Completely factor the expression. w^2

a sequence of numbers begins at 400. If the pattern increases by consecutive multiples of 5 starting with 5, then find the next

bazaltina [42]

Given :

A sequence of numbers begins at 400.

To Find :

If the pattern increases by consecutive multiples of 5 starting with 5, then find the next 3 numbers in the sequence 400, ___, ___, ___ .

Solution :

This is the a question of arithmetic progression .

The first term is , a = 400 .

Now , it is given that the next numbers increase by the multiples of 5 starting with 5 .

So , common difference is , d = 5 .

Now , we know , $n^{th}$ number in A.P is given by :

$a_n=a+(n-1)d$

Putting value of n = 2 , 3 , 4 .

We get :

$a_2=a+(2-1)d=400+5=405\\\\a_3=a+(3-1)d = 400 + (5\times 2) = 410\\\\a_4=a+(4-1)d = 400 +(5\times 3)=415$

Therefore , the next 3 numbers in the sequence is 400 , 405 , 410 , 415 .

Hence , this is the required solution .

8 0

3 years ago

Help fast please

Lady_Fox [76]

Answer:

Acute and Obtuse..I cant see any right

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and

balu736 [363]

Answer:

(a) The sample size required is 43.

(b) The sample size required is 62.

Step-by-step explanation:

The (1 - α) % confidence interval for population mean is:

$CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

The margin of error for this interval is:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

(a)

The information provided is:

σ = 4 minutes

MOE = 72 seconds = 1.2 minutes

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size required as follows:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}$

$=[\frac{1.96\times 4}{1.2}]^{2}\\\\=42.684\\\\\approx 43$

Thus, the sample size required is 43.

(b)

The information provided is:

σ = 4 minutes

MOE = 1 minute

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size required as follows:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}$

$=[\frac{1.96\times 4}{1}]^{2}\\\\=61.4656\\\\\approx 62$

Thus, the sample size required is 62.

3 0

2 years ago

A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 3 stocks?

Gala2k [10]

Answer:

There are 27 different possible outcomes.

Step-by-step explanation:

Assuming that you have 3 different stocks:

First, we need to find the number of events and the number of possible outcomes for each event.

Here we can assume that each one of the stocks is a event, and the number of possible outcomes for each one are:

Stock 1: 3 options (up, down, stay)

Stock 2: 3 options (up, down, stay)

Stock 3: 3 options (up, down, stay)

The total number of possible outcomes is equal to the product of the numbers of options for all the events.

Then the total number of possibilities is:

C = 3*3*3 = 27

4 0

2 years ago

Find the value of 4^2 + 6 ÷ 2

lorasvet [3.4K]

Answer:

19

Step-by-step explanation:

Follow PEMDAS

4^2 + 6 ÷ 2

16 + 6 ÷ 2

16 + 3

19

4 0

3 years ago

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Completely factor the expression. w^2 - 15w + 54