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forsale [732]
3 years ago
11

I need help with this question

Mathematics
1 answer:
Novay_Z [31]3 years ago
3 0

Answer:

$ \frac{\sqrt{3} - 1}{2\sqrt{2}} $

$ \frac{-(\sqrt{3} + 1)}{2\sqrt{2}} $

$ - \frac{\sqrt{3} - 1}{\sqrt{3} + 1} $

Step-by-step explanation:

Given $ \frac{11 \pi}{12} = \frac{3 \pi}{4} + \frac{\pi}{6} $

(A) $ sin(\frac{11\pi}{12}) = sin (\frac{3 \pi}{4}  + \frac{\pi}{6}) $

We know that Sin(A + B) = SinA cosB + cosAsinB

Substituting in the above formula we get:

$ sin (\frac{3\pi}{4} + \frac{\pi}{6}) = \frac{1}{\sqrt{2}} . \frac{\sqrt{3}}{2} + \frac{-1}{\sqrt{2}}. \frac{1}{2} $

$ \implies \frac{1}{\sqrt{2}} (\frac{\sqrt{3} - 1}{2}) = \frac{\sqrt{3} - 1}{2\sqrt{2}}

(B) Cos(A + B) = CosAcosB - SinASinB

$ cos(\frac{11\pi}{12}) = cos(\frac{3\pi}{4} + \frac{\pi}{6}}) $

$ \implies \frac{-1}{\sqrt{2}}. \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}} . \frac{1}{2} $

$ \implies cos(\frac{11\pi}{12}) = cos(\frac{3\pi}{4} + \frac{\pi}{6}) $

$ = \frac{-(\sqrt{3} + 1)}{2\sqrt{2}}

(C) Tan(A + B) = $ \frac{Sin(A +B)}{Cos(A + B)} $

From the above obtained values this can be calculated and the value is $ - \frac{\sqrt{3} - 1}{\sqrt{3} + 1} $.

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A scale on a map shows that 2.52.52, point, 5 centimeters represents 151515 kilometers.
Dmitry_Shevchenko [17]

Answer:

  105 km

Step-by-step explanation:

Written as a proportion, the ratio of km to cm will be the same for both distances:

  (x km)/(17.5 cm) = (15 km)/(2.5 cm)

  x km = (15 km)(17.5/2.5) = 105 km

105 actual kilometers are represented by 17.5 cm on the map.

5 0
3 years ago
G(x)=(x^2+1)(3x-5) what is the value of g(4)?
MAVERICK [17]

g(x) = x^2 + 1(3x - 5)

<em><u>Replace all x's with 4.</u></em>

g(4) = 4^2 + 1(3 * 4 - 5)

g(4) = 16 + 1(12 - 5)

g(4) = 17(7)

g(4) = 119 (This is your answer.)

5 0
3 years ago
A given population proportion is .25. What is the probability of getting each of the following sample proportions
anyanavicka [17]

This question is incomplete, the complete question is;

A given population proportion is .25. What is the probability of getting each of the following sample proportions

a) n = 110 and = p^ ≤ 0.21, prob = ?

b) n = 33 and p^ > 0.24, prob = ?

Round all z values to 2 decimal places. Round all intermediate calculation and answers to 4 decimal places.)

Answer:

a) the probability of getting the sample proportion is 0.1660

b) the probability of getting the sample proportion is 0.5517

Step-by-step explanation:

Given the data in the questions

a)

population proportion = 0.25

q = 1 - p = 1 - 0.25 = 0.75

sample size n = 110

mean = μ = 0.25

S.D = √( p( 1 - p) / n ) = √(0.25( 1 - 0.25) / 110 ) √( 0.1875 / 110 ) = 0.0413

Now, P( p^ ≤ 0.21 )

= P[ (( p^ - μ ) /S.D) < (( 0.21 - μ ) / S.D)

= P[ Z < ( 0.21 - 0.25 ) / 0.0413)

= P[ Z < -0.04 / 0.0413]

= P[ Z < -0.97 ]

from z-score table

P( X ≤ 0.21 ) = 0.1660

Therefore, the probability of getting the sample proportion is 0.1660

b)

population proportion = 0.25

q = 1 - p = 1 - 0.25 = 0.75

sample size n = 33

mean = μ = 0.25

S.D = √( p( 1 - p) / n ) = √(0.25( 1 - 0.25) / 33 ) = √( 0.1875 / 33 ) = 0.0754

Now, P( p^ > 0.24 )  

= P[ (( p^ - μ ) /S.D) > (( 0.24 - μ ) / S.D)

= P[ Z > ( 0.24 - 0.25 ) / 0.0754 )

= P[ Z > -0.01 / 0.0754  ]

= P[ Z > -0.13 ]

= 1 - P[ Z < -0.13 ]

from z-score table

{P[ Z < -0.13 ] = 0.4483}

1 - 0.4483

P( p^ > 0.24 )  = 0.5517

Therefore, the probability of getting the sample proportion is 0.5517

6 0
3 years ago
The probability of randomly selecting a female from a group of 25 elementary school teachers is . Which of the following describ
nirvana33 [79]

Answer:

it is likely that a female will be picked

Step-by-step explanation:

the probability of selecting a female = 21/25....or 84%

7 0
3 years ago
An arrow on a spinner is spun 250 times. Some of the results are shown below. The relative frequency of landing on a 4 is the sa
N76 [4]

Answer:

11/50

Step-by-step explanation:

The frequency numbers for landing on 1, 2, and 3 are:

25, 53, 62.

We add them up to get: 25 + 53 + 62 = 140

Since 250 spins were made, and 140 of them landed on 1, 2, or 3, then

250 - 140 = 110,

so 110 landed on 4 or 5.

We are told the numbers of spins landing on 4 and 5 are equal, so

110/2 = 55,

so the spinner landed 55 times on 4 and 55 times on 5.

relative frequency = 55/250 = 11/50

5 0
3 years ago
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