The two processes that caused the puddle to form and then disappear were evaporation and infiltration.
Evaporation is the process in which liquid water turns into vapor and rises into the atmosphere. It occurs when the air around the puddle is warmer than the liquid, causing the water molecules to move faster and spread out. This allows the water to evaporate into a gas. The rate of evaporation is proportional to the water surface area and the difference in temperature between the air and the water.
Infiltration is the process in which water is absorbed into the ground. It occurs when the water in the puddle is drawn into the soil due to gravity and capillary action. This process is influenced by the soil type, the amount of water, and the soil's porosity. The rate of infiltration is proportional to the soil's permeability, which is a measure of how quickly water can move through the soil.
The combination of evaporation and infiltration caused the puddle to form and then disappear. As the water evaporated, the puddle shrank until it was gone. Simultaneously, the water that remained was absorbed into the ground until all of the puddle was gone.
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Find the vector equation for the line of intersection of the planes x+4y-4z=-3 and x+z=5. r= < , ,0> +t <4, , >.
The vector equation for the line of intersection of the planes x+4y-4z=-3 and x + z = 5 is r = <5, -2, 0> + t <-1, 5/4, 1>
The equations of the planes are:
x + 4y - 4z = -3 ..............(1)
and x + z = 5 .............(2)
Subtract equation (2) from equation (1),
( x + 4y - 4z + 3) - (x + z - 5 ) = 0
4y - 5z + 8 = 0
we can rewrite is as,
4y = 5z - 8
y = 5/4 z - 8/4
y = 5/4 z - 2 ...............(3)
Here, we don't have enough equations to uniquely solve for either y or z. So, we set z = t, where t can be any real number.
The variable t is the free parameter for the parametrization of the line.
Substitute z = t in equation (3) we get,
y = 5/4 t - 2
From equation (2),
x = 5 - z
For z = t,
x = 5 - t
Thus, the parametrization of the line would be,
(x, y, z) = (5 - t, -2 + 5/4 t , t)
= <5, -2, 0> + t<-1, 5/4, 1>
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What i the 8th term in the arithmetic equence defined by the explicit formula an=6n−4?
Answer:
a₈ = 44
Step-by-step explanation:
to find a₈, substitute n = 8 into the explicit formula
a₈ = 6(8) - 4 = 48 - 4 = 44
a radio tower is located 275 feet from a building. from a window in the building, a person determines that the angle of elevation to the top of the tower is and that the angle of depression to the bottom of the tower is . how tall is the tower?
The height of the tower is equal to the length of the side opposite the angle of elevation plus the length of the side opposite the angle of depression.
The angle of elevation and angle of depression in this problem can be used to solve for the height of the tower.
Since the angle of elevation is the angle from the window to the top of the tower and the angle of depression is the angle from the window to the bottom of the tower, the height of the tower can be determined by finding the length of the side opposite the angle of elevation and adding it to the length of the side opposite the angle of depression.
Using trigonometry, we can solve for the two lengths using the sine and cosine functions. The sine of the angle of elevation is equal to the length of the side opposite the angle divided by the hypotenuse. The hypotenuse is the distance from the window to the tower, which is known to be 275 feet. Therefore, we can solve for the side opposite the angle of elevation by multiplying the sine of the angle of elevation by 275. The cosine of the angle of depression is equal to the length of the side opposite the angle divided by the hypotenuse. We can solve for the side opposite the angle of depression in the same way.
Once the two lengths are calculated, we can add them together to find the height of the tower.The height of the tower is equal to the length of the side opposite the angle of elevation plus the length of the side opposite the angle of depression.
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16 x 6 equals 92 How do I find 6?!?
The area of the rectangle would be 96 square inches.
Option (D) is correct.
What is the area of the rectangle?
The formula for the area of a rectangle is:
Area = length x width
where length is the distance along the longer side of the rectangle and width is the distance along the shorter side of the rectangle.
In the given figure,
The length of the rectangle = 8 + 8 = 16 inches.
Now by using the Pythagoras theorem, we can find the height
[tex]Height= \sqrt{(10)^2-(8)^2} \\\\=\sqrt{100-64}\\\\=\sqrt{36}\\\\=6[/tex]
So the base would be 6 inches.
Now we can find the area of the rectangle
Area = 16 * 6
Area = 96 square inches.
Hence, the area of the rectangle would be 96 square inches.
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keith drove 320 miles using 12 gallons of gas. at this rate, how many gallons of gas would he need to drive 296 miles?
Answer:
9.87 Gallons
Step-by-step explanation:
Start by finding how far mr. keith here can drive with one gallon of gas.
to do this you will:
360 ÷ 12 = 30
For one gallon of gas, he can drive 30 miles.
Now that we know the rate for 1 gallon of gas, you just apply that rate to the new mileage:
296 (new distance) ÷ 30 (how many he can do in one mile) = 9.87 (how many times that 30 miles goes into 296 (recall that this is the rate))
To drive 296 miles, keith will use 9.87 gallons of gasoline.
hope this helped :)
May I have help on this one please? thank you if you do!
Answer:
I believe you answer would b B!
The number of gallons of gas used every 1 mile traveled.
Step-by-step explanation:
Hope it helps! =D
Select the linear function that describes the relationship between the domain and range in the table below.
x f(x)
−1 5
0 3
1 1
The linear function that describes the relationship is y = -2x + 3
How to determine the linear functionFrom the question, we have the following parameters that can be used in our computation:
x f(x)
−1 5
0 3
1 1
A linear function is represented as
y = mx + c
Where
c = y when x = 0
This means thar
c = 3
So, we have
y = mx + 3
From the table, we can see that
As x increases by 1, y decrease by 2
This means that
m = -2
So, we have
y = -2x + 3
Hence, the equation is y = -2x + 3
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A boss wants to estimate the proportion of her employees who are satisfied with the company's
parking policy. She puts all 600 employees' names into a hat and picks 50 different names out of
the hat. Of the 50, 47 are satisfied with parking policy and 3 are not satisfied with it.
Which condition for constructing a l-sample z-interval for proportions has the boss failed to
satisfy?
For the given case The boss has failed to satisfy the condition of random sampling without replacement. This condition states that the samples must be taken randomly and with replacement, meaning that each sample is replaced after it has been selected.
In this case, the boss picked the 50 names out of the hat without replacing them, which means that the same names could have been picked more than once. This can lead to a sample bias, as the same names may be overrepresented in the sample. This lack of randomness can lead to an inaccurate estimate of the proportion of employees who are satisfied with the company's parking policy.
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A recipe for lemonade is shown. Select the two true statements about the ratios in this recipe.
Lemonade recipe
2 cups sugar
3 cups lemon juice
8 cups water
Answer:
The ratio of sugar to lemon juice is 2 cups sugar : 3 cups lemon juice.
The ratio of lemon juice to water is 3 cups lemon juice : 8 cups water.
The first statement is true because the recipe calls for 2 cups of sugar and 3 cups of lemon juice. The ratio of sugar to lemon juice is therefore 2:3, or 2 cups sugar : 3 cups lemon juice.
The second statement is true because the recipe calls for 3 cups of lemon juice and 8 cups of water. The ratio of lemon juice to water is therefore 3:8, or 3 cups lemon juice : 8 cups water.
It's important to note that these ratios are in the context of this specific recipe, and may differ from other lemonade recipes.
Step-by-step explanation:
If you invest $10,000 in a bank which one is a better investment? A) 9% compounded monthly b) 9. 3% compounded annually
If you invest $10000 in a bank , then the better investment plan is (a) 9% compounded monthly .
The amount to be invested in bank is = $10000 ;
the formula to calculate the final amount by compounding is given as :
A = P(1 + r/n)^(nt) ;
Where: (A) = final amount , (P) = initial amount ,
⇒ r is interest rate (in decimal form) , n is number of times the interest is compounded per year and
⇒ t is number of years investment is made
(a) the rate of interest is 9% compounded monthly ;
in this case n = 12 , because there are 12 months in 1 year ;
So , Amount = 10000(1 + 0.09/12)^(12×t)
Amount = 10000 × (1.0075)^(12×t)
Suppose t = 1 ;
we get , Amount = 10000 × (1.0075)¹² ≈ 10938 .
(b) the rate of interest is 9% compounded annually ;
in this case n = 1 , because compounded annually ;
So , Amount = 10000 × (1 + 0.09)^(1×t)
Amount = 10000 × (1.09)^t
Suppose t = 1 ; we get , Amount = 10000 × (1.09)¹ ≈ 10900 ;
On comparing both the interest value we observe that ,
the monthly compounding returns more value than compounding annually .
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Nikki gathered data about the length of time she spent listening to the radio and the number of commercials she heard. She organized the data in a scatter plot, where x represents the minutes spent listening and y represents the number of commercials. Then she used the graphing tool to find the equation of the line of best fit:
HELP!!
By using the equation of the line of best fit, the number of minutes Nikki would need to listen to the radio is equal to 63.275 minutes.
How to determine the number of minutes Nikki would need to listen to the radio?In order to determine the number of minutes Nikki would need to listen to the radio, we would have to substitute the value representing the number of commercials (y) into the linear equation and then evaluate as follows;
y = 0.338x − 1.387
When the value of y = 20 commercials, the number of minutes (x) in feet is given by;
20 = 0.338x − 1.387
By rearranging and collecting like terms, we have the following:
0.338x = 20 + 1.387
0.338x = 21.387
Number of minutes (x) = 21.387/0.338
Number of minutes (x) = 63.275 minutes.
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Complete Question:
Nikki gathered data about the length of time she spent listening to the radio and the number of commercials she heard. She organized the data in a scatter plot, where x represents the minutes spent listening and y represents the number of commercials. Then she used the graphing tool to find the equation of the line of best fit: y = 0.338x − 1.387. Based on the line of best fit, for approximately how many minutes will Nikki need to listen to the radio to hear 20 commercials?
a bag contains 8 red marbles, 8 white marbles, and 10 blue marbles. you draw 5 marbles out at random, without replacement. what is the probability that all the marbles are red?
The probability of all 5 marbles being red is (8/26) x (7/25) x (6/24) x (5/23) x (4/22) = 0.000766.
This can also be written as P(RRRRR) = 8/26 x 7/25 x 6/24 x 5/23 x 4/22. This probability is very small, as the chances of randomly selecting only red marbles from the bag is low.
This calculation is based on the formula for combinations, which states that the probability of selecting r items from a group of n items is nCr x Pr, where nCr is the number of combinations of selecting r items from n items and Pr is the probability of selecting a specific item. In this case, n = 26 and r = 5, so the number of combinations of selecting 5 items from 26 items is 26C5. This is equal to 8x7x6x5x4/5x4x3x2x1, or 8x7x6x5x4/120. The probability of selecting a specific item is 1/26, as there are 26 items in the bag. Therefore, P(RRRRR) = 8/26 x 7/25 x 6/24 x 5/23 x 4/22.
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3. In the MN Daily 3 lottery, players are given a ticket based upon 3 digits that they pick. If their
3 digits match the winning digits in the correct order, then the player wins $500. If the digits
don't match, then the player loses. The game costs $1 to play. What is the expected value for
a player of this lottery game. (Hint find the probability of winning the Daily 3)
On average, a player can expect to lose $0.50 for every ticket they play in the Daily 3 lottery. Therefore, the Daily 3 lottery game is not a good investment, as the expected value is negative, and players are likely to lose money in the long run.
How to find the expected value?To find the expected value of the Daily 3 lottery game, we need to calculate the probability of winning and the expected payout for winning.
The probability of winning the Daily 3 game with a single ticket is 1/1000, since there are 1000 possible 3-digit number combinations and only one of them is the winning combination.
The expected payout for winning is $500, since this is the prize for matching the winning digits in the correct order.
To calculate the expected value, we can use the formula:
Expected Value = (Probability of Winning) x (Payout for Winning) - (Cost of Playing)
Plugging in the values we found, we get:
Expected Value = (1/1000) x ($500) - ($1)
= $0.50 - $1
= -$0.50
This means that, on average, a player can expect to lose $0.50 for every ticket they play in the Daily 3 lottery. Therefore, the Daily 3 lottery game is not a good investment, as the expected value is negative, and players are likely to lose money in the long run.
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The explicit rule for an arithmetic sequence is an = 8. 7 + (-1. 4)(n-1). What is the value of the 47th term? round to the nearest tenth, if necessary.
answer: A) -55. 7
The value of the 47th term of the given arithmetic sequence is -55.7
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is always the same.
We are given the explicit rule for an arithmetic sequence as follows -
[tex]a_n[/tex] = 8.7 - 1.4(n-1)
We have to find the value of the 47th term in the series.
So, we have the value of n = 47
The equation will become -
[tex]a_{47}[/tex] = 8.7 - 1.4(47-1)
[tex]a_{47}[/tex] = 8.7 - 1.4(46)
[tex]a_{47}[/tex] = 8.7 - 64.4
[tex]a_{47}[/tex] = -55.7
Thus, the value of the 47th term of the given arithmetic sequence is -55.7
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Lucia and Danna both recently purchased fitness watches. The watches count the number of steps they walk in a day. At lunchtime, Lucia has 5445 steps and Danna has 4995 steps. Lucia averages 800 steps per hour and Danna averages 900 steps per hour.
A. Write and solve a system of linear equations that represent the total number of steps each person takes.
B. Interpret the meaning of the solution in terms of the problem situation.
The system of linear equations is y = 800x + 5445, and y = 900x + 4995. The solution is 4.50. This states that the number of steps taken by Danna and Lucia will be equal after 4.50 hours.
What is system of linear equation?The set of two or more linear equations containing the same variables is known as a system of linear equations in mathematics. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation.
Let us suppose the number of hours = x.
Let us suppose the total number of steps = y.
Given that, Lucia has 5445 steps and Lucia averages 800 steps per hour.
For Lucia the linear equation is:
y = 800x + 5445
For Danna, Danna has 4995 steps and Danna averages 900 steps per hour.
For Danna the linear equation is:
y = 900x + 4995
The system of linear equations is:
y = 800x + 5445 (equation 1)
y = 900x + 4995 (equation 2)
Substitute the value of y of equation 1 in equation 2:
800x + 5445 = 900x + 4995
5445 - 4995 = 900x - 800x
450 = 100x
x= 4.50
B. The solution of the linear equation is 4.50. This states that the number of steps taken by Danna and Lucia will be equal after 4.50 hours.
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Lysosomes break open during the process of digestion, releasing enzymes into the cytoplasm. Which statement may explain why the entire cell may not be digested?
1: the acidic environment of the cytoplasm destroys the enzymes
2: antibodies in the cytoplasm break down foreign enzymes.
3: The pH of the cytoplasm causes the enzymes to function less effectively
4: Enzymes can function only ind the location where they are synthesized
If Lysosomes break open during the process of digestion, releasing enzymes into the cytoplasm. The statement that may explain why the entire cell may not be digested is: 3. The pH of the cytoplasm causes the enzymes to function less effectively.
What is Lysosomes?Lysosomes can be defined as vesicles that is made up of enzyme. This Lysosomes enables the process of digestion to take place and the enzyme found in lysosomes also help to break down biological molecule.
The reason why the whole cell may not be digested in an situation where enzymes are released into the cytoplasm is that the pH of the cytoplasm led to the enzymes not to function effectively. Optimum PH is required for cytoplasm to function more effectively.
Therefore the correct option is B.
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2. How many points
of intersection are there
on the graph
of
y=x² + 3x-2
y -x=4
There is one point of intersection on the graph of y = x² + 3x - 2 and y - x = 4
To find the point of intersection, we need to set the two equations equal to each other and solve for x and y.
y = x² + 3x - 2
y - x = 4
x² + 3x - 2 - x = 4
x² + 2x - 6 = 0
(x-3)(x+2)=0
x =3 or x=-2
When x = 3, we substitute it into the first equation y = x² + 3x - 2
y = 3² + 3(3) - 2
y = 9 + 9 - 2
y = 16
When x = -2, we substitute it into the first equation y = x² + 3x - 2
y = -2² + 3(-2) - 2
y = 4 -6 -2
y = -4
So the point of intersection is (3,16) or (-2,-4)
Hence there is only one point of intersection on the graph of y = x² + 3x - 2 and y - x = 4
Please help me. Answer ASAP!! all info you need to solve the problem is in the photo
If f(0) = 18 and f(1) = 13 then f(0) be the largest value.
What is meant by function?A function is a relationship between a number of inputs where each input has exactly one output, according to one definition.
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions denoted the idealized relationship between two changing quantities.
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). If f exists typically utilized to denote a function (x).
Let the function f(x) = 18 - 5x
a) f(-4) = 18 - 5(-4) = 38
b) f(0) = 18 - 5(0) = 18
f(1) = 18 - 5(1) = 13
Therefore, f(0) be the largest value.
The complete question is:
Given the function f(x) = 18 - 5x
a. What is the value of function f given an input of -4 ?
b. Which is larger, f(0) or f(1)? Show your work to justify your answer.
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How do the values compare? Order the values from least to greatest.
30
314
4
-1
14
4
314
14
14
-2.
14
1-2-11
Answer: -2, -1, 4, 4, 14, 14, 14, 30, 314, 314
The values are arranged in increasing order from least to greatest.
Check the picture below.
5. Rafael had 25 golf balls in a bucket. He used 20% of them at the driving range. How many balls did he use at the driving range?
Answer:
5
Step-by-step explanation:
To find out how many golf balls Rafael used at the driving range, we can use the following formula:
number of balls used at the driving range = total number of balls x percentage used
Given:
Total number of balls = 25
Percentage used = 20%
So we can substitute these values into the formula:
number of balls used at the driving range = 25 x 20% = 25 x 0.20 = 5
Therefore, Rafael used 5 golf balls at the driving range.
A bakery sells different packages of muffins. The number of muffins, , and the price in dollars, , of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.
The bakery is considering adding a new package of muffins. Which of these combinations would make the relation NOT a function? Select TWO that apply.
A relation might or might not be a function. The connection would cease to be a function because of b. (6, 8) and d. (4, 3).
What are combinations?Combinations are mathematical procedures that count how many different ways a collection of items could be arranged when the order in which they are chosen is immaterial.
Combos' components can be chosen in any hierarchy.
Combinations and permutations can coexist.
Hence, the ordered pair is given:
(x, y) = (1, 2); (2, 3); (4, 5); (6, 7); (12, 13)
For a relation to be a function, all of the x-values must be unique (i.e. no repetition)
From the list of alternatives, options (b) and (d), with x values (6, 7) and (d), already exist in the ordered pair (4,5)
In light of this, (b) and (d) would stop the connection from being a function.
Therefore, a relation might or might not be a function. The connection would cease to be a function because of b. (6, 8) and d. (4, 3).
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Correct question:
A bakery sells different packages of muffins. The number of muffins, x, and the price in dollars, y, of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.
{(1,2),(2,3),(4,5),(6,7),(12,13)}
The bakery is considering adding a new package of muffins. which ordered pairs would make the relation NOT a function? Choose all that are correct.
a. (10,13)
b. (6,8)
c. (8,12)
d. (4,3)
e. (24,18)
A local news story claims that 53% of high school
males agree with the statement "I am ok with a girl
playing on the football team because there is not a
football team for girls. " To investigate this claim, an SRS
of 100 males from a large local high school is selected.
In the sample, 38 males agreed with the statement. We
used technology to simulate choosing 240 SRSs of size
n = 100 from a population of males where 53% agreed
with the statement. The dotplot shows p = the sample
proportion of males who agree with the statement for
each of the 240 samples.
Find the mean and standard deivation of the sampling
distribution.
The mean is 24 and standard deviation is 10 of the sampling distribution.
The term in math called standard deviation is defined as the standard deviation of the sampling distribution is also known as the standard error and it is inversely proportional to the sample size in which is as the sample size increases the standard deviation of the sample means decreases.
Here we know that the value of n is 100 and the number of samples 240.
Agreed count = 38.
Here we have to assuming the expected population standard deviation to be 10, and a population size of 100, the study would require a sample size of 24 to estimate a mean with 53% confidence and a precision of 1.5.
Then the standard deviation is 10.
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When we are concerned with whether we are correct in inferring that a cause produced an effect, we are concerned with the:
The concept here is the Research method, it is the main extent to which a concept, conclusion, or measurement is well-founded The answer is validity.
Research methods are strategies, processes, or ways used to collect data or substantiation for analysis to uncover new information or better understand the content.
Validity is the lesser degree to which an idea, conclusion, or action is reasonable and likely to directly reflect reality. The word" valid" comes from the Latin Validus, which means strong.
The validity of a dimension instrument is the extent to which the instrument measures what it's intended to measure. Validity refers to the relationship between the study thing and the data the experimenter chooses to use to quantify that thing. Some confines similar to physical strength, aren't naturally related to intelligence.
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Jill and Jessica are bike riding at the park. Jill rides her bike around the two edges of the rectangular park while Jessica takes the short cut. How much farther does Jill ride than Jessica? Round to the nearest tenth.
Jill ride 43.39 meters farther than Jessica.
What is the Pythagorean theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.
Given, Jill and Jessica are bike riding at the park. Jill rides her bike around the two edges of the rectangular park while Jessica takes the shortcut
Given the length of the Rectangular park = 100m
The width of the park = 60m
Thus jill ride total = 60 + 100
Jill ride total = 160m
Jessica took a shortcut since she rides diagonally.
From the Pythagorean theorem:
hypotaneus² = base² + height²
Thus,
total distance Jessica covers = √(60² + 100²)
total distance Jessica covers = √3600 + 10000
total distance Jessica covers = √13600
total distance Jessica covers = 116.61
Difference between their distances = 160 - 116.61
Difference between their distances = 43.39
therefore, 43.39 m farther does Jill ride than Jessica.
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Complete question:
Solve for x to the nearest tenth.
By calculating , The value of x is 5√5.
What is triangle?
Triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.
From the given figure,
When we draw a line inside the figure than it becomes into rectangle and one another triangle.
so,
In the right angled triangle,
with base 10 and opposite side 5
We have to find the hypothenuse that is x .
so,
from pythagorean theorem
we can say that
Sum of squares of two sides is equal to square of hypothenuse
so,
10*10 + 5*5 = x*x
100+25 = x*x
x*x = 125
x = 5√5 .
Hence, The value of x is 5√5
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complete the description of the piecewise function graphed below
The supplied input should simply be replaced in the function definition for that precise interval.
What best describes a piecewise function?An equation or set of equations, rather than a single equation, defines a piecewise-defined function. For a specific interval, each equation is valid.
Find out to which of the above intervals (or inequalities) the supplied input belongs before evaluating a piecewise function at any given input. The function definition for that specific interval should therefore just have the specified input replaced.
When a rule or relationship changes as an input value passes specific "boundaries," we refer to these instances as piecewise functions. For instance, scenarios where the price per piece of a specific item is decreased once the quantity requested exceeds a given amount are frequent in business.
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1. If mA = 3x° and
m
what is the value
of x?
Answer: I'm sorry, but the information provided is not enough to determine the value of x. The statement "mA = 3x°" does not provide enough context to understand what "mA" and "x" represent, and what the relationship between them is. Additionally, the statement "m" does not provide any information that can help determine the value of x. Can you please provide more information or context?
Step-by-step explanation:
The same type of dinner plate is sold in two different packs. Small pack contents 3 plates £5. 25. Large pack contents 12 plates £21. 24 which size packet is the better value for money?
Large pack with 12 plates has better value of money with $1.77 for each plate comparison to smaller pack with $1.75 for each plate.
Number of plates in smaller pack is equal to 3 .
Cost of smaller pack with three plates = $5.25
Cost of each plate in smaller pack = $5.25 / 3
= $1.75
Number of plates in larger pack is equal to 12 .
Cost of larger pack with twelve plates = $21.24
Cost of each plate in larger pack = $21.24 / 12
= $1.77
$1.77 is greater than $1.75.
Larger pack of plates have better value of money for each plate comparing the smaller pack.
Therefore, the larger pack has better value of money than the smaller pack .
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What is the distance between AB and CD?
√5 is the minimum distance between the line AB and CD.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given Two lines AB and CD,
Since, The minimum distance between two lines is the distance between B and C As we can see in the graph
Since, coordinates of B and C are, (1, 2) and (3, 1)
From the formula of distance between two coordinates:
Distance = √((x₂ -x₁)² + (y₂ -y₁)²)
in our case,
Distance = √((3 - 1)² + (1-2)²)
Distance = √4 + 1)
Distance = √5
Therefore, the minimum distance between the line AB and CD is √5.
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Eagle Airlines flies charter planes all over the world. Susan, one of the airlines' top pilo
routes in Europe and North Africa. Susan's plane uses 2 kilograms of fuel for every kil
she flies.
There is a proportional relationship between the distance Susan flies (in kilometers), x
the amount of fuel her plane uses (in kilograms), y.
Graph this relationship. Select two points to draw a line.
What is the slope of the line?
The proportional relationship that models this situation is given as follows:
y = 2x.
The graph is given by the image presented at the end of the answer.
How to model the proportional relationship?A proportional relationship is modeled as follows:
y = kx.
In which k is the constant of proportionality.
Susan's plane uses 2 kilograms of fuel for every unit she flies, hence the constant is given as follows:
k = 2.
The relationship is:
y = 2x.
The domain is:
x >= 0, as the number of units flied cannot be negative.
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