Order from the smallest to the largest: 3/4, 2/3, 5/9, 5/6

Out of-pocket spending in a country for health care increased between 2003 and 2008. The function fox)-2574models average annual

lidiya [134]

Answer:

(a) The total expenditures per household in the year 2008 were approximately $3,080.

(b) The spending reached $2875 per household in 2006.

Step-by-step explanation:

Note: This question is not complete, and the part c is not another question but the same question as part a. The complete question is therefore provided before answering the question as follows:

Out of-pocket spending in a country for health care increased between 2003 and 2008. The function f(x) = 2574e^(0.0359x) models average annual expenditures per household, in dollars. In this model, x represents the year, where x = 0 corresponds to 2003.

(a) Estimate out-of-pocket household spending on health care in 2008.

(b) Determine the year when spending reached $2875 per household

The explanation to the answer is now given as follows:

(a) Estimate out-of-pocket household spending on health care in 2008.

Given;

f(x) = 2574e^(0.0359x) ........................ (1)

Since x = 0 corresponds to 2003; by counting from 2003 to 2008, it implies that x = 5 corresponds to 2008.

Substituting x = 5 into equation (1) to estimate out-of-pocket household spending on health care in 2008, we have:

f(6) = 2574e^(0.0359 * 5)

f(6) = 2574 * 1.19661890406748

f(6) = 3,080.09705906969

Rounding to the nearest dollar as needed, we have:

f(6) = $3,080

Therefore, the total expenditures per household in the year 2008 were approximately $3,080.

(b) Determine the year when spending reached $2875 per household

This can be determined using equation (1) in part a by equating f(x) to $2875 solve for x as follows:

2875 = 2574e^(0.0359x)

2875 /2574 = e^(0.0359x)

1.11693861693862 = e^(0.0359x)

Taking the natural log of both sides, we have:

ln(1.11693861693862) = ln(e^(0.0359x))

0.110591565075382 = 0.0359x

x = 0.110591565075382 / 0.0359

x = 3.0805449881722

Approximating to a whole number, we have:

x = 3

Since x = 0 corresponds to 2003; by counting from 2003, x = 3 corresponds to 2006.

Therefore, the spending reached $2875 per household in 2006.

3 0

3 years ago

Four circles of unit radius are drawn with centers $(1,0)$, $(-1,0)$, $(0,1)$, and $(0,-1)$. a circle with radius 2 is drawn wit

Reika [66]

Check the picture 1.

The regions contained in an odd number of these 5 circles are

the pink colored region, contained only in the circle with radius 2,

and the yellow regions, each contained in the intersection of 2 small circles and the third large circle.

So what we need to determine is the "area pink + area yellow".

Consider the second picture.

Let A2 be the area of the right isosceles triangle, and A1 be half of the yellow region.

the region A2 + A1 is called a sector, and it is 1/4 of the area of a unit circle.

$A1=A_{sector}-A2= \frac{1}{4} \pi r^2- \frac{1}{2}.1.1= \frac{1}{4} \pi 1^2- \frac{1}{2}= \frac{1}{4}\pi- \frac{1}{2}$

Thus, the overall yellow region is $8A1=8(\frac{1}{4}\pi- \frac{1}{2})=2\pi-4$

The purple area is:

Area of large circle - 4*(Area of 1 small circle) + yellow region.

(because subtracting all 4 small circles means that each of the 4 separate yellow regions have been subtracted twice)

$A_{purple}=\pi.2^2-4(\pi.1^2)+2\pi-4=4\pi-4\pi+2\pi-4=2\pi-4$

Finally, the total area is : $2\pi-4+2\pi-4=4\pi-8$ (units squared)

Answer: $6\pi-8$ square units

6 0

4 years ago

3+20×5+4+6×2 what is it

Alexus [3.1K]

Answer:

The answer is 119

Step-by-step explanation:

Lets go by BODMAS

Step 1 : Multiplication

3+[(20*5)=100]+4+[(6*2)=12]

=3+100+4+12 = 119

8 0

4 years ago

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Four calculators cost $160 the Unit rate

Agata [3.3K]

The unit rates is $40 $160 divides by 4 calculators gets you $40

4 0

3 years ago

Find the value of X in the parallelogram below.

nignag [31]

Answer:

28

Step-by-step explanation:

In paralellograms, the lengths of the parallel sides are equal to each other

As seen in the figure, the side that is parallel to the side that is represented with x has a length of 28 units, so the value of x is also equal to 28

4 0

2 years ago

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