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jok3333 [9.3K]
2 years ago
13

Graph each equation. 56) y = |x-31-3 I if it if it it of .

Mathematics
1 answer:
BabaBlast [244]2 years ago
3 0

Step-by-step explanation:

The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Find the values of m m and b b using the form y=mx+b y = m x + b .

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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
It takes 54 minutes for 4 people to paint 6 walls. How many minutes does it take 6 people to paint 7 walls?
Nady [450]
It takes 35 mins for 6 people to paint 7 walls if you would like this answer described to you let me know please 
6 0
3 years ago
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The total number of items sold by each student who participated in the fundraiser is showing in the stem and leaf plot
kenny6666 [7]

The statement that is best supported by the data in the stem and leaf plot is D. The most common number of items sold is 15.

<h3>How to illustrate the information?</h3>

It should be noted that the stem and plot diagram is important to illustrate the data given.

Based on the information given, the most common number of items sold is 15.

In conclusion, the correct option is D.

Learn more about stem plot on:

brainly.com/question/23450543

#SPJ1

The total number of items sold by each student who participated in a fund-raiser is shown in the stem and leaf plot.

Which statement is best supported by the data in the stem and leaf plot?

The number of students who sold between 10 and 20 items is greater than the number of students who sold more then 40 items.

The number of students who sold more than 30 items is greater than the number of students who sold fewer than 30 items.

The most common number of items sold is 30.

The most common number of items sold is 15.

4 0
1 year ago
A large water tank holds 210 liters of water. About how many gallons of water does the same tank hold, if there are approximatel
shusha [124]

Answer:

Step-by-step explanation:

Set up a proportion

15 Liters / 4 gallons = 210 Liters / x      Cross Multiply

15x = 4 * 210                                           Combine the right

15x = 840                                                Divide by 15

x = 840 / 15

x = 56 gallons

4 0
3 years ago
Is X=3 calculate the value of X3+X btw the 3 is a small three
Naddik [55]
The only 'small number' that I know that would affect the answer is an exponent that looks like ³ so the problem would be x³+x

remember that x³=x times x times x
if x=3 then
3³+3=27+3=30
3 0
3 years ago
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