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blsea [12.9K]
3 years ago
5

In a class of 24 students, 25 percent of them failed a test. How many students failed a test

Mathematics
2 answers:
scZoUnD [109]3 years ago
8 0
25 is 1/4 and 1/4 of 24 is 6 ( that is the easy way)

Tcecarenko [31]3 years ago
4 0
X/24 = 25/100
100x = 600
100x/100 = 600/100
x = 6
6 students failed the test
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Solve for XX. Assume XX is a 2×22×2 matrix and II denotes the 2×22×2 identity matrix. Do not use decimal numbers in your answer.
sveticcg [70]

The question is incomplete. The complete question is as follows:

Solve for X. Assume X is a 2x2 matrix and I denotes the 2x2 identity matrix. Do not use decimal numbers in your answer. If there are fractions, leave them unevaluated.

\left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]· X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =<em>I</em>.

First, we have to identify the matrix <em>I. </em>As it was said, the matrix is the identiy matrix, which means

<em>I</em> = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

So, \left[\begin{array}{cc}2&8\\-6&-9\end{array}\right]· X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right] =  \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

Isolating the X, we have

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]= \left[\begin{array}{cc}2&8\\-6&-9\end{array}\right] -  \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

Resolving:

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]= \left[\begin{array}{ccc}2-1&8-0\\-6-0&-9-1\end{array}\right]

X·\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]=\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Now, we have a problem similar to A.X=B. To solve it and because we don't divide matrices, we do X=A⁻¹·B. In this case,

X=\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]⁻¹·\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Now, a matrix with index -1 is called Inverse Matrix and is calculated as: A . A⁻¹ = I.

So,

\left[\begin{array}{ccc}9&-3\\7&-6\end{array}\right]·\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]

9a - 3b = 1

7a - 6b = 0

9c - 3d = 0

7c - 6d = 1

Resolving these equations, we have a=\frac{2}{11}; b=\frac{7}{33}; c=\frac{-1}{11} and d=\frac{-3}{11}. Substituting:

X= \left[\begin{array}{ccc}\frac{2}{11} &\frac{-1}{11} \\\frac{7}{33}&\frac{-3}{11}  \end{array}\right]·\left[\begin{array}{ccc}1&8\\-6&-10\end{array}\right]

Multiplying the matrices, we have

X=\left[\begin{array}{ccc}\frac{8}{11} &\frac{26}{11} \\\frac{39}{11}&\frac{198}{11}  \end{array}\right]

6 0
3 years ago
Giving brainliest <br><br><br> C<br> Plz help
Vitek1552 [10]

Answer:

D. 42

Step-by-step explanation:

Base = 10+4 (ft)

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4 0
3 years ago
Two families went to the event. The first family bought two children's tickets and one adult ticket and paid a total of 8.2 euro
blagie [28]

Answer:

Step-by-step explanation:

step a system of two equations         c = child ticket     a = adult ticket

eq 1)  2c + 1a = 8.2            multiply by 2

eq 2) 3c + 2a = 14.1

I will multiply eq 1 times TWO and subtract eq 2 from eq 1a)

         eq 1a)  4c + 2a = 16.4

          eq 2)  3c + 2a = 14.1

subtract  (4c - 3c) + (2a -2a)  = 16.4 - 14.1  

                    c      +       0       =   2.3 euros     for one child ticket

Now find the adult ticket price,  plug 2.3 for c into eq 1)

     eq 1)  2c + 1a = 8.2

     eq 1)  2(2.3) + 1a = 8.2         solve for a

                 4.6  + a   =  8.2         substract 4.6 from both sides

                             a =  8.2 - 4.6

                               =   3.6 euros    for one adult ticket

double check using eq 2)    we know c and a values

    eq 2)  3c + 2a = 14.1

    eq 2)  3(2.3) + 2(3.6) = 14.1

                   6.9 + 7.2    =  14.1

                          14.1    =  14.1

5 0
3 years ago
John's goal is to have more then -7 dollars in his bank account by the end of the month.The variable d is the number of dollars
Alona [7]

Answer:

i need more info

Step-by-step explanation:

6 0
3 years ago
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Your round trip drive to school is 3 7/10 miles.how many miles do you drive to and from school in 5 days?
riadik2000 [5.3K]

Answer:

18 1/2 miles

Step-by-step explanation:

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37/2

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2 goes into 37 18 times with 1 left over

18 1/2

5 0
3 years ago
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