Answer:
<h2>
11.2≤
12.8 </h2>
Step-by-step explanation:
Confidence interval for the population mean is expressed by the formula;
CI = xbar ± Z(S/√n) where;
xbar is the sample mean = 12.5
Z is the z score at 99% confidence = 2.576
S is the standard deviation = √variance
S = √2.4 = 1.5492
n is the sample size = 25
Substituting the given values into the formula given above,
CI = 12.5 ± 2.576(1.5492/√25)
CI = 12.5 ± 2.576(0.30984)
CI = 12.5 ± 0.7981
CI = (12.5-0.7981, 12.5+0.7981)
CI = (11.2019, 12.7981)
Hence the 99% confidence interval for the population mean is 11.2≤12.8 (to 1 decimal place)
The solution of this question will make use of the Two Tangents from Point Theorem which states that "the measure of an angle formed by two tangents drawn from a point outside the circle is half the the difference of the intercepted arcs".
We can also see that the measure of arcs are: 
and
Thus, as per the theorem, the measure of the 
can be calculated as:
Therefore, we get:
Thus, out of the given options, option B is the correct option.
Answer:
Since,
Length is 4 times Breadth
Let Breadth be x
Therefore,Length=4x
Perimeter=50m
Therefore,
50m=2(l+b)
50m=2(4x+x)
50m=2(5x)
50m=10x
x=5m.
Therefore,
Breadth=5m
Length=4x=4×5=20m
You are given the equation 36 = 9x² + 4y². You are asked to find the slopes of the asymptotes of the hyperbola. A hyperbola has the following general equation x²/a² + y²/b² = 1. the goal here is to find the slopes of the hyperbolic equation. So divide both sides by 36
36 = 9x² + 4y²
(1/36)[36 = 9x² + 4y²]
1 = x²/4 + y²/9
a² = 4
a = 2
and
b² = 9
b = 3
To find the slope, divide a/b and you will get 2/3.
The interest rate is 3.5%.
EXPLANATION
We substitute the given values into the formula;
to obtain
We divide through by 6000 to obtain,
This implies that,
We take the square root of both sides,
This gives us,
Add -1 to both sides of the equation to obtain
Multiply through by 100 to obtain;
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