The hypotenuse of a right triangle is 4 times the smallest side. the third side is 4√15 cm. find the length of the smallest side of the triangle.

x=4 cm

Step-by-step explanation:

x=smallest side

4x=hypotenuse

4√15=third side

use the Pythagorean Theorem

(4x)^2=x^2+(4√15)^2

16x^2=x^2+240

16x^2-x^2=240

15x^2=240

x^2=240/15

x^2=16

x=√16

x=4 cm is the smallest side

the hypotenuse is 16 cm

the third side is 4√15 cm

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation:

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.