The population after 12 years is 98448 and the formula is[tex]P(t) = 25000(1.121)^{t}[/tex].
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the population of the town is 25000 and increasing at the rate of 1.121.
The expression will be written as:-
[tex]P(t) = 25000(1.121)^{t}[/tex]
[tex]P(12) = 25000(1.121)^{12}[/tex]
P(12) = 98448
Hence, the population after 12 years will be 98448.
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write the word sentence as an equation: 5 is one-forth of a number c
(don't solve. just write an equation)
The equation of the word sentence, "5 is one-fourth of a number c" is: 5 = 1/4c.
How to Write a Word Sentence as an Equation?To write a word sentence as an equation, you need to identify the variables and the operations being described in the sentence, and then use mathematical symbols to represent them.
For example, we are given the sentence "5 is one-fourth of a number c,", in this case, the variable is "c" and the operation is "one-fourth of," which is represented by the fraction 1/4 or the multiplication by 1/4.
Therefore, the equation would be:
5 = 1/4c.
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Question 6
Find the area of triangle ABC:
AD is 1cm and BC is 1cm and D is 90
The area of triangle ABC is 0.5cm² where base and height are given.
Describe Area.Triangle area is used to measure the size of a region on a surface. The area of a form or planar lamina is referred to as the plane region or plane area, as opposed to surface area, which denotes the area of an open surface or the boundary of a three-dimensional object.
The area of a triangle can be compared to the volume of material at a specific thickness needed to make a model of the form or the amount of paint needed to cover a surface in a single coat. It is equivalent to a solid's volume or a curve's length in two dimensions (a three-dimensional concept).
From the given figure, we can say that
Height = AD = 1cm
Base = BC = 1cm
Area of Triangle = Base × Height/2
Area = 1 × 1 /2
Area = 0.5 cm²
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-86
8
6 8
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
008
Clear all
Enter the correct answer.
+00
+?
DONE
The equation of the linear function in this problem is given as follows:
y = 0.5x + 4.
How to define the linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.When x = 0, y = 4, hence the intercept b is given as follows:
b = 4.
When x increases by 8, y increases by 4, hence the slope m is given as follows:
m = 4/8 = 0.5.
Missing InformationThe linear function goes through the points (-8,0) and (0,4).
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P(A)=0.60, p(b)=0..25 and p(A and B)=.15 what is p(A or B)?
Answer:
0.70
Step-by-step explanation:
You want p(A+B) given that p(A) = 0.60, p(B) = 0.25, and p(A·B) = 0.15.
ProbabilityThe relevant formula is ...
p(A+B) = p(A) +p(B) -p(A·B)
p(A+B) = 0.60 +0.25 -0.15
p(A+B) = 0.70
__
Additional comment
In the attached Venn diagram, the sum of the numbers inside the circle labeled A is p(A) = 0.45 +0.15 = 0.60. Likewise, the sum of the numbers inside circle B is p(B) = 0.15 +0.10 = 0.25.
As the attachment shows, the event A includes the event 'A and B'. Likewise, event B includes the event 'A and B'. Simply adding the probabilities of A and B will cause p(A and B) to be counted twice.
FILL IN THE BLANK when calculating the confidence interval for the mean using a sample size of 30 or greater with a known population standard deviation, the ____ is used
The standard normal distribution is used when calculating the confidence interval for the mean using a sample size of 30 or greater with a known population standard deviation.
The Z-distribution (also known as the standard normal distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. When the population standard deviation is known, the sample mean follows a normal distribution and the standard error is given by the population standard deviation divided by the square root of the sample size. So, the Z-score is given by (x - μ) / (σ / √(n)) where x is the sample mean, μ is the population mean and σ is the population standard deviation and n is the sample size.
With a sample size of 30 or greater, the central limit theorem states that the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. So, a Z-score can be used to find the probability that a sample mean falls within a certain range of the population mean, which is commonly used to construct a confidence interval.
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In how may years ₹ 4,000 will amount to ₹ 14,400 at 10% p.a. Compounded interest payable quarterly ?
Answer:
P = ₹4,000
F = ₹14,400
r = 10% = 0.10
m = 4 (because interest is compounded quarterly)
So, we can plug in these values into the formula:
n = (log(14400 / 4000)) / (log(1 + 0.10 / 4))
n = (log(3.6)) / (log(1.025))
n = 2.59
Therefore, it will take approximately 2.59 years for the investment of ₹4,000 to grow to ₹14,400 at a 10% annual interest rate compounded quarterly.
based on the histogram shown, of the following, which is closest to the average (arithmetic mean) number of seeds per apple?
The closest to the average(arithmetic mean) number of seeds per apple is 6.
What is average ?
An average, also known as a mean, is a measure of central tendency that represents the typical value of a set of data. To calculate the average of a set of numbers, you add them up and then divide by the number of items in the set. For example, the average of the numbers 2, 4, 6, and 8 is (2 + 4 + 6).
Average = Total number of seeds/12
⇒ Average = 2×3+4×5+1×6+2×7+3×9/12
⇒ Average = 73/12
⇒ Average ≈6
The closest to the average(arithmetic mean) number of seeds per apple is 6.
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Which of the following statements is true about the first quartile (Q1) value of a box and whisker plot?
Group of answer choices
One-quarter of the data lies below Q1 and three-quarters of the data lies above Q1.
Q1 means the same as Q3.
Half of the data lies below Q1 and half of the data lies above Q1.
Three-quarters of the data lies below Q1 and one-quarter of the data lies above Q1.
The correct option regarding the first quartile of a data-set is given as follows:
One-quarter of the data lies below Q1 and three-quarters of the data lies above Q1.
What is the first quartile of a data-set?The first quartile Q1 of a data-set is the 25th percentile, meaning that:
25% of the data lies below Q1.100 - 25 = 75% of the data lies above Q1.This means that the correct option is given by the first option.
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how to Solve the following Systems of Linear Equations 4X + 3Y= 7
Answer:
4x−3y+4=0
⟹x=
4
−4+3y
Let, y=4, then x=
4
−4+3(4)
=2
Similarly, when y=0,x=−1
4x+3y−20=0
⟹x=
4
20−3y
Let, y=4, then x=
4
20−3(4)
=2
Similarly, when y=0,x=5
In order to determine whether this horizontal position of the pumpkin trajectory represents a minimum or maximum, evaluate at Im. View Available Hint(s) dy a = -8.0 x 10-3m (negative, so this is a minimum) d=2a = –16 x 10-3 (negative, so this is a minimum) ay=2a = -16 x 10-4 (negative, so this is a maximum) = -8.0 x 10m (negative, so this is a maximum)
A projectile have a minimum speed at the highest point of its trajectory. This is because horizontal speed of the projectile remains constant.
Since the only force exerted on the projectile is gravity, which is
9.8 ms ^2 acting downwards and has no effects on the horizontal velocity.The maximum height the pumpkin reaches occurs at 62.5 horizontal meters from its launching spot.
The calculation is as follows;
The equation is y = -0.008x^2 +x
that corresponds to a curve presented by a parabola.
Now we can determine the maximum of this parabola with arms pointing down requesting the derivative slope of the tangent line to
the curve to be zero
So,= 62.5m
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(PLEASE HELP IM GIVING OUT BRAINLIST PLEASE help help).
The number of papers ms. Motley grades increases exponentially as
time goes on. On the first day she grades 9 papers , on the second day she grades 27 papers and on the third day she grades 31 papers
How many will she grade in five days?
After many days will it take her to grade 6,000 papers?
The papers graded exponentially at the end of 5 days are 134, and it will take approximately around 12 days to complete 6000 papers.
What is exponential function?A function is considered to be exponentially growing if its value rises faster than any polynomial. The function e^x, serves as a good illustration.
The exponential growth is given by the following formula:
[tex]A = Pe^{rt}[/tex]
where, A is the final amount, P is the initial amount, r is the rate and t is the time.
For t = 0, the number of papers graded are, 9, hence the value of P = 9.
To calculate the rate at which the work is done, substitute the value of P = 9, A = 27 and t = 2 in the equation:
[tex]27 = 9 e^{2r}\\3 = e^{2r}[/tex]
Taking ln on both sides of the equation:
[tex]ln (3) = ln(e^{2r})\\\\ln(3) = 2r[/tex]
1.09 = 2r
r = 0.54
To calculate the number of papers graded in five days, substitute the value of P = 9, t = 5 and r = 0.54.
[tex]A = 9 e^{(0.54)(5)}[/tex]
A = 134
Hence, the papers graded at the end of 5 days are 134.
To complete grading 6000 papers, the time taken will be:
6000 = 9e^(0.54)(t)
666.66 = e^(0.54)(t)
Taking ln on both sides of the equation:
ln (666.66) = ln(e^(0.54)(t))
6.50 = (0.54)(t)
t = 12.04
Hence, it will take approximately around 12 days to complete 6000 papers.
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find the measurements of the angles
all the mentioned angles have been found.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angles of triangle = 180
∠ICA =180-20 =160
∠EAF = 20
∠ICB =180
∠GAF = 120 -20 =100
∠CAB= 180-80=100
∠HAG=180-120 =60
∠CBA=180-120=60
∠HAC.= 20
Hence all the mentioned angles have been found.
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find the unit vector orthogonal to the plane through the points p, q and r which has a positive y-component.
The unit vector orthogonal to the plane can be found by taking the cross product of the vectors p-q and p-r. The vector should have a positive y-component if the cross product points in the positive y direction.
To find a unit vector orthogonal to the plane through the points p, q, and r, with a positive y-component, we will use the cross product of two of the vectors. The cross product of two vectors is a vector perpendicular to both of them. First, we will create vector p-q, which is a vector from point p to point q. We can do this by subtracting the coordinates of point q from the coordinates of point p. Next, we will create vector p-r, which is a vector from point p to point r. We can do this by subtracting the coordinates of point r from the coordinates of point p. Finally, we will take the cross product of the two vectors. This will give us a vector orthogonal to the plane through the three points. If the vector has a positive y-component, then it is the unit vector orthogonal to the plane that we are looking for.
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Find the average of the following set of integers. −20,−54,−93,37,45
The average of given set of integers is -17.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
The given set of integers are -20, -54, -93, 37 and 45.
Here, average = Sum of all the observations/Number of observations
= (-20-54-93+37+45)/5
= -85/5
= -17
Therefore, the average of given set of integers is -17.
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Which of the following describes dependent events?
✔
a.) Rufus spins a spinner and it randomly lands on the number
7. Rufus spins the spinner again, and it lands on the
number 7 again.
32°F
b.) Rudolph randomly picks names out of a hat. He chooses
"Mark" first. He puts Mark's name back in the hat and
chooses again. This time he chooses "Indira."
c.) Renata randomly chooses a chocolate chip cookie from a
cookie jar. She eats the cookie and chooses again. This
time she gets a sugar cookie.
d.) Rocky tosses a six-sided die that lands on the number 1.
Next, he picks a card from a standard deck of playing
The situation that can be described as dependent events is c.) Renata randomly chooses a chocolate chip cookie from a cookie jar. She eats the cookie and chooses again. This time she gets a sugar cookie.
What are dependent events ?Events that are dependent upon prior events are called dependent events. The results of earlier events have an impact on these current ones. For example, two or more occurrences that are interdependent are referred to as dependent events. An event generally qualifies as being reliant if it offers details about another event. If an event provides no information about other events, it is considered independent.
The dependent event would be Renata picking a sugar cookie the second time she chooses another cookie because she ate from the first cookie and so was able to avoid it the second time.
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9x-20=3x+32 solve for x
Answer:
[tex]x=\frac{26}{3}[/tex]
Step-by-step explanation:
Lets solve for [tex]x[/tex].
Subtract [tex]3x[/tex] from both sides of the equation.
[tex]9x-20-3x=32[/tex]
Add 20 to both sides of the equation.
[tex]9x-3x=32+20[/tex]
Simplify both sides.
[tex]6x=52[/tex]
Divide both sides of the equation by 6.
[tex]x=\frac{52}{6}[/tex]
Write the fraction in simplest form.
[tex]52 \div 2 = 26\\6 \div 2 = 3[/tex]
[tex]x=\frac{26}{3}[/tex]
Answer:
x=26/3Step-by-step explanation:
9x-20=3x+32
9x-20+20=3x+32+20
9x=3x+52
9x-3x=3x+52-3x
6x=52
6x/6=52/6
x=26/3
Nancy has to mark 1 1/2 and-1 1/2 on this number line. How many parts does she need between the integers 1 and 2, and between -1 and -2, to show1 1/2 and-1 1/2 on the number line?
Answer:
1
Step-by-step explanation:
according to hooke's law and Pythagorean theorem your answer is should be most definitely will be or is it honestly I don't know. but the answer should be too is in the number not the figure of speech.
32.- The high costs of the California real estate market have caused families who cannot afford to buy larger houses to consider backyard sheds as an expansion option. Many are using their patio structures to build their studios, art rooms, and hobby areas, as well as for additional storage. The median price for a custom-built backyard clapboard frame is $3,100 (Newsweek, September 29, 2003). Assume that the standard deviation is $1,200.
The z-score for a backyard structure costing $2300 is -0.67.
How to calculate the z score?The standard score in statistics is the amount of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.
The Z-score quantifies the deviation between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a given data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data set.
The z score will be:
= (2300 - 3100) / 1200
= -0.67.
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The high costs in the California real estate market have caused families who cannot afford to buy bigger homes to consider backyard sheds as an alternative form of housing expansion. Many are using the backyard structures for home offices, art studios, and hobby areas as well as for additional storage. The mean price of a customized wooden, shingled backyard structure is $3100 (Newsweek, September 29, 2003). Assume that the standard deviation is $1200.
a. What is the z-score for a backyard structure costing $2300?
When assessing schedule feasibility, a systems analyst must consider the interaction between time and costs.true or false
True, When assessing schedule feasibility, a systems analyst must consider the interaction between time and costs.
When assessing the viability of scheduling a project, an organisation determines the anticipated completion time. The feasibility analysis assists in identifying any potential obstacles the proposed project may encounter, such as: Internal project constraints, including those related to technology, finances, and resources
The expansion and acceptance of project management training have undergone significant changes over the past few years, and it is projected that these developments will continue and accelerate. And as project management becomes more popular, feasibility studies become more important. It may be exhilarating to begin a difficult, extensive project that will have a significant influence on your organization.
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help pls now now pls
The change in the function per unit over a specific period of time is the average rate of change. Between x is 5 and x is 7, the average rate of change is -4.
What is a specific period of time is the average rate of change?The y = f graph
The points on f(x) that connect x = 5 to x = 7 are in the attachment. A green line serves as the line segment's representation.
The following values can be used to calculate the line segment's average rate of change.
If x = 5, then y = 8.
Y Equals 0 when x = 7
Consequently, the typical rate of change (m) is
(Delta*y/(Delta*x)) = m
Where:
Delta*y equals y 2 - y 1.
Sigma*y = 0 to 8
Delta*y equals -8
Delta*x equals x 2 - x 1.
x = 7 - 5 for delta.
x*Delta = 2
We therefore have:
(Delta*y/(Delta*x)) = m
m = - 8/2 m = - 4
Hence, the average rate of change from x = 5 to 7 is -4
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Suppose your MP3 player contains 100 songs. 10 of those songs ae by your favorite group (say U2). Suppose the shuffle feature is used to play the songs in random order: What is the probability that the first U2 song heard is the Sth song played? What is the probability that one of the first five songs played is U2 song?
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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Please, very important for me, I’ll give brainliest if you want
The quartic function y = 0.5 · x⁴ - x³ - 15.5 · x² + 30 · x + 21 contains roots 4 - √2 and - 3 + √6 and intercept - 21.
How to derive a quartic function
Quartic functions are polynomials of grade 4, whose factor form is introduced below:
y = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)
Where:
a - Lead coefficientr₁, r₂, r₃, r₄ - RootsAccording to statement, the quartic equation has an intercept of - 21 and two real roots: 4 - √2, - 3 + √6. The two remaining roots can be found based on features exhibited by quadratic formula and that quartic functions are the product of two quadratic functions: 4 + √2, - 3 - √6
Now we proceed to expand the quartic function:
y = a · (x - 4 + √2) · (x - 4 - √2) · (x + 3 - √6) · (x + 3 + √6)
y = a · (x² - 8 · x + 14) · (x² + 6 · x + 3)
y = a · [x² · (x² - 8 · x + 14) + 6 · x · (x² - 8 · x + 14) + 3 · (x² - 8 · x + 14)]
y = a · (x⁴ - 8 · x³ + 14 · x² + 6 · x³ - 48 · x² + 84 · x + 3 · x² - 24 · x + 42)
y = a · (x⁴ - 2 · x³ - 31 · x² + 60 · x + 42)
And we find the lead coefficient:
- 21 = 42 · a
a = - 0.5
And we obtain the quartic function in standard form:
y = 0.5 · x⁴ - x³ - 15.5 · x² + 30 · x + 21
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Please I can't seem to get this. It's really hard
The number of notepads per department used in the Southeast location is given as follows:
6.
How to obtain the number of notepads per department?The number of notepads per department is obtained applying the proportions in the context of this problem, considering the graph.
The number of departments of the Southeast location is given as follows:
6.
Which is given from the table given in the second image for this problem.
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If you divide a whole number greater than 10 by a fraction, the result is always larger than the original number.
Answer:
Yes
Step-by-step explanation:
This only works for positive integers. For example, 11/0.5 equals 22, but if you were to negate the 11 then the answer would be -22 which is less than negative 11 so the answer is yes it is true for whole positive integers.
NO LINKS!! NOT MULTIPLE CHOICE!!
For each of the functions below, find the following information. Then sketch a graph.
a. x- int and y-int.
b. vertical asymptote(s) or any holes
c. end behavior asymptotes
d. domain and range
33. g(x) = (x - 2)/(x^2 - 2x - 3)
34. k(x)= (x^2 - x - 2)/(x - 3)
35. f(x)= -x/(x^3 - 4x)
Answer:
Question 33
a) x-int (2, 0). y-int (0, 2/3)
b) Vertical asymptotes: x = -1 and x = 3
Horizontal asymptote: y = 0
c) f(x) → -∞, as x → -1⁻
f(x) → +∞, as x → -1⁺
f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
d) Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)
Range: (-∞, ∞)
Question 34
a) x-int (-1, 0) and (2,0). y-int (0, 2/3)
b) Vertical asymptote: x = 3
c) f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
d) Domain: (-∞, 3) ∪ (3, ∞)
Range: (-∞, 1] ∪ [9, ∞)
Question 35
a) No axis intercepts
b) Vertical asymptotes: x = -2 and x = 2. Hole at (0, ¹/₄).
c) f(x) → -∞, as x → -2⁻
f(x) → +∞, as x → -2⁺
f(x) → +∞, as x → 2⁻
f(x) → -∞, as x → 2⁺
d) Domain: (-∞, -2) ∪ (-2, 0) ∪ (0, 2) ∪ (2, ∞)
Range: (-∞, 0) ∪ (¹/₄, ∞)
Step-by-step explanation:
Definitions
The x-intercepts are the points at which the curve crosses the x-axis, so when y = 0.The y-intercept is the points at which the curve crosses the y-axis, so when x = 0.The domain of a function is the set of all possible input values (x-values).The range of a function is the set of all possible output values (y-values).A vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.A horizontal asymptote occurs at y = 0 if the degree of the numerator is less than the degree of the denominator.A hole occurs when a rational function has a factor with an x that is in both the numerator and the denominator.Question 33Given rational function:
[tex]g(x) =\dfrac{x - 2}{x^2 - 2x - 3}[/tex]
x-intercept
[tex]\begin{aligned}y=0 \implies \dfrac{x - 2}{x^2 - 2x - 3}&=0\\x - 2&=0\\x&=2\end{aligned}[/tex]
y-intercept
[tex]x=0 \implies \dfrac{0 - 2}{0^2 - 2(0) - 3}=\dfrac{2}{3}[/tex]
Vertical asymptotes
Set the denominator to zero and solve for x:
[tex]\implies x^2-2x-3=0[/tex]
[tex]\implies x^2-3x+x-3=0[/tex]
[tex]\implies x(x-3)+1(x-3)=0[/tex]
[tex]\implies (x+1)(x-3)=0[/tex]
[tex]\implies x+1=0 \implies x=-1[/tex]
[tex]\implies x-3=0 \implies x=3[/tex]
Horizontal asymptote
As the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at y = 0.
Holes
Factor the denominator:
[tex]g(x) =\dfrac{x - 2}{(x+1)(x-3)}[/tex]
There are no holes as there is no common factor in the numerator and the denominator.
End behaviour near the vertical asymptotes
f(x) → -∞, as x → -1⁻
f(x) → +∞, as x → -1⁺
f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
Domain
As there are vertical asymptotes at x = -1 and x = 3, the domain is restricted:
Interval notation: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)Range
The range is unrestricted:
Interval notation: (-∞, ∞)Question 34Given rational function:
[tex]k(x)= \dfrac{x^2 - x - 2}{x - 3}[/tex]
x-intercepts
[tex]\begin{aligned}y=0 \implies \dfrac{x^2 - x - 2}{x - 3}&=0\\x^2 - x - 2&=0\\x^2-2x+x-2&=0\\x(x-2)+1(x-2)&=0\\(x+1)(x-2)&=0\\\\x+1&=0 \implies x=-1\\x-2&=0 \implies x=2\end{aligned}[/tex]
y-intercept
[tex]x=0 \implies \dfrac{(0)^2 - 0 - 2}{0 - 3}=\dfrac{2}{3}[/tex]
Vertical asymptotes
Set the denominator to zero and solve for x:
[tex]\implies x-3=0[/tex]
[tex]\implies x=3[/tex]
Holes
Factor the numerator:
[tex]k(x)= \dfrac{(x+1)(x-2)}{x - 3}[/tex]
There are no holes as there is no common factor in the numerator and the denominator.
End behaviour near the vertical asymptote
f(x) → -∞, as x → 3⁻
f(x) → +∞, as x → 3⁺
Domain
As there is vertical asymptote at x = 3, the domain is rest:
Interval notation: (-∞, 3) ∪ (3, ∞)Range
The extreme points are (1, 1) and (5, 9). Therefore, the range is restricted:
Interval notation: (-∞, 1] ∪ [9, ∞)Question 35Given rational function:
[tex]f(x)= -\dfrac{x}{x^3 - 4x}[/tex]
x-intercepts
As the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at y = 0. Therefore, there are no x-intercepts.
y-intercept
Substitute x = 0 and solve for y:
[tex]x=0 \implies -\dfrac{0}{0(x+2)(x-2)}=\dfrac{0}{0}=\textsf{unde\:\!fined}[/tex]
Therefore, there is no y-intercept.
Factor the denominator:
[tex]f(x)= -\dfrac{x}{x(x+2)(x-2)}[/tex]
Cancel the common factor x:
[tex]f(x)= -\dfrac{1}{(x+2)(x-2)}[/tex]
Vertical asymptotes
Set the denominator to zero and solve for x:
[tex]\implies (x+2)(x-2)=0[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Holes
Factor the denominator:
[tex]f(x)= -\dfrac{x}{x(x+2)(x-2)}[/tex]
As the numerator and denominator have a common factor of x, the function is not defined when x = 0. Therefore, there is a hole when x = 0.
To find the y-value of the hole, cancel the common factor x and input x = 0 into the resulting function:
[tex]x=0 \implies -\dfrac{1}{(0+2)(0-2)}=\dfrac{1}{4}[/tex]
Therefore, there is a hole at (0, ¹/₄).
End behaviour near the vertical asymptotes
f(x) → -∞, as x → -2⁻
f(x) → +∞, as x → -2⁺
f(x) → +∞, as x → 2⁻
f(x) → -∞, as x → 2⁺
Domain
As there are vertical asymptotes at x = -2 and x = 2, and a hole at (0, ¹/₄), the domain is restricted:
Interval notation: (-∞, -2) ∪ (-2, 0) ∪ (0, 2) ∪ (2, ∞)Range
As there is a hole at (0, ¹/₄) and a horizontal asymptote at y = 0, the range is restricted:
Interval notation: (-∞, 0) ∪ (¹/₄, ∞)find the y intercepts of the graph shown. (5.6,0) (-3.3,0) (0.4) (-5,0)
A's x- intercept is 3 and y-intercept is 5. Both are favourable.
How can you determine a graph's y-intercept?shown. (5.6,0) (-3.3,0) (0.4) (-5,0) (-5,0)Finding the value of y at x=0 on a graph will reveal the y-intercept. At this location, the graph passes across the y-axis.The slope (m) and the y-intercept (b) of a line are highlighted in the slope-intercept form of linear equations (y=mx+b).I Plotting point A (5.6,0)(0.4) (-5,0) (-5,0)In this instance, A's x-coordinate is 3 and y-coordinate is 5. Both are favourable. As a result, the point A (0.4) is in quadrant I.ate is 3 and y-coordinate is 5. Both are favourable. As a result, the point A (-5,0) is in quadrant I. begin at the beginning. Along the x-axis, move three units to the right. Then, turn, travel parallel to the Y-axis by 5 units, and mark point A.To learn more about y intercepts refer to:
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If nm, find the value of x and the value of z.
In the triangles value of x is 10.39 and z is 2.6.
What are the sides of right angle triangle?We can see from the diagram that both triangles are right triangles. As a result, we can use Pythagorean theorems. The longest side of a right triangle is the hypotenuse. In the diagram, those are sides with lengths of 4 and 12. The formula for this is:
c² = (a²+ b²), where c is the hypotenuse and the other shorter sides are a and b.
c = [tex]\sqrt{(a^{2} + b^{2} )}[/tex]
To calculate z,
By substituting the values,
4² = (z² + 3²)
16 = (z² + 9)
z² = 16 - 9
z² = 7
z = √7
z = 2.6
To find x,
use the following formula: 12² = (x² + 6²)
144 = x² + 36
x² = 144 - 36 = 10.39
x = 10.39
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the following question is from the four steps of statistical inference. if you respond with a summary of all four steps, you will receive no credit on this problem:
One of the steps in statistical inference, to check the claim is hypothesis testing. In this method, we determine whether to reject or accept the null hypothesis.
Hypothesis testing is the procedure in statistical inference that helps to decide whether the result of the research study supports a particular hypothesis when applied to a population. This helps to test the relationship between two statistical variables.
This includes two types null and alternate hypotheses. If the results say that there is no relationship seen between the two variables, then the null hypothesis is accepted. But if the results so there is a relationship seen between two variables, then an alternate hypothesis is accepted. So to check our claim, we do hypothesis testing.
The complete question is -
The following question is from the four steps of statistical inference. If you respond with a summary of all four steps, you will receive no credit on this problem:
What do we do to check a claim?
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2 x – 3 y = 7 –4 x + y = –5 What is the x -value of the solution to this system of equations?
The value of x which holds true for the given system of equations as required is; x = 4 / 5.
What is the value of x which holds true for the system of equations?It follows from the task content that the value of x which holds true for the given system of equations be determined.
Since the given system is;
2x - 3y = 7........(i)
-4x + y = -5........(ii)
The value of x which holds true for the given system of equations can be determined by making y the subject of the formula in (ii) and substitution into (i) as follows;
y = 4x - 5.
Therefore;
2x - 3 (4x - 5) = 7
2x - 12x + 15 = 7
-10x = -8
x = 4/5
Ultimately, the value of x which holds true for the given system of equations is; x = 4 / 5.
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2 x – 3 y = 7 –4 x + y = –5 Wh
Aiden asked a group of students to choose their favorite type of music from the choices of rock, hip-hop, and country. The results of the survey are shown in the graph.
Based on the graph, how many students in a class of 360 students would be expected to choose hip-hop or rock as their favorite type of music?
Number of students who are expected to choose hip hop or rock as their favorite type of music is 240.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Percentage is usually denoted by the symbol '%'.
From the graph,
Number of students who choose rock music = 20
Number of students who choose hip hop music = 40
Number of students who choose country music = 30
Total number of students = 20 + 40 + 30 = 90
Percentage of students who choose rock or hip hop = (20+ 40) / 90
= (60 / 90)
= 66.67%
Out of 360 students, 66.67% of students will chose hip hop or rock.
360 × (60/90) = 240
Hence 240 students choose either hip hop or rock as their favorite music.
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