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3 years ago

Which Pythagorean identity is correct?

Mathematics

2 answers:

Alla [95]3 years ago

5 0

Answer:

Option 2:

tangent squared (theta) + 1 = secant squared (theta)

Step-by-step explanation:

1 + tan²X

1 + sin²X/cos²X

(cos²X + sin²X)/cos²X

1/cos²X

sec²X

navik [9.2K]3 years ago

5 0

Answer:

tangent squared (theta) + 1 = secant squared (theta)

e2020

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An airplane has 100 seats for passengers. Assume that the probability that a person holding a ticket appears for the flight is 0

zmey [24]

Answer:

96.33% probability that everyone who appears for the flight will get a seat

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 105, p = 0.9$

$\mu = E(X) = np = 105*0.9 = 94.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{105*0.9*0.1} = 3.07$

What is the probability that everyone who appears for the flight will get a seat

100 or less people appearing to the flight, which is the pvalue of Z when X = 100. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{100 - 94.5}{3.07}$

$Z = 1.79$

$Z = 1.79$ has a pvalue of 0.9633

96.33% probability that everyone who appears for the flight will get a seat

7 0

2 years ago

At the North campus of a performing arts school 30% of students are music majors at the South campus 80% of the students are mus

OLEGan [10]

Answer:

It should be option B

Step-by-step explanation:

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3 years ago

Complete the Square and express the quadratic as a square.

Shtirlitz [24]

Answer:

Step-by-step explanation:

x² - 6x + 13 = 0

x² - 2(x)(3) + 3² - 3² + 13 = 0

(x - 3)² = -4

6 0

3 years ago

Is 31/50 greater than 1/2

KengaRu [80]

Yes 31/50 is greater than 1/2

5 0

3 years ago

Read 2 more answers

What are the postulates for congruent triangles

Delvig [45]

Hi there!

There are 5 ways to find if two triangles are congruent :

SSS, SAS, ASA, AAS & HL

1. SSS (Side, Side, Side)

Means that we have two triangles with 3 sides equal.

⇒ If 3 sides of one triangle are equal to 3 sides of another triangle, the triangles are congruent.

2. SAS (Side, Angle, Side)

Means that we have two triangles where we know 2 sides and the included angle are equal.

⇒ If 2 sides and the includent angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

3. ASA (Angle, Side, Angle)

Means that we have two triangles where we know 2 angles and the included side are equal.

⇒ If 2 angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

4. AAS (Angle, Angle, Side)

Means thant we have two triangles where we know 2 angles and the non-included side are equal.

⇒ If 2 angles and the non-included side of one triangle are equal to the coresponding angles and side of another triangle, the triangles are congruent.

5. HL (Hypotenuse, leg)

** This one only applies to right-angled triangles.**

Hypotenuse: The longest side of a right-angled triangle.

Legs: The other 2 sides of the right-angled triangle.

Means we have two right-angled triangles with the same length of hypotenuse and the same length for one of the other 2 legs (it doesn't matter which leg since the triangles could be rotated).

⇒ If the hypotenuse and one leg of one right-angled triangles are equal to the corresponding hypotenuse and leg of another right-angled triangles, the two triangles are congruent.

There you go! I really hope this helped, if there's anything just let me know! :)

7 0

3 years ago