Help plz on question 6

Mathematics

1 answer:

ycow [4]3 years ago

8 0

<u>Answer:</u>

a. look attachment

i. P(choclate)

P(choclate) = 1/2 × (3/8 + 1/2)

P(choclate) = 3/16 + 1/4

P(choclate) = 3/16 + 4/16

P(choclate) = 7/16

ii. P(mints)

P(mints) = 1/2 × (5/8 + 1/2)

P(mints) = 5/16 + 1/4

P(mints) = 5/16 + 4/16

P(mints) = 9/16

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Three interior angles of a quadrilateral have measures of 120°, 100°, and 75°. What's the measure of the fourth interior angle?

SpyIntel [72]

Answer:

The answer is A.

Step-by-step explanation:

Given that the total interior angles in a quadrilateral is 360°. So in order to find the 4th angle, you have to subtract the remaining angles from 360° :

$θ + 120 + 100 + 75 = 360$

$θ + 295 = 360$

$θ = 360 - 295$

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4 years ago

Problem 8) In the diagram, RQ ⊥ PQ, m∠QPS = 32°, m∠RPS = 24°, and PQ = 14.Find RS to the nearest tenth of a unit. Image is provi

Sav [38]

Since S is a point on the segment QR, then:

$QS+SR=QR$

Use the diagram and trigonometric relationships to find the value of QS and QR. Then, use the above equation to solve for SR.

In the right triangle PQS, the side QS is opposite to the angle of 32º, and the side PQ is adjacent to the angle of 32º. Then, use the tangent trigonometric function to relate PQ to QS:

$\tan\left(32º\right)=\frac{QS}{PQ}$

Isolate QS and replace PQ=14:

$\begin{gathered} \Rightarrow QS=PQ\cdot\tan\mleft(32º\mright) \\ \operatorname{\Rightarrow}QS=14\tan\mleft(32º\mright) \end{gathered}$

On the other hand, notice that the side QR in the right triangle PQR is opposite to the angle QPR, which has a measure of 32º+24º=56º.

Then, by a similar reasoning, we can use again the tangent function to find QR:

$\begin{gathered} \tan\mleft(56º\mright)=\frac{QR}{PQ} \\ \Rightarrow QR=PQ\cdot\tan\mleft(56º\mright) \\ \Rightarrow QR=14\cdot\tan\mleft(56º\mright) \end{gathered}$

We have found expressions for QS and QR in terms of trigonometric relationships. Then, we can find an expression for SR: