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svp [43]
3 years ago
14

Given sinθ = 2/5 and cosθ < 0: 1. Find cscθ 2. Find cotθ

Mathematics
1 answer:
Tems11 [23]3 years ago
5 0

Recall that

sin²(<em>θ</em>) + cos²(<em>θ</em>) = 1

for all <em>θ</em>, and given that cos(<em>θ</em>) < 0, we find that

cos(<em>θ</em>) = -√(1 - sin²(<em>θ</em>)) = -√(1 - (2/5)²) = -√(21)/5

Now,

csc(<em>θ</em>) = 1/sin(<em>θ</em>) = 1/(2/5) = 5/2

and

cot(<em>θ</em>) = cos(<em>θ</em>)/sin(<em>θ</em>) = (-√(21)/5)/(2/5) = -√(21)/2

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Suppose thatAnn selects a ball by first picking one of two boxes at random and then selecting a ball from this box. The first bo
Natalka [10]

Answer:

35/68

Step-by-step explanation:

The first box contains 3 orange balls and 4 black balls.

The second box contains 5 orange balls and 6 black balls

Total number of boxes = 2

Let Pr(F) be the probability that the first box is picked.

Let Pr(S) be the probability that the second ball is picked

Let O be the orange ball selected

Pr(F) = 1/2

Pr(S) = 1/2

Pr(O|S) = n(O) / n(S)

= 5/ 6+5

5/11

Pr(O|F) = n(O) / n(F)

= 3/ 4+3

= 3/7

Pr(S|O) = [Pr( O|S).P(S)] / [Pr( O|S).P(S) + Pr( O|F).P(F)]

= (5/11*1/2) / (5/11*1/2) +(3/7*1/2(

= (5/22) / (5/22 + 3/14)

= (5/22) / (136/308)

= 35/68

3 0
3 years ago
Pete can type 80 words in the same time that Ralph can type 50 words. If they type at those rates
tamaranim1 [39]

Answer:

After the extended period of time, Pete would have typed 6400  words.

Step-by-step explanation:

Given the data in the question;

In the same time;

number typed word of Pete = 80

type word of Ralph = 50

After a period time;

number of typed word of Pete = ?

number of typed word of Ralph = 4000

so, let x represent the number of typed word by Pete after an extended period.

so

80 words = 50 words

x words =    4000 words

we cross multiply

x × 50 = 4000 × 80

x = ( 4000 × 80 ) / 50

x = 320000 / 80

x = 6400

Therefore, After the extended period of time, Pete would have typed 6400  words.

3 0
3 years ago
The number of right-handed students in a math class is nine times the number of left-handed students. The total number of studen
nirvana33 [79]
R - Right Handed 
L - Left Handed 

R = 9L ( the number of right handed kids is equal to having 9*number of left handed kids) 
9L + L = 30  ( since total number of people in class is 30) 
10L = 30 
( Divide by 10 both sides )
L = 3 

so... There are 3 Left Handed kids and 27 Right Handed kids ( since R = 9L , R = 9(3) = 27)

Hope this helped!
5 0
3 years ago
The figures are similar. Find x.
DaniilM [7]

Answer:

My own answer to your question is x=10

4 0
2 years ago
Identify the lateral area and surface area of a regular triangular pyramid with base edge length 14 cm and slant height 15 cm
posledela

Answer:

D) L = 315 cm2 ; S = 399.9 cm2

Step-by-step explanation:

Lateral area;

3 × (½)(14)(15)

315 cm²

Surface area:

315 + (½)(14)(14)sin(60)

399.8704896 cm²

6 0
3 years ago
Read 2 more answers
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