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4 years ago

Determine which relation is a function.

Mathematics

2 answers:

GrogVix [38]4 years ago

8 0

Letter A is the function because the input has exactly 1 output

anyanavicka [17]4 years ago

7 0

Answer choice a is a function because none of its x values repeat at all. There is only one -4 in the function. and same with all the x values

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For the years from 2002 and projected to 2024, the national health care expenditures H, in billions of dollars, can be modeled b

dmitriy555 [2]

Answer:

2019.

Step-by-step explanation:

We have been given that for the years from 2002 and projected to 2024, the national health care expenditures H, in billions of dollars, can be modeled by $H = 1,500e^{0.053t}$ where t is the number of years past 2000.

To find the year in which national health care expenditures expected to reach $4.0 trillion (that is, $4,000 billion), we will substitute $H=4,000$ in our given formula and solve for t as:

$4,000= 1,500e^{0.053t}$

$\frac{4,000}{1,500}=\frac{ 1,500e^{0.053t}}{1,500}$

$\frac{8}{3}=e^{0.053t}$

$e^{0.053t}=\frac{8}{3}$

Take natural log of both sides:

$\text{ln}(e^{0.053t})=\text{ln}(\frac{8}{3})$

$0.053t\cdot \text{ln}(e)=\text{ln}(\frac{8}{3})$

$0.053t\cdot (1)=0.9808292530117262$

$\frac{0.053t}{0.053}=\frac{0.9808292530117262}{0.053}$

$t=18.506212320$

So in the 18.5 years after 2000 the expenditure will reach 4 trillion.

$2000+18.5=2018.5$

Therefore, in year 2019 national health care expenditures are expected to reach $4.0 trillion.

7 0

4 years ago

Suppose that $1800 is borrowed for three years at an interest rate of 2% per year, compounded continuously. Find the amount owed

Schach [20]

1908

Step-by-step explanation:2% of 1800 is 36 36 x 3 is 108 + 1800 =1908

5 0

2 years ago

Solve |3x - 5] = 2 - 1/2x

bekas [8.4K]

Answer:

x=2

Step-by-step explanation:

First multiply both sides by 2:

6x-10=4-x

Move the variable to the left-hand side and change its sign:

6x-10+x=4

Move the constant to the right-hand side and change its sign:

6x+x=4+10

Collect like terms:

7x=14

Divide both sides of the equation by 7:

x=2

8 0

3 years ago

a movie theater sells ticket for 16 each. the theater also sell beverages for 3. the theater needs to make 1900 in all oreder to

lesya692 [45]

Answer:

let t be tickets and b be beverages

Step-by-step explanation:

16t + 3b = 1900

6 0

3 years ago

Find the circumference and the area of a circle with diameter <br> 2ft

rosijanka [135]

Circumference: 6.28 feet ~rounded to the nearest hundredth

To find circumference, multiply the diameter by pi.

Area: 3.14 feet squared ~rounded to the nearest hundredth

To find area, divide the diameter by 2 and multiply by pi.

3 0

3 years ago

Read 2 more answers