Answer:
x ≤ -3 or 1 < x
Step-by-step explanation:
Solve an inequality the same way you would solve an equation, with one exception. If you multiply or divide by a negative number, the inequality symbol is reversed.
... x + 7 ≤ 4 . . . . . left inequality
... x ≤ -3 . . . . . . . subtract 7 to get the x-term by itself
___
... 5 - 3x < 2 . . . . right inequality
... -3x < -3 . . . . . . subtract 5 to get the x-term by itself
... x > 1 . . . . . . . . . divide by -3. Since -3 is negative, we reverse the inequality symbol
The problem statement says the solution is the OR of these, so ...
... x ≤ -3 . . or . . 1 < x
_____
These are graphed on a number line with a solid dot at -3, and an arrow to the left from there; and an open dot at +1, and an arrow to the right from there. (The dot at 1 is open because x=1 is not in the solution set.)
Answer:
At any given moment, the red ant's coordinates may be written as (a, a) where a > 0. The red ant's distance from the anthill is 
. The black ant's coordinates may be written as (-a, -a) and the black ant's distance from the anthill is . This shows that at any given moment, both ants are units from the anthill.
Step-by-step explanation:
Given:
red ant's coordinates written as (a,a)
black ant's coordinates are written as (-a, -a)
To find:
The distance of red and black ants from anthill
Solution:
Compute the distance of red ant from the anthill using distance formula
d (red ant) = 
= 
= 
=
So distance of red ant from anthill is
Compute the distance of black ant from the anthill using distance formula
d (black ant) = 
= 
=
=
=
So distance of black ant from anthill is
Hence both ants are
units from the anthill.
<span>The width is 6 inches and the length is 26 inches.
Explanation:
L=4w+2, since the length is 2 more than 4 times the width.
The perimeter is given by P=2L+2w; using our equation for L, we have
P=2(4w+2)+2w.
Using the distributive property, we have
P=2*4w+2*2+2w
P=8w+4+2w.
Combining like terms, we have P=10w+4.
We know the perimeter is 64, so we have
64=10w+4.
Subtract 4 from both sides:
64-4=10w+4-4
60=10w.
Divide both sides by 10:
60/10 = 10w/10
6=w.
Substitute this into the equation for length: L=4*6+2=24+2=26</span>
I have no idea on D. Sorry. I hope this helps. They may not be right I didn’t quite understand the directions.
Answer:
(a) 0.1414
(b) 0.1010
Step-by-step explanation:
(a)
The density curve is rectangular in shape.
This implies that the distribution of donations is Uniform.
(b)
Compute the probability of donations at least 85 cents as follows:
![=\frac{1}{99}\times [x]^{99}_{85}\\\\=\frac{99-85}{99}\\\\=0.1414\\\\](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B99%7D%5Ctimes%20%5Bx%5D%5E%7B99%7D_%7B85%7D%5C%5C%5C%5C%3D%5Cfrac%7B99-85%7D%7B99%7D%5C%5C%5C%5C%3D0.1414%5C%5C%5C%5C)
Thus, the proportion of donations that are at least 85 cents is 0.1414.
(b)
Compute the probability of donations between 30 and 40 cents as follows:
![=\frac{1}{99}\times [x]^{40}_{30}\\\\=\frac{40-30}{99}\\\\=0.1010](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B99%7D%5Ctimes%20%5Bx%5D%5E%7B40%7D_%7B30%7D%5C%5C%5C%5C%3D%5Cfrac%7B40-30%7D%7B99%7D%5C%5C%5C%5C%3D0.1010)
Thus, the probability of donations between 30 and 40 cents is 0.1010.
