Factor (z-5) (z+4)=52

Mathematics

1 answer:

stich3 [128]3 years ago

4 0

Answer:

$\large\boxed{(z-9)(z+8)=0\to z=9,\ z=-8}$

Step-by-step explanation:

$(z-5)(z+4)=52\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\(z)(z)+(z)(4)+(-5)(z)+(-5)(4)=52\\\\z^2+4z-5z-20=52\qquad\text{subtract 52 from both sides}\\\\z^2-z-72=0\\\\z^2-9z+8z-72=0\\\\z(z-9)+8(z-9)=0\\\\(z-9)(z+8)=0\iff z-9=0\ \vee\ z+8=0\\\\z=9\ \vee\ z=-8$

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just olya [345]

Given Information:

Mean time to finish 400 meter dash = μ = 65 seconds

Standard deviation to finish 400 meter dash = σ = 2.5 seconds

Confidence level = 95%

Required Information:

95% confidence interval = ?

Answer:

$CI = 60 \: to \: 70 \: seconds$

Step-by-step explanation:

In the normal distribution, the empirical rule states approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.

The confidence interval for 95% confidence limit is given by

$CI = \mu \pm 2\sigma$

Since approximately 95% of all the data lie within 2 standard deviations from the mean. μ is the mean time Carson takes to finish 400 meter dash and σ is the standard deviation.

$CI = 65 \pm 2(2.5)$