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-Dominant- [34]
3 years ago
14

(geometry) This zigzag crystal vase has a height of 12 inches. The cross sections parallel to the base are always rectangles tha

t are 5 inches wide by 4 inches long.
(a) If we assume the crystal itself has no thickness, what would be the volume of the base?
(b) The crystal is actually half an inch thick on each of the sides and on the bottom. Approximately how much space is contained within the vase?
Mathematics
1 answer:
enot [183]3 years ago
7 0

Answer:

A. 9

B. 7

Step-by-step explanation:

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andrew-mc [135]

Answer:

1) x = 8

2) ∠RPS = 36°

Step-by-step explanation:

<u>GIVEN :-</u>

  • ∠QPS = 180°
  • ∠QPR = 7x + 88
  • ∠RPS = 3x + 12

<u>TO FIND :-</u>

  1. Value of x
  2. Measure of ∠RPS

<u>FACTS TO KNOW BEFORE SOLVING :-</u>

In a straight line , if there are two angles such that their sum is equal to straight angle (or 180° in other words) , then those angles are known as linear pair.

<u>PROCEDURE :-</u>

1)

Measure of ∠QPS = 180° and it comprises of ∠QPR & ∠RPS.

⇒ ∠QPR & ∠RPS are linear pair.

⇒ ∠QPR + ∠RPS = 180°

⇒ 7x + 88 + 3x + 12 = 180°

⇒ 10x + 100 = 180

⇒ 10x = 180 - 100 = 80

⇒ x = 80/10 = 8

2)

x = 8. So,

∠RPS = 3×8 + 12 = 24 + 12 = 36°

8 0
3 years ago
A financial advisor is analyzing a family's estate plan. The amount of money that the family has invested in different real esta
Pachacha [2.7K]

Answer:

The amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.

Step-by-step explanation:

Let the random variable <em>X</em> represent the amount of money that the family has invested in different real estate properties.

The random variable <em>X</em> follows a Normal distribution with parameters <em>μ</em> = $225,000 and <em>σ</em> = $50,000.

It is provided that the family has invested in <em>n</em> = 10 different real estate properties.

Then the mean and standard deviation of amount of money that the family has invested in these 10 different real estate properties is:

\mu_{\bar x}=\mu=\$225,000\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{50000}{\sqrt{10}}=15811.39

Now the lowest 80% of the amount invested can be represented as follows:

P(\bar X

The value of <em>z</em> is 0.84.

*Use a <em>z</em>-table.

Compute the value of the mean amount invested as follows:

\bar x=\mu_{\bar x}+z\cdot \sigma_{\bar x}

   =225000+(0.84\times 15811.39)\\\\=225000+13281.5676\\\\=238281.5676\\\\\approx 238281.57

Thus, the amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.

6 0
3 years ago
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