(x) = [9.99, 21.24]
Answer:
C(x) = 8.74 + 1.25x
Domain: 1 ≤ x ≤ 10
Range: [9.99, 21.24]
Why does the graph look like a series of steps rather than a smooth curve? Why is a hollow circle needed at the beginning of each step(except the first)?
Answer:
the cost function is defined as a step function
Step-by-step explanation:
You want to know why a cost graph has steps.
Cost StepsIn the US, current first class postage rates for appropriately sized envelopes are 60¢ for the first ounce, and 24¢ for each additional ounce.
Envelopes below a certain weight cannot be mailed, and above that minimum (up to at most one ounce), the cost will be 60¢. That is, the first step is at cost=60¢, and extends from some minimum weight up to 1 ounce at that cost.
Above one ounce -- even very slightly above, the cost is 84¢. There is no weight where the cost is 61¢ or 62¢ or any other number between 60¢ and 84¢.
For the purpose of determining cost, the weight is rounded up to the next higher ounce. This guarantees that cost values will be a discrete set of values.
Continuous weightsThe weight can take on any real value. This is reflected in the continuous horizontal line at each level of cost.
The hollow circle at 1 ounce on the second step means that the cost for one ounce is not the value of that second step. The filled circle indicates the cost for one ounce is the value of the first step. The hollow circle also indicates that weights arbitrarily close to 1 ounce, but greater, will cost the same as for 2 ounces.
__
Additional comment
The minimum weight envelope that can be mailed first class will be a function of its size. Outside a certain size and weight range, the envelope will not be "machinable," so will incur an extra charge.
The sum of the ages of Steve and Ali is
three times the difference of their ages.
What is the ratio of Ali's age to Steve's
age if Ali is older?
The ratio of Ali's age to Steve's is 2 to 1.
How to find the ratio of Ali age to Steve age ?The sum of the ages of Steve and Ali is three times the difference of their ages.
Therefore,
let
x = age of Steve
y = age of Ali
Hence,
x + y = 3(y - x)
x + y = 3y - 3x
Therefore,
x + 3x = 3y - y
4x = 2y
divide both side by 2
4x / 2 = 2y / 2
2x = y
The ratio of Ali's age to Steve's is 2 to 1.
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Yu Yan competes in a sprint triathlon. The race consists of three parts: a 0.5-mile swim, a 12.4-mile bike ride, and a 3.1-mile run. a. Yu Yan completes the swim portion of the sprint triathlon in 25 minutes. What is her average swimming speed in miles per minute?
The average swimming speed of Yu Yan is 0.02 miles per minute.
We are given that:
Yun Yan needs to swim 0.5 miles in the race.
She completed it in 25 minutes.
We need to find the average speed of Yu Yan in swimming in meter / minute.
We will do this by dividing the number of miles that she needed to swim with the number of minutes she took to complete it.
Average swimming speed = 0.5 miles / 25 minutes
Average swimming speed = 0.02 miles / minute
Therefore, the average swimming speed of Yu Yan is 0.02 miles per minute.
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or Brendan watched a beetle on the sidewalk. It crawled 5/6 of a yard, then rested for a bit, and then crawled 1/3 of a yard farther. How far did the beetle crawl in all? Simplify your answer and write it as a fraction or as a whole or mixed number.
Answer:
5/9 dydgsusg6xhsxigdsys5suxts7xysustx7s
Answer:
Mixed number - 1 1/6
Improper fraction - 7/6
Step-by-step explanation:
The goal of the question is to get you to add the 2 distances the beetle crawled together.
First you have to give the fractions the same denominator.
5/6 & 2/6 (to change 1/3 to 2/6 multiply the top and bottom by 2)
Then you simply add the numerators.
5+2/6
7/6
Since this can't be simplified anymore that is your answer.
Mixed number - 1 1/6
Improper fraction - 7/6
Linear relationships graph
Answer: Linear graph definition
Step-by-step explanation: A linear graph is a straight line that connects the x and y coordinates
Ordered: 130 mg. Available: 1 gr/tablet. How many tablets should be given? ________
Answer:
2
Step-by-step explanation:
1gr=100mg
130-100=30
No tablets should be given since the ordered quantity of 130 mg is less than the available quantity per tablet of 1 g.
How many tablets should be given?We have the following data:
Ordered amount: 130 mg
Available amount per tablet: 1 g
To decide the number of tablets to be given, we have to be make sure the units are steady. Let's change over the ordered amount to grams:
130 mg = 130/1000 g = 0.13 g
Presently, we are able calculate the number of tablets:
Number of tablets = Ordered amount / Available amount per tablet
Number of tablets = 0.13 g / 1 g = 0.13 tablets
Since we cannot administer a fraction of a tablet, we round the result to the closest whole number. In this case, 0.13 is less than 0.5, so we round down:
Number of tablets to be given = tablets
Hence, no tablets ought to be given since the ordered amount of 130 mg is less than the available amount per tablet of 1 g.
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Kim multiplied 8 x 0.952 and got 76.16. How can you estimate to show that kim answer is incorrect
a bottle contains 2 litter of water.The bottle leaks 80 milliliters of water every 3 minutes.will the bottle be empity in one hour?
Answer:
No, the bottle will not be empty
Suppose a study is completed that finds that the number of cockroaches in chandler decreases by 18% every 12 years. I’m 2020, there were approximately 3.5 million cockroaches in chandler.
The number of cockroaches in Chandler in the year 2025 will be 3237500 or 3.23 million approx
Approx number of cockroaches in the year 2020 in Chandler = 3500000 or 3.5 million
Percentage decrease in cockroaches every 12 years = 18%
Percentage decrease in cockroaches every year = 18/12 = 1.5%
So, in 5 years the percentage decrease in cockroaches will be = Percentage decrease every year*No. of years = 1.5*5 = 7.5%
The number of cockroaches in 2025 will be: 3500000 - 7.5% of 3500000
= 3500000 - 7.5/100*3500000
= 3500000 - 262500
= 3237500
Hence, the number of cockroaches in Chandler in the year 2025 will be 3237500 or 3.23 million approx
Although a part of your question is missing, you might be referring to this full question: Suppose a study is completed that finds that the number of cockroaches in chandler decreases by 18% every 12 years. I’m 2020, there were approximately 3.5 million cockroaches in chandler.
Assuming the number of cockroaches is changing exponentially, how many cockroaches do you estimate there will be in 2025 (5 years later)
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H=at-0.25vt*, solve for a
46•2^3-3•2^3
O 344
O2,920
086
1,840
Answer:
Answer is A. 0344
Step-by-step explanation:
46*8 - 3* 8
= 43*8
= 344
1. The graph of a certain geometric sequence can be described as a curve that is decreasing from left to right. Which sequence would have a similar graph?
A {1,1/3,1/9,1,27…}
B{1/16,1/8,1/4,1/2,..,}
The sequence A, 1, 1/3, 1/9, 1/27 shows the similar graph decreasing from left to right. Option a is correct.
Geometric progression abbreviated as GP is type of sequence and series that has common and equal ratio between preceding values in series.
Here,
The only geometric sequence seems from observation having decreasing from left to right, that implies the curve is also decreasing from left to right is 1, 1/3, 1/9, 1/27, having common ratio of 1/3 with preceding values.
Thus, the sequence 1, 1/3, 1/9, 1/27 shows the similar graph decreasing from left to right which can be described as a curve that is decreasing from left to right.
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Which inequality is true?
A. 7TT > 21
B. T +4<7
C. 12/1 >1
D. 37-19
C. 12/1 > 1 is the inequality which is true as 12/1 is 12 and 12 is obviously greater than 1.
What is inequality?Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. Inequality issues can be expressed as either questions or theorems, and both can be resolved using techniques that are similar to those used to resolve equations.
The triangle inequality, for instance, stipulates that the length of the remaining side of a triangle is more than or equal to the sum of the lengths of any two of its sides. Many of these inequalities are used in the proofs of mathematical analysis' most significant theorems.
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67 is the difference of Rita's height and 7.
Answer: 7=r-67
Step-by-step explanation:
r=Rita's height
7=r-67
Give the sample statistic for the percentage of voters surveyed who said they would vote for Brown. Round your answer to the nearest tenth of a percent.
Answer:
34%
Step-by-step explanation:
In the sample of 300 voters, 102 said they would vote for brown. The sample statistic is just the percent given by the sample. Find the percent by dividing the voters who said they'd vote for brown by the entire sample group:
[tex]\frac{102}{300}=0.34[/tex]
Convert this to a percentage:
34%
the sample statistic for the percentage of voters surveyed who said they would vote for Brown is 34%.
How do we explain?we start by divide the number of voters who said they will vote for Brown by the total number of voters surveyed and then multiply by 100.
Number of voters surveyed (n) = 300
Number of voters who said they'd vote for Brown = 102
The Sample statistic for the percentage of voters who said they would vote for Brown:
Percentage of voters for Brown = (Number of voters for Brown / Number of voters surveyed) * 100
Percentage of voters for Brown = (102 / 300) * 100
Percentage of voters for Brown = 34%
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complete question:
The city of Raleigh has
11
,
900
11,900 registered voters. There are two candidates for City Council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of
300
300 randomly selected registered voters was conducted.
102
102 said they'd vote for Brown,
195
195 said they'd vote for Feliz, and
3
3 were undecided.
a) Give the sample statistic for the percentage of voters surveyed who said they would vote for Brown. Round your answer to the nearest tenth of a percent.
can you sum 58.91 570 42,769 994.8
Answer: Yes, i think. you add 0's to 58.91 -----> 58.910. 570-------->570.000. 42,769-------->42,769.000. 994.800. to line them perfectly. greatest are always on top smallest are in the bottom
The sum of numbers 58.91, 570, 42,769, 994.8 will be
⇒ 44392.71
What is Addition?
The process of combining two or more numbers is called the Addition.
Given that;
The number are,
58.91, 570, 42,769, 994.8
Now,
The sum of numbers 58.91, 570, 42,769, 994.8 is,
⇒ 58.91 + 570 + 42,769 + 994.8
⇒ 44392.71
Thus, The sum of numbers 58.91, 570, 42,769, 994.8 will be
⇒ 44392.71
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What is the domain of the function y = square root x+6 -7?
Answer:
-6 ≤ x < ∞
Step-by-step explanation:
You want the domain of the function y = √(x+6) -7.
DomainThe domain of a function is the set of x-values for which the function is defined. On a graph, it is the horizontal extent of the graph.
The square root function is undefined for negative arguments, so that limits the domain of the given function:
x+6 ≥ 0
x ≥ -6 . . . . . domain of the given function
__
Additional comment
When the domain is written in interval notation, both the left and right ends of the interval must be specified.
[-6, ∞)
The square bracket identifies -6 as being part of the domain. The parenthesis is used with ∞, because that number has no specific value.
Keep the Old Car or Buy a Used Car
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 110 miles per week to commute to work. With gas prices currently at $ 2.05 per gallon, he is considering buying a more fuel-efficient car, and wants to know if it would be a good financial decision.
The old car Manny owns currently gets 17 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $ 870 per year (as long as nothing serious goes wrong).
The newer, more fuel-efficient car that he is looking at to purchase will cost a total of $ 8,000 over a three-year loan process. This car gets 32 miles per gallon and would only require an average of $ 10 per month for general maintenance. To help make a decision, Manny wants to calculate the total cost for each scenario over three years. He decides to use the quantitative reasoning process to do this.
The total cost of using the old car is $4,679.29
The total cost of using the newer car is $ 8,896.25.
What are the total costs?The total cost of using the old car: (cost of maintenance x number of years) + ( miles driven to work / miles per gallon x cost per gallon x number of weeks in a year x number of years)
($870 x 3) + (110 / 17 x $2.05 x 52 x 3)
$2,610 + 2069.29 = $4,679.29
The total cost of using the newer car : purchase price + (cost of maintenance per month x number of months in year x number of years) + (miles driven to work in a week / number of miles per gallon x weeks in year x number of year)
$8000 + ($10 x 12 x 3) + (110 / 32 x 52 x 3)
$8000 + 360 + 536.25 = 8,896.25
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How can you find all the factors (or divisors) of a number?
Answer:
Step-by-step explanation:
Find the measure of a negative angle coterminal with 180°.
The measure of a negative angle which is coterminal with the angle 180° as given in the task content is; -180°.
Which negative angel is coterminal with the angle 180°?It follows from the task content that the negative angle which is coterminal with 180°.
On this note, it follows that the negative angle corresponds to a clockwise direction while the positive corresponds to an anticlockwise direction.
Hence, the required angle which is coterminal is; -180°.
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En nuestro sistema solar 6 de los 8 planetas
tienen lunas.
¿Qué porcentaje de los planetas tiene
lunas?
Answer:
75%
Step-by-step explanation:
% = (6/8)(100) = 600/8 = 75
Hope this helps
QUESTION 5
The owner of an older house wants to put new tile in the kitchen. At a local hardware store the tile the owner wants to putdown is on sale for $2.50 per square foot. If the owners kitchen is in the shape of the figure below, how much will it cost to tile the floor?
13ft
12ft
5ft
convert into power notation 243/1,00,000
Answer:
243=3^5
100000=5^5*2^5
So answer is- 3^5/5^5*2^5
Step-by-step explanation:
Hope it helps!!!
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A certain triangle has a perimeter of 3064mi the shortest side measures 79mi less than the middle side and the longest side measures 377mi more than the middle side. find the lengths of the three sides
Answers:
smallest = 843 milesmedium = 922 mileslargest = 1299 miles=========================================================
Work Shown:
x = smallest side
y = medium side
z = largest side
x = y-79
z = y+377
x+y+z = perimeter
x+y+z = 3064
(y-79) + (y) + (y+377) = 3064
3y + 298 = 3064
3y = 3064-298
3y = 2766
y = 2766/3
y = 922
x = y-79
x = 922-79
x = 843
z = y+377
z = 922+377
z = 1299
------------------
Summary:
x = 843, y = 922, z = 1299
Check:
x+y+z = 843+922+1299 = 3064
which matches the given perimeter, so the answer is confirmed.
Help please!!!?!?!?!
The amount borrowed is $87,000, the annual interest rate is 6%, the number of payments per year is 12, the loan term is 19 years, and the payment amount is $145,920.
Given that, an individual borrowed $87,000 an APR of 6%, which will be paid off with monthly payments of $640 for 19 years.
What is APR?APR is annual percentage rate. APR can be found with the formula, APR = ((Interest + Fees / Principal or Loan amount) / N or Number of days in loan term)) x 365 x 100.
From the given question,
P=$87,000, R=6%, monthly payment=$640 and loan term = 19 years.
Total amount = Total number of months × Monthly payment
= 19 × 12 × 640
=$1,45,920
Therefore, the amount borrowed is $87,000, the annual interest rate is 6%, the number of payments per year is 12, the loan term is 19 years, and the payment amount is $145,920.
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If Melinda wanted to build a patio in her backyard that was 14 feet long, 6 feet wide
and 4 inches deep using pervious concrete mix that is 4 parts aggregate to 4.5 parts
loose cement, with some water added then how many cubic feet of aggregate would
she need to build the walkway?
Round the final answer to the hundredths place. If you answer doesn't have a
hundredths place include zeros so that it does
The volume of aggregate that she needs to build the patio is 13.18 ft^3
How many cubic feet of aggregate would she need to build the walkway?
We know that the backyard is 14ft long, 6 feet wide and 4 inches deep.
Rememeber that:
1ft = 12 in
Then:
4 in = (4/12) ft = (1/3) ft
Then the volume of the backyard is:
V = (14ft)*(6ft)*(1/3 ft) = 28ft^3
Now we know that we have a mix of 4 parts aggregate to 4.5 parts loose cement that need to fill these 28 cubic feet.
Note that:
4 + 4.5 = 8.5
How many times we have 8.5 in 28?
28/8.5 = 3.294
Now for each of these we have 4 parts of aggregate, then the volume of aggregate that we need is:
4*3.294 ft^3 = 13.18 ft^3
The volume of aggregate that she needs to build the patio is 13.18 ft^3
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A kinara is a candle holder used during Kwanzaa celebrations. The graph shows the
number of kinaras, rounded to the nearest 500, an online store sold each year for 15
years. A line of fit is drawn to show the trend of the data. What does the slope of the line
represent?
Answer:C
Step-by-step explanation:
if angle 2=6x+8 and angle 4=4x+11 what is the value of angle 2?
Find the total surface area of the following square pyramid. Base is 12 and slant is 10 cm.
The surface area of the square pyramid when the base is 12 and slant is 10 cm is 384cm².
How to calculate the area?It should be noted that the total surface area will be:
= b² + 2bs
where b = base length
s = slant height
Surface area = (12)2 + 2(12)(10)
Surface area = 144 + 240
Surface area = 384cm².
In conclusion, the surface area of the square pyramid when the base is 12 and slant is 10 cm is 384cm².
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The second angle of a triangle is five times as large as the first. The measure
of the third angle is 12 degrees greater than that of the first angle. What is
the measurement of the largest angle?
Answer:
120
Step-by-step explanation:
consider
1st angle= a
2nd angle = b
3rd angle = c
now,
b=5a ............. equation 1
c = a+12 ........ equation 2
as we know in a triangle, sum of all angle is 180.
so
a+b+c = 180
=> a +5a + (a+12 ) = 180
=> 7a = 180-12 =168
=> a = 168/7 = 24
so a= 24
b = 5(24) = 120
c = a+12 = 24+12 =36
so b = largest = 120