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3 years ago

What are the roots of the polynomial equation x^2+8x-48=0

Mathematics

1 answer:

____ [38]3 years ago

4 0

Given polynomial x^2+8x-48 = 0

x^2+12x-4x-48 = 0

x(x+12)-4(x+12) = 0

(x+12)(x-4) = 0

x+12 = 0

Subtract 12 from each side.

x+12-12 = 0-12

x = -12

and x-4 = 0

Add 4 to each side.

x-4+4 = 0+4

x = 4

Roots are -12,4.

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2 years ago

One measure of an athlete’s ability is the height of his or her vertical leap. Many professional basketball players are known fo

almond37 [142]

Answer:

(1) P( $\bar X$ < 26 inches) = 0.0436

(2) P(27.5 inches < $\bar X$ < 28.5 inches) = 0.2812

Step-by-step explanation:

We are given that the mean vertical leap of all NBA players is 28 inches. Suppose the standard deviation is 7 inches and 36 NBA players are selected at random.

Firstly, Let $\bar X$ = mean vertical leap for the 36 players

Assuming the data follows normal distribution; so the z score probability distribution for sample mean is given by;

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

where, $\mu$ = population mean vertical leap = 28 inches

$\sigma$ = standard deviation = 7 inches

n = sample of NBA player = 36

(1) Probability that the mean vertical leap for the 36 players will be less than 26 inches is given by = P( $\bar X$ < 26 inches)

P( $\bar X$ < 26) = P( $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{26-28}{\frac{7}{\sqrt{36} } }$ ) = P(Z < -1.71) = 1 - P(Z $\leq$ 1.71)

= 1 - 0.95637 = 0.0436

(2) Now, here sample of NBA players is 26 so n = 26.

Probability that the mean vertical leap for the 26 players will be between 27.5 and 28.5 inches is given by = P(27.5 inches < $\bar X$ < 28.5 inches) = P( $\bar X$ < 28.5 inches) - P( $\bar X$ $\leq$ 27.5 inches)

P( $\bar X$ < 28.5) = P( $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{28.5-28}{\frac{7}{\sqrt{26} } }$ ) = P(Z < 0.36) = 0.64058 {using z table}

P( $\bar X$ $\leq$ 27.5) = P( $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{27.5-28}{\frac{7}{\sqrt{26} } }$ ) = P(Z $\leq$ -0.36) = 1 - P(Z < 0.36)

= 1 - 0.64058 = 0.35942

Therefore, P(27.5 inches < $\bar X$ < 28.5 inches) = 0.64058 - 0.35942 = 0.2812

6 0

3 years ago

Find the missing coordinates y+7x=1 (-1, ) (4, )

Pachacha [2.7K]

Answer:

(-1,8)

(4,-27)

Step-by-step explanation:

y+7x=1

Let x = -1 and find y

y+7(-1)=1

y -7 =1

Add 7 to each side

y-7+7 = 1+7

y = 8

(-1,8)

Let x = 4 and find y

y+7(4)=1

y +28 =1

Subtract 28 from each side

y+28-28 = 1-28

y = -27

(4,-27)

6 0

2 years ago