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3 years ago

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Biruk wants to buy a book for $15.25 and a book for $4.85. He wants to pay with one $20 bill. Use estimation to decide if this i

s reasonable. Explain to what place value to round for an estimate that is useful in this situation.

2 answers:

ycow [4]3 years ago

8 0

First round 15.25 to 15.30 and round 4.85 to 4.90 and then add you get 21.20 no it is not reasonable and you round to the decimal ones

Aloiza [94]3 years ago

6 0

Answer: It's not reasonable.

Step-by-step explanation:

Hi, to answer this question we have to add both book’s prices:

15.25 + 4.85 = $20.1

If he wants to pay with one $20 bill, it wouldn’t be reasonable, because:

20 <20.1

For an useful estimate, estimate to the nearest tenth:

15.30 +4.90 = 20.2

Still, he can’t afford the books because he is lacking 20 cents.

Feel free to ask for more if needed or if you did not understand something.

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3 years ago

A researcher is interested in knowing the average height of the men in a village. To the researcher, the population of interest

Anna11 [10]

Answer:

The population mean height of men in the village is 5.78 feet.

The sample mean height of men in the village is 7.8 feet.

Step-by-step explanation:

It is provided that the researcher's interest is in knowing the average height of the men in a village.

To the researcher, the population of interest is the <em><u>men</u></em><em> </em>in the village, the relevant population data are the <em><u>height of men</u></em> in the village, and the population parameter of interest is the <em><u>mean height of men</u></em>.

It is also provided that there are 590 men in the village, and the sum of their heights is 3,410.2 feet.

Compute the average height as follows:

$\bar X_{H}=\frac{3410.2}{590}=5.78\ \text{feet}$

Thus, the population mean height of men in the village is 5.78 feet.

It is given that the researcher measured the heights of 18 village men and calculated the average to estimate the average height of all the village men.

The sample for his estimation is <em><u>18 men</u></em>, the relevant sample data are the <em><u>heights of the 18 men</u></em>, and the sample statistic is the <em><u>sample mean height</u></em>.

It is also given that the sum of the heights of the 18 village men is 104.4 feet.

Compute the average height of the 18 men as follows:

$\bar x_{H}=\frac{104.4}{18}=7.8\ \text{feet}$

Thus, the sample mean height of men in the village is 7.8 feet.

8 0

2 years ago

For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;

Dmitrij [34]

Answer:

a.

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

$ax+by=c$

Suppose integers x0 and yo satisfy the equation; that is,

$ax_0+by_0 = c$

what other values

$x = x_0+h$ and $y=y_0+k$

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

$as+bt=gcd(a,b)$

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

$a(sk) + b(tk) = gcd(a,b)k = c$

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

$a(x_1-x) + b(y_1-y)=0$

Therefore,

$a(x_1-x) = b(y-y_1)$

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

$y = y_1+r(\frac{a}{gcd(a, b)})$ for some integer r. Substituting into the equation

$a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba$

or

$x = x_1-r(\frac{b}{gcd(a, b)} )$

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

In order to find all integer solutions to 6x + 15y = 12

we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

$15 = 6*2+3\\6=3*2+0$

Therefore gcd(6,15) = 3. Since 3|12, the equation has integral solutions.

We then find a way of representing 3 as a linear combination of 6 and 15, using the Euclidean algorithm computation and the equalities, we have,

$3 = 15-6*2$

Because 4 multiplies 3 to give 12, we multiply by 4

$12 = 15*4-6*8$

So one solution is

$x=-8$ & $y = 4$

All other solutions will have the form

$x=-8+\frac{15r}{3} = -8+5r\\y=4-\frac{6r}{3} =4-2r$

where $r$ ∈ Ζ

Hence by putting r values, we get many (x, y)

3 0

3 years ago