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2 years ago

Choose the answer to complete each statement

Mathematics

1 answer:

NeTakaya2 years ago

7 0

Answer:

1. The slope of the line is 7/3

2. y intercept is -3

3. y= 7/3x -3

Step-by-step explanation:

To find the slope of the line you use the equation y2-y1/x2-x1

y2 and y1 are y coordinates of the 2 coordinates on the same line that you want to find the slope of and the same with x2 and x1

The y-intercept is the point where the line crosses the y axis and x= 0

the equation of a line is y= mx+b

m= slope

b= y intercept

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Answer:

Leon is correct. (Option 1)

Step-by-step explanation:

Given that Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.

Step 1: Find the greatest common factor of the given lengths: 7

Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5

Step 3: Verify that the lengths found in step 2 form a Pythagorean triple.

we have to explain whether or not Leon is correct.

As, 3,4,5 forms a Pythagorean triplet i.e satisfies the Pythagoras theorem

$Hypotenuse^2=Base^2+Perpendicular^2$

⇒ $5^2=3^2+4^2$

Let a, b, c forms a Pythagorean triplet

$a^2+b^2=c^2$

Multiplied by 4 on both sides

⇒ $4a^2+4b^2=4c^2$

⇒ ${2a}^2+{2b}^2={2c}^2$

Hence, we say 4a, 4b and 4c also forms a Pythagorean triplet.

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Answer:

a) $p$ represent the real population proportion of people who showed partial or complete resistance to the antibiotic

b) $\hat p=\frac{973}{1714}=0.568$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

c) We are confident (95%) that the true proportion of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic is between 54.5% to 59.1%.

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part a

Description in words of the parameter p

$p$ represent the real population proportion of people who showed partial or complete resistance to the antibiotic

$\hat p$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

n=1714 is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part b

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the number of people with a characteristic and n the total sample size selected.

$\hat p=\frac{973}{1714}=0.568$ represent the estimated proportion of people who showed partial or complete resistance to the antibiotic

Part c

The confidence interval for a proportion is given by this formula

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.568 - 1.96 \sqrt{\frac{0.568(1-0.568)}{1714}}=0.545$

$0.568 + 1.96 \sqrt{\frac{0.56(1-0.56)}{1714}}=0.591$

And the 95% confidence interval would be given (0.545;0.591).

We are confident that about 54.5% to 59.1% of individuals in Florida diagnosed with a strep infection was tested for resistance to the antibiotic penicillin present partial or complete resistance to the antibiotic.

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