There are 28 people on a martial arts course. 13 are female and 15 are male. What fraction of the people are male? ​

(5x - 3y)(25x² + 15xy + 9y²) Step-by-step explanation: 125x³ - 27y³ is a difference of cubes and can be factored as a³ - b³ = (a - b)(a² + ab + b²). Given 125x³ - 27y³ = (5x)³ - (3y)³, it can be written as (5x - 3y)((5x)² + (5x)(3y) + (3y)²) = (5x - 3y)(25x² + 15xy + 9y²).

Distance formula:


5 units-4.5 units=0.5 units

Segment LM exceeds segment JK by 0.5 units.

Answer: Zeno consumed 51 hot dogs.

The total number of hot dogs consumed was 676.

Step-by-step explanation:

Al started by eating one hot dog. Bob then outperformed him by devouring three hot dogs. Carl, not wanting to fall behind, ate five hot dogs. This pattern continued, with each participant consuming two hot dogs more than the previous one. This indicates that the quantity of hot dogs eaten by each contestant followed an arithmetic sequence.

The formula for finding the nth term in an arithmetic series is given by

Tn = a + (n - 1)d

Where

a denotes the first term in the sequence.

d signifies the common difference.

n stands for the total terms in the sequence.

<pBased on the details provided,

a = 1 hot dog

d = 3 - 1 = 2 hot dogs

We aim to find how many hot dogs the 26th contestant, T26, consumed. Thus,

T26 = 1 + (26 - 1)2 = 1 + 50

T26 = 51 hot dogs

The formula to calculate the sum of n terms in an arithmetic sequence is

Sn = n/2[2a + (n - 1)d]

Hence, to find the total number of hot dogs consumed by 26 contestants, S26 is calculated as

S26 = 26/2[2 × 1 + (26 - 1)2]

S26 = 13[2 + 50]

S26 = 13 × 52 = 676 hot dogs

Detailed explanation:

Information provided:

Tran possesses a credit card that allows up to $2000 in spending with an APR of 12%.

In the initial month, Tran incurred charges of $450 and settled $150 within that billing period.

The formula to determine the interest that will accrue for Tran in the first month is (0.012)(300)

Here, 0.01 signifies the monthly interest rate.

The 300 reflects the outstanding balance, as Tran charged $450 but only paid back $150.

To calculate the mean absolute deviation of
1,2,3,4,5,6,7
, we start by finding the mean;
 (1+2+3+4+5+6+7) =28/7
                               = 4
. Next, we determine the absolute differences of each data point from the mean (x-μ)
 = -3,-2,-1,0,1,2,3
. The absolute values are 3,2,1,0,1,2,3
. Now we compute the mean of these absolute differences,
3+2+1+0+1+2+3 = 12
                           = 12/7
                           = 1.7143
. Thus, the mean is 4, and the Mean absolute deviation comes out to be 1.7143