Find two numbers whose sum is 15 and whose product is as large as possible.

1 answer:

6 0

If one number is x the other is 15-x so their product is 15x-x².
This can be written -(x²-15x+225/4)+225/4=(15/2)²-(x-15/2)².
The largest value of this expression is when x=15/2=7.5 so the other number is also 7.5.
Let’s pick two other numbers and check their product: 7 and 8, product=56 but the product of 7.5 and 7.5=56.25 which is larger, therefore the two numbers are 7.5 and 7.5.

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In a poll, 6 out of 13 children said they read every night before bed, whereas 54% of the adults said they read every night befo

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Which expression should you simplify to find the 90% confidence interval,

Alex787 [66]

Answer:

$0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.287$

$0.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613$

And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

Step-by-step explanation:

The estimated proportion of interest is $\hat p=0.45$

We need to find a critical value for the confidence interval using the normla standard distributon. For this case we have 95% of confidence, then the significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value is: