Answers
Answer:
Let 'a' be the first term, 'r' be the common ratio and 'n' be the number of terms
Series = 2+6+18.......= 2+2•3¹+ 2•3².......= 728
Now,
[tex]Sum = \frac{a( {r}^{n} - 1) }{(r - 1)} \\ [/tex]
So,
[tex] \frac{a( {r}^{n} - 1)}{(r - 1)} = 728 \\ \frac{2( {3}^{n} - 1) }{(3 - 1)} = 728 \\ \frac{2( {3}^{n} - 1) }{2} = 728 \\ {3}^{n} - 1 = 728 \\ {3}^{n}=728+1\\ {3}^{n} = 729 \\ {3}^{n} = {3}^{6} \\ \boxed{ n = 6}[/tex]
Therefore, number of terms is 6
6 is the right answer.Its a GP given by 2+6+18
First term=a=2Common ratio=r=
[tex]\\ \bull\tt\looparrowright \dfrac{6}{2}=3[/tex]
Now
[tex]\\ \bull\tt\looparrowright S_n=728[/tex]
[tex]\\ \bull\tt\looparrowright \dfrac{a(r^n-1)}{r-1}=728[/tex]
[tex]\\ \bull\tt\looparrowright \dfrac{2(3^n-1)}{3-1}=728[/tex]
[tex]\\ \bull\tt\looparrowright \dfrac{2(3^n-1)}{2}=728[/tex]
Cancel 2[tex]\\ \bull\tt\looparrowright 3^n-1=728[/tex]
[tex]\\ \bull\tt\looparrowright 3^n=728+1[/tex]
[tex]\\ \bull\tt\looparrowright 3^n=729[/tex]
[tex]\\ \bull\tt\looparrowright 3^n=3^6[/tex]
[tex]\\ \bull\tt\looparrowright n=6[/tex]
Related Questions
please I can't understand this question ⁉️
please help
Answers
Answer:
gauth math
got it perfect answer
Explain how you can use absolute value to tell whether
the sum of two integers is positive or negative.
Answers
Answer:
Let the integers are p and q.
In case both integers are positive or negative, you add the numbers up and apply their sign to the sum.
Examples:
10 + 88 = 98-20 + (-15) = -35In case one of the integers is negative and one positive.
p < 0, q > 0Use absolute value in this case.
Subtract the numbers and apply the sign of the number with the greater absolute value.
Examples:
- 10 + 15 = |15 - 10| = |5| = 5- 15 + 10 = - |15 - 10| = - |5| = -5Step-by-step explanation:
Let the numbers be x and y
If both are of same signs then
|x + y| = x + y
-|x + y| = -(x + y) = -x - y
If one is negative and one is positive
-|x + (-y)| = -|x - y| = -x + y
-|y + (-x)| = -|y - x| = -y + x
You are offered an hourly job making $19 per hour. If you are scheduled to work 45
hours per week. What would the weekly gross pay for this job be?
Answers
Answer: 855 is the answer
AAAAAAAAAAHHHHHHHHHHHH!!!!!!!!!
Answers
Answer:
[tex] \sqrt{12} \times \sqrt{27} \\ = 2 \sqrt{3} \times 3 \sqrt{3} \\ 6 \sqrt{3 } \times \sqrt{3} \\ = 6 \times 3 \\ = 18 \\ thank \: u[/tex]
Answer:
18
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
its correct i solved it by paper im lazy typing it here lol, anyways 18 has to be the correct answer.
hope i helped
Problem 10
(a) A teacher selects a team of three from a group of students. She also
selects a team of two (students can be in more than one team). The
teacher notices that there are twice as many ways of choosing the
team of three as there are the team of two. How many students are
in the group?
(b) For another group of students, there are three times as many teams
of three which can be selected as there are teams of two. How many
teams of three can be selected from this group?
Answers
Using the combination formula, it is found that:
a) There are 8 students in the group.b) 165 teams of three can be selected from this group.---------------------------
The order in which the students are chosen is not important, which means that the combination formula is used to solve this question.
Combination formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
---------------------------
Question a:
3 students from a set of n, thus: [tex]C_{n,3}[/tex]2 students from a set of n, thus: [tex]C_{n,2}[/tex]Twice as many ways to choose the teams of 3 than the teams of 2, thus:
[tex]C_{n,3} = 2C_{n,2}[/tex]
[tex]\frac{n!}{3!(n-3)!} = 2\frac{n!}{2!(n-2)!}[/tex]
We have to solve for n, thus:
[tex]2!n!(n-2)! = 2(3!)(n!)(n-3)![/tex]
[tex](n-2)! = 3!(n-3)![/tex]
From the factorial concept: [tex](n-2)! = (n-2)(n-3)![/tex], thus:
[tex](n-2)! = 3!(n-3)![/tex]
[tex](n-2)(n-3)! = 3!(n-3)![/tex]
[tex]n - 2 = 3![/tex]
[tex]n - 2 = 6[/tex]
[tex]n = 8[/tex]
There are 8 students in the group.
---------------------------
Question b:
First we have to find the total number of students, using the same logic as item a.
[tex]C_{n,3} = 2C_{n,2}[/tex]
[tex]\frac{n!}{3!(n-3)!} = 3\frac{n!}{2!(n-2)!}[/tex]
[tex]2!n!(n-2)! = 3n!3!(n-3)![/tex]
[tex]2(n-2)(n-3)! = 18(n-3)![/tex]
[tex]n - 2 = 9[/tex]
[tex]n = 11[/tex]
---------------------------
The number of teams of three is:
[tex]C_{11,3} = \frac{11!}{3!8!} = 165[/tex]
165 teams of three can be selected from this group.
A similar problem is given at https://brainly.com/question/23302762
The diner sells 4 different sandwiches, 6 different drinks, and 3
different deserts. How many different orders could you place if you
decided to buy a sandwich and a desert?
Answers
Answer:
sandwich and drink only (no dessert)
so 4 x 6 = 24
you have 24 different combinations you can do
hope this helps
Step-by-step explanation:
Find the measure of unknown angle
Answers
Answer:
120 + z = 180 (linear pair)
=> z = 180 - 120
=> z = 60
130 + y = 180 (linear pair)
=> y = 180 - 130
=> y = 50
50 + 60 + x = 180 (Angle sum property of a triangle = 180)
=> 110 + x = 180
=> x = 180 - 110
=> x = 70
write 19.6 as a fraction
Answers
The answer would be 98/5
ayudenme con esto por favor
Answers
Answer:
the answer is on the computer
Step-by-step explanation:
please help!!! the question is in the picture above— this is geometry
Answers
Use the co‐interior rule, corresponding angle rule, alternate angle rule and vertical opposite angle rule to solve the question above.
angle G5 = angle K1 reason : corresponding angles
angle J1 = angle H3 reason: vertical opposite angles
angle J2 = angle K4 reason: vertical opposite angles
angle G5 = angle K4 reason: co‐ interior angles
angle F6 = angle K4 reason: alternate angle
Calculate the area of each figure.
(PLS HELP )
Answers
Then u calculate the rectangle part L x B which is 10 x 17 = ? Then when you have the ans already, add them!
starting at school, you and your friend ride bikes in different directions- you ride 4 blocks north and your friend rides 3 blocks west. at the end of the adventure, how far apart are you and your friend?
Answers
Which of the following rules should be used to find the area of a triangle?
Divide area by length.
Divide the sum of the upper and lower sides by 2.
Multiply length by width by height.
Multiply base by altitude.
none of these
Answers
Answer:
none of these
Step-by-step explanation:
area of the triangle =height ×base and then divide by 2
2f - 3(4f - 5g) + 5g + 7fg
Help pls how to solve it?
Answers
Step-by-step explanation:
2f - 3(4f - 5g) + 5g +7fg
multiply the 3 in
2f - 12f - 15g + 5g + 7fg
add or subtract common terms
-10f -10g +7fg will be your final answer
Answer:
Step-by-step explanation:
As the question did not say how to 'solve the question', I would assume it will be to simplify the equation, as there is no way of solving an expression without an answer.
Simplify:
2f - 3(4f-5g) + 5g +7fg
Get rid of the parentheses
2f - 12f - 15g + 5g +7fg
Simplify similar expressions
-10f - 10g + 7fg
Therefore, 2f - 3(4f-5g) + 5g +7fg simplified is equal to -10f - 10g + 7fg.
Write the perimeter of the rectangle in simplest form
Answers
Answer:
6v+16
Step-by-step explanation:
2(2v+13) + 2(v-5) > 4v+26+2v-10 > 6v+16
Answer:
Perimeter is 6v + 16
Step-by-step explanation:
Perimeter formular of rectangle:
[tex]{ \sf{perimeter = 2(length + width)}} \\ { \sf{p = 2(l + w)}}[/tex]
length is (2v + 13)
width is v - 5
[tex]{ \sf{p = 2 \{(2v + 13) + (v - 5) \}}} \\ { \sf{p = 2 \{(2v + v) + (13 - 5) \}}} \\ { \sf{p = 2(3v + 8)}} \\ { \sf{p = 6v + 16}}[/tex]
Will give brainliest! Simplify 6 ÷ 2 · 3 - 6² ÷ 2² - 3²
Thanks!
Answers
. is written as ×
Step-by-step explanation:
6 ÷ 2 × 3 - 6² ÷ 2² - 3²
6 ÷ 2 × 3 - 36 ÷ 4 - 9
3 × 3 - 9 - 9
9 - 9 - 9
0 - 9
- 9
Answer:
Enter the expression you want to simplify into the editor.
The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. The calculator works for both numbers and expressions containing variables.
Step-by-step explanation:
HELP DUE IN 15 MINS!
Solve for x:
2x - 5 = -x + 19
Answers
Answer:
I HOPE IT WILL HELP YOU.
Have a great day ahead.
Please help quickly!
Answers
Answer:
Step-by-step explanation:
Stop doing it
The factorization of x² + x + xy + y + zx + z is
answer meenu plz
Answers
Answer:
[tex]x2+x+xy+y+zx+z \\ =x(x+1+y+y+z)+z \\ =x(x+2y+z+1)+z
[/tex]
Step-by-step explanation:
take like terms together..
x²+x+zx+xy+y+z
x(x+z+y)+y(x+y+z)
(x+y)(x+y+z)
hope it helps
Chose the correct property
(8•3)4 = 8(3•4)
A) Commutative Property Of Multiplication
B) Associative Property Of Multiplication
C) Neither
Answers
Answer:
B) Associative Property of Multiplication
Step-by-step explanation:
The associative property states you can change where the parentheses (grouping terms) are in a multiplication statement, and you'll get the same product.
More generally:
(a * b) * c = a * (b * c)
Answer:
B) Associative Property Of Multiplication
Step-by-step explanation:
The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
Therefore, changing the grouping of (8x3) or (3x4) does not change the product.
If the surface area of a cylinder is given by SA =
2nr^2+2nrh, calculate the height if the surface area is 30n and the radius is 2.
Answers
Answer:
The height is 11/2
Step-by-step explanation:
We know SA = 30n
and r = 2
We are solving for h. So plug in our values
30n = 2n(2)^2 + 2n(2)h
Multiply and square on the right side terms
30n = 8n + 4nh
Divide everything by n
30 = 8 + 4h
Subtract 8 on both sides
22 = 4h
Divide by 4 on both sides
h = 22/4 = 11/2
Check:
30n = 2n(2)^2 + 2n(2)(11/2)
30n = 8n + 22n
30n = 30n
solve please this question
Answers
Step-by-step explanation:
[tex]sum \: of \: angles \: in \: a \: circle = 360 \\ so \\ 5a + 2a + 2a + 5a + 4a = 360 \\ 18a = 360 \\ a = \frac{360}{18} \\ a = 20 \\ thank \: you[/tex]
60 CHALLENGE The Queen Isabella Memorial Bridge connects South Padre Island, Texas, to
Port Isabel on the mainland. Suppose one crew began building from South Padre Island,
and another crew began building from Port Isabel. The two crews met 6256.5 feet from the
South Padre Island side of the bridge approximately 2.5 years after construction began.
a. Suppose the South Padre Island crew built an average of 208.5 feet per month.
Together the two crews built 12,513 feet of bridge. Determine the average number of
feet built per month by the Port Isabel crew.
307
b. About how many miles of bridge did each crew build?
c. Is this answer reasonable? Explain.
2,513
Answers
With some give information, we need to solve some algebraic problems that involve a change of units, lets see step by step how we do that:
A) First, we know that:
The bridge was constructed in 2.5 years
Knowing that 1 year = 12 months, we can rewrite:
2.5 years = (2.5)*(12 montsh) = 28 months
The two crews built, together, 12,513 ft of the bridge.
Now, we know that the South Padre Island crew built an average of 208.5 per month.
Then in the 28 months for the whole construction, they built 28 times that amount:
D = (28 months)*(208.5 per month) = 5,838 ft
Then the rest was constructed by the Port Isabel Crew.
They constructed 12,513 ft - 5,838 ft = 6,675ft
So that crew constructed 6,675 ft in 28 months, then the average number of feet built per month (the quotient between the total amount built and the number of months in which that was built) is:
6,675 ft/28 months = 238.39 ft per month.
b)
South Padre Island crew constructed 5,838 ft
Port Isabel Crew constructed 6,675ft
Now we want to transform these to miles.
Remember that;
1 mille = 5280 ft.
Then to transform from ft to miles, we just need to divide our measures by 5280 ft
Then:
South Padre Island crew constructed 5,838 ft = (5,838ft/5280ft) mi = 1.11 mi
Port Isabel Crew constructed 6,675ft = (6,675ft/5280ft) mi = 1.26 mi
c) Is this answer reasonable?
Mathematically, yes, both crews constructed about the same in about the same time, with a small difference that may be related to the sizes of each crew or something like that.
We could conclude that this would not be reasonable if the monthly rates were dramatically different.
If you want to learn more, you can read:
https://brainly.com/question/15051367
Someone please help :))
Answers
PLZ help me 15 points
Answers
Answer:
[tex]\frac{12}{3} - 5 +16 : 4 = 3[/tex]
Step-by-step explanation:
[tex]\sqrt{144} = 12\\\sqrt[5]{243} = 3\\\\\sqrt[3]{64}= 4[/tex]
Hey guys I need help in these. Thanks in advance^^
1) In which operations does the order of the numbers make a difference to the
final answer? Find out what this rule is called.
2) If evaluating the sum 2+3+4 does it make a difference which two numbers !
add first? Is the same true for the other operations? What's this rule called?
Answers
Answer:
Read explanation
Step-by-step explanation:
The two operations that you will get the same answer for no matter what order you do it is addition and multiplication.
Bonus: Technically, if you had something like 1-2-3 you could rewrite it as 1 + (-2) + (-3) and now it won't matter the order and for something like 1/2/3 you could rewrite as 1 * (1/2) * (1/3) and not it wont matter the order too!
This propetie is called the associative property of addition and multiplication.
In the second question since its addition the order you do it in does not matter.
Why: If you think of it logically adding in a diffrent order than the question does not matter since in the end your still adding the same ammount.
Remember: You can only swap the orders if everything is addition or multiplication and remember your order of operations when using this propety in the years to come.
Hoped this helped, Eddie K.W.
Solve the following: -7x + 5 = 8x - 25
Answers
Answer:
x=30
Step-by-step explanation:
Subtract 5 from both sides of the equ
(X^8/yz^5)^m=1 find the value of m
Answers
Answer:
0
Step-by-step explanation:
Any nonzero number to 0 power results in 1.
This implies m is simply 0 since it would give
(x^8/yz^5)^0 which is 1.
Answer:
the value of "m" is 0
Step-by-step explanation:
the entire fraction is equal to 1, the fraction is raised to a power of 0, non-zero
raised to the power of 0 is always equal to 1 so then its
(\frac{x^{8}}{yz^{5}})^0 =1
now then this gives us the value of "m" = 0
hope that helps>3
please help me with this
I will give brainlist
questions number 12 and 13
Answers
Answer:
hope this helps you have a great
Help please, would be much appreciated
Answers
Hey there! I'm happy to help!
We see that all of our y-values go negative and our x-values stay the same. It isn't a rotation because then our x-values will switch, but they haven't switched in our problem, so A and D are incorrect.
Reflecting over the line y=x is just reflecting over a diagonal line, and that will switch the x-value as well.
The correct answer is B. reflect over the x-axis. All of the x-values stay the same here, but the y-values are all on the other side of the x-axis, so they are all negative now, and this matches the change we see with our points.
Have a wonderful day and keep on learning! :D