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3 years ago

BRAINLIESTT ASAP! PLEASE HELP ME :)

Mathematics

1 answer:

sukhopar [10]3 years ago

6 0

Answer: A) none of the equations are identities

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

Part 1

Plug in theta = 0

sin(theta+pi/2) - cos(theta+pi/6) = 2*cos(theta) - sin(theta)

sin(0+pi/2) - cos(0+pi/6) = 2*cos(0) - sin(0)

1 - sqrt(3)/2 = 2*1 - 0

0.13 = 2

which is a false equation

So we do not have an identity in equation 1.

-------------------------------------------

Part 2

Plug in theta = 0

sin(theta+pi/6) + cos(theta+pi/3) = (sqrt(2)/3)*sin(theta) + 2*cos(theta)

sin(0+pi/6) + cos(0+pi/3) = (sqrt(2)/3)*sin(0) + 2*cos(0)

1/2 + 1/2 = 0 + 2

1 = 2

which is also false

This is not an identity either.

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A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the l

Anna [14]

Answer:

a) 0.4452

b) 0.0548

c) 0.0501

d) 0.9145

e) 6.08 minutes or greater

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.7 minutes

Standard Deviation, σ = 0.50 minutes.

We are given that the distribution of length of the calls is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(calls last between 4.7 and 5.5 minutes)

$P(4.7 \leq x \leq 5.5) = P(\displaystyle\frac{4.7 - 4.7}{0.50} \leq z \leq \displaystyle\frac{5.5-4.7}{0.50}) = P(0 \leq z \leq 1.6)\\\\= P(z \leq 1.6) - P(z$

$P(4.7 \leq x \leq 5.5) = 44.52\%$

b) P(calls last more than 5.5 minutes)

$P(x > 5.5) = P(z > \displaystyle\frac{5.5-4.7}{0.50}) = P(z > 1.6)\\\\P( z > 1.6) = 1 - P(z \leq 1.6)$

Calculating the value from the standard normal table we have,

$1 - 0.9452 = 0.0548 = 5.48\%\\P( x > 5.5) = 5.48\%$

c) P( calls last between 5.5 and 6 minutes)

$P(4.7 \leq x \leq 5.5) = P(\displaystyle\frac{5.5 - 4.7}{0.50} \leq z \leq \displaystyle\frac{6-4.7}{0.50}) = P(1.6 \leq z \leq 2.6)\\\\= P(z \leq 2.6) - P(z$

$P(5.5 \leq x \leq 6) = 5.01\%$

d) P( calls last between 4 and 6 minutes)

$P(4 \leq x \leq 6) = P(\displaystyle\frac{4 - 4.7}{0.50} \leq z \leq \displaystyle\frac{6-4.7}{0.50}) = P(-1.4 \leq z \leq 2.6)\\\\= P(z \leq 2.6) - P(z$

$P(4 \leq x \leq 6) = 91.45\%$

e) We have to find the value of x such that the probability is 0.03.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 4.7}{0.50})=0.03$

$= 1 -P( z \leq \displaystyle\frac{x - 4.7}{0.50})=0.03$

$=P( z \leq \displaystyle\frac{x - 4.7}{0.50})=0.997$

Calculation the value from standard normal z table, we have,

P(z < 2.75) = 0.997

$\displaystyle\frac{x - 4.7}{0.50} = 2.75\\x = 6.075 \approx 6.08$

Hence, the call lengths must be 6.08 minutes or greater for them to lie in the highest 3%.

8 0

3 years ago

Help asp

Svetradugi [14.3K]

<h3>The temperature drop from the morning to the night is -16.8 F</h3>

<em><u>Solution:</u></em>

Given that,

The temperature in the morning was -4 F

At night the temperature dropped to -12.8 F

To find: temperature drop from the morning to the night be represented

From given,

Morning = -4 F

Night = -12.8 F

Therefore,

Temperature drop from the morning to the night = -4 - 12.8 = -16.8 F

Thus the temperature drop from the morning to the night is -16.8 F

3 0

3 years ago

Grace ran 8 laps and walked 3 laps around the gym track. Grace ran twice as many laps as Tami ran. Then Tam walked twice as many

GrogVix [38]

Answer:

Grace

Step-by-step explanation:

Grace ran 11 since 8 + 3= 11. Tam ran 4 laps and walked 6 and 4 + 6 = 10. Grace did 11 laps while Tam did 10 laps.

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3 years ago

Read 2 more answers

Please help me. Noura is redecorating her house. She needs to work out the area of the wall around her triangular window in orde

Vinvika [58]

Answer:

a. 277.3 m²

b. $307.86

Step-by-step explanation:

a. Area of the wall to be painted = area of rectangle - area of triangle

= L × W + ½×a×b×sin θ

L = 17 m

W = 14 m

a = 8.7 m

b = 9.5 m

θ = 72°

Plug in the values into the equation

Area of the wall = (17×14) + (½*8.7×9.5×sin 72)

Area of the wall = 238 + 39.3024105

Area of the wall to paint ≈ 277.3 m²

b. 20 liters of paint of 1 container cost $21.99

If 1 liter of paint covers 1m², therefore,

277.3 m² will need = 277.3 × 1 = 277.3 liters of paint.

20 liters = 1 container of paint

277.3 liters = 277.3/20 = 13.865 ≈ 14 containers

1 container = $21.99

14 containers = 21.99 × 14 = $307.86

8 0

3 years ago

There are four students, all of different heights, who are to be randomly arranged in a line. What is the probability that the t

notka56 [123]

Answer:

Hey there!

The answer is 1/12

1/4(1/3)=1/12

Let me know if this helps :)

6 0

3 years ago