A three digit number is formed at random using the digits 2, 3 and 4. If no digit can be repeated in any one number, find the probability that the number formed is greater than 300.

2/3, or 66.7%

Step-by-step explanation:

There are 2 options for the first digit (3 or 4).

After the first digit is selected, it cannot be repeated, so there are 2 options left for the second digit.

After the first two digits are selected, there is only 1 option for the third digit.

So there are 4 permutations greater than 300.

The total number of permutations is 3! = 6.

So the probability is 4/6 = 2/3.

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.

45.36 feet per second.

step-by-step explanation:

to find the most accurate determination for the number of feet per second tyrone traveled on his way to work let us convert miles to feet and minutes to seconds.

1 mile = 5280 feet.

1 minute = 60 seconds.

now we will divide 158400 by 3492 to find the most accurate determination for the number of feet per second tyrone traveled on his way to work.

therefore, tyrone traveled on his way to work at the rate of 45.36 feet per second.