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Orlov [11]
2 years ago
9

The figure below is from a quilting pattern. The indicated angles are Supplementary. What is the news he or N and the two angles

; 8n-16 and 6n.

Mathematics
1 answer:
VashaNatasha [74]2 years ago
3 0

Answer:

  • <u>The value of N is 8</u>

<u></u>

  • <u>The value of the angles is 48º</u>

Explanation:

The two indicated angles are supplementary because they could be drawn as two interior angles on the same side of two parallel sides cut by a transversal.

Thus, those measure of those two angles add up 180º, which lets you to write an equation and solve for N:

  • 8N - 16 = 6N
  • 8N - 6N = 16
  • 2N = 16
  • N = 16 / 2
  • N = 8

And the value of the angles is:

  • 8N - 16 = 8(8) - 16 = 48, or
  • 6N = 6(8) = 48
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2 years ago
A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measurin
Ratling [72]

Answer:

The standard deviation of weight for this species of cockroaches is 4.62.

Step-by-step explanation:

Given : A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams.

To find : What is the approximate standard deviation of weight for this species of cockroaches?

Solution :

We have given,

Mean \mu=50

The sample mean x=55

A lab assistant reports that 14% of the cockroaches weigh more than 55 grams.

i.e. P(X>55)=14%=0.14

The total probability needs to sum up to 1,

P(X\leq 55)=1-P(X>55)

P(X\leq 55)=1-0.14

P(X\leq 55)=0.86

The z-score value of 0.86 using z-score table is z=1.08.

Applying z-score formula,

z=\frac{x-\mu}{\sigma}

Where, \sigma is standard deviation

Substitute the values,

z=\frac{x-\mu}{\sigma}

1.08=\frac{55-50}{\sigma}

1.08=\frac{5}{\sigma}

\sigma=\frac{5}{1.08}

\sigma=4.62

The standard deviation of weight for this species of cockroaches is 4.62.

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