Find the value of t and s

Which expression is equivalent to 2(a+3) when a equals 3 2(3) 5(3) 2(3)+3 2(3)+6

sammy [17]

2(3+3) or 2(3)+6, so the answer is the third option. It’s just using the distributive property.

8 0

3 years ago

Read 2 more answers

Find the slope of the line that passes through the points (0, 6) and (20, 14).

mihalych1998 [28]

Answer:

2/5

Step-by-step explanation:

4 0

2 years ago

Recall, we have five connectives in propositional logic ¬, ∧, ∨, →, ↔ (negation, conjunction, disjunction, conditional and bicon

Free_Kalibri [48]

Answer:

(a) ¬(p→¬q)

(b) ¬p→q

(c) ¬((p→q)→¬(q→p))

Step-by-step explanation

taking into account the truth table for the conditional connective:

p | q | p→q

T | T | T

T | F | F

F | T | T

F | F | T

(a) and (b) can be seen from truth tables:

for (a) p∧q:

p | q | ¬q | p→¬q | ¬(p→¬q) | p∧q

T | T | F | F | T | T

T | F | T | T | F | F

F | T | F | T | F | F

F | F | T | T | F | F

As they have the same truth table, they are equivalent.

In a similar manner, for (b) p∨q:

p | q | ¬p | ¬p→q | p∨q

T | T | F | T | T

T | F | F | T | T

F | T | T | T | T

F | F | T | F | F

again, the truth tables are the same.

For (c)p↔q, we have to remember that p ↔ q can be written as (p→q)∧(q→p). By replacing p with (p→q) and q with (q→p) in the answer for part (a) we can change the ∧ connector to an equivalent using ¬ and →. Doing this we get ¬((p→q)→¬(q→p))

4 0

3 years ago

175,000 In Scientific notation

Nataly [62]

Answer:

1.75*10 to the power of 5

Step-by-step explanation:

start by moving the decimal over until only one number is in front of the decimal. this is because in scientific notation a number can't be higher than 9.

check how many places you move the decimal over (5). 1.75000 needs to be simplified (since that's the point of scientific notation) and can be simplified to 1.75.

the answer is 1.75 multiplied by ten to the power of digits the decimal moved (5) so the answer is 1.75*10 to the power of 5

4 0

3 years ago

Suppose a normally distributed set of data with 4800 observations has a mean of 195 and a standard deviation of 12. Use the 68-9

Artemon [7]

Answer:

The number of observations in the data set expected to be below a value of 231 is of 4793.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 195

Standard deviation = 12

The normal distribution is symmetric, which means that 50% of the observations are above the mean and 50% are below.

Proportion of observations below 231:

231 = 195 + 3*12

So 231 is three standard deviations above the mean.

Of the 50% of observations below the mean, all are below 231.

Of the 50% of observations above the mean, 99.7% are between the mean of 195 and three standard deviations above the mean(231).

So, the proportion of observations below 231 is:

$P = 0.5*1 + 0.5*0.997 = 0.9985$

Out of 4800:

0.9985*4800 = 4793

The number of observations in the data set expected to be below a value of 231 is of 4793.

4 0

2 years ago