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grandymaker [24]
3 years ago
13

Lin has a pet German shepherd that weighs 38 when measured in one unit and 84 when measured in a different unit. which measureme

nt is in pounds, and which is in kilograms?
Mathematics
1 answer:
harkovskaia [24]3 years ago
7 0

Given :

Lin has a pet German shepherd that weighs 38 when measured in one unit and 84 when measured in a different unit.

To Find :

Which measurement is in pounds, and which is in kilograms.

Solution :

We know, mass in kg and pounds are related as :

m_P = 2.2m_{kg}

Putting, m_{kg}=38 and m_P=84 , we get :

LHS = 84

RHS = 2.2 × 38 = 83.6 ≈ 84

Since, LHS = RHS .

Therefore, 38 units is Kg and 84 units in Pounds.

Hence, this is the required solution.

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Carlo and Anita make mailboxes and toys in their wood shop. Each mailbox requires 1 hour of work from Carlo and 4 hours from Ani
Natali [406]

Answer:

$80

Step-by-step explanation:

Let the number of hours required to make a mailbox = x

Let the number of hours required to make a toy = y

Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita.

Each toy requires 1 hour of work from Carlo and 1 hour from Anita.

The table below summarizes the information for ease of understanding.

\left|\begin{array}{c|c|c|c}&$Mailbox(x)&$Toy(y)&$Maximum Number of Hours\\--&--&--&------------\\$Carlo&1&1&12\\$Anita&4&1&24\end{array}\right|

We have the constraints:

x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0

Each mailbox sells for $10 and each toy sells for $5.

Therefore, Revenue, R(x,y)=10x+5y

The given problem is to:

Maximize, R(x,y)=10x+5y

Subject to the constraints

x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0

The graph is plotted and attached below.

From the graph, the feasible region are:

(0,0), (6,0), (4,8) and (0,12)

At (6,0), 10x+5y=10(6)+5(0)=60

At (4,8), 10(4)+5(8)=80

At (0,12), 10(0)+5(12)=60

The maximum revenue occurs when they use 4 hours on mailboxes and 8 hours on toys.

The maximum possible revenue is $80.

5 0
3 years ago
A 2X2 square is centered at the origin. It is dilated by a factor of 3. What are coordinates of the vertices of the square?
Vesna [10]

Answer:

The vertices are:

A' = (-3, -3)

B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

Step-by-step explanation:

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1),  B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

B(1, -1) = 3(1, -1) = B'(3, -3)

C(1, 1) = 3(1, 1) = C'(3, 3)

D(-1, 1) = 3(-1, 1) = D'(-3, 3)

7 0
3 years ago
Simplify.<br><br> f-1g-1<br><br> a. f/g<br> b.g/f<br> c.1/fg<br> d.fg
fiasKO [112]
You can rewrite this equation as "f - g - 1". That's all that I see that you can do with this.
4 0
3 years ago
Due today HELP PLEASEEEEE!!!
Deffense [45]

Answer:

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4 0
3 years ago
A 2 -gallon container of window costs 31.36. what is the price per cup
irinina [24]

Answer:

0.98 $/cup

Step-by-step explanation:

The final answer asks for price/cup, as "per" means "divided by".

So, our final units will be in $/cup.

We are given that for every 2 gallons, it will cost $31.36.

In order to get from gallons to cups, we need to convert units.

In 1 gallon, there are 16 cups.

So, our conversion factor will be 16 cups/1 gallon.

\frac{31.36}{2} *\frac{1}{16} \\\\= 0.98$/cup

Important things to note:

- With these types of problems, it makes it much easier if you just figure out what units you need in the final answer, and then use conversions and dimensional analysis to get the answer

8 0
2 years ago
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