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rodikova [14]
3 years ago
5

A small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded. The results showed that 150

of the adults who were parents and 40 of the adults who were not parents thought the park should be expanded.
Use this information to complete the two-way table.

Enter your answer by filling in the boxes to complete the table.

Should the park be expanded?
Yes No
Parents
Not parents
Mathematics
2 answers:
quester [9]3 years ago
8 0

Answer:

Yes, the park should be expanded

Explanation:

180 adults said yes.

250 - 180 = 70

70 people thought the park shouldn't be expanded, but there are more people who want the mark to expand.

nignag [31]3 years ago
7 0

Answer:

its 70

Step-by-step explanation:

70 goes in the yes 0 for no and 40 for yes and 0 for no

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3 years ago
Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).
insens350 [35]

Answer:

\cos{\theta} = \dfrac{1}{52}

\csc{\theta} = \dfrac{52}{\sqrt{2703}}

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

\sec{\theta} = \dfrac{1}{\cos{\theta}}

we can substitute the value of sec(θ) in this equation:

52 = \dfrac{1}{\cos{\theta}}

and solve for for cos(θ)

\cos{\theta} = \dfrac{1}{52}

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by \theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ

b) since right triangle is mentioned in the question. We can use:

\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

  • length of the adjacent side = 1
  • length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2

(52)^2=(1)^2+(\text{opp})^2

\text{opp}=\sqrt{(52)^2-1}

\text{opp}=\sqrt{2703}

  • length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}

\sin{\theta} = \dfrac{\sqrt{2703}}{52}}

and since \csc{\theta} = \dfrac{1}{\sin{\theta}}

\csc{\theta} = \dfrac{52}{\sqrt{2703}}

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