Let F(x) = { x2 − 9 x + 3 x ≠ −3 k x = −3 Find ""k"" so that F(−3) = lim x→ −3 F(x)
Answers
The limit of F(x) as x approaches −3 does not exist because the limits from both sides are not equal. So, we cannot find a value of k that would make F(−3) = lim x → −3 F(x).
Given function F(x) = { x² − 9x + 3 for x ≠ −3k for x = −3
To find k such that F(−3) = lim x → −3 F(x), we need to evaluate the limit of F(x) as x approaches −3 from both sides. First, we find the limit from the left-hand side: lim x → −3−(x² − 9x + 3)/(x + 3)
Let g(x) = x² − 9x + 3.
Then,Lim x → −3−(g(x))/(x + 3)
Using the factorization of g(x), we can write it as:
g(x) = (x − 3)(x − 1)
Thus,lim x → −3−[(x − 3)(x − 1)]/(x + 3)
Factor (x + 3) in the denominator and simplify, we get:
lim x → −3−(x − 3)(x − 1)/(x + 3)= (−6)/0- (a negative value with an infinite magnitude)
This means that the limit from the left-hand side does not exist. Next, we find the limit from the right-hand side:lim x → −3+(x² − 9x + 3)/(x + 3)
Again, using the factorization of g(x), we can write it as:g(x) = (x − 3)(x − 1)
Thus,lim x → −3+[(x − 3)(x − 1)]/(x + 3)
Factor (x + 3) in the denominator and simplify, we get:
lim x → −3+(x − 3)(x − 1)/(x + 3)= (−6)/0+ (a positive value with an infinite magnitude)
This means that the limit from the right-hand side does not exist.
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Related Questions
Combine the following expressions. 1/3√45- 1/2√12 +√20+2/3√27 3 + 4 + 3 +
Answers
The combination of the expression is \(5\sqrt{5} + \sqrt{3} + 10\)
We are given that;
The expression= 1/3√45- 1/2√12 +√20+2/3√27 3 + 4 + 3
To combine the expressions, we need to simplify the radicals and find the common factors.
Rewrite the radicals as fractional exponents
= \(\frac{1}{3}(45)^{\frac{1}{2}} - \frac{1}{2}(12)^{\frac{1}{2}} + (20)^{\frac{1}{2}} + \frac{2}{3}(27)^{\frac{1}{2}} + 3 + 4 + 3\)
Simplify the coefficients and combine the like terms:
\(=5\sqrt{5} + \sqrt{3} + 10\)
Therefore, the expression will be \(5\sqrt{5} + \sqrt{3} + 10\).
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Beads cost $2.40 per pound. How many pounds of beads can Sam buy with $18?
Answers
Answer: 7 pounds
Step-by-step explanation: Since you have 18 dollars and buy $2.40 beads, your equation is 18 divided by 2.40.
18 divided by 2.40 is 7.5
But since it’s asking how many pounds, not half a pound, the answer is simple 7 pounds of beads.
Noah has a coupon for 30% off at his favorite clothing store . He uses it to buy a hoodie . The regular price of a hoodie is $27. What did Noah pay for the hoodie?
Answers
Answer:
$18.90
Step-by-step explanation:
The way to do percentages is actually pretty easy.
since it's taking 30% of you are left with 70%. Take 70 and divide it by 100. This gives you .70
Now what you do is you take the price of the time and multiply it by the .70
So 27.00 * .7 = 18.90
So Noah paid 18.90
The graph of y=x^2is the solid black graph below. Which function represents the dotted graph?
Answers
Answer:
\(y=-(x+5)^{2}\)
Step-by-step explanation:
This is a transformation of the function, y=x^2. Since the vertex, (h, k), is (-5, 0), you would just have to plug them in into the formula \(y=a(x-h)^{2} +k\), with a=-1.
\(y=-1(x+5)^{2}\)
a line intercepts the point ( -11, 4) and has a slope of -2 fill in the formula y - ? = ? (x - ? )
Answers
The point-slope form is;
\(y-4\text{ = -2(x+11)}\)Here, we want to write the slope intercept formula for the given line and point
We have the general point-slope form as;
\(\begin{gathered} y-y_1=m(x-x_1) \\ \\ m\text{ is slope = -2} \\ (x_1,y_1)\text{ = (-11,4)} \\ \\ y-4\text{ = -2(x-(-11))} \\ y\text{ - 4 = -2(x+11)} \end{gathered}\)x - 3y = 17
x = 2y + 13
What are the steps for solving these?
Answers
Answer:
(x, y) = (5, -4)
Step-by-step explanation:
The second equation gives you an expression for x that can be substituted into the first equation.
(2y +13) -3y = 17 . . substitute for x in the first equation
-y = 4 . . . . . . . . . . . subtract 13 and simplify
y = -4
x = 2(-4) +13 = 5 . . . use the second equation to find the value of x
The solution is (x, y) = (5, -4).
_____
Additional comment
When faced with a system of linear equations, the first step is to look at them and observe where the variable terms are, and any relationships between coefficients. Several options are generally open to you for solving the equations. Methods generally taught first are ...
substitutioneliminationSubstitution is handy when one of the variables or variable terms can be written (easily) in terms of the other variable. Elimination is handy when some simple multiple of one of the equations can be added to the other equation to cancel one of the variable terms (eliminate it).
Other available methods include matrix methods, Cramer's rule, and graphing. Working knowledge of all of these methods will help you identify the one that will be easiest to use in any given situation.
The availability of calculators able to use these methods greatly simplifies the task of finding a solution. It is simply a matter of entering the equations in the appropriate form.
One of my favorites is the graphing calculator, which only requires you type in the given equations and click on the solution point to find its coordinates.
In a rectangle KLMN, the diagonals KM and LN intersect at O.
(i) If KO = 4y + 6 and ON = 3y + 11, find the lengths of its diagonals.
(ii) If ∠NKM = 32°, find ∠KON and ∠KMN.
guys, pls answer. it's very urgent. I have to submit tomorrow. pls don't give wrong ans.
Answers
Answer:
8y°±94°⊂⊂100°
Step-by-step explanation:
18. Express the first amount as a percentage of second.
a) 600 m of 3 km
………………………………….
b) In a local election there were 8000 registered voters.
Of these 3200 voted.
What was the percentage that voted?
………………………………….
Answers
Answer:
a. 20%
b. 40%
Step-by-step explanation:
a. 3km =3000m
600/3000×100=20%
b. 3200/8000×100=40%
Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.
N(2,
M(4, C
The perimeter is about
units.
L
Answers
According to the given statement,
the perimeter is 10.99 units.
What is perimeter?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.
There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose a yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter. Similar to this, the circumference of a spool is related to the length of string looped around it; if the string's length were correct, it would match the circumference.
According to the given value ,
We have a triangle with points in:
X // Y
N 2 // 0
P -1 // -2
M 4 // 0
We can solve for the side of the triangle by subtracting the points to calculate the distance between them, AKA the side of the triangle.
M - N = NM = 4 - 2 = 2 units of X
M - N = NM = 0 - 0 = 0 units of Y
This has a length of 2 units of X and 0 units of Y thus, we already have a line of size 2.
Next side:
N - P = 2 -(-1) = 3 units of x
N - P = 0 - (-2) = 2 units of Y
We have a length of 3 units of X and 2 of Y we use Pythagoras to get the length of NP:
Now, we do the same with MP:
M - P = 4 - (-1) = 5 units of X
M - P = 0 - (-2) = 2 units of Y
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Please helplike fr I don’t understand :((
It’s for question 4
Answers
Answer:
$6,000
Step-by-step explanation:
We have to start by finding the conversation rate.
So, we can divide 9,600 by 8 to find how much the ratio is being multiplied by.
9,600 / 8 = 1200
Now that we know the conversion rate, we can multiply by five to find how much the expenses really cost, according to the ratio.
1200 * 5 = 6000
Their expenses this month are 6000
Convert the decimal or whole number to a percent.
1.15 7/8
Answers
Answer:
1.15 is 115%
Step-by-step explanation:
7/8 is 0.875 so it makes it 87.5%
The percentage form of the given number is:
1.15 as a percent is 115%
7/8 as a percent is 187.5%
To convert a decimal to a percent,
we need to multiply it by 100.
So for 1.15,
Multiply it by 100 to get 115%.
To convert a mixed number to a percent,
We have to convert it to an improper fraction first.
To do that, we multiply the denominator by the whole number and add the numerator.
Then we put that answer over the original denominator.
For 7/8, the improper fraction would be,
(8 x 1) + 7 = 15/8.
To convert this to a percentage,
We need to divide the numerator by the denominator and multiply by 100.
So 15/8 as a decimal is 1.875, and when we multiply that by 100 we get 187.5%.
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A fruit plantation has two types of fruit trees: apple trees and orange trees. 3
5
of the fruit trees are orange trees. There are 4515 orange trees on the plantation. The apple trees bear apples of two different colours. There are 342 more trees bearing red apples than trees bearing green apples. How many trees with green apples are there?
Answers
If there are 342 more trees bearing red apples than trees bearing green apples, then the number of trees with green apples are 1336.
The 3/5 of fruit trees are orange trees, then 2/5 of the fruit trees are apple trees.
Let the total number of fruit trees be = x. Then we can write two equations based on the given information that, there are 4515 orange trees and there are 342 more red apple trees than green apple trees,
The equations are :
⇒ 3/5 x = 4515 ...equation(1)
⇒ x - 4515 = (G + 342) + G ...equation(2)
Where G is the number of trees bearing green apples.
From equation(1), we can solve for x:
x = (4515)/(3/5) = 7525
Substituting this value of "x" into equation(2),
We get,
⇒ 7525 - 4515 = (G + 342) + G
⇒ 3010 = 2G + 342
⇒ 2668 = 2G
⇒ G = 1334.
Therefore, there are 1336 trees with green apples.
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The given question is incomplete, the complete question is
A fruit plantation has two types of fruit trees: apple trees and orange trees. 3/5 of the fruit trees are orange trees. There are 4515 orange trees on the plantation. The apple trees bear apples of two different colors. There are 342 more trees bearing red apples than trees bearing green apples.
How many trees with green apples are there?
If I had 39inches and 28inches how many inches and all
Answers
Answer:
67 inches
Step-by-step explanation:
Since the question is asking how many inches total do you have, we need to add up the 2 values given:
39 inches + 28 inches = 67 inches.
We can convert this to feet by dividing by 12:
67 in /12 in/ft ≈ a little over 5 and a half feet
Which of the following correlation coefficients indicates the strongest relationship between two variables? a.−1.0 b. 0.80 c.0.1 d.−0.45
Answers
The correlation coefficient that indicates the strongest relationship between two variables is a. -1.0.
The correlation coefficient is a numerical measure that quantifies the relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.
In this case, a correlation coefficient of -1.0 represents a perfect negative correlation, meaning that the two variables have a strong, linear relationship where as one variable increases, the other decreases in a perfectly predictable manner. This indicates a very strong and consistent inverse relationship between the variables.
In comparison, a correlation coefficient of 0.80 indicates a strong positive correlation, but it is not as strong as a perfect negative correlation of -1.0. A correlation coefficient of 0.1 suggests a weak positive correlation, while a correlation coefficient of -0.45 indicates a moderate negative correlation.
Therefore, out of the given options, the correlation coefficient of -1.0 represents the strongest relationship between two variables.
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The faculty senate at a large university wanted to know what proportion of the employees thought the food services at the university are satisfactory. The statistics department offered to cooperate in conducting a survey, and a simple random sample of 100 faculty members was selected. A survey form was sent by email to these 100 employees. In this case, the sampling frame is:
A. all the employees who are faculty members.
B. all the employees at the university.
C. all the employees who think the food services at the university are satisfactory.
D. the 100 employees who got the email survey.
E. the employees who responded to the email survey.
Answers
The sampling frame in this case is option D: the 100 employees who received the email survey.
The sampling frame refers to the specific group or population from which a sample is selected. In this scenario, the faculty senate wanted to survey the proportion of employees who believed the food services at the university were satisfactory. Therefore, the sampling frame should consist of individuals who are eligible to provide their opinions on the food services.
Option A, "all the employees who are faculty members," is incorrect because the survey is focused on faculty members' opinions, not all employees.
Option B, "all the employees at the university," is incorrect because the survey is specifically targeting faculty members and not all employees.
Option C, "all the employees who think the food services at the university are satisfactory," is incorrect because the survey aims to determine the proportion of employees who find the food services satisfactory, and this information is not known in advance.
Option E, "the employees who responded to the email survey," is incorrect because it refers to the individuals who actually responded to the survey, rather than the initial group of faculty members who received the email survey.
Thus, option D, "the 100 employees who received the email survey," is the correct sampling frame since it represents the specific group of faculty members who were selected to participate in the survey.
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Given the parametric equations, answer the following. x=8t,y=t+2 Part 1. Explain how you will write these parametric equations into one rectangular equation. Part 2. What is the graph of the the resulting rectangular equation? Part 3. What is the rectangular equation?
Answers
Part 1: To write the given parametric equations into one rectangular equation, we can eliminate the parameter \(\(t\)\)by solving one equation for\(\(t\)\) and substituting it into the other equation. we can start with \(\(x = 8t\):\)
And the isolated part is to be \(t\) as follows:
\(\(t = \frac{x}{8}\)\)
\(now \(t\)will be classified \(y = t + 2\):\)
\(\(y = \frac{x}{8} + 2\)\)
So, the resulting rectangular equation is\(\(y = \frac{x}{8} + 2\).\)
Part 2:Straight line is the rectangular equations graph\(\(\frac{1}{8}\)\)and a y-intercept of 2. It has a positive slope, indicating that the line is ascending from left to right.
Part 3: The rectangular equation is\(\(y = \frac{x}{8} + 2\).\)
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If f(x)=x⁴ + 3x³ - x² + 6, find f(-3)
Answers
Answer:
3x^{3} -66
Step-by-step explanation:
Factor 2x^3-12x^2+16x
Answers
Answer:
2x ( x-4) (x-2)Step-by-step explanation:
Jane said that 6(64) = 6(50) + 6(14). Is she correct? Use the Distributive Property to explain your answer.
Answers
Answer:
Yes.
Step-by-step explanation:
6(64) = 6(50+14)
Using the Distributive Property, 6 needs to be multiplied by both 50 and 14.
6(50+14) = 6(50) + 6(14)
Thus, Jane is correct.
Work out the circumference of this circle.
Take a to be 3.142 and give your answer to 1 decimal place.
9m
Answers
Answer:
28.3 (explaination below)! :)
Step-by-step explanation:
Use the formula for cicrumfrence: C=2πr
Radius can be found by splitting the given number in half, (unless you were given the radius already, then you'd just multiply by 2).
Plug in our numbers. C= 2π4.5
Then, multiply.
You'd get 28.27433388230814.
Rounding to the first decimal place, you'd have a final answer of 28.3.
Hope this helps!
.Does education really make a difference in how much money you will earn? Reseachers randomly selected 100 people from each of three income categories—"marginally rich," "comfortably rich," and "super rich"—and recorded their education levels. The data is summarized in the table that follows.10
a Describe the independent multinomial populations whose proportions are compared in the χ 2 analysis.
b Do the data indicate that the proportions in the various education levels differ for the three income categories? Test at the α = .01 level.
c Construct a 95% confidence interval for the difference in proportions with at least an undergraduate degree for individuals who are marginally and super rich. Interpret the interval.
Answers
a. The independent multinomial populations whose proportions are compared in the chi-square analysis are the proportions of individuals with different levels of education (high school, some college, bachelor's degree, and advanced degree) in the three income categories (marginally rich, comfortably rich, and super rich).
To construct a 95% confidence interval for the difference in proportions with at least an undergraduate degree for individuals who are marginally and super rich, we can use the following formula:
(p1 - p2) ± zsqrt(p1(1-p1)/n1 + p2*(1-p2)/n2)
where p1 and p2 are the sample proportions with at least an undergraduate degree for marginally rich and super rich individuals, n1 and n2 are the sample sizes, and z is the critical value from the standard normal distribution for a 95% confidence level (z = 1.96).
From the table, we can see that there are 42 individuals in the marginally rich group and 72 individuals in the super rich group with at least an undergraduate degree. The sample proportions are:
p1 = 42/100 = 0.42
p2 = 72/100 = 0.72
Substituting these values into the formula, we get:
(p1 - p2) ± zsqrt(p1(1-p1)/n1 + p2*(1-p2)/n2)
= (0.42 - 0
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Find the 25th term for the sequence a1=5 and d=0.5
Answers
Answer:17
Step-by-step explanation:
We can tell from the question, that the problem is an arithmetic progression type because of presence of d=common difference.
The nth term of an arithmetic progression is given as
Tn=a1 +(n-1)d
putting the given vales we have
T₂₅=5 +(25-1)0.5
T₂₅=5 +(24)0.5
T₂₅=5 +12
T₂₅=17
The 25th term for this sequence is 17
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A project has an initial cost of $30 million.The project is expected to generate a cash flow of $2.85 million at the end of the first year.All the subsequent cash flows will grow at a constant growth rate of 3.85% forever in future.If the appropriate discount rate of the project is 11%,what is the profitability index of the project? a.1.917 b.1.328 c.1.387 d.1.114 ortcehov e. None of the above
Answers
Profitability index is 1.387. Thus, the correct option is (c) 1.387.
The formula for calculating the profitability index is:
P.I = PV of Future Cash Flows / Initial Investment
Where,
P.I is the profitability index
PV is the present value of future cash flows
The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.
The present value of cash flows can be calculated using the formula:
PV = CF / (1 + r)ⁿ
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
n is the number of periods
For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.
Substituting the values, we get:
PV = 2.85 / (1 + 0.11)¹ = $2.56 million
To calculate the present value of all future cash flows, we can use the formula:
PV = CF / (r - g)
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
g is the constant growth rate
For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.
Substituting the values, we get:
PV = 2.85 / (0.11 - 0.0385) = $39.90 million
The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.
PV of future cash flows = $39.90 million + $2.56 million = $42.46 million
Profitability index (P.I) = PV of future cash flows / Initial investment
= 42.46 / 30
= 1.387
Therefore, the correct option is (c) 1.387.
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Jen, Heather, and Bob are auditioning for the same role. Jen auditions 10 minutes before four, Heather auditions 30 minutes before Jen, and Bob auditions 5 minutes before four. Order the three by who will audition first..
Answers
The required order for the three according to the turn of the audition is Heather, Jen, and bob.
Given that,
Jen, Heather, and Bob are auditioning for the same role. Jen auditions 10 minutes before four, Heather auditions 30 minutes before Jen, and Bob auditions 5 minutes before four. Order the three by who will audition first.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let's order the timeline,
Jen's audition was 10 minutes before the 4, so the time is 3:50
Heather's audition was 30 minutes before so the time would be 3:20
Bob's audition was 5 minutes before the 4 so the time would be 3:55
So from the above calculation. the order of the audition is Heather, Jen, and bob.
Thus, the required order for the three according to the turn of the audition is Heather, Jen, and bob.
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the mean number of hours that a jetblue pilot flies monthly is 49 hours. assume that this mean was based on actual flying times for a sample of 100 jetblue pilots and that the sample standard deviation was 8.5 hours. * at 95% confidence what is the margin of error? * what is the 95% confidence interval estimate of the population mean flying time for the pilots?
Answers
To calculate the margin of error at a 95% confidence level, we will use the formula: Margin of Error = (Critical Value) * (Standard Deviation / Square Root of Sample Size).
Given that the sample size is 100, the mean flying time is 49 hours, and the sample standard deviation is 8.5 hours, we can calculate the margin of error. First, we need to determine the critical value for a 95% confidence level. Since the sample size is large (n > 30), we can use the z-distribution. The critical value for a 95% confidence level is approximately 1.96. Now, we can plug in the values into the margin of error formula:
Margin of Error = 1.96 * (8.5 / √100) = 1.96 * (8.5 / 10) = 1.66 hours.
Therefore, the margin of error is 1.66 hours.
At a 95% confidence level, the margin of error for the mean flying time of JetBlue pilots is 1.66 hours. This means that we can estimate the population mean flying time by taking the sample mean of 49 hours and subtracting the margin of error (1.66 hours) to get the lower bound and adding the margin of error to get the upper bound. The 95% confidence interval estimate of the population mean flying time for the pilots is approximately (47.34, 50.66) hours.
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\(how \: can \: you \: use \: dimensional \: analysis \: to \: convert \: between \: measurment \: systems\)
Helppppppppp
Answers
Lines AB and BC intersect at point B. Ray BD bisects angle ABC. (4x-24) B (x+6) What is the value of x?
Answers
If line AB and BC are intersecting at point B and ray BD bisect the angle ABC, then the value of x is 23
The line AB and BC are intersecting at point B.
Ray BD bisect the angle ABC
∠ABD = x+8 degrees
∠ABD=∠DBC = x+8
Because the ray BD bisect the ∠ABC, so ∠ABD and ∠DBC will be equal
∠ABD+∠DBC= 4x-30 degrees
Because both are vertically opposite angles
Substitute the values in the equation
x+8 + x+8 = 4x-30
2x+16 = 4x-30
2x-4x = -30-16
-2x = -46
x = 23
Hence, if line AB and BC are intersecting at point B and ray BD bisect the angle ABC, then the value of x is 23
The complete question is
Line AB and BC are intersecting at point B and ray BD bisect the angle ABC. What is the value of x?
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help asap!! <3 no working out required^^
Answers
Step-by-step explanation:
3×100000 or
300000
hope it's correct
What is the slope and the y intercept for the graph y=7x-2
Answers
Answer:
slope = 7
Y intercept = 2
Step-by-step explanation:
Solve the system of linear equations using substitution:
-15x + 7y = 83
5x + y = -8
Answers
Answer:
-15x + 7y = 83
Step-by-step explanation:
Mostly what I get is 0 because what i was taught was moving the constant to the left ( -83=0) and by changing the signs (- +) but like there are different things in this problem I get from the root (-83/15,0) xeR is domain and range yeR so I say 0. I'm sorry if its wrong.