Which word best completes the following sentence?

1. (Sec. 6.1) In a random sample of 80 components of a certain type, 12 are found to be defective. (a) Give a point estimate for

denis-greek [22]

Answer:

(a) 0.85

(b) 0.7225

Step-by-step explanation:

(a) The point estimate for the proportion of all such components that are not defective is given by the number of non-defective units in the sample divided by the sample size:

$p=\frac{80-12}{80}\\p=0.85$

The proportion is 0.85.

(b) Assuming that the sample is large enough to accurately provide a point estimate for the whole population, this can be treated as a binomial model with probability of success (non-defective part) p = 0.85. Since both components must be non-defective for the system to work, the probability of two successes in two trials is:

$P(x=2) = 0.85^2\\P(x=2) = 0.7225$

An estimate of 0.7225 for the proportion of all such systems that will function properly.

4 0

3 years ago

Convert: 38 inches = feet and inches all together

kirza4 [7]

Answer: 3 ft. and 2 inches

38÷12=3.2

12×3=36

38-36

8 0

3 years ago

Read 2 more answers

The GCD(a, b) = 9, the LCM(a, b)=378. Find the least possible value of a+b.

denis-greek [22]

$\mathrm{gcd}(a,b)=9\implies9\mid a\text{ and }9\mid b\implies9\mid a+b$

which means there is some integer $k$ for which $a+b=9k$ .

Because $9\mid a$ and $9\mid b$ , there are integers $n_1,n_2$ such that $a=9n_1$ and $b=9n_2$ , and

$\mathrm{lcm}(a,b)=\mathrm{lcm}(9n_1,9n_2)=9\mathrm{lcm}(n_1,n_2)=378\implies\mathrm{lcm}(n_1,n_2)=42$

We have $42=2\cdot3\cdot7$ , which means there are four possible choices of $n_1,n_2$ :

1, 42
2, 21
3, 14
6, 7

which is to say there are also four corresponding choices for $a,b$ :

9, 378
18, 189
27, 126
54, 63

whose sums are:

387
207
153
117

So the least possible value of $a+b$ is 117.

6 0

4 years ago

Can someone please help? Only answer the question correctly, please! Question is down below.

DIA [1.3K]

Answer:

Step-by-step explanation:

Given, 

$\frac{1}{ {6y}^{ - 2} }$

Since,

${x}^{ab} = {( {x}^{a} )}^{b}$

Hence,

$= \frac{1}{ {( {6y}^{2} )}^{ - 1} }$

Since,

$\frac{1}{ {x}^{ - 1} } = x$

Hence,

$= {6y}^{2} (ans)$

7 0

3 years ago

I just need help with this problem

sashaice [31]

Keeping in mind that the area of a circle is πr².

the actual area will just be the area of the rectangular backyard plus the pool, namely (10*20) + (π15²), which gives us an actual area of 200 + 225π.

now, we know the model and actual are on a 1:20 ratio.

$\bf \cfrac{model}{actual}\qquad 1:20\qquad \cfrac{1}{20}\qquad \qquad \cfrac{m}{200+225\pi }=\cfrac{1}{20}
\\\\\\
m=\cfrac{(200+225\pi )1}{20}\implies m=\cfrac{200+225\pi }{20}\implies m=\cfrac{200}{20}+\cfrac{225\pi }{2}
\\\\\\
m=10+112.5\pi$

5 0

4 years ago