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Ira Lisetskai [31]
2 years ago
15

Write an explicit formula for an,the Nth term of the sequence 4,12,36

Mathematics
1 answer:
Rudik [331]2 years ago
6 0

Answer:

3^{n}+3^{n-1}

Step-by-step explanation:

Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be x^n + yn

Because the sequence multiplies by 3 each time, The base number in that equation would be 3^n +yn.

So 3^n of the equation would be:
3, 9, 27.

Compare the 2 equations:
4, 12, 36

3, 9 ,27

The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is: 3^{n-1}.

Combine these 2 equations together and you get:

3^{n}+3^{n-1}.

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The area of a door is 3024 square inches. If the length of the door is 48 inches longer than the width of the door, what is the
borishaifa [10]

Answer:

The width of the door is 36 inches

Step-by-step explanation:

The given parameters are;

The given area of the door = 3024 in.²

The length of the door = 48 + The width of the door

Let W represent the width of the door

Therefore, we have;

The length of the door = 48 + W

The area of the door = The length of the door × The width of the door

∴ By substitution, the area of the door = 3024 = W × (48 + W)

3024 = W × (48 + W) = 48·W + W²

48·W + W² = 3024

∴ 48·W + W² - 3024 = 0

Rearranging, we get;

W² + 48·W - 3024 = 0

By trial and error, we have;

(W + 84)×(W - 36) = 0

Therefore, given that the width of the door is a natural number, we have;

The width of the door, W = 36 inches

7 0
3 years ago
Determine the absolute value. Type the numerical answer only. -l12l​
mote1985 [20]

Answer:

-12

cause l12l is 12 then u add the negative sign.

Step-by-step explanation:

7 0
3 years ago
The drama club can wash 9 cars in 40 minutes.  At this rate, how many cars can they wash in 2 hours? Caution: turn hours to minu
Natali [406]

Answer:

l am pretty sure the answer is 27

6 0
3 years ago
Pls for the love of god someone explain how to do this to me
viva [34]
I’m not sure...but I think

x+y=5
If x =15
Then 15+y=5
Y= 10
The 2nd robot can do the task in 10min
5 0
3 years ago
A study conducted by the Center for Disease Control that asked 15,000 students about
BaLLatris [955]

Answer:

The sampling distribution of \hat p is: \hat p\sim N(p,\ \frac{p(1-p)}{n}).

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

\mu_{\hat p}=p

The standard deviation of this sampling distribution of sample proportion is:

\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}

The study was conducted using the data from 15,000 students.

Since the sample size is so large, i.e. <em>n</em> = 15000 > 30, the central limit theorem is applicable to approximate the sampling distribution of sample proportions.

So, the sampling distribution of \hat p is: \hat p\sim N(p,\ \frac{p(1-p)}{n}).

5 0
3 years ago
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