Answer:
13
Step-by-step explanation:
The average of any 5 consecutive numbers is the 3rd one (the middle one of the group). The third consecutive number starting from 11 is 13.
The average of {11, 12, 13, 14, 15} is 13.
There are 30 students in a class and 18 of them at least have 1 pet. what fraction of the class has pets Give your answer in its simplest form
Answer:
3/5
Step-by-step explanation:
3/5 pet is the exact fraction of pet that each student will have.
18 pets out of 30 students
= total pets divided by total students that would be 18/30
Simplifying 18/30 would make
9/15 first and then 3/5
So 3/5 is the answer
Consider the following function.
f(x) = 1 + 5/x - 4/x2
(a) Find the vertical asymptote(s).
(b) Find the interval where the function is increasing.
Find the interval where the function is decreasing.
(c) Find the local maximum and minimum values.
(d) Find the interval where the function is concave up.
Find the interval where the function is concave down.
Find the inflection point.
(e) Use the information from parts (a)-(d) to sketch the graph of f.
Answer:
See below
Step-by-step explanation:
I assume the function is [tex]f(x)=1+\frac{5}{x}-\frac{4}{x^2}[/tex]
A) The vertical asymptotes are located where the denominator is equal to 0. Therefore, [tex]x=0[/tex] is the only vertical asymptote.
B) Set the first derivative equal to 0 and solve:
[tex]f(x)=1+\frac{5}{x}-\frac{4}{x^2}[/tex]
[tex]f'(x)=-\frac{5}{x^2}+\frac{8}{x^3}[/tex]
[tex]0=-\frac{5}{x^2}+\frac{8}{x^3}[/tex]
[tex]0=-5x+8[/tex]
[tex]5x=8[/tex]
[tex]x=\frac{8}{5}[/tex]
Now we test where the function is increasing and decreasing on each side. I will use 2 and 1 to test this:
[tex]f'(2)=-\frac{5}{2^2}+\frac{8}{2^3}=-\frac{5}{4}+\frac{8}{8}=-\frac{5}{4}+1=-\frac{1}{4}[/tex]
[tex]f'(1)=-\frac{5}{1^2}+\frac{8}{1^3}=-\frac{5}{1}+\frac{8}{1}=-5+8=3[/tex]
Therefore, the function increases on the interval [tex](0,\frac{8}{5})[/tex] and decreases on the interval [tex](-\infty,0),(\frac{8}{5},\infty)[/tex].
C) Since we determined that the slope is 0 when [tex]x=\frac{8}{5}[/tex] from the first derivative, plugging it into the original function tells us where the extrema are. Therefore, [tex]f(\frac{8}{5})=1+\frac{5}{\frac{8}{5}}-\frac{4}{\frac{8}{5}^2 }=\frac{41}{16}[/tex], meaning there's an extreme at the point [tex](\frac{8}{5},\frac{41}{16})[/tex], but is it a maximum or minimum? To answer that, we will plug in [tex]x=\frac{8}{5}[/tex] into the second derivative which is [tex]f''(x)=\frac{10}{x^3}-\frac{24}{x^4}[/tex]. If [tex]f''(x)>0[/tex], then it's a minimum. If [tex]f''(x)<0[/tex], then it's a maximum. If [tex]f''(x)=0[/tex], the test fails. So, [tex]f''(\frac{8}{5})=\frac{10}{\frac{8}{5}^3}-\frac{24}{\frac{8}{5}^4}=-\frac{625}{512}<0[/tex], which means [tex](\frac{8}{5},\frac{41}{16})[/tex] is a local maximum.
D) Now set the second derivative equal to 0 and solve:
[tex]f''(x)=\frac{10}{x^3}-\frac{24}{x^4}[/tex]
[tex]0=\frac{10}{x^3}-\frac{24}{x^4}[/tex]
[tex]0=10x-24[/tex]
[tex]-10x=-24[/tex]
[tex]x=\frac{24}{10}[/tex]
[tex]x=\frac{12}{5}[/tex]
We then test where [tex]f''(x)[/tex] is negative or positive by plugging in test values. I will use -1 and 3 to test this:
[tex]f''(-1)=\frac{10}{(-1)^3}-\frac{24}{(-1)^4}=-34<0[/tex], so the function is concave down on the interval [tex](-\infty,0)\cup(0,\frac{12}{5})[/tex]
[tex]f''(3)=\frac{10}{3^3}-\frac{24}{3^4}=\frac{2}{27}>0[/tex], so the function is concave up on the interval [tex](\frac{12}{5},\infty)[/tex]
The inflection point is where concavity changes, which can be determined by plugging in [tex]x=\frac{12}{5}[/tex] into the original function, which would be [tex]f(\frac{12}{5})=1+\frac{5}{\frac{12}{5}}+\frac{4}{\frac{12}{5}^2 }=\frac{43}{18}[/tex], or [tex](\frac{12}{5},\frac{43}{18})[/tex].
E) See attached graph
solve for m -7/9 m = 11/6
Answer:
19/18
Step-by-step explanation:
substitute the value of m(11/6) in m-7/9
which is equal to 11/6 -7/9 =19/18
what percent of 75cm is 5cm
Answer:
6.67%
Step-by-step explanation:
5 / 75 = 0.066667
(0.066667)(100) = 6.67%
What is the value of
negative 3/4 with negative 4 as a exponent
Answer:
=[tex]\frac{256}{81}[/tex]
(Decimal: 3.160494)
Step-by-step explanation:
[tex](\frac{3}{4} )^-4[/tex]
[tex](\frac{4}{3} )^4[/tex]
[tex]\frac{4^4}{3^4}[/tex]
=[tex]\frac{256}{81}[/tex]
(Decimal: 3.160494)
:)
I hope this helps
How much would you have to deposit today to have an accumulated amount 20,000 in 20 years if yearly interest is 4.75% compounded continuously?
The principal investment required to get a total amount of $20,000.00 from compound interest at a rate of 4.75% per year compounded 12 times per year over 20 years is $7,749.34
Given dataPrincipal =?
Final amount = $20,000
rate = 4.75%
Time = 20 years
First, convert R as a percent to r as a decimal
r = R/100
r = 4.75/100
r = 0.0475 per year,
Then, solve the equation for P
P = A / (1 + r/n)^(nt)
P = 20,000.00 / (1 + 0.0475/12)^(12)(20)
P = 20,000.00 / (1 + 0.003958333)^(240)
P = $7,749.34
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What is correct A, B or C
Answer:
A is the correct solution
Step-by-step explanation:
3x³ + 4x² + 0x - 1 / x - 2
3 10 20
-2 | 3 4 0 -1
- (3 -6)
10 0
- (10 -20)
20 -1
- (20 -40)
39
3x² + 10x + 20 + 39/(x - 2)
round to nearest ten thousand
887,173
Which of the following describes exponential decay?
A. The amount at a given time can be calculated by multiplying the previous amount
by a value greater than 1.
B. The amount at a given time can be calculated by multiplying the previous amount by a value less than 1.
C. The amount at a given time can be calculated by adding an amount to the previous amount.
D. The amount at a given time can be calculated by subtracting an amount from the previous amount.
The amount at a given time can be calculated by multiplying the previous amount by a value less than 1, which represents exponential decay. Hence, option B is the right choice.
What does linear function mean?A quantity grows (or depreciates) linearly if it increases (or decreases) by the same amount per unit of time.
What does exponential function mean?A quantity grows (or depreciates) exponentially if the increase (or decrease) in the amount is a multiple of the previous amount.
How to solve the question?In the question, we are asked to identify the option that best describes an exponential decay.
We assess each option and try to identify the exponential decay among them.
A. The amount at a given time can be calculated by multiplying the previous amount by a value greater than 1: This is an exponential function as it is multiplied by the previous amount, but it shows exponential growth as the quantity multiplied is greater than 1.B. The amount at a given time can be calculated by multiplying the previous amount by a value less than 1: This is an exponential function as it is multiplied by the previous amount, and it shows exponential decay as the quantity multiplied is less than 1.C. The amount at a given time can be calculated by adding an amount to the previous amount: This is a linear function as a fixed quantity is added.D. The amount at a given time can be calculated by subtracting an amount from the previous amount: This is a linear function as a fixed quantity is subtracted.Therefore, the amount at a given time can be calculated by multiplying the previous amount by a value less than 1, which represents exponential decay. Hence, option B is the right choice.
Learn more about exponential functions at
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Mr. Herman's class is selling candy for a school fundraiser. The class has a goal of raising $500 by selling c
boxes of candy. For every box they sell, they make $2.75.
Write an equation that the students could solve to figure out
how many boxes of candy they need to sell.
Answer:
500=2.75c
Step-by-step explanation:
500= 2.75c
Isolate c by dividing 2.75 on each side
500/2.75 =181.818181818 which is about 181.8
So the students need to sell about 181.8 boxes of candy in order to reach their goal of $500.
20 kilograms increased by 25%
Answer:
25 kilograms
Step-by-step explanation:
Emilio has 8 large bottles of soda and 12 large jugs of water. Emilio wants to set up identical tables and have no drinks left over. What is the greatest number of tables that he can set up?
Answer:
4
Step-by-step explanation:
Think about the ratio between the current number of large bottles of soda(8) and the current number of jugs of water (12)
By finding the GCF (Greatest Common Factor) of the two numbers, we can conclude that if both numbers were to be divided by the GCF, 4, we would get a 2:3 ratio.
For every 2 bottles of soda, 3 jugs of water will be placed. Keep doing this until we run out of both sources of liquid, in this case, 4 tables where we would use all the bottles of soda and the jugs of water.
Graph the function g(x) = 2x2 + 8x - 1
Answer:
(-2,-9)
(0,-1)
Step-by-step explanation:
I solved in desmos.
Mrs. Harris treated her 1st period with donuts for averaging the highest on the midterm exam. She bought 25 donuts, By the end of the period, there were 3 donuts remaining. What is the percent decrease?
Answer:
88% decrease
Step-by-step explanation:
3 is only 12% of 25 so there was a 88% decrease
Solve for x. 2^4x-7=16
Answer:
23/16
Step-by-step explanation:
2*4 x x-7 = 16
16x - 7 = 16
16x = 16 + 7
16x = 23
x = 23/16
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NEED NOW PLEASE.....
Tell which value of the variable is the solution of the equation.
s−4.3=0; s=4.3, 4.4, 4.5, 4.6
Question content area bottom
Part 1
Which of the following is the solution of the equation?
A. 4.3
B. 4.5
C. 4.4
D. 4.6
E. No solution is given in the set of values
Answer:
a
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.shshs
I need help this is easy tho!
Answer:
it is true
it's a quadralateral
One mom has 3 children, and each child attends a different level of school. If the mom plans to pick her children up, what would be her total distance traveled if she starts at the high school, then goes to the elementary school, and finally the middle school? (Write your answer as a decimal rounded to the nearest tenths place). *
Answer: I need the map good sir please show it
Step-by-step explanation:
Question Write an equation of the line passing through the point A(0, 3) that is perpendicular to the line y = −1/2x−6
Answer:
The equation would be y=2x+3 I am pretty sure
Step-by-step explanation:
This is because you take the slope which is 2 from the line y=-1/2x-6. To find the slope perpendicular to the line, you need to find the exact opposite of the slope: -1/2, and in this case, it would be 2.
(Ex: if it was -3/4, you would need to use a slope of 4/3 since it is the opposite)
Then you take that slope (2) and the point (0, 3) and put it into "y-y1=m(x-x1)"
y-y1=m(x-x1)
y-3=2(x-0)
-distribute the 2-
y-3=2x-0
-add 3 on both sides-
so equation would be y=2x+3
Not sure if this is all correct, but I hope it helps! :)
Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire station receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are under 3 minutes? Find the z-table here. 6.68% 10.56% 89.44% 93.32%
Answer:
mean = 4.5
SD = 1.2
Z value = (3-4.5)/1.2 = - 1.25
Percentage based on z value = 1 - pnorm(1.25) = 0.1056498 = 10.56498%
The response times under 3 minutes is 10.56%
What is Normal Distribution?'Normal distribution is a continuous probability distribution wherein values lie in a symmetrical fashion mostly situated around the mean.'
According to the given problem,
mean = 4.5
SD = 1.2
Z value = [tex]\frac{3 - 4.5}{1.2}[/tex] = - 1.25
Percentage based on z value = 1 - pnorm(1.25)
= 0.1056498
= 10.56498%
Hence, we can conclude that the response time of fire station under 3 minutes is 10.56%.
Learn more about normal distribution here: https://brainly.com/question/11876263
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Recall the method that the video showed to solve Gavin’s word problem. The video showed how we can use numerical expressions (with the help of a diagram) to arrive at a solution.
Compare the expression method from the video with the equation method that uses the variable b. Do both methods use the same sequence of operations?
Answer:
There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method.
Step-by-step explanation: hope this helps :)
Help help math please I don’t understand
Answer:
45°
Step-by-step explanation:
it's a mirror angle to the known angle
Find the length of the second base of a trapezoid with one base measuring 12 feet,a height of 4,and an area of 58 square feet.
Answer:
Step-by-step explanation:
A = ½(b₁ + b₂)h
b₂ = 2A/h - b₁
b₂ = 2(58)/4 - 12
b₂ = 17 ft
Mandy has 37 red markers and 24 green markers. She wants to place an equal number of markers on 4 tables. What is the greatest number of markers she could place on each table ? Explain please
Answer:
15 marker's
Step-by-step explanation:
37+24=61
61÷4=15.25
because she wants an even number of makers the answer is 15.
if h(x) =5 for the function h(x) =2x+1, what is the value of x?
12
11
2
Answer:
2
Step-by-step explanation:
5=2x+1
5-1=2x
2x=4
x=2
Answer:
x = 2
Step-by-step explanation:
2x+1 = 5
-1 -1
-------------
2x = 4
x = 2
hope this helps! :D
have a miraculous day, and brainliest is immensely appreciated!! <3
Which of the following is an equilateral triangle based on the given figure?
Check the picture below.
Answer:
ΔABEStep-by-step explanation:
In ΔBCD,
Two sides are equal, i.e,
BC = CD
therefore, it is a Isoceles Triangle.
In ΔBDE,
No sides are equal,
therefore, it is Scalene Triangle.
In ΔABE,
AB = BE = AE
Therefore, it is equilateral triangle.
Hope it helps you!!Given the line segment AD. AD=24 BC=12,AB=CD Find AB ?
Answer:
I think its 6
Step-by-step explanation:
emma is finding 7/2 x 2/5
Answer:
14/10
OR
7/5
Step-by-step explanation:
(7*2)/(2*5) = 14/10
(14/2) / (10/2) = 7/5
Answer:
Mixed fraction: 1 2/5
Decimal form: 1.4
Hope this helps :)
Write an equation involving absolute value or the graph
Answer:
Step-by-step explanation:
2 AND 4