find the sum of the first 41 terms of the following series, to the nearest integer 11,19,27
Answers
Input data
11, 19, 27
An arithmetic sequence is a sequence in which the difference between each consecutive term is constant. An arithmetic sequence can be defined by an explicit formula in which an = d (n - 1) + c, where d is the common difference between consecutive terms, and c = a1.
Procedure
d = 19 - 11 = 8
d = 27 - 19 = 8
a1 = 11
\(a_n=11+8(n-1)\)for n = 41
To find the sum of the first n terms of an arithmetic series use the formula, n terms of an arithmetic sequence use the formula,
\(\begin{gathered} S_n=\frac{n(a_1+a_n)}{2} \\ \end{gathered}\)a41 = 11+8(41-1)
a41 = 11+8*40
a1 = 331
\(\begin{gathered} S_{41}=\frac{41(11+331)}{2} \\ S_{41}=\frac{41(342)}{2} \\ S_{41}=6642 \end{gathered}\)Related Questions
21 20 15 22 19 23 17 what is the median and range
Answers
The median would be 22:
Step-by-step explanation: The median is the number that is in the middle
Simply defined, the median is the number right in the middle of a set.
But before I get down to finding the median, I will order the numbers from least to greatest:
15, 17, 19, 20, 21, 22, 23
Now, the middle number is 20. So that's the median.
As for the range, it's the difference between the largest number and the smallest one:
Range = Greatest number - Smallest number
= 23 - 15
= 6
In summary, the median, the number in the middle, is 20, and the range, the difference between the largest number and the smallest one, is 6.
The owner of a computer repair shop has determined that their daily revenue has mean $7200 and standarddeviation $1200. The daily revenue totals for the next 30 days will be monitored. What is the probability thatthe mean daily revenue for the next 30 days will be between $7000 and $7500
Answers
Answer:
\(P(7000<\bar X<7500)\)
And we can use the z score formula to solve this problem
\(z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\)
And replacing we got:
\( z = \frac{7000-7200}{\frac{1200}{\sqrt{30}}}= -0.913\)
\( z = \frac{7500-7200}{\frac{1200}{\sqrt{30}}}= 1.369\)
And we can find this probability with the normal standard distribution and with this difference:
\(P(-0.913<z<1.369)=P(z<1.369)-P(z<-0.913)= 0.9145 -0.1806= 0.7339\)
Step-by-step explanation:
Let X the random variable that represent the daily revenue of a population, and for this case we know the distribution for X is given by:
\(X \sim N(7200,1200)\)
Where \(\mu=7200\) and \(\sigma=1200\)
We are interested on this probability
\(P(7000<\bar X<7500)\)
And we can use the z score formula to solve this problem
\(z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\)
And replacing we got:
\( z = \frac{7000-7200}{\frac{1200}{\sqrt{30}}}= -0.913\)
\( z = \frac{7500-7200}{\frac{1200}{\sqrt{30}}}= 1.369\)
And we can find this probability with the normal standard distribution and with this difference:
\(P(-0.913<z<1.369)=P(z<1.369)-P(z<-0.913)= 0.9145 -0.1806= 0.7339\)
The tables of ordered pairs represent some points on the graphs of two lines. What is the solution to the system of equations represented by the two lines? There are no zeroes on the chart. What do I do
Answers
To find the solution to the system of equations represented by the two lines based on the given tables of ordered pairs, you can follow these steps:
Examine the tables and identify a pattern or relationship between the x-values and y-values for each line.Determine the slope (rate of change) of each line by calculating the difference in y-values divided by the difference in x-values for any two points on the line.Once you have the slopes, compare them to see if they are equal or different.If the slopes are different, the lines intersect at a single point, which represents the solution to the system of equations.If the slopes are equal, the lines are parallel, and there is no solution to the system of equations.If the slopes are different, you can find the intersection point by solving the system of equations using either substitution, elimination, or another suitable method.For such more question on equations
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BOOMER GENERATION: At 84%, Boomers are the highest amongst all the generations that want to shop in-store. In a sample size of 75 people in the Boomer Generation, estimate how many of them prefer to shop in-store.
Answers
In a sample size of 75 people in the Boomer Generation, proportionately, the estimated number of people who prefer to shop in-store is 63.
What is proportion?Proportion shows the relative number of objects or people in the whole.
Proportions are ratios equated to each other.
They are expressed as fractional values, in decimals, percentages, and fractions.
The percentage of Boomers who want to shop in-store = 84%
The sample size of the Boomer Generation = 75
The estimated number of Boomers in the sample size who want to shop in-store = 63 (75 x 84%)
Thus, 63 Boomers representing 84 percent of 75 want to shop in-store.
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Find the unit price of 48 golf balls for $38.97. Round your answer to the nearest cent if necessary.
Answers
Answer:
.81
Step-by-step explanation:
38.97/48=.811875
Answer:
$0.81
Step-by-step explanation:
Hi there!
To find the unit price of the golf balls, divide the total cost by the total number of golf balls:
$38.97 ÷ 48
= $0.81 (approximately)
Therefore, the unit price is $0.81.
I hope this helps!
9. A has some amount of money with him. He gave one half of one third from that amount One half of the amount received by B is 20. What is the amount that A originally had?
Answers
Using the expression 5x/12 = 20, the amount that A originally had was $48.
We have,
Let x be the amount of money that A originally had.
Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.
The amount received by B is 1/2 of the remaining amount,
which is (x - x/6)/2 = 5x/12.
We know that 5x/12 = 20,
Solving for x.
5x/12 = 20
5x = 240
x = 48
Therefore,
The amount that A originally had was $48.
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pls answer I will give brainliest
Answers
Which inequality is represented by the number line?
A.
|2x + 1| ≥ 7
B.
2|x + 1| ≤ 8
C.
|2x − 1| ≥ 9
D.
2|x − 1| ≤ 10
Answers
The inequality represented by the graph is |2x − 1| ≥ 9
How to determine the inequality represented by the graph?The number line represents the given parameter
On the number line, we have the following endpoints
x = -4 and x = 5
So, we test the above solutions in the list of options (representing them as an equation)
So, we have
|2x + 1| = 7
When x = -4
|2(-4) + 1| = 7 ⇒ 7 = 7 --- true
When x = 5
|2(5) + 1| = 7 ⇒ 11 = 7 --- false
2|x + 1| ≤ 8
When x = -4
2|(-4) + 1| = 8 ⇒ 6 = 8 --- false
|2x − 1| ≥ 9
When x = -4
|2(-4) - 1| = 9 ⇒ 9 = 9 --- true
When x = 5
|2(5) - 1| = 9 ⇒ 9 = 9 --- true
Hence, the inequality is (c) |2x − 1| ≥ 9
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Find the percent increase. Round to the nearest percent.
From $25 to $40
The percent increase is
Answers
Answer:
Step-by-step explanation:
40 minus 25 is 15
15/25 is .6
.6 times 100
60% is the percent increase
elliot scores 65 out of 80 in a mats test. write this as afraction
Answers
Answer:
\(\huge\boxed{\sf \frac{65}{80} => \frac{13}{16} }\)
Step-by-step explanation:
Obtained Marks = 65
Total Marks = 80
Fraction:
=> \(\sf \frac{65}{80}\)
=> \(\sf \frac{13}{16}\)
Hope this helped!
~AnonymousHelper1807
Telephone Company Project
Answers
IT IS USED TO STEAL PERSONAL INFORMATION
4.6w - 3 + 6.4x - 1.9y
Answers
Answer:
What do you want me to do? Its already simplified to its lowest terms
Answer:
w = 0.652173913 + -1.391304348x + 0.4130434783y
Step-by-step explanation:
I am pretty sure this is it.
A committee of four people is formed by selecting members from a list of 12 people.
How many different committees can be formed?
__ committees
Answers
The number of different committees that can be formed is 495
How many different committees can be formed?From the question, we have the following parameters that can be used in our computation:
People = 12
Committee = 4
These can be represented as
n = 12 and r = 4
The number of different committees that can be formed is
Number = nCr
So, we have
Number = 12C4
Evaluate
Number = 495
Hence, the committee are 495
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If electricity is billed at a rate of $0.75 per KWH and you used on average 120 KWHs per month, what would you expect to pay each month?
Answers
You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.
How to find the expected monthly payTo calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.
Given:
Cost per KWH: $0.75
Average monthly usage: 120 KWHs
To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:
Monthly Cost = Cost per KWH * Average monthly usage
Plugging in the values, we have:
Monthly Cost = $0.75/KWH * 120 KWHs
Calculating the result:
Monthly Cost = $90
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Find the value of x that makes quadrilateral ABCD a rectangle if BE = 3x+1 and ED = 5x-3
Answers
The value of x that makes quadrilateral ABCD a rectangle if BE = 3x+1 and ED = 5x-3 is x = 2.
What is a rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
There are four vertices and four sides.
Every vertex has an angle of 90 degrees.
Equal and parallel opposed sides are bisected by a diagonal.
We know that the diagonals of a rectangle bisect each other.
Thus, for the quadrilateral to be a rectangle we have:
BE = ED
3x + 1 = 5x - 3
1 + 3 = 5x - 3x
4 = 2x
x = 2
Hence, the value of x that makes quadrilateral ABCD a rectangle if BE = 3x+1 and ED = 5x-3 is x = 2.
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AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.
Answers
When a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency. This means that triangle ABD is a right triangle with AB as the hypotenuse.
We can use the Pythagorean theorem to find the length of AB:
AB^2 = AD^2 + BD^2
Since AD = x + 9 and BD = 8x - (x + 9) = 8x - x - 9 = 7x - 9, we can substitute these values into the equation:
(8x)^2 = (x + 9)^2 + (7x - 9)^2
64x^2 = x^2 + 18x + 81 + 49x^2 - 126x + 81
64x^2 = 50x^2 - 108x + 162
14x^2 + 108x - 162 = 0
Dividing the equation by 2, we get:
7x^2 + 54x - 81 = 0
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
a = 7, b = 54, c = -81
x = (-54 ± √(54^2 - 4 * 7 * -81)) / (2 * 7)
x = (-54 ± √(2916 + 2268)) / 14
x = (-54 ± √5184) / 14
x = (-54 ± 72) / 14
Now we solve for x:
Case 1: x = (-54 + 72) / 14 = 18 / 14 = 9 / 7
Case 2: x = (-54 - 72) / 14 = -126 / 14 = -9
Since the length of a segment cannot be negative, we discard the second case and focus on the positive solution.
Therefore, x = 9/7.
Substituting this value back into AB = 8x:
AB = 8 * (9/7) = 72/7 ≈ 10.29
Rounding to 2 decimal places, the length of AB is approximately 10.29 units.
Answer:
To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:
8x = x + 9
Solving for x, we get:
x = 1.5
Therefore, AB = 8x = 8(1.5) = 12.
To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:
AB^2 + BD^2 = AD^2
Substituting the values, we get:
12^2 + BD^2 = (1.5 + 9)^2
Simplifying, we get:
BD^2 = 56.25
Taking the square root of both sides, we get:
BD = 7.5
Hence, the length of AB is 12 and the length of BD is 7.5.
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175+14.25x=200+11z solve the problem
Answers
Answer:
x = 7.69
Step-by-step explanation:
We need to solve the given problem. It is as follows :
175+14.25x=200+11x
Here, x is a variable. We can take on one side of an equation and constants to the other side such that,
14.25x-11x = 200-175
3.25x=25
x = 25/3.25
x = 7.69
Hence, the solution of the given equation is 7.69.
Find the volume of the right triangular prism.
A) 120 cubic centimeters
B) 90 cubic centimeters
C) 60 cubic centimeters
D) 150 cubic centimeters
Answers
help me please! i’m giving brainliest! :)
A desk measures 3 feet in height. How many inches does the desk measure in height?
Answers
Answer:
36 Inches
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
it would just be 12×3=36
(-2/3)(6/7)
Please show work if possible!
Answers
Multiply the top x top / bottom x bottom, then simplify by dividing both the top and bottom by a common factor of three.
Get me right twinnnn
Answers
Answer:
\( \frac{9x { }^{2 } - 63x}{ 3x} \\ = \frac{3x(3x - 21)}{3x} \\ = 3x - 21 \)
hope it helps:)
Answer:3x-21
Step-by-step explanation:
\(\frac{9x^{2} - 63x }{3x}\) ⇒ \(\frac{3x * (3x - 21) }{3x}\) ⇒ cancel out 3x ⇒ 3x - 21
The sales tax rate on a new vehicke is 6.5 percent. If the vehicle is priced at 12,000, how much will you be charged for sales tax?
Answers
If sales tax rate on a new vehicle is 6.5 percent. If the vehicle is priced at 12,000, then 780 will be charged for sales tax
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The sales tax rate on a new vehicle is 6.5 percent.
The price of the vehicle is 12000
We need to find the how much will you be charged for sales tax
Let us convert 6.5 percent to the decimal value by dividing it with 100
6.5/100×12000
0.065×12000
780
Hence, 780 will be charged for sales tax.
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An IAS question. Add 10 and 4 and you get 2. how
Answers
Answer:
you make them into groups
Step-by-step explanation:
Answer:
Make them into groups
Step-by-step explanation:
Hope this helped have an amazing day!
URGENT!!!! Find the y-intercept of the line that passes through the points (-3, 7) and (3, −9).
Answers
Answer:
\(m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} \)
\(7 = - \frac{8}{3} ( - 3) + b\)
\(7 = 8 + b\)
\(b = - 1\)
\(y = - \frac{8}{3} x - 1\)
The y-intercept is -1.
you realize your scale was calibrated too low by 7 grams meaning each birth weight needs to be increased by 7 grams how would this change the rage median iqr of the data set
Answers
If we increase each value by 7 grams, we get: {2507, 2707, 2807, 2907, 3107} this would change the rage median iqr of the data set.
what is the median?
The median is a measure of central tendency in a set of data, which represents the middle value of the data when it is arranged in order.
If each birth weight needs to be increased by 7 grams due to a calibration error in the scale being too low, this would affect all the values in the dataset equally, without changing the distribution of the data. Therefore, the range and median of the data set would be increased by 7 grams, while the IQR (interquartile range) would remain the same since it is calculated based on the middle 50% of the data.
For example, suppose we have the following birth weight data set:
{2500, 2700, 2800, 2900, 3100}
The range of the data set was originally 600 (3100 - 2500) but now it is 607 (3107 - 2507), an increase of 7. Similarly, the median of the data set was originally 2800 but now it is 2807, an increase of 7. However, the IQR of the data set, which is the difference between the third quartile (Q3 = 3000) and the first quartile (Q1 = 2700), remains the same at 300 - 270 = 30.
Therefore, If we increase each value by 7 grams, we get:
{2507, 2707, 2807, 2907, 3107}
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Complete Question:
You realize your scale was calibrated too low by 7 grams meaning each birth weight needs to be increased by 7 grams. How would this change the rage median IQR of the data set?
a number is tripled and then increased by four. the result is seventy-nine. what is the original number?
Answers
Answer:
3x+4=79
Step-by-step explanation:
3x+4=79
3x=79-4
3x=75
Divide both sides by three
3x/3 = 75/3
x=25
Therefore the original number is 25.
Hope it helps.✨✨
Jerome biked 1.2 miles. Then he ran 0.75 mile. How far did Jerome go you brainlyest if answerd by you
Answers
Answer:
The answer would be 1.95
Step-by-step explanation:
he returns on share A follow the market model with coefficients αA = 0.01, βA =
1.25. If at time t, R~ MT = 0.02 and the actual return on share A is 0.025, calculate
∈�At (the error term)
Answers
Answer:
2 or more so it's be like 3 I guess he doesn't have the right for the tiger and in the heights block he it is a great game and to
find the length of segment BC
Answers
Answer:
Well B is 6 and c is 12. So if you are finding out line segment Bc then all you have to do is combine bot h B and C. So you would get 6x12. If you could peroxide a graph that would be great.
So therefore the answer is 12
Step-by-step explanation:
A triangle has a side with length 9 feet and another side with length 7 feet. The
angle between the sides measures 69°. Find the area of the triangle. Round your
answer to the nearest tenth
Answers
Answer:
63
Step-by-step explanation: