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Pavlova-9 [17]
3 years ago
7

Prove csc(pi/2 -x) = sec x

Mathematics
1 answer:
kifflom [539]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

Consider the left side

Using the trigonometric identities

csc x = \frac{1}{sinx} and sec x = \frac{1}{cosx}

Note that sin( \frac{\pi }{2} - x) = cos x

Hence

csc(\frac{\pi }{2} - x)

= \frac{1}{sin(\frac{\pi }{2}-x) }

= \frac{1}{cosx}

= sec x = right side ⇒ proven

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Out of 450 applicants for a job, 206 are male and 62 are male and have a graduate degree.
xxMikexx [17]

Answer:

0.3009 is the  probability that the applicant has graduate degree given he is a male.                                                              

Step-by-step explanation:

We are given he following in the question:

M: Applicant is male.

G: Applicant have a graduate degree

Total number of applicants = 450

Number of male applicants = 206

n(M) = 206

Number of applicants that are male and have a graduate degree = 62

n(M\cap G) = 62

\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}

P(M) = \dfrac{206}{450} = 0.4578

P(M\cap G) = \dfrac{n(M\cap G)}{n} = \dfrac{62}{450} = 0.1378

We have to find the probability that the applicant has graduate degree given he is a male.

P(G|M) = \dfrac{P(G\cap M)}{P(M)} = \dfrac{\frac{62}{450}}{\frac{206}{450}} = \dfrac{62}{206} = 0.3009

Thus, 0.3009 is the  probability that the applicant has graduate degree given he is a male.

5 0
3 years ago
clayton uses 34 of a bottle of hot sauce for every batch of salsa he makes. yesterday, he used 214 bottles of hot sauce. how man
Aleks [24]
If he used 34 bottles for every batch just divide 214 bottles he used by 34 it takes for a batch 
he made 6.3 batches 
8 0
3 years ago
Someone help me please
garri49 [273]

Answer:

  • 42 seats

Step-by-step explanation:

This represents an arithmetic progression with the first term of a = 15 and common difference of d = 3.

<u>The tenth row is the 10th term:</u>

  • aₙ = a + (n - 1)d

<u>The row 10 has:</u>

  • a₁₀ = 15 + 9*3 = 15 + 27 = 42 seats
7 0
2 years ago
Read 2 more answers
(5.6x - 4) + (16 - 2.1x)<br><br> What is the sum of this expression?
Damm [24]

\huge\text{Hey there!}

\large\textsf{(5.6x - 4) + (16 - 2.1x)}

\large\text{DROP the PARENTHESES}

\large\textsf{5.6x - 4 + 16 - 2.1x}

\large\text{COMBINE the LIKE TERMS}

\large\textsf{5.6x - 2.1x - 4 + 16}

\large\textsf{5.6x - 2.1x = \bf  3.5x}

\large\textsf{-4 + 16 = \bf  12}

\large\textsf{=  \bf 3.5x + 12 }

\boxed{\boxed{\large\text{Answer: \huge \bf 3.5x + 12}}}\huge\checkmark

\text{Good luck on your assignment and enjoy your day!}

~\frak{Amphitrite1040:)}

7 0
3 years ago
Plzzz HELP will give brainliest 9^-53*9^37
slamgirl [31]

Answer: The exact form is 5.3965953e-16. But in exponential form: 9^(-16).

Step-by-step explanation:

Use your calculator to plug in the negative powers and to multiply. Do it one step at a time. If you want exponential form, then here:

9^(-53) * 9^(37)

Add exponents keep base

9^(-16)

Hope this helps

3 0
3 years ago
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