63/63 into mixed number

Find the truth value of (p ^ q) v r. (Make a truth table.)

alexgriva [62]

Answer:

p: (-4)2 > 0

q: An isosceles triangle has two congruent sides.

r: Two angles, whose measure have a sum of 90, are supplements.

Step-by-step explanation:

p: (-4)2 > 0

q: An isosceles triangle has two congruent sides.

r: Two angles, whose measure have a sum of 90, are supplements.

4 0

3 years ago

Which characteristic of a data set makes a linear regression model unreasonable?

LiRa [457]

Which characteristic of a data set makes a linear regression model unreasonable?

Answer: A correlation coefficient close to zero makes a linear regression model unreasonable.

If the correlation between the two variable is close to zero, we can not expect one variable explaining the variation in other variable. For a linear regression model to be reasonable, the most important check is to see whether the two variables are correlated. If there is correlation between the two variable, we can think of regression analysis and if there is no correlation between the two variable, it does not make sense to apply regression analysis.

Therefore, if the correlation coefficient is close to zero, the linear regression model would be unreasonable.

6 0

3 years ago

Read 2 more answers

1.) (-6) (-7) =

Jobisdone [24]

$\left(-6\right)\left(-7\right)=42$

$46=2\quad :\quad \mathrm{False}$

$\left(-9\right)+25=16$

$\left(13\right)\left(-3\right)=-39$

$14+3=17$

5 0

2 years ago

Read 2 more answers

Evaluate 5p+cd when c=1/5 and d=15

Anna [14]

Answer: If solving for P it is p = -3/5

If you are just wanting the equation it is 5p+3

Step-by-step explanation: Plug in c and d into 5p+cd

You get 5p+(1/5)(15)

Once done with the math it is 5p+3

7 0

3 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago