I'm a little lost on this one Galen wrote the statement "If the sum of the digits in a number is divisible by 3, the original number is divisible by 3." Which statements are true regarding his work? Select three options. 1. The hypothesis of the statement is "If the sum of the digits in a number is divisible by 3 2. An equivalent statement is "If the sum of the digits in a number is divisible by 3, then the original number is divisible by 3." 3. The statement is not a conditional statement because it does not include both an "if" and a "then" clause. 4. The statement can be proven true or false. 5. The conclusion of the statement is written before the hypothesis. Any help would be appreciated.

note: I wasn't sure about statement 2. I think your teacher made a typo with that.

Let's go through the five statements to see if they are true or not.

Statement 1) The hypothesis of the statement is "If the sum of the digits in a number is divisible by 3"

This is a true statement as conditionals are of the basic form "if hypothesis, then conclusion". A hypothesis is an educated guess or assumption, and it leads to the conclusion which is often directly (or somewhat directly) tied to the hypothesis.

Statement 2) An equivalent statement is "If the sum of the digits in a number is divisible by 3, then the original number is divisible by 3."

This is a bit baffling as this is an identical copy of the statement Galen wrote at the top. It seems like your teacher made a typo here (probably didn't realize they cut/pasted the wrong thing). I'm not sure what to do here. I would ask your teacher for clarification.

Statement 3)  The statement is not a conditional statement because it does not include both an "if" and a "then" clause.

This is false. It is indeed a conditional even if it doesn't fit the exact parameters of "if ..., then " format. You could have a conditional that reads "it gets wet outside if it rains", which can be rearranged into "if it rains, then it gets wet outside". Both are considered conditionals even though the first one doesn't have "then".

Statement 4) The statement can be proven true or false

This is true. We can prove Galen's statement to be true or false. In this case, it can be proven to be true. This is one of the many divisibility rules.

Statement 5) The conclusion of the statement is written before the hypothesis.

This is false. The conclusion in this case is "the original number is divisible by 3" which is written after the hypothesis. There is a way to write the conclusion first by saying "a number is divisible by 3 if the sum of its digits are divisible by 3". But that isn't the case here.

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!