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3 years ago

Find the slope and the y-intercept of the line with equation 9x + 10y = 91.

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

6 0

y=mx+b

M is also slope. b= y-intercept

9x + 10y = 91

move 9x to the other side

sign changes from +9x to- 9x

9x-9x+10y=-9x+91

10y=-9x+91

Divide both sides by 10 to get y by itself

10y/10=-9/10x+91/10

y=-9/10x+91/10

y-intercept (x=0)

9x + 10y = 91

9(0)+10y=91

0+10y=91

10y=91

Divide both sides by 10

10y/10=91/10

y=91/10

Answer:

slope (m)=-9/10

y-intercept :(0, 91/10)

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<h2>Answer:</h2>

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Area of the shaded sector of the circle = 31.2 cm²

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Read 2 more answers

A selective university advertises that 96% of its bachelor’s degree graduates have, on graduation day, a professional job offer

OLEGan [10]

Answer:

The probability is $P( p < 0.9207) = 0.0012556$

Step-by-step explanation:

From the question we are told

The population proportion is $p = 0.96$

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The number of graduate who had job is k = 209

Generally given that the sample size is large enough (i.e n > 30) then the mean of this sampling distribution is

$\mu_x = p = 0.96$

Generally the standard deviation of this sampling distribution is

$\sigma = \sqrt{\frac{p (1 - p )}{n} }$

=> $\sigma = \sqrt{\frac{0.96 (1 - 0.96 )}{227} }$

=> $\sigma = 0.0130$

Generally the sample proportion is mathematically represented as

$\^ p = \frac{k}{n}$

=> $\^ p = \frac{209}{227}$

=> $\^ p = 0.9207$

Generally probability of obtaining a sample proportion as low as or lower than this, if the university’s claim is true, is mathematically represented as

$P( p < 0.9207) = P( \frac{\^ p - p }{\sigma } < \frac{0.9207 - 0.96}{0.0130 } )$

$\frac{\^ p - p}{\sigma } = Z (The \ standardized \ value\ of \ \^ p )$

$P( p < 0.9207) = P(Z< -3.022 )$

From the z table the area under the normal curve to the left corresponding to -3.022 is

$P(Z< -3.022 ) = 0.0012556$

=> $P( p < 0.9207) = 0.0012556$

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