The sum of finite arithmetic series 8+9+10+. . . . . . +15 is 92
Suppose we are given an arithmetic series:
a(1) + a(2) + ... + a(n)
Then the sum is:
S(n) = n/2 (a(1) + a(n))
Where: a(1) = first term
a(n) = nth term
The given series is:
8+9+10+. . . . . . +15
We need to find n such that a(n) = 15.
Recall that in an arithmetic sequence:
a(n) = a(1) + (n -1) . d
where d = difference between 2 consecutive terms.
Substituting a(1) = 8, and d = 9 - 8 =1 into the formula:
a(n) = 8 + (n -1) . 1
15 = 7 + n
n = 8
Substitute n = 8 into the sum formula:
S(n) = n/2 (a(1) + a(n))
S(8) = 8/2 . (8 + 15)
= 4 . 23 = 92
Learn more about arithmetic series here:
https://brainly.com/question/28144402
#SPJ4
1/2+sqrt(3 Que harias para racionalizar esta expresion?
After calculating we have come to find that [tex]\frac{1 + 2 \sqrt3 }{2}[/tex] is the rationalized form of the expression 1/2 + √3
What is rationalization?Rationalizing is the process of multiplying one surd by another similar surd to produce a rational number. The rationalizing factor is the surd used to multiply (RF).
We rationalize the denominator to make it easier to perform any calculation on the rational number. When we rationalize the denominator of a fraction, we remove any radical expressions from the denominator, such as square roots and cube roots.
We have been asked to rationalize 1/2 + √3
⇒ 1/2 + √3
= [tex]\frac{1 + 2 \sqrt3 }{2}[/tex]
As the denominator is a rational number 1/2 + √3 has been rationalized
Learn more about Rationalizing
https://brainly.com/question/17121733
#SPJ9
A 36-inch diameter pie is cut into 6 slices. What is the area of one of the slices?
A. 54 inches
B. 216 inches
C. 6 inches
D. 24 inches
E. None of the above
Answer:
6 inches
Step-by-step explanation:
it's just 36/6 which equals 6
PLEASE HELP!!!
Noor needs to build a pen for her chickens. She wants the pen to be rectangular, 3 meters longer than it is wide. Write the equation Noor should use to determine the width of a pen which has an area of 70 square meters
Given the area, the equation that Noor should use to determine the width of pen is x² + 3x = 70.
The length and width of the rectangular pen are 10m and 7m respectively.
What is the width of the rectangular pen?The area of a rectangle is expressed as;
A = l × w
Where l is length and w is width.
Given the data in the question;
Let the width of the rectangular pen be 'x'
Width = w = xLength = l = x + 3Area = 70m²To determine the equation that Noor will use to find the width of the pen, plug the values into the equation above.
A = l × w
70 = (x+3) × x
70 = x² + 3x
x² + 3x = 70
We can go further and solve for the width of the pen.
x² + 3x = 70
x² + 3x - 70 = 0
Factor sing AC method; find two integer whose addition gives 3 and multiplication gives -70.
-7 and 10
(x-7) (x+10) = 0
x - 7 = 0, x + 10 = 0
x = 7, x = -10
But the dimension of the width can not be negative.
Hence
x = 7
Width = x = 7m
Length x + 3 = 7 + 3 = 10m
Given the area, the equation that Noor should use to determine the width of pen is x² + 3x = 70.
The length and width of the rectangular pen are 10m and 7m respectively.
Learn more about rectangles here: https://brainly.com/question/28572793
#SPJ1
Which is true about dividing integers?
A If there is an odd number of negative signs, then the quotient is positive.
B The quotient of integer division is always positive.
C If there is an even number of negative signs, then the quotient is positive.
D The quotient of integer division is always negative.
Answer: C
Step-by-step explanation:
A says an odd number (neg) + (neg)+ (neg) = positive and that is not right
B. quotients are not always positive
C. A even number of negatives (neg) + (neg) = a positive
D. is not true
Prepare Sangreens bank reconciliation at may 31, 2022
ok:).
poop
.........
Q 11. Luis and Baca have been weightlifting with each other and want to see how long it will take them to be the same weight. Luis weighs 194 pounds and gains 0.6 pounds of muscle per week. Baca weighs 218 pounds and gains 0.2 pounds of muscle per week. Create an equation that Luis and Baca can use to determine how long it will take for them to be the same weight. In the text box, write about how you formed the equation used to determine when Luis and Baca would be the same weight. BI
Luis and Baca would be the same weight after 60 weeks of weightlifting.
What is a linear Equation?A linear equation is one in which the highest power of the variable is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation.
To create an equation that Luis and Baca can use to determine how long it will take for them to be the same weight:
Let the time taken by Luis and Baca to be of the same weight be x weeks,
Given:
Initial weight of Luis = 194 pounds
Initial weight of Baca = 218 pounds
Then,
Weight gained by Luis in x weeks = 0.6x pounds
Weight gained by Baca in x weeks = 0.2x pounds
Total weight of Luis after x weeks = (194 + 0.6x ) pounds
Total weight of Baca after x weeks = (218 + 0.2x) pounds
For Luis and Baca to be of the same weight,
Total weight of Luis after x weeks = Total weight of Baca after x weeks
Therefore, we equate the total weight gained by Luis and Baca after x weeks to determine the value of x
⇒ 194 + 0.6x = 218 + 0.2x
⇒ 0.6x - 0.2x =218 - 194
⇒ 0.4x = 24
⇒ x = 60
Hence, Luis and Baca would be the same weight after 60 weeks of weightlifting.
To know more about Linear Equations visit:
https://brainly.com/question/13738061
#SPJ9
Find the specified value for each infinite geometric series.
b. S=12, r= 1/6 ; find a₁
An infinite geometric series is the outcome of an unlimited geometric sequence. If the value of S = 12 and r = 1/6 then the value of a₁ = 10.
What is an infinite geometric series?An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.
The sum of an infinite geometric series be S = a/1-r
S be the sum = 12
a₁ be the first term = ?
r -be the common ratio = 1/6
We know,
S = a₁/1-r
substitute the values in the above equation, we get
12 = a₁/1-(1/6)
simplifying the equation,
12 = 6a₁/5
a₁ = 60/6 = 10
If the value of S = 12 and r = 1/6 then the value of a₁ = 10.
To learn more about infinite geometric series, refer to:
https://brainly.com/question/12742266
#SPJ4
Carmenjello went to the secret panda company in Alabama to purchase pandas for his community. He bought 39
1/4 pandas on Monday, 17 1/5 pandas on Tuesday, and 52 ½ pandas on Wednesday. On Thursday 7 3/4 pandas ran away from his back to their home. There are 5 neighborhoods in his community that will evenly split the pandas
between one another. How many pandas will each neighborhood receive?
Each neighbourhood will receive 23.34 pands.
What are fractions?In mathematics, a fraction is defined as a portion of the whole. If a pizza is cut into four equal pieces, each piece is represented by ¼. Fractions make it easier to distribute and judge numbers and speed up calculations. There are three major types of fractions in mathematics. Proper fractions, improper fractions, and mixed fractions are the three types. Fractions are terms that have a numerator and a denominator.So, 39¼ + 17⅕ + 52½ + 7¾.
Now, solve the above mathematical operation as follows:
39¼ + 17⅕ + 52½ + 7¾157/4 + 86/5 + 105/2 + 31/4LCM of 4, 5, 2, and 4: 20
Now,
5(157) + 4(86) + 10(105) + 5(31)/20785 + 344 + 1050 + 155/202334/20116.7Now, divide 116.7 by 5:
116.7 ÷ 5 = 23.34Therefore, each neighbourhood will receive 23.34 pands.
Know more about fractions here:
https://brainly.com/question/17220365
#SPJ9
A rectangular sticker has a perimeter of 30 centimeters. Its area
is 54 square centimeters. What are the dimensions of the sticker?
The dimensions of the sticker are 6 centimeters and 9 centimeters, respectively.
What are the dimensions of a rectangular sticker?
According to the statement, we find a rectangular sticker whose perimeter and area are known. By the perimeter and area formulas of the rectangle we have the following system of equations:
x · y = 54 (1)
2 · (x + y) = 30 (2)
By (2):
2 · x + 2 · y = 30
2 · x = 30 - 2 · y
x = 15 - y
(2) in (1):
(15 - y) · y = 54
15 · y - y² = 54
y² - 15 · y + 54 = 0
(y - 9) · (y - 6) = 0
The solutions are y₁ = 9 and y₂ = 6, respectively.
By (2):
x₁ = 15 - y₁
x₁ = 15 - 9
x₁ = 6
x₂ = 15 - y₂
x₂ = 15 - 6
x₂ = 9
The solutions are x₁ = 6 and x₂ = 9, respectively.
The dimensions of the sticker are 6 centimeters and 9 centimeters, respectively.
To learn more on algebraic equations: https://brainly.com/question/24875240
#SPJ1
C: (4, -8, 16, -32,...}
Find a 10
Answer:
i think 10 is in between -8 and
Step-by-step explanation:
hope this
2. If h(x)=x²-4, what is h(-3)?
(1)-13
(2) -10
(3) 5
(4) 2
John is painting his house. It has taken him 5 days to paint 2/5 of his house. How many more days will it take john to finish painting his house?
A. 5 days
B. 7.5 days
C. 6.5 days
D. 8 days
E. None of the above
Answer:
B. will take 7.5 more days
Booker owns 85 video games. He has 3 shelves to put the games on.
Each shelf can hold 40 video games. How many more video games does he have room for? (Brainliest Question)
Answer:
5
Step-by-step explanation:
it's because one shelf is 40 then the second shelf is 80 and then the third is 5.
Determine whether the following statements are sometimes, always, or never true. Explain.
How can triangle classifications help you prove triangle congruence?
Triangle classification will always help us to prove congruency in triangle. Each of the three angles in an acute triangle is acute. One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle.
What is triangle congruence?The triangles are congruent when two sets of corresponding sides and the corresponding angles between them are in agreement. Two triangles that have a congruent angle in the middle and two congruent sides.
Instead of using the unit measure, it is based on the proportion of the side lengths to one another. As a result, triangles are categorized according to how many of their sides are the same length as one another or not at all equal.
Angles are another way to categorize triangles. Each of the three angles in an acute triangle is acute (less than 90 degrees). One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle (greater than 90 degrees).
To learn more about Triangle congruence refer to:
https://brainly.com/question/2938476
#SPJ4
3. Change the digit 5 to zero in each number. Show the operation that will make it zero
a. 478 578 = b. 353 897 = c. 294 025 = d. 500 000 = e. 893 257 = 0 1 2 3 4
Place value is defined as the value of a digit in a number which depends on its position in the number. On the other hand, Total value is the product of a digit and its place value.
Rounding off entails changing a number into an approximation such that it has fewer significant numbers. To change the digit 5 in this question to 0, we will need to round off the given numbers to the most appropriate place value.
a. 478 578
We round off to the nearest thousands, this becomes 479 000
b. 353 897
We round off to the nearest tens of thousands, this becomes 400 000
c. 294 025
We round off to the nearest ones, this becomes 294 030
d. 500 000
The 5 in this value cannot be converted to 0 since 5 is the largest place value in the number.
Read more: https://brainly.com/question/14631150?referrer=searchResults
#SPJ4
14 POINTS!!!!!!!!!!!!!
PLS HELP
Answer:
1) y = 6
2) Paul has 20 quarters
Step-by-step explanation:
What is the length and width of the sandy island beach snak shack
30m by 90m is the length and width of the sandy island beach snak shack.
What is a rectangle shape?
An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.20 x 1 = 20
20 x .5 = 10
20 + 10 = 30
60 x 1 = 60
60 x .5 = 30
60 + 30 = 90..
Learn more about rectangle
brainly.com/question/15019502
#SPJ9
The complete question is -
Sandy Island Beach is building a new Snack Shack based on a scale drawing that is 20 centimeters by 60 centimeters and uses the scale 1 cm : 1.5 m.
The product of 6 and Gail’s height is 66
Use g to represent Gail’s height
Answer:
The product of 6 and Gail’s height is 66
Use g to represent Gail’s height
Step-by-step explanation:
in straightedge and compass construction of the parallel line below which of the following reasons can you use to prove that JK and LN are parallel
The correct option is (C) ∠ MJK ≅ ∠ MKJ by construction.
When two parallel lines have a transversal cutting those parallel lines, the alternate angle theorem holds true. According to the alternate angle theorem, all alternate angles are equal.
We have a similar circumstance here, where we are employing the alternate angle theorem approach to design and build two parallel lines. To prove that the two alternate angles are equal and the lines are parallel, we must first identify the two alternate angles.
The two alternate angles are:
∠ MLN and ∠ MJK
Therefore, for the lines, JK and LN to be parallel the two angles must be congruent.
Hence, ∠ MLN ≅ ∠ MJK
Learn more about parallel lines here:
https://brainly.com/question/25087745
#SPJ9
The complete question is mentioned below:
In the straightedge and compass construction of the parallel line below, which of the following reasons can you use to prove that JK and LN are parallel?
A. ∠ MLN ≅ ∠ MNL by construction.
B. ∠ NLJ ≅ ∠ MJK by construction.
C. ∠ MJK ≅ ∠ MKJ by construction.
D. ∠ MLN ≅ ∠ MJK by construction.
need help with inequalities problem
ll and lll is the answer.
never said anything about
Find the first five terms of each sequence. aₙ =-2 n-1
The first five terms of the sequence are -3, -5, -7, -9, -11
What is a sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given,
aₙ =-2 n-1
a1 = -2 - 1 = -3
a2 = -4 -1 = -5
a3 = -6 -1 = -7
a4 = -8 -1 = -9
a5 = -10 - 1 = -11
To learn more about sequences from given link
https://brainly.com/question/7882626
#SPJ4
Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
∠4 and ∠ 6
The relationship between the ∠4 and ∠6 is that both are alternate interior angle.
Given,
The angles = ∠4 and ∠6
Here,
The ∠4 and ∠6 lie on the opposite sides of the transversal and both are nonadjacent interior angles
So, ∠4 and ∠6 are alternate interior angle.
Hence, The relationship between the ∠4 and ∠6 is that both are alternate interior angle.
Complete question is:
Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
∠4 and ∠ 6
Learn more about alternate interior angle here
brainly.com/question/2656732
#SPJ4
y varies directly with x .
If y=6 when x=2 , find x when y=12 .
The required value of x is 4 by using constant of proportion.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of y
When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion —-- 1
Now, find k for given x = 2 and y = 6, we need to put these values in equation 1, i.e.
6 = k(2)
k = 6/2
k = 3
Further calculate x for given y = 12 and constant of variation = 3 i.e.
12 = (3)x
x = 4
Hence, the required value of x is 4.
To learn more about the constant of proportion, visit the link:
https://brainly.com/question/24868934
#SPJ4
Solve this multi-step problem. A runner completes of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?
The runner completes a 10 miles race in 16 minutes.
According to the question we have been given that,
Runner takes 8 minutes to complete = 5 miles race
We need to find that if the runner is in the same pace then how many miles the runner completes in 16 minutes
This multi-step problem can be solved using the unitary method. That is,
8 minutes = 5 miles
1 minute = 5/8 miles
16 minutes = 5/8*16 miles
= 5*2 miles
= 10 miles
Hence runner completes a 10miles race in 16 minutes
Learn more about unitary method here : https://brainly.com/question/8083231
#SPJ9
the first box is either greater than or less than and the second box is either including or not including
The interpretation of the interval is that the solution set is all real numbers equal or greater to -4.
What is the standard interval notation?The standard interval notation of an interval of lower bound a and upper bound b is given by:
[a,b].
For the interval given in this problem, we have that:
The lower bound is x = -4.There is no upper bound, the interval goes to infinity.Hence the interpretation of the interval is that the solution set is all real numbers equal or greater to -4.
More can be learned about interval notations at https://brainly.com/question/28261641
#SPJ1
Solve for x in terms of y
4x+2y=7
Answer:
x= -(2y+7)/(4)
Step-by-step explanation:
4x+2y=7
4x = -2y+7
x= -(2y+7)/(4)
Answer:
x = [tex]\frac{7-2y}{4}[/tex]
Step-by-step explanation:
4x + 2y = 7 ( subtract 2y from both sides )
4x = 7 - 2y ( divide both sides by 4 )
x = [tex]\frac{7-2y}{4}[/tex]
What is an equation of the line that passes through the point (4,1)(4,1) and is perpendicular to the line 2x-y=42x−y=4?
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line is given below.
2x - y = 4
Then the slope of the perpendicular line will be
y = 2x - 4
m = 2
Then the equation of line will be
y = -(1/2)x + d
Then the line is passing through (4, 1), then we have
1 = -(1/2)4 + d
3 = d
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3
More about the equation of a perpendicular line link is given below.
https://brainly.com/question/14200719
#SPJ1
An investment portfolio is shown below.
Investment Amount Invested ROR
Savings Account $2,600 1.7%
Municipal Bond $3,700 3.2%
Preferred Stock $575 12.9%
Common Stock A $1,225 −5.6%
Using technology, calculate the weighted average ROR of the investments. Round to the nearest tenth of a percent.
2.1%
3.1%
5.9%
7.5%
Using technology, the weighted average ROR of the investment, rounded to the nearest tenth of a percent is 2.1%
What is the weighted average ROR?
The weighted average ROR means the rate of return of the four investments combined together to give a single return, which is computed as the sum of the RORs multiplied by the percentage of total portfolio invested in each security.
total investment=$2600+$3700+$575+$1225
total investment=$8100
% invested in each security=amount invested in each security/total investment
weighted average ROR=(1.7%*$2600/$8100)+(3.2%*$3700/$8100)+(12.9%*$575/$8100)+(-5.6%*$1225/$8100)
weighted average ROR=2.1%
Find out more about weighted average ROR on:https://brainly.com/question/28683603
#SPJ1
At Bell High School, 43% of the students own a CD player and 28 % own a CD player and an MP3 player. What is the probability that a student owns an MP3 player if he or she also owns a CD player?
According to the question, Let us assume the total number of students is [tex]100[/tex]. In which [tex]43[/tex] students own a CD player. And [tex]28[/tex] students own both CD player as well as MP3 Player.
Now, to calculate the probability that a student owns an MP3 player and also they own a CD player. It is clear from the given data, the percentage is higher than [tex]28[/tex] percent.
Using conditional probability rule:
[tex]P(MP3|CD) = \frac{P(MP3 and CD)}{P(CD)} = \frac{0.28}{0.43} = 0.65[/tex]
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
To learn more about the Probability from the given link:
https://brainly.com/question/13604758
#SPJ4
Graph the line with the equation y = -4/3x+1
Answer: coordinates would be 0,1 and 3,-3
Step-by-step explanation:
