It is not possible for the area to change with a translation because translations are simply movements. They are not changing anything about the object's form, like something such as scaling does.

8 0

3 years ago

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Bridget, Jim and Krutika share some sweets in the ratio 4:5:1. Bridget gets 39 more sweets than Krutika. How many sweets does Ji

Yakvenalex [24]

Step-by-step explanation:

Let Bridget, Jim and Krutika's shares be 4x, 5x and x respectively.

According to the given information:

4x = x + 39

4x - x = 39

3x = 39

x = 39/3

x = 13

5x = 5*13 = 65

Hence, Jim got 65 sweets.

8 0

3 years ago

The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 ci

Olenka [21]

Answer:

The correct answer is

(0.0128, 0.0532)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

For this problem, we have that:

In a random sample of 300 circuits, 10 are defective. This means that $n = 300$ and $\pi = \frac{10}{300} = 0.033$

Calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool.

So $\alpha$ = 0.05, z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 - 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0128$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 + 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0532$

The correct answer is

(0.0128, 0.0532)

4 0

3 years ago