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3 years ago

What’s a real life example of dilation for geometry?

2 answers:

8 0

The pupil of the eye can dilate. Pupils dilate if you are in darker locations to let more light enter the eye for site. However, if the pupils are very dilated, even when a light is shined on the eye, this indicates something is wrong with the patient. Pupil dilation is measured in millimeters.

valentinak56 [21]3 years ago

3 0

Answer:

A balloon being filled with gas and expanding.

Step-by-step explanation:

The shape of the balloon does not change as it gets bigger but it's size grows.

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Write <img src="https://tex.z-dn.net/?f=%28-%20x%5E%7B2%7D%29%20-4x%2B2" id="TexFormula1" title="(- x^{2}) -4x+2" alt="(- x^{2})

marin [14]

Because the coefficient of x^2 is -1, we know that a will be -1. Knowing that the coefficient of x is -4, we can calculate that p=2. Thus, we have -1(x+2)^2+q is our equation. This is equal to -x^2-4x-4+q. As the constant term must be 2, we can then see that q is 6.

As such, we have -1(x+2)^2+6=0 as our factorization.

To solve this equation, we can use the quadratic formula. Plugging in values, we have:

$\frac{4+-2 \sqrt{6} }{-2}$
which is equal to: (when the fraction is simplified)
$-2+- \sqrt{6}$

7 0

3 years ago

Kim is 5 years older than her brother Jack. If the sum of their ages is 21, find each of their ages.

yarga [219]

9514 1404 393

Answer:

Kim is 13
Jack is 8

Step-by-step explanation:

Let k represent Kim's age. Then Jack's age is k-5 and the total of their ages is ...

k + (k -5) = 21

2k = 26 . . . . . . . add 5, collect terms

k = 13 . . . . . . . . . divide by 2; Kim's age

k -5 = 8 . . . . . . . Jack's age

Kim is 13; Jack is 8.

7 0

3 years ago

A company surveyed 2400 men where 1248 of the men identified themselves as the primary grocery shopper in their household. a) E

polet [3.4K]

Answer:

a) With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

b) The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

c) $\alpha =1-0.98=0.02$

Step-by-step explanation:

If np' and n(1-p') are higher than 5, a confidence interval for the proportion is calculated as:

$p'-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }\leq p\leq p'+z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }$

Where p' is the proportion of the sample, n is the size of the sample, p is the proportion of the population and $z_{\alpha/2}$ is the z-value that let a probability of $\alpha/2$ on the right tail.

Then, a 98% confidence interval for the percentage of all males who identify themselves as the primary grocery shopper can be calculated replacing p' by 0.52, n by 2400, $\alpha$ by 0.02 and $z_{\alpha/2}$ by 2.33

Where p' and $\alpha$ are calculated as:

$p' = \frac{1248}{2400}=0.52\\\alpha =1-0.98=0.02$

So, replacing the values we get:

$0.52-2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\leq p\leq 0.52+2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\\0.52-0.0238\leq p\leq 0.52+0.0238\\0.4962\leq p\leq 0.5438$

With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

Finally, the level of significance is the probability to reject the null hypothesis given that the null hypothesis is true. It is also the complement of the level of confidence. So, if we create a 98% confidence interval, the level of confidence $1-\alpha$ is equal to 98%