Four spinners are spun 40 times. Which spinner is most likely to produce actual results closest to the predicted results?

Find the first term and common difference of an AP, whose 7th term is 29/6 and 15th term is 11/2.

777dan777 [17]

Answer:

The first term is 13/3 and the common difference is d = 1/12

The formula is a(n) = 13/3 + (1/12)(n - 1)

Step-by-step explanation:

The general equation for an arithmetic progression is:

a(n) = a(1) + d(n - 1), where d is the common difference/

Case 1: n = 7: 29/6 = a(1) + d(7 - 1), or 29/6 = a(1) + d(6)

Case 2: n = 15: 11/2 = a(1) + d(15 - 1) = a(1) + d(14)

Then our system of linear equations is:

a(1) + 6d = 29/6

a(1) + 14d = 11/2

Let's solve this by elimination by addition and subtraction. Subtract the first equation from the second. We get:

Substituting 1/12 for d in the first equation, we get:

a(1) + 14(1/12) = 11/2 or 66/12 (using the LCD 12)

Then a(1) = 66/12 - 14/12 = 52/12 = 13/3

The first term is 13/3 and the common difference is d = 1/12

The arithmetic sequence formula for this problem is thus:

a(n) = 13/3 + (1/12)(n - 1) 8

5 0

3 years ago

Assume the exponential growth model A(t)equals=Upper A 0 e Superscript ktA0ekt and a world population of 5.95.9 billion in 2006

Whitepunk [10]

Answer:

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

Step-by-step explanation:

We are given the following in the question:

The exponential growth model is given by:

$A(t) = A_0e^{kt}$

where k is the growth rate, t is time in years and $A_0$ is constant.

The world population is 5.9 billion in 2006.

Thus, t = 0 for 2006

$A_0 = 5.9\text{ billions}$

We have to find the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

Putting these values in the growth model, we have,

$24 = 5.9e^{100k}\\\\k = \dfrac{1}{100}\ln \bigg(\dfrac{24}{5.9}\bigg)\\\\k = 0.01403\\k = 0.01403\times 100\% = 1.4\%$

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

8 0

3 years ago

Two partners agree to invest equal amounts in their business. One will contribute $10,000 immediately. The other plans to contr

krek1111 [17]

Answer:

She should contribute $ 8369.38 ( approx )

Step-by-step explanation:

Let P be the amount invested by the other partner,

∵ The amount formula in compound interest,

$A=P(1+\frac{r}{n})^{nt}$

Where,

r = annual rate,

n = number of compounding periods in a year,

t = number of years,

Here, r = 9% = 0.09, n = 4 ( quarters in a year ), t = 2 years,

Then the amount after 2 years,

$A = P(1+\frac{0.09}{4})^{8}$

According to the question,

A = $ 10,000,

$P(1+\frac{0.09}{4})^{8}= 10000$

$P(1+0.0225)^8 = 10000$

$\implies P = \frac{10000}{1.0225^8}\approx \$ 8369.38$

6 0

3 years ago

Convert y-3=(1/3)(x+1) to slope intercept form

Mekhanik [1.2K]

Slope-intercept form is $y=mx+b$ , where m is the slope and b is the y-intercept.

Here, we first need to distribute the 1/3.

$y-3= \frac{1}{3} x+\frac{1}{3}$

Next, we add 3 to both sides of the equation.

$y= \frac{1}{3} x+\frac{10}{3}$

8 0

3 years ago

Jessica pours 1/3 of a cup of water into a pot. She does this 5 times. How many

nydimaria [60]

She poured 1 full cup and 2/3 of another cup. The answer would be 1 and 2/3 cups.

5/3= 1 and 2/3

4 0

3 years ago