1. A researcher is interested in studying whether or not listening to music while jogging makes people run faster. He thinks tha
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1) set up a problem
you know you want to get an avg of 94 but how do you do avg in the first place. you add up the numbers then divde by the total number of numbers used lol
so
92.5 is the avg number for the last 3 tests
"x" is the 4th test score which we want to find out
"2" is the total number of numbers being added together
so now lets get x to one side
92.5+ x=94*2 (multiply 2 to both sides)
92.5+x=188
x=188-92.5 (subtract 92.5 from both sides)
x= 95.5 this is the score she need to make to avg 94%
2) you can draw a tree diagram. for example Flower1 branches off into 3 diff greens and then each of those greens branch off into 2 for with or with babies breath.
or you can simple multiply 4*3*2. you can do this because all choices are included with no restriction
your total number of options is 24
you know you want to get an avg of 94 but how do you do avg in the first place. you add up the numbers then divde by the total number of numbers used lol
so
92.5 is the avg number for the last 3 tests
"x" is the 4th test score which we want to find out
"2" is the total number of numbers being added together
so now lets get x to one side
92.5+ x=94*2 (multiply 2 to both sides)
92.5+x=188
x=188-92.5 (subtract 92.5 from both sides)
x= 95.5 this is the score she need to make to avg 94%
2) you can draw a tree diagram. for example Flower1 branches off into 3 diff greens and then each of those greens branch off into 2 for with or with babies breath.
or you can simple multiply 4*3*2. you can do this because all choices are included with no restriction
your total number of options is 24
Refer to the diagram below.
Because ray NP bisects ∠MNQ, therefore
∠MNP = ∠PNQ = 2x + 1.
Therefore
∠MNQ = 2*∠PNQ = 2(2x + 1) = 4x + 2.
Because ∠MNQ is given as x² - 10, therefore
x² - 10 = 4x + 2
x² - 4x - 12 = 0
(x + 2 )(x - 6) = 0
x = -2, or x = 6
When x = -2,
∠MNQ = 4*(-2) + 2 = -6°
This answer is not acceptablle, therefore x = -2 should be rejected.
When x = 6,
∠MNQ = 4*6 + 2 = 26°
Answer: x = 6, and ∠MNQ = 26°
Because ray NP bisects ∠MNQ, therefore
∠MNP = ∠PNQ = 2x + 1.
Therefore
∠MNQ = 2*∠PNQ = 2(2x + 1) = 4x + 2.
Because ∠MNQ is given as x² - 10, therefore
x² - 10 = 4x + 2
x² - 4x - 12 = 0
(x + 2 )(x - 6) = 0
x = -2, or x = 6
When x = -2,
∠MNQ = 4*(-2) + 2 = -6°
This answer is not acceptablle, therefore x = -2 should be rejected.
When x = 6,
∠MNQ = 4*6 + 2 = 26°
Answer: x = 6, and ∠MNQ = 26°
The problem is modelled in the diagram below
Question 1:
The largest area of the pool is half of the area of the circle
Area of circle = πr², where r is the radius given by 1/2 of the diameter
Area of circle = π(60)² = 11309.73355 feet
Area of half of the circle is 11309.73355/2 = 5654.866... ≈ 5654.87 feet (2dp)
Question b:
The area of the pool is the area of the circle subtracts the area of the triangle.
The area of the circle is 11309.73²
The area of the triangle is 1/2 (60×103.92) = 3117.6 feet²
The area of the pool is 11309.73 - 3117.6 = 7922.13 feet²
The volume of the pool = 7922.13 × 4 = 31688.52 feet³
Note: there isn't any information on the fish tank part so the answer above is assumed for the whole pool.
Question 1:
The largest area of the pool is half of the area of the circle
Area of circle = πr², where r is the radius given by 1/2 of the diameter
Area of circle = π(60)² = 11309.73355 feet
Area of half of the circle is 11309.73355/2 = 5654.866... ≈ 5654.87 feet (2dp)
Question b:
The area of the pool is the area of the circle subtracts the area of the triangle.
The area of the circle is 11309.73²
The area of the triangle is 1/2 (60×103.92) = 3117.6 feet²
The area of the pool is 11309.73 - 3117.6 = 7922.13 feet²
The volume of the pool = 7922.13 × 4 = 31688.52 feet³
Note: there isn't any information on the fish tank part so the answer above is assumed for the whole pool.