❗️❗️❗️❗️❗️the length of the hypotenuse of a right triangle is 157 units. the length of one leg of the triangle is 132 units. lara wrote the following steps find the length of the unknown leg:
length of the unknown leg= 157^2 - 132^2=24,649 - 17,424= 7,225 units
which statement best explains whether lara’s step is correct or incorrect?
a. it is correct because the length of the unknown side is the difference of the lengths of the sides
b. it is correct because the length of the unknown side is the difference of the squares of the sides
c. it is incorrect because the length of the unknown side is the square root of 42,073
d. it is incorrect because the length of the unknown side is the square root of 7,225

In pqr the obtuse angle is 105 and the shorter sides measure 4 and 7 units rounded to the nearest tenth what is the area of triangle pqr

6.(q^9)^2 a. 2q^18 b. q^18 c. q^81 d.q^11 7.(6q^6)^-4 a. 6q^1296 b. 1296q^2 c. 1/1296q^24 d. 6q^-24 8. what is the value of 12x^-3 y^-1 for x = -1 and y = 5? a. -12/5 b.-10 c.-0 d.5/12 9. (y^-5)^10y^10 a. y^-60 b. y^60 c. y^-150 d. y^150 find the simplified form of each expression. 10. (4/7^5)^2 a.8/14^10 b.16/49^25 c.16/49y^10 d.8/14y^25 11. determine if the number 3.43 times 10^-6 is written in scientific notation. if not, explain. a. yes; the number is written scientific notation. b. no; the first factor is not a number between 1 and 10. c. no; it is not written as a number times a power of 10

The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. complete parts (a) and (b) below. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is nothing. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is nothing. (round to three decimal places as needed.)