Answer:
The 99.7% confidence interval for the mean here is
[tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].
Step-by-step explanation:
The data in this question comes from random samples. In other words, the true population data are not known. Assume that both the sample average and the sample stdev are unbiased estimates for the population mean and stdev.
The sample size 196 is sufficient large, such that the central limit theorem will apply. By the central limit theorem, the distribution of the mean (as well as the sum) of a sufficiently large samples resembles normal distributions. However, since stdev is only an estimate, the confidence interval can only be found using the Student's t-distribution.
What is the confidence interval for the mean of a random variable that follows the t-distribution?
[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex],
where
[tex]\bar{x}[/tex] is the unbiased estimate of the population mean (a.k.a sample mean.) For this question, [tex]\bar{x} = 12[/tex]. [tex]s_{n-1}[/tex] is the unbiased estimate of the standard deviation (the square root of variance) of the population. For this question, [tex]s_{n-1} = 3.5[/tex].[tex]n[/tex] is the sample size. For this question, [tex]n = 196[/tex].What is not given is
[tex]t[/tex], the test statistics of the t-distribution. This value depends on the confidence level of the estimate (99.7% in this case.)Start by determining the degree of freedom [tex]df[/tex] of [tex]t[/tex]. The degree of freedom for a one-variable estimate is usually equal to [tex]n -1[/tex] (that is: sample size minus one.) For this question, [tex]n = 196[/tex] so [tex]df = 196 - 1 = 195[/tex].
If [tex]T[/tex] represent a random variable that follows the [tex]t_{195}[/tex]-distribution, the value of t shall ensure that
[tex]P(-t \le T \le t) = \text{Confidence Interval} = 0.997[/tex].
The t-distribution is symmetric. As a result,
[tex]\displaystyle P(T > t) = 0.997 + \frac{1}{2}\times (1 - 0.997) = 0.9985[/tex].
Find the value of [tex]t[/tex] either with a t-distribution table or with technology. Keep in mind that for this question, [tex]df = n - 1 = 195[/tex].
[tex]t \approx 3.00549[/tex].
Apply the formula for the confidence interval:
[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex].
Lower bound:
[tex]\displaystyle \bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 - 3.00549\times \frac{3.5}{\sqrt{196}}\approx 11.2[/tex].
Upper bound:
[tex]\displaystyle \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 + 3.00549\times \frac{3.5}{\sqrt{196}}\approx 12.8[/tex].
In other words, the 99.7% confidence interval for the actual concentration is [tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].
1.) Is y= cosx/x an even, odd , or neither
2.) Is y=sinx/x and even, odd , or neither
The given options are 1) y = (cos x) / x is neither and 2) y = (sin x) / x is even.
What are the six trigonometric ratios?
Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right-angled (not of 90 degrees).
The slanted side is called the hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.
1) y = (cos x) / x is neither, since cos x is even and x is odd.
2) y = (sin x) / x is even since sin x and x would either both be positive at the same time or negative at the same time.
We know that (-) / (-) is positive, just as (+) / (+) is positive.
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Final answer:
1. The function y=cos(x)/x is neither even nor odd due to its lack of symmetry properties
2. y=sin(x)/x is an odd function as it satisfies the symmetry condition about the origin.
Explanation:
To determine if the functions y=cos(x)/x and y=sin(x)/x are even, odd, or neither, we need to understand the definitions of even and odd functions and apply them accordingly.
Even and Odd Functions:
An even function satisfies the condition f(-x) = f(x), meaning the function's graph is symmetric about the y-axis. An odd function satisfies the condition f(-x) = -f(x), indicating symmetry about the origin.
Analysis of y=cos(x)/x:
To determine if y=cos(x)/x is even, odd, or neither, replace x with -x:
y=cos(-x)/(-x) = cos(x)/(-x) because cos(-x) = cos(x), an even function property.
This contradicts the definitions of both even and odd functions; hence, y=cos(x)/x is neither even nor odd.
Analysis of y=sin(x)/x:
Similarly, for y=sin(x)/x, replace x with -x:
y=sin(-x)/(-x) = -sin(x)/(-x) because sin(-x) = -sin(x), an odd function property.
This simplifies to y=sin(x)/x, which satisfies the condition for an odd function.
Therefore, y=sin(x)/x is an odd function.
Which polygons are similar?
1,2,3,4
Answer:
1 and 4
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
The corresponding angles of Triangle 1 and Triangle 4 are congruent
therefore
Both triangles are similar
Answer:
similar polygons are 1 and 4
Step-by-step explanation:
From the figure we can see some triangles and angles are given
Similar triangles means that the angles are same and their corresponding sides are in proportion.
To find the correct answer
From the figure we get 1 and 2 are similar triangle, because angles of triangle 1 are 10°, 60° and 110°,
and angles of triangle 4 are 10°, 60° and 110°,
Therefore the correct answer is 1 and 4
Which inequality is equivalent to 4 x − 2 y ≤ 8 ?
Answer:
y≥2-4
Step-by-step explanation:
Simplify your equation.
4x-2y≤8
-4x -4x
-2y≤-4x+8
/-2 /-2
y≥2-4
What is the solution of Square -4x =100?
For this case we have the following expression:
[tex](-4x) ^ 2 = 100[/tex]
To look for the solution:
We apply root to both sides of the equation to eliminate the exponent:
[tex]-4x = \pm \sqrt {100}\\-4x = \pm10[/tex]
Then we have two solutions:
[tex]-4x = 10[/tex]
Dividing between -4 on both sides of the equation:
[tex]x = \frac {10} {- 4}\\x = - \frac {5} {2}[/tex]
The second solution:
[tex]-4x = -10[/tex]
Dividing between -4 on both sides of the equation:
[tex]x = \frac {-10} {- 4}\\x = \frac {5} {2}[/tex]
Answer:
[tex]x_ {1} = - \frac {5} {2}\\x_ {2} = \frac {5} {2}[/tex]
If g(x) = x+1/ x-2 and h (x) =4 - x , what is the value of ( g*h) (-3)?
Answer:
g (h (x) ) = 5/8
Step-by-step explanation:
We are given the following two functions and we are to find the value of [tex] g ( h ( - 3 ) ) [/tex]:
[tex] g ( x ) = \frac { x + 1 } { x + 2 } [/tex]
[tex] h ( x ) = 4 - x [/tex]
Firstly, we need to find the function :
[tex] g ( h ( x ) ) = \frac { ( 4 - x + 1 ) } { ( 4 - x - 2 ) } = \frac { 5 - x } { 2 - x } [/tex]
Now substituting the value [tex]x=-3[/tex] in it:
[tex] g ( h ( x ) ) = \frac { 5 - (-3) } { 2 - (-3) } [/tex]
g (h (x) ) = 5/8
Answer:
8/5
Step-by-step explanation:
If g(x) = (x+1)/(x-2) and h(x) = 4 - x
(g*h)(-3) = g(h(-3))
h(-3) = 4 - -3 = 4 + 3 = 7
g(7) = (7 + 1)/(7 - 2) = 8/5
Which is the solution to the inequality |x-4|<3
Answer:
[tex]\large\boxed{1<x<7\to x\in(1,\ 7)}[/tex]
Step-by-step explanation:
[tex]|x-4|<3\iff x-4<3\ \wedge\ x-4>-3\qquad\text{add 4 to both sides}\\\\x<7\ \wedge\ x>1\Rightarrow1<x<7[/tex]
you have to make a negative and positive equation for this situation
x-4<3 and x+4<3
for the first equation you have to add 4 to both sides to get x<7
for the second equation you have to subtract 4 from both sides to get x<-1
hope this helps
a bookcase contains 2 statistics books and 5 biology books if 2 books are chosen at random the chance that both are statistics books is
Answer 1 (without replacement) :
P(2 books)=P(first)*P(second)=2/7*1/6=2/42=1/21 this is if you don't put the book back on the shelf after taking it off the first time
Answer 2 (with replacement) :
P(2 books)=P(first)*P(second)=2/7*2/7=4/49 this is if you put the book back on the shelf after taking it off the first time
I put he probably didn't put the book back on the shelf after this first time but I don't know without those details in the question
Find the scale factor of the larger figure to the bigger figure.5-8 solve for x. The polygons in each pair are similar.
Answer:
See below in BOLD.
Step-by-step explanation:
What you need to do is identify the corresponding sides in the polygon than divide the larger length by the smaller.
3. The side length 8 corresponds to the 4 in the other polygon.
So the scale factor is 8/4 = 2.
4. Scale Factor = 24/20 = 1.2.
5. 40/32 = 5x / 24
5x = 40*24 / 32
5x = 30
x = 6.
6. 25/30 = 4x + 7 / 42
5/6 = 4x + 7 / 42
6(4x + 7) = 210
24x = 210 - 42 = 168
x = 168/24
x = 7.
7. 40/24 = 3x + 5 / 21
5/3 = (3x + 5) / 21
9x + 15 = 105
9x = 90
x = 10.
8. 24 / 40 = (x + 3) / 15
3/5 = (x + 3) / 15
5x + 15 = 45
5x = 30
x = 6.
Which inequality describes the graph
Answer:
y < 1/2x - 2
Step-by-step explanation:
Find the slope of the graph, we can find the slope of the graph by using the formula y2 - y1/x2 - x1. But in order to do so, we must find two perfect points.
Point 1: (0,-2)
Point 2: (4,0)
Now, we would put these points into the formula.
0 -(-2) = 2
4 - 0 = 4
2/4 = 1/2
Therefore, the slope of this graph is 1/2
Now we must find the y intercept, which can be found based on where the line intersects with a y coordinate (ex: 0,y). Based on that, we can come to the conclusion that -2 is our y-intercept
In order to proceed we must know what a linear equation is. A linear equation contains the following:
y = mx + b
m of mx represents the slope, you would leave x as it is.
b represents the y intercept
We have already found what each is, so we can go ahead and put in our slope and y-intercept into the linear equation.
y = 1/2x + -2
Because, we are dealing with an inequality problem, the equal sign must be replaced with an inequality sign and that is determined based on the area of the graph that is shaded.
Since, the graph is shaded downwards we will be using the "less than sign", in addition if you haven't noticed, the line is dotted so we will NOT be using any "equal to symbols"
So, after applying all of this together, we can conclude that the inequality that describes this graph is y < 1/2x - 2
Should you have any further questions, please let me know in the comment section below.
find the area of a rectangular garden that measures 4 feet by 6/7 feet
Answer:
A=3.43 ft^2
Step-by-step explanation:
A=lw
A=4(6/7)
A=3.43 ft^2
To find the area of a rectangular garden 4 feet by 6/7 feet, multiply the length by the width to get 24/7 square feet.
The area of a rectangular garden measuring 4 feet by 6/7 feet can be calculated as follows:
Area = Length x WidthArea = 4 ft × (6/7) ftArea = 24/7 ft²Therefore, the area of the rectangular garden is 24/7 square feet.
The length of a rectangle is 24 units. Can the perimeter P of the rectangle be 60 units when its width w is 11 units?
How can 7 go into 424 as a whole number
Answer:
Step-by-step explanation:
It can't.
The answer is 60 with a remainder of 4
Which graph represents the function f(x) = −|x − 2| − 1? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f\left(x\right)=-\left|x-2\right|-1[/tex]
The function represents an inverted V-shaped graph
The vertex of the function is the point (2,-1)
The y-intercept of the function is the point (0,-3)
The domain is all real numbers -----> (-∞,∞)
The range is all real numbers less than or equal to -1 ----> (-∞,-1]
Using a graphing tool
The graph in the attached figure
A savings account earns 4% annual interest compounded quarterly. How much interest would $500 earn if it was invested for one year?
Amount obtained in Compound interest is given by :
[tex]\bigstar\;\;\boxed{\mathsf{Amount = Principal\bigg(1 + \dfrac{Rate\;of \;interest}{100}\bigg)^{Conversion\;periods}}}[/tex]
Note : Conversion period is the time from one interest period to the next interest period. If the interest is compounded annually then there is one conversion period in an year. If the interest is compounded semi-annually then there are two conversion periods in an year. if the interest is compounded quarterly then there are four conversion periods in an year.
Problem :
Given : $500 is invested for one year at 4% annual interest
[tex]\implies\boxed{\begin{minipage}{4 cm}\bigstar\;\;\textsf{Principal = 500}\\\\\bigstar\;\;\textsf{Time period = 1 year}\\\\\bigstar\;\;\textsf{Rate of interest = 4\%}\end{minipage}}[/tex]
As the question mentions the term ''compounded quarterly'', there are 4 conversion periods in a year.
If the interest is compounded quarterly, then the rate of interest per conversion period (quarter) will be :
[tex]\implies \mathsf{\left(\dfrac{1}{4} \times 4\%\right) = 1\%}[/tex]
Substituting all the values in the Amount formula of C.I, We get :
[tex]\mathsf{\implies Amount = 500\bigg(1 + \dfrac{1}{100}\bigg)^4}[/tex]
[tex]\mathsf{\implies Amount = 500\left(1 + 0.01\right)^4}[/tex]
[tex]\mathsf{\implies Amount = 500\left(1.01\right)^4}[/tex]
[tex]\mathsf{\implies Amount = 520.30}[/tex]
We know that : Interest = Amount - Principal
[tex]:\implies[/tex] Interest = 520.30 - 500
[tex]:\implies[/tex] Interest = $20.30
If $500 is invested in a savings account with a 4% annual interest rate compounded quarterly for one year, it would earn $20.04 in interest.
Explanation:To calculate the interest earned on a savings account, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is $500, the annual interest rate is 4% (or 0.04 as a decimal), the interest is compounded quarterly (so n = 4), and the investment period is one year (so t = 1).
Plugging the values into the formula, we get:
A = 500(1 + 0.04/4)^(4×1)
Simplifying the equation, we calculate that the final amount after one year is $520.04. To find the amount of interest earned, we subtract the initial investment ($500) from the final amount ($520.04):
Interest = $520.04 - $500 = $20.04.
Therefore, $500 would earn $20.04 in interest if invested for one year in a savings account with a 4% annual interest rate compounded quarterly.
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Graph: y - 10 = -2(x - 10)
Answer:
The line would start at 30 on the Y axis and go through 15 on the X axis
Answer: First dot (0,30) Second dot (15,0)
Multiply the polynomials (x-7)(x^2+3x-3)
A. x^3-4x^2-24x+21
B. x^3-7x^2-24x+21
C. x^3-4x^2-3x+21
D. x^3-7x^2-3x+21
[tex]\bf (x-7)(x^2+3x-3)~\hfill \begin{array}{cll} x^2+3x-3\\ \times x\\ \cline{1-1} x^3+3x^2-3x \end{array}~~+~~ \begin{array}{cll} x^2+3x-3\\ \times -7\\ \cline{1-1} -7x^2-21x+21 \end{array}~\hfill \\\\[-0.35em] ~\dotfill\\\\ (x^3+3x^2-3x) +(-7x^2-21x+21)\implies x^3-4x^2-24x+21[/tex]
notice that all you do is simply multiply the terms of either one by the terms of the other sequentially, then add like-terms.
5.(04.07)
Two different plants grow each year at different rates, which are represented by the functions f(x) = 4* and g(x) = 5x + 2. What is the first year the f(x) height is greater than
the g(x) height?
Year 3
Year 0
Year 2
Year 1
Answer:
Year 2
Step-by-step explanation:
The graph that I attached shows the growth over time. The height of the blue line (f(x)) surpasses g(x) at 1.63 years. We can say that year 2 is the first year that f(x) is greater than g(x).
what are the zeros of the function f (x)=x^2+5x+5 written in simplest radical form
Answer:
The zeros are
[tex]x1=\frac{-5+\sqrt{5}} {2}[/tex] and [tex]x2=\frac{-5-\sqrt{5}} {2}[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]f(x)=x^{2} +5x+5[/tex]
To find the zeros equate the function to 0
[tex]x^{2} +5x+5=0[/tex]
so
[tex]a=1\\b=5\\c=5[/tex]
substitute in the formula
[tex]x=\frac{-5(+/-)\sqrt{5^{2}-4(1)(5)}} {2(1)}[/tex]
[tex]x=\frac{-5(+/-)\sqrt{5}} {2}[/tex]
[tex]x1=\frac{-5+\sqrt{5}} {2}[/tex]
[tex]x2=\frac{-5-\sqrt{5}} {2}[/tex]
What is the perimeter of the rectangle?
2 + square root 5 cm
6 +3 square root 5 cm
Answer:
Just add up the measurements of the sides and then double the result.
(2 + √5 + 6 + 3√5) · 2
= (8 + 4√5) · 2
= 16 + 8√5 (cm)
To answer your question, we first need to understand that the perimeter of a rectangle is calculated by adding up all its sides or simply twice the sum of its length and width.
From the information given, the width of the rectangle is equal to 2 cm plus the square root of 5 cm, while the length is 6 cm plus 3 times the square root of 5 cm.
So now, let's sum up the length and the width:
= (2 + √5 cm) + (6 + 3√5 cm)
= 8 + 4√5 cm
We then multiply this result by 2 (to account for both sets of opposite sides of the rectangle):
Perimeter = 2 * (8 + 4√5 cm)
Perimeter ≈ 33.89 cm
Therefore, the perimeter of the rectangle is roughly 33.89 cm.
what is the answer to (( 5 x 12)/3)+30-50
I believe the correct answer is 0
Step-by-step explanation:
To solve this question, we use an abbreviation formula called BODMAS which is:
B = Brackets
O = Of
D = Division
M = Multiplication
A = Addition
S = Subtraction
We solve each element that is available in the order of the abbreviated letter.
1. We solve the brackets:
[tex](5\times12) = 60[/tex]
2. We solve the second bracket:
[tex](60\div3) = 20[/tex]
The equation now is [tex]20+30-50[/tex]
3. We now solve addition first:
[tex]20+30=50[/tex]
4. Now we solve the subtraction:
[tex]50-50=0[/tex]
The answer then = 0
Answer:
The value of given expression is 0.
Step-by-step explanation:
We have to evaluate the given expression:
[tex]\bigg(\displaystyle\frac{(5\times 12)}{3}\bigg)+30-50[/tex]
We use the BODMAS rule to evaluate the given expression.
B-Bracket
O-of
D-Division
M-Multiplication
A-Addition
S-Subtraction
[tex]\bigg(\displaystyle\frac{(5\times 12)}{3}\bigg)+30-50\\\\=\bigg(\displaystyle\frac{60}{3}\bigg)+30-50\\\\=20+30-50\\\\=50-50\\\\=0[/tex]
The value of expression is 0.
determine the number of solutions the system has.
2x = 2y -6
y = x + 3
[tex]2x = 2y -6|\div 2\\y = x + 3 \\\\x=y-3\\y=x+3\\\\y=x+3\\y=x+3[/tex]
Both equations are identical, so there are infinitely many solutions.
Is 30/5 an integer number
Answer: Yes.
Step-by-step explanation:
30/5 or 30 divided by 5 simplifies to 6. 6 is a whole number and therefore it is an integer.
Is the number 128.439 a rational number
Answer:
Yes
Step-by-step explanation:
Yes terminating and repeating decimals are rational numbers.
This is a terminating decimal. It ends, so it is rational.
Anything that can be written as a fraction where the top and bottom are integers is rational.
Some examples:
-1 =-1/1
5 =5/1
5.23 =523/100
.3333333333333333333333333333333333333....=1/3
1 2/3 =5/3
Since there seems to be more that need convincing, the number 128.439 can be written as 128439/1000
that is a fraction where the top and bottom are integers
so 128.439 is rational
The number 128.439 is a rational number
If f(x) =3x+10, find f(4) A.f(4)=17 B.f(4)=22 C.22 D.f(4)=17
Answer:
[tex]\large\boxed{B.\ f(4)=22}[/tex]
Step-by-step explanation:
[tex]f(x)=3x+10\\\\f(4)-\text{put x = 4 to the equation of the function}\\\\f(4)=3(4)+10=12+10=22[/tex]
PLEASE HELP! 8 POINTS!! Find the value
Answer:
-sqrt(3)/2
Step-by-step explanation:
Use double angle identity for sin(2x)
sin(2x)=2sin(x)cos(x)
We are given sin(x)=-1/2 so we already have so far that:
sin(2x)=2(-1/2)cos(x)
sin(2x)=-1*cos(x)
We just need to find cos(x).
x is in the fourth quadrant so cosine will be positive there
knowing the unit circle we should know that if sin(x)=-1/2 then cos(x)=sqrt(3)/2 while in 4th quadrant.
So the answer is sin(2x)=-1*sqrt(3)/2=-sqrt(3)/2
How many ounces are in 3.5 pounds?
Hint: 16 ounces = 1 pound
Answer:
56 ounces
Step-by-step explanation:
16 ounces = 1 pound
There are 3.5 pounds so 16 x 3 = 48
Then, the other .5 of the pound would be 16/2 or 8.
48 + 8 + 56
Answer:
56
Step-by-step explanation:
16x3=48
Half of 16 is 8.
Since there is 3 1/2 pounds
You would add the 8 and 48.
48 from the 3 pounds and 8 ounces for 1/2 a pound.
Hence, the answer is 56.
48+8=56
factor the common factor out of -56x4 + 16x2 + 16x
Answer:
The common factor is 8x or -8x ( I forgot if the first number needs to positive or not.
Step-by-step explanation:
-8x(7x^3-2x-2)
or
8x(-7x^3+2x+2)
Hope this is what you are looking for?
Answer:
The common factor is 8x or -8x
Step-by-step explanation:
-8x(7x^3-2x-2)
or
8x(-7x^3+2x+2)
Hope this is what you are looking for!! Stay Safe!!
Tomer owns a daycare center called kidz kare. One afternoon he collected the age of each person in kidz kare. The following histogram summarizes the data he collected. Based on this data, what is a reasonable estimate of the probability that the next person to enter kidz kare is between 10 and 15 years old?
Choose the best answer:
A) 2/10
B) 2/7
C) 3/10
D) 3/7
Answer:
3/10
Step-by-step explanation:
Using it's concept, it is found that the probability that the next person to enter kidz kare is between 10 and 15 years old is given by:
C) 3/10.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
From the histogram, we have that out of a total of 10 students, 3 are between 10 and 15 years old, hence:
p = 3/10, which means that option C is correct.
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what is The best decimal to represent 5 3/7
Step-by-step explanation:
First, change the mixed fraction into an improper fraction:
5 3/7 =
5 x 7 = 35 + 3 = 38/7
Next, divide:
38/7 = 5.42857...
5.43 (rounded) is your answer.
Of course, the more digits behind it the better, so it is up to your discretion and your answer choices.
~
Answer:
5*7+3 = 38/7 ~5.43
we can multiple 5 by 7 and add them by 3
At which values of X does the function F(x) have a vertical asymptote? Check all that apply
Answer:
The values of x are -6 , 0 , 1 ⇒ Answers C , D , E
Step-by-step explanation:
* Let revise how to find the vertical asymptote
- Vertical asymptotes of a rational function f(x)/g(x) can be found by
solving the equation g(x) = 0 ⇒ the denominator of the fraction
- Note: this only applies if the numerator f(x) is not zero for the same
x value
* Lets solve the problem
∵ F(x) = 1/x(x + 6)(x - 1)
∵ The denominator of the fraction is x(x + 6)(x - 1)
- To find the equation of the vertical asymptote Put the
denominator = 0
∴ x(x + 6)(x - 1) = 0
- The denominator has three factors, equate each by 0
∴ x = 0
OR
∴ x + 6 = 0 ⇒ subtract 6 from both sides
∴ x = -6
OR
x - 1 = 0 ⇒ add 1 to both sides
∴ x = 1
∴ From all above there are 3 vertical asymptotes at x = -6 , 0 , 1
* The answers are C, D , E
Answer:
Step-by-step explanation:
-6 0 1