Eric had 13 tiles to arrange in a rectangular design how does Erics drawing show that 13 is a prime number

Blababa [14]

80-30=50 your answer would be 50

4 0

3 years ago

Tacoma's population in 2000 was about 200 thousand, and had been growing by about 9% each year. a. Write a recursive formula for

KIM [24]

Answer:

a) The recurrence formula is $P_n = \frac{109}{100}P_{n-1}$ .

b) The general formula for the population of Tacoma is

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) In 2016 the approximate population of Tacoma will be 794062 people.

d) The population of Tacoma should exceed the 400000 people by the year 2009.

Step-by-step explanation:

a) We have the population in the year 2000, which is 200 000 people. Let us write $P_0 = 200 000$ . For the population in 2001 we will use $P_1$ , for the population in 2002 we will use $P_2$ , and so on.

In the following year, 2001, the population grow 9% with respect to the previous year. This means that $P_0$ is equal to $P_1$ plus 9% of the population of 2000. Notice that this can be written as

$P_1 = P_0 + (9/100)*P_0 = \left(1-\frac{9}{100}\right)P_0 = \frac{109}{100}P_0$ .

In 2002, we will have the population of 2001, $P_1$ , plus the 9% of $P_1$ . This is

$P_2 = P_1 + (9/100)*P_1 = \left(1-\frac{9}{100}\right)P_1 = \frac{109}{100}P_1$ .

So, it is not difficult to notice that the general recurrence is

$P_n = \frac{109}{100}P_{n-1}$ .

b) In the previous formula we only need to substitute the expression for $P_{n-1}$ :

$P_{n-1} = \frac{109}{100}P_{n-2}$ .

Then,

$P_n = \left(\frac{109}{100}\right)^2P_{n-2}$ .

Repeating the procedure for $P_{n-3}$ we get

$P_n = \left(\frac{109}{100}\right)^3P_{n-3}$ .

But we can do the same operation n times, so

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) Recall the notation we have used:

$P_{0}$ for 2000, $P_{1}$ for 2001, $P_{2}$ for 2002, and so on. Then, 2016 is $P_{16}$ . So, in order to obtain the approximate population of Tacoma in 2016 is

$P_{16} = \left(\frac{109}{100}\right)^{16}P_{0} = (1.09)^{16}P_0 = 3.97\cdot 200000 \approx 794062$

d) In this case we want to know when $P_n>400000$ , which is equivalent to

$(1.09)^{n}P_0>400000$ .

Substituting the value of $P_0$ , we get

$(1.09)^{n}200000>400000$ .

Simplifying the expression:

$(1.09)^{n}>2$ .

So, we need to find the value of $n$ such that the above inequality holds.

The easiest way to do this is take logarithm in both hands. Then,

$n\ln(1.09)>\ln 2$ .

So, $n>\frac{\ln 2}{\ln(1.09)} = 8.04323172693$ .

So, the population of Tacoma should exceed the 400 000 by the year 2009.

8 0

3 years ago

Read 2 more answers

I need help pleeeeeeeeeeeeeease

dsp73

Answer:

Tj hit 85% of the balls pitched to him

Step-by-step explanation:

6 0

3 years ago

The width of a rectangle measures (6.9a+8.5)(6.9a+8.5) centimeters, and its length measures (3.8a+9.8)(3.8a+9.8) centimeters. Wh

Colt1911 [192]

Answer:

P = (21.4a+36.6) cm

Step-by-step explanation:

Given that,

The width of a rectangle, b = (6.9a+8.5) cm

The length of a rectangle, l = (3.8a+9.8) cm

We need to find the perimeter of the rectangle. Perimeter is the sum of all sides. So,

P = 2(l+b)

Put all the values,

P = 2(6.9a+8.5+3.8a+9.8)

= 2(6.9a+3.8a+8.5+9.8)

= 2(10.7 a+18.3)

= (21.4a+36.6)

So, the perimeter of the rectangle is (21.4a+36.6) cm.

5 0

3 years ago

Help please! factoring polynomials

alexgriva [62]

Answer:

B

Step-by-step explanation:

you can use foil and the graph,

because you can see (in the graph) that the lines intersect at 1 and 4.

just use foil to help figure out which matches the slope.

something else (the normal way) is find which 2 numbers equal to the last coefficient, in this case it can be

-2 and -2, 2 and 2, 4 and 1 or -4 and -1, multiply them and if they make up the last coefficient, and added it equals the second coefficient it is correct.

6 0

3 years ago

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