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Soloha48 [4]
3 years ago
6

There are 15 students in a social studies class. Two students will be selected to present their term projects today. In how many

different orders can two students be selected?
Mathematics
1 answer:
xz_007 [3.2K]3 years ago
5 0
Given:
15 students
2 students must be chosen.
No repetition, no order

This is a combinations problem. We use this formula: n! / (n-r)!(r!)

n = 15 ; r = 2

15! / (15-2)!(r!) ⇒ 15! / 13! * 2! = 105 
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If a woman takes an early pregnancy test, she will either test positive, meaning that the test says she is pregnant, or test neg
k0ka [10]

Answer:

0.0098

Step-by-step explanation:

Probability of being pregnant:100/1000

=1/10.

98% chance:=98/100 ×1/10

=98/1000

Therefore the probability that she really is pregnant is: 0.098

3 0
3 years ago
Solve the given initial-value problem. x' = 1 2 0 1 − 1 2 x, x(0) = 2 7
Ilia_Sergeevich [38]
I'll go out on a limb and guess the system is

\mathbf x'=\begin{bmatrix}\frac12&0\\1&-\frac12\end{bmatrix}\mathbf x

with initial condition \mathbf x(0)=\begin{bmatrix}2&7\end{bmatrix}^\top. The coefficient matrix has eigenvalues \lambda such that

\begin{vmatrix}\frac12-\lambda&0\\1&-\frac12-\lambda\end{vmatrix}=\lambda^2-\dfrac14=0\implies\lambda=\pm\dfrac12

The corresponding eigenvectors \eta are such that

\lambda=\dfrac12\implies\begin{bmatrix}\frac12-\frac12&0\\1&-\frac12-\frac12\end{bmatrix}\eta=\begin{bmatrix}0&0\\1&-1\end{bmatrix}\eta=\begin{bmatrix}0\\0\end{bmatrix}
\implies\eta=\begin{bmatrix}1\\1\end{bmatrix}

\lambda=-\dfrac12\implies\begin{bmatrix}\frac12+\frac12&0\\1&-\frac12+\frac12\end{bmatrix}\eta=\begin{bmatrix}1&0\\1&0\end{bmatrix}\eta=\begin{bmatrix}0\\0\end{bmatrix}
\implies\eta=\begin{bmatrix}0\\1\end{bmatrix}

So the characteristic solution to the ODE system is

\mathbf x(t)=C_1\begin{bmatrix}1\\1\end{bmatrix}e^{t/2}+C_2\begin{bmatrix}0\\1\end{bmatrix}e^{-t/2}

When t=0, we have

\begin{bmatrix}2\\7\end{bmatrix}=C_1\begin{bmatrix}1\\1\end{bmatrix}+C_2\begin{bmatrix}0\\1\end{bmatrix}=\begin{bmatrix}C_1\\C_1+C_2\end{bmatrix}

from which it follows that C_1=2 and C_2=5, making the particular solution to the IVP

\mathbf x(t)=2\begin{bmatrix}1\\1\end{bmatrix}e^{t/2}+5\begin{bmatrix}0\\1\end{bmatrix}e^{-t/2}

\mathbf x(t)=\begin{bmatrix}2e^{t/2}\\2e^{t/2}+5e^{-t/2}\end{bmatrix}
5 0
4 years ago
Find an explicit formula for the geometric sequence 96, 24, 6, 1.5
kirill115 [55]

Answer:

This is a geometric sequence since there is a common ratio between each term. in this cade, multiplying the previous term in the sequence by 1/4 gives the next term.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A square field has an area of 479ft^2. What is the approximate length of a side of the field? Give your answer to the nearest fo
ikadub [295]
Area of a square= length^2
479=length^2
√479= length
so length= 21.89ft rounded to 22ft
4 0
3 years ago
-5 5/6 - (-2 1/3) + 5 1/6
Ket [755]

Answer:

1.6 with the bar on top of the 6

Step-by-step explanation:

5 0
3 years ago
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