Apply the Pythagorean Theorem to find the distance between points A and C.

A crew of loggers cleared 1/2 acre of lumber in 4 days. How long will it take the same crew to clear 2 3/4 acres of lumber?

krok68 [10]

Set up a proportion of acres to days. 1/2 acre is to 4 days as 2 3/4 acres is to x days.

x= # days to clear 2 3/4 acres
2 3/4 to improper fraction= 11/4

(1/2)/4 = (11/4)/x
cross multiply

(1/2 * x) = (4 * 11/4)
on the right, the 4 "cancels out"

1/2x= 11
divide both sides by 1/2

x= 11 ÷ 1/2
to divide fractions, multiply by reciprocal/inverse of 1/2

x= 11 * 2/1
x= 22 days

ANSWER: It would take 22 days to clear 2 3/4 acres.

Hope this helps! :)

6 0

4 years ago

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10. A random sample of 10 fibers is taken from a collection of 92 fibers that consists of 43 fibers of polymer A, 17 fibers of p

vazorg [7]

Answer:

0.1150 = 11.50% probability that the sample does not contain any fibers of polymer B

Step-by-step explanation:

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

Fibers are chosen without replacement, which means that we use the hypergeometric distribution.

92 fibers means that $N = 92$

Sample of 10 means that $n = 10$

No polymeter B which means that $x = 0$

17 fibers of polymeter B which means that $k = 17$

a. What is the probability that the sample does not contain any fibers of polymer B

This is P(X = 0).

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,92,10,17) = \frac{C_{17,0}*C_{75,10}}{C_{92,10}} = 0.1150$

0.1150 = 11.50% probability that the sample does not contain any fibers of polymer B

4 0

3 years ago

Which graphs display a directly proportional relationship? Check all that apply.

Vedmedyk [2.9K]

The one that goes from corner to corner......i think if i get it wrong sorry

8 0

4 years ago

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Because the three sides are congruent, what foes that make each angle measure according to the equilateral triangle theorem.

m_a_m_a [10]

Answer : 60 degrees
Explanation: All triangles's angles add up to 180. Since all angles are equal, you can divide 180 by 3. 180/3 is 60

3 0

3 years ago

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The line integral of xydx×x^2y^3dy where c is the triangle with points (0,0) (1,0) (1,2) using green's theorem

lyudmila [28]

If $\mathcal C$ is the boundary of the triangle $D$ , then by Green's theorem

$\displaystyle\int_{\mathcal C}xy\,\mathrm dx+x^2y^3\,\mathrm dy=\iint_D\left(\frac{\partial(x^2y^3)}{\partial x}-\frac{\partial(xy)}{\partial y}\right)\,\mathrm dA$
$=\displaystyle\int_{x=0}^{x=1}\int_{y=0}^{y=2x}(2xy^3-x)\,\mathrm dy\,\mathrm dx$
$=\displaystyle\int_{x=0}^{x=1}x\int_{y=0}^{y=2x}(2y^3-1)\,\mathrm dy\,\mathrm dx$
$=\displaystyle\int_{x=0}^{x=1}x(8x^4-2x)\,\mathrm dx=\frac23$

4 0

3 years ago