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2 years ago

Does anyone know how to do this?

Mathematics

2 answers:

Digiron [165]2 years ago

8 0

Answer: 13

explanation: 3 match sticks are added every time. multiply by 2 to get 6.

7+6 = 13

hope this helps :)

xenn [34]2 years ago

6 0

Answer:

Step-by-step explanation:

4th- 7+3=10

5th- 10+3=13

(There is a pattern of +3)

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Which one is greater explain why. 8/10 and 0.91

BARSIC [14]

Answer:

0.91 because 8/10 as a decimal is 0.8

Step-by-step explanation:

so 0.91 is bigger than 0.8

7 0

3 years ago

Read 2 more answers

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

You usually buy a 16.5-ounce bottle of shampoo. There is a new bottle that says it gives you 30% more free.

Katarina [22]

Answer:

$\frac{x-16.5}{16.5}=0.30$

Hopefully, this is your desired setup. (I noticed the formula you have to fill in there.)

Have a good day.

Step-by-step explanation:

Hi.

You could use the percent change formula.

Since we know it is a percent increase then we will do new-old instead of old-new:

$\frac{\text{new}-\text{old}}{\old}$

x is the new amount of shampoo.

16.5 is the original amount (old) of shampoo.

The percent increase is 30%=0.30 .

So we have the following equation:

$\frac{x-16.5}{16.5}=0.30$

We could have found the equation like this:

$16.5+16.5(0.30)=x$

Subtract 16.5 on both sides:

$16.5(0.30)=x-16.5$

Divide both sides by 16.5:

$0.30=\frac{x-16.5}{16.5}$

By us of symmetric property of equality:

$\frac{x-16.5}{16.5}=0.30$

5 0

3 years ago

Read 2 more answers

Calculate the following absolute value |-1-1+2|-|-1+2|-|-2|

Softa [21]

Answer:

-3

Hope This Helps!

8 0

3 years ago

I really need help please answer

belka [17]

Answer: Choice B) between 6:48 AM and 5:12 PM

=========================================================

Explanation:

I've seen this problem before, and the first part states that if the temperature is above 25 degrees C, then the air conditioner turns on to start cooling the castle.

We want to find values of t that satisfy f(t) > 25

This is the same as trying to solve f(t) - 25 > 0

So we have,

$f(t) = 24 - 5\cos\left(\frac{\pi}{12}t\right)\\\\ f(t)-25 = 24 - 5\cos\left(\frac{\pi}{12}t\right)-25\\\\ f(t)-25 = -1 - 5\cos\left(\frac{\pi}{12}t\right)\\\\ f(t)-25 > 0\\\\ -1 - 5\cos\left(\frac{\pi}{12}t\right) > 0\\\\$

To solve this inequality, we can graph using Desmos as I've done so below. See the attached image.

Note how I used x in place of t. This is because the graphing calculator graphs (x,y) coordinates.

Furthermore, note how I marked the two points (6.769, 0) and (17.231, 0)

Between these two points is when the curve is above the x axis, when f(t) > 25 is true. This is when the temperature is above 25 degrees C, and when the air conditioner is working.

When t = 6.769, this means that roughly 6.769 hours have passed since midnight which means we're somewhere between 6 am and 7 am. The only value that works from the answer choices is 6:48 AM.

Note how 0.769*60 = 46.14 is fairly close to 48. This error is likely due to how things are rounded.

Then focusing on the point (17.231, 0) means that t = 17.231. So 17.231 hours have elapsed since midnight and we're now at roughly 1700 hours

1700 hours in military time = 17-12 = 5 pm

The time value t = 17.231 is between 5 pm and 6 pm. The only thing that works is 5:12 pm.

We can then note how 0.231*60 = 13.86 which is also probably due to rounding error (it's fairly close to 12 though).

--------------------------

In short, we found the function for f(t)-25 and graphed it as shown below. The two points (6.769, 0) and (17.231, 0) help us see when the AC is turned on, which is roughly between 6:48 AM and 5:12 PM. This seems like a reasonable time for the AC to be operational. Something like between 5:12 PM and 6:48 AM seems like a bad idea because the AC would be working mostly at night, instead of during the day.

Anything beyond t = 24 represents the next day, which is when the cycle starts all over again. So we only need to focus on the window from t = 0 to t = 24. Specifically, the portion of the f(t)-25 curve that is above the x axis.

8 0

3 years ago

Does anyone know how to do this?​

Does anyone know how to do this?