Step-by-step explanation:
Add using Scratch Addition. 45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 3
2 answers:
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Answer:
65°
Step-by-step explanation:
Radii CA and CB are perpendicular to tangent lines AT and BT, so
Since angle BAT is equal to 65°, angle CAB has measure
Consider triangle ACB. This triangle is isosceles, because CA=CB as radii of the circle. Two angles adjacent to the base are congruent, thus
The sum of the measures of all interior angles in triangle is always 180°, so
Angle ACB is central angle subtended on the minor arc AB, angle APB is inscribed angle subtended on the same minor arc AB. The measure of inscribed angle is half the measure of central angle subtended on the same arc, so
Answer:
(a) The probability that <em>Y</em>₂₀ exceeds 1000 is 3.91 × 10⁻⁶.
(b) <em>n</em> = 28.09
Step-by-step explanation:
The random variable <em>Y</em>ₙ is defined as the total numbers of dollars paid in <em>n</em> years.
It is provided that <em>Y</em>ₙ can be approximated by a Gaussian distribution, also known as Normal distribution.
The mean and standard deviation of <em>Y</em>ₙ are:
(a)
For <em>n</em> = 20 the mean and standard deviation of <em>Y</em>₂₀ are:
Compute the probability that <em>Y</em>₂₀ exceeds 1000 as follows:
**Use a <em>z </em>table for probability.
Thus, the probability that <em>Y</em>₂₀ exceeds 1000 is 3.91 × 10⁻⁶.
(b)
It is provided that P (<em>Y</em>ₙ > 1000) > 0.99.
The value of <em>z</em> for which P (Z < z) = 0.01 is 2.33.
Compute the value of <em>n</em> as follows:
The last equation is a quadratic equation.
The roots of a quadratic equation are:
a = 16
b = -805.4289
c = 10000
On solving the last equation the value of <em>n</em> = 28.09.
ANSWER
1. k=13
2. x=-10
EXPLANATION
The given function is
To find f(x+5), plug in (x+5) wherever you see x.
This implies that:
Expand:
Simplify to obtain
We now compare with,
This implies that:
To find the smallest zero of f(x+5), we equate the function to zero and solve for x.
The smallest zero is -10.