Answer: 2 years 1 month
Step-by-step explanation:
2 years 1 month at $100 a month = $2,500
$720 x 2 years = $1,440
$720 / 12 months = $60
$1,440 + $60 = $1,500
$4,000 - $1,500 = $2,500
Answer:
a)0.099834
b) 0
Step-by-step explanation:
To solve for this question we would be using , z.score formula.
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
A candy maker produces mints that have a label weight of 20.4 grams. Assume that the distribution of the weights of these mints is normal with mean 21.37 and variance 0.16.
a) Find the probability that the weight of a single mint selected at random from the production line is less than 20.857 grams.
Standard Deviation = √variance
= √0.16 = 0.4
Standard deviation = 0.4
Mean = 21.37
x = 20.857
z = (x-μ)/σ
z = 20.857 - 21.37/0.4
z = -1.2825
P-value from Z-Table:
P(x<20.857) = 0.099834
b) During a shift, a sample of 100 mints is selected at random and weighed. Approximate the probability that in the selected sample there are at most 5 mints that weigh less than 20.857 grams.
z score formula used = (x-μ)/σ/√n
x = 20.857
Standard deviation = 0.4
Mean = 21.37
n = 100
z = 20.857 - 21.37/0.4/√100
= 20.857 - 21.37/ 0.4/10
= 20.857 - 21.37/ 0.04
= -12.825
P-value from Z-Table:
P(x<20.857) = 0
c) Find the approximate probability that the sample mean of the 100 mints selected is greater than 21.31 and less than 21.39.
Answer:
Step-by-step explanation:
We are given that Volume of spherical balloon in cubic meters
We have to find the value of volume of the balloon after t seconds.
We are given that radius of spherical balloon after t seconds
Substitute the value then we get
Hence, the volume of spherical balloon is given by the formula
we know that
<u>The Side-Splitter Theorem</u>: States that If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally
so
in this problem
therefore
<u>the answer is</u>
The segment length is GJ
We are given the parametric equations:
x = 6 cos θ
y = 6 sin θ
We know that the derivative of cos a = - sin a and the
derivative of sin a = cos a, therefore taking the 1st and 2nd
derivates of x and y:
d x = 6 (-sin θ) = - 6 sin θ
d^2 x = -6 (cos θ) = - 6 cos θ
d y = 6 (cos θ) = 6 cos θ
d^2 y = 6 (-sin θ) = - 6 sin θ
Therefore the values we are asked to find are:
dy / dx = 6 cos θ / - 6 sin θ = - cos θ / sin θ = - cot θ
d^2 y / d^2 x = - 6 sin θ / - 6 cos θ = sin θ / tan θ =
tan θ
We can find the value of the slope at θ = π/4 by using
the dy/dx:
dy/dx = slope = - cot θ
dy/dx = - cot (π/4) = - 1 / tan (π/4)
dy/dx = -1 = slope
We can find the concavity at θ = π/4 by using the d^2 y/d^2
x:
d^2 y / d^2 x = tan θ
d^2 y / d^2 x = tan (π/4)
d^2 y / d^2 x = 1
Since the value of the 2nd derivative is
positive, hence the concavity is going up or the function is concaved upward.
Summary of Answers:
dy/dx = - cot θ
d^2 y/d^2 x = tan θ
slope = -1
concaved upward
