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jasenka [17]
2 years ago
8

If the hypotenuse of a right triangle is 2

lt="\sqrt{3}" align="absmiddle" class="latex-formula"> units long and one of the legs is \sqrt{3} units long, then how long is the other leg?
\sqrt{3}

2\sqrt{3}

3
Mathematics
1 answer:
Svetradugi [14.3K]2 years ago
5 0

Answer:

3

Step-by-step explanation:

a = the other leg:

a^{2} =(2\sqrt{3} )^{2} -(\sqrt{3}) ^{2} =(4)(3)-3=12-3

a^{2} =9

a=\sqrt{9}

a=3

Hope this helps

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Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. The mean length of
julia-pushkina [17]

Answer:

Due to the higher z-score, Stewart caught the longer fish, relative to fish of the same species

Step-by-step explanation:

Problems of normally distributed samples are 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}

The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Who caught the longer fish, relative to fish of the same species?

Whosoever fish's had the higher z-score.

Stewart caught a bluefish that was 283mm

The mean length of a bluefish is 264 millimeters with a standard deviation of 57mm.

So we have to find Z when X = 283, \mu = 264, \sigma = 57

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

Z = \frac{283 - 264}{57}

Z = 0.33

Gina caught a pompano that was 152mm long.

For pompano, the mean is 157mm with a standard deviation of 28mm.

So we have to find Z when X = 152, \mu = 157, \sigma = 28

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

Z = \frac{152 - 157}{28}

Z = -0.18

Due to the higher z-score, Stewart caught the longer fish, relative to fish of the same species

8 0
4 years ago
4 (k - 6) = 6 (-4 - 5k)<br> a) 10<br> b) 0<br> c) -2<br> d) 8
user100 [1]

Step-by-step explanation:

step 1. what is the question? solve for k? okay.

step 2. 4(k - 6) = 6(-4 - 5k)

step 3. 4k - 24 = -24 - 30k

step 4. 34k = 0

step 5. k = 0.

3 0
3 years ago
Rationalise the denominator <br>​
Margaret [11]

Step-by-step explanation:

1. \frac{2 \sqrt{3} }{ \sqrt{5} }

multiply

\sqrt{5}

do both the numerator and denominater

\frac{2 \sqrt{3} }{ \sqrt{5} }   \times  \frac{ \sqrt{5} }{ \sqrt{5} }  =  \frac{2 \sqrt{15} }{ \sqrt{25} }  =  \frac{2 \sqrt{15} }{5}

8 0
3 years ago
In a right triangle, the acute angles measure ×+15 and 2× degrees. What is the measure of the larger acute angle of the triangle
harkovskaia [24]

Sum of angles in a triangle is 180°


90 + (x + 15) + (2x) = 180

90 + x + 15 + 2x = 180

105 + 3x = 180

3x = 180 - 105

3x = 75

x = 75 ÷ 3

x = 25


Smaller angle = x + 15 = 25 + 15 = 40°

Larger angle = 2x = 2(25) = 50°


Answer: 50°


5 0
3 years ago
the ratio of dogs to cat at a shelter is 42 to 26. The total number of dogs and cats at your local shelter is 272. How many dogs
frozen [14]

There are 168 dogs and 104 cats

6 0
3 years ago
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