Answers
By the alternating series test, this series converges: for [tex]k\in\Bbb N[/tex],
[tex]\dfrac{k^5+1}{k^6+11}[/tex]
is a positive, decreasing sequence that converges to 0.
However,
[tex]\displaystyle \sum_{k=2}^\infty \left| (-1)^{k+1} \frac{k^5+1}{k^6+11} \right| = \sum_{k=2}^\infty \frac{k^5+1}{k^6+11} \approx \sum_{k=2}^\infty \frac1k[/tex]
is a divergent series by comparison to the harmonic series.
So the given series is conditionally convergent.
The given series is conditionally convergent. This can be obtained by using alternating series test first and then comparing the series to the harmonic series.
Determine if diverges, converges, or converges conditionally:Initially we need to know what Absolute convergence and Conditional convergence,
If [tex]\sum|a_{n} |[/tex] → converges, and [tex]\sum a_{n}[/tex] → converges, then the series is Absolute convergence
If [tex]\sum|a_{n} |[/tex] → diverges, and [tex]\sum a_{n}[/tex] → converges, then the series is Conditional convergence
First use alternating series test,
[tex]\lim_{k \to \infty} \frac{k^{5} +1}{k^{6}+11 }[/tex] = [tex]\lim_{n \to \infty} \frac{5}{6k}[/tex] = 0,
The series is a positive, decreasing sequence that converges to 0.
Next by comparing the series to harmonic series,
[tex]\sum^{\infty} _{k=2}|(-1)^{k+1} \frac{k^{5} +1}{k^{6}+11 }|=\sum^{\infty} _{k=2}\frac{k^{5} +1}{k^{6}+11 }[/tex] ≈ [tex]\sum^{\infty} _{k=2}\frac{1}{k}[/tex] = 0
This implies that the series is divergent by comparison to the harmonic series.
First we got that the series is converging and then we got the series is divergent. Therefore the series is conditionally convergent.
[tex]\sum|a_{n} |[/tex] → diverges, and [tex]\sum a_{n}[/tex] → converges, then the series is Conditional convergence.
Hence the given series is conditionally convergent.
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Related Questions
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
Answer:
○ [tex]F = \frac{S + 24}{3}[/tex]
Step-by-step explanation:
We know that:
[tex]S = 3F -24[/tex],
where F is the length of the foot of a person, and S is their shoe size.
To solve for the length of a person's foot, we have to rearrange the given equation to make F the subject:
[tex]S = 3F -24[/tex]
⇒ [tex]S + 24 = 3F[/tex] [adding 24 to both sides]
⇒ [tex]\frac{S + 24}{3} = F[/tex] [dividing both sides by3]
⇒ [tex]F = \frac{S + 24}{3}[/tex] [swapping the sides]
I really don't know what to do for this question! :( help?
Answers
The amount of money she should deposit is 6131.14 dollars.
How to find the compound interest ?The amount she should deposit can be found as follows:
[tex]p = \frac{A}{(1+\frac{r}{n} )^{nt} }[/tex]
where
A = amount to depositr = raten = number of timest = timep = principalTherefore,
p = [tex]\frac{20000}{(1+\frac{0.12}{4}{} )^{40} }[/tex]
[tex]p=\frac{20000}{(1+0.03)^{40} }[/tex]
[tex]p = \frac{20000}{1.03^{40} }[/tex]
[tex]p=\frac{20000}{3.262037792}[/tex]
Hence,
p = $6,131.14
Therefore, she should deposit 6131.14 dollars.
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What is the maximum value of the transformed function, y = -3cos (2x - 8) + 5
A. 3 units
B. 5 units
C. 8 units
D. 11 units
Answers
Answer:
C. 8 units.
Step-by-step explanation:
The maximum value of the cosine ( cos) function is 1
So, for y = 3cos(2x - 8) + 5
Maximum value is 3 *1 + 5 = 8.
y = -3cos(2x - 8) + 5 is the above graph reflected in the y axis so the maximum value is also 8.
30 metres is percentage of 100 metres
Answers
Answer:
30%
Step-by-step explanation:
1) Based on the given conditions, formulate:
30 meters/100 meters
2) Calculate 30 meters/100 meters:
3/10
3) Convert to percentage:
- 3/10 x 10/10
- 3x10/10x10
30/100
30/100 = 30%
You’re done!
Also, if you could label this brainliest that would be a great help!
Thanks xx
-Dante
Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→[infinity] (5x − ln(x))
Answers
The limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.
According to the given question.
We have to find the limit of [tex]\lim_{x \to \infty} 5x - lnx[/tex]
As we know that L'hospital rule is a theorem which provides a technique to evaluate limits of indeterminate forms.
And the formual for L'hospital rule is
[tex]\lim_{x \to \ c} \frac{f_{x} }{g_{x} } = \lim_{x \to \ c} \frac{f^{'}( x)}{g^{'} (x)}[/tex]
[tex]\lim_{x \to \infty} 5x - lnx[/tex] can be written as
[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]
If we put the value of limit in lnx/x we get an indeterminate form ∞/∞.
Therefore, [tex]\lim_{x \to \infty} \frac{lnx}{x} = \frac{\frac{1}{x} }{1}[/tex]
[tex]\implies \lim_{x \to \infty} \frac{1}{x} = 0[/tex] (as x tends to infinity 1/x tends to 0)
So,
[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]
[tex]= \lim_{x \to \infty}x(5 -0)[/tex]
[tex]= \lim_{n \to \infty} 5x \\= \infty[/tex](as x tends to ∞ 5x also tends to infinity)
Therefore, the limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.
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Four out of 5 students passed the entrance exam. On the same trend, if 252 students got passing mark, how many students took the examination?
Answers
Answer:
315 students
Step-by-step explanation:
Based on the question, we can deduce:
[tex] \frac{4}{5} = 80percent \: passing \: rate[/tex]
Next we can find out the total number of students who sat for the examination.
80% = 252
[tex]1percent \: = \frac{252}{80} \\ 100 \: percent = \frac{252}{80} \times 100 = 315 \: students [/tex]
A group of 65 baseball players were surveyed about which hand they favor for batting. The data from the survey are shown in the Venn diagram.
Determine the value for each variable in the two-way table.
a =
b =
c =
d =
e =
Answers
The value of each variable in the two-way table is:
a = 7
b = 31
c = 28
d = 13
e = 65
What are the value of the variables?A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.
The following have to be established:
a player can either be male or female
a player favors either the left or the right
a = females that favor the left. Looking at the Venn diagram, this number is 7.
b = total number of females : 24 + 7 = 31
c = males that favor the right = total number of males - males that favor the left
34 - 6 = 28
d = Total number of people who favor the left = 7 + 6 = 13
Total number of baseball players = 65
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The height of an equilateral triangle is 4 startroot 3 endroot. what is the perimeter of the equilateral triangle?
Answers
Answer:
perimeter = 24
Step-by-step explanation:
formula:
In an equilateral triangle with sides of lengths ‘a’
The height of the triangle is equal to :
[tex]= \frac{\sqrt{3} }{2} a[/tex]
……………………………………………
Calculating ‘a’ :
We have to solve the equation:
[tex]4\sqrt{3} =\frac{\sqrt{3} }{2} a[/tex]
[tex]\Longleftrightarrow 4=\frac{1 }{2} a[/tex]
[tex]\Longleftrightarrow a = 8[/tex]
Calculating the perimeter:
= 3a
= 3 × 8
= 24
Exponential Growth
Find f(4), where f(x) = 3x.
Answers
f(x) = 3^x
f(4) = 3^4
f(4) = 3 * 3 * 3 * 3
f(4) = 9 * 9
f(4) = 81
Hope this helps!
Which of the following measurements would be MOST likely to have a negative exponent in scientific notation?
a. The distance the Earth is from the sun in meters.
b. The length of a needle in millimeters
c. The length of a football field in inches.
d. The length of an amoeba in meters.
Answers
The measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.
Given four measurements:
The distance the Earth is from the sun in meters.The length of a needle in millimetersThe length of a football field in inches.The length of an amoeba in meters.We are required to choose one measurement which would most likely to have a negative exponent in scientific notation.
A negative exponent is defined as the multiplicative inverse of the base,raised to the power which is of the opposite sign of tthe given power.It is expressed as [tex]e^{-x}[/tex].
We know that exponent shows continuous growth or continuous decay.
Among all the measurement the measurement which is most likely to have a negative exponent in scientific notation is the length of an amoeba in meters because among all the option amoeba can grow continously or decay continuously.
Hence the measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.
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Round to the nearest whole number
763.9
Answers
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
First let us revise the rounding rules before getting down to the process of rounding :
if the number you're rounding to is followed by a number from 0 to 4, then you drop that number.if the number you're rounding to is followed by a number that's 5 or more, you add 1 to that number.∴[tex]\sf{763.9 \ to \ the \ nearest \ whole \ number :}\\\hfill\stackrel{\small\text{add 1 }}{3^{+1}}.\\\hfill\stackrel{\small\text{drop it}}{9}}[/tex]
∴[tex]\sf{763.9\approx764}[/tex]
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
yvette uses 6 grams of tea leaves to make 24 fluid ounces of tea. last week she made 288 fluid ounces of tea. how many grams of tea leaves did yvette use to make tea last week
Answers
72 grams tea is needed to prepare 288 fluid ounces of tea.
According to the statement
we have given that the yvette uses 6 grams of tea leaves to make 24 fluid ounces of tea.
And we have to find that the how much grams of tea uses to make 288 fluid ounces of tea.
So, For this purpose,
the given terms are:
6 grams tea = 24 fluid ounces of tea
Now, we use division method
1 gram of tea = 4 fluid ounces of tea
It means
4 fluid ounces of tea prepared by 1 gram of tea.
then
288 fluid tea prepared = ?
So,
288 fluid tea prepared by grams of tea = 288/4
288 fluid tea prepared by grams of tea = 72.
So, 72 grams tea is needed.
So, 72 grams tea is needed to prepare 288 fluid ounces of tea.
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What is the last digit of the product of all the numbers between 11 and 29?
Answers
we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.
What is the last digit of the product of all the numbers between 11 and 29?
Here we want to find the last digit of the product between all the whole numbers larger than 11 and smaller than 29.
Then we have the product:
P = 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28
Now, notice that there is a 20 there.
Any number times 20 will end with a zero, then:
P = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)
Only with that, we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.
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The daily high temperature of Elk Creek drops by 1.2°C every day. What is the net change in the daily high temperature after two calendar weeks?
Answers
[tex]1.2 \: degrees \: drop \: a \: day \\ 14 \: days \: in \: two \: weeks \\ net \: change = 14 \times 1.2 = 16.8 \: deg[/tex]
If you were a travel agent and a client asked about the daily cost of renting a condominium on maui, what average would you use? explain.
Answers
The average mean cost used for the condominium on maui is 132.5
According to the statement
we have given that the some data values and we have to find the mean of the data and tell the how much expensive is condominium on maui.
So, The given data set is
89 50 68 60 375 55 500 60 50 250 45 45 125 235 1 40 350 65 60 120
So, For this purpose we know that the
Average Mean is a middle point or something (as a place, time, number, or rate) that falls at or near a middle point
Formula to calculate mean is sum of terms / total number of terms.
So,
Mean = 89+ 50+ 68+ 60+ 375+ 55+ 500+ 60+ 50+ 250+ 45+ 45+ 125+ 235+ 1+ 40+ 350+ 65+ 60+ 120 / 20
Mean = 2643 / 20
Mean = 132.5
So, The average mean cost used for the condominium on maui is 132.5
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Maui Vacation How expensive is Maui? If you want a vacation rental condominium
(up to four people), visit a Maui tourism web site. The Maui News gave the following costs in dollars per day for a random sample of condominiums located throughout the island of Maui.
89 50 68 60 375 55 500 60 50 250 45 45 125 235 1 40 350 65 60 120
what average mean would you use?
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200 σ j=1 2j( j 3) describe the steps to evaluate the summation. what is the sum?
Answers
The sum of the equation is = 5494000.
What does summation mean in math?The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.
Briefing:Distribute 2j to (j+3).
Rewrite the summation as the sum of two individual summations.
Evaluate each summation using properties or formulas from the lesson.
The lower index is 1, so any properties can be used.
The sum is 5,494,000.
Calculation according to the statement:[tex]\sum_{j=1}^{200} 2 j(j+3)[/tex]
simplifying them we get:
[tex]\sum_{j=1}^{200} 2 j^{2}+6 j[/tex]
Split the summation into smaller summations that fit the summation rules.
[tex]\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j[/tex]
[tex]\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}[/tex]
The formula for the summation of a polynomial with degree 2
is:
[tex]\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}[/tex]
Substitute the values into the formula and make sure to multiply by the front term.
[tex](2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$[/tex]
we get: 5373400
Evaluating same as above : [tex]6 \sum_{j=1}^{200} j[/tex]
we get: 120600
Add the results of the summations.
5373400 + 120600
= 5494000
The sum of the equation is = 5494000.
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A lampshade made from a piece of sheet plastic has a radius of the inner circle to be 7cm and that of the outer circle is 28cm. if its arc subtends an angle of 315 degree at the center, what is the area of the plastic used to form the lampshade
Answers
The area of the plastic used to form the lampshade is 2021.25 square centimeters
How to determine the area of the plastic used to form the lampshade?The given parameters in the question are:
Outer radius, R = 28 cm
Inner radius, r = 7 cm
Angle, ∅ = 315
The area of the plastic used to form the lampshade is calculated using the following area of sector formula
A = ∅/360 * π(R² - r²)
Substitute the known values in the above equation
A = 315/360 * 22/7 * (28² - 7²)
Evaluate the exponents
A = 315/360 * 22/7 * (784 - 49)
Evaluate the difference
A = 315/360 * 22/7 * 735
Evaluate the product
A = 2021.25
Hence, the area of the plastic used to form the lampshade is 2021.25 square centimeters
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please help 20 points!!!!!
hree students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. The samples are shown in the table. (a)Fill in the sample means in the table. Do not round your answers. Sample Backpack weight (in pounds) Sample mean 1 3, 7, 8, 3, 7, 9, 6, 8 2 8, 6, 4, 7, 9, 4, 6, 7 3 9, 4, 5, 8, 7, 5, 9, 6
(b)Use the table to calculate the range of the sample means. Rangeofsamplemeans:
(c)The students are going to use the sample means to estimate the mean backpack weight of their schoolmates. Select all the true statements below.
A single sample mean will tend to be a worse estimate than the mean of the sample means.
The mean of the sample means will tend to be a worse estimate than a single sample mean.
The closer the range of the sample means is to 0, the less confident they can be in their estimate.
The farther the range of the sample means is from 0, the less confident they can be in their estimate.
Answers
Three students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. Then as per the given sample data,
(a) The sample means of the backpacks are: 6.375,6.375,6.625
(b) Range of sample means: 0.25
(c)The true statement is: The closer the range of the sample means is to 0, the less confident they can be in their estimate.
For the first sample, mean= 6.375
For the second sample, mean= 6.375
For the third sample, mean= 6.625
Range of sample means=Maximum Mean- Minimum Mean
= 6.625 - 6.375
= 0.25
The students will estimate the average backpack weight of their classmates using sample means, the true statement is:
The closer the range of the sample means is to 0, the more confident they can be in their estimate.
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At the break-even point of 2000 units, variable costs are $45000, and fixed costs are $35000. how much is the selling price per unit? $40. 00 $17. 50 $22. 50 $5. 0
Answers
Answer:
$40/unit?
Step-by-step explanation:
I'll assume the the fixed and variable costs are for 2000 units.
Fixed Costs = $35,000
Variable Costs = $45,000
Tota Costs = $80,000
The selling price can be anything. Free and we lose $80,000; $40 each, net profit of $0; $100 each for a net profit of $120,000.
In the absence of any infoprmation regarding selling price (e.g., 50% profit margin), I'd select the $40/unit selling price since that is breakeven.
Jacob is cutting a tile in the shape of a parallelogram. two opposite angles have measures of (6n − 70)° and (2n 10)°. what are the two different angle measures of the parallelogram-shaped tile?
Answers
The measures of the two different angles are 70° and 110°.
What is angle in parallelogram ?
A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.Thus from the given question, we have:
(6n − 70)° + (2n + 10)° = 180°
8n - 60 = 180° + 60
8n = 240
n = 240/8
n = 30°
So that,
i. (6n − 70)° = (6[30] − 70)°
= 180 - 70
= 110°
ii. (2n + 10)° = (2[30] + 10)°
= 60 + 10
= 70°
Therefore, the measures of the two different angles are 70° and 110°.
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Please help me fast
Determine an exact value for the expression and include a complete solution
(sin 225°) ² - cos 330° cos 240°
Answers
Answer:
1.187991
Step-by-step explanation:
sin^2(225)−(cos(330))(cos(240))
=(−0.930095)2−(cos(330))(cos(240))
=0.865076−(cos(330))(cos(240))
=0.865076−−0.991199(cos(240))
=0.865076−(−0.991199)(0.325781)
=0.865076−(−0.322914)
=1.187991
Jenny packaged 108 eggs in 9 cartons. Write this statement as a ratio
Answers
108:9
108/9 (simplest form = 12)
108 eggs to 9 cartons
I hope that this is what you were looking for!
Answer:
12:1
Step-by-step explanation:
each pack contains 12 eggs
108/9 = 12
Hope this helps
The following figure is made of 2 triangles.
9
5
A
Figure
Triangle A
Triangle B
Whole figure
7
B
Find the area of each part of the figure and the whole figure.
Area (square units)
Answers
area is 1/2 times base times height
triangle A
1/2 times 7 times 9
answer 31.5
Triangle B
1/2 times 7 times 5
answer 17.5
Triangle A: 31.5 units squared
Triangle B: 17.5 unites squared
But you really should start memorizing formulas
50 points!!!
Someone help pls, I can’t understand it and it’s due tomorrow :c
Answers
[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}[/tex]
[tex]\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}[/tex]
❍ Arrange the given data in order either in ascending order or descending order.
2, 3, 4, 7, 9, 11
❍ Number of terms in data [n] = 6 which is even.
As we know,
[tex]\star \: \sf Median_{(when \: n \: is \: even)} = {\underline{\boxed{\sf{\purple{ \dfrac{ { \bigg (\dfrac{n}{2} \bigg)}^{th}term +{ \bigg( \dfrac{n}{2} + 1 \bigg)}^{th} term } {2} }}}}}[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ { \bigg (\dfrac{6}{2} \bigg)}^{th}term +{ \bigg( \dfrac{6}{2} + 1 \bigg)}^{th} term } {2} }[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \dfrac{6 + 2}{2} \bigg)}^{th} term } {2} }[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \cancel{ \dfrac{8}{2}} \bigg)}^{th} term } {2} }[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ 4}^{th} term } {2} }[/tex]
• Putting,
3rd term as 4 and the 4th term as 7.
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 4 + 7 } {2} }[/tex]
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 11} {2} }[/tex]
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} = \purple{5.5}[/tex]
[tex]\\[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}[/tex]
[tex]\star\:{\underline{\underline{\sf{\red{Solution:}}}}}[/tex]
❍ Arrange the given data in order either in ascending order or descending order.
1, 2, 3, 4, 5, 6, 7
❍ Number of terms in data [n] = 7 which is odd.
As we know,
[tex]\star \: \sf Median_{(when \: n \: is \: odd)} = {\underline{\boxed{\sf{\red{ { \bigg( \frac{n + 1}{2} \bigg)}^{th} term}}}}}[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: odd)} = {{ \bigg(\dfrac{ 7 + 1 } {2} \bigg) }}^{th} term[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: odd)} = { \bigg(\cancel{\dfrac{8}{2}} \bigg)}^{th} term[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: odd)} ={ 4}^{th} term[/tex]
• Putting,
4th term as 4.
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: odd)} = \red{ 4}[/tex]
[tex]\\[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}[/tex]
[tex]\star\:{\underline{\underline{\sf{\green{Solution:}}}}}[/tex]
The frequency distribution table for calculations of mean :
[tex]\begin{gathered}\begin{array}{|c|c|c|c|c|c|c|} \hline \rm x_{i} &\rm 3&\rm 1&\rm 7&\rm 4&\rm 6&\rm 2 \rm \\ \hline\rm f_{i} &\rm 4&\rm 6&\rm 2&\rm 2 & \rm 1&\rm 1 \\ \hline \rm f_{i}x_{i} &\rm 12&\rm 6&\rm 14&\rm 8&\rm 6&\rm \rm 2 \\ \hline \end{array} \\ \end{gathered} [/tex]
☆ Calculating the [tex]\sum f_{i}[/tex]
[tex] \implies 4 + 6 + 2 + 2 + 1 + 1[/tex]
[tex] \implies 16[/tex]
☆ Calculating the [tex]\sum f_{i}x_{i}[/tex]
[tex] \implies 12 + 6 + 14 + 8 + 6 + 2[/tex]
[tex]\implies 48[/tex]
As we know,
Mean by direct method :
[tex] \: \: \boxed{\green{{ { \overline{x} \: = \sf \dfrac{ \sum \: f_{i}x_{i}}{ \sum \: f_{i}}}}}}[/tex]
here,
• [tex]\sum f_{i}[/tex] = 16
• [tex]\sum f_{i}x_{i}[/tex] = 48
By putting the values we get,
[tex]\sf \longrightarrow \overline{x} \: = \: \dfrac{48}{16}[/tex]
[tex]\sf \longrightarrow \overline{x} \: = \green{3}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Note\: :}}}}}}[/tex]
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[tex]\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}[/tex]
greatest common factor of 6,12, and 21
Answers
Answer:
3
Step-by-step explanation:
[tex]6=2 \times 3 \\ \\ 12=3 \times 2^2 \\ \\ 21=3 \times 7[/tex]
which of the following tools is used to construct an angle bisector
Answers
Answer:
Tools used to construct a bisector are 1》pencil ,2》Eraser ,3》protector ,4》Compass ,5》Sharpner etc ....
Which has no real roots?
Answers
[tex] \sqrt[4]{ - 8} [/tex]
Explanation:The input of a radical should be strictly positive or equal to zero when the nth root is even.Select the correct answer from the drop-down menu. consider the equations y = |x − 1| and y = 3x 2. the approximate solution of this system of equations is .
Answers
The approximate solution of this system of equations is
(x,y)=(-0.25,1.25)
What is an equation?Equation is defined as the state of being equal and is often shown as a math expression with equal values on either side, or refers to a problem where many things need to be taken into account.
Given that,
y = |x − 1| and y = 3x+2
y = |x − 1|
= (x-1) , for (x-1)>0 or x>1
and
y = -(x-1) , for(x-1)<0 or x<1
y = -x+1
Now, For x>1
y = x-1 ......(1)
y = 3x+2 ......(2)
Solving for x by equaliting's method:
3x+2 = x-1
→ 3x-x = -1-2
→ 2x = -3
→ x = -3/2
→ x = -1.5 which is <1.
For x<1
y = -x+1 ......(1)
y = 3x+2 ......(2)
Solving for x by equaliting's method:
3x+2 = -x+1
→ 3x+x = 1-2
→ 4x = -1
→ x = -1/4
→ x= -0.25 which is <1.
substitute the value of x = -0.25 in equation 1 for x<1.
y = -x+1
= -(-0.25)+1
y = 1.25
Hence, The approximate solution of this system of equations is
(x,y)=(-1/4,5/4)=(-0.25,1.25).
To learn more about equation from the given link:
https://brainly.com/question/9475812
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A mini-lottery involves selecting 2 numbers between 1 and 10. What is the probability of correctly picking the two numbers?
a) 2/10
b) 1/30
c) 2/90
d) 2/100
Answers
The probability of correctly picking the two numbers is 2/10.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability of correctly picking the two numbers = (numbers that have to be selected to win / total numbers)
2/10
To learn more about probability, please check: https://brainly.com/question/13234031
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There are 20 points on a line, each spaced two inches apart. How far, in inches, is it from the first point to the last one?
Answers
Answer: 40 inches
Step-by-step explanation: If the 20 points on the line were spaced 1 inch apart, the result would be 20 inches. Each point you're going to is 1 inch in spacing and there is only going to be 20 inches of spacing (1 inch per point.)
For 2 inches spaced apart, the result would be simply 40 inches. You just need to add the distance of 20 more to the already distance of 20 points, since if 2 were to be divided, it would be 1, which is 20 inches in distance as stated. Another 20 points would be another inch in distance, and adding them gives you 2 inches in distance or 40 inches all together.
I apologize if I wasn't clear enough, I couldn't find a way to explain it as good as I thought it was in my mind.
Hope it helped though!