Identify which of the twelve basic functions listed below fit the description given.
Answers
Answer:
The correct option is;
b. y = x², \(y = \left | x \right |\)
Step-by-step explanation:
The equations are
1) y = x
\(\lim_{x\rightarrow -\infty }f\left (x \right )=-\infty\)
2) y = x²
\(\lim_{x\rightarrow -\infty }f\left (x \right )=+\infty\)
3) y = x³
\(\lim_{x\rightarrow -\infty }f\left (x \right )=-\infty\)
4) \(y = \left | x \right |\)
\(\lim_{x\rightarrow -\infty }f\left (x \right )=+\infty\)
5) y = 1/x
\(\lim_{x\rightarrow -\infty }f\left (x \right )=0\)
6) y = eˣ
\(\lim_{x\rightarrow -\infty }f\left (x \right )\rightarrow 0\)
7) y = √x
\(\lim_{x\rightarrow -\infty }f\left (x \right )= \infty\sqrt{(-1)}\)
8) y = ㏑x
\(\lim_{x\rightarrow -\infty }f\left (x \right )= \infty\sqrt{(-1)}\)
9) y = sin x
\(\lim_{x\rightarrow -\infty }f\left (x \right )=\) undefined
10) y = cos x
\(\lim_{x\rightarrow -\infty }f\left (x \right )=\) undefined
11) y int (x)
\(\lim_{x\rightarrow -\infty }f\left (x \right )=-\infty\)
12) \(y = \dfrac{1}{1 + e^{-x}}\)
\(\lim_{x\rightarrow -\infty }f\left (x \right )=0\)
Therefore, the correct options are y = x² and \(y = \left | x \right |\)
Related Questions
Carson has $50 in the bank to put towards a new e-bike. If every three
months afterwards he saves $20 additional dollars to put towards the
bike, how much will he have saved up for it after three years?
Answers
Select all the points which are relative minimums of this graph of a polynomial function.
a
Point A
b
Point B
c
Point C
d
Point D
e
Point E
f
Point F
g
Point G
Answers
The relative minimum are
d. Point D and f .Point FHow to find the relative minimums of the polynomial function?To find the relative minimum, the point has to satisfy the following conditions
The tangent at that point must be equal to zeroThe tangent at that point must be increasingSo, at point A, we see that the tangent is not equal to zero, so it is not a minimum point
At point B, we see that the tangent equals zero but it is decreasing so it is not a minimum point
At point C, we see that the tangent is not equal to zero but negative so it is not a minimum point
At point D, we see that the tangent is equal to zero and it is increasing, so it is a minimum point
At point E, we see that the tangent equals zero but it is decreasing so it is not a minimum point
At point F, we see that the tangent is equal to zero and it is increasing, so it is a minimum point
at point G, we see that the tangent is not equal to zero and it is increasing, so it is not a minimum point
So, the only points that satisfy the condition for minimum point are Points D and point F
So, the relative minimum are
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-9(m+3) +14=-49 please show work
Answers
Answer:
m=4
Step-by-step explanation:
−9(m+3)+14=−49
Step 1: Simplify both sides of the equation.
−9(m+3)+14=−49
(−9)(m)+(−9)(3)+14=−49(Distribute)
−9m+−27+14=−49
(−9m)+(−27+14)=−49(Combine Like Terms)
−9m+−13=−49
−9m−13=−49
Step 2: Add 13 to both sides.
−9m−13+13=−49+13
−9m=−36
Step 3: Divide both sides by -9.
−9m
−9
=
−36
−9
m=4
Select the cone(s) that are similar to a cone with a height of 10 meters and a radius of 6 meters.
cone with a height of 20 meters and a radius of 12 meters
cone with a height of 11 meters and a radius of 7 meters
cone with a height of 6 meters and a radius of 4 meters
cone with a height of 5 meters and a radius of 3 meters
Answers
Answer:
I do strongly believe that it is none other than option 4: cone with a height of 5 meters and a radius of 3 meters
Step-by-step explanation:
Solve for x
5(3+x)=5+7x
Answers
A rectangular prism has a length of 8 meters, a width of 6 meters, and a height of 3 meters.
Which equations could be used to determine the volume, V, of the prism?
Select each correct answer.
(A) V = 8 × 6 × 6
(B) V = 8 × 6 × 3
(C) V = 8 × 9
(D) V = 48 × 3
Answers
Answer:
(B) V = 8 x 6 x 3
Step-by-step explanation:
The formula to find the volume of a rectangular prism is, V = Length x Width x Height cubic units.
V = 8 x 6 x 3 cm 3.
V = 192 cm 3.
Brainliest?!
what expression can be used to add 1/2 plus 5/6?
Answers
Step-by-step explanation:
You can add the two fractions by turning 1/2 and 5/6 to have the same denominator. Turn 1/2 into a fraction with a denominator of 6. That simplifies to 1 1/3. Hope this helps yo
V I’mhjhvcbjvcvjhvvvggujvvcghhhvcccgggghh
Answers
Answer:
the like terms were not grouped together.
Apple trees need to be planted in an orchard. The process takes two hours per tree. The orchard owner wants to find out how many apple trees can be planted in a given amount of time. Which graph correctly represents this relationship between time ( y ) and apples trees planted ( x )?
Graph D
Graph A
Graph C
Graph B
Answers
Answer:
Graph C. Hope this is correct!!!
Step-by-step explanation:
Answer: It should be "B". the vertical axis is the time and the horizontal axis is number of trees.
This is what my teacher sent me.
Select the correct answer. There are three cell phone models in a store. When selecting a new cell phone, 25% of the customers choose model A, 33% choose model B, and 32% choose model C. The remaining customers buy from an old collection on which the average profit is $50. If the average profit earned on models A, B, and C is $60, $75, and $40, respectively, what is the expected value of the profit earned on all models?
Answers
Given the average profits on the different cell phone models, the expected value of profit to be earned on all models is $57.55
How to find the expected value?The expected value of the profit on these models of cell phones can be found based on the number of customers who choose the model and the profit of that model.
The expected value of the profit on all the models is:
= ∑ ( percentage of customers x Profit per model)
= (Percentage of customers model A x Profit from model A) + (Percentage of customers model B x Profit from model B) + (Percentage of customers model C x Profit from model C) + (Percentage of customers old collection x Profit from old collection)
= (25% x 60) + (33% x 75) + (32% x 40) + ( (1 - 25% - 33% - 32%) x 50)
= $57.55
Options for this question are:
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3.48 Referring to Exercise 3.39, find
(a) f(y|2) for all values of y;
(b) P(Y = 0 | X = 2).
this is 3.39
3.39 From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in the sample, find (a) the joint probability distribution of X and Y ; (b) P[(X, Y ) ∈ A], where A is the region that is given by {(x, y) | x + y ≤ 2}.
Answers
Referring to Exercise 3.39,
(a) f(y|2) for all values of y is f(2|2) = P(Y=2|X=2) = P(X=2, Y=2) / P(X=2) = (1/14) / (3/14) = 1/3
(b) P(Y = 0 | X = 2) = 1
To find f(y|2), we need to first calculate the conditional probability of Y=y given that X=2, which we can do using the joint probability distribution we found in part (a) of Exercise 3.39:
P(Y=y|X=2) = P(X=2, Y=y) / P(X=2)
We know that P(X=2) is equal to the probability of selecting 2 oranges out of 4 fruits, which can be calculated using the hypergeometric distribution:
P(X=2) = (3 choose 2) * (2 choose 0) / (8 choose 4) = 3/14
To find P(X=2, Y=y), we need to consider all the possible combinations of selecting 2 oranges and y apples out of 4 fruits:
P(X=2, Y=0) = (3 choose 2) * (2 choose 0) / (8 choose 4) = 3/14
P(X=2, Y=1) = (3 choose 2) * (2 choose 1) / (8 choose 4) = 3/14
P(X=2, Y=2) = (3 choose 2) * (2 choose 2) / (8 choose 4) = 1/14
Therefore, f(y|2) is:
f(0|2) = P(Y=0|X=2) = P(X=2, Y=0) / P(X=2) = (3/14) / (3/14) = 1
f(1|2) = P(Y=1|X=2) = P(X=2, Y=1) / P(X=2) = (3/14) / (3/14) = 1
f(2|2) = P(Y=2|X=2) = P(X=2, Y=2) / P(X=2) = (1/14) / (3/14) = 1/3
To find P(Y=0|X=2), we can use the conditional probability formula again:
P(Y=0|X=2) = P(X=2, Y=0) / P(X=2) = 3/14 / 3/14 = 1
Therefore, P(Y=0|X=2) = 1.
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A baseball team plays the same opponent six times in a season. The set {0,1,2,3,4,5,6} describes the possible number of wins for the six games.
Set A contains the number of wins when exactly four games are won.
Set B contains the number of wins when at least four games are won.
Which of these statements are true? Choose all that are correct.
The union of set A and B is an empty set
The complement of the union of set A and B is {0,1,2,3} set A
The complement of set B is {0,1,2,3}
The intersection of set A and set B is an empty set
The complement of set B is {1,2,3}
Answers
- The complement of set B is {0,1,2,3}
- The complement of set B is {1,2,3}
the travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. the probability that she will finish her trip in 60 minutes or less is
Answers
The probability that the student will finish her trip in 60 minutes or less is 0.4
To find the probability that the student will finish her trip in 60 minutes or less, we need to find the proportion of the total area under the uniform distribution curve that lies to the left of 60 minutes.
Since the travel time is uniformly distributed between 40 and 90 minutes, the probability density function is
f(x) = 1/(90-40) = 1/50, for 40 ≤ x ≤ 90
The probability of finishing the trip in 60 minutes or less is therefore
P(X ≤ 60) = ∫[40, 60] f(x) dx
= (60-40)/50
Do the arithmetic operations
= 0.4
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Random sample of 30 days and finds that the site now has an average of 124,247 unique listeners per day. calculate the p-value. t.test(a2:a31,b2:b31,2,3)
Answers
The p-value is 0.0064
Given that a random sample of 30 days and finds that the site now has an average of 124,247 unique listeners per day. Let us first understand the t-test(a2:a31, b2:b31, 2, 3) formula:
t-test stands for student's t-test.
a2:a31 is the first range or dataset.
b2:b31 is the second range or dataset.
2 represents the type of test (i.e., two-sample equal variance).
3 represents the type of t-test (i.e., two-tailed).
Now, let's solve the problem at hand using the formula given by putting the values into the formula:
P-value = 0.0064
The p-value calculated using the t.test(a2:a31, b2:b31, 2, 3) formula is 0.0064.
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What is the slope of the line perpendicular to y 1 4x 10?
Answers
The slope of the line perpendicular to the given line is equal to -4/1.
The equation is in the form y=mx+b
so, y=(1/4)x -10
First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4
To find the slope perpendicular to the line you must find the negative reciprocal of 1/4. (Which just means change the sign then flip the fraction)
Multiplying 1/4 by -1 which is -1/4
Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1
Thus, the slope of the line perpendicular to the given line is equal to -4/1.
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The equation is in the form y=mx+b
so, y=(1/4)x -10
First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4
Multiplying 1/4 by -1 which is -1/4
Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1
find a function whose square plus the square of its derivative is 1.
Answers
A function that satisfies the condition of having its square plus the square of its derivative equal to 1 is given by f(x) = sin(x).
The function f(x) = sin(x) has the property that its square, sin^2(x), is equal to 1 when added to the square of its derivative, \($\frac{d}{dx}\sin(x))^2 = \cos^2(x)$\).
This can be seen by directly evaluating the expression: \(sin^{2}(x) + cos^{2}(x) = 1\), which is a fundamental identity in trigonometry.
The sine function is periodic with a period of 2π, and its derivative, cosine function, also has the same period. This means that for any x, the function sin(x) and its derivative cos(x) will satisfy the given condition.
Geometrically, the sine function represents the y-coordinate of a point on the unit circle as the corresponding angle is varied. Its derivative, the cosine function, represents the rate of change of this y-coordinate with respect to the angle. The squares of the sine and cosine functions add up to 1, which is the square of the radius of the unit circle. This property is fundamental in trigonometry.
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A sterilization procedure yields a decimal reduction time of
0.65 minutes. Calculate the minimum sterilization time required to
yield 99.9% confidence of successfully sterilizing 50 L of medium
containing 10^6 contaminating organisms using this procedure.
Answers
The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.
To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.
The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.
To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.
To calculate the minimum sterilization time, we can use the following formula:
Minimum Sterilization Time = D-value × log10(N0/Nf)
Where:
D-value is the decimal reduction time (0.65 minutes).
N0 is the initial number of organisms (10^6).
Nf is the final number of organisms (10^6 × 10^-3).
Let's calculate it step by step:
Nf = N0 × 10^-3
= 10^6 × 10^-3
= 10^3
Minimum Sterilization Time = D-value × log10(N0/Nf)
= 0.65 minutes × log10(10^6/10^3)
= 0.65 minutes × log10(10^3)
= 0.65 minutes × 3
= 1.95 minutes
Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes
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Find the surface area of a pentagon-based pyramid with slant height of 11 m.
Apothem of the pentagon = 3.5 m
Answers
Answer:
108.75 square meter.
Step-by-step explanation:
Surface area of pentagon based pyramid:\(\sf \boxed{\text{\bf Surface area of pentagonal pyramid = $ \bf \dfrac{5}{2}*b*(a + s)$}}\)
Here, b is the base length of the pyramid. b = 3 m
a is the apothem of the pyramid. a = 3.5 m
s is the slant height of the pyramid. s = 11 m
\(\sf Surface \ area = \dfrac{5}{2}*3*(11 + 3.5)\)
\(\sf = \dfrac{5}{2}*3*14.5\\\\ = 108.75 \ m^2\)
What’s the sum of 45 and ^
Answers
Answer:
45+π ≈ 48.1415926536
Step-by-step explanation:
Maybe you want the sum of 45 and pi:
45+π ≈ 48.1415926536
The sum is irrational, so cannot be expressed exactly, except in the form 45+π.
Lula is planting her spring garden. It takes nineteen giant bags of soil to fill five flower beds. How much soil is in each flower bed?
Answers
Answer:
19/5 = 3 4/5 soils for each flower bed.
Step-by-step explanation:
Answer is 3 4/5 soils in each flower bed.
Which of the following equations has infinitely many solutions?
A
2x + 3 = 5 + 2x
B
2x + 3 = 5 + 3x
C
3x - 5 = -5 + 3x
D
2x - 5 = -5 + 3x
Answers
A. 2x + 3 = 5 + 2x has infinitely many solutions because the variable terms cancel out, leaving the statement 3 = 3, which is always true, regardless of the value of x.
Please help urgent ~~
Answers
Answer:
False
Step-by-step explanation:
I need help with problem 9
Answers
Answer: The triangles are not congruent.
Step-by-step explanation:
We are given that the two triangles both contain a congruent angle and two congruent sides. The triangles have two congruent sides with a non-included congruent angle among them.
However, because the two triangles only have two congruent sides, and the angle shared by each triangle is not included between the two sides, the triangle would be "congruent" by SSA, which is not a triangle congruency theorem or postulate.
Therefore, the two triangles are not congruent.
I hope this helps!
A die is rolled 3 times. What is the probability of getting a "1" on the first roll, a "2" on the second roll, and a "3" on the third roll?
Write your answer as a reduced fraction.
Answer:
Answers
Answer:
1/216
Step-by-step explanation:
1/6 * 1/6 * 1/6
1/216
3. Which represents the least percent of change?
A. A $125 watch selling for $90.
B. The speed limit changing from
40 mph to 55 mph.
C. The stock market dropping from
250 to 175 points.
D. Marissa's math grade increasing
from 75 to 99.
Answers
Answer: B. The speed limit changing from 40 mph to 55 mph represents the least percent of change.
In A, a watch selling for $90 from $125 represents a 28% decrease,
In C, the stock market dropping from 250 to 175 points represents a 30% decrease,
In D, Marissa's math grade increasing from 75 to 99 represents a 32% increase.
While in B, the speed limit changing from 40 mph to 55 mph represents a 37.5% increase.
So, B represents the least percent of change.
Step-by-step explanation:
8.) Antonio is going to the carnival. He can spend no more than $20.00. If the ticket to g in is $7.50, and each ride costs $1.25, how many rides could Antonio ride at the carnival?
Answers
20-7.50 =12.50
12.50/1.25=10
Because of the question it is
to find a power series for the function, centered at 0. f(x) = 1 (1 − x)2
Answers
The power series expansion for \(f(x) = 1/(1 - x)²\),
centered at 0, is:
\($$f(x) = \sum_{n=0}^{\infty}(n+1)x^n(1 - 2x + x^2).$$\)
To find a power series for the function, centered at 0.
\(f(x) = 1(1 − x)²,\)
we can begin with the formula for a geometric series. Here's how we can derive a power series expansion for this function. We'll use the formula for the geometric series:
\($$\frac{1}{1-r} = 1+r+r^2+r^3+\cdots,$$\)
where |r| < 1. We start with the expression
\(f(x) = 1(1 − x)²,\)
and we can write it as:
f(x) = 1/((1 − x)(1 − x))
Using the formula for a geometric series, we can write:
\($$\frac{1}{1-x} = \sum_{n=0}^{\infty}x^n,$$\)
and substituting x with x², we get:
\($$\frac{1}{(1-x)^2} = \sum_{n=0}^{\infty}(n+1)x^n.$$\)
Substituting x with -x, we get:
\(f(x) = 1/(1 - x)² = 1/(1 + (-x))²\)
So we can write:
\($$\frac{1}{(1+x)^2} = \sum_{n=0}^{\infty}(n+1)(-x)^n.$$\)
Now, we want the series for \(1/(1 - x)²\), not for 1/(1 + x)².
So we multiply by \((1 - x)²/(1 - x)²:\)
\($$\frac{1}{(1-x)^2} = \frac{1}{(1+x)^2} \cdot \frac{(1-x)^2}{(1-x)^2} = \sum_{n=0}^{\infty}(n+1)(-x)^n \cdot (1-x)^2.$$\)
Multiplying out the last term gives:
\($$(1-x)^2 = 1 - 2x + x^2,$$\)
so we have:
\($$\frac{1}{(1-x)^2} = \sum_{n=0}^{\infty}(n+1)(-x)^n(1 - 2x + x^2).$$\)
Simplifying, we get the power series expansion:
\($$\frac{1}{(1-x)^2} = \sum_{n=0}^{\infty}(n+1)x^n(1 - 2x + x^2).$$\)
Thus, the power series expansion for \(f(x) = 1/(1 - x)²\),
centered at 0, is:
\($$f(x) = \sum_{n=0}^{\infty}(n+1)x^n(1 - 2x + x^2).$$\)
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Find the equation of the line.
Use exact numbers.
y=y=y, equals
x+x+x, plus
\small{1}1\small{2}2\small{3}3\small{4}4\small{5}5\small{6}6\small{7}7\small{8}8\small{9}9\small{\llap{-}2}-2\small{\llap{-}3}-3\small{\llap{-}4}-4\small{\llap{-}5}-5\small{\llap{-}6}-6\small{\llap{-}7}-7\small{\llap{-}8}-8\small{\llap{-}9}-9\small{1}1\small{2}2\small{3}3\small{4}4\small{5}5\small{6}6\small{7}7\small{8}8\small{9}9\small{\llap{-}2}-2\small{\llap{-}3}-3\small{\llap{-}4}-4\small{\llap{-}5}-5\small{\llap{-}6}-6\small{\llap{-}7}-7\small{\llap{-}8}-8\small{\llap{-}9}-9yyxx
Answers
On solving the provided question, we can say that Slope is 1/2, so equation is y=1/2x+0 or y=1/2x.v
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
We can utilize the slope-intercept version of the equation. It is written as y=mx+b. B is the y-intercept, and m stands for the slope. The line intersects the y-axis at (0,0). the y-intercept is consequently 0.
the slope by equation, we have
m = y2 - y1 / x2 - x1
m = 2-1/4-2
m = 1/2
Slope is 1/2, so equation is y=1/2x+0 or y=1/2x.
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The correct question is
Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus 5
on her first six test, Sandra's scores were 75 70 80 80 85 and 90 find the mean of the six scores
Answers
Explanation:
First add up the scores: 75+70+80+80+85+90 = 480
Then divide by n = 6 because there are 6 scores. We get 480/n = 480/6 = 80 as the mean.
The set of ordered pairs a where
t is the time in seconds after
someone jumps out of a plane at
4000 meters to go skydiving, and d
is the displacement above the
ground
I need to find the domain and Range.
Answers
Answer: Domain is \([0,\infty)\) and range is [0,4000].
Step-by-step explanation:
It is given that, the set of ordered pairs (t,d), where
t = the time in seconds after someone jumps out of a plane at 4000 meters to go skydiving
d = is the displacement above the ground.
It means t is independent variable and it is represented on the x-axis.
d is dependent variable and it is represented on the y-axis.
We need to find the domain and Range.
Domain is the set of input values.
Here, input is time and time can not be negative.
Domain \(=0\leq t=[0,\infty)\)
Range is the set of output values.
Here, output is displacement above the ground which can not be negative or more than 4000 meters.
Range \(=0\leq d\leq 4000=[0,4000]\)
Therefore, domain is \([0,\infty)\) and range is [0,4000].