Answers
Answer:
See Below.
Step-by-step explanation:
We want to use the Squeeze Theorem to show that:
[tex]\displaystyle \lim_{x \to 0}\left(x^2\sin\left(\frac{2}{x}\right)\right)=0[/tex]
Recall that according to the Squeeze Theorem, if:
[tex]\displaystyle g(x)\leq f(x) \leq h(x)[/tex]
And:
[tex]\displaystyle \lim_{x\to c}g(x) =\lim_{x\to c}h(x) = L[/tex]
Then:
[tex]\displaystyle \lim_{x\to c}f(x)=L[/tex]
Recall that the value of sine is always ≥ -1 and ≤ 1. Hence:
[tex]\displaystyle -1 \leq \sin\left(\frac{2}{x}\right) \leq 1[/tex]
We can multiply both sides by x². Since this value is always positive, we do not need to change the signs. Hence:
[tex]\displaystyle -x^2\leq x^2\sin\left(\frac{2}{x}\right)\leq x^2[/tex]
Let g = -x², h = x², and f = x²sin(2 / x). We can see that:
[tex]\displaystyle \lim_{x \to 0}g(x) = \lim_{ x \to 0}h(x) = 0[/tex]
And since g(x) ≤ f(x) ≤ h(x), we can conclude using the Squeeze Theorem that:
[tex]\displaystyle \lim_{x \to 0}f(x) = \lim_{x \to 0}x^2\sin\left(\frac{2}{x}\right)=0[/tex]
Related Questions
The following function represents exponential growth or decay.
P= 2.9(1.05)^t
a. The initial quantity is :_______________
b. The initial quantity is :__________
c. Is the quantity growing or decaying?
Answers
Answer:
a) The initial quantity is 2.9.
b) The initial quantity is 2.9.
c) The multiplier is 1.05 > 1, and thus, the quantity is growing.
Step-by-step explanation:
Exponential equations:
Have the following format:
[tex]A(t) = A(0)(k)^t[/tex]
In which A(0) is the initial amount and k is the multiplier.
If k > 0, the quantity is growing.
If k < 0, the quintity is decaying.
In this question:
[tex]P(t) = 2.9(1.05)^t[/tex]
a, b. The initial quantity is
P(0). So
[tex]P(0) = 2.9(1.05)^0 = 2.9*1 = 2.9[/tex]
The initial quantity is 2.9.
c. Is the quantity growing or decaying?
The multiplier is 1.05 > 1, and thus, the quantity is growing.
I’m looking at one of my past tests and I don’t remember how I solved this. Can someone explain please :)
Answers
Answer:
Step-by-step explanation:
588000-540000=48000
48000/540000=8.8%
8.8%/2 years =4.4%
can you help me?
(4n+13)+(6+7n)
i will mark brailest first to answer correct if you tell how to do it??
Answers
Answer:
11n + 19
Step-by-step explanation:
The parentheses can be removed immediately without affecting the clarity of this expression:
4n + 13 + 6 + 7n
Next we combine like terms, obtaining:
11n + 19
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{(4n + 13) + (6 + 7n)}\\\\\large\textsf{ = 4n + 13 + 6 + 7n}\\\\\large\textsf{COMBINE the LIKE TERMS}\\\\\large\textsf{(4n + 7n) + (13 + 6)}\\\\\large\textsf{4n + 7n = \boxed{\large\textsf{\bf 11n}}}\\\\\large\textsf{13 + 6 = \boxed{\large\textsf{\bf 19}}}\\\\\\\boxed{\huge\textsf{= 11n + 19}}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 11n + 19}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
CNNBC recently reported that the mean annual cost of auto insurance is 1049 dollars. Assume the standard deviation is 275 dollars. You take a simple random sample of 72 auto insurance policies.
Find the probability that a single randomly selected value is less than 962 dollars.
P(X < 962) =
Find the probability that a sample of size
n
=
72
is randomly selected with a mean less than 962 dollars.
P(M < 962) =
Enter your answers as numbers accurate to 4 decimal places.
Answers
Answer:
0.3745 = 37.45% probability that a single randomly selected value is less than 962 dollars.
0.0037 = 0.37% probability that a sample of size 72 is randomly selected with a mean less than 962 dollars.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
CNNBC recently reported that the mean annual cost of auto insurance is 1049 dollars. Assume the standard deviation is 275 dollars.
This means that [tex]\mu = 1049, \sigma = 275[/tex]
Find the probability that a single randomly selected value is less than 962 dollars.
This is the p-value of Z when X = 962. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{962 - 1049}{275}[/tex]
[tex]Z = -0.32[/tex]
[tex]Z = -0.32[/tex] has a p-value of 0.3745
0.3745 = 37.45% probability that a single randomly selected value is less than 962 dollars.
Sample of 72
This means that [tex]n = 72, s = \frac{275}{\sqrt{72}}[/tex]
Probability that the sample mean is les than 962.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{962 - 1049}{\frac{275}{\sqrt{72}}}[/tex]
[tex]Z = -2.68[/tex]
[tex]Z = -2.68[/tex] has a p-value of 0.0037
0.0037 = 0.37% probability that a sample of size 72 is randomly selected with a mean less than 962 dollars.
Need help ASAP .............
Answers
Answer:
A
Step-by-step explanation:
-4n(2n-7)=0
Simplif your answer
Answers
Answer:
n=3.5, n=0
Step-by-step explanation:
Open the parenthesis
2n(-4n)-7(-4n)=0
-8n^2+28n=0
Factor:
n(-8n+28)=0
Solve:
n=0, or -8n+28=0
-8n=-28
8n=28
n=28/8
n=3.5
n can be either 3.5 or 0
Answer:
0, 7/2
Step-by-step explanation:
See image below:)
What is the volume, in cubic in, of a rectangular prism with a height of 19in, a width of 17in, and length of 18in?
Answers
Answer:
5814
Step-by-step explanation:
V= width x height x length
V=17·19·18=5814
Statins are used to keep cholesterol in check and are a top-selling drug in the U.S. The equation:
S
−
1.3
x
=
6
gives the amount of sales (
S
) of statin in billions of dollars
x
years after 1998. According to this equation, how much will/did people in the U.S. spend on statins in the year 2008?
Answers
Answer:
19 billion dollars
Step-by-step explanation:
Given the equation :
S - 1.3x = 6
Where, S = amount of sale of statin in billions of dollars ; x = number of years after 1998
Amount spend in 2008
x = 2008 - 1998 = 10
Put x = 10 in the equation ;
S - 1.3x = 6
S - 1.3(10) = 6
S - 13 = 6
S = 6 + 13
S = 19
People will spend about 19 billion dollars on statin in 2008
A basket contains five apples, five peaches, and three pears. You randomly select a piece of fruit. what is the chance you pick an apple or a peach?
Answers
Answer:
10/13
Step-by-step explanation:
The chance that you pick an apple is 5/13 and the chance it's a peach is 5/13 because in total there's 13 fruits.
Since it says what's the chance it's either an apple OR peach you add these two fractions: 5/13+5/13 = 10/13
If the question said what's the probability you pick an apple AND a peach then you'd mutiply not add.
y'+y=y^2; y(0)=-1/3
Giải phương trình trên
Answers
Step-by-step explanation:
[tex]y' + y = y^2[/tex]
We can rewrite the differential equation above as
[tex]\dfrac{dy}{dx} + y = y^2[/tex]
[tex]dy = (y^2 - y)dx[/tex]
or
[tex]\dfrac{dy}{y^2 -y} = dx[/tex]
We can rewrite the left side of the equation above as
[tex]\dfrac{dy}{y^2-y}=\dfrac{dy}{y(y-1)}= \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy[/tex]
We can the easily integrate this as
[tex]\displaystyle \int \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy = \int dx[/tex]
or
[tex]\displaystyle \int \dfrac{dy}{y-1} - \int \dfrac{dy}{y} = \int dx[/tex]
This will then give us
[tex]\ln |y-1| - \ln |y| + \ln |k| = x[/tex]
where k is the constant of integration. Combining the terms on the left hand side, we get
[tex]\ln \left|\dfrac{k(y-1)}{y} \right| = x[/tex]
or
[tex]\dfrac{y-1}{y} = \frac{1}{k}e^x[/tex]
Solving for y, we get
[tex]y= \dfrac{1}{1- \frac{1}{k} e^x}=\dfrac{k}{k-e^x}[/tex]
We know that [tex]y(0)= \frac{1}{3}[/tex], so when we substitute [tex]x=0[/tex], we find that [tex]k = -\frac{1}{2}[/tex].
Therefore, the final form of the solution to the differential equation above is
[tex]y = \dfrac{1}{1+2e^x}[/tex]
PLEASE HELP WILL MARK BRAINLIEST.Write the log equation as an exponential equation. You do not need to solve for x.
In (5) = 2x
Answers
Answer:
10x ÷ 5x=2x
10x ÷ 5x = 2x
10x÷ 5x = 2x
Answer:
[tex]e^{2x}=5[/tex]
Step-by-step explanation:
Recall that [tex]\log_b a=c\implies b^c=a[/tex].
In this case, we need to find the base of the logarithm. The logarithm [tex]\ln[/tex] denotes natural [tex]\log[/tex] with a base of [tex]e[/tex], a mathematical constant.
Therefore, we can re-write the equation as:
[tex]\log_e5=2x[/tex]
To write the equation as an exponential equation, recall the definition of log (first sentence of explanation):
[tex]\boxed{e^{2x}=5}[/tex]
HELP PLEASE ON NUMBER 5!
Answers
Answer:
2.5 hours is the time it will take.
Step-by-step explanation:
50t + 55t-30 = 235
105t = 265
T = 2.5 hours (rounded to one d.p)
I need help with this fast
Answers
Answer:
1. positive
2. No
(for number 3, I'm not sure if my answer to it is going to be correct)
Step-by-step explanation:
1. the dots look like they are going up
2. there are no outlying dots that look unusual
A research team conducts a survey to determine the area of land used for farming in Iowa. The team randomly selects house addresses and sends the survey by mail. Which type of sampling method is the research team using?
A. Systematic random sampling.
B. Simple random sampling.
C. Multi-stage sampling.
D. Cluster sampling.
Answers
Answer:
B. Simple random sampling.
Step-by-step explanation:
From the question we are informed about a research team conducts a survey to determine the area of land used for farming in Iowa. The team randomly selects house addresses and sends the survey by mail. In this case, the type of sampling method used is the Simple random sampling. A simple random sample can be regarded as a subset of a statistical population, whereby each member of this subset posses an equal probability of them being chosen. A simple random sample can be portrayed as an unbiased representation of a group.
Simple random sampling is utilized in to culling smaller sample size out of larger population so that it can be used to research and make generalizations as regards larger group.
PLS HELP!!!! I NEED TO FIND THE SURFACE AREA OF THIS CYLINDER!!!!!
Answers
Step-by-step explanation:
SA=
[tex]2\pi \gamma {2} + 2\pi \gamma h[/tex]
[tex]2\pi(7){2} + 2\pi(7)(20)[/tex]
[tex]2\pi(49) + 2\pi(140)[/tex]
[tex]98\pi + 280\pi[/tex]
[tex]378\pi[/tex]
[tex]1187.52cm[/tex]
A national survey of 1516 respondents reached on land lines and cell phones found that the percentage of adults who favor legalized abortion has dropped from 55% a year ago to 45%. The study claimed that the error
atributable to sampling is 4 percentage points. Would you claim that a majority of people are not in favor of legalized abortion?
Answers
Answer:
The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion
Step-by-step explanation:
Confidence interval:
Sample proportion plus/minus margin of error.
In this question:
Sample proportion of 0.45, margin of error of 0.04. So
0.45 - 0.04 = 0.41
0.45 + 0.04 = 0.49
The confidence interval is of (0.41,0.49). The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion
need an answer show work please thank you
Answers
Answer:
[tex]\text{C. }1[/tex]
Step-by-step explanation:
In the question, we're given that the notation [tex]\#\#(a,b,c)[/tex] produces a number [tex]a[/tex] less than the product of [tex]b[/tex] and [tex]c[/tex] raised to the [tex]a[/tex] power. Let the number produced be [tex]n[/tex]. As a mathematical equation, we can write this production as [tex]n=(bc)^a-a[/tex]
For [tex]\#\#(2, 5, x)[/tex], we can assign:
[tex]a\implies 2[/tex] [tex]b\implies 5[/tex] [tex]c\implies x[/tex]Substituting these values into [tex]n=(bc)^a-a[/tex], we get:
[tex]23=(5x)^2-2[/tex]
Add 2 to both sides:
[tex]25=(5x)^2[/tex]
Take the square root of both sides:
[tex]5=|5x|[/tex]
For [tex]y=|z|[/tex], there are two cases:
[tex]\begin{cases}y=z,\\y=-z\end{cases}[/tex]
Therefore, we have:
[tex]\begin{cases}5=5x, x=\boxed{1}\\5=-(5x), 5=-5x, x=\boxed{-1}}\end{cases}[/tex]
The only answer choice applicable is [tex]\boxed{\text{C. }1}[/tex].
calculate to the nearest million m³.the current amount of water in the berg river dam
Answers
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the dimension of the dam is not given.
However, a general way of calculating volume is to calculate the base area and the multiply by height.
Take for instance,the dam has a rectangular base of 20m by 30m.
The base area will be
Area = 20m * 30m = 600m²
If the height of the water in the dam is 40m, then the volume is:
Volume = 600m² * 40m
Volume = 24000m³
Find the length of the arc
in terms of pi.
A
90°
B AB = [?]π
C
10
Hint: The arc is only part of the circle.
Enter
Answers
Answer:
5pi
is answer
Step-by-step explanation:
hear is your answer in attachment
HELP!!! Please simplify: 4^(x+1)*2^(2x)
Answers
Answer:
24x+2
Step-by-step explanation:
NEED HELP FAST!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
A. f(x) = -0.5(x+3) (x-5)
Translate and solve: 82% of what number is 369?
Answers
Answer:
82% of what number is 369
82% of 450 is 369
Answer:
number is 450
Step-by-step explanation:
let the number be x
82% of x=369
[tex]\frac{82}{100}[/tex]x = 369
82x=369*100
x=36900/82
x=450
Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)
Answers
Answer: Part A: Find a rational number that is between 9.5 and 9.7. Explain why it is rational.
Step-by-step explanation:
Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth
PLS HELP ASAP !!!! PLS !! will mark whoever gets it right as brainliest !
Answers
Answer:
128° because its vertical with ∠1
I think, but I'm not sure.
it took thandile 30minutes to fly the distance of 192,4kilometers between pilanesburg nationalpark an johannesburg.calculate the average speed of the aircraft in kilometres per hour
Answers
Answer:
Average speed = 3848 km / h
Step-by-step explanation:
Given:
It took Thandile 30 minutes to fly the distance of 1924 km between Pilanesburg National Park and Johannesburg.
To find:
Calculate the average speed.
Solution:
Average speed = distance / time
30 min = 0.5 h => 1924 / 0.5
= 3848 km / hours
Answer:
Average speed = 3848 km / h
hope this helps.....
If ⃗ = + + is perpendicular to both ⃗ = 5 + − 2 and = 3 − 3 + 6 , find and .
Answers
Answer:
The values of [tex]m[/tex] and [tex]n[/tex] are 0 and 2, respectively.
Step-by-step explanation:
If [tex]\vec {c} = m\,\hat{i} + n\,\hat{j} + \hat{k}[/tex] is perpendicular to [tex]\vec {a} = 5\,\hat{i} + \hat{j} -2\,\hat{k}[/tex] and [tex]\vec {b} = 3\,\hat{i} - 3\,\hat{j} + 6\,\hat{k}[/tex], then the following relationships must be observed:
[tex]\vec {c}\,\bullet\,\vec {a} = 0[/tex] (1)
[tex]\vec{c}\,\bullet \,\vec{a} = 0[/tex] (2)
Then, we expand the previous expressions:
[tex](m, n, 1)\,\bullet\,(5, 1, -2) = 0[/tex]
[tex]5\cdot m + n = 2[/tex] (1b)
[tex](m, n, 1)\,\bullet\,(3, -3, 6) = 0[/tex]
[tex]3\cdot m - 3\cdot n = -6[/tex] (2b)
Then, we solve for [tex]m[/tex] and [tex]n[/tex]:
[tex]m = 0, n = 2[/tex]
The values of [tex]m[/tex] and [tex]n[/tex] are 0 and 2, respectively.
When Riley goes bowling, her scores are normally distributed with a mean of 160 and
a standard deviation of 13. Using the empirical rule, determine the interval that
would represent the middle 68% of the scores of all the games that Riley bowls.
Answers
Answer:
The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 160, standard deviation of 13.
Middle 68% of the scores of all the games that Riley bowls.
Within 1 standard deviation of the mean, so:
160 - 13 = 147.
160 + 13 = 173.
The interval that would represent the middle 68% of the scores of all the games that Riley bowls is (147, 173).
Help please If f(x) = -3x - 5 and g(x) = 4x-2, find (1-9)(x).
Answers
9514 1404 393
Answer:
-7x -3
Step-by-step explanation:
(f -g)(x) = f(x) -g(x) = (-3x -5) -(4x -2)
(f -g)(x) = -3x -5 -4x +2 = (-3-4)x +(-5+2)
(f -g)(x) = -7x -3
Use this table of values for the rate of rainfall over time.
Rate of Rainfall (mm per hour) Time 6:00 am 20 6.15 am 28 630 am 3.0 645 am 35 7:00 am 3.8 7:15 am 42 7:30 am 4.8 7:45 am 5.6 8:00 am 4.0 8.15 am 3.3 8:30 am 1.8 8:45 am 0.4 9:00 am 1.2.
An approximation of the total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is
a. 9.3 mm.
b. 9.6 mm.
Answers
Solution :
Here the subintervals of equal length will be :
[tex][6:00, 6:30], [6:30, 7:00], [7:00, 7:30], [7:30, 8:00], [8:00, 8:30], [8:30, 9:00][/tex]
So thee mid points are
[tex]x_1 = 6:15, \ x_2=6:45, \ x_3=7:15, \ x_4=7:45, \ x_5, 8:15, \ x_6 = 8:45[/tex]
The length of each sub-interval is = [tex]\frac{9-6}{6} = \frac{3}{6} = 0.5[/tex]
So, total amount of rainfall will be :
[tex]$=0.5 \sum^6_{i=1} f(x_i)$[/tex]
[tex]$=0.5\left( f(x_1)+f(x_2)+....+ f(x_6)\right)$[/tex]
= 0.5 (2.8 + 3.5 + 4.2 + 5.6 + 3.3 + 0.4)
= 0.5 (19.8)
= 9.9
The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is 9.9.
Given that,
The rate of rainfall (mm per hour) over time.
Rate of rainfall;
6;00 6;15 6;30 6;45 7;00 7;15 7;30 7;45 8;00 8;15 8;30 8;45 9;00
Time
2.0 2.8 3.0 3.5 3.8 4.2 4.8 5.6 4.0 3.3 1.8 0.4 1.2
We have to determine,
0.4 9:00 am 1.2.
The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is?
According to the question,
Rate of rainfall;
6;00 6;15 6;30 6;45 7;00 7;15 7;30 7;45 8;00 8;15 8;30 8;45 9;00
Time
2.0 2.8 3.0 3.5 3.8 4.2 4.8 5.6 4.0 3.3 1.8 0.4 1.2
Here, the midpoints sum with 6 equal subintervals are,
[tex]\rm x_1 = 6;15, \ x _2 = 6;45, \ x_3 = 7;15, \ x_4 = 7;45, x_5 = 8;15 , \ x_6 = 8;45[/tex]
Then, the length of each subinterval is,
[tex]= \dfrac{9-6}{6}\\\\= \dfrac{3}{6}\\\\= \dfrac{1}{2}[/tex]
The total amount of rainfall that falls between 6;00 to 9;00 am using the midpoint subinterval is,
[tex]\rm = \dfrac{1}{2} \sum^{6}_{i=0} f(x_i)\\\\= \dfrac{1}{2} \sum^{6}_{i=0} f(x_1)+ f(x_2) + f(x_3) + f(x_4) +f(x_5)+f(x_6)\\\\= \dfrac{1}{2} (2.8+ 3.5+4.2+ 5.6+3.3+0.4}\\\\= \dfrac{1}{2} \times 19.8\\\\= 9.9[/tex]
Hence, The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is 9.9.
For more details refer to the link given below.
https://brainly.com/question/795909
Two cars are parked at the points (4, 5) and (8, 7). Find the midpoint between the two cars. O (12, 12) O (-6, -6) O (6,6) O (-2,-1) < Previous 00:00 / 00:00
Answers
Answer:
(6,6)
You can use the midpoint formula.