Answer:

Step-by-step explanation:
Given that from a well shuffled set of playing cards (52 in number) a card is drawn and without replacing it, next card is drawn.
A - the first card is 4
B - second card is ace
We have to find probability for

P(A) = no of 4s in the deck/total cards = 
After this first drawn if 4 is drawn, we have remaining 51 cards with 4 aces in it
P(B) = no of Aces in 51 cards/51 = 
Hence

(Here we see that A and B are independent once we adjust the number of cards. Also for both we multiply the probabilities)
Answer: The value of x in trapezoid ABCD is 15
Step-by-step explanation: The trapezoid as described in the question has two bases which are AB and DC and these are parallel. Also it has sides AD and BC described as congruent (that is, equal in length or measurement). These descriptions makes trapezoid ABCD an isosceles trapezoid.
One of the properties of an isosceles trapezoid is that the angles on either side of the two bases are equal. Since line AD is equal to line BC, then angle D is equal to angle C. It also implies that angle A is equal to angle B.
With that bit of information we can conclude that the angles in the trapezoid are identified as 3x, 3x, 9x and 9x.
Also the sum of angles in a quadrilateral equals 360. We can now express this as follows;
3x + 3x + 9x + 9x = 360
24x = 360
Divide both sides of the equation by 24
x = 15
Therefore, in trapezoid ABCD
x = 15
<h3>
Answer: 123 meters is the longest </h3>
============================
Work Shown:
Convert everything to the same unit. I'm going to convert everything to meters
0.1203 km = 120.3 meters (multiply by 1000)
1230 cm = 12.3 meters (divide by 100)
12030 mm = 12.03 meters (divide by 1000)
------------------
The four distances we have are: 120.3 meters, 123 meters, 12.3 meters, 12.03 meters. We see that 123 meters is the longest.
Answer:
The answer is 103
Step-by-step explanation:
The given expression is:
300-7[4(3+5)]+3 to the 3rd power
3 to the 3rd power means 3^3
Therefore,
300-7[4(3+5)]+3^3
First we will solve the round bracket and find the cube
300-7[4(8)]+27
Now we will solve square bracket
300-7[32]+ 27
300-224+27
76+27
103
Thus the answer we get is 103....
Answer:
29119.66666...+14561.3333...=43681, 209ft^2, not square feet.
Step-by-step explanation:
<em>"One side of a rectangle is 3 feet shorter than twice the other side find the sides if the area is 209 feet squared"</em>
Ok, so this is a tricky one- <em> 209 feet squared, </em>not 209 square feet, therefore the area is 209^2, or 43,681.
Next, let's define our variables-
<em>x= the "other side"</em>
<em>z= 3 feet shorter than twice side</em>
We can now make these (useful) equations
z=2x-3
43681= (2x-3)+x
We will focus on the latter for now-
Simplify
43681= (2x-3)+x
43681= 2x-3+x
43681= 3x-3
+3
43684=3x
/3
14561.3333...=x
z=2x-3
z=2*(14561.3333)-3
z=29119.66666....
29119.66666...+14561.3333...=43681