Question

1. currency on the first day of 2007, the value of one us - dollar was equivalent to 0.76 euro. on the same day, one us - dollar was equivalent to 1.22 swiss francs.

a. write a function to represent the value of francs in euros.
b. what is the value of the function for an input of 5 rounded to the nearest euro, and what does it represent?
c. how can you tell from the given data that your answer makes sense?

1. a. which is the greater percent change: from 50 to 60 or from 60 to 50?

b. analyze how can the answer to part a be found without actually finding the percents?

1. error analysis find and explain the error in solving the equation below. correct the error and solve:

7x−14 = −9 + 12x
7x = −23 + 12x
−5x = −23
x=\frac{23}{5}

1. geometry the length of a rectangle equals x + 4 and the width equals 5 inches. the perimeter of the rectangle can be calculated as shown below. which properties of real numbers are demonstrated?

p = 2(x + 4)+2(5)=2(x + 4 + 5)=2(x + 9)=2x + 18.

1. statistics the mean for the list of numbers below is 11.8. use the formula for mean to create a linear equation to solve for the missing data point.

12, 15, 8,?, 20

1. predict the weight of an object on neptune varies directly with the weight of that object on earth. an object that weighs 5 g on earth, weighs 6 g on neptune. without doing any calculations, predict the weight of an object on neptune that weighs 10 g on earth. explain your prediction.
2. in 2002, the average height of a 15 - year - old boy was 1.737×10³ mm. about how many 15 - year - old boys lying head - to - toe would it take to equal the circumference of the earth at the equator, if its circumference measures about 4.0076×10⁴ km? write the answer in scientific notation rounded to the nearest ten - thousandth.
3. verify the circumference of a circle varies directly with the radius. the table below shows the circumference and radius of three different circles. verify that the constant of variation is 6.283.

circumference | radius
12.566 cm | 2 cm
94.245 cm | 15 cm
232.471 cm | 37 cm

Explanation:

17.

Step1: Define variables

Let $d$ be the value of US - dollar, $e$ be the value of euro and $s$ be the value of Swiss - franc. We know $d = 0.76e$ and $d = 1.22s$. So, $e=\frac{d}{0.76}$ and $s=\frac{d}{1.22}$.

Step2: Write the function

The function to convert US - dollars to euros is $f(d)=\frac{d}{0.76}$, and to convert US - dollars to Swiss - francs is $g(d)=\frac{d}{1.22}$.

Step3: Evaluate the function for $d = 5$

For the euro - conversion function $f(5)=\frac{5}{0.76}\approx6.58$ euros. For the Swiss - franc conversion function $g(5)=\frac{5}{1.22}\approx4.10$ Swiss - francs.

Step4: Check the answer

Since 1 US - dollar is worth 0.76 euros, 5 US - dollars should be worth $5\times0.76 = 3.8$ (but we are using the inverse relationship $e=\frac{d}{0.76}$). Similarly, for Swiss - francs, since 1 US - dollar is worth 1.22 Swiss - francs, 5 US - dollars should be worth $\frac{5}{1.22}$. The values we calculated are consistent with the given exchange - rate relationships.

Step1: Calculate percent change formula

The percent change formula is $\text{Percent Change}=\frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\times100\%$.

Step2: Calculate percent change from 50 to 60

$\text{Percent Change}_1=\frac{60 - 50}{50}\times100\%=\frac{10}{50}\times100\% = 20\%$.

Step3: Calculate percent change from 60 to 50

$\text{Percent Change}_2=\frac{50 - 60}{60}\times100\%=\frac{- 10}{60}\times100\%\approx - 16.67\%$. The magnitude is $\frac{10}{60}\times100\%\approx16.67\%$.

Step4: Analyze without calculating percents

The change of 10 from 50 to 60 is a larger fraction of 50 than the change of 10 from 60 to 50 is of 60.

Step1: Identify the error

The error is in the first step. When moving $-14$ from the left - hand side to the right - hand side of the equation $7x−14=-9 + 12x$, it should be $7x=-9 + 12x+14$, not $7x=-23 + 12x$.

Step2: Correct the solution

Starting with $7x−14=-9 + 12x$, we get $7x=-9 + 12x+14$. Then $7x=5 + 12x$. Subtracting $12x$ from both sides gives $7x-12x=5$, or $-5x = 5$. Dividing both sides by $-5$, we have $x=-1$.

Answer:

a. The function to convert US - dollars to euros is $y=\frac{x}{0.76}$ (where $x$ is the amount in US - dollars and $y$ is the amount in euros), and to convert US - dollars to Swiss - francs is $y=\frac{x}{1.22}$.
b. For the euro - conversion, $y=\frac{5}{0.76}\approx6.58$ euros; for the Swiss - franc conversion, $y=\frac{5}{1.22}\approx4.10$ Swiss - francs.
c. The calculations are consistent with the given exchange - rate relationships.

18.