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victus00 [196]
3 years ago
12

If P( A or B) = 2/5, P(B)=1/4 and P( A and B) = 1/10 find P(A)

Mathematics
1 answer:
natulia [17]3 years ago
5 0

Answer:

p(a) = -3/20

Step-by-step explanation:

p ( a +b) = p(a)+p(b)

1/10= p(a) +1/4

1/10 - 1/4 = p(a)

p(a) = -3/20

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What is the y-intercept, axis of symmetry and vertex of the following function.
Pepsi [2]

Complete the square:

F(x) = -3x² - 6x - 5

F(x) = -3 (x² + 2x) - 5

F(x) = -3 (x² + 2x + 1 - 1) - 5

F(x) = -3 ((x + 1)² - 1) - 5

F(x) = -3 (x + 1)² + 3 - 5

F(x) = -3 (x + 1)² - 2

The y-intercept has x-coordinate equal to 0, so it corresponds to the value of F(0) :

F(0) = -3 (0 + 1)² - 2 = -3 - 2 = -5

The axis of symmetry is the vertical line running through the vertex of this parabola, so we'll come back to this.

The vertex of the parabola is (-1, -2). This represents the maximum value of F(x), which follows from

(x + 1)² ≥ 0   ⇒   -3 (x + 1)² ≤ 0   ⇒   -3 (x + 1)² - 2 ≤ -2

This is to say, every point on the parabola has a y-coordinate no greater than -2.

As mentioned earlier, the axis of symmetry is the vertical line through the vertex, and its equation is determined by the x-coordinate of the vertex. Hence the AoS is the line x = -1.

4 0
2 years ago
Read 2 more answers
2/3x - 1/9x + 5 = 20
BabaBlast [244]

Answer:I think the answer is x=27

Step-by-step explanation:

6 0
3 years ago
If y varies directly as x and y = 21 when x = 5, find x when y = 42.
Lorico [155]

Answer: 10

<u>Step-by-step explanation:</u>

varies directly means: \frac{y}{x} = k

Step 1: solve for k   ⇒  \frac{21}{5} = k

Step 2: plug in the given value and k to solve for the missing value: \frac{42}{x} = \frac{21}{5}

42(5) = 21(x)

\frac{42(5)}{21} = \frac{21(x)}{21}

2(5) = x

10  = x


5 0
3 years ago
Alan, Bianca, and Charles are counting in turn. Alan says "one," Bianca says "two," and Charles says "three." Then it's Alan's t
timama [110]
Bianca would say fifty nine
8 0
3 years ago
You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o
Aleksandr [31]

Answer:

Therefore the circumference of the circle is =\frac{20\pi}{4+\pi}

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

⇒2s+πr =10

\Rightarrow s=\frac{10-\pi r}{2}

The area of the circle is = πr²

The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

A=\pi r^2+ (\frac{10-\pi r}{2})^2

\Rightarrow A= \pi r^2+(\frac{10}{2})^2-2.\frac{10}{2}.\frac{\pi r}{2}+ (\frac{\pi r}{2})^2

\Rightarrow A=\pi r^2 +25-5 \pi r +\frac{\pi^2r^2}{4}

\Rightarrow A=\pi r^2\frac{4+\pi}{4} -5\pi r +25

For maximum or minimum \frac{dA}{dr}=0

Differentiating with respect to r

\frac{dA}{dr}= \frac{2\pi r(4+\pi)}{4} -5\pi

Again differentiating with respect to r

\frac{d^2A}{dr^2}=\frac{2\pi (4+\pi)}{4}    > 0

For maximum or minimum

\frac{dA}{dr}=0

\Rightarrow \frac{2\pi r(4+\pi)}{4} -5\pi=0

\Rightarrow r = \frac{10\pi }{\pi(4+\pi)}

\Rightarrow r=\frac{10}{4+\pi}

\frac{d^2A}{dr^2}|_{ r=\frac{10}{4+\pi}}=\frac{2\pi (4+\pi)}{4}>0

Therefore at r=\frac{10}{4+\pi}  , A is minimum.

Therefore the circumference of the circle is

=2 \pi \frac{10}{4+\pi}

=\frac{20\pi}{4+\pi}

4 0
2 years ago
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