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Mademuasel [1]
3 years ago
9

Determine whether each argument is valid. if the argument is valid, give a proof using the laws of logic. if the argument is inv

alid, give values for the predicates p and q over the domain {a, b} that demonstrate the argument is invalid. (a) ∃x (p(x) ∧ q(x)) ∴ ∃x q(x) ∧ ∃x p(x) hegg
Mathematics
1 answer:
Ede4ka [16]3 years ago
6 0
FGYYFFHHFFUYTREDVUYTDCVBYTRSXCJYTRDHFGCT
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Use trig identities to transform the left side of the equation to the right side.
Taya2010 [7]

<u>Answer and explanation</u>

(1+sinθ)(1-sinθ)=cos²θ

We are to prove that the left hand side is equal to the right hand side.

(1+sinθ)(1-sinθ) = 1(1-sinθ) + sinθ(1-sinθ)

                         = 1 - sinθ + sinθ - sin²θ

                          = 1 - sin²θ

From the trigonometric identity sin²θ + cos²θ = 1,

1 - sin²θ = cos²θ


7 0
3 years ago
Adult female height is normally distributed with a mean of 65.3 inches and a standard deviation of 2.32 inches. a) If an adult f
emmasim [6.3K]

Answer:

0.0423 is the probability that the adult female has a height less than 61.3 inches.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 65.3 inches

Standard Deviation, σ = 2.32 inches

We are given that the distribution of adult female height is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(adult female has a height less than 61.3 inches)

P( x < 61.3) = P( z < \displaystyle\frac{61.3 - 65.3}{2.32}) = P(z < -1.7241)

Calculation the value from standard normal z table, we have,  

P(x < 61.3) =0.0423 = 4.23\%

0.0423 is the probability that the adult female has a height less than 61.3 inches.

5 0
4 years ago
Linear function, pls help
True [87]

Answer:

A

Step-by-step explanation:

4 0
3 years ago
5 times the sum of F amd 13 equala 125
Zolol [24]

Answer:

5(F+13)=125 F=12

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
At a small college somewhere on the East coast, 20% of the girls and 30% of the boys smoke at least once a week.
Nezavi [6.7K]

Answer: Required mean would be 15.

Step-by-step explanation:

Since we have given that

Number of girls G= 75

Number of boys B= 100

Probability that girls smoke = P₂ = 0.20

Probability that girls don't smoke = P'₂=1-0.20=0.80

Probability that boys smoke = P₁ = 0.30

Probability that boys don't smoke = P'₁=1-0.30=0.70

We need to find the mean of the sampling distribution of the difference in the sample proportion of girl smokers and boys smokers.

So, it becomes,

E[P_1-P_2]=E[P_1]-E[P_2]\\\\=B\times P_1-G\times P_2\\\\=100\times 0.30-75\times 0.20\\\\=30-15\\\\=15

Hence, required mean would be 15.

6 0
3 years ago
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