Are -1/2, 3/4 and -1.5 rational numbers if not what are they?

In one town, 47% of all voters are Democrats. If three

34kurt

Answer:

The probability that the all three votes are Democrats

P(X=3) = 0.1038

Step-by-step explanation:

Step(i):-

Given that the all voters are democrats

The probability that the all voters are democrats

p = 47% =0.47

q = 1-p =1-0.47 = 0.53

Step(ii):-

Let 'X' be the random variable in binomial distribution

$P(X=r) = n_{C_{r} } p^{r} q^{n-r}$

The probability that the all three votes are Democrats

P(X=3) = 0.1038

n=3 and r=3

$P(X=3) = 3_{C_{3} } (0.47)^{3} (0.53)^{3-3}$

$P(X=3) = 1 (0.47)^{3}$

P(X=3) = 0.1038

Final answer:-

The probability that the all three votes are Democrats

P(X=3) = 0.1038

5 0

3 years ago

Given the set points K+1:(-1,8),(1,0) and (2,5), find the quadratic polynomial interpolate

Sauron [17]

Answer:

The interpolating polynomial is $p(x) = 1-4x+3x^2$ .

Step-by-step explanation:

We want to find a quadratic polynomial $p(x)$ such that $p(-1)=8$ , $p(1)=0$ and $p(2)=5$ . In order to do this let us write $p(x) = a_0+a_1x+a_3x^2$ .

Now, evaluating the polynomial in the points -1, 1 and 2 we get

$\begin{cases} 8 = p(-1) &= a_0-a_1+a_2\\ 0 = p(1) &= a_0+a_1+a_2\\ 5 = p(2) &= a_0+2a_1+4a_2\end{cases}$

This relations give us a linear system of equations:

$\begin{cases} 8 &= a_0-a_1+a_2\\ 0 &= a_0+a_1+a_2\\ 5&= a_0+2a_1+4a_2\end{cases}$

where the $a_0$ , $a_1$ and $a_2$ are the unknowns.

The augmented matrix of the system is

$\begin{pmatrix}1 & -1 & 1 & 8\\ 1 & 1 & 1 & 0\\ 1 & 2 & 4 & 5\end{pmatrix}$

In this matrix it is easy to eliminate the 1's of the first column and get

$\begin{pmatrix} 1 & -1 & 1 & 8\\ 0 & 2 & 0 & -8\\ 0 & 3 & 3 & -3\end{pmatrix}$

From this matrix we can find the values of each unknown. Notice that the second row gives us $2a_2=-8$ that yields $a_1=-4$ .

Then, the third row means $3a_1+3a_2=-3$ that gives $-12+3a_2=-3$ . So, $a_2=3$ .

Finally, the first row is $a_0-a_1+a_2=8$ and substituting is $a_0+7=8$ that yields $a_0=1$ .

Therefore, the interpolating polynomial is

$p(x) = 1-4x+3x^2$ .

8 0

3 years ago

If x=6 find the value of x+4. 3x. x/2 all as different answer please

Archy [21]

Answer:

x+4=10 3x=18 and x/2=3

Step-by-step explanation:

x=6 substituting the value,

x+4

=6+4

=10

3x

=3×6

=18

x/2

=6/2

=3

4 0

2 years ago

Please help meee I’m bad at math!!!!!

Crank

the answer to this question is C

y=2x+6×

6 0

3 years ago

somebody can help me with this problem p;lz i really really need help if you answer thius question you gonnna be the best person

Iteru [2.4K]

The length of FD = 0.76 feet.

Step-by-step explanation:

Given that in ΔDEF, the angle F measures 90° and the angle D measures 83° and EF=6.2 feet

To find the length of FD, let us use the tangent function. The tangent of an angle is the length of opposite side divided by the length of the adjacent side.

$\tan \theta=\frac{o p p}{a d j}$