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1 year ago

Alex, Bob and Carl go for a walk every day. If Alex doesn't wear a hat, then Bob wears

Mathematics

1 answer:

bazaltina [42]1 year ago

3 0

Answer:

Carl and Alex are wearing hats.

Step-by-step explanation:

If Bob doesn't isn't wearing a hat, then Carl is, so Carl clearly is wearing a hat.

Now let's look at Alex. If he wasn't wearing a hat, then Bob would be wearing one. (If Alex doesn't wear a hat, then Bob wears

a hat). The logical conclusion is that Alex must be wearing a hat as well.

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6/9 9/12 wich one is bigger

Alexxandr [17]

Answer:

9/12

Step-by-step explanation:

because I is the biggest number

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3 years ago

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An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it takes the carpenters 2 days. How

AleksAgata [21]

Answer:

6 days

Step-by-step explanation:

Let the time taken by Carpenter working alone = $C$ days

Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2 $C$ days

Time taken working together = 2 days

Work done in one day working together = $\frac{1}{2}$

Work done in one day by Carpenter working alone = $\frac{1}{C}$

Work done in one day by apprentice working alone = $\frac{1}{2C}$

Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone = $\frac{1}{C}$ + $\frac{1}{2C}$ = Work done in one day working together = $\frac{1}{2}$

$\dfrac{1}{C}+\dfrac{1}{2C}=\dfrac{1}{2}\\\Rightarrow \dfrac{2+1}{2C}=\dfrac{1}{2}\\\Rightarrow C = 3\ days$

Time taken by Carpenter alone to complete the work = 3 days

Time taken by Apprentice alone to complete the work = 3 $\times$ 2= 6 days

4 0

3 years ago

2. Solve the system of equations. Write your answer in parametric vector notation. X, +5x2 + 4x3 + 3x4 +9xs = 18 2x, +6x2 + 4x3

ratelena [41]

Answer:

The system is inconsistent.

Step-by-step explanation:

The system is

$x_1+5x_2+4x_3+3x_4+9x_5=18\\2x_1+6x_2+4x_3+6x_4+6x_5=28\\3x_1+7x_2+4x_3+10x_4+x_5=41\\4x_1+6x_2+2x_3+7x_4+4x_5=29$

The associated matrix to the system is

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\2&6&4&6&6&28\\3&7&4&10&1&41\\4&6&2&7&4&29\end{array}\right]$

Now we use row operations to find the echelon form of the matrix:

1. We substract to row 2, two times the row 1.

We substract to row 3, three times the row 1.

We substract to row 4, four times the row 1 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&-4&-4&0&-12&-8\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

2. We multiply the second row of the preview step by -1/4. We obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

We add to row 3, eight times the row 2.

We add to row 4, fourtheen times the row 2 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&-5&10&-155\end{array}\right]$

4. We add to row 4 of the preview step, five times the row 3 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&0&0&-140\end{array}\right]$

Using backward substitution we have that

$0x_5=-140$ , then $0=-140$ and this is absurd. Then The system is inconsistent.

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3 years ago

Give the digits in the ones place and the tenths place 23.91

Andru [333]

Answer:

Ones place: 3, Tenths place: 0.9

Step-by-step explanation:

Simple math

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2 years ago

6. Suppose that a password for a computer system must have at least 6, but no more than 9 characters, where each character in th

Verizon [17]

Answer:

How many of these passwords contain at least one occurrence of at least one of the five special characters?

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2 years ago

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