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jasenka [17]
3 years ago
13

Simplify square root of negative 48.

Mathematics
1 answer:
kvv77 [185]3 years ago
3 0
We want to simplify √(-48).

Note that
i² = -1 by definition.
Therefore
\sqrt{-48} =  \sqrt{i^{2}.16.3} = \sqrt{i^{2}}  \sqrt{16}  \sqrt{3} =4i \sqrt{3}

Answer: c.  4i \sqrt{3}

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Please answer both questions and show all your work. Thank you!!! :)
nignag [31]

(1) let "r" denote number of rabbits, "c"  number of chickens

Set up the equations:

r + c = 1000\\4r + 2c = 3150\\\\-2r -2c = -2000\\4r + 2c = 3150\\\\2r = 1150\implies r = 575\implies c = 425

Answer: There are 575 rabbits and 425 chickens

(2) m - number of Mike's stamps, a - number of Andrew's stamps.

Set up equations:

m = 4a\\m-8 = 2(a+8)\\\\4a-8=2a + 16\\2a = 24\implies a = 12\implies m = 48\\

Answer:  Mike has 48 stamps. Andrew has 12 stamps.

4 0
3 years ago
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I need help with the circled table
Dima020 [189]

Step-by-step explanation:

you multiply the number of lemonades by 1.80 because you're just basically adding 1.80 from each lemonade you sell

5 0
3 years ago
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g A researcher wants to construct a 95% confidence interval for the proportion of children aged 8-10 living in Atlanta who own a
Helga [31]

Answer:

The sample size needed is 2401.

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 level of 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}.

The margin of error of the interval is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

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.

Estimate the sample size needed if no estimate of p is available so that the confidence interval will have a margin of error of 0.02.

We have to find n, for which M = 0.02.

There is no estimate of p available, so we use \pi = 0.5

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.02\sqrt{n} = 1.96*0.5

\sqrt{n} = \frac{1.96*0.5}{0.02}

(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.02})^{2}

n = 2401

The sample size needed is 2401.

7 0
3 years ago
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The intersection of 2 planes can be defined as a_____?
tamaranim1 [39]

The intersection of two planes is a line.   That's not necessarily the definition of a line, but that's probably what they're looking for.


Answer: line


5 0
2 years ago
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9 x 10 *9 or 3 x 10 *-4
Mademuasel [1]
The first one is 810

The second is -120
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3 years ago
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