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serious [3.7K]
3 years ago
6

Write the equation of an exponential function that passes through the points (2,48) and (5,750).

Mathematics
1 answer:
Otrada [13]3 years ago
7 0
Ok, so the function form is y = a * bx.
Substitute in the values:
750 = a * b5
and
48 = a * b2
Then divide the two equations:
750/ 48 = (a * b5) / (a * b2)
So:
15.625 = b3
Take the cube root of both sides:
2.5 = b
Now, substitue b into one of the equations (the one with 48 has smaller numbers and is easier to work with.)
48 = a * 2.52
Simplify.
48 = a * 6.25
Divide both sides by 6.25
7.68 = a
Now substitute in a and b to write the exponential function:
y = 7.68 * 2.5x
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Which of the following ordered pairs could be the y-intercept of the function?
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Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls on the skin, is essential for stro
tigry1 [53]

Answer:

a) The 98% confidence interval would be given (0.182;0.218).

b) We are 98% confident that the true proportion of of England people who are deficient in Vitamin D is between 0.182 and 0.218.

c) If repeated samples were taken and the 98% confidence interval computed for each sample, 98% of the intervals would contain the population proportion.

d) Yes since the confidence interval not contains the value 0.25, we can refute the claim at 2% of significance.

Step-by-step explanation:

Data given and notation  

n=2700 represent the random sample taken    

X represent the people in England who are deficient in Vitamin D

\hat p=0.2 estimated proportion of England people who are deficient in Vitamin D

\alpha=0.02 represent the significance level

Confidence =0.98 or 98%

z would represent the statistic (variable of interest)    

p= population proportion of England people who are deficient in Vitamin D

Part a

The confidence interval would be given by this formula

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

For the 98% confidence interval the value of \alpha=1-0.98=0.02 and \alpha/2=0.01, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=2.33

And replacing into the confidence interval formula we got:

0.20 - 2.33 \sqrt{\frac{0.2(1-0.2)}{2700}}=0.182

0.20 + 2.33 \sqrt{\frac{0.2(1-0.2)}{2700}}=0.218

And the 98% confidence interval would be given (0.182;0.218).

Part b

We are 98% confident that the true proportion of of England people who are deficient in Vitamin D is between 0.182 and 0.218.

Part c

If repeated samples were taken and the 98% confidence interval computed for each sample, 98% of the intervals would contain the population proportion.

Part d

Yes since the confidence interval not contains the value 0.25, we can refute the claim at 2% of significance.

3 0
3 years ago
Amir says the graph of<br> y= x2 + 16 has -4 as a zero. Is Amir correct?<br> Explain.
sukhopar [10]

Answer:

  • Amir is wrong

Step-by-step explanation:

The function y = x² + 16 is positive for any value of x, hence the graph has no intersection with the x-axis and therefore has no real zero's.

If no zero's, -4 also can't be its zero.

8 0
2 years ago
Read 2 more answers
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