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1 year ago

Combine these radicals. √27- √3

Mathematics

2 answers:

Alex73 [517]1 year ago

8 0

Square root 27 is 3squer root 3 so the answer is 2 square root three

mixas84 [53]1 year ago

5 0

$\sqrt{9 \times 3} - \sqrt{3} \\ 3 \sqrt{3} - \sqrt{3} \\ 2 \sqrt{3}$
combined

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The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in n

devlian [24]

Answer:

The length of the longest 15% of Atlantic cod in this area is 53.79cm, roundeed to 2 decimal places.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X.

In this problem, we have that:

A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm, so $\mu = 49.9, \sigma = 3.74$ .

What is the length in cm of the longest 15% of Atlantic cod in this area?

We have to find the value of X for the value of Z that has a pvalue of 0.85.

Looking at the zscore table, we have that Z = 1.04 has a pvalue of 0.8508. So, we have to find the value of X when $Z = 1.04, \mu = 49.9, \sigma = 3.74$ .

$Z = \frac{X - \mu}{\sigma}$

$1.04 = \frac{X - 49.9}{3.74}$

$X - 49.9 = 3.8896$

$X = 53.7896$

The length of the longest 15% of Atlantic cod in this area is 53.79cm, roundeed to 2 decimal places.

8 0

1 year ago

If a person invests $220 at 7% annual interest, find the approximate value of the investment at the end of 10 years.

frez [133]

$\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$220\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &10 \end{cases} \\\\\\ A=220[1+(0.07)(10)]\implies A=220(1.7)\implies A=374$

5 0

1 year ago

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To control pollination, pollen-producing flowers are often removed from the top of corn in a process called detasseling. The hou

____ [38]

Answer: <u>Last option</u>

$Z_ {13} = 0.5,\ Z_ {17} = 2.5$

Step-by-step explanation:

The z-scores give us information about how many standard deviations from the mean the data are. This difference can be negative, if the data are n deviations to the left of the mean, or it can be positive if the data are n deviations to the right of the mean.

To calculate the Z scores, we calculate the difference between the value of the data and the mean and then divide this difference by the standard deviation.

$Z = \frac{x- \mu}{\sigma}$ .

Where x is the value of the data, μ is the mean and σ is the standard deviation

In this case :

μ = 12 $/h

$\sigma$ = 2 $/h

We need to calculate the Z-scores for $x = 17$ and $x = 13$

Then for $x = 17$ :

$Z_{17} = \frac{17-12}{2}$ .

$Z_{17} = 2.5$

Then for $x = 13$ :

$Z_{13} = \frac{13-12}{2}$ .

$Z_{13} = 0.5$

Therefore the answer is:

$Z_ {13} = 0.5,\ Z_ {17} = 2.5$

8 0

1 year ago

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You plan to accumulate 100,000 at the end of 42 years by making the follow-

Mariana [72]

Answer:

Y = 479.17

Step-by-step explanation:

At the end of year 14, the balance from the deposits of X can be found using the annuity due formula:

A = P(1+r/n)((1 +r/n)^(nt) -1)/(r/n)

where P is the periodic payment, n is the number of payments and compoundings per year, t is the number of years, and r is the annual interest rate.

A = X(1.07)(1.07^14 -1)/0.07 ≈ 24.129022X

This accumulated amount continues to earn interest for the next 28 years, so will further be multiplied by 1.07^28. Then the final balance due to deposits of X will be ...

Ax = (24.129022X)(1.07^28) = 160.429967X

The same annuity due formula can be used for the deposits of Y for the last 10 years of the interval:

Ay = Y(1.07)(1.07^10 -1)/.07 = 14.783599Y

Now we can write the two equations in the two unknowns:

Ax +Ay = 100,000

X - Y = 100

From the latter, we have ...

X = Y +100

So the first equation becomes ...

160.429967(Y +100) +14.783599Y = 100000

175.213566Y +16,043.00 = 100,000

Y = (100,000 -16,043)/175.213566 ≈ 479.17

Y is 479.17

7 0

1 year ago

If you can buy 1/3 of a box of chocolates for 6 dollars, how much can you buy for 4 dollars?

lys-0071 [83]

Answer:

Given that 1/3 of a box is 6 dollars, we can say that per dollar is 1/18 of a box. If you have 4 dollars, this would mean that you can buy 4/18 of a box to 2/9 of a box. Hope this answers your question. Have a great day ahead!

Step-by-step explanation:

6 0

1 year ago

Read 2 more answers