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777dan777 [17]
3 years ago
6

- 11/5 -2.4 1.6 15/10 - 2.25 in order from least to greatest

Mathematics
2 answers:
tatuchka [14]3 years ago
8 0

Answer (least to greatest):

  1. -2.4
  2. -2.25
  3. -11/5
  4. 15/10
  5. 1.6

I hope this helps!

Dvinal [7]3 years ago
8 0

Answer:

1.6,- 11/5 ,2.25 , -2.4 15/10

Step-by-step explanation:

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Determine whether the statements in (a) and (b) are logically equivalent.
Andru [333]

Answer:

The two statements are logically equivalent.

Step-by-step explanation:

Let X be the statement that Bob is a double math and computer science major.

Y be the statement that Ann is a maths major.

Z be the statement that Ann is a double maths and computer science major.

The two statements written in terms of X, Y and Z now

a. Bob is a double math and computer science major and Ann is a math major, but Ann is not a double math and computer science major.

(x and y) and not z

b. It is not the case that both Bob and Ann are double math and computer science majors, but it is the case that Ann is a math major and Bob is a double math and computer science major.

not (x and z) and (x and y)

Noting that for logical statements,

Negation is represented by ~

And is represented by conjunction sign Λ

Or is represented by disjunction sign V

(x and y) and not z

(x Λ y) Λ (~z)

not (x and z) and (x and y)

~(x Λ z) Λ (x Λ y)

We can then simplify the second statement to obtain the first statement and prove the equivalence of both sides

~(x Λ z) Λ (x Λ y)

Using DE MORGAN'S theory, ~(x Λ z) = (~x) V (~z)

~(x Λ z) Λ (x Λ y) = ((~x) V (~z)) Λ (x Λ y)

Then applying the distributive law to the expression, we can open the bracket up

((~x) V (~z)) Λ (x Λ y)

= ((~x) Λ (x Λ y)) V ((~z) Λ (x Λ y))

Opening the first bracket up further

((~x) Λ (x Λ y)) V ((~z) Λ (x Λ y))

= ((~x) Λ x) Λ y) V ((~z) Λ (x Λ y))

The NEGATION law shows that (~x Λ x) = c (where c is a negation law parameter for when two opposite statements are combined in this manner, it works like a 0 in operation)

((~x) Λ x) Λ y) V ((~z) Λ (x Λ y))

= (c Λ y) V ((~z) Λ (x Λ y))

But (c Λ y) = (y Λ c) = c (according to the UNIVERSALLY BOUND law, see how c works like a 0 now?)

(c Λ y) V ((~z) Λ (x Λ y))

= c V ((~z) Λ (x Λ y))

= ((~z) Λ (x Λ y)) V c (commutative)

And one of the foremost IDENTITY laws is that (any statement) V c = c

((~z) Λ (x Λ y)) V c

= ((~z) Λ (x Λ y))

= (x Λ y) Λ (~z)

Which is the same as the first statement!

PROVED!!!

Hope this Helps!!!

5 0
3 years ago
Read 2 more answers
Classify the following is rational or irrational(a) √45​
marshall27 [118]

The numbers that can be expressed in the form of a fraction are called rational numbers. While that numbers that cannot be expressed in the form of a fraction are called irrational numbers.

\sqrt{45} =\sqrt{3 \times 3 \times 5}

\sqrt{45} =3\sqrt{5}

3\sqrt{5} is an irrational number, it cannot be expressed in the form of a fraction.

3 0
3 years ago
There are 60 minutes in an hour. The total number of minutes is a function of the number of hours, as shown in the table. Does t
Alexxx [7]

Answer:

Step-by-step explanation:

It represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.

Here, number of hours represents input value and minutes represents the output value,

Now, By the given table,

The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),

Also,

⇒  The rate of change output value with respect to input value remains constant,

Hence, It represents a linear function because there is a constant rate of change.

3 0
2 years ago
The cost c, for manufacturing x flags is given by c=x? -24x +39. Find the number of flags manufactured if the cost is $120.
IRINA_888 [86]

9514 1404 393

Answer:

  27

Step-by-step explanation:

You want to find x when c = 120.

  120 = x^2 -24x +39

  x^2 -24x -81 = 0 . . . . . . subtract 120 to put in standard form

  (x -27)(x +3) = 0 . . . . .  .factor it

Solutions are ...

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The number of flags manufactured for a cost of $120 is 27 flags.

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2 years ago
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OLga [1]
Sina - (cosa)(tanb)/cosa + (sina)(tanb)
sina ≡ (tana)(cosa)

(tana)(cosa) - (cosa)(tanb)/cosa + (tana)(cosa)(tanb)
= cosa(tana - tanb)/cosa(1 + tanatanb)
(cosas cancel out)
= (tana - tanb)/(1 + tanatanb) ≡ tan(a-b)
7 0
3 years ago
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