Hey there mate :)
As per question,
Options (a), (b) and (d) are correct.
Proof :-(a) The cost per visit to a community pool.
Considering x = number of visits to the pool
a = fixed cost of visit.
So, the cost per visit to the pool y will be ax
Therefore, this represents a linear function.
And
The neighborhood charges a yearly fee to use the pool.
Assuming x = number of years
a = fixed fee to use the pool
So the yearly fee to use the pool y will be ax
Therefore, this represents a linear function.
(b) The cost to attend a show at the local theater. Tickets are $12 each.
Let x = number of shows
Let the cost of one show = $12.
Now, the cost of x shows y will be 12x
So, it represents a linear function.
(d) The distance a bicyclist travels when cycling at a constant speed of 30 mph.
Assuming x= time
Speed = 30 mph.
Since the distance (y) is given as:-
Distance = Speed×time, so,
=> y = 30x
Hence, this also represents a linear function.
Hence, all correct option are proved
Write the equation of the parabola that has a vertex at (4,6) and passes through (5,8)
A parabola has vertex at (4,6) and passes through the point (5,8).
The general equation of the parabola is:
\(y=a(x-h)^2+k\)Where (h,k)=(4,6) in this case so it follows:
\(y=a(x-4)^2+6\)Also it passes through (5,8) so it follows:
\(\begin{gathered} 8=a(5-4)^2+6 \\ a=2 \end{gathered}\)Hence the equation is:
\(y=2(x-4)^2+6\)solving quadratic equation using the completing the square method. (a)-6h²+5h+2=0
...........................................................................................................................................................................................................................................................................................................................................................................
\(-6h^{2}+5h+2=0\\h^{2} -\frac{5}{6} h-\frac{1}{3} =0\\h^{2} -\frac{5}{6} h+(\frac{5}{12} )^{2} -(\frac{5}{12} )^{2}-\frac{1}{3} =0\\(h-\frac{5}{12} )^{2} =\frac{1}{3} +(\frac{5}{12} )^{2}\\(h-\frac{5}{12} )^{2} =\frac{73}{144} \\\)
\(h-\frac{5}{12} = \sqrt{\frac{73}{144}} \\h=\sqrt{\frac{73}{144}} +\frac{5}{12}\)
or
\(h-\frac{5}{12} = -\sqrt{\frac{73}{144}} \\h=-\sqrt{\frac{73}{144}} +\frac{5}{12}\)
Determine f(-1) (3). Use the following table of values
Answer:
-5
Step-by-step explanation:
The value of x that gives f(x) = 3 is -5.
\(f^{-1}(3)=-5\)
solve. 3 is less than y minus 2
Answer:
\(\bold{3 < (y - 2)} \\ \bold{y > 3 + 2} \\\bold{ y > 5}\)
hope helpful~
Answer:
3 is less than y minus 2 => 3 < y - 2
Step-by-step explanation:
If an expression has an equal sign, it is called an equation.
If it has less than or greater than sign, then it is called inequality.
It is also an inequality if it has greater than or equal to or less than or equal to signs. ( ≥, ≤).
Now y minus 2 means
y - 2
Now it says 3 is less than (y-2)
So we get
3 < y - 2
a box in a shape of a rectangle prism has a length of 3 5/8 inches a width of 2 1/2 inches and a height of 4 inches. what is the volume of the box
Answer:
volume is 36.25inches
145/4
Step-by-step explanation:
L= 3 5/8inches
W= 2 1/2inches
H= 4inches
VOLUME = L×W×H
3 5/8 × 2 1/2 × 4 =
29/8 × 5/2 × 4 = 36.25inches
36.25→145/4
Express 602.16 dam in decimeters
The expression of 602.16 dam in decimeters can be written as 60216 decimeter.
How can the expression of 602.16 dam be converted to decimeters?The concept that will be used in the calculation is conversion. to perform this conversion, it is important to note that 1 Decimeter (dm) is equal to 0.01 dekameter (dam).
Then, if 1dm = 0.01 dam
Xdm = 602.16 dam
Where x is the value in decimeter.
Then we can cross multiply as :
X= (602.16 dam * 1dm)/ 0.01 dam
= 60216 decimeter.
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Does this graph represent a function? Why or why not?
For the following expression, a) Determine the number of terms. b) Write down each term. c) Write down the coefficient for each term. Make sure you simplify the expression before answering. 2x-13
Answer:
a) 2
b) 2x, -13
c) 2, -13
Step-by-step explanation:
Term means mathematical equations that are separated by arithmetic symbols like (+,-,x,/).
For example, there is 2 terms in the following example because there is two values separated by arithmetic symbols: 3x+5.
More examples of terms: 7, 5x, x, \(7x^2\), \(x^2\)
Coefficient means the value that you multiply the variable by. The coefficient in the variable: 5x is 5 because you are multiplying x by 5.
Which product is greater, (-4).(-6) or
(-7) • (-8)? Explain.
Answer:
(-7) times (-8)
Step-by-step explanation:
when you multiply two negatives they become positive so 7 times 8 is 56 which is greater than 4 times 6 that is 24.
Hope that helps!
how many inches is 2 1/6 ft
Answer:
26 inches
Step-by-step explanation:
You find out that 1 foot equals 12 inches
times 2 by 12 equaling 24
24 added by 2 is 26
1/6 as a decimal is 1.83 infinitive 3 which is rounded to 2 as the whole number
makes your answer 26 inches
Hope that helps
Samantha is comparing scooter prices with two different DC scooter companies. With the UBER scooters, the equation c = 1.80m gives the relationship between m, the number of minutes per ride, and the total cost, in dollars. With the LYET scooters, the cost of 5 minutes is $3.75 and the cost of 10 minutes is $7.50. If Samantha rides for 12 minutes, how much money would she save by renting the less expensive scooter? Explain your reasoning.
Answer:
yes!
Step-by-step explanation:
how do beans cost in 12 pounds?
Answer:
are u high bruv
Step-by-step explanation:
Please hurry!
Polygons LMNO and L'M'N'O' are shown on the following coordinate grid:
What set of transformations is performed on LMNO to form L'M'N'O'?
A. A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
B. A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
C. A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin
D. A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin
Answer:
Step-by-step explanation:
i think the answer is the 3rd one
How does estimation help to solve
Fermi Problems?
Answer:
Fermi estimates generally work because the estimations of the individual terms are often close to correct, and overestimates and underestimates help cancel each other out.
Step-by-step explanation:
A researcher tests whether cocaine use increases impulsive behavior in a sample of cocaine-dependent and cocaine-inexperienced mice.
Independent Variable: ________
Quasi-Independent Variable: ________
Dependent Variable: ________
Answer:
Independent variable: Cocaine Use
Quasi-Independent Variable: Cocaine-dependent and cocaine-inexperienced mice
Dependent variable: Increase in impulsive behavior
If √x has a decimal approximation of 3.4, then x is between which two integers? In your final answer, include all calculations.
Step-by-step explanation:
b Jawaban
semoga bermanfaat ✨⬅️
explain adpose tissue
Answer:
Adipose tissue is commonly known as body fat. It is found all over the body. It can be found under the skin (subcutaneous fat), packed around internal organs (visceral fat), between muscles, within bone marrow and in breast tissue.
Adipose tissue is commonly known as body fat. It is found all over the body. It can be found under the skin (subcutaneous fat), packed around internal organs (visceral fat), between muscles, within bone marrow and in breast tissue.
(tan^(2)x)/(secx)=secx-cosx how do i verify the identity
Answer:
sec x − cos x = sin x tan x? First convert all terms into sinx and cosx. Second apply fraction sum rules to the LHS. and replace secx with 1 cosx. The LHS, secx − cosx becomes 1 cosx − cosx. The RHS, sinxtanx becomes sinx sinx cosx or sin2x cosx.
Step-by-step explanation:
Help for a cookie!:D
Answer:
0.305
0.097
Step-by-step explanation:
…..………....
36 divided by m over x times 9
Answer:
Step-by-step explanation:
4/mx
The floor of a swimming pool is covered in 525 blue, 300 green and 75 white tiles. What is the ratio of blue to white tiles?
What is the ratio of the blue and white tiles
the line with a slope of 9/7 & containing a midpoint of the segment whose end points are (2, -3) & (-6, 5)
Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:
y = (9/7)x + 25/7.
Step-by-step explanation:Step 1: Find the midpoint of the line segment.
The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:
Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)
Midpoint = (-4 / 2, 2 / 2)
Midpoint = (-2, 1)
So, the midpoint of the line segment is (-2, 1).
Step 2: Write the equation of the line using the slope-intercept form.
The slope-intercept form of a line is given by:
y = mx + b
where m is the slope and b is the y-intercept.
Given the slope as 9/7, we have:
y = (9/7)x + b
Step 3: Substitute the coordinates of the midpoint to find the value of b.
Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:
1 = (9/7)(-2) + b
1 = -18/7 + b
To find the value of b, we can solve this equation:
1 + 18/7 = b
25/7 = b
Step 4: Write the final equation of the line.
Using the value of b, the equation becomes:
y = (9/7)x + 25/7
Question content area top
Part 1
Felix is slicing a tortilla Española (Spanish omelet) by cutting diameters through the center. He plans on cutting 1 to 8 diameters. The number of slices is a function of the number of diameters. Describe the domain and range of the function.
The function from which the number of slices can be found based on the number of diameters, can be obtained from the function, f(n) = 2·n, which indicates;
The domain = [1, 8]
The range = [2, 16]
What is the domain and range of a function?The domain is the set of the possible input of the function, while the range is the set of possible output of the function.
The number of diameters Felix plans to slice into the tortilla = 1 to 8
The number of arcs formed by a diameters of a circle = 2
The number of arcs formed by 8 diameters = 2 × 8
Therefore, the number of arcs formed by n diameters of a circle = 2·n
Each arc of the tortilla represents a slice, therefore:
The number of slices formed by n diameters = 2·n slices
The function of the number of slices Felix gets from cutting n number of diameters is; f(n) = 2·n
The domain is the possible number of inputs, which is the number of diameters, therefore;
The domain is; 1 ≤ n ≤ 8When n = 1, f(n) = f(1) = 2 × 1 = 2
When n = 8, f(8) = 2 × 8 = 16
The range is the possible number of slices obtained from the tortilla, therefore;
The range is; 2 ≤ f(n) ≤ 16Learn more about the domain and range of a function here:
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Ashley’s car weighs more than Joseph’s car Joseph wrote the following equation for the weight of his car 24x10
In a large population, 69 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Give your answer as a decimal (to at least 3 places) or fraction.
The required probability is 0.970 (approx.) or 97/100 (in fraction).
Given that 69% of people in a large population have been vaccinated. We are required to determine the probability of at least one person being vaccinated if three people are randomly selected. Let's solve it using the complement rule.
The complement rule states that the probability of an event occurring is equal to 1 minus the probability of that event not occurring. That is, if A is an event, then P(A) = 1 - P(A').
We can solve the given problem using the complement rule as follows: Let P(A) be the probability of at least one person being vaccinated.
Then, the probability of no one being vaccinated is P(A') = (100 - 69) = 31%.
To find the probability of at least one person being vaccinated, we can subtract the probability of none of them being vaccinated from 1. That is, P(A) = 1 - P(A') = 1 - 0.31 × 0.31 × 0.31 = 1 - 0.029791 = 0.97021.
Hence, the probability of at least one person being vaccinated if three people are randomly selected is 0.97021 (rounded to 3 decimal places).
Therefore, the required probability is 0.970 (approx.) or 97/100 (in fraction).
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For which of the following displays of data is it not possible to find the mean histogram frequency, table, stem, and leaf plot doc plot
The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.
A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.
A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.
A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.
A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.
In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
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Mrs Gallo weighs 94 kg. Her doctor says she has to reduce her weight! If she
reduces her weight by 16% what will her new weight be (to the nearest
kilogram)?
Carlos drove 200 miles in 5 hours. If he drove at a constant rate, how many miles did Carlos drive per hour?
Answer:
40
Step-by-step explanation:
200/5=x/1
Answer:
40
Step-by-step explanation:
200/5 = 40
nice dumb questions
Experiment 1: Select ONE card from a deck of cards Create two events A and B. For example: Let A = observing a card with an odd number on it B = observing a king Mix and match two events anyway you like.
Answer:
The answer is "64".
Step-by-step explanation:
Let A= look at the number of a card on it {3,5,7,9}
\(\to 4 \times 4 = 16 \ odd \ numbers\)
Let B= look at the king of the card = \(4 \ Cards\)
Choose one card A = 16 ways
Choose one card B= 4 ways
selecting one card, either A and B:
\(=A \times B \\\\= 16 \times 4 \\\\= 64\)
Many of the pesticides for citrus trees are toxic to fish. When the citrus groves on a large farm were treated with pesticides, high winds deposited 100 gallons of pesticides into a lake stocked with fish. To ensure survival of the fish, 95% of the pesticides must be removed from the lake within 96 hours of contamination. There are two methods of removal.
A: Add a chemical reagent to the pond to neutralize the pesticide. This chemical reagent removes the pesticide at the rate of 11 gal/hr. B: Fit the pond with a filtration system. This system removes 4% of the remaining pesticides each hour. Method A sound reasonable but I am not sure and I also don't know how to create an equation for the method. Please help.
In the scenario above, the best method to use is A by the Addition of a chemical reagent to the pond to neutralize the pesticide. This chemical reagent removes the pesticide at the rate of 11 gal/hr.
What removes pesticides from water?Pesticides can be removed from ponds water via chemical reagent through Chemical degradation and other ways.
Note that the first option is useful as the Addition of a chemical reagent to the pond to neutralize the pesticide because there are lot of chemical against that can eat up other chemicals that are harmful to the pond.
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