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Prove that the two circles shown below are similar.

tiny-mole [99]

Answer:

We can prove the similarity of two circles by mapping one circle onto the other (i.e. making a circle look exactly like the other one) by a translation and a scale factor.

Let's map circle Y onto circle X for example. We need to make sure we have the same radii for both circles, so let's expand circle Y by a scale factor of 2. Then shift circle Y 6 units up and 6 units to the left to move the center point of circle Y over to that of circle X.

Now, since we could map circle Y onto circle X using transformations (scaling and translation), we know that the two circles are similar.

3 0

3 years ago

Only about 75% of all donated human blood can be used in hospitals. The remaining 25% cannot be used because of various infectio

Tresset [83]

Answer:

a) 0.02739

b) 0.00034

Step-by-step explanation:

If it is believed that at least 6 of the 10 pints are usable, then the 75% of “good” pints that can be used from this sample reduces to 60% of 75% = 0.6*0.75 = 0.45

Now for this sample we use a binomial distribution with probability of “success” (finding a “good” pint) of 0.45% and

the probability of getting exactly r good pints out of 10 is

$\bf \binom{10}{r}0.45^r(1-0.45)^{10-r}=\binom{10}{r}0.45^r0.55^{10-r}$

where

$\bf \binom{10}{r}$ are combinations of 10 taken r at a time.

a)

The probability that at least 8 of the pints are usable is P(r>7)

$\bf \binom{10}{8}0.45^80.55^2+\binom{10}{9}0.45^90.55^1+\binom{10}{10}0.45^{10}0.55^0=\\0.02289+0.00416+0.00034=0.02739$

b)

Here we want P(r=10)

$\bf \binom{10}{10}0.45^{10}0.55^0=0.00034$

7 0

3 years ago

Consider the following scenario:

Sladkaya [172]

Answer:

1. P(C AND D) = 0.3

2. (C.) C and D are not mutually exclusive because P(C AND D) ≠ 0

3. (A.) The events are not independent because P(C | D) ≠ P(C)

4.P(D | C) = 0.5

Step-by-step explanation:

• Let P(C) = 0.4

• Let P(D) = 0.5

• Let P(C | D) = 0.6

1.) Find P(C AND D).

$P(C | D) = \frac{P(C n D)}{P(D)} \\P(C n D) = P(C | D) * P(D)\\P(C n D) = 0.6 * 0.5\\P(C n D) = 0.3$

2.) Events can be mutually exclusive meaning the both event cannot happen at the same time. So, P(A and B) = 0

3.) Events can be "Independent", meaning each event is not affected by any other events.

4.) Find P(D | C)

$P(D | C) = \frac{P (D n C)}{P(C)}\\P(D n C) = 0.5 * 0.4 = 0.2\\P(D | C) = \frac{0.2}{0.4}\\P(D | C) = 0.5$

6 0

4 years ago

Juan told Sylvia he got a $0.50 raise this week and his new hourly rate will be $10.25 an hour. Sylvia wants to know what Juan’s

zhenek [66]

Answer:

The correct answer is:

r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.

This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).

6 0

3 years ago

Read 2 more answers

Show me the equation for 3 less than 5 times a number is 12 use X for the variable

ANEK [815]

Answer:

The required equation is 5x - 3 = 12

Step-by-step explanation:

We have to find the equation for the given condition

Let the number be x as given in the equation

Now according to the condition

5 time the Number is 5 *x = 5x

Three less then 5 time the Number would be 5x - 3

And all of it is equal to 12

Which gives us the equation

5x - 3 =12

The required equation is <em>5x - 3 = 12</em>

7 0

3 years ago