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2 years ago

23:

Mathematics

2 answers:

irina [24]2 years ago

8 0

Answer:

$(-\frac{3}{7}, 0)$ -- x intercept

$(0,3)$ -- y intercept

Step-by-step explanation:

Given

$y = 7x + 3$

Required

Determine the x and y intercept

For x intercept.

Set $y = 0$

So, we have:

$y = 7x + 3$

$0 = 7x + 3$

Collect Like Terms

$7x = -3$

Make x the subject

$x = -\frac{3}{7}$

Hence, the x intercept is: $(-\frac{3}{7}, 0)$

For the y intercept;

Set $x = 0$

So, we have:

$y = 7x + 3$

$y = 7*0 + 3$

$y = 0 + 3$

$y = 3$

Hence, the y intercept is: $(0,3)$

RUDIKE [14]2 years ago

6 0

AnswerB

Step-by-step explanation:

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In a survey of 603 adults, 98 said that they regularly lie to people conducting surveys. Create a 99% confidence interval for th

marysya [2.9K]

Answer:

The population proportion is estimated to be with 99% confidence within the interval (0.1238, 0.2012).

Step-by-step explanation:

The formula for estimating the population proportion by a confidence interval is given by:

$\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}$

Where:

$\hat{p}$ is the sample's proportion of success, which in this case is the people that regularly lie during surveys,

$z_{\alpha /2}$ is the critical value needed to find the tails of distribution related to the confidence level,

$n$ is the sample's size.

<u>First</u> we compute the $\hat{p}$ value:

$\hat{p}=\frac{successes}{n}=\frac{98}{603}=0.1625$

<u>Next</u> we find the z-score at any z-distribution table or app (in this case i've used StatKey):

$z_{\alpha /2}=2.576$

Now we can replace in the formula with the obtained values to compute the confidence interval:

$\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}=0.1625\pm 2.576\times\sqrt{\frac{0.1625\times(1-0.1625)}{603}}=(0.1238, 0.2012)$