Answer:
It means [tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex] also converges.
Step-by-step explanation:
The actual Series is::
[tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex]
The method we are going to use is comparison method:
According to comparison method, we have:
[tex]\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n[/tex]
If series one converges, the second converges and if second diverges series, one diverges
Now Simplify the given series:
Taking"n^2"common from numerator and "n^6"from denominator.
[tex]=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}[/tex]
[tex]\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}[/tex]
Now:
[tex]\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}[/tex]
So a_n is finite, so it converges.
Similarly b_n converges according to p-test.
P-test:
General form:
[tex]\sum_{n=1}^{inf}\frac{1}{n^p}[/tex]
if p>1 then series converges. In oue case we have:
[tex]\sum_{n=1}^{inf}b_n=\frac{1}{n^4}[/tex]
p=4 >1, so b_n also converges.
According to comparison test if both series converges, the final series also converges.
It means [tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex] also converges.
joey collects 100 seashells. 45% of them are pink. how many shells are not pink. how many are pink .
Answer:
45 are pink 55 are not pink
Step-by-step explanation:
a) The number of pink seashells is A = 45
b) The number of seashells that are not pink = 55
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the total number of seashells be = 100
Let the percentage of the seashells that are pink = 45 %
If 45% of the 100 seashells are pink, then the remaining 55% must be not pink. We can find the number of pink shells by multiplying 100 by 45%:
Number of pink shells = 100 x 0.45 = 45
To find the number of shells that are not pink, we can subtract the number of pink shells from the total number of shells:
Number of shells not pink = 100 - 45 = 55
Hence , there are 55 seashells that are not pink and 45 seashells that are pink.
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Simplify (2+3)^2+8/2
Answer:
Exact Form: − 29 30 Decimal Form: − 0.9 ¯ 6
Hoped I helped
HELPPPPPP doing a last attempt
Answer:
irational number, non-repeating
Andrew drove 45 more miles than Nicole. If they drove a combined total of 111 miles, how many miles did Nicole drive?
Answer:
Nicole drove 66 miles.
Step-by-step explanation:
You can set of an equation of 45 - x = 111 x representing the amount of miles Nicole drove. You would subtract 45 from both 45 and 111 and get that x = 66.
The average temperature in a northern Canadian city is 1 degree Fahrenheit. The actual temperature in January differs by 10 degrees. (use x as the variable |x(+or-)#|=# | -------- | = ----------
Answer:
x+10
Step-by-step explanation:
How do you do this Please Explain how you did
Answer:
Domain : (- ∞, - 5), and (3 / 2, ∞),
Range : (∞, 0.4437]
Step-by-step explanation:
Assuming that we want our answer in interval notation, let's start by determining the domain. Remember that the domain can be found where the function is undefined.
Given : f(x) = (2x - 7) / (2x² + 7x - 15)
Alternative Form : (2x - 7) / (x + 5)(2x - 3)
To receive this 'alternative form' we can simply factor the expression 2x² + 7x - 15. See the procedure below,
[tex]\mathrm{Given : 2x^2+7x-15} ,[/tex]
[tex]\mathrm{Break\:the\:expression\:into\:groups : \left(2x^2-3x\right)+\left(10x-15\right)} ,[/tex]
[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-3x\mathrm{:\quad }x\left(2x-3\right),\\\mathrm{Factor\:out\:}5\mathrm{\:from\:}10x-15\mathrm{:\quad }5\left(2x-3\right),[/tex]
[tex]x\left(2x-3\right)+5\left(2x-3\right) = \left(2x-3\right)\left(x+5\right) - \mathrm{Factored\:expression}[/tex]
Now let's find the domain using the expression '(x + 5)(2x - 3) = 0.' If the denominator equals 0, the function is considered undefined.
[tex]\mathrm{Given : \left(x+5\right)\left(2x-3\right)=0} ,\\x+5=0:\quad x=-5, 2x-3=0:\quad x=\frac{3}{2}\\\mathrm{The\:solutions\:are: x=-5,\:x=\frac{3}{2}}[/tex]
Knowing these solutions the domain has the intervals (- ∞, - 5), and (3 / 2, ∞). The range is the set of values that correspond to the domain, so in this case the range would be (∞, 42 + 8√17 / 169]. 42 + 8√17 / 169 = (About) 0.4437, so it lies on the interval (∞, 0.4437].
The images below represent the plotted function in two areas. There are 3 curves in this graph.
PLZ ANSWER FAST!! CORRECT ANSWER GETS BRAINLIEST!!
Answer:
(Weight (lb), Price ($) ) = (0.45,2.3)
That means :
Weight (lb) = 0.45 when Price ($) = 2.31) So, if we want to find the price per pound, we'll divide 2.3 by 0.45:
=> [tex]\frac{\$ 2.3}{0.45 \ lb}[/tex] [True]
2) Second Statement: [False]
The weight of every 0.45 lb of bag is 2.3 pounds not for per bag.
3) Third Statement: [False]
2.3 pounds of almonds cost $0.45
This is incorrect according to the graph.
4) Fourth Statement: [False]
Almonds cost $0.45 per pound
Let's check it out
0.45 lb = $2.3
Dividing both sides by 0.45
1 lb = $5.11
It is not $4.5
5) Fifth Statement: [True]
0.45 pounds of almond costs $2.30
For every 0.45 pounds, there are $2.30 . So, this statement is true!
Sam owns a vegetable stand. He tracks the price of potatoes, p, in dollars per pound
throughout the year. In the beginning of the year, the price of potatoes rose gradually
until it peaked in the third month. After that, the price declined until it bottomed out in
the seventh month of the year. Then, the price of potatoes rose to peak again near the
end of the year.
Answer:
What's the question, what are you meant to find??
What is the volume of the pyramid shown below?
Step-by-step explanation:
Given:
h=7in
w=9in
l=6in
Required:
v=?
Formula:
v=l*w*h
Solution:
v=l*w*h
v=6in*9in*7in
v=54in^2*7in
v=378in^3
Hope this helps ;) ❤❤❤
A car, starting from a city, traveled east for 100 km and then west for
130 km. How far from City was the car at the end of the trip?
Fill in the blank. In a _______ distribution, the frequency of a class is replaced with a proportion or percent.
Answer:
Relative frequency
Step-by-step explanation:
In a relative frequency distribution, the frequency of a class is replaced with a proportion or percent.
A relative frequency distribution displays how the proportion of totality of the observations related to each class is correlated to the probability distribution. A relative frequency distribution shows the proportion of times a value occurs in each class. It can be determined by the division of the frequency with the total number of data values.
When we are choosing a random sample and we do not place chosen units back into the population, we are
If the population does not follow the normal probability distribution, the Central Limit Theorem tells us that the sample means will be normally distributed with sufficiently large sample size. In most cases, sample sizes of 5 or more will result in sample means being normally distributed, regardless of the shape of the population distribution.a) trueb) false
Answer:
The correct option is false
Step-by-step explanation:
Generally the Central Limit Theorem tells us that the sample means will be normally distributed with sufficiently large sample size( i.e [tex]n \ge 30[/tex] ) regardless of the shape of the population distribution.
But the question states that the mean is normally distributed if the sample size is 5 or more which is false hence the statement is false
PLS HELP BEST ANSWER GETS BRAINLIEST Find the volume of the rectangular prism with edge lengths of 1/2, 2/3, and 4/3.
Answer:
4/9 cubic units
Step-by-step explanation:
The volume of a rectangular prism is the product of its edge lengths:
V = LWH
V = (1/2)(2/3)(4/3) = (1·2·4)/(2·3·3) = 4/9 . . . . cubic units
Find the rate of change of f(x, y, z) = xyz in the direction normal to the surface yx2 + xy2 + yz2 = 3 at (1, 1, 2).
Answer:
Rate of change = 18/√74
Step-by-step explanation:
The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v
Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;
∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)
So;
∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))
This gives;
∇g(1, 1, 2) = (3, 7, 4)
Now,
||∇g(1, 1, 2)|| = √(3² + 7² + 4²)
||∇g(1, 1, 2)|| = √74
Normal vector would be given by the formula;
v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]
Thus;
v = (3, 7, 4)/√74
Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)
Thus, rate of change is given by;
∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74
This gives;
Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74
Form the union for the following sets.
M={ }
N = {6, 7, 8, 9, 10)
MUN=
MUN = {6, 7, 8, 9, 10}
Step-by-step explanation:
M={ }
N = {6, 7, 8, 9, 10)
MUN = {6, 7, 8, 9, 10} .. (because A∪∅=A)
Find the area of the triangle whose base is 12 cm and height is 4 cm.
Answer:
A = 24 cm^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
A = 1/2 (12)*4
A = 24 cm^2
Answer:
1/2bh.
1/2×12×4= 1/2×48.
=24cm^2
A 17ft ladder leans against the side of a house. The top of the ladder is 15 ft off the ground. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree
Answer:
SOHCAHTOA.
We are to use SOH in this question because we have the opposite which is 15 and the hypotenuse which is 17.
which will be Sin theta =15/17.
Sin theta =0.8823~1.
then Sin theta =1.
which is theta = (inverse of sin) sin^-1(1).
theta =90°.
Answer:x = theta =90°.
Step-by-step explanation:
Need Help on this Part
To determine the 'intervals of increase' and 'intervals of decrease' we can refer to the graph with respect to the x - axis.
• Knowing that t = x - axis, the 'intervals of increase' as an inequality would be 1 < x < 3, and 4 < x < ∞. Therefore we have our intervals of increase as (1,3) and (4, ∞).
• Respectively our 'intervals of decrease' as inequalities would be - ∞ < x < 1, and 3 < x < 4. Our intervals of decrease would then be (- ∞, 1) and (3,4).
• We are left with our local extrema and absolute extrema. Now remember the absolute extrema is the absolute lowest point in the whole graph, while the local extrema is the lowest point in a restricted interval. In this case our local extrema is our maximum, (3,1). But this maximum is not greater than the starting point (0, 4) so it appears, and hence their is no absolute extrema.
Write the mixed number as a decimal. 4 9/20
120 = -5 (2m - 7) + 5 Multi - Step
Answer:
Step-by-step explanation:
-10m + 35 + 5 = 120
-10m + 40 = 120
-10m = 80
m = -8
Solve 12x + 4y = 20 for y.
A. y=-3x+ 20
B. y = -12x+ 20
C. y= 12x+ 5
D. y=-3x+ 5
Answer:
D. y= -3x+ 5
Step-by-step explanation:
[tex]12x + 4y = 20[/tex]
Move 12x to the right and change its sign
[tex]4y =20-12x[/tex]
Divide through by 4
[tex]\frac{4y}{4} = \frac{20}{4} -\frac{12x}{4} \\\\Simplify\\y = 5-3x\\y =-3x+5[/tex]
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{y = - 3x + 5}}}}}[/tex]
Option D is the correct option.
Step-by-step explanation:
[tex] \sf{12x + 4y = 20}[/tex]
Move 12x to right hand side and change it's sign
⇒[tex] \sf{4y = - 12x + 20}[/tex]
Divide both sides of the equation by 4
⇒[tex] \sf{ \frac{4y}{y} = \frac{ - 12x + 20}{4} }[/tex]
⇒[tex] \sf{y = \frac{ - 12x}{4} + \frac{20}{4} }[/tex]
Divide -12x by 4 . Also divide 20 by 4
⇒[tex] \sf{y = - 3x + 5}[/tex]
Hope I helped!
Best regards!! :D
what is thirty two percent of fifty six
Answer: 17.92
Step-by-step explanation:
32% of 56
Change to fraction
32 /100 x 56
Change to decimal
0.32 x 56
= 17.92
what do 16 and 24 have in common
Answer:
both are positive even composite integers with a common factor of 8.
Step-by-step explanation:
Both are positive even composite integers with a common factor of 8. They are solutions to the quadratic equation (x-16)(x-24) = 0. Their cube roots (or any root of index greater than 2) are irrational. They are divisors of 48.
There are also many things that both numbers are not. They are not the lengths of sides of a right triangle with integer side lengths. They are not negative or irrational. They are not triangle numbers or elements of the Fibonacci sequence.
x + y = 12 and y = x - 1.
Find the value of 2x + 2y.
Answer:
2x + 2y = 24
Step-by-step explanation:
You have to isolate y and then use substitution.
x + y = 12 and y = x - 1
-x -x
y = -x + 12 and y = x - 1
-x + 12 = x - 1
+x +x
--------------------
12 = 2x - 1
+1 +1
----------------
13 = 2x
2x = 13 [ divide both sides by 2]
x = 6.5
Now, you have to plug x (6.5) into y = x - 1.
y = x - 1
y = 6.5 - 1
y = 5.5
Finally, plug both x (6.5) and y (5.5) into 2x + 2y.
2x + 2y
= 2 (6.5) + 2 (5.5)
= 13 + 11
= 24
Jimmy is putting in tile floors in his living room. He ordered 20 boxes of tiles, but only 16 arrived. What percent of the order is missing?
Answer:
400%
Step-by-step explanation:
20-16=4
4*100%=400%
Why is it important to line up the decimal points?
In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 75% of adults say that it is morally wrong to not report all income on tax returns.a. What is the null and alternative hypothesis?b. What is the test statistic?c. What is the P-value?d. What is the Conclusion?
Answer:
a
The null hypothesis is [tex]H_o : p = 0.75[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.75[/tex]
b
[tex]t = 2.51[/tex]
c
[tex]p-value = 0.01207[/tex]
d
There no sufficient evidence to conclude that 75% of adults say that it is morally wrong to not report all income on tax returns
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 745[/tex]
The number that said it is morally wrong is [tex]k = 589[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The population proportion is [tex]p = 0.75[/tex]
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
=> [tex]\r p = \frac{589}{745}[/tex]
=> [tex]\r p = 0.79[/tex]
The null hypothesis is [tex]H_o : p = 0.75[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.75[/tex]
The standard error is mathematically represented as
[tex]SE = \sqrt{\frac{p(1-p)}{n} }[/tex]
=> [tex]SE = \sqrt{\frac{0.75(1-0.75)}{745} }[/tex]
=> [tex]SE =0.0159[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\r p - p }{SE}[/tex]
=> [tex]t = \frac{0.79 - 0.75 }{0.0159}[/tex]
=> [tex]t = 2.51[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(Z > 2.51)[/tex]
From the the z-table
[tex]P(Z > 2.51) = 0.0060366[/tex]
=> [tex]p-value = 2 * 0.0060366[/tex]
=> [tex]p-value = 0.01207[/tex]
From the calculation [tex]p-value >\alpha[/tex]
Hence we fail to reject the null hypothesis
Thus there no sufficient evidence to conclude that 75% of adults say that it is morally wrong to not report all income on tax returns
What is the distance between (-1, -2) and (2, 2)?
Answer: The distance would be, (3, 4)
2. True False 6(10 + 5) - 6.10 + 6.5
[tex]10 + 5 - 6.10 + 6.5 \times 6[/tex]
Answer:
47.9Step-by-step explanation:
[tex]10 + 5 - 6.10 + 6.5 \times 6 \\ [/tex]
Follow PEDMAS
[tex]10 + 5 - 6.10 + 39[/tex]
[tex]15 - 6.10 + 39 \\ 15 + 39 - 6.10 \\ 54 - 6.10 \\ = 47.9[/tex]