From a group of ten boys and twelve girls, a committee of students is chosen at random. what is the probability that

Suppose that the functions p and q are defined as follows.p(x) = -2x + 1q(x)=-x?Find the following.

MariettaO [177]

First let us find

$(q\mathrm{}p)(x)$ $\begin{gathered} q(p(x))=q(-2x+1) \\ =-(-2x+1)^2 \\ So\text{ } \\ (q\mathrm{}p)(5)=-(-2\times5+1)^2 \\ =-(9)^2 \\ =-81 \end{gathered}$

Now let;s solve the second part

$\begin{gathered} (p\mathrm{}q)(x)=p(q(x)) \\ =p(-x^2) \\ =-2(-x^2)+1 \\ =2x^2+1 \\ So\text{ (p.q)(5) will be } \\ (p\mathrm{}q)(5)=2(5)^2+1 \\ =51 \end{gathered}$

6 0

1 year ago

(Old furniture sold for cash Rs. 1500)

atroni [7]

What’s the question?

6 0

3 years ago

Ashley will tend a car for the weekend.she can choose one of two plans.the first plan has an initial fee of $49.96 and cost an a

Rom4ik [11]

First, you multiply $55.96 by $0.12 and you get $6.7152. Then, multiply $49.96 by $0.14 and you get $6.9944. If you subtract $69944-$6.7152 you get your answer which is $0.2792.

5 0

3 years ago

(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.

valentinak56 [21]

Find the intersection of the two planes. Do this by solving for z in terms of x and y ; then solve for y in terms of x ; then again for z but only in terms of x.

-4x + 2y - z = 1 ==> z = -4x + 2y - 1

3x - 2y + 2z = 1 ==> z = (1 - 3x + 2y)/2

==> -4x + 2y - 1 = (1 - 3x + 2y)/2

==> -8x + 4y - 2 = 1 - 3x + 2y

==> -5x + 2y = 3

==> y = (3 + 5x)/2

==> z = -4x + 2 (3 + 5x)/2 - 1 = x + 2

So if we take x = t, the line of intersection is parameterized by

r(t) = ⟨t, (3 + 5t )/2, 2 + t⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩

(a) The tangent vector to r(t) is parallel to this line, so you can use

v = dr/dt = d/dt ⟨2t, 3 + 5t, 4 + 2t⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in x = -1, y = 1, and z = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩

3 0

3 years ago

Anely and Sandra get paid per project. Anely is paid a project fee of $40 plus $11.50 per hour. Brenda is paid a project fee of

alexdok [17]

Answer:

$68 to hire and 28.25 per hour to hire both

Step-by-step explanation:

7 0

3 years ago