The given series Σ((-1)^n * n / n^3 * 5) where n starts from 1 and goes to infinity converges by the Alternating Series Test.
To test the given series for convergence or divergence, we will use the Alternating Series Test. The series can be written as:
Σ((-1)^n * n / n^3 * 5), where n starts from 1 and goes to infinity.
Now, let's check the two conditions for the Alternating Series Test:
1. The sequence of absolute values of the terms, a_n = n / n^3 * 5, must be decreasing. This can be simplified to a_n = 1 / (n^2 * 5). Since the denominator increases as n increases, the sequence of absolute values is indeed decreasing.
2. The limit of the absolute values of the terms must be 0 as n approaches infinity. Taking the limit as n -> ∞, we get lim (1 / (n^2 * 5)) = 0, which satisfies this condition.
Since both conditions are met, the series converges by the Alternating Series Test.
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Paki answer po fi d the value of k mentally
Answer:
We have 5 equations where we want to find the value of k. To find the value of k first solve the term that is multiplicating k, and when we know the term, we can divide both sides to isolate k in one side of the equation.
1) 30 = k*(15/4)
To solve this, we can just multiply by (4/15) in both sides, so we get:
30*(4/15) = k*(15/4)*(4/15)
(30/15)*4 = k
2*4 = k
8 = k
2) 360 = k*√36
Here you need to remember that:
6*6 = 36
then √36 = 6
We could just replace that in the equation:
360 = k*6
now let's divide both sides by 6.
360/6 = k*6/6
60 = k
3) 64 = k*(4²)*(2²)
Here we need to remember that:
4² = 16
2² = 4
We can replace these in the equation to get:
64 = k*16*4
and 4*16 = 64
then:
64 = k*64
Now let's divide both sides by 64.
64/64 = k*64/64
1 = k
4) 100 = k*(25)*(4)
Here we know that 4*25 = 100
So replacing that in the equation we get a similar expression to the above one.
100 = k*100
Now let's divide both sides by 100
100/100 = k*100/100
1 = k
5) 6 = k*3
Here just divide both sides by 3.
6/3 = k*3/3
2 = k
Find the coordinates of the point P that divides the directed line segment from A to B in the given ratio. A(−9, −1), B(11, 9); 3 to 2
Answer:
(-2.5, 7.5)
Step-by-step explanation:
Find the coordinates of the point P that divides the directed line segment from A to B in the given ratio. A(−9, −1), B(11, 9); 3 to 2
Using the formula for calculating the mid point segment expressed as;
X = ax1+bx2/a+b
Y = ay1+by2/a+b
Given
x1 = -9, y1 = -1, x2 = 11, y2 = 9, a = 3 and b = 2
Substitute
X = 3(-9)+2(11)/2
X = -27+22/2
X = -5/2
X = -2.5
Similarly
Y = 3(-1)+2(9)/2
Y = -3+18/2
Y = 15/2
Y = 7.5
Hence the required coordinate point is (-2.5, 7.5)
Which of the following best describes the solution to the system of equations below?
6x + 5y=8
6x + 5y=15
A. The system of equations has infinitely many solutions.
B. The system of equations has exactly one solution where x=0 and y =8/5
C. The system of equations has no solution.
D. The system of equations has exactly one solution where x = 8 and y= 15.
Answer:
the correct answer is C the system of equations has no solution.
6 74/500 as a decimal (giving another chance for brainliest)
Answer:
6.148
Step-by-step explanation:
Desmond spends $800 per month on fixed expenses. Desmond earns $10,00 per hour,
How many hours does Desmond need to work each month to spend 50% of his/her income
on fixed expenses?
Answer: 160 hours
============================================================
Explanation:
He earns $10.00 an hour. Let x be the number of hours worked in a month. So 10x represents how much he earns after working x hours.
If he spends $800 per month on fixed expenses, and wants this to be 50% of his total earnings, then this must mean that the other 50% is for other things (eg: spending on a vacation or putting it to savings). So his goal is to earn 800+800 = 1600 dollars per month.
Set 10x equal to this and solve for x
10x = 1600
x = 1600/10
x = 160
He needs to work 160 hours a month.
-------------------------------
Extra info:
Divide 160 over 4 (the approximate number of weeks in a month) and we see that he'll need to work 160/4 = 40 hours a week
If he only works Monday through Friday, that's 5 days of the week. So he'll put in 40/5 = 8 hours per day.
So his goal of working 160 hours per month is reasonable. Keep in mind that this doesn't include factors like him missing time from work due to being sick (unless he has paid sick leave).
Enter the correct answer in the box.
What is the standard form of function f?
[tex]f(x)=4(x+6)^2+5[/tex]
Substitute numerical values into the equation for a, b, and c.
[tex]f(x)=ax^{2} +bx+c[/tex]
Answer:
f(x) = 4x² + 48x + 149
Step-by-step explanation:
Given
f(x) = 4(x + 6)² + 5 ← expand the factor using FOIL
= 4(x² + 12x + 36) + 5 ← distribute parenthesis by 4
= 4x² + 48x + 144 + 5 ← collect like terms
= 4x² + 48x + 149 ← in standard form
Answer:
Have a great rest of your day ;)
Step-by-step explanation:
A square is cut diagonally into two equal parts. If each part has an area of 50 cm^2, then what is the perimeter of each part?
I tried it isn't 30 cm
Answer:
30cm
Step-by-step explanation:
Given data
When are square is cut diagonally into two parts
The resulting shape is a triangle
hence the area of the square = 50+50 = 100cm^2
The length of each side of the square = √100= 10cm
likewise the diagonal of the square = 10cm
Hence the perimeter of the resulting triangle= 10+10+10= 30cm
Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she
drinks in a week?
There are 16 cups in a gallon.
Answer:
Katie drinks 56 cups (3.5 gallons) of water in one week.
Step-by-step explanation:
16 - 0.5 (1/2) = 0.5 (1/2)
16 - 1/2 = 8
8 x 7 days (1 week)
= 56 cups
Katie drinks 56 cups (3.5 gallons) of water in one week.
Your teacher asked your class to describe a real world situation in which a y-intercept is 100 and the slope is 5. Your partner gave the following description: My younger brother originally had 100 small building blocks, but he has lost 5 of them every month since. What mistake did your partner make?
Answer:
He should have said that his small brother had 100 small building bricks, but lost 5 in total now.
how many times can 1/4 go into 6
Answer:
24 times
Step-by-step explanation:
Answer:24
Step-by-step explanation:
I need a lot of help please ):
And if u don’t know the answers do not comment anything because i'm really looking for help!
Answer:
The answer are
CX=10/3
ML=76
Step-by-step explanation:
NUMBER 4
We know that the averages are divided 1 to 2 by the base
[tex]then \: \\ xc = \frac{1}{3} xf \\ = \frac{1}{3} \times 1 0 = \frac{10}{3} [/tex]
NUMBER 5
[tex]ml = \frac{2}{3} mr \\ then \\ 10x - 4 = \frac{2}{3} (12x + 18) \\ 30x - 12 = 24x + 36 \\ 6x = 48 \\ x = 8 \\ then \\ ml = 10 \times 8 - 4 = 76[/tex]
please help!
In right triangle ABC, angle C is a right angle, AB = 13, and BC = 5.
What is the length of AC?
Answer:
Step-by-step explanation:
AC=[tex]\sqrt{13^{2} -5^{2} }[/tex]
=12
graph x<2/9 on a number line
Answer:
The line should begin on the right side 2 dashes (the small lines tht go throught the number line. There are 9 dashes between each whole number.)
Then the line should go left because it says x is less than 2/9. (which is right)
The line segment you should choose is the one with the open circle with an arrow going to the left.
<---O (looks like this lol.)
Half of Ethan string is equal to 2/3 of Kayla stream the total length of the string is 10 feet how much longer is Ethan string Kayla string
Answer:
10/7 feet
Step-by-step explanation:
Let e = Ethan
k = Kayla
The following equations can de derived from the equation :
1/2 e = 2/3k
multiply both sides of the equation by 2
e = 4/3k --- 1
e + k = 10 --- 2
Substitute for e in equation 2
4/3k + k = 10
7/3k = 10
multiply both sides of the equation by 3/7
k = 30/7
Substitute for k in equation 1
e = (4/3) x 30/7 = 40/7
difference in length = 40/7 - 30/7 = 10/7
what is m
A.
B.
C.
D.
Answer: .B.
Step-by-step explanation
Please please help I will give brainliest
Answer:
67
4*4*4=64
64+3=
67
2(3x-9)=2x+10 what's x
Answer:
x = 7
Step-by-step explanation:
2(3x-9)=2x+10
6x - 18 = 2x + 10
4x = 28
x = 7
Answer:
x = 7
Step-by-step explanation:
In order to find the value of x, isolate it in the equation.
1) First, distribute the 2 to the terms inside the set of parentheses.
[tex]2 (3x - 9) = 2x + 10 \\6x - 18 = 2x + 10 \\[/tex]
2) Next, move all the x terms to one side and all the other terms to the other side. Subtract both sides by 2x and add both sides by 18.
[tex]6x - 18 = 2x + 10 \\4x = 28[/tex]
2) Divide both sides by 4 to finally isolate x.
[tex]4x = 28 \\x = 7[/tex]
Thus, x = 7.
The surface area of a rectangular prism is increased by a factor of 16.
By what factor is the volume of the figure increased?
O4
O 8
O 32
O 64
Answer:
C. 32
Explanation:
The square-cube law states that "When an object undergoes a proportional increase in size, its new surface area is proportional to the square of the multiplier and its new volume is proportional to the cube of the multiplier." This means that if the surface area of the cube is increased by a certain amount, the volume of the cube will increase by the cube of that.
Please give Brainliest
Works Cited:
https://en.wikipedia.org/wiki/Square%E2%80%93cube_law#:~:text=The%20square%E2%80%93cube%20law%20can,the%20cube%20of%20the%20multiplier.
The solution is, the volume of the figure increased by factor C. 32 , when The surface area of a rectangular prism is increased by a factor of 16.
What is scale factor?A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.
here, we have,
The square-cube law states that "When an object undergoes a proportional increase in size,
its new surface area is proportional to the square of the multiplier and its new volume is proportional to the cube of the multiplier.
" This means that if the surface area of the cube is increased by a certain amount, the volume of the cube will increase by the cube of that.
Hence, The solution is, the volume of the figure increased by factor C. 32 , when The surface area of a rectangular prism is increased by a factor of 16.
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4 minutes 53 seconds to seconds
Answer: 293 Seconds
Step-by-step explanation:
Answer:
293 seconds
Step-by-step explanation:
one minute = 60 seconds
4 x 60 = 240 seconds -------> use the equation above to multiply per min
240 + 53 = 293 seconds -------> add the remaining seconds to find total
Determine the geometric mean of 11 and 8.
Answer:
[tex]\sqrt{88}[/tex]
Step-by-step explanation:
The geometric mean of 11 and 8 is equal to [tex]\sqrt{88}[/tex].
According to the question it is clear that we have to calculate the geometric mean of two positive numbers 11 and 8.
The geometric mean of two positive numbers a and c is the positive number b in such a way that it satisfies the condition
[tex]\frac{a}{b}=\frac{b}{c}[/tex]
The geometric mean of a and b is √ab if a and b are both positive numbers and it will be −√ab if a and b are negative numbers.
The geometric mean is the positive square root of the product of two numbers.
For a square the geometric mean of two numbers a and b, is the length of one side of a square whose area is equal to the area of a rectangle with the sides of a and b lengths.
If we talk about the n numbers then the geometric mean is the nth root of the product of n numbers. If n positive values are given then the geometric mean is the nth positive root of the product of that n numbers.
So, the geometric mean is equal to [tex]\sqrt{a.b}[/tex]
Here, a = 11 and b = 8
The geometric mean of this is equal to = [tex]\sqrt{11.8}[/tex] = [tex]\sqrt{88}[/tex]
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I really need someone's help please!
Answer:
Felipe subtracted 3x from both sides of the equation.
Answer:
-2
Step-by-step explanation:
first, you will subtract the 2x from 3x then take 6 away from - 8 so it would be 8 and subtract it from 6 because of where the = is and get your answer
how do I solve this
Answer:
113
Step-by-step explanation:
DQ= 180-112= 68
and sum of ang in quad add to 360 so
lets call what we have to find x
so x+ 68+56+123= 360
x+247=360
x= 113
Write the equation of the line.
Help me find the slope to 0,0 and 6,1
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Slopes and gradient.
slope, m = y2-y1/ x2-x1
hence, m = 1-0/ 6-0
m = 1/6
hence slope = 0.166
Which side lengths form a right triangle?
Answer:
B
Step-by-step explanation:
1^2+8^2=[tex]\sqrt 65\\[/tex]
The following data show the scores Gina obtained on 12 IQ tests:
93, 83, 74, 74, 83, 92, 93, 94, 90, 87, 83, 86
The box plot below represents these data:
74
76
78
80
82
84
86
88
90
92
94
96
98
Which of the following is shown incorrectly in the box plot? (5 points)
Оа
Median
Ob
Lower quartile
ос
Upper quartile
Od
Maximum value
Answer:
Median
Step-by-step explanation:
74,83,87,90,92,93,94
Add them together then divide by how many are there to get the median. Then check the data.
simplify (8x^3 + 7x^2 - 3x + 6) + ( -2x^2 - 5x + 4 )
Answer:
hello! :) have a good day!
8x³ + 5x² − 8x + 10
2 A town park has two biking trails. Marsh Trail is 5 miles long. Woodland Trail is
2 miles long. How much longer is Marsh Trail than Woodland Trail?
Show your work.
How do I show my work and what is the answer
Answer:
25/10
Step-by-step explanation:
Make the fractions improper by multiplying the whole number by the denominator and then adding the numerator (if this makes sense).
This makes 5x10=50+3=53/10
Do the same for the second fraction. 2x5=10+4=14/5
Then make the denominators the same, and in this case all you need to do is multiply both sides of 14/5 by 2, so that makes 28/10.
Now, just take it away.
53/10-28/10=25/10, which can be then simplified into 2 1/2 or 5/2.
please help me , I am so confused my head is hurting from this problem...
Answer:
For the first one you could do 1 and 3/5 for the second one you ca do 2/5 3/5 and 3/5 again to get the answer
Step-by-step explanation:
1 + 3/5 = 1 3/5
2/5 + 3/5 + 3/5 = 1 3/5
(5x-8)
+
(2x+19)
Find the value of x.
OA.5
B.7
C.9
D.11
Answer:
x=9 option C
Step-by-step explanation:
explanation above
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