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3 years ago

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.

The tenth row is the 10th term:

aₙ = a + (n - 1)d

The row 10 has:

a₁₀ = 15 + 9*3 = 15 + 27 = 42 seats

7 0

2 years ago

Read 2 more answers

(5.6x - 4) + (16 - 2.1x) 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