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QveST [7]
3 years ago
5

The sides of a parallelogram are 24cm and 16cm. The distance between the 24cm sides is 8 cm. Find the distance between the 16cm

sides
Mathematics
1 answer:
Stolb23 [73]3 years ago
7 0

Answer:

12 cm.

Step-by-step explanation:

The distance between the opposite sides is a perpendicular line so we can form a right angled triangle by drawing a perpendicular line from one corner of the parallelogram  to the opposite 24 cm side.

So  one angle of the parallelogram will have a sine of 8/16 = 1/2 so this angle =  30 degrees.

In a similar way to the above we form a right angled triangle  from the same corner by drawing a perpendicular line to the opposite 16 cm side.

This has an angle of 30 degrees (  opposite angles in a parallelogram are congruent).

So sine 30 = x / 24

1/2 = x /24

x = 12 feet.

Another way to do this is by noting that the 2 triangles are similar (because  2 corresponding angles are equal).

So  8/ 16 = x/24

16x = 192

x = 12 feet.

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The average daily jail population in the United States is 706,242. If the distribution is normal and the standard deviation is 5
Karolina [17]

a. The probability that on a randomly selected day, the jail population

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b. The probability that on a randomly selected day, the jail population is

between 600,000 and 700,000 is 43.2%

Step-by-step explanation:

The given is:

1. The average daily jail population in the United States is 706,242

2. The distribution is normal and the standard deviation is 52,145

3. We need to find the probability that on a randomly selected day,

    the jail population is greater than 750,000

4. We need to find the probability that on a randomly selected day,

    the jail population is between 600,000 and 700,000

a.

At first find z-score

∵ z = (x - μ)/σ, where x is the score, μ is the mean and σ is the standard

   deviation

∵  x = 750,000 , μ = 706,242 and σ = 52,145

∴ z = \frac{750,000-706,242}{52,145} ≅ 0.84

Use the normal distribution table of z to find the area to the right of

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∵ The corresponding area to z-score of 0.84 is 0.79955

- But we are interested in x > 750,000, we need the area to the

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∴ P(x > 750,000) = 1 - 0.79955 = 0.2005

∴ P(x > 750,000) = 0.2005 × 100% = 20.1%

The probability that on a randomly selected day, the jail population is

greater than 750,000 is 20.1%

b.

We will find z-score for 600,000 < x < 700,000

∵ z = \frac{600,000-706,242}{52,145} ≅ -2.04

∵ z = \frac{700,000-706,242}{52,145} ≅ -0.12

Use the normal distribution table of z to find the area between

the two z-values

∵ The corresponding area to z-score of -2.04 is 0.02068

∵ The corresponding area to z-score of -0.12 is 0.45224

- To find P(600,000 < x < 700,000) subtract the two values above

∴ P(600,000 < x < 700,000) = 0.45224 - 0.02068 = 0.4316

∴ P(600,000 < x < 700,000) = 0.4316 × 100% = 43.2%

The probability that on a randomly selected day, the jail population is

between 600,000 and 700,000 is 43.2%

Learn more:

You can learn more about z-score in brainly.com/question/7207785

#LearnwithBrainly

5 0
3 years ago
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kotykmax [81]

Answer:

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2w(w+17)

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