The probability that the first MP3 song heard is the fifth song played is:
[tex]\frac{C^9^0_4.C^1^0_1}{C^1^0^0_5}[/tex] = [tex]\frac{2,555,190. 10}{75,287,520}[/tex] ≈ 0.3394
The probability that there are exactly two MP3 songs in the first five songs played is:
[tex]\frac{C^1^0_2.C^9^0_3}{C^1^0^0_5}[/tex] [tex]= \frac{45.117,480}{75,287,520}[/tex] ≈ 0.0702
Now, According to the question:
The 1st MP3 player songs heard is the 5th song played means that first 4 songs are not MP3 songs (there are 100 - 10 = 90 such songs) and the 5th song is MP3 song (there are 10 such songs). Hence, the probability that the first MP3 song heard is the fifth song played is:
[tex]\frac{C^9^0_4.C^1^0_1}{C^1^0^0_5}[/tex] = [tex]\frac{2,555,190. 10}{75,287,520}[/tex] ≈ 0.3394
There are exactly two MP3 songs in the first five songs played means there are 2 MP3 songs and 3 not MP3 songs (the number when these songs are played do not matter). Hence, the probability that there are exactly two MP3 songs in the first five songs played is:
[tex]\frac{C^1^0_2.C^9^0_3}{C^1^0^0_5}[/tex] [tex]= \frac{45.117,480}{75,287,520}[/tex] ≈ 0.0702
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The owner of a public golf course is concerned about slow play, which clogs the course and results in selling fewer rounds. She believes the problem lies in the amount of time taken to sink putts on the green. To investigate the problem, she randomly samples 10 foursomes and measures the amount of time they spend on the 18th green. The data are listed here. Assuming that the times are normally distributed with a standard deviation
of 2 minutes, test to determine whether the owner can infer at the 5% significance level that the mean amount of time spent putting on the 18thgreen is greater than 6 minutes
If the calculated value is less than the table value, we fail to reject the null hypothesis.
What is the null hypothesis?
The null hypothesis is a statement or assumption that there is no statistically significant difference or relationship between two variables or groups being studied. It is usually denoted by the symbol H₀. It serves as a starting point for a statistical hypothesis test, and it is the opposite of the alternative hypothesis, which states that there is a statistically significant difference or relationship between the variables or groups being studied.
for the given sample :
mean=6.6
S.D=2.31
n=10
Mean of population:6
t0=(6.6-6)/2.31/sqrt(10)=0.82
for 95% confidence and 9 df
t value is:2.26
Hence, if the calculated value is less than the table value, we fail to reject the null hypothesis.
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Mason has 2/3 of a foot of ribbon. He needs to divide the ribbon into 1/6 -foot pieces.
How many pieces can he cut from the ribbon?
Based on the information provided, Mason can cut four pieces of ribbon.
How much ribbon does Mason have?Based on the information provided, Mason has 2/3 of a foot ribbon, which is equivalent to 0.66.
How many pieces can he cut out of the total ribbon he has?To know the answer, use a division with the following formula:
Total ribbon/ size of the desired pieces
0.66 / 2/3 or 0.166 (2/3 = 0.166)
0.66 / 0.166
4 pieces
Based on this, it can be concluded that Mason will be able to get 6 1/6 feet long pieces.
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x-2 for x = 8
help pls
Answer:
6
Step-by-step explanation:
since x=8, 8-2 equals 6
Find the slope of a line perpendicular to the line whose equation is 4x - 3y = -3.
Fully simplify your answer.
The slope of the line having the equation 4x - 3y = -3 is calculated to be
4/3
How to find the slope of the lineThe slope of the line is gotten by rewriting the equation of the line in the standard form Ax + By = C. to equation of a line in slope intercept form which is y = mx + c
The equation of line in the problem is 4x - 3y = -3
The equation is rewritten as follows
4x - 3y = -3
-3y = -3 - 4x
Isolating y by dividing trough by -3
y = 1 + 4/3 x
y = 1.33x + 1
comparing with y = mx + c where m is the slope we can see that m = 4/3
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Suppose your city is building a new park, and issues bonds to raise the money to build it. You obtain a $1,000 bond that pays 5% interest annually that matures in 5 years. How much interest will you earn?
Answer:
To find out how much interest you will earn, you need to multiply the bond principal amount ($1,000) by the interest rate (5%) and the number of years the bond matures (5).
The interest rate is expressed as a percentage, so you need to convert it to a decimal by dividing it by 100.
Interest = Principal x Interest Rate x Time
Interest = $1,000 x 0.05 x 5
Interest = $1,000 x 0.05 x 5 = $250
So, you will earn $250 in interest over the 5-year period.
You are inflating a balloon in a room. The volume of the balloon is
given by V(m, θ) = sqrtθ [ln(m)],
where m is the mass of the air in the balloon, and θ is the temperature of the room.
Suppose that at time t, the mass of air in the balloon is m(t) = t^2+3 and the temperature of the room is θ(t) = e^t.
Use the chain rule to find the rate at which the volume is
changing at time t.
According to the question rate at which the volume is dV/dt = dV/dm * dm/dt + dV/dθ * dθ/dt.
What is the straightforward meaning of volume?The space covered within an object's borders in three dimensions is referred to as its volume. It is refereed as the object's capability on occasion.
How is volume measured?Volume, which is measured in cubic units, is the three dimensional volume occupied by matter or encircled by a surface. The cubic centimeter (m3), a derived unit, is the Standard unit of volume.
Substituting in the given information, we have:
V(m, θ) = sqrt(θ) * ln(m)
m(t) = t^2 + 3
θ(t) = e^t
Therefore:
dV/dm = (1/m) * sqrt(θ)
dm/dt = 2t
dV/dθ = (1/2sqrt(θ)) * ln(m)
dθ/dt = e^t
plugging in the values of m(t) = t^2 + 3 and θ(t) = e^t
dV/dt = (1/(t^2+3)) * sqrt(e^t) * 2t + (1/2sqrt(e^t)) * ln(t^2+3) * e^t
So the rate at which the volume is changing at time t is given by dV/dt
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Quadrilateral GFHE and quadrilateral TRQS are similar. Which pair of angles are corresponding congruent angles of these quadrilaterals?
The following pair of angles are corresponding congruent angles of these quadrilaterals:
∠G ≅ ∠T
∠F ≅ ∠R
∠H ≅ ∠Q
∠E ≅ ∠S
What is quadrilateral?A quadrilateral in geometry is a four-sided polygon with four edges and four corners.
Given:
Quadrilateral GFHE and quadrilateral TRQS are similar.
The figures are given in the attached image.
The following pair of angles are corresponding congruent angles of these quadrilaterals:
∠G ≅ ∠T
∠F ≅ ∠R
∠H ≅ ∠Q
∠E ≅ ∠S
Therefore, all the pairs are given above.
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let x be a numeric vector. create a new vector y which consists of all entries of x between -3 and 3 (including -3 and 3), in order of appearance as in the vector x. for example, if
For the creation of y, we first need to know the placement of the numbers and then write an R code to create a subset for the same.
To create another vector y which contains all the numbers between 3 and -3 in order of appearance, we first need to know exactly what is the order of the appearance of 3 and -3.
Hence we will write the R code
which(x == 3)
which(x == -3)
These commands will return us the specific position of the numbers 3 and -3
Let us assume that 3 is the fourth number and -3 is the 31st number. Then we will write y as a function that contains the subset of x from the fourth to the 31st number as follows.
y <- x[4:31]
Typing this command will give us the required subset.
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Complete Question
Let x be a numeric vector and suppose you want to extract all the entries of x that are between -3 and 3 (including both boundaries -3 and 3). Create a new vector y which consists of all entries of x between -3 and 3 (including -3 and 3), in order of appearance as in vector x. For example, if X = c(-5, 7, 9, 3, 14, 9, 5, 10, -2, 0, 12) then, printing y should read у [1] 0 3 -2 0
The table at the right shows the random sample that Jeremy generated from the same population as Morgan's and Maddy's samples. Compare Jeremy's sample to Morgan's and Maddy's.
When Jeremy's sample is being compared to the sample collected by Morgan and Maddy by the left, about 6 Jeremy samples ranges from 81-10 while only 2 samples ranges from 81-100 in Morgan's and Maddy's.
What is a histogram?A histogram is defined as one of the graphical way of representation of data for an easy analysis, comparison and interpretation of results.
From the two histogram given above, the comparison of both results shows that about 6 Jeremy samples ranges from 81-10 while only 2 samples ranges from 81-100 in Morgan's and Maddy's.
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Before you work on your homework each week, please make sure you've read through the assigned sections in the book.
The assigned reading for this lesson begins with this quote:
Quote:
Human beings only use ten percent of their brains. Ten percent! Can you imagine how much we could accomplish if we used the other sixty percent?
According to the textbook, who said this quote?
Please help 30 points
The quote that "Human beings only use ten percent of their brains. Ten percent! Can you imagine how much we could accomplish if we used the other sixty percent?" was made by Ellen DeGeneres.
What is a quote?The representation of an utterance in oral speech that is preceded by a quotative marker, such as a verb of saying, is known as a paraphrase. When doing a brainstorming exercise, quotes can help spark ideas that then influence the ideas for the piece.
Through the presentation of other people's ideas, they can steer you in new directions. Finally, using short quotes that won't keep a writer from writing for too long can help them as they put a piece together.
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The temperature, t, of water and the number of minutes, m, the water is in the freezer
Which is the dependant variable
Answer:
Temperature.
Step-by-step explanation:
The temperature of the water depends on the minutes the water is in the freezer. If the water is frozen for longer, the water will be colder and if the water is frozen for less time, the water will be less cold.
3x + 5y = - 9 + -6x - 5y = 18?
Answer: The given equations are not valid because there is no equal sign between the first and second equation. If you are trying to solve a system of equations it should be in the form of
3x + 5y = - 9
-6x - 5y = 18
You can solve for x and y by using different methods such as substitution, elimination or graphing.
In this case, you can add the first equation to the second equation:
3x + 5y = -9
-6x - 5y = 18
-3x = 27
x = -9
Now you can substitute this value of x into one of the equations to find the value of y.
3x + 5y = -9
3(-9) + 5y = -9
-27 + 5y = -9
5y = 18
y = 3.6
So, the solution is x = -9 and y = 3.6
It's important to check your solution by substituting the values of x and y in the original equations to make sure that the solution is consistent.
Step-by-step explanation:
A teacher in a summer school program notices that her students seem less able to pay attention
when the temperature in the classroom gets warmer. The teacher decides to record the
temperature every day (utilizing Fahrenheit degrees) to track classroom heat conditions. The
measurement of the temperature used here used here is
1.
2.
3.
C
Nominal
r
Ordinal
Interval
Save
Ratio
The level of measurement used for the temperature is given as follows:
Interval.
How to obtain the levels of measurement of the data?There are four levels of measurement for the data, given as follows:
Nominal.Ordinal.Interval.Ratios.The measures of central tendency for each level are given as follows:
Nominal: ModeOrdinal: Mode and median.Interval: Arithmetic mean, mode and median.Ratios: Arithmetic mean, geometric mean, mode and median.For the temperature, we obtain the arithmetic mean, hence it has the level of measurement of interval.
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What was Di's average velocity, in miles per hour, from the interval
t = 10 min
to
t = 15 min?
(Round your answer to two decimal places.)
Average velocity between the interval t = 10 min to t = 15 min is; 52.5 miles per hour
How to find the average velocity?The expression showing Di's average velocity, in miles per hour, t minutes after entering the interstate highway is;
v(t) = ¹/₂₀₀t³ + ³/₂₀t² - ³/₈t + 60
At t = 10 minutes, we have;
v(10) = ¹/₂₀₀(10³) + ³/₂₀(10²) - ³/₈(10) + 60
v(10) = 5 + 15 - 7.5 + 60
v(10) = 52.5 miles per hour
At t = 15 minutes, we have;
v(15) = ¹/₂₀₀(15³) + ³/₂₀(15²) - ³/₈(15) + 60
v(15) = 16.875 + 33.75 - 5.625 + 60
v(15) = 105 miles per hour
Thus;
Average velocity between the interval t = 10 min to t = 15 min is;
v(15) - v(10) = 105 - 52.5
= 52.5 miles per hour
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Reuben is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Reuben has been adding money. Suppose that x and y are related by the equation 750=40x.
Based on equation 750=40x, the value of x is 18.75 weeks.
What is an equation?An equation is a mathematical statement that two or more algebraic expressions are equal or equivalent.
Equations must have the equation symbol (=) to show the equality of the mathematical expressions.
Equations are started with let statements, defining the variables.
Let the total amount of money in the account = y (in dollars)
Let the number of weeks Reuben has been adding money = x
Equation:750 = 40x
40x = 750
x = 18.75 (750/40)
Thus, based on the solution to the equation, we know that Reuben has added money into the account for 18.75 weeks.
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Question Completion:Compute the number of weeks Reuben has been putting money into the account.
Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is 60 . For one performance, 40 advance tickets and 15 same-day tickets were sold. The total amount paid for the tickets was 1400. What was the price of each kind of ticket?
Answer: Let's call the price of an advance ticket "a" and the price of a same-day ticket "s". We know that the combined cost of one advance ticket and one same-day ticket is 60, so we can set up the equation: a + s = 60.
We also know that 40 advance tickets and 15 same-day tickets were sold for a total of 1400 dollars. So we can set up the equation: 40a + 15s = 1400
We have a system of two equations with two variables. We can use substitution or elimination method to solve for the unknowns.
Using substitution:
Solve the first equation for s, s=60-a
substitute it into the second equation, 40a + 15(60-a) = 1400
Expanding the second equation: 40a + 900 - 15a = 1400
25a = 500
a = 20
substitute a back into the first equation: s = 60 - 20 = 40
So the price of an advance ticket is $20, and the price of a same-day ticket is $40.
Step-by-step explanation:
twelve people each spin a coin. find the number of ways in which exactly five heads may be obtained
the probability exactly five heads may be obtained is 77%.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
twelve people each spin a coin.
n = number of trials = 12
x = number of successes(head) among n trials = 5
p = probability of success(head) in any one trial = 1/2
probability of failure in any one trial (q = 1 - p) = 1/2
exactly five heads may be obtained 12 C 5 * (1/2)[tex].{5}[/tex] *(1/2)[tex].{5}[/tex] = 792/1024 =0.77
Hence the probability exactly five heads may be obtained is 77%.
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given triangle xyz and triangle pqr with measurements as marked below. determine whether or not triangle xyz is similar to triangle pqr
The Pythagorean Theorem holds true for both triangles, then the triangles are not only similar, but also congruent.
Triangle xyz has sides of length x, y, and z and triangle pqr has sides of length p, q, and r.
To determine if triangle xyz is similar to triangle pqr, we must calculate the ratios of corresponding sides. This is done using the formula:
Ratio of sides = (Side length x) / (Side length y)
We can calculate the ratios for each side of the triangles and compare them. If the ratios are equal for all sides, then the triangles are similar. For example, if the ratio of side x to side y in triangle xyz is equal to the ratio of side p to side q in triangle pqr, then the triangles are similar. If the ratios are not equal for all sides, then the triangles are not similar.
We can use the Pythagorean Theorem to determine if the triangles are not only similar, but also congruent. The Pythagorean Theorem states that a2 + b2 = c2, where c is the longest side and a and b are the other two sides. If the Pythagorean Theorem holds true for both triangles, then the triangles are not only similar, but also congruent.
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m = 6
point = (12, -8)
b = ?
solve it
Step-by-step explanation:
you mean the slope-intercept form of a line equation ?
y = mx + b
or what is the problem ?
if my assumption is correct, then m is the slope of the line.
and we got a point on the line.
so, we could start with the point-slope form and then transform.
the point-slope form is
y - y1 = m(x - x1)
again, m is the slope, (x1, y1) is a given point on the line.
so, we have
y - -8 = 6(x - 12)
y + 8 = 6x - 72
y = 6x - 80
that means b = -80
what of the following statements is not true about samples? group of answer choices wording and ordering of questions can affect results samples should reflect the population being studied samples picked randomly are more representative of a population a variety of ways can be used to contract the samples larger samples are more accurate
The statement that is not true about samples is: "samples picked randomly are more representative of a population."
To determine this:
While random sampling is one way to ensure that a sample is representative of a population, it is not the only way. There are other methods of sampling such as stratified sampling, cluster sampling, and systematic sampling that can also be used to obtain a representative sample.
It is important to note that, even with random sampling, a sample may not be representative of the population if the sample size is too small or if there is a significant amount of bias in the sampling process.
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what is the solution set of y= x^2 + 2x + 7 and y = x + 7?
Answer:
Step-by-step explanation:
(0, 7) and (-1, 6)
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“One-third of a herd of elephants and three times the square root of the remaining part of the herd were seen on a mountain slope; and in a lake was seen a male elephant along with three female elephants constituting the ultimate(last) remainder. How many were the elephants here?”
The total number of elephants in the herd is 24.
How did we arrive at the value?This is a math problem that can be solved using algebra. To start, let x be the total number of elephants in the herd.
From the first part of the problem, we know that:
x/3 = a herd of elephants seen on a mountain slope
From the second part of the problem, we know that:
3 * √(x - x/3) = a herd of elephants seen on a mountain slope
From the third part of the problem, we know that:
1 + 3 = 4 = the ultimate remainder of the herd seen in a lake.
We can then use these equations to solve for x.
x/3 + 3 * √(x - x/3) + 4 = x, where x is the total number of elephants in the herd.
x = 3 * (1 + √(x - x/3) + 4)
Solving for x, we get x = 24
So, the total number of elephants in the herd is 24.
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A graphing calculator is recommended.
Find the maximum and minimum values of the function. (Round your answer to two decimal places)
y=3x-4sin3x, 0x2π
The Maximum value of the function is 5.71 and the Minimum value of the function is -2.71. To find the maximum and minimum values of the function y=3x-4sin3x, 0x2π, we used a graphing calculator.
first, we set the range of x from 0 to 2π and graphed the function. By looking at the graph, I could identify the maximum and minimum values of the function. The maximum value was 5.71 and the minimum value was -2.71. This can be seen at the peak and trough of the graph respectively. I then used the calculator to find the exact values of the maximum and minimum.
To do this, I used the 'maximum' and 'minimum' functions on the graphing calculator. This allowed me to input the function and the range of x and the calculator was able to output the exact maximum and minimum values. The output was 5.71 and -2.71. The calculator used was able to identify the maximum and minimum values of the function by using a process called calculus.
Calculus is the study of how functions change and by using the maximum and minimum functions, the calculator can identify the peak and trough of the graph.
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Can you guys help me with this one?
The ratio table can be completed as follows :
2 flowers - 10 petals 4 flowers - 20 petals 3 flowers - 15 petals How to complete the ratio table ?The ratio table shows that every flower would have 5 petals.
2 flowers would therefore have ;
= 2 flowers x 5 petals
= 10 petals
4 flowers would have :
= 4 flowers x 5 petals
= 20 petals
15 petals would belong to :
= 15 / 5 petals per flower
= 3 flowers
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nscribed and Circumscribed Circles: Tutorial
?
Answer the question below. Type your response in the
space provided.
In quadrilateral QRST, m¿Q > is 68°, m¿R is (3x + 40)º, and m¿T is (5x
52)°. What are the measures of ZR, ZS, and
values in that order with the measures separated by commas.
Done
Clear
The angle ∠R, ∠S, and ∠T for the quadrilateral are ∠R, ∠S, ∠T = 112°, 112°, 68°.
what are quadrilaterals?
A quadrilateral is a polygon with four sides, four vertices, and four angles.
It is formed by joining four non-collinear points. The sum of the interior angles of quadrilaterals is always equal to 360 degrees. The word quadrilateral is derived from the Latin words ‘Quadra’ which means four and ‘Latus’ means ‘sides’. Not all the four sides of a quadrilateral need to be equal in length. Hence, we can have different types of quadrilaterals based on sides and angles.
Five special quadrilaterals are shown below in the image, along with their definitions and pictures, and points for them to get proven.
Now,
TQRS is an inscribed quadrilateral.
5 x - 52° + 3 x + 40° = 180°
8 x - 12° = 180°
8 x = 180° + 12°
8 x = 192°
x = 192° : 8 = 24°
m∠ R = 3 · 24° + 40° = 112°
m∠ T = 5 · 24° - 52° = 68°
m∠ S = 360° - ( 68° + 68° + 112° ) = 112°
Answer:
∠R, ∠S, ∠T = 112°, 112°, 68°.
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Right question:-
"In quadrilateral QRST, m∠Q is 68°, m∠R is (3x + 40)°, and m∠T is (5x − 52)°. What are the measures of ∠R , ∠S , and ∠T ? Write the numerical values in that order with the measures separated by commas.
The linear equation y=2x represents the cost y for x pounds of apples. Which ordered pair lies on the graph of the equation
The ordered pair that lies on the graph of the equation is (1, 2)
How to determine the ordered pair lies on the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
y = 2x
The point in the ordered pair lies on the graph of the equation is the solution set
Take for instance, we set x = 2
So, we have
y = 2 * 1
Evaluate the product
This gives
y = 2
When repesented as an ordered pair, we have
(1, 2)
Hence, the point is (1, 2)
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Three women can bake 75 cakes in 5 days. How many cakes
can 6 women bake in 6 days?
Answer:
108 sorry there no more explanation!
Answer:
Step-by-step explanation:
180
if sum a n and sum b n are series with positive terms, and lim a n/b n does not exist, and sum b n diverges, then sum a n diverges
Since lim a n/b n does not exist, it means that the ratio between a n and b n can be larger or smaller depending on the terms.
This implies that the rate of growth of a n and b n are not necessarily the same. If the series b n diverges, it means that the terms of b n increase without bound. Therefore, the terms of a n will also increase without bound, and sum a n will also diverge.
Formally, if lim a n/b n = ∞, then ∑ a n is divergent. We can prove this by contradiction. Suppose ∑ a n converges. Then by the comparison test, lim a n/b n must converge and be finite, which is a contradiction. Therefore, ∑ a n must diverge.
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In the preivous activity you used a table of coordinates to determine that the baseball Billy hit followed a nonlinear path.I’m this activity you will use a graphical means to make the same determination
This equation represents the path of the ball that billy
Y=-1/300 x2 +x+3
Answer:
Part a: Answer is 1/2
78-3/1500 = 75/150
= 1/2
Part b: Answer is -1/2
3-78/300-150
=-75/150
= -1/2
Part c: No, the two rates aren't the same,
because one is positive and the other is
negative.
Part d: The rate of change of the function
determined by using the two pairs of
coordinates is not the same. So, the
function modeling the movement of the
ball is a nonlinear function
2. The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s)
when f(x) = g(x)? Explain your answer(s).
The solutions when the function f(x) = g(x) is x = -3 and x = -1, since the output of the function is similar.
What are functions?With the condition that each input is associated to exactly one output, a function is a relationship between a collection of inputs and a set of allowed outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
As we can observe from the given table, the two values for which the two function produce a similar output are at x = -3 and x = -1.
Hence, the solutions when the function f(x) = g(x) is x = -3 and x = -1, since the output of the function is similar.
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