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4 years ago

If sin θ = cos 40°, 0<θ<90°, what is θ?

Mathematics

1 answer:

Bezzdna [24]4 years ago

3 0

Answer:

θ = 50 degrees

Step-by-step explanation:

we have sin θ = cos 40°

θ = arcsin ( cos 40°)

and make sure θ is less than 90 and greater than 0

θ = arcsin (0.766044443)

θ = 50 degrees

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4 years ago

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3 years ago

BRAINLIEST ANSWER WINS! A satellite is to be put into an elliptical orbit around a moon as shown below. A vertical ellipse is sh

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Answer:

D. x²/1953² + y²/ 1466² = 1

Step-by-step explanation:

==>Given:

Radius of spherical moon = 1000km

Distance of satellite from moon surface = 953km to 466km

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Derived equation of ellipse

==>Solution:

The formula for driving an equation of ellipse is given as:

x²/a² + y²/b² = 1

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a = length of the semi-major axis, while,

b = length of the semi-major axis

Since we are told that the satellite distance to the surface of the moon varies from 953km to 466km, values of a and b is calculated by summing each length to the radius of the moon as follows:

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3 years ago

In right triangle ∆ABC, ∠A = 42°. Find the measure of ∠B which is the other non right angle.

Zigmanuir [339]

Answer:

48 degrees

Step-by-step explanation:

A triangle has three angles that add up to 180 degrees. In a right triangle, one of the angles in 90 degress, and the other 2 add up to 90. In this case, we have 2 given angles, 90 degree angle and 42 degree angle. If we do 90+42 it gives us 132. We then subtract that from 180 to give us 48 degrees.

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3 years ago

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp

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Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305$