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2 years ago

List the 8 numbers between 4 and 40 in a sequence of 10 numbers a common difference

Mathematics

1 answer:

yuradex [85]2 years ago

3 0

Answer:

8, 12, 16, 20, 24, 28, 32, 36

Step-by-step explanation:

the nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

a₁ is the first term and d the common difference

given a₁ = 4 and a₁₀= 40 , then

4 + 9d = 40 ( subtract 4 from both sides )

9d = 36 ( divide both sides by 9 )

d = 4

add d to each term to obtain the next term

4 + 4 = 8

8 + 4 = 12

12 + 4 = 16

16 + 4 = 20

20 + 4 = 24

24 + 4 = 28

28 + 4 = 32

32 + 4 = 36

the 8 terms between 4 and 40 are

8, 12, 16, 20, 24, 28, 32, 36

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The current in a circuit element is i(t) = 3(1 - e-2t) A when t ≥ 0 and i(t) = 0 when t < 0. The total charge that has entere

lesantik [10]

Answer:

A=-3/2

B=3

c=3/2

a=-2

Step-by-step explanation:

Knowing that for $t>0$ $i(t)=2\left(1-e^{-2t}\right) A$ , $i(t)=0$ when t<0 and using the definition of charge

$q(t)=\int_{-\infty}^0i(t')dt'+\int_0^t i(t')dt'=0+\int_0^t i(t')dt'$

The first term corresponds to q(0), the charge accumulated before t=0, in this case it luckily gives zero so we don't have to worry about it.

Let's proceed and integrate $i(t)$ then when t>0

$i(t)=3\int_0^t \left[ \int_0^tdt'-\inte_0^t e^{-2t'}dt' \right]dt'=3\left[ t+\frac{1}{2}\left( e^{-2t}-1 \right) \right]=3t+\frac{3}{2}e^{-2t}-\frac{3}{2}\,\, C$

It is clear that:

A=-3/2

B=3

c=3/2

a=-2

4 0

3 years ago

Can you please answer to this question I really need help please I need it right now please this is 4 time I was sending this qu

Viefleur [7K]

Answer:

Total number of baseball game players =(p) = $16$ .

Step-by-step explanation:

Let the total number of baseball players be (p).

So as we have been given that, $\frac{3}{4}$ of them have taken bottle of water.

And this $\frac{3}{4}$ is also equivalent to $12$ .

So we can say that $\frac{3}{4} \times (p) = 12$

From here we can find the value of (p).

To find (p) multiply both sides with $4$ and divide with $3$ .

Now

$(p)=\frac{12\times 4}{3}=16$

So here we have the total number of baseball players that is (p) and $p=16$ .

We can also say that the number of players who have taken box of juice at the end of the game $=(16-12)=4$ .

5 0

3 years ago

(Someone please answer this time, I don't want to waste my points again)

BlackZzzverrR [31]

Given: first day amount=$3,000,000.

It is given that amount double that amount the next day.

Note: The double amount is added to the amount present initially.

Each time we need to add $3,000,000 to the double amount to get the final amount for a particular day.

For second day amount will be 3,000,000+ double of 3,000,000, that is = 3,000,000 + 6,000,000 = $9,000,000.

Third day amount = 3,000,000 + 2*9,000,000 = $21,000,000.

Fourth day amount = 3,000,000 + 2*21,000,000 = $45,000,000.

Fifth day amount = 3,000,000 +2*45,000,000 = $93,000,000.

Sixth day amount = 3,000,000 +2*93,000,000 = $189,000,000 .

3 0

3 years ago

In the 1992 presidential election, Alaska’s 40 election districts averaged 1956.8 votes per district for President Clinton. The

torisob [31]

Answer:

(a) The distribution of X is N (1956.8, 90.49²).

(b) The value 1956.8 is the population mean.

(d) The probability that a randomly selected district had between 1,800 and 2,000 votes for President Clinton is 0.6426.

(e) The third quartile for votes for President Clinton is 2018.3.

Step-by-step explanation:

The random variable X is defined the number of votes for President Clinton for an election district.

The information provided is:

$n=40\\\bar x=1956.8\\\sigma=572.3$

(a)

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

$\mu_{x}=\mu = \bar x=1956.8$

And the standard deviation of the distribution of sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{572.3}{\sqrt{40}}=90.49$

Thus, the distribution of X is N (1956.8, 90.49²).

(b)

A mean of the distribution of sample mean is given by,

$\mu_{x}=1956.8$

The mean value, 1956.8 is the population mean of the sampling distribution of sample mean.

This is because the law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample ( $\bar x$ ) approaches the whole population mean ( $\mu_{x}$ ).