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3 years ago

A(n) ______ line is a line that relates points on the line with numbers.

Mathematics

1 answer:

choli [55]3 years ago

4 0

Answer:

A number line is a line that relates points on line with numbers :)

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4 years ago

Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±11)

Katen [24]

Answer:

$\frac{y^{2} }{81} -\frac{x^{2} }{40} }=1$ is standard equation of hyperbola with vertices at (0, ±9) and foci at (0, ±11).

Step-by-step explanation:

We have given the vertices at (0, ±9) and foci at (0, ±11).

Let (0,±a) = (0,±9) and (0,±c) = (0,±11)

The standard equation of parabola is:

$\frac{y^{2} }{a^{2} } -\frac{x^{2} }{b^{2} }=1$

From statement, a = 9

c² = a²+b²

(11)² = (9)²+b²

121-81 = b²

40 = b²

Putting the value of a² and b² in standard equation of parabola, we have

$\frac{y^{2} }{81} -\frac{x^{2} }{40} }=1$ which is the answer.

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4 years ago

A city hosted a music festival that included three concerts. According to the sales database, 28% of the audience attended the f

Vitek1552 [10]

Answer:

$P(X\cap Y\cap Z)=0.05$

Step-by-step explanation:

From the question we are told that:

Percentage of audience in first concert $P(X)=0.28$

Percentage of audience in second concert $P(Y)=0.42$

Percentage of audience in third concert $P(Z)=0.30$

Audience Percentage at at-least one concert $P(X \cup Y \cup Z)=0.80$

Percentage of audience at first & second concert $P(X \cap Y)=0.10$

Percentage of audience in first & third concert $P(X \cap Z)=0.08$

Percentage of audience in second & third concert $P(Y\cap Z)=0.07$

Generally the equation for probability of attending all concerts $P(X\cap Y\cap Z)$ is mathematically given by

$P(X \cup Y \cup Z)=P(X)+P(Y)+P(Z)-P(X \cap Y)-P(X \cap Z)-P(Y\cap Z)+P(X\cap Y\cap Z)$

$P(X\cap Y\cap Z)=P(X \cup Y \cup Z)-P(X)-P(Y)-P(Z)+P(X \cap Y)+P(X \cap Z)+P(Y\cap Z)$

$P(X\cap Y\cap Z)=0.80-0.28-0.42-0.30+0.10+0.80+0.70$

$P(X\cap Y\cap Z)=0.05$

Therefore the probability that a randomly selected audient attended all the concerts

$P(X\cap Y\cap Z)=0.05$

8 0

3 years ago