Ask question

Ask question

All categories

3 years ago

15

Felicity's dog eats no more than two cups of dog food per day. Felicity's dog eats at least one-quarter cup more than one-half o

f the amount Martin's dog eats. If the amount of food that Martin's dog eats is represented by using m, which inequality represents the situation?

1 answer:

horrorfan [7]3 years ago

3 0

Answer:

$\frac{1}{4}+\frac{m}{2} \leq x\leq 2$

$x$ denotes amount of food that Felicity's dog eats

Step-by-step explanation:

Given:

Felicity's dog eats no more than two cups of dog food per day.

Felicity's dog eats at least one-quarter cup more than one-half of the amount Martin's dog eats.

The amount of food that Martin's dog eats is represented by using $m$

To find: the inequality that represents the situation

Solution:

Amount of food that Martin's dog eats = $m$

Amount of food that Felicity's dog eats ≤ 2

Also,

Amount of food that Felicity's dog eats $\geq \frac{1}{4}+\frac{m}{2}$

Therefore,

$\frac{1}{4}+\frac{m}{2}\leq$ Amount of food that Felicity's dog eats ≤ 2

Let $x$ denotes amount of food that Felicity's dog eats.

$\frac{1}{4}+\frac{m}{2}$ ≤ $\frac{1}{4}+\frac{m}{2} \leq x\leq 2$

You might be interested in

The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

$V = \frac{1}{3}\pi r^{2}h$

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

$V = \frac{1}{3}\pi r^{2}h$

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

3 years ago

Coach Chapman has 54 students signed up for a jump rope competition. He only has 18 jump ropes. What is the ratio of jump ropes

Andrei [34K]

Answer:

1:3

Step-by-step explanation:

The question is asking what the ratio of jump ropes to students is.

The order of the question matters.

Since they ask for the jump ropes first and then the students, we

get a ratio of 18:54.

Find the GCF (Greatest Common Factor)

The GCF is 18.

Divide 18:54 by 18.

18/18=1

54/18=3

The answer is 1:3.

6 0

3 years ago

How many toys were stuffed animals

Umnica [9.8K]

Answer:

It would be the first one.

Step-by-step explanation:

The way you figure it out is that it said that there was a total of 80 stuffed animals, so model B is out. Then, you change the percent into a decimal by moving the decimal point over to the right 2 times and you get 0.30. Finally, you multiply 80 by 0.30 and you get 24 stuffed animals.

4 0

3 years ago

Read 2 more answers

A bag has 2 blue marbles and 16 red marbles. half of the red marbles are made of plastic. a marble is selected a random from the

bija089 [108]

there are 2 blue marbles, 8 red marbles, and 8 plastic red marbles

there are 18 marbles in total

8/18

6 0

3 years ago

Read 2 more answers

Find the side length of a cube with a volume of 166 m

marin [14]

The answer is 5.5 m.

Cube
Volume = length x width x height

Since the length, width and the height are the same in cube, the formula can be:

Volume = length^3

Let x metres be the side length of the cube.

166 = x^3

x = ∛166

x = 5.495864.....

x = 5.5 (nearest tenth)

8 0

3 years ago