-1/5, 5/6,1.3,1 1/3, 5/3 -4/3 least to greatest
2 answers:
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The simplification form of the provided expression is 108 after applying the integer exponent properties.
<h3>What is integer exponent?</h3>In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
We have an expression:
= 108
Thus, the simplification form of the provided expression is 108 after applying the integer exponent properties.
Learn more about the integer exponent here:
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Answer:
The degree measure of ∠ACP is 112.5°
Step-by-step explanation:
The total area of the given diagram is the sum of two semicircles with arc AB and arc CB having radius R and r respectively
Where:
R = AC
r = DB
R = 2 × r
Therefore the area of the semicircles are given as follows;
For the semicircle with arc AB, we have;
Area, A₁ = π × R²/2 = π × (2×r)²/2 = 2×π×r²
For the semicircle with arc CB, we have;
Area, A₂ = π × r²/2 = 1/2×π×r²
The ratio of the two semicircles is presented in the following relation;
Therefore, the area of A₁ is four times that of A₂ or A₁ = 4 × A₂
The total area of the given diagram = A₁ + A₂ = 4 × A₂ + A₂ = 5·A₂
∴ Half of the area of the diagram, = 5·A₂/2 = 2.5·A₂ = 2.5 × 1/2×π×r² = 1.25×π×r²
The ratio of half of the diagram of the figure to the area of the semicircle with arc AB is found as follows;
/A₁ = (1.25×π×r²)/(2×π×r²) = 5/8
Therefore, the half of the diagram of the figure given by segment PAC is equivalent to 5/8 of the semicircle with arc AB
Given that the arc AB subtends an angle of 180° at the center (angle subtended by a semicircle), the arc AP will subtend 5/8×180 = 112.5°
To verify we have;
Area of a segment of a circle is presented in the following relation;
As segment PAC is 5/8 of a semicircle, it is therefore 5/(8×2) or 5/16 of the whole circle
Hence;
Therefore the degree measure of ∠ACP is 112.5°.
Answer:
a
The 95% confidence bounds is
b
It was not necessary to make any assumption about the shape of the travel time distribution
Step-by-step explanation:
From the question we are told that
The sample size is n = 30
The sample mean is
The standard deviation is
From the question we are told the confidence level is 95% , hence the level of significance is
=>
Generally from the normal distribution table the critical value of is
Generally the margin of error is mathematically represented as
=>
=>
Generally 95% confidence bounds is mathematically represented as
=>
=>
This 95% confidence bounds show that there is 95% confidence that the true mean lies within this bound hence there is it was not necessary to make any assumption about the shape of the travel time distribution