Suppose you like to keep a jar of change on your desk. currently, the jar contains the following:

18 pennies 24 dimes

7 nickels 25 quarters

what is the probability that you reach into the jar and randomly grab a dime and then, without replacement, a nickel? express your answer as a fraction or a decimal number rounded to four decimal places.

0.0959

Step-by-step explanation:

There are 18+24+7+25=74 coins in the jar

Let's call

P(p) = 18/74 the probability of grabbing a penny

P(d) = 24/74 the probability of grabbing a dime

P(n) = 7/74 the probability of grabbing a nickel

P(q) = 25/74 the probability of grabbing a penny

What is the probability that you reach into the jar and randomly grab a dime and then, without replacement, a nickel?

Here we want to find P(n | d) the probability of grabbing a nickel given that you already grabbed a dime.

By the Bayes' Theorem

Now,

P(d | p) = 24/73 since there are now 73 coins and 24 dimes.

Similarly,

P(d | d) = 23/73 for you already grabbed a dime

P(d | n) = 24/73

P(d | q) =24/73

Replacing in the Bayes' formula

So

P(n | d) = 0.0959

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .