All categories

4 years ago

A jar contains 2 orange balls, 5 black balls, and 3 pink balls.

2 answers:

7 0

The probability of Event A is 5/10 which simplifies to 1/2.

The probability of Event B is 3/9 which simplifies to 1/3.

Because it says "and" we need to multiply them which gives us 1/2*1/3=1/6

galben [10]4 years ago

7 0

$|\Omega|=10\cdot9=90\\
|A\cap B|=5\cdot3=15\\\\
P(A\cap B)=\dfrac{15}{90}=\dfrac{1}{6}$

You might be interested in

600 is deposited in an account that pays 7% annual interest,compunded continuosly.what is the balance after 5 years?

netineya [11]

Year 1 $642.00
Year 2 $686.94
Year 3 $735.03
Year 4 $786.48
Year 5 $841.53

8 0

3 years ago

Read 2 more answers

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 23 in. by 13 in. by

faltersainse [42]

Answer:

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is 361.19 $in^3$ .

Step-by-step explanation:

Given that the dimensions of a cardboard is 23 in by 13 in.

Let the side of the square be x in.

Then the length of the box= (23-2x) in

and the width of the box =(13-2x) in

and height = x in.

The volume of the box is = length ×width × height

=[(23-2x)(13-2x)x] $in^3$

=(299x-72x² +4 $x^3$ ) $in^3$

∴V=299x-72x² +4x³

Differentiating with respect x

V'= 299-144x+12x²

Again differentiating with respect x

V''= -144+24x

To find the dimensions, we set V'=0

∴299-144x+12x²=0

Applying Sridharacharya formula that is the solution of a quadratic equation ax²+bx+c is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here a=12, b=-144 , c=299

$\therefore x=\frac{-(-144)\pm\sqrt{(-144)^2-4.12.299}}{2.12}$

$\Rightarrow x= 9.33, 2.67$

If we take x=9.33 in, then the width of the box [13-(2×9.33)] will negative.

∴x = 2.67 in

If at x = 2.67, V''<0 , then the volume of the box will be maximum or V''>0 then volume of the box will be minimum.

$V''|_{x=2.67}=-144+(24\times 2.67)=-79.92$

Therefore at x = 2.67, the volume of the box maximum.

The length of the box =[23-(2×2.67)] in

=17.66 in

The width of the box =[13-(2×2.67)] in

=7.66 in

The height of the box= 2.67 in

The dimension of the box is 17.66 in by 7.66 in by 2.67 in.

Therefore the volume of the box is =(17.66×7.66×2.67) $in^3$

=361.19 $in^3$

8 0

3 years ago

Rose is making chocolate chip cookies for dessert the recipe for one batch of chocolate chip cookies calls for 2 1/2 cups of sug

lilavasa [31]

Answer:

8.75 cups

Step-by-step explanation:

3.5:1 (the ratio of batches to 1 batch)

x:2.5 (the ratio of cups of sugar used to the amount used for only 1 batch)

3.5/1=x/2.5 (proportion)

x= 8.75

3 0

3 years ago

(33) Please check my answer in geo thanks I am not 100% about this one

Reil [10]

Yes this is using the transitive property
Point A leads to point B, B goes to C, so overall A goes to C. Think of it connecting a chain.

Nice job on getting the correct answer.

5 0

3 years ago

F(x)=-1/2(x-2)^2-4 Graph the function

telo118 [61]

Answer:

see below

Step-by-step explanation:

The function is written in vertex form. It has a negative vertical scale factor, so you know ...

the vertex is (2, -4)
the vertical scale factor is 1/2
the parabola opens downward

Vertex form is ...

f(x) = a(x -h)^2 +k . . . . . . . . . . vertical scale factor "a", vertex (h, k)

Since you know the vertex and scale factor, you can plot some points on the graph. I find it convenient to think in terms of units either side of the vertex. These are values of x that would make (x-2)^2 be 1^2, 2^2, 3^2, 4^2 and so on. The vertical scale factor of -1/2 tells you that the y-differences for these points will be -1/2, -4/2, -9/2, -16/2 from the vertex. Then we have ...

vertex: (2, -4)

1 unit either side of the vertex: (1, -4.5), (3, -4.5)

2 units either side of the vertex: (0, -6), (4, -6)

3 units either side of the vertex: (-1, -8.5), (5, -8.5)

4 units either side of the vertex: (-2, -12), (6, -12)

You can plot these points and draw a smooth curve through them. Or, you can let a graphing calculator do it. The result will be similar to that shown below.

6 0

4 years ago