Answer:
thw answer is -3/2 and in decimal form its -1.5
Step-by-step explanation:
hoped I helped:)
Answer:
P(A) = 0.2
P(B) = 0.25
P(A&B) = 0.05
P(A|B) = 0.2
P(A|B) = P(A) = 0.2
Step-by-step explanation:
P(A) is the probability that the selected student plays soccer.
Then:
P(B) is the probability that the selected student plays basketball.
Then:
P(A and B) is the probability that the selected student plays soccer and basketball:
P(A|B) is the probability that the student plays soccer given that he plays basketball. In this case, as it is given that he plays basketball only 10 out of 50 plays soccer:
P(A | B) is equal to P(A), because the proportion of students that play soccer is equal between the total group of students and within the group that plays basketball. We could assume that the probability of a student playing soccer is independent of the event that he plays basketball.
Answer:
15%
Step-by-step explanation:
vat amount
= 1380 - 1200
=180
finding the rate of vat
= 1380/1200 *100
= 115%
NB : the 115% shows that 1200 8 115% = 1380 , this give total amount including vat , we only want vat hence we have to deduct the 100% which indicates the amount of article)
hence 115 - 100 = <u>15%</u>
15% * 1200= 180
OK. You asked for it. Here we go.
First, let's gather up the tools we might use ...
some things that we know about triangles:
-- Every triangle: Area = (1/2) x (length of the base) x (the height)
-- Isosceles triangle: It has two sides that are the same length.
-- Right triangle: It has one right angle in it.
The sides that meet at the right angle are called the "legs".
They form a corner there, like this _| .
-------------------------------------------
Now we can start using these tools to hack away at the problem.
Farmer Ted has an isosceles right triangle garden.
The problem asks us to figure out how long the legs are.
Before he changes anything, it looks like this _| and both of
those sides are the same length. Call it 'x' until we figure out
what it really is.
Notice that one of them is the base of the triangle, and the other one
is the height. So the area of this triangle is
(1/2) (x) (x) or (1/2) x² .
-------------------------------
Farmer Ted is never satisfied. Suddenly, one day without warning, he
comes along and makes the garden bigger. He makes one of the legs
7 ft longer, and he makes the other one 5 ft longer.
Now the length of one leg is (x + 7) and the other one is (x + 5) .
They're still the base and height of the triangle, so the area of the
bigger garden is
(1/2) (x + 7) (x + 5).
The problem says that this area is 55 square feet more than the original
area, so look out, here comes the <em>equation </em>:
new area = old area + bigger
(1/2) (x + 7) (x + 5) = (1/2) x² + 55
Locked in the mysterious shadowy crevices of this equation is
everything we need in order to figure out the original length of the legs ...
what we called 'x'.
At this point, we can forget about Farmer Ted, forget about the garden,
and just go back to our laboratory with this equation and solve it to find 'x'.
Let's take it slow and easy, one little step at a time:
<u>(1/2) (x + 7) (x + 5) = (1/2) x² + 55</u>
Multiply each side by 2 : (x + 7) (x + 5) = x² + 110
Expand (FOIL) the left side: x² + 12x + 35 = x² + 110
Subtract x² from each side: 12x + 35 = 110
Subtract 35 from each side: 12x = 75
Divide each side by 12 : <em>x = 6.25 feet</em>
==============================================
OK. That's a very nice number. How do we know whether it's correct ?
Let's check it out, and see if it fits the story:
Original area = (1/2 x base x height) = (0.5 x 6.25 x 6.25) = 19.53125 sq ft
One new leg = (6.25 + 7) = 13.25 ft
Other new leg = (6.25 + 5) = 11.25 ft
New area = (1/2 x base x height) = (0.5 x 13.25 x 11.25) = 74.53125 sq ft
How much bigger is the new area ?
74.53125 - 19.53125 = <em>55 sq ft </em> yay !
When we start with legs that are 6.25-ft and go through the whole story,
the new area is exactly what the problem says it was. So 6.25-ft is the
correct original length of the legs, before Farmer Ted messed with it.
