A given shape that is <u>bounded</u> by three sides and has got three <em>internal angles</em> is referred to as a <u>triangle</u>. Thus the <em>value</em> of PB is <u>8.0</u> units.
A given <u>shape</u> that is <em>bounded</em> by three <em>sides</em> and has got three <em>internal angles</em> is referred to as a <em>triangle</em>. Types of <u>triangles</u> include right angle triangle, isosceles triangle, equilateral triangle, acute angle triangle, etc. The<em> sum</em> of the <u>internal</u> <u>angles</u> of any triangle is
.
In the given question, point P is such that <APB = <APC = <BPC =
. Also, line PB bisects <ABC into two <u>equal</u> measures. Thus;
<ABP = 
Thus,
<ABP + <APB + <BAP = 
30 + 120 + <BAP = 
<BAP =
- 150
<BAP = 
Apply the <em>Sine rule</em> to determine the <u>value</u> of <em>PB</em>, such that;
= 
= 
BP = 
= 
BP = 8.0
Therefore, the <u>value</u> of <u>BP</u> = 8 units.
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Answer 24a + 6
Step-by-step explanation:
8 + 18a -2 + 6a
18a + 6a = 24a
8 - 2 = 6
24a + 6
Answer:
The length = The width = The height ≈ 5.8 cm
Step-by-step explanation:
The volume of a rectangular pyramid, V = l × w × h
The surface area of the pyramid = 2 × l × h + 2 × w × h + 2 × l × w = 200
∴ l × h + w × h + l × w = 200/2 = 100
We have that the maximum volume is given when the length, width, and height are equal and one length is not a fraction of the other. Therefore, we get;
At maximum volume, l = w = h
∴ l × h + w × h + l × w = 3·l² = 100
l² = 100/3
l = 10/√3
Therefore, the volume, v = l³ = (10/√3)³
The length = The width = The height = 10/√3 cm ≈ 5.8 cm
Answer:
Step-by-step explanation:
- x² - 16 = 0
- x² = 16
- x = √16
- x = ± 4
Answer:
And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613
Step-by-step explanation:
The estimated proportion of interest is 
We need to find a critical value for the confidence interval using the normla standard distributon. For this case we have 95% of confidence, then the significance level would be given by
and
. And the critical value is:
The confidence interval for the true population proportion is interest is given by this formula:
Replacing the values provided we got:
And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613