Answer:
b. [tex]a_{12}=-177147[/tex]
Step-by-step explanation:
This is a geometric sequence:
[tex]a_n=a_1x^{n-1}[/tex]
where n is the index in the sequence and x is the common scale factor.
In the given sequence here, the common factor is 3:
[tex]-3\div-1=3\\-9\div-3=3\\-27\div-9=3[/tex]
That's the factor, and we know the first term is -1, so you can write the equation for this sequence:
[tex]a_n=(-1)(3)^{n-1}[/tex]
Finally, plug in 12 for n and solve:
[tex]a_{12}=(-1)(3)^{12-1}\\a_{12}=(-1)(3)^{11}\\a_{12}=(-1)177147\\a_{12}=-177147[/tex]
It costs $8 for admission to the Park City Ice Arena. In addition, renting skates costs $4 per hour.
Write an equation that shows how the total cost, y, depends on the length of the rental in hours, x.
Do not include dollar signs in the equation.
40 dollars
Step-by-step explanation:
Answer:
y = 8 + 4x
Step-by-step explanation:
y is the total cost of 1 skating experience.
y = 8 + 4x
This can be read as: the total cost, y, is equal to the admission, $8, plus $4 times the number of hours the skates are rented. No snacks included.
What is 7x + 15 = 9x + 15 - 2x + 1 and how many solutions are there
Answer:
no solutions
Step-by-step explanation:
7x + 15 = 9x + 15 - 2x + 1
Combine like terms
7x+15 = 7x+16
Subtract 7x from each side
7x+15-7x = 7x+16-7x
15 =16
This is not a true statement so there are no solutions
Drag the numbers below to put them in order from least to greatest:
-9 -12 -4
–4 20 -1 -6
Answer:
-12, -6, -4, -1, 9, 20
Step-by-step explanation:
9, -12, -4, 20 -1, -6
putting them in order from least to greatest means that negatives should go to the left (1st), largest should go to the right (last).
The number -9, -12, -4, 20, -6, -1 in the order from least to greatest is -12, -9, -6, -4, -4, -1, 20.
Given data: -9, -12, -4, 20, -6, -1
Starting from the smallest number:
-12 is the smallest number.
Next is -9, which is larger than -12 but smaller than -6.
Then comes -6, larger than -9 but smaller than -4.
After that, we have two occurrences of -4.
Following that is -1, greater than -4.
Finally, the largest number is 20.
So, the numbers in ascending order are: -12, -9, -6, -4, -4, -1, 20.
Learn more about ascending order here:
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Peggy earned $20 for each lawn she mowed last summer. This summer, she raised her price to $23 per lawn. What is the percent increase of Peggy’s charges?
Answer:
15 percent
Step-by-step explanation: You will substract the new value from the old value.
23-20
Now you will get the difference between them and divide that by the original amount.
3/20
This will equal 0.15 in which you now multiply by 100
15 percent
Divide 120ml into the ratio 3:7
Answer:
Step-by-step explanation:
sum of ratio=3+7=10
total=120 ml
first part=3/10×120=36 ml
second part=7/10×120=84 ml
What is 1/3 of 9/5 please help.
How do you solve : 3x^4 - 11x^3 -x^2 + 19x + 6
You can't use long division in this equation.
Step-by-step explanation:
This is a polynomial so we can use rational roots Theorem to solve the equation.
The rational roots simply states that the roots of a polynomial, in the form of
[tex]p{x}^{n} + ax {}^{n - 1} + bx {}^{n - 2} .....r {}^{0} [/tex]
The possible roots of the polynomial are the factors of
p/r.
We say r^0 to represent the constant and p to represent the leading coeffceint.
So the rational roots states the possible roots of a polynomial is
the factors of leading coeffceint/ the factors of the constant.
In this case, the polynomial leading coeffecient is 3 and its constant is 6 so we do the factors of 3 divided by the factors of 6.
The factors of 3, are plus or minus 1 and 3. divided by factors of 6 which are plus or minus 1,2,3,6. So our possible roots are
positive or negative (1,1/2, 1/3,1/6, 3, 3/2).
Now, we see which of the following roots will that the polynomial, P will equal zero.
It seems that -1 can work so by definition, (x+1) is the a factor of the polynomial. So now we use synetheic or long division to cancel out that factor.
So our factored version of the polynomial is
[tex](x + 1)(3x {}^{3} - 14 {x}^{2} + 13x + 6)[/tex]
Now can we continue and factor the right side of the factors.
3 also works so x-3 is a factor as well so
[tex](3 {x}^{2} - 5x - 2)(x + 1)(x - 3)[/tex]
Now factor the quadratic using factoring by grouping
[tex]3 {x}^{2} - 5x - 2 = 3 {x}^{2} - 6x + x - 2 = 3x(x - 2) + 1(x - 2) [/tex]
So our factor are
[tex](3x + 1)(x - 2)[/tex]
So in conclusion our factors are
[tex](3x + 1)(x - 2)(x + 1)(x - 3)[/tex]
And our x values are -1/3, 2, -1, and 3.
Find the value of x in the given figure
Answer:
32°
Step-by-step explanation:
Its pretty strait forward.
2x + 60° + 3x - 40° = 180°
5x + 20° = 180°
5x = 160°
x = 160°/5
x = 32°
Actually I am from India, Please Mark me as brainliest.....
Lynne walks dogs every day to earn money. The fees she charges per month are 1 dog,$40;2 dogs,$37.25 each;3 dogs,$34.50 each;4 dogs,$31.75 each. A pet store wants her to walk 8 dogs if the pattern continues, how much will Lynne charge to walk each of the 8 dogs.
Answer:
The answer is $20.75
A dog: 40$
2: $37.25
3: $34.50
4: $31.75
5: $29
6: $26.25
7: $23.50
8: $ 20.75
Step-by-step explanation:
Minus $2.75 is the pattern
Answer:
$ 59.25
Step-by-step explanation:
The given rates form an AP (Arithmetic Progression).
Let the cost of walking 1 dog be taken as the first term
and,
cost of walking 2 dogs as second term,
we notice that the price per dog is decreasing by 2.75 $ each time the number of dogs is increasing by 1.
So, it's safe to say that
In the AP:
First term is $ 40
Common difference is $ 2.75
Finding the charge to walk each of the eight dogs is like finding the 8th term of the given Series.
Formula for n-th term of a depreciating AP in terms of common difference(d) and first term(a):
[tex] \boxed{ \mathsf{a _{n} = a - (n - 1)d}}[/tex]
[tex] \implies \mathsf{a _{8} = 40 - (8 - 1) \times 2.75}[/tex]
[tex] \implies \mathsf{a _{8} = 40 - 7 \times 2.75}[/tex]
[tex] \implies \mathsf{a _{8} = 40 - 19.25}[/tex]
[tex] \implies \mathsf{a _{8} = \underline{20.75}}[/tex]
Answer:Hence, the charge to walk each of the eight dogs is $ 20.75
Carlos can read 30 pages per hour in the 270 page book he is reading. At this rate, how long will it take him to finish his book?
Answer:
9 hours
Step-by-step explanation:
270/30=9
2x + 3y = 9
3x - y = 8
[tex]\left \{ {{2x + 3y = 9} \atop {3x - y = 8}} \right. <=>\left \{ {{2x + 3y = 9} \atop {9x-3x=24}} \right. <=>\left \{ {{2x+9x+3x-3x=9+24} \atop {9x-3x=24}} \right. \\<=>\left \{ {{11x=33} \atop {9x-3x=24}} \right. <=>\left \{ {{x=3} \atop {y=1}} \right.[/tex]
ok done. Thank to me :>
How can I solve this?
Answer:
This is not possible with 2 equal symbols
i suck at this stuff
pls help asap
ty <3
Answer:
12*2=24
Step-by-step explanation:
A group of 493 people is going on a boat tour. If each boat holds 7 people, how many people will be on the last boat?
Answer:
3 people.
Step-by-step explanation:
493÷7=70 with 3 remaining.
Colin invests £2350 into a savings account. The bank gives 4.2% compound
interest for the first 4 years and 4.9% thereafter. How much will Colin have after
10 years to the nearest pound?
Answer:
£3691 (nearest pound)
Step-by-step explanation:
Consider the rate of compound interest is r and the initial amount of savings is P, hence
[tex]P \ + \ P \ \times \ r \ = \ P \ (\ 1 \ + \ r \ ) \qquad (Final \ amount \ for \ the \ 1st \ year ) \\ \\ \ P \ (\ 1 \ + \ r \ ) \ + \ P \ (\ 1 \ + \ r \ ) \ \times \ r \ = \\ \ P\ ( \ 1\ + \ r \ ) \ ( \ 1 \ + \ r \ ) \ = \ P \ {( \ 1 \ + \ r \ )}^2 \qquad (Final \ amount \ for \ the \ 2nd \ year) \\ \\ \ P \ {(\ 1 \ + \ r \ )}^2 \ + \ P \ {(\ 1 \ + \ r \ )}^2 \ \times \ r \ = \\ \ P\ {( \ 1\ + \ r \ )}^2 \ ( \ 1 \ + \ r \ ) \ = \ P \ {( \ 1 \ + \ r \ )}^3 \\ \\ (Final \ amount \ for \ the \ 3rd \ year)...[/tex]
Therefore, the final amount of savings after nth years of compund interest is
[tex]P \ {( \ 1 \ + \ r \ )}^n[/tex].
Given that 4.2% compound interest was used for the first 4 years to a savings of £2350, thus
[tex]Final \ amount \ for \ the \ first \ 4 \ years \ = \ 2350 \ {( \ 1 \ + \ \frac{4.2}{100} \ )}^4 \ = \ 2770.36[/tex]
Then, taking the final amount of savings previously into an initial amount for the next 6 years with 4.9% compound interest.
[tex]2770.36 \ {( \ 1 + \frac{4.9}{100} \ )}^6 \ = \ 3691.40 \ = \ 3691 \ (nearest \ pound)[/tex]
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Nick and Sally run on the 100m straight track,Nicks's speed is 3m/s,Sally's soeed is 2m/s.If they both start from two sides of the track, running towards each other continuously.Then they would meet each other ... times after 10 minutes
They would meet 30 times after 10 minutes.
Since Nick and Sally run on the 100m straight track, and Nicks's speed is 3m / s, while Sally's speed is 2m / s, if they both start from two sides of the track, running towards each other continuously, to determine how many times they would meet each other after 10 minutes the following calculation should be performed:
30 x 20 + 2 x 20 = 60 + 40 = 100 10 minutes = 600 seconds 600/20 = X 30 = X
Therefore, they would meet 30 times after 10 minutes.
Learn more about maths in https://brainly.com/question/25849676
Please help me with this
Answer:
h,c
Step-by-step explanation:
I NEED HELP I NEED HELP I NEED HELP I NEED HELP I NEED HELP
What do you mean? What’s the question?
Answer:
Unknown
Step-by-step explanation:
Question, not provided.
If 7 out of 25 students have a pet, what percent of the class has a pet?
Answer:
28%
Step-by-step explanation:
(25%-7%)×4
100%-28%
Two boxes are similar. The longest dimension of the smaller box is 6 inches and its volume is 48 in3. The longest dimension of the larger box is 12 inches. What is the volume of the larger box?
Answer:96
Step-by-step explanation:
Last season, your
favorite basketball
team won 20 games. This
season, your favorite
basketball team won 31
games. What is the
percent change in the
number of games that
your favorite team won
from last season to this
season?
Answer:
55%
Step-by-step explanation:
The percent change formula is written like this:
[tex]|\frac{change - original }{original}|[/tex]. In this scenario, the "change" or new value is 31, because it is this season, and the original is last season. Now, 31-20 = 11, and 11/20 = 55%.
HI GUYS CAN SOMEONE PLEASE HELP...
TYSM IT WUD MEAN SO MUCH
Answer:
what do you need help with??
Step-by-step explanation:
i would be happy to help : )
What is the area of 30x40 rectangle in square units?? Will give BRAINLIEST if only correct!!!
Answer:
1200 units 30 times 40 is 1200
1200 sq units
hope this helps
While flying against the wind, the plane covered 1800 km in 2 hours and 40 minutes. On the return flight it spent 16 minutes less because the plane was moving on the direction of the wind. What was the speed of the wind and the speed of the plane?
Answer:
PLANE SPEED --
While flying against the wind - 675 km/h
While flying along with the wind - 750 km/h
WIND SPEED --
Speed of the wind - EXPLANATORY LOOK AT ABOVE DATA
Step-by-step explanation:
If you need the explanation, just comment yes :)
It's a bit long, so I'm not sure if you just wanted the answer or the whole step-by-step explanation.
what is cosec32°/sec58°=
Answer:
1
Step-by-step explanation:
Using the cofunction identity
sec(90 - x) = cosecx , then
sec(90 - 58)° = cosec32° , so
[tex]\frac{cosec32}{sec58}[/tex]
= [tex]\frac{cosec32}{cosec32}[/tex]
= 1
In a certain town, 80% of all married men are working, and 75% of all married men are over 35 years old. Among working married men, 70% are over 35 years old. What proportion of non-working married men are over 35 years old?
answer: 95%
working is needed
It helps to set up a two way table as shown below. Such tables compare 2 different variables. In this case, we're comparing the variables "working status" and "age".
Specifically, the working status separates the men into "working vs non-working". The age variable splits the men into groups of "35 or younger" and "over 35". Usually, but not always, each variable will take on two values.
Let's say this town had 1000 married men. 80% of this is 0.80*1000 = 800 to indicate there are 800 married working men. So we write this in the "total" column for the "working" row. This leaves 1000-800 = 200 nonworking married men, which will go right under the 800.
We're told that 75% of the married men are over 35, so 0.75*1000 = 750 married men are over 35. This goes in the "total" row for the "over 35" column. There are 1000-750 = 250 married men who are 35 and under.
As you can see, the stuff in the total column and the total row must add back to the grand total of 1000 married men overall.
--------------------------------
Another bit of info given is that "Among the working married men, 70% are over 35". We'll only focus on the "working" row. We have 800 total and 70% of this is 0.70*800 = 560 which is the number of working married men over 35. This leaves 800-560 = 240 married men who are not over 35.
At this point, we have 2 spots left in the table. Through guess and check, or using algebra, you should find that there are 190 non-working men over 35 and 10 non-working men who aren't over 35. Make sure that each row and column total checks out.
--------------------------------
By now, the table is fully filled out. See below.
Your teacher now asks "what proportion of non-working married men are over 35 years old?" which means we'll only focus on the "non-working" row. There are 200 men total here, and of this total, 190 are over 35.
So, 190/200 = 0.95 = 95% of the non-working married men are over 35.
Mr. Allen says that the equation y=2x+1 has a solution of (4, 9). Is Mr. Allen right or wrong?
Answer:
right
Step-by-step explanation:
y=2x+1
9=2(4)+1
9=8+1
9=9
What is the greatest common factor of 3 and 33?
Answer:
3
Step-by-step explanation:
Step 1: Find the factors of 3 and 33.
3: 1, 333: 1, 3, 11, 33Step 2: Find the largest common factor they share.
As you can see, the largest common factor they share is 3.Therefore, the GCF of 3 and 33 is 3.
Convert 53 grams to kilograms. 53,000 kg 0.053 kg 5.3 kg 530 kg
Answer:
0.053 kg
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3