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3 years ago

Show that cos 30 degree + sin 60 degree / 1+ sin 30 degree + cos 60 degree is equal to cos 30 degree

Mathematics

1 answer:

Soloha48 [4]3 years ago

5 0

Answer:

cos 30

Step-by-step explanation:

cos 30 + sin 60 / 1+ sin 30 + cos 60

= root3 / 2 + root3/2 / 1 + 1/2 + 1/2

= root 6/2 by 4/2

= root 6/4

= root 3/2

= cos 30

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The probability that a randomly selected box of a certain type of cereal has a particular prize is 0.20.

MatroZZZ [7]

Answer:

a) the probability is 0.0734 (7.34%)

b) the probability is 0.7382 (73.82%)

c) 10 boxes

Step-by-step explanation:

Since each box is independent of the others and defining the random variable X= number of boxes of cereal purchased without prices until having 2 prices , then X has a negative binomial distribution . Thus

P(X=k)= C(k+r-1,k)*p^k *(1-p)^r

where

p= probability to not obtain a price when a box is purchased = 1- 0.2 = 0.8

C ( ) = combinations

k = number of boxes without prices

r= number of boxes with prices=2

P(X=k) = probability of purchasing k boxes without prices until obtaining r boxes with prices

a) for k= 8 - r = 6

P(X=6)= C(7,6)*0.8^6*0.2^2 = 7*0.8^6*0.2^2 = 0.0734 (7.34%)

b) for k≥9-2=7

P(X≥7) = 1- P(X<7)= 1- Fn(X=7)

where Fn(X) is the cumulative negative binomial distribution. We can calculate it through its relationship with the cumulative binomial distribution Fb(X) that is easily found in tables :

Fn(k=7,r=2,p=0.8) = Fb(k=7,n=k+r=9,p=0.8) = 0.2618

thus

P(X≥7) = 1- P(X<7)= 1- Fn(X=7) = 1- 0.2618 = 0.7382 (73.82%)

c) the expected value E(X) for a negative binomial distribution is

E(X)= p*r/(1-p) = 0.8*2/0.2 = 8 boxes that do not contain prices

thus

n=k+r = 8 + 2 = 10 boxes

6 0

3 years ago

L E N 4 8 1 O k M What is the value of k? k=

s2008m [1.1K]

Answer: 2

Step-by-step explanation:

By the geometric mean theorem,

$\sqrt{8k}=4\\\\8k=16\\\\k=\boxed{2}$

6 0

2 years ago

What is the value of the numerical expression 5/8-5/12(3-1/4)+2/3

vlabodo [156]

Make bottom numbers same
find least common multipules of 8,12,4 and 3
8=2 times 2 times 2
12=2 times 2 times 3
4=2 times 2
3=3
lcm=2 times 2 times 2 times 3=24

5/8 times 3/3=15/24
5/12 times 2/2=10/24
3/1 times 24/24=72/24
1/4 times 6/6=6/24
2/3 times 8/8=16/24
we now have
15/24-10/24(72/24-6/24)+16/24
pemdas
simplify parenthasees first
72/24-6/24=66/24

now we have
15/24-10/24(66/24)+16/24
multiply
15/24-660/576+16/24
make same bottom number
15/24 times 24/24=360/576
16/24 times 24/24=384/576
360/576-660/576+384/576
84/576
7/48

answer is 7/48

3 0

3 years ago

WORTH 50 POINTS!!

cluponka [151]

Answers: Choice A and Choice E

0.82B and B-0.18B

========================================================

Explanation:

B is the cost of the game (some unknown amount). Subtract off 0.18B to indicate a 18% reduction in the price. That's how we get choice E.

Simplifying choice E leads us to choice A. Notice that 1 - 0.18 = 0.82; which represents 100% - 18% = 82%. After the discount, Bo is paying 82% of the original price.

Side note: Choice B indicates an 18% increase. Choices C and D don't represent percentage decreases (rather they're decreasing by a fixed amount regardless of what B is).

4 0

2 years ago

The endpoints of a diameter of a circle are (6,2) and (−2,5) . What is the standard form of the equation of this circle?

Paul [167]

Answer:

The standard form of the given circle is

$(x-2)^2+(y-\frac{7}{2})^2=73$