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3 years ago

Their sum is −7 and their difference is 14 what are my numbers

Mathematics

1 answer:

Mashcka [7]3 years ago

8 0

Answer:

Answer: 3 1/2 and -10 1/2 are the two numbers.

Step-by-step explanation:

Let x and y be the two unknown numbers.

x+y=-7 [Given]

x-y=14 [Given]

x=y+14 [Add y to both sides]

x+y=-7 [Given]

(y+14)+y=-7 [Subtitution]

2y+14=-7 [Combine like terms]

2y=-21 [Subtract 14 from both sides]

y=-21/2 [Divide both sides by 2]

y=-10 1/2 [Division]

x-y=14 [Given]

x=y+14 [Add y to both sides]

x=-10 1/2 + 14 [Substitution]

x= 3 1/2 [Addition]

Check:

x+y=-7 [Given]

3 1/2 + -10 1/2?=-7 [Substition]

-7=-7 [Addition]

QED

x-y=14 [Given]

3 1/2 - -10 1/2?=14 [Substitution]

3 1/2 + 10 1/2?=14 [Change the sign of the subtrahend and add]

14=14 [Addition]

QED

Answer: 3 1/2 and -10 1/2 are the two numbers.

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2 years ago

Of 585 samples of seafood purchased from various kinds of food stores in different regions of a country and genetically compared

Dafna1 [17]

Answer:

a) The 99% confidence interval is from 14.8% to 23.2%.

b) The confidence interval tells us that the true proportion of mislabeled is within 14.8% and 23.2%, with a 99% confidence. In other words, if we take samples of the same size, 99% of the samples will have a proportion within 0.148 and 0.232.

c) The confidence interval calculation take into account the sample size, so the width (or precision) of the interval depends on the sample size.

The only criticism that could be analyzed is to see if the sample is representative of the population.

Step-by-step explanation:

a) We have to calculate a 99% confidence interval for the proportion.

The sample proportion is p=0.19.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.19*0.81}{585}}\\\\\\ \sigma_p=\sqrt{0.000263}=0.016$

The critical z-value for a 99% confidence interval is z=2.576.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=2.576 \cdot 0.02=0.042$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.19-0.042=0.148\\\\UL=p+z \cdot \sigma_p = 0.19+0.042=0.232$

The 99% confidence interval for the population proportion is (0.148, 0.232).

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2 years ago