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Amanda [17]
2 years ago
5

in 2000, Jonesville had a population of 15,000. in 2001, the population was 16250 and in 2002, the population was 17,500. if the

population grew at the same constant rate each year, which model describes the population growth for n years after 2000?
Mathematics
2 answers:
lesya [120]2 years ago
8 0
Population (p) = 1,250n + 15,000
tester [92]2 years ago
4 0

In year 2000, the population was 15,000.

In year 2001, the population was 16,250.

In year 2002, the population was 17,500.

The population growth from year 2000 to year 2001 was (16,250-15,000) = 1,250.

The population growth from year 2001 to year 2002 was (17,500-16,250) = 1,250.

So the slope of the line would be m = 1250.

And y-intercept would be the initial population i.e. b = 15,000.

So the equation of line is y = 1250x + 15000.

Hence, n years after 2000, the population would be P = 1250n + 15000.

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Make x the subject of the following relations. 2y+3=5x-18​
nekit [7.7K]

Step-by-step explanation:

2y+3=5x-18

swap both sides

5x-18=2y+3

add 18 to both sides

5x-18+18=2y+3+18

5x=2y+21

divide both sides by

5x/5=2y+21/5

X=2y+21/5

6 0
2 years ago
a(0.3−y)+1.1+2.4x (y−1.2) ​ =0 =−1.2(x−0.5) ​ Consider the system of equations above, where aaa is a constant. For which value o
Veseljchak [2.6K]

Answer:

For a = 1.22 there is one solution where y = 1.3

Step-by-step explanation:

Hi there!

Let´s write the system of equations:

a(0.3 - y) + 1.1 +2.4x(y-1.2) = 0

-1.2(x-0.5) = 0

Let´s solve the second equation for x:

-1.2(x-0.5) = 0

x- 0.5 = 0

x = 0.5

Now let´s repalce x = 0.5 and y = 1.3 in the first equation and solve it for a:

a(0.3 - y) + 1.1 +2.4x(y-1.2) = 0

a(0.3 - 1.3) + 1.1 + 2.4(0.5)(1.3 -1.2) = 0

a(-1) + 1.1 + 1.2(0.1) = 0

-a + 1.22 = 0

-a = -1.22

a = 1.22

Let´s check the solution and solve the system of equations with a = 1.22. Let´s solve the first equation for y:

1.22(0.3 - y) + 1.1 +2.4(0.5)(y-1.2) = 0

0.366 - 1.22y + 1.1 + 1.2 y - 1.44 = 0

-0.02y +0.026 = 0

-0.02y = -0.026

y = -0.026 / -0.02

y = 1.3

Then, the answer is correct.

Have a nice day!

4 0
2 years ago
Randolph is creating parallelogram WXYZ so that XY has an equation of y = 2 over 3x −5. Segment WZ must pass through the point (
GalinKa [24]

Step-by-step explanation:

its y-(-6)= 3 over 2(x-(-1))

7 0
2 years ago
The function f(x) = 1/2 x + 3/2 is used to complete this table.
Mrac [35]

Answer:

a) f(-1/2)  = -2 is NOT TRUE.

b)  f(0)  =3/2 is  TRUE.

c)   f(1)  = -1 is NOT TRUE.

d)   f(2)  = 1 is NOT TRUE.

e)   f(4)  = 7/2  is  TRUE.

Step-by-step explanation:

Here, the given function is  f(x) = (\frac{1}{2}) x+\frac{3}{2}

Now, checking for each values for the given function:

a) Putting x  = (-1/2):

 f(\frac{-1}{2} ) = (\frac{1}{2})(\frac{-1}{2} ) +\frac{3}{2}   = \frac{-1}{4}  + (\frac{3}{2} )\\\implies f(x) = \frac{-1 + 6}{4}  = (\frac{5}{4} )

and (5/4) ≠  -2

Hence, f(-1/2)  = -2 is NOT TRUE.

b)Putting x  = 0 :

f(0) = (\frac{1}{2})(0 ) +\frac{3}{2} = (\frac{3}{2} )

Hence, f(0)  =3/2 is  TRUE.

c) Putting x  = 1:

f(1 ) = (\frac{1}{2})(1 ) +\frac{3}{2}   = \frac{1}{2}  + (\frac{3}{2} )\\\implies f(x) = \frac{3 + 1}{2}  = (\frac{4}{2} )   = 2\implies 2   \neq -1

Hence, f(1)  = -1 is NOT TRUE.

d)Putting x  = 2:  

f(2 ) = (\frac{1}{2})(2 ) +\frac{3}{2}   = 1+ (\frac{3}{2} )\\\implies f(x) = \frac{2 + 3}{2}  = (\frac{5}{2} )

and (5/2) ≠  1

Hence, f(2)  = 1 is NOT TRUE.

e)Putting x  = 4:

 f(4 ) = (\frac{1}{2})(4 ) +\frac{3}{2}   = 2  + (\frac{3}{2} )\\\implies f(x) = \frac{4 + 3}{2}  = (\frac{7}{2} )

Hence, f(4)  = 7/2  is  TRUE.

4 0
2 years ago
A teacher wants to see if a new unit on factoring is helping students learn. She has five randomly selected students take a pre-
sergiy2304 [10]

Answer:

The <em>t</em>-value used for the 95% confidence interval of paired data is 2.776.

Step-by-step explanation:

The confidence interval formula for mean difference for a paired data is as follows:

CI=\bar x_{d}\pm t_{\alpha/2, (n-1)}\times \frac{s_{d}}{\sqrt{n}}

Here,

\bar x_{d} = sample mean of the difference,

s_{d} = sample standard deviation of the difference,

<em>n </em>= sample size (both samples are of same size).

t_{\alpha/2, (n-1)} = critical value of <em>t</em>

(<em>n</em> - 1) = degrees of freedom

The information provided is:

<em>n</em> = 5

Confidence level = 95%

The critical value of <em>t</em> is:

t_{\alpha/2, (n-1)}=t_{0.05/2, (5-1)}

               =t_{0.025, 4}

               =2.776

*Use a <em>t</em>-table for the critical value of <em>t</em>.

Thus, the <em>t</em>-value used for the 95% confidence interval of paired data is 2.776.

4 0
2 years ago
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