Simplify this expression: 4(1 - 3x) + 7 x-8. : 0101 + - . x a

Timmy is building a new website. Right after he starts, he has 2 visitors. He expects his visitors to increase according to a mo

Alex73 [517]

Answer:

He gets 42 visitors 4 weeks after starting to build his website.

He gets 10 new visitors per week.

Step-by-step explanation:

Equation for the number of visitors:

The equation for the number of visitors Timmy's new website receives after t weeks is:

$v(t) = 10t + b$

In which b is the number of visitors rightly after he starts.

Timmy is building a new website. Right after he starts, he has 2 visitors.

This means that $b = 2$ , so:

$v(t) = 10t + 2$

How many visitors does he get 4 weeks after starting to build his website?

This is v(4). So

$v(4) = 10(4) + 2 = 40 + 2 = 42$

He gets 42 visitors 4 weeks after starting to build his website.

How any new visitors does he get per week?

After 0 weeks:

$v(0) = 10(0) + 2 = 0 + 2 = 2$

After 1 week:

$v(1) = 10(1) + 2 = 10 + 2 = 12$

2 weeks:

After 2 week:

$v(2) = 10(2) + 2 = 20 + 2 = 22$

22 - 12 = 12 - 2 = 10

He gets 10 new visitors per week.

5 0

3 years ago

What's the explicit formula for 5,10,15,20,25,30

vivado [14]

Answer:

$a_{n}$ = 5n

Step-by-step explanation:

There is a common difference d between consecutive terms

d = 10 - 5 = 15 - 10 = 20 - 15 = 25 - 20 = 30 - 25 = 5

This indicates the sequence is arithmetic with explicit formula

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 5 and d = 5 , then

$a_{n}$ = 5 + 5(n - 1) = 5 + 5n - 5 = 5n

4 0

3 years ago

The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years.

laiz [17]

Answer:

208.82 ; 61.33

Step-by-step explanation:

Given the data:

Year Quarter Profit ($1000s)

1 1 45

1 2 51

1 3 72

1 4 50

2 1 49

2 2 45

2 3 79

2 4 54

3 1 42

3 2 58

3 3 70

3 4 56

The 3 period moving average :

Yr Qtr Profit ($1000s)Pt ____ Ft ____ e=(PT-Ft)²

1 _ 1 ___45 __

1 _ 2 __ 51 __

1 _ 3 __ 72 __

1 _ 4 __ 50 ______________56 ____ 36

2 _ 1 __ 49 ______________57.67__ 75.17

2 _ 2__ 45 ______________57 ____ 144

2 _ 3__ 79 ______________48 ____961

2 _ 4__ 54 ______________57.67 _ 13.47

3 _ 1__ 42 ______________59.33__300.33

3 _2 __ 58 ______________58.33__ 0.11

3 _ 3__ 70 ______________51.33__ 348.57

3 _ 4 __56 ______________56.67__0.45

MSE = Σ(Pt - Ft)² ÷ n

MSE = (36+75.17+144+961+13.47+300.33+0.11+348.57+0.75) ÷ 9

= 208.82

Forecast for next quarter :

(58 + 70 + 56) / 3 = 184 /3 = 61.33

8 0

3 years ago

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean leng

alexandr402 [8]

Complete Question

From a random sample of size 18, a researcher states that (11.1, 15.7) inches is a 90% confidence interval for mu, the mean length of bass caught in a small lake. A normal distribution was assumed. Using the 90% confidence interval obtain:

a. A point estimate of $\mu$ and its 90% margin of error.

b. A 95% confidence interval for $\mu$ .

Answer:

a

$\= x = 13.4$ . $E = 2.3$

b

$10.7 < \mu < 16.1$

Step-by-step explanation:

From the question we are told that

The sample size is n = 18

The 90% confidence interval is (11.1, 15.7)

Generally the point estimate of $\mu$ is mathematically evaluated as

$\= x = \frac{11.1 + 15.7 }{2}$

=> $\= x = 13.4$

Generally the margin of error is mathematically evaluated as

$E = \frac{15.7 - 11.1}{2 }$

=> $E = 2.3$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the equation for the lower limit of the confidence interval is

$\= x - Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{18} } = 11.1$

=> $13.4 - 0.3877 s = 11.1$

=> $s = 5.932$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * \frac{5.932}{\sqrt{18} }$

=> $E = 2.7$

Generally 95% confidence interval is mathematically represented as

$\= x -E < \mu < \=x +E$

=> $13.4 - 2.7 < \mu < 13.4 + 2.7$

=> $10.7 < \mu < 16.1$

3 0

3 years ago

Use the x-intercept method to find all real solutions of the equation -9^3-72^2-96x+36=3x^3+x^2-3x+8

Vadim26 [7]

Answer:

x ≈ 0.290640965127

Step-by-step explanation:

y subtracting the right side of the equation, we get a function that is zero at a real solution for x. The only x-intercept is at approximately 0.290640965127.

___

The graph shows the x-intercept to be 0.2906. The value above was obtained by Newton's method iteration. The roots of this cubic will all be irrational.

7 0

3 years ago