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3 years ago

Brainliest plus 10 points! simplify 6y^2-6/8y^2+8y÷3y-3/4y^2+4

Mathematics

1 answer:

lesya692 [45]3 years ago

6 0

Answer:

(y² +1)/y

Step-by-step explanation:

Invert the denominator fraction and multiply. Factor the difference of squares.

$\displaystyle\frac{\left(\frac{6y^2-6}{8y^2+8y}\right)}{\left(\frac{3y-3}{4y^2+4}\right)}=\frac{6(y^2-1)}{8y(y+1)}\cdot\frac{4(y^2+1)}{3(y-1)}\\\\=\frac{24(y+1)(y-1)(y^2+1)}{24y(y+1)(y-1)}=\frac{y^2+1}{y}$

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Step-by-step explanation:

We are given that the longest one-way travel time is in New York City, where the mean time is 38.5 minutes.

Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.2 minutes.

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The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

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P(X < 26 minutes) = P( $\frac{X-\mu}{\sigma}$ < $\frac{26-38.5}{7.2}$ ) = P(Z < -1.74) = 1 - P(Z $\leq$ 1.74)

= 1 - 0.9591 = 0.0409 = 4.09%

The above probability is calculated by looking at the value of x = 1.74 in the z table which has an area of 0.9591.

(2) The percent of the New York City commutes that are between 26 and 32 minutes is given by = P(26 min < X < 32 min) = P(X < 32 min) - P(X $\leq$ 26 min)

P(X < 32 min) = P( $\frac{X-\mu}{\sigma}$ < $\frac{32-38.5}{7.2}$ ) = P(Z < -0.90) = 1 - P(Z $\leq$ 0.90)

= 1 - 0.8159 = 0.1841

P(X $\leq$ 26 min) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{26-38.5}{7.2}$ ) = P(Z $\leq$ -1.74) = 1 - P(Z < 1.74)

= 1 - 0.9591 = 0.0409

The above probability is calculated by looking at the value of x = 0.90 and x = 1.74 in the z table which has an area of 0.8159 and 0.881 respectively.

Therefore, P(26 min < X < 32 min) = 0.1841 - 0.0409 = 0.1432 or 14.32%.

(3) The percent of the New York City commutes that are between 26 and 40 minutes is given by = P(26 min < X < 40 min) = P(X < 40 min) - P(X $\leq$ 26 min)

P(X < 40 min) = P( $\frac{X-\mu}{\sigma}$ < $\frac{40-38.5}{7.2}$ ) = P(Z < 0.21) = 0.5832

P(X $\leq$ 26 min) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{26-38.5}{7.2}$ ) = P(Z $\leq$ -1.74) = 1 - P(Z < 1.74)

= 1 - 0.9591 = 0.0409

The above probability is calculated by looking at the value of x = 0.21 and x = 1.74 in the z table which has an area of 0.5832 and 0.881 respectively.

Therefore, P(26 min < X < 40 min) = 0.5832 - 0.0409 = 0.5423 or 54.23%

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