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3 years ago

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Sam will spend at most $27 on gifts. So far, he has spent $18. What are the possible additional amounts he will spend? Use c for

the additional amount

2 answers:

saw5 [17]3 years ago

7 0

$\text{We could turn this scenario into an equation}\\\\27\geq18+c\\\\\text{You would solve for c to find how much more Sam can spend on gifts:}\\\\27\geq18+c\\\\\text{Subtract 18 from both sides:}\\\\9\geq\,c\\\\\text{This means that the additional amount Sam has is \$9}\\\\\boxed{\$9}$

Assoli18 [71]3 years ago

5 0

Answer:$9

Step-by-step explanation:

Let the additional amount be c

Total amount to spend on gift is $27

He had spent $18 so far

$18+c= $27

C= $27-$18

C=$9

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HELP!! 50 POINTS!!!

aalyn [17]

Step-by-step explanation:

We have been given a table, which represents the projected value of two different houses for three years.

Part A:

$\text{Increase in value of house 1 after one year}=294,580-286,000$

$\text{Increase in value of house 1 after one year}=8580$

$\text{Increase in value of house 1 after two years}=303,417.40-294,580$

$\text{Increase in value of house 1 after two years}=8837.4$

We can see from our given table that the value of house 1 is not increasing at a constant rate, while a linear function has a constant rate of change, therefore, an exponential function can be used to describe the value of the house 1 after a fixed number of years.

$\text{Increase in value of house 2 after one year}=295,000-286,000$

$\text{Increase in value of house 2 after one year}=9,000$

$\text{Increase in value of house 2 after two years}=304,000-295,000$

$\text{Increase in value of house 2 after two years}=9,000$

We can see from our given table that the value of house 2 is increasing at a constant rat that is $9,000 per year. Since a linear function has a constant rate of change, therefore, a linear function can be used to describe the value of the house 2 after a fixed number of years.

Part B:

Let x be the number of years after Dominique bought the house 1.

Since value of house 1 is increasing exponentially, so let us find increase percent of value of house 1.

$\text{Increase }\%=\frac{\text{Final value-Initial value}}{\text{Initial value}}\times 100$

$\text{Increase }\%=\frac{294,580-286,000}{286,000}\times 100$

$\text{Increase }\%=\frac{8580}{286,000}\times 100$

$\text{Increase }\%=0.03\times 100$

$\text{Increase }\%=3$

$\text{Increase }\%=\frac{303,417.40-294,580}{294,580}\times 100$

$\text{Increase }\%=\frac{8837.4}{294,580}\times 100$

$\text{Increase }\%=0.03\times 100$

$\text{Increase }\%=3$

Therefore, the growth rate of house 1's value is 3%.

Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For growth b is in form (1+r), where, r is rate in decimal form.

$3\%=\frac{3}{100}=0.03$

Upon substituting our values in exponential function form we will get,

$f(x)=286,000(1+0.03)^x$ , where, f(x) represents the value of the house 1, in dollars, after x years.

Therefore, the function $f(x)=286,000(1.03)^x$ represents the value of house 1 after x years.

Let x be the number of years after Dominique bought the house 2.

We can see that when Dominique bought house 2 it has a value of $286,000. This means that at x equals 0 value of house will be $286,000 and it will be our y-intercept.

Since value of house 2 is increasing 9000 per year, therefore, slope of our line be 9000.

Upon substituting these values in slope-intercept form of equation $(y=mx+b)$ we will get,

$f(x)=9000x+286,000$ , where, f(x) represents the value of the house 2, in dollars, after x years.

Therefore, the function $f(x)=9000x+286,000$ represents the value of house 2 after x years.

Part C:

Since values in exponential function increases faster than linear function, so the value of house 1 will be greater than value of house 2.

Let us find the value of house 1 and house 2 by substituting x=25 in our both functions.

$f(25)=286,000(1.03)^{25}$

$f(25)=286,000*2.0937779296542148$

$f(25)=598820.48788$

We can see that value of house 1 after 25 years will be approx $598,820.48.

$f(25)=9000*25+286,000$

$f(25)=225,000+286,000$

$f(25)=511,000$

We can see that value of house 2 after 25 years will be approx $511,000.

Since $511,000 is less than $598820.48, therefore, value of house 1 is greater than value of house 2.

6 0

3 years ago

Read 2 more answers

-18 = -6n - 6 + 2n Solve for n.

vodomira [7]

Answer:

n = 3

Step-by-step explanation:

-18 = -6n - 6 + 2n

-18 = -6n +2n -6 (Combine like terms)

-18= -4n -6

-18+6= -4n -6+6 (Addition Property of Equality)

-12 = -4n

-12/-4 = -4n/-4 (Division Property of Equality)

3=n

The value of 'n' is 3.

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3 years ago

find the probability of picking 5 vowels and 3 consonants when 8 letters are picked with replacement from a set of alphabet tile

loris [4]

Approximately 0.01%, explication in the photo

5 0

3 years ago

Need help geometric sequences see pic for details

LenKa [72]

Given:

The recursive formula of a geometric sequence is

$a_n=a_{n-1}\cdot (\dfrac{1}{8})$

$a_1=-3$

To find:

The explicit formula of the given geometric sequence.

Solution:

We know that, first term of geometric sequence is $a_1=-3$ .

Recursive formula of a geometric sequence is

$a_n=a_{n-1}\times r$ ...(i)

where, r is common ratio.

We have,

$a_n=a_{n-1}\cdot (\dfrac{1}{8})$ ...(ii)

On comparing (i) and (ii), we get

$r=\dfrac{1}{8}$

The explicit formula of a geometric sequence is

$a_n=a_1r^{n-1}$

Putting $a_1=-3$ and $r=\dfrac{1}{8}$ , we get

$a_n=-3\left(\dfrac{1}{8}\right)^{n-1}$

Therefore, the correct option is D.

5 0

3 years ago

Lisa paid $35.00 to join an online music service. If she purchases 18 songs each month at a cost of $0.75 per song, what will be

nignag [31]

Answer:

Hi there!

Your answer is:

$89

Step-by-step explanation:

35+18x(.75)

Plug in 4 for x.

35+ 18(4) × (.75)

35+ 54

89$

Hope this helps

7 0

4 years ago