Answer:
a) 10th term is 0.051
b) The sum of first 18 terms of given sequence is 51.48
Step-by-step explanation:
We are given the sequence 26, 13, 6.5, ..... we need to find
a) 10th term
b) Sum of first 18 terms
Before solving we need to determine if the sequence is arithmetic or geometric
The sequence is arithmetic if common difference d is same.
The sequence is geometric if common ratio r is same.
Finding common difference d: 13-26 = -13, 6.5-13= -6.5
As common difference is not same so, the sequence is not arithmetic.
Finding common ratio r : 13/26 =0.5, 6.5/13= 0.5
As common ratio is same so, the sequence is geometric.
a) Finding common difference: 13-26 = -13, 6.5-13= -6.5
As common difference is not same so, the sequence is not arithmetic.
a) 10th term
The formula to find 10th term is: [tex]a_n=a_1r^{n-1}[/tex]
We have a₁=26 and r = 0.5 n=10
[tex]a_n=a_1r^{n-1}\\a_{10}=26(0.5)^{10-1}\\a_{10}=26(0.5)^{9}\\a_{10}=0.051[/tex]
So, 10th term is 0.051
b) Sum of first 18 terms
The formula to find sum of geometric series is: [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
where a= 1st term, r = common ratio and n= number of terms
In the given sequence we have
a=26, r=0.5 and n=18
Finding sum of first 18 terms
[tex]S_n=\frac{a(1-r^n)}{1-r}\\S_{18}=\frac{26(1-(0.5)^{18}}{1-0.5}\\S_{18}=\frac{26(0.99)}{0.5}\\S_{18}=\frac{25.74}{0.5}\\S_{18}=51.48[/tex]
So, sum of first 18 terms of given sequence is 51.48
The new post office has an area that is 6.5 times the area of the old post office. Let p represent the area of the old post office. Write an expression to represent the area of the new post office?
Answer:
[tex]Area = 6.5p[/tex]
Step-by-step explanation:
Given
[tex]Area\ of\ Old = p[/tex]
[tex]Area\ of\ New = 6.5 * Area\ of\ Old[/tex]
Required
Write an expression for the area of new post office
From the question, we have the following:
[tex]Area\ of\ Old = p[/tex]
and
[tex]Area\ of\ New = 6.5 * Area\ of\ Old[/tex]
Substitute p for Area of Old in the second equation
[tex]Area\ of\ New = 6.5 * p[/tex]
[tex]Area\ of\ New = 6.5 p[/tex]
Hence, the expression is:
[tex]Area = 6.5p[/tex]
Olivia needs 54 ticks for every 3 lollipops she eats. Complete the table using equivalent ratios. Lollipops
Answer:
36:2
90:5
Step-by-step explanation:
I got 2 because if we figure out how many licks she gets for every 1 lollipop that will help find the other numbers. When we divide 54 by 3 we get 18. For every 1 lollipop she lickes 18 times. To figure out how many lollipops for 36 I added 18 plus 18 which gives me 36. I added it twice or multiples by 2. Since I multiplied by 2 the lollipops will be 2. Since we know the rate of change which is 18. We know that for 3 lollipops the person will lick 54 times. I added 54 plus 18 two times which gave me 90. So for 90 licks the person will have 5 lollipops. I hope this helps.
Arianna correctly simplified an expression. When she substituted x=2 into the simplified expression, the value was –4. Which could be Arianna’s original expression? One-sixth (negative 3 x minus 24)
One-sixth (negative 5 x minus 8)
One-sixth (negative 10 x minus 4)
One-sixth (negative 12 x minus 16)
Answer:
Step-by-step explanation: 1/6(-10x-4) or C
Answer: C
Step-by-step explanation:
PLEASE HELP ME ! ! ! ! :(
The slope would be -3/1.
Why do all verified people who answer, are always wrong
Answer:
they probably do it just to get more answer points or whatever the brianily thing is called
Step-by-step explanation:
What is the inverse function F(x)=-1/2(x+3)?
The inverse of the function f(x) is
[tex]f^{-1}[/tex] (x) = 2x - 3
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 1/2 (x + 3)
Put f(x) = y
y = 1/2 (x + 3)
Replace y and x.
x = 1/2 (y + 3)
Find y.
2x = y + 3
y = 2x - 3
This means,
[tex]f^{-1}[/tex] (x) = 2x - 3
Thus,
The inverse of f(x) is 2x - 3.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ2
Hi, I will give brainliest if someone can help me with this problem.
Answer:
(C)Zero
Step-by-step explanation:
Because of the zero on top of the y in the division anything that you multiply or divides is always zero even a negative so the answer is zero
Answer:
Zero
Step-by-step explanation:
Anything multiply or divide by 0 is always 0
HELP ASAP TIMED! GIVING BRAINLIEST
Answer:
4680
Step-by-step explanation:
65% of 7200 is 4680
Answer:
4680
Step-by-step explanation:
65% of 7200 is 4680
If two triangles are congruent, which of the following statements must be
true? Check all that apply.
Answer:
A, C, D are true.
Step-by-step explanation:
Answer: A,B,C,D
Step-by-step explanation:
ALL ARE TRUE I JUST TOOK THE TEST A P E X
Which of the following equations is equivalent to 4(a + 2) – 2(a – 8) = 24?
Answer:
Step-by-step explanation:
4a + 8 - 2a + 16 = 24
Solving like terms
2a + 24 = 24
2a = 24 - 24
2a = 0
Answer: 2a+24=24
Step-by-step explanation: How to get the CORRECT answer:
4(a+2)-2(a-8)
4a + 8 - 2 (a-8)
4a + 8 - 2a + 16
2a + 8 + 16
2a + 24
Final Answer: 2a + 24
I also got it correct on my test, hope this helps :)
What is the equation of the line parallel to the given line.
3. Evaluate the expression. (1 point) 6(x+7) for x=9
A. 12
b. 42
c. 96
d. 16
Answer:
C. 96
Step-by-step explanation:
x = 9, so we have:
6 · (9 + 7) = 6 · 16 = 96
Please give me Brainlest!
The sum of two numbers is 60. The greater number is 6 more than the smaller number. Which equation can be used to solve for the smaller number?
1) x + (x + 6) = 60
2) x- (x + 6) = 60
3) x(x + 6) = 60
04) x(x-6) = 60
Answer:
1) x + (x + 6) = 60Step-by-step explanation:
Let the numbers be x and y
x + y = 60y = x + 6Then, substituting y:
x + (x + 6) = 60Correct option is 1)
An airport shuttle service charges $15 plus $1.15 per mile. An equation is written as y=mx+b, where y is the cost for x miles.
Answer: See explanation
Step-by-step explanation:
You didn't really say what you need to calculate but let me try to help out.
From the question, we are informed that an airport shuttle service charges $15 plus $1.15 per mile and that an equation is written as y=mx+b, where y is the cost for x miles.
The equation can be expressed as:
y = 15 + 1.15x
where,
15 = y intercept and this is the initial fixed cost
1.15 = slope and this is the cost per mile
x = number of miles
What value should go in the empty box to complete the calculation fro finding the product or of 23.456 * 0.86
Can anyone help me I did it I'm just checking :)
Answer:
x = 12Step-by-step explanation:
2x + 5 = 3x - 7
5 + 7 = 3x - 2x
12 = x
Maya will deposit $1,650 in an account that earns 5% simple interest every year. Her brother, James, will deposit $1,600 in an account that earns 8% interest compounded annually. The deposits will be made on the same day, and no additional money will be deposited or withdrawn from the accounts. Compare and contrast the two siblings' accounts after four years
Answer:
each year james gets 3% more interest than maya. over 4 years james gets 34% interest and maya gets 20%. over 4 years james gets 16% more than maya.
Sneezy's bank account increased from $1,200 to $1,800. By what percent did the amount of money in his bank account increase?
Answer:
66.6
Step-by-step explanation:
1200/1800x100 = 66.6
Answer:
increased by 50%
Step-by-step explanation:
($1,800/$1,200)*100= 150%
150%-100%=50%
4 Ted finished 1/8 of his homework this
morning and 3/4this afternoon. How
much homework does Ted have left?
Answer:
6 /1
Step-by-step explanation:
1/8+3/4= 24/4 = 6 or 6/1
After Thanksgiving, Fernando had 3/8 of a pumpkin pie left. Later that night, 1 point
Fernando ate 2/3 of the remaining pie. How much of the pumpkin pie did
Fernando eat?*
3/8 of the pie
9/16 of the pie
1/4 of the pie
06/24 of the pie
Answer:
(C) 1/4 of the pie.
Step-by-step explanation:
Given that Fernando had 3/8 of a pumpkin pie left.
So, the remaining pie= 3/8 of a pie.
As Fernando ate 2/3 of the remaining pie, so,
the portion of a pie that Fernando ate = 2/3 x 3/8 of a pie = 1/4 of a pie.
So, Fernando ate 1/4 of a pie.
Hence, option (C) is correct.
Ricky is solving a multiplication problem where both terms include decimal values. The first term has 4 digits after the decimal. The second term has 5 digits after the decimal. The product will have how many digits after the decimal?
Answer:
9 digits
Step-by-step explanation:
when doing multiplication with decimals the amount of digits after the decimal in the final product will be the sum of the amounts of digits after the decimal in the two numbers being multiplied together
For example, If you were to multiply 6.789 by 10.321 the answer would be 70.069269. There are six digits after the decimal because the numbers being multiplied each have three digits after their decimals
(If that makes sense. If not, I'm sorry)
At one gas station, gas costs $2.75 per gallon. Write an equation that relates the total cost, C, to the number of gallons of gas purchased, g.
Answer:
2.75g=c
Step-by-step explanation:
not quite sure what your asking, but this is my best answer you take the 2.75 base cost, add the variable G for the gallons purchased which gives you 2.75g which in the end would give you the total cost (C) giving you the equation 2.75g=c
if this isnt what you were asking id be happy to help if you elaborate more or post the exact question your needing help on
(4y + 5) + (-7y - 1)
Answer:
-3y+4
Step-by-step explanation:
(4y + 5) + (-7y - 1)=
4y-7y+5-1=
-3y+4
Identify the value of the 4 in the number : 45,348
Answer:
I wasn't sure which 4 you were talking about, but I hope this helps! xx
Step-by-step explanation:
4- hundred-thousands
5- ten-thousands
3- thousands
4- hundreds
8- tens
HELP!!!!! I will mark Brainly
Answer:
D
Step-by-step explanation:
2x + 3 > -9
2x > -12
x > -6
Choice D represents x > -6
Answer: i think its the last one but if not then the second to last
Step-by-step explanation:
Find three consecutive odd integers such that when the third is subtracted from five times
the sum of the first and second, the result is 798 more than the first.
9514 1404 393
Answer:
99, 101, 103
Step-by-step explanation:
Let x represent the smallest. Then the sum of the first two is (x+x+2) and the third is x+4. The problem statement tells us the relation ...
5(2x +2) -(x +4) = x +798
10x +10 -x -4 = x +798
8x = 792
x = 99
The integers are 99, 101, 103.
__
Check
5(99 +101) -103 = 99 +798
897 = 897 . . . . answer checks OK
PLZZZZ HELPPPPPP THIS IS TIMEDDDD!!!! *look at picture*
A person and a building cast a shadow at the same time of day. The person is 5.8 feet tall in case the shadow of 3.2 feet. The building cast a shadow of 28 feet.
Find the height of the building.
round your answer to the nearest 10th of a foot.
Answer:
Height of the building = 50.8 ft
Step-by-step explanation:
A person and a building are casting the shadows at the same time of the day.
Triangles formed by the person and his shadow and the building and its shadow will be similar.
Therefore, corresponding sides of the similar triangles will be proportional.
[tex]\frac{x}{28}=\frac{5.8}{3.2}[/tex]
x = [tex]\frac{5.8\times 28}{3.2}[/tex]
x = 50.75
x ≈ 50.8 ft
Answer:
50.8 feet is correct
Step-by-step explanation:
test says so
Marks football team has scored about 24 points each game. They played 12 games this season. What is the best estimate for the total numbers of points they scored in the season?
Answer:
About 300 Points
Step-by-step explanation:
24x12=288
288 rounded up is 300
40 passengers in cars = 4 passengers per car
Answer:
if there is 40 passengers and 4 passengers per car there are 10 cars
what is -2(4x+3)-(x-7) = 6
Answer:
It should be x= -5/9
Step-by-step explanation:
-2(4x+3)-(x-7) = 6
Distribute: -8x-6-x+7=6
Solve: -9x+1=6
-9x=5
x=5/-9
2(4x+3)}}-1(x-7)=62(4x+3)−1(x−7)=6
8+6−1(−7)=6