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3 years ago

Let p: The number is even.

Mathematics

1 answer:

Gemiola [76]3 years ago

8 0

<u>Answer:</u>

The statement represented by p ∧ q is number is even and prime. Hence statement 1 is correct

<u>Solution:</u>

Given that

p means number is even

q Means number is prime.

We need to find meaning of p ∧ q

lets see what is meaning of symbol ∧.

∧ is a conjunction symbol which joins two statement with and operator.

In our case two statements are p means number is even and q means number is prime.

So p ∧ q means p and q means number is even and number is prime. that is number is even and prime.

Hence first statement in the given option that is number is even and prime is represented by p ∧ q.

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zloy xaker [14]

Part A: $y=-\frac{5}{4} x+\frac{35}{2}$ is the equation of the line.

Part B: Anika worked 17.5 hours on day 0.

Part C: The setup time decreases with 1 hour and 15 min per day.

Explanation:

Part A: Let us find the equation of the line using the points (2,15) and (6,10)

The equation of the line is given by,

$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \cdot\left(x-x_{1}\right)$

Substituting, we get,

$y-15=\frac{10-15}{6-2} (x-2)$

Simplifying, we have,

$y-15=-\frac{5}{4} (x-2)$

$y-15=-\frac{5}{4} x+\frac{5}{2}$

Subtracting both sides by 15, we get,

$y=-\frac{5}{4} x+\frac{35}{2}$

Hence, the equation of the line is $y=-\frac{5}{4} x+\frac{35}{2}$

Part B: To determine the number of hours Anika worked on day 0, let us substitute x = 0 in the equation of the line.

Thus, we get,

$y=\frac{35}{2}\\y=17.5$

Hence, Anika worked 17.5 hours on day 0.

Part C: The setup time decrease per day can be determined using the slope.

The formula for slope is given by

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting , we have,

$m=\frac{10-15}{6-2}=-\frac{5}{4}$

Converting the fraction into hours and minutes, we get,

$-\frac{5}{4}\times60=-75 min$

Since, 1 hour = 60 min

Subtracting 60 and 75 = 15 min

Thus, the setup time decreases with 1 hour and 15 min per day.

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What is the value of x2+9x+20 when x could be -5, -3 or -6

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Answer:

Step-by-step explanation:

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