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3 years ago

6

kaylie has 164 stamps in her collection.her friend nellie has 229 more stamps than kaylie.how many stamps do kaylie and nellie h

ave?

1 answer:

STALIN [3.7K]3 years ago

3 0

657 stamps is what they would have combined

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For each of the following, use logic laws to decide whether the statement is a tautology contradiction, or neither. a (a) (A B)

spayn [35]

Answer:

The statement $(A\rightarrow \lnot B)\land (B\rightarrow A)$ is a contingency.

The statement $(P\rightarrow \lnot P)\land P$ is a contradiction.

Step-by-step explanation:

A tautology is a proposition that is always true.

A contradiction is a proposition that is always false.

A contingency is a proposition that is neither a tautology nor a contradiction.

a) To classify the statement $(A\rightarrow \lnot B)\land (B\rightarrow A)$ , you need to use the logic laws as follows:

$(A\rightarrow \lnot B)\land (B\rightarrow A) \equiv$

$\equiv (\lnot A \lor\lnot B)\land(\lnot B \lor A)$ by the logical equivalence involving conditional statement.

$\equiv (\lnot B\lor \lnot A )\land(\lnot B \lor A)$ by the Commutative law.

$\equiv \lnot B \lor (\lnot A \land A)$ by Distributive law.

$\equiv \lnot B \lor (A \land \lnot A)$ by the Commutative law.

$\equiv \lnot B \lor F$ by the Negation law.

Therefore the statement $(A\rightarrow \lnot B)\land (B\rightarrow A)$ is a contingency.

b) To classify the statement $(P\rightarrow \lnot P)\land P$ , you need to use the logic laws as follows:

$(P\rightarrow \lnot P)\land P \equiv$

$\equiv (\lnot P \lor \lnot P)\land P$ by the logical equivalence involving conditional statement.

$\equiv P \land (\lnot P \lor \lnot P)$ by the Commutative law.

$\equiv (P \land \lnot P) \lor (P \land \lnot P)$ by Distributive law.

$\equiv F \lor F \equiv F$ by the Negation law.

Therefore the statement $(P\rightarrow \lnot P)\land P$ is a contradiction.

8 0

3 years ago

Write a matrix equation for the given systems of equations.

REY [17]

Answer:

<em></em> $\left[\begin{array}{ccc}2&-6&2\\0&3&-2\\0&2&2\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\-5\\-3\end{array}\right]$ <em></em>

Step-by-step explanation:

Given system of equations are

2x-6y-2z = 1

3y - 2z = -5

2y + 2z = -3

given

2 x - 6 y - 2 z = 1

0 x + 3 y - 2z = -5

0 x +2y + 2 z = - 3

<em>The Matrix form of the given system of equations </em>

<em>A X = B</em>

<em></em> $\left[\begin{array}{ccc}2&-6&2\\0&3&-2\\0&2&2\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\-5\\-3\end{array}\right]$ <em></em>

4 0

3 years ago

Which pair of ratios are equal?6/15 and 3/17 3/4 and 9/11 2/5 and 12/35 or 2/3 and 8/12

Elanso [62]

The last pair.
Because 2*4/3*4=8/12

7 0

3 years ago

How many different ways can you make change for $.50 using only nickels,dimes, and quarters?

yanalaym [24]

Answer:

10 ways

Step-by-step explanation:

5 0

3 years ago

Can anyone help me with this page i can’t find the answers

Dvinal [7]

1) f(x)=2x

when x=3 then f(x) =3×2=<em><u>6</u></em>

when x=4 then f(x)=4×2=<em><u>8</u></em>

2)At y=35(no. of mangoes),x corresponds to y=60(amount)

so$<em><u>6</u></em><em><u>0</u></em><em><u>,</u></em><em><u> </u></em><em><u>amount</u></em><em><u> </u></em><em><u>he</u></em><em><u> </u></em><em><u>need</u></em><em><u> </u></em><em><u>to</u></em><em><u> </u></em><em><u>spend</u></em><em><u>!</u></em>

3) f(x)= x+2

for x=1, f(x)=1+2=<em><u>3</u></em>

for x=2,f(x)=2+2=<em><u>4</u></em>

✌️:)

8 0

3 years ago