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3 years ago

Two statements are logically equivalent when:

Mathematics

1 answer:

-BARSIC- [3]3 years ago

7 0

<h2>Answer:</h2>

C. The two statements agree in point of truth or falsehood in virtue of their logical structure alone, i.e. the two statement are true or false in exactly the same conditions.

<h2>Step-by-step explanation:</h2>

For two statements to be logically equivalent, their truth values (true or false) must be the same for every variation of their constituent variables. In other words, if the truth tables of both statements are the same for every possible value of their variables, then they are logically equivalent.

For example;

The two statements P ∩ (Q U R) and (P ∩ Q) ∪ (P ∩ R) are logically equivalent.

If P, Q and R are all true, then;

P ∩ (Q U R) = true

(P ∩ Q) ∪ (P ∩ R) = true

If P, Q and R are all true, then;

P ∩ (Q U R) = false

(P ∩ Q) ∪ (P ∩ R) = false

If P = false, Q = true and R = true, then;

P ∩ (Q U R) = false

(P ∩ Q) ∪ (P ∩ R) = false

Checking for all other possible combinations of truth values of P, Q and R will always give the same results for the two statements, therefore, they are logically equivalent.

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3 years ago

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Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally

rusak2 [61]

Answer:

(a) The probability that the thickness is less than 3.0 mm is 0.119.

(b) The probability that the thickness is more than 7.0 mm is 0.119.

(c) The probability that the thickness is between 3.0 mm and 7.0 mm is 0.762.

Step-by-step explanation:

We are given that thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.0 millimeters (mm) and a standard deviation of 1.7 mm.

Let X = thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village.

So, X ~ Normal( $\mu=5.0,\sigma^{2} =1.7^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean thickness = 5.0 mm

$\sigma$ = standard deviation = 1.7 mm

(a) The probability that the thickness is less than 3.0 mm is given by = P(X < 3.0 mm)

P(X < 3.0 mm) = P( $\frac{X-\mu}{\sigma}$ < $\frac{3.0-5.0}{1.7}$ ) = P(Z < -1.18) = 1 - P(Z $\leq$ 1.18)

= 1 - 0.8810 = 0.119

The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.

(b) The probability that the thickness is more than 7.0 mm is given by = P(X > 7.0 mm)

P(X > 7.0 mm) = P( $\frac{X-\mu}{\sigma}$ > $\frac{7.0-5.0}{1.7}$ ) = P(Z > 1.18) = 1 - P(Z $\leq$ 1.18)

= 1 - 0.8810 = 0.119

The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.

(c) The probability that the thickness is between 3.0 mm and 7.0 mm is given by = P(3.0 mm < X < 7.0 mm) = P(X < 7.0 mm) - P(X $\leq$ 3.0 mm)

P(X < 7.0 mm) = P( $\frac{X-\mu}{\sigma}$ < $\frac{7.0-5.0}{1.7}$ ) = P(Z < 1.18) = 0.881

P(X $\leq$ 3.0 mm) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{3.0-5.0}{1.7}$ ) = P(Z $\leq$ -1.18) = 1 - P(Z < 1.18)

= 1 - 0.8810 = 0.119

The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.

Therefore, P(3.0 mm < X < 7.0 mm) = 0.881 - 0.119 = 0.762.

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4 years ago

Which of the following equations describes the line shown below? Check all that apply.

scoundrel [369]

Answer:

B. y = 2x - 2

E. $y + 4 = 2(x + 1)$

F. $y - 6 = 2(x - 4)$

Step-by-step explanation:

The equation of the line can be found using either the point-slope equation or the slope-intercept equation.

✔️Equation of the line in point-slope using the slope and the coordinates of the point (4, 6):

Slope = m = change in y/change in x

Using (4, 6) and (-1, -4),

m = (-4 - 6)/(-1 - 4)

m = -10/-5

m = 2

Substitute m = 2, and (a, b) = (4, 6) into the point-slope equation form $y - b = m(x - a)$

Thus:

$y - 6 = 2(x - 4)$

✔️Equation of the line in point-slope using the slope and the coordinates of the point (-1, -4):

Slope = m = 2

Substitute m = 2, and (a, b) = (-1, -4) into the point-slope equation form $y - b = m(x - a)$

Thus:

$y - (-4) = 2(x - (-1))$

$y + 4 = 2(x + 1)$

✔️Equation of the line in slope-intercept form, y = mx + b

Where,

m = slope = 2

b = y-intercept = -2 (the point where the line intercepts the y-axis)

Thus, substitute m = 2 and b = -2 into y = mx + b

y = 2x + (-2)

y = 2x - 2

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

SHAYNA FREEL PLANS TO BUY $17.45 WORTH OF STATIONERY SUPPLIES. IF THE SALES TAX IS 13%, HOW MUCH WILL SHAYNA PAY?

Rainbow [258]

9514 1404 393

Answer:

$19.72

Step-by-step explanation:

The sales tax is 13% of $17.45:

0.13 × $17.45 = $2.27 . . . . . . rounded (up) to the nearest cent

Then the total Shayna will pay is ...

$17.45 +2.27 = $19.72

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