Assume that random guesses are made for seven multiple choice questions on an sat test, so that there are nequals 7 trials, each with probability of success (correct) given by pequals 0.25 . find the indicated probability for the number of correct answers. find the probability that the number x of correct answers is fewer than 4 .

0.929.

Step-by-step explanation:

The event x fewer than 4 is 0, 1 2 or 3 correct answers.

Probability of the first 3 being correct and the last 4 incorrect

= (0.25)^3 * (0.75)^4 = 0.00494385

There are  7C3 = 7*6*5/ 3*2*1 = 35 ways in which this can happen so the required probability for 3 correct answers is 35 * 0.00494385 = 0.17303.

In a similar fashion we can find the probability of  0, 1 and 2 successes:

P(0) = (0.75)^7 =  0.13348

P(1) =  7 * 0.25*(0.75)^6 = 0.31146

P(2) = 21* (0.25)^2(0.75)^5 = 0.31146

So probability of 1 2 or 3 successes = sum of the above 4 probabilities

=  929.

d. 9

step-by-step explanation:

in the table given in the picture, x is the input of the function and f(x) is the output on the given input. in the given table, it can be read as the value of function at -3 is it's respective value of f(x) which is -9.

as we have to find the value of f(3), we will see that what is the value of output on input 3. we can see in the table that the output value at x=3 is 9.

so, option d is the correct answer ..

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )