Question 1 of 5

Mathematics

1 answer:

nydimaria [60]3 years ago

3 0

Answer:

hypotenuse =

$\sqrt{a {}^{2} } + b {}^{2}$

$\sqrt{} 24 {}^{2} + 10 {}^{2}$

= 26mi

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The firm is requested to send 3 employees who have positive indications of asbestos on to a medical center for further testing.

Rus_ich [418]

Answer:

0.0645 = 6.45% probability that exactly 10 employees will be tested in order to find 3 positives

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

40% of the employees have positive indications of asbestos in their lungs

This means that $p = 0.4$

a) Find the probability that exactly 10 employees will be tested in order to find 3 positives

2 within the first 9( $P(X = 2)$ when $n = 9$ ), and the 10th, with 0.4 probability. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{9,2}.(0.4)^{2}.(0.6)^{7} = 0.1612$

0.4*0.1612 = 0.0645

0.0645 = 6.45% probability that exactly 10 employees will be tested in order to find 3 positives

4 0

3 years ago

Compare the perimeter and area of the original figure to the perimeter and area of the reduced figure using the scale factor. A

Serggg [28]

Answer:

- The scale factor is one-half

- The perimeter of the model is the product of the scale factor and the perimeter of the original rectangle

-The area of the reduced figure is (1/2)^2 = 1/4 times the area of the original figure

Step-by-step explanation:

The ratio of the length of the original rectangle to that of the reduced rectangle is 6 to 3, or a factor of 1/2. The ratio of the width of the original rectangle to that of the reduced rectangle is 2 to 1, or, again, a factor of 1/2. So, because this ratio of 1/2 is constant, we know the total scale factor is 1/2, making B correct.

The perimeter of a rectangle is: $P=2l+2w$ , where l is the length and w is the width. The perimeter of the reduced figure is: P = 2 * 3 + 2 * 1 = 6 + 2 = 8 units. The perimeter of the original figure is: P = 2 * 6 + 2 * 2 = 12 + 4 = 16 units.

Notice that 16 * (1/2) = 8, which means that the perimeter of the scale-factored, reduced rectangle is "the product of the scale factor (which is 1/2) and the perimeter of the original rectangle (which is 16)". So, C is correct.

The area of a rectangle is: $A=lw$ , where l is the length and w is the width. The area of the reduced figure is: A = 3 * 1 = 3 units squared. The area of the original figure is: A = 6 * 2 = 12 units squared.