Ask question

Ask question

All categories

3 years ago

6

Let p: The integer has one digit. Let q: The integer is less than 10. Which represents "The integer has one digit if and only if

the integer is less than 10”? p ∨ q p ∧ q p → q p ↔ q

1 answer:

Vinil7 [7]3 years ago

8 0

The double implication "if and only if" is graphically represented by an arrow pointing in both direction, so the correct writing is

$p \iff q$

You might be interested in

In 2 hours the minutes hand of a clock rotates through an angel of how many degrees?

Ipatiy [6.2K]

720° cause in 1 hour it rotates 360° meaning of you multiple by 2 it's 720°

3 0

3 years ago

Read 2 more answers

A glass bottle filled with oil weighs 590 grams. After Sophia uses 200 milliliters of oil, the bottle weighs 400 grams. The weig

iris [78.8K]

Answer: The answer is $M=590-\dfrac{19}{20}V.$

Step-by-step explanation: Given that a glass bottle is filled with oil weighs 590 grams. After that, Sophia uses 200 millilitres of oil and then the bottle weighs 400 grams.

Therefore, the weight of the oil that Sophia uses = 590 - 400 = 190 grams.

That is, 190 grams = 200 millilitres, so

$1~\textup{ ml}=\dfrac{190}{200}~\textup{grams},\\\\\textup{V ml}=\dfrac{19}{20}\textup{V}~\textup{grams}.$

So, the relation between the weight 'M' of the bottle of oil, in grams, is a function of 'V', the volume of oil Sophia used is given by

$\textup{M}=590-\dfrac{19}{20}\textup{V}.$

7 0

3 years ago

como calcular la cantidad de horas por proyecto si un contratista tiene 5,000 horas-hombres y el costo es de $10 y $12 por proye

Tju [1.3M]

Answer:

Each project has 2.500 man-hours

Step-by-step explanation:

Available man hours: 5000

For two projects Costs $

X: project A 10

Y: project B 12

Approach:

X + Y = 5000 => X = 5000 - Y

10 * X + 12 * Y = 55000

replacing:

10 * (5000 - Y) + 12 * Y = 55000

50000 - 10 * Y + 12 * Y = 55000

2 * Y = 55000 - 50000

Y = 5000/2

Y = 2500

For X:

X = 5000 - 2500

X = 2500

The number of hours available for each project are:

Projects Man hours

X: project A 2500

Y: project B 2500

6 0

3 years ago

If p and q are both true, then which of the following statements has the same truth-value as ~p → q?

olganol [36]

If p and q are both true, then

$\neg p \implies q$

is an implication of the form

$F \implies T$

which is true, because every implication starting with false is true, i.e.

$F \implies T = T,\quad F \implies F = T$

So, we're looking for an expression evaluating to true. Let's see what we have:

A) is an AND proposition. Logical AND is true only if both parts are true. So, you have

$\neg P \land \neg Q = F \land F = F$

So it's not the right option.

B) is an OR proposition. Logical OR is true whenever one of the two parts is true. So, you have

$\neg P \lor\neg Q = F \lor F = F$

So it's not the right option.

C) is again an AND proposition. You have

$P \land \neg Q = T \land F = F$

So this is not the right option.

D) Finally, the last one is again an implication, and again it starts with false:

$\neg Q \implies P = F \implies T = T$

So this is true, and thus is the correct option.

8 0

3 years ago

Lines a and b are perpendicular. The equation of line a is y=1/3x+3. What is the equation of line b

kykrilka [37]

Perpendicular lines have slopes that are negative reciprocals to each other, that is, if one slope is a/b, the other is -b/a
in this case, the given slope is 1/3, so the other line's slope is -3/1, which is -3
from the graph we see that the y intercept of line b is -4, so the equation of line b is: y=-3x-4

6 0

4 years ago