The graph of a system of equations with the same slope will have no solutions.

Kiran earns $8.50 per hour.

Let x represent Kiran's pay. He worked 23 hours last week, so his pay would be given by 23x.

Kiran's cousin is paid 30% more. 30% = 30/100 = 0.3. We add this to the x per hour that Kiran is paid:

x + 0.3x = 1.3x

This is multiplied by 27, since Kiran's cousin works 27 hours:
27(1.3x)

This gives us the following equation:
23x + 27(1.3x) = 493.85
23x + 35.1x = 493.85
58.1x = 493.85

Divide both sides by 58.1:
58.1x/58.1 = 493.85/58.1
x = 8.5

Thus Kiran earns 8.50 per hour.

8 0

2 years ago

Of 560 samples of seafood purchased from various kinds of food stores in different regions of a country and genetically compared

frutty [35]

Answer:

a) (0.5256,0.5944)

c) Criticism is invalid

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 560

Proportion of mislabeled = 56%

$\hat{p} = 0.56$

a) 90% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.64$

Putting the values, we get:

$0.56\pm 1.64(\sqrt{\dfrac{0.56(1-0.56)}{560}}) = 0.56\pm 0.0344\\\\=(0.5256,0.5944)$

b) Interpretation of confidence interval:

We are 90% confident that the true proportion of all seafood in the country that is mislabeled or misidentified is between 0.5256 and 0.5944 that is 52.56% and 59.44%.

c) Validity of criticism

Conditions for validity:

$np > 10\\n(1-p)>10$