Answer:
Area of trapezium = 4.4132 R²
Step-by-step explanation:
Given, MNPK is a trapezoid
MN = PK and ∠NMK = 65°
OT = R.
⇒ ∠PKM = 65° and also ∠MNP = ∠KPN = x (say).
Now, sum of interior angles in a quadrilateral of 4 sides = 360°.
⇒ x + x + 65° + 65° = 360°
⇒ x = 115°.
Here, NS is a tangent to the circle and ∠NSO = 90°
consider triangle NOS;
line joining O and N bisects the angle ∠MNP
⇒ ∠ONS = 
= 57.5°
Now, tan(57.5°) = 
⇒ 1.5697 = 
⇒ SN = 0.637 R
⇒ NP = 2×SN = 2× 0.637 R = 1.274 R
Now, draw a line parallel to ST from N to line MK
let the intersection point be Q.
⇒ NQ = 2R
Consider triangle NQM,
tan(∠NMQ) = 
⇒ tan65° =
⇒ QM = 
QM = 0.9326 R .
⇒ MT = MQ + QT
= 0.9326 R + 0.637 R (as QT = SN)
⇒ MT = 1.5696 R
⇒ MK = 2×MT = 2×1.5696 R = 3.1392 R
Now, area of trapezium is (sum of parallel sides/ 2)×(distance between them).
⇒ A = (
) × (ST)
= (
) × 2 R
= 4.4132 R²
⇒ Area of trapezium = 4.4132 R²
The simplified form of the expression is -10x - 16
<h3>Factorizing expressions</h3>
Given the expression -2(5x + 8)
In order to factorize the expression, we will use the distributive property. Distribute -2 over 5x and 8 to have:
Step 1: Distribute -2 to 5x and 8
-2(5x + 8) =-2(5x) -2(8)
Simplify
-2(5x + 8) = -10x - 16
Hence the simplified form of the expression is -10x - 16
Learn more on factoring here: brainly.com/question/24734894
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Add 24 to both sides<span><span>x≥9+24</span>Simplify <span>9+24</span><span> to </span><span>33
</span><span><span>x≥33</span><span>
</span></span></span>
Answer:
864
Step-by-step explanation:
A=6a^2=6·12^2=864
Answer:
A <u>z-score</u> indicates how far an individual raw score falls from the mean of a distribution; the <u>standard deviation</u> indicates how the scores in general scatter around the mean.
Step-by-step explanation:
We have been given an incomplete statement. We are supposed to complete the given statement.
We know that z-score of a data set indicates that a sample score or raw score is how many standard deviation away from the mean. Z-score indicates the distance of a raw score is above or below mean in units.
Therefore, the correct word for 1st blank would be "z-score".
We also know that standard deviation represents the variation of a data set. It tells that data points of a data set are how much close or away from mean of the data set.
Therefore, the correct word for 2nd blank would be "standard deviation".
