The value of the partial sum of geometric sequence with terms a3 = 36 and a6 = 288 is given by 297. This is obtained by using the concept of partial sum of a geometric progression.
What is geometric progression?
Geometric progression is defined as a series of numbers having a fixed ratio between each term and its preceding term. It is also known as a geometric sequence or G.P., and is exemplified as a1, a2, a3, ….., an
Here, the first term is denoted by a1 and its common ratio is shown by r, which is calculated using the formula a2 by a1. The partial sum of a G.P. is given by a1 ( rn - 1 ) / ( r - 1 ), when r > 1 and a1 ( 1 - rn ) / ( 1 - r ), when r < 1
Calculation of the partial sum of the geometric sequence that satisfies the given conditions. a3 = 36, a6 = 288, n = 5
Given:
Value of a3 = 36
Value of a6 = 288
n = 5
a3 = ar2 — 1
a6 = ar5
Now, a6 / a3 = ar5 / ar2 = 288 / 36
r3 = 8
Taking cube root both sides, we get,
r = 2
Putting the value of r in equation 1,
a3 = a(2)2
36 = 4a
a = 9
As r > 1, using the formula for Sn as a(rn - 1) / (r - 1)
Sn = 9(2n - 1) / (2 - 1)
Sn = 9(2n - 1)
Using n = 5, we have,
Sn = 9[(2)5 - 1]
Sn = 9(32 - 1)
Sn = 9 × 33
Sn = 297
Hence, the value of the partial sum of a G.P. is 297
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ASAP help please!!!
Answer:
linear
Step-by-step explanation:
Ravi drove 536 miles in 8 hours. At the same rate, how long would it take him to drive 871 miles?
Answer:
13 hours
Step-by-step explanation:
536/8=67
871/67=13
Select the verb that is in the incorrect tense.
Lydia grabbed her jacket and ran out the door. She had planed to leave at 8:00 but it was 8:15. She sighs
please please pleasee help me if u cann i need this asap <33
Answer:
"Sighs" should be "Sighed"
Pls pls help whoever gets it right gets a crown
Answer: 76b2
Step-by-step explanation: hope this helps!!!!
Answer:
C
Step-by-step explanation:
(-4b)(-19b)
76b^2
PEMDAS
Determine the correct METRIC length of the cockroach in this image.
A 1.0 in
B 2.5 cm
C 7.5 cm
D 3.0 in
Answer:
I think 7.5 answer is right
Answer:
2.5 cm.
Step-by-step explanation:
7.5 - 5
= 2.5
a health and fitness company is testing a newly designed exercise and weight loss program. it is suspected that the new program is more effective in assisting weight loss. a group of 220 volunteers is first separated into 6 groups, labeled a to f, based upon age and weight such that these qualities are similar within each group. the age and weight of the volunteer is initially measured. within each group, participants are randomly assigned to either undergo the new exercise program or undergo a conventional exercise program. in addition, the daily calorie intake is set to a particular amount, either low, moderate or high, and maintained at that level for the duration of the program. at the end of six months, the percentage of weight lost is measured for each unit and the results are collected and compared.
This testing procedure is an example of a randomized block design experiment.
What do we mean by randomized block design experiment?A randomized block design is a research study in which the experimental units are organized into groups known as blocks. The treatments are assigned at random to the experimental groups within each block. We have a completely randomized block design when all treatments appear at least once in each block. A vaccine trial to check the efficacy of a new vaccine is an instance of block randomization. There are two treatments in this trial scenario: a placebo and a drug. A placebo is a non-therapeutic drug that is given to a doctor in place of the real drug.So, the given situation of a health and fitness company in the testing procedure is an example of a randomized block design experiment.
Therefore, this testing procedure is an example of a randomized block design experiment.
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The correct question is given below:
A health and fitness company is testing a newly designed exercise and weight loss program. It is suspected that the new program is more effective in assisting weight loss. A group of 220 volunteers is first separated into 6 groups, labeled A to F, based upon age and weight such that these qualities are similar within each group. The age and weight of the volunteer is initially measured. Within each group, participants are randomly assigned to either undergo the new exercise program or undergo a conventional exercise program. In addition, the daily calorie intake is set to a particular amount, either low, moderate or high, and maintained at that level for the duration of the program. At the end of six months, the percentage of weight lost is measured for each unit and the results are collected and compared.
This testing procedure is an example of a ____.
In the diagram below of triangle LMN, O is the midpoint of LN and P is the midpoint of MN. If OP = 31 - 2x, and LM = 38 + 4x, what is the measure of LM?
Answer: LM= ?
If O is the midpoint of LN and P is the midpoint of MN and if OP = 31 - 2x, and LM = 38 + 4x, then the measure of LM = 88
As per the question statement, Triangle LMN where O is the midpoint of LN and P is the midpoint of MN and if OP = 31 - 2x, and LM = 38 + 4x, we are supposed to find the measure of LM.
As O is the mid point of LN and P is the midpoint of OP the using the Mid point theorem, we can say that in Triangle LMN
[tex]OP=\frac{LM}{2}[/tex]
Substituting values,
[tex]31-2x=\frac{38+4x}{2} \\2(31-2x)=38+4x\\62-4x=38+4x \\8x = 100\\x=12.5[/tex]
LM = 38 + 4x
[tex]LM = 38 + 4(12.5)\\LM=38 + 50\\LM=88[/tex]
Hence value of LM is 88
This question is a classic example of how to solve linear equations.
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a rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x 5)x
The length and width of the rectangle are: 10 inches and 5 inches.
What is a rectangle?Rectangle refers to a plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Given:
Area of the rectangle = 104 sq. inchesLength of the rectangle is 5 inches more than the width.To find: the length and width of the rectangle.
Finding:
Let the width of the rectangle be 'x'
Then the length of the rectangle = x + 5
Now, area of the rectangle = width (length)
=> 104 = x ( x + 5)
=> x² + 5x - 104 = 0
=> x² + 13x - 5x - 104 = 0
=> (x + 13) (x - 5) = 0
Since the lengths can't be negative, x = 5, i.e., the width of the rectangle = 5 inches
=> Length = 5 + 5 = 10 inches
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please help ill give points !!!!!! porfa
Answer:D
Step-by-step explanation:
Answer:B (8)
Step-by-step explanation:
OVER 50 means anything higher than 50, NOT OLDER THAN 70 means anything that's 70 or lower. So we have a range of 51-70. Now, when we look at the diagram, we can tell that there are 4 people who are 51-60 years old which fits to the range we are looking for. Same with the 4 people in the 61-70 range.
Is -51/5 rational or irrational
Answer: rational
Step-by-step explanation: If a number is terminating number or repeating decimal, then it is rational.
Answer:
Rational
Step-by-step explanation:
If a number has a finite number of digits or could be written in a fraction that consists of numbers with a finite number of digits(-51 and 5 have a finite number of digits), then it is a rational number. Hence, -51/5 is a rational number.
A gallon of paint covers 400 square feet.how many square feet will 2 3/8 gallons of paint cover? 1 point
2 3/8 gallons of paint will cover 950 square feet by unitary method.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
By unitary method,
1 gallon paint covers 400 sq feet.
2 3/8 = [tex]\frac{19}{8}[/tex] gallons of paint will cover: [tex]400(\frac{19}{8})[/tex] = 950 sq. feet
Hence, 2 3/8 gallons of paint will cover 950 square feet by unitary method.
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A hotel business center charges $40 per hour to rent a computer plus a $65 security deposit. The total rental charge is represented by f(X)=40+65. How would the equation change if the business center increased the security deposit by $15?
Answer:
The equation would change to f(x)=40x+80
Step-by-step explanation:
you add 15 to the 65 as that is the security deposit
Answer: It is Yes
Step-by-step explanation:
1. Since y = 40x + 65 was the original equation, when added 15 dollars to the security deposit, the equation changed by adding 15 into 65, changing it's y-int.
Yogurt Express charges $0.27 per ounce for yogurt. Maria pays $8.37 for her yogurt. How many ounces of yogurt did Maria get?
Answer:
31 oz.
Step-by-step explanation:
8.37/0.27 = 31
if one ounce equals $0.27, then Maria bought 31 ounces with the $8.37
unless she had to pay taxes on it, which wasn;t mentioned so I guess she didn't pay taxes :)
Can someone answer this please It's due in 30 minutes
Which square root could be the number shown on the number line?
O A. √15
O B. √17
O C. √26
O D. √24
The square root that could be the number shown on the number line is √17
Which square root could be the number shown on the number line?On the number line, the position of the point is
Point = 4.1
Square both sides of the above equation
So, we have"
Point^2 = 4.1^2
This gives
Point^2 = 16.81
Approximate
Point^2 = 17
Hence, the square root that could be the number shown on the number line is √17
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a elevator at a construction site has a maximum capacity of 2030 pounds. if the elevator operator weighs 230 pounds and each cement bag weighs 75 pounds how many bags of cement can safely lifted on the elevator in one trip
Answer:
Step-by-step explanation:
2030-230=1800
1800/75=24
The ratio of the measures of the three sides of a triangle is 9: 7: 5 . Its perimeter is 191.1 inches. Find the measure of each side.
Answer:
81.9 inches, 63.7 inches, 45.5 inches respectively
Step-by-step explanation:
Total number of units = 9+7+5 = 21
21 units = 191.1 inches
1 unit = 191.1/21 = 9.1 inches
9 units = 9.1 x 9 = 81.9 inches
7 units = 9.1 x 7 = 63.7 inches
5 units = 9.1 x 5 = 45.5 inches
If x - 4y = -10 and 2x + 9y= -3 are true equations, what would be the value of 3x+5y?
The value of the expression 3x + 5y will be 47.
How to calculate the equation?It should be noted that an equation is used in Mathematics to show the relationship the exist between different variables.
The given equations are:
x - 4y = -10 ...... i
2x + 9y= -3 ....... ii
Multiply equation i by 2
Multiply equation ii by 1
2x - 8y = -20 ...... iii
2x + 9y = -3. ..... iv
Subtract equation iv from iii
(2x - 2x) (-8y - 9y) = (-20 + 3)
-17y = -17
Then, we have to divide by the coefficient.
y = -17/-17
y = 1
Since x - 4y = -10.
We will then put the value of y = 1 into the equation
x - 4(1) = 10
x = 10 + 4
x = 14
Therefore, 3x + 5y will be:
=3(14) + 5(1)
= 42 + 5
= 47.
In conclusion, the value of 3x + 5y is 47.
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How many times greater is 700,000 than 70,000?
Answer:
100 times more
help me !!!!!!!!!!!!!!!!!!!!!!!!
Answer:
a. 1.37
b. 1.37
c. 1.37
all of them are 1.37 or they are all 137
Step-by-step explanation:
PLS HELP ME
SHOW WORK
Answer: Equation: 3x-2=4
Solutoin: x=2
Step-by-step explanation:
[tex]x+x+x-1-1=1+1+1+1\\3x-2=4\\3x-2+2=4+2\\3x=6[/tex]
Divide both parts of the equation by 3:
[tex]x=2[/tex]
Write an equation of the line and interpret the slope and y intercept (Will award brainiest answer)
Answer:
[tex]y = 120x [/tex]
Step-by-step explanation:
Equation of a straight line is
[tex]y = mx + b[/tex]
m= slope of line = rise/run which can be computed by taking two points on the line, finding the difference I the y coordinate values and dividing by the correspoding difference in their x coordinate values
b is the y-intercept where the line crosses the y-sxis
Looking at the graph we can see that the line crosses the y-sxis at the origin (0, 0) so the y-intercept is at y=0
The slope is determined by examining the two highlighted points (3, 360) and (2, 240)
Slope =
[tex] \frac{360 - 240}{3 - 2} = \frac{120 }{1} = 120[/tex]
So equation of line is
[tex]y = 120x + 0[/tex]
or
[tex]y = 120x[/tex]
R
On his first three tests Al averaged 76 out of 100.
What score out of 100 must he get on the fourth
test so his average will be 81?
Al must score 96 in his final test to get an average of 81.
An average or mean is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.
If every number in a list is the same number, then the average of the numbers in the list is also this number. Every one of the diverse varieties of average shares this characteristic.
The sum of the of the numbers 2, 3, 4, 7, and 9 is 25, the average of the numbers is equal to 25 divided by 5=5.
Let Al scores x on final test.
Average score on first 3 tests=76
Total score on first 3 tests=76×3=228
Total score in 4 tests=228+x
Average score of 4 tests=(228+x)÷4
Average to be obtained in 4 tests=81
therefore we can equate the two expressions to calculate x.
(228+x)÷4=81
or, 228+x=324
or,x=324-228
or, x=96
Hence Al needs to get 96 on his final test so that his average is 81.
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When she was practising for the 10K, Mirin timed herself.
Her times ranged from 66 minutes down to 54 minutes.
a) Write her times in tolerance notation as in (.... ± ...) minutes.
b) Now calculate her tolerance using percentages as.... mins (± ...%).
Using the percentage concept, it is found that:
a) Her tolerance is of (60 ± 6 minutes).
b) As a percentage, her tolerance times are of 60 minutes (± 10%).
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
For this problem, the interval is between 54 and 66 minutes, that are both within 6 minutes of the mean of 60 minutes, thus:
a) Her tolerance is of (60 ± 6 minutes).
For item b, we want to find the tolerance as a percentage, that is, the percentage that the tolerance of 6 minutes is from the time of 60 minutes, hence:
P = 6/60 x 100% = 0.1 x 100% = 100%.
Hence:
b) As a percentage, her tolerance times are of 60 minutes (± 10%).
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math work that i need help with please
Step-by-step explanation:
B: translated across the y axis and shifted upwards 2 units.
100 points and brainlyiest
ANSWER:
[tex]y=3x+5[/tex]
draw a point at (0,-5). then move up 3 units, and right one unit. draw a pont there. using a ruler, connect the dots and draw arrows on each end to show it continues.
[tex]y=-\frac{3}{2} x+3[/tex]
draw a point at (0,3). move down 3 units, and right 2 units. draw a point there. connect them as before
EXPLANATION:
[tex]y=mx+b[/tex] is the slope-intercept form of an equation, where m is the slope, and b is the y-intercept.
i used desmos, a web application, for the graph
Answer:
y=3x+5
Step-by-step explanation:
Prove: The sum of two multiples of 3 is a multiple of 3.
3m+3n=[?](m+n)
= a multiple of []
The sum of two multiples of 3 is a multiple of 3. This shows the proof is correct.
How to illustrate the information?It should be noted that the information given is to prove that the sum of a multiple of 3 is also a multiple of 3.
This will be illustrated thus. Let's use the numbers 6 and 15. It should be noted that the addition of the numbers will be:
= 6 + 15
= 21
It should be noted that 21 is a multiple of 3. Therefore, the proofing is correct.
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5. Rewrite 252 + 108 in the form A(B+C) where a is the greatest common factor of 252 and 108
and b and care whole numbers.
(Responses: 2, 4, 6, 36, 42, 54, 63)
252 +108 =
Responses: 2, 4, 6, 7, 42, 63, 126)
(
(Responses: 2, 3, 18, 27; 36, 54, 108)
The values of A, B and C are 36, 7 and 3, respectively.
What is the simplified form of the sum of two positive integers?
In this problem we have the addition of two positive integers that are divisible to 2. First, we proceed to decompose each element of the addition as a product of prime numbers:
252 = 2² × 3² × 7
108 = 2² × 3³
The greatest common factor is the greatest integer that can be removed from the addition by distributive property. Then, the greatest common factor is 2² × 3² = 36 and finally:
(2² × 3²) · (7 + 3)
36 · (7 + 3)
The values of A, B and C are 36, 7 and 3, respectively.
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There are twenty marbles in a jar: some are red, some are
blue. You are blindfolded and choose two marbles. No matter how
you choose, at least one marble is guaranteed to be blue. Is it
possible to figure how many blue marbles are in the jar? If so,
how
many are there?
The number of blue marbles in the jar are 8.
Given, the total number of marbles in the jar = 24.
therefore, total number of all possible outcomes = 24.
Let the number of green marbles in Jar be x.
therefore, the number of favourable outcomes = x.
The probability that the marble drawn is green = x/24
But we have the probability of drawing a green marble = 2/3
x/24 = 2/3
3x = 2 (24)
x = 16
Thus , the number of green marbles in the jar = 16
The number of blue marbles = 24 - 16 = 8
Hence, the number of blue marbles in the jar is 8.
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Your question is incomplete.Please find the missing content below.
There are 24 marbles in a jar out of them some are green and remaining are blue. If a marble is drawn from the jar at random, the probability that the green marble drawn is 2/3.Find the number of blue marbles in the jar.
15 + 1.50 = 55 - 4.50
Answer: 6x=40
x=40/6
x=6+2/3
Step-by-step explanation: hope this helps!!!
Step-by-step explanation:
4.50+1.50=55-15
6=40 ........
BRAINLIEST ANSWER IF ANSWERED PROPERLY WITH NO SPAM
Answer:
m = e/c^2
Step-by-step explanation:
e = mc^2
m = e/c^2