Write a comparison sentence that includes the words as long as and compares

A bucket has 16 inches of water in it but there is a hole in the bottom. Use interval notation to write the domain and range of

Dennis_Churaev [7]

Answer: range: {0in, 16in}

domain {0min, 12.8 min}

Step-by-step explanation:

When we have a function:

f(x) = y.

The range is the set of possible values of y and the domain is the set of all the possible values of x.

In this case, our function is:

H(x) = 16 - 1.25*x

which is a linear equation, and we know that the linear equations are defined (for range and domain) in the set of all the real numbers, but this is a physical situation, so we must see at the real problem.

The bucket can not have more water than the initial amount, 16 inches, so this is the maximum in the range.

The minimum height of water that we can find in the bucket is 0 inches (so the bucket is empty) then this is the minimum of the range.

Then we can write the range as:

R: 0in ≤ y ≤ 16in. = {0in, 16in}

Now we can find the extremes of the domain by using the extremes of the range:

y = 16 = 16 - 1.25*x

0 = -1.25*x

then we have x = 0min, this will be the minimum of the domain.

Now using the minimum of the range y = 0 we have:

y = 0 = 16 - 1.25*x

1.25*x = 16

x = 16/1.25 = 12.8 mins

This is the maximum time in the domain (because after this time, there is no water in the bucket)

Then the domain is:

D: 0min ≤ x ≤ 12.8 min

5 0

3 years ago

A company has 31 salespeople. A board member at the company asks for a list of the top 4 salespeople, ranked in order of effecti

kvv77 [185]

Answer:

31465 ways

Step-by-step explanation:

Given data

Let us apply the combination formula

nCr = n! / r! * (n - r)!

n= 31

r= 4

substitute

= 31!/4!(31-4)!

= 31!/4!(27)!

= 31*30*29*28*27!/ 4!(27)!

= 31*30*29*28/4!

=31*30*29*28/4*3*2*1

=755160/24

=31465 ways

Hence there are 31465 possible ways to rank it

8 0

3 years ago

A ball of mass 0.4 kg flies through the air at low speed, so that air resistance is negligible. What is the net force acting on

arsen [322]

Answer:

-3.92 N

Step-by-step explanation:

We are given that

Mass of ball=0.4 kg

Acceleration due to gravity= $-9.8m/s^2$

Because the ball flies against to gravity

We have to find the net force acting on the ball while it is in motion.

We know that when there is no air resistance then the net force acts on the ball is equal to weight of ball.

Net force,F =mg

Substitute the values then we get

$F=0.4(-9.8)$

$F=-3.92N$

Hence, the net force acting on the ball while it is on motion=-3.92 N

6 0

3 years ago

Carlos is using the quadratic formula to find the solutions of y=3x^2-5x-2. Which of the following will simplify to the correct

Nana76 [90]

Answer:

$Fx=\frac{5\pm\sqrt{25+24} }{6}$

Step-by-step explanation:

A quadratic equation in one variable given by the general expression:

$ax^2+bx+c$

Where:

$a\neq 0$

The roots of this equation can be found using the quadratic formula, which is given by:

$x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

So:

$y(x)=3x^2-5x-2=0$

As you can see, in this case:

$a=3\\b=-5\\c=-2$

Using the quadratic formula:

$x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}=\frac{-(-5)\pm\sqrt{(-5)^2-4(3)(-2)} }{2(3)}=\frac{5\pm\sqrt{25+24} }{6}$

Therefore, the answer is:

$Fx=\frac{5\pm\sqrt{25+24} }{6}$

4 0

3 years ago

Find the missing lengths and leave answers as radicals in simplest form?

ElenaW [278]

Answer:

x=6

y=3

Step-by-step explanation:

y(side)= x

x(side)=2x

3rd side (3 $\sqrt{3}$ ) = x $\sqrt{3}$

x=3;

x= 2(3)=6

y=(3)=3

5 0

3 years ago

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