Answer:
A, E
Step-by-step explanation:
There should be 2^8-1 proper subsets of A. Its every one besides { }
An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth rate during those 9 years is approximated by
dh/dt = 1.8t + 3,
where t is the time (in years) and h is the height (in centimeters). The seedlings are 10 centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) =
(b) How tall are the shrubs when they are sold?
cm
Answer:
(a) After t years, the height is
18t² + 3t + 10
(b) The shrubs are847 cm tall when they are sold.
Step-by-step explanation:
Given growth rate
dh/dt = 1.8t + 3
dh = (18t + 3)dt
Integrating this, we have
h = 18t² + 3t + C
When t = 0, h = 10cm
Then
10 = C
So
(a) h = 18t² + 3t + 10
(b) Because they are sold after every 9 years, then at t = 9
h = 18(9)² + 3(9) + 10
= 810 + 27 + 10
= 847 cm
A line runs tangent to a circle at the point (4, 2). The line runs through the origin. Find the slope of the tangent line.
Answer:
Slope of the tangent line (m) = 1 / 2
Step-by-step explanation:
Given:
Point A = (4,2)
Origin point = (0,0)
Find:
Slope of the tangent line (m)
Computation:
Slope of the tangent line (m) = (y2-y1) / (x2-x1)
Slope of the tangent line (m) = (2-0) / (4-0)
Slope of the tangent line (m) = 2 / 4
Slope of the tangent line (m) = 1 / 2
The chief business officer of a construction equipment company arranges a loan of $9,300, at 12 1 /8 % interest for 37.5 months. Find the amount of interest. (Round to the nearest cent)
a. $2,761.21
b. $3,583.83
c. $3,523.83
d. $3,722.47
Answer:
C). $3523.83
Step-by-step explanation:
loan of principles p= $9,300,
at rate R= 12 1 /8 % interest
Rate R = 12.125%
for duration year T = 37.5 months
T= 37.5/12 = 3.125 years
Interest I=PRT/100
Interest I =( 9300*12.125*3.125)/100
Interest I = (352382.8125)/100
Interest I = 3523.83
Interest I= $3523.83
The probability density function for random variable W is given as follows: Let x be the 100pth percentile of W and y be the 100(1 – p)th percentile of W, where 0
Answer:
Step-by-step explanation:
A probability density function (pdf) is used for continuous random variables. That is why p is between 0 and 1 (the two extremes - 0 and 1 - exclusive).
X = 100pth percentile of W
Y = 100(1-p)th percentile of W
Expressing Y as a function of X;
Y = 100(1-p)th = 100th - 100pth
Recall that 100pth is same as X, so substitute;
Y = 100th - X
where 100th = hundredth percentile of W and X = 100pth percentile of W
Point E lies within rectangle ABCD. If AE = 6, BE = 7, and CE = 8, what is the length of DE?
Answer:
[tex]\sqrt{51}[/tex] units.
Step-by-step explanation:
Point E is inside a rectangle ABCD.
Please refer to the attached image for the given statement and dimensions.
Given that:
Sides AE = 6 units
BE = 7 units and
CE = 8 units
To find:
DE = ?
Solution:
For a point E inside the rectangle the following property hold true:
[tex]AE^2+CE^2=BE^2+DE^2[/tex]
Putting the given values to find the value of DE:
[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]
Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
Find the missing side or angle.
Round to the nearest tenth.
Answer:
b=2.7
Step-by-step explanation:
using sine rule,,,
Step-by-step explanation:
So for this problem, we need the missing angle A. From there, we can use the law of sines to compute length of b.
So the sum of the interior angles of a triangle is 180. With that in mind, we can make an equation to fine the measure of angle A.
53 + 80 + A = 180
133 + A = 180
A = 47
Now that we have the angle of A, we can use the law of sines to fine the length of b.
b / sin(B) = a / sin(A)
b = sin(B) * a / sin(A)
b = sin(80) * 2 / sin(47)
b = 2.693
Now round that to the nearest tenth to get
b = 2.7
Cheers.
PLEASE HELP!!!
Evaluate the expression when b=4 and y= -3
-b+2y
Answer: -10
Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.
1. -4+2(-3)
2. -4+(-6)
3.-4-6
4.-10
Answer:
8
Step-by-step explanation:
-b + 2y
if
b = 4
and
y = 3
then:
-b + 2y = -4 + 2*6 = -4 + 12
= 8
