Divide through the limand by the highest power of t :
[tex]\displaystyle \lim_{t\to\infty} \frac{t^3-t+2}{(2t-1)(t^2+t+1)} = \lim_{t\to\infty} \frac{1 - \frac1{t^2} + \frac2{t^3}}{\left(2-\frac1t\right) \left(1+\frac1t + \frac1{t^2}\right)}[/tex]
(I distributed 1/t³ in the denominator as 1/t (2t - 1) and 1/t² (t² + t + 1).)
As to goes to infinity, these 1/tⁿ terms will converge to 0, and you're left with
[tex]\displaystyle \lim_{t\to\infty} \frac{1 - \frac1{t^2} + \frac2{t^3}}{\left(2-\frac1t\right) \left(1+\frac1t + \frac1{t^2}\right)} = \frac{1 - 0 + 0}{(2-0)(1+0+0)} = \boxed{\frac12}[/tex]
G(X)
Graph the function.
g(x) 1/2 x 2
See attachment for the graph of g(x) = 1/2x^2
How to graph the function?The equation of the function is:
g(x) = 1/2x^2
The above function is a quadratic function that has only one term
Next, we plot the graph using a graphing tool
See attachment for the graph of g(x)
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Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x?
For the function, f(x) = 4x² − 7x + 13, find the value of f(-2).
43
29
15
4
Answer: 43
Step-by-step explanation: subsitute -2 into x
4(-2)^2 - 7(-2) + 13 = 43
Help me with this question please
An associate in a scatter plot tells us the relation between the two variables. The points that are true about the given scatter plot are F and C.
What is an associate?An associate in a scatter plot tells us the relation between the two variables. There are 4 types of associates:
Positive associate: If the value of one variable is increasing the value of another increase as well, but the relation is not linear.
Negative associate: If the value of one variable is decreasing with the value of another increasing as well, but the relation is not linear.
Linear Associate: If the value of one is dependent on the other such that they follow a function of line, and all the data points are on that function line.
Non-linear Associate: If the data points of the plot are scattered and random, such that there is no relationship between the points.
The points that are true about the given scatter plot are:
F.) A cluster appears to be at the bottom left corner.
C.) There appears to be a positive association.
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Joe's Fabric Store purchased 6 bolts of fabric at $150.00 per bolt. Each bolt contained 50 m of fabric. If the fabric was retailed at $8.00 per metre, calculate the profit or loss.
what's the difference between dy/dx and d/dx?
Answer:
There is a slight difference but the result is the same.
In the notation ddx(y) the ddx part is an operator which says ‘the function which is the differential with respect to x of ⋯’ and y is the function being operated on. The ddx and y are two separate entities in this notation.
In the notation dydx we mean the function that is the result of differentiating the function y with respect to x. In this case, there is only a single entity: dydx.
Both notations mean ‘the function which is the differential of function y by x
Are the ratios 4:8 and 1:2 equivalent?
Answer:
yes
Step-by-step explanation:
yes they are i can see this because, 4/8 is the same as 1/2.
I know this because if you reduce 4/8, you will get 1/2.
theres 2 parts i need a awnser and i need to you to show your work please!!! WILL GIVE BRAINLIST!!!!!!!!!
Answer:
Part 1: See below ↓↓
You have two given data available here: the actual height of the Empire State Building measuring 1,450 feet, and the height of the block measuring 2 feet. To find how many blocks stacked together would make up 1,450 feet, just divide 1,450 by 2.
Number of blocks=1,450 feet * (1 block/2 feet)
Number of blocks = 725 blocks
Part 2 (kinda work)
What I did was I divided 1,450 by 5 and I got 290 so you would have to use 290 blocks to build the Empire State building out of blocks. The scale factor is 1 block per 5ft
Step-by-step explanation:
Eliminate the parameter in the equations x = 5cos(t) – 7 and y = 5sin(t) 9. how can the rectangular equation be described? circle ellipse parabola hyperbola
The equation here can be described to be a circle.
How to solve for the parameterWe have the following equations
x = 5cos(t) - 7, and
y = 5sin(t) + 9
When rearranged we have
x + 7 = 5cos(t),
y - 9 = 5sin(t)
Square both equations
(x + 7)² = 25cos²(t), and
(y - 9)² = 25sin²(t)
Sum the equations
(x + 7)² + (y - 9)² = 25cos²(t) + 25sin²(t)
(x + 7)² + (y - 9)² = 25
(x + 7)² + (y - 9)² = 5²
The equation above is that of a circle. The radius is 5 units. The center is (-7,9)
The formula for the equation of a circle is
(x -a)² + (y - b)² = R², this is similar to (x + 7)² + (y - 9)² = 5²
The equation can be described as a circle.
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Answer: cirlce
Step-by-step explanation:
did it
How much does Craig earn each month,in dollars?
Answer:
Craig must be rich LOL cuz It says its 1/20 of his paycheck each month so u have to multiply by 20
Step-by-step explanation:
720*20 = 14440
Good evening every one sorry to brother u but can someone answer this
3 - 3 / 1/3 + 1
Thank u very much
Answer:
-5
Step-by-step explanation:
3 - 9 + 1 = -6 + 1 = -5
Hope this helped! I would appreciate a Brainliest!
(BTW, if you can, can you please answer my question? It's due today!)
Which of the following measurements could be the side lengths of a right triangle? A. 65 in, 104 in, 130 in B. 78 in, 104 in, 130 in C. 78 in, 104 in, 156 in D. 78 in, 117 in, 130 in
Answer:
B
Step-by-step explanation:
from right angle triangle we know
(greater side)=√one side^2+remaining side^2
130=√78^2+104^2
130=130
hence b is correct
A numerical measure computed from a sample, such as sample mean, is known as a.
Answer:
Sample statistic
on marks first day, he ran 5 laps without stopping after several weeks of training he ran 9 weeks without stopping. what is the percent increase.
The percentage increase from 5 laps of race on the first day to 9 laps after several weeks is 80%
How to determine the percentage increase?The distance ran are given as:
Initial = 5 laps
Final= 9 laps
The percentage increase is calculated using:
Percentage = (Final - Initial)/Initial
So, we have:
Percentage = (9 - 5)/5
Evaluate
Percentage = 0.8
Express as percentage
Percentage = 80%
Hence, the percentage increase is 80%
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Find the dependent value
for the graph
y = 12 + 5x
when the independent value is 3.
y = [?]
Answer:
Y = 27
Step-by-step explanation:
In the equation (y = 12 + 5x) the X is the independent value. When you replace this by 3 you will multiply 3*5 which will give you 15 and then you will want to add 12 as that is your y intercept. Giving the value of your Y a 27, or the point would be (3,27)
WILL MARK BRAINLIEST . PLEASE HELP . Pigeons can fly at a rate of 168ft every 6 minutes, and ravens can fly at a rate of 472ft every 12.5 mins. Which unit rate, per hour, represents the speed of the faster bird?
Answer:
2,265.60 ft/hr
Step-by-step explanation:
168ft/6min = 28ft/min * 60min= 1,680ft/hr
472ft/12.5min= 37.76ft/min * 60min= 2,265.60ft/hr
helppppp ....Simpson Office Furniture pays Sam Hughes a $840 monthly salary plus a 7% commission on merchandise he sells each month. Assume Sam's sales were $18,600 for last month. Calculate the following amounts:
Answer:
$2,142
Step-by-step explanation:
7% of 18,600 is 1,302
Add this to 840 and you get a total of $2,142
Commission is $1,302
Gross pay is $840
Question Progress 10 Homework Progress 17/ x: y = 2:3 Which is the correct equation? A 2x = 3y B 2y = 3x C y = x - 1 D y = x + 1
I need help on this it's only 1 attempt or I'll get a 1hr detention
Answer: 2y = 3x
Reason:
The equation x:y = 2:3 is the same as saying x/y = 2/3
Cross multiply to get 3x = 2y which flips to 2y = 3x
What would be the volume of a sphere with a radius of 16 yd
Answer:
v=13117.69 m3
Step-by-step explanation:
Hope this helps.
Answer:
The answer is 803.84
Step-by-step explanation:
Carry on learning i hope this helps..
50 points Select the correct answer
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
Answer:The answer is A: b^4/a
Step-by-step explanation:now i dont rly have an explaination but i got this in my test so ik its right!
100% verrified!
What multiplies to 14 and adds to 15
14 and 15
to find:which number multiplies to 14 and add up to 15.
solution:[tex]1 + 14 = 15[/tex]
[tex]1 \times 14 = 14[/tex]
[tex] = 1[/tex]
therefore, the number which multiplies to 14 and add up to 15 is 1
= 1
because,
14×1 = 14
14+1= 15
You have been given data about gas prices in 15 states.
2018 Gas Price Data
Max: $2.42
Min: $2.03
Mean: $2.098
Median: $2.06
Mode: $2.04
Variance: 0.0121
Standard Deviation: $0.1098
What does the mean and median of the data say about gas prices in 2018?
Both the mean and the median can be used to describe where the “center” of a dataset is located. It’s best to use the mean when the distribution of the data values is symmetrical and there are no clear outliers. It’s best to use the median when the distribution of data values is skewed or when there are clear outliers.
Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 10 students per hour, and the average service rate is 20 students per hour. A student has just entered the system. How long is she expected to stay in the system (in minutes)?
The amount of time that she is expected to stay in the system is; 7.5 Minutes
How to find the average of Exponential Functions?We are given;
The average number of arrivals of customers, λ = 12 students/hour.
The average service rate of a single server; μ = 20 students/hour.
The average of an exponential distribution is given by the formula:
E(X) = 1/μ
However, the amount of time that she is expected to stay in the system is;
t = 1/(μ - λ)
t = 1/(20 - 12)
t = 0.125 hours
Converting to minutes gives;
t = 0.125 * 60
t = 7.5 minutes
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Triplets Peter, Reeta and Nikita have two ways for getting home from school each day: cycle on a tandem bike or walk. The bike can carry either one or two riders at a time. Regardless of the number of people pedalling, cycling speed is 5 times walking speed. The triplets always leave school at the same time and always use the same path between school and home, whether walking or cycling. The school is 5 km from home and their walking speed is 4 kilometres per hour. a On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way home the bike gets a puncture, so Nikita and Peter walk the rest of the way home. How far from school is Reeta when the cyclists arrive home? b On Tuesday, Peter and Reeta ride the bike and Nikita walks. When the cyclists arrive home, Peter hops off the bike and Reeta rides back towards school to collect Nikita. How far from school is Nikita when Reeta reaches her? c On Wednesday, Reeta and Nikita take the bike and Peter walks. When the cyclists are halfway home, Reeta off and walks the rest of the way, while Nikita heads back to pick up Peter. How far from school is Reeta when her siblings pass her on the bike? d On Thursday, it is Reeta's turn to walk. Peter drops Nikita off at a certain point leaving her to walk home. Meanwhile he returns to pick up Reeta and they cycle home together. If all three arrive home at the same time, how far from school are the drop-off and pick-up points?
The distance between Reeta and the school when the cyclists arrive the home for this case is found to be 2 km
How to form mathematical expressions from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example, if it is asked to increase some items by 4, then you can add 4 in that item to increase it by 4. If something is, for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert descriptions to mathematical expressions.
How to find the speed of an object?
If the object is going linearly, and at a constant speed, then the speed of that object is given by the distance it travelled to the time it took to travel that distance.
If the object travelled D distance in T units of time, then that object's speed is
[tex]Speed = \dfrac{D}{T}[/tex]
Given that:
Distance from school to home = 5 kmWalking speed = 4 km / hoursCycling speed = 5 times walking speed = 20 km / hourThey all go and come together to and from school/home.On Monday: Nikita and Peter are coming by cycle, and Reeta walks.Cycle punctures at four-fifth of the way home = [tex]\dfrac{4}{5}\times 5[/tex] from school (as they're coming towards home, so went from school)After a puncture, cyclists walk to homeTo find the Distance of Reeta from school when the cyclist reaches home.Suppose at time 0 hours, all three people departed from school (on that Monday).
After 't' hours, suppose the cycle gets punctured.
Then, as the cycle was going by 20 km/hour speed, so in 't' hours, it must have covered d kilometres (suppose),
then we get:
[tex]S =\dfrac{D}{T}[/tex]
[tex]20=\dfrac{d}{t}[/tex]
d = 20t
This distance is measured from school. But we know that this distance is 4 km, so we get:
20t = 4
t = 1 / 4
The remaining 1 km (as the home is 5 km away from school and 4 km is already travelled) is walked by Cyclists. And walking speed is 5 km/hour, so let they take T hours to travel that 1 km walking, then we get:
5 = 1 / T
t = 0.2 hours
So, the total time cyclists took to reach home from school is: 0.2+0.2=0.4 hours
Reeta is walking that whole 5 km.
The time the cyclist reached home, Reeta had walked for 0.4 hours as they had started at the same time, and it took cyclists 0.4 hours to reach home.
Thus, we have:
Time is taken 0.4 hours, speed of Reeta = walking speed= 5 km/hour, then we get:
D = S x T
D = 5 x 0.4 = 2 km
So Reeta was 2 km away from school when cyclists reached home on that Monday.
Thus, the distance between Reeta and the school when the cyclists arrive at the home for this case is found to be 2 km
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A random sample of n 1 = 249 people who live in a city were selected and 87 identified as a democrat. a random sample of n 2 = 113 people who live in a rural area were selected and 58 identified as a democrat. find the 98% confidence interval for the difference in the proportion of people that live in a city who identify as a democrat and the proportion of people that live in a rural area who identify as a democrat.
Answer:
[tex]CI=\{-0.2941,-0.0337\}[/tex]
Step-by-step explanation:
Assuming conditions are met, the formula for a confidence interval (CI) for the difference between two population proportions is [tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z^*\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}[/tex] where [tex]\hat{p}_1[/tex] and [tex]n_1[/tex] are the sample proportion and sample size of the first sample, and [tex]\hat{p}_2[/tex] and [tex]n_2[/tex] are the sample proportion and sample size of the second sample.
We see that [tex]\hat{p}_1=\frac{87}{249}\approx0.3494[/tex] and [tex]\hat{p}_2=\frac{58}{113}\approx0.5133[/tex]. We also know that a 98% confidence level corresponds to a critical value of [tex]z^*=2.33[/tex], so we can plug these values into the formula to get our desired confidence interval:
[tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z^*\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\CI=\biggr(\frac{87}{249}-\frac{58}{113}\biggr)\pm 2.33\sqrt{\frac{\frac{87}{249}(1-\frac{87}{249})}{249}+\frac{\frac{58}{113}(1-\frac{58}{113})}{113}}\\\\CI=\{-0.2941,-0.0337\}[/tex]
Hence, we are 98% confident that the true difference in the proportion of people that live in a city who identify as a democrat and the proportion of people that live in a rural area who identify as a democrat is contained within the interval {-0.2941,-0.0337}
The 98% confidence interval also suggests that it may be more likely that identified democrats in a rural area have a greater proportion than identified democrats in a city since the differences in the interval are less than 0.
6 tractors take 10 days to collect the harvest. How long would it take 10 tractors to do the same work?
Answer:
6 days
Step-by-step explanation:
Relation :
Number of tractors ∝ 1/Number of days6 tractors took 10 days. Now, we have 10 tractors. This means the number of tractors has increased by 10/6 = 5/3. Therefore, the number of days will become 3/5 of the original time.
Solving :
10 × 3/52 × 36 daysKyle is considering a 7/1 ARM. What does 7 represent?
Answer:
The number of years the fixed interest rate will be applied to the loan
Step-by-step explanation:
I just guessed the answer was (The number of years the fixed interest rate will be applied to the loan)
The value of a in the equation, a-6=9 is
PLS HELP ME!!!
Answer:
15
Step-by-step explanation:
15-6=9 so a-6=9
Answer:
17
Step-by-step explanation:
17-6=9 (to double check your work and make sure it's right you do the opposite [9+6=17] )
Consider the system of equations. 3x + 2y = 16, x + y = 4 Which numerical values could you multiply the second equation by to eliminate a variable? Select all that apply. 2 -2 03 D-3 34 -4
Answer:
-2 and -3
Step-by-step explanation:
Answer:
answer in picture
Step-by-step explanation:
Deshawn earned $48 raking leaves last October. He decided to save 3/8 of his money. How much money did Deshawn save?