In Δ ABC, ∠A=120°, AB=AC=1
To draw a circumscribed circle Draw perpendicular bisectors of any of two sides.The point where these bisectors meet is the center of the circle.Mark the center as O.
Then join OA, OB, and OC.
Taking any one OA,OB and OC as radius draw the circumcircle.
Now, from O Draw OM⊥AB and ON⊥AC.
As chord AB and AC are equal,So OM and ON will also be equal.
The reason being that equal chords are equidistant from the center.
AM=MB=1/2 and AN=NC=1/2 [ perpendicular from the center to the chord bisects the chord.]
In Δ OMA and ΔONA
OM=ON [proved above]
OA is common.
MA=NA=1/2 [proved above]
ΔOMA≅ ONA [SSS]
∴ ∠OAN =∠OAM=60° [ CPCT]
In Δ OAN
OA=1
∴ OA=OB=OC=1, which is the radius of given Circumscribed circle.
Because you went from 41.5 to 47.6 when the granite was placed in the graduated cylinder, using displacement:
47.6 - 41.5 = 6.1
I don't know about the cubic centimeters part, I don't know for sure if mL and cubic cm are the same, sorry. :(
Answer :
The shape of the distribution of the sample usually contains the given two points :
1. The sampling distribution is skewed for small sample sizes. Also, the distribution will be non-normal if the sample size is small
2. The shape of the sampling distribution gets more and more normal-like (bell shaped) as the sample size increases
For sample size, n = 2
The sampling distribution will be skewed for this sample size
For sample size, n = 70
The shape of the sampling distribution for sample size of 70 will be more normal as compared to that of sample size of 2
<h3>There are 96 roses altogether</h3>
<em><u>Solution:</u></em>
Let "x" be the number of roses
From given,
<em><u>1/4 of the roses are red</u></em>
<em><u>1/3 of the remainder are yellow</u></em>
Therefore,
<em><u>Rest are pink</u></em>
Therefore,
There are 24 more pink roses than red roses
Therefore,
Number of pink roses = 24 + red roses
Thus there are 96 roses altogether
Answer:
a) 0.88
b) 0.35
c) 0.0144
d) 0.2084
e) 0.7916
Step-by-step explanation:
a) The probability of a peanut being brown is 12/100 = 0.12. Hence the probability of it not being brown is 1-0.12 = 0.88
b) 12% of peanuts are brown, 23% are blue. So 35% are either blue or brown. The probability of a peanut being blue or brown is, therefore 35/100 = 0.35.
c) 12% of peanuts are red, so the probability of a peanut being red is 12/100 = 0.12. In order to calculate the probability of 2 peanuts being both red, we can assume that the proportion doesnt change dramatically after removing one peanut (because the number of peanuts is absurdly high. We can assume that we are replenishing the peanuts). To calculate the probability of 2 peanuts being both red, we need to power 0.12 by 2, hence the probability is 0.12² = 0.0144.
d) Again, we will assume that the probability doesnt change, because we replenish. The probability of a peanut being blue is 0.23. The probability of it not being blue is 0.77, so the probability of 6 peanuts not being blue is obtained from powering 0.77 by 6, hence it is 0.77⁶ = 0.2084
e) The event 'at least one peanut is blue' is te complementary event of 'none peanuts are blue', so the probability of this event is 1- 0.2084 = 0.7916
