<span>Let the extension of the length and width be x.
The new dimensions are: Length = 8+x
Width =3+x
Area = 104 ft squared
Area of a rectangle = Length x Width
Therefore,
(8+x)(3+x) = 104
x^2 +11x +24=104
x^2 +11x +24-104=0
x^2 +11x-80=0
Factorize using splitting the middle term method.
X^2 +16x-5x-80=0
x(x+16)-5(x+16)=0
(x-5)(x+16)=0
either x-5 = 0 or x+16=0
x=5 or x=-16
length and width measure cannot be negative.
Therefore, the extension of the length and width is 5 feet each.</span>
Answer:
(a) 
and 
are indeed mutually-exclusive.
(b) 
, whereas 
.
(c) 
.
(d) 
, whereas 
Step-by-step explanation:
<h3>(a)</h3>
means that it is impossible for events and to happen at the same time. Therefore, event and are mutually-exclusive.
<h3>(b)</h3>
By the definition of conditional probability:
.
Rearrange to obtain:
.
Similarly:
.
<h3>(c)</h3>
Note that:
.
In other words, and are collectively-exhaustive. Since and are collectively-exhaustive and mutually-exclusive at the same time:
.
<h3>(d)</h3>
By Bayes' Theorem:
.
Similarly:
.
It is 100. There is many ways to find this answer. One way would be to divide 1000 by 10 to get a 100. Another way is to take the decimal form of 1/10 which is .10 and times it by 1000 to get 100.
<span>We have to find the value of x if the measures of the angles of a triangle are: 2 x, 3 x and 4 x. We know that the sum of the measures of the angles of a triangle is 180 degrees. A + B + C = 180. Here we have: A = 2 x, B = 3 x and C = 4 x; 2 x + 3 x + 4 x = 180; 9 x = 180; x = 180 : 9. Answer: x = 20 degrees.</span>
I recommend going to desmos graphing calculator and put those in and it should show
