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3 years ago

To get a 100 kilograms of a 48% fat content chocolate how many kilograms of a 30% and 50% mix should be used

1 answer:

8 0

A kilogram %30 chocolate,
b kilogram %50 chocolate,
a+b = 100 kilogram chocolate,

48.(a+b) = 30.a + 50.b
48a + 48b = 30a + 50b
18a = 2b
b = 9a

a+b = a + 9a = 10a = 100 kg
a = 10 kg
b = 9.a = 90 kg

You should use,

10 kg %30 chocolate,
90 kg %50 chocolate

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Deci (símbolo d) es un prefijo del Sistema Internacional que indica un factor de 10−1 (1/10) o una décima parte.

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10 months ago

Which is the correct algebraic expression after combining like terms? 6+8x-7-x

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Answer:

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6+8x-7-x

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3 years ago

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2 years ago

What is your sister’s total cost under each of the two plans?2. Suppose your sister doubles her monthly usage to 3,500 minutes a

chubhunter [2.5K]

Answer:

(1) The total cost under Plan A is $92 and the total cost under Plan B is $515.

(2) The total cost under Plan A is $92 and the total cost under Plan B is $1,030.

Step-by-step explanation:

The question is incomplete, so the complete question is below:

$A\ cell \ phone \ company\ offers\ two \ different \ plans.$

$Plan\ A\ costs\ \$92\ per\ month\ for\ unlimited\ talk\ and\ text.\ Plan\ B\ costs \ $0.20\ per\ minute\ plus\ \$0.10\ per\ text\ message\ sent.$ $You\ need \ to\ purchase \ a \ plan \ for\ your \ 14-year-old \ sister$ $.Your\ sister\ currently \ uses\ 1,750 \ minutes\ and \ sends\ 1,650 \ texts\ each \ month.$ $(1) What\ is\ your \ sister's\ total\ cost\ under \ each\ of\ the\ two\ plans?$

$(2) Suppose\ your\ sister\ doubles\ her\ monthly\ usage \ to\ 3,500\ minutes \ and\ sends\ 3,300 \ texts.$ $What \ is \ your \ sister's \ total \ cost \ under \ each \ of \ the \ two \ plans?$

Now, to find (1) total cost for each of the two plans. (2) Total cost under each of the two plans, if sister doubles her monthly usage to 3,500 minutes and sends 3,300 texts.

As, the Plan A is for unlimited talk and text

Cost of the Plan A = $92.

Now, to find the cost under Plan B:

According to question:

Rate of call per minute is $0.20 and per text is $0.10.

Calls she uses currently is 1,750 minutes and text 1,650.

So, to get the cost of Plan B:

$0.20\times 1750+0.10\times 1650$

$=350+165$

$=515.$

Thus, Plan B costs $515.

Now, to get the total cost as, sister doubles her monthly usage to 3,500 minutes and sends 3,300 texts.

As, the Plan A is same in both cases and is for unlimited text and calls.

So, cost of Plan A = $92.

As, the monthly usage is double.

Calls in minutes are 3,500.

Texts are 3,300.

Now, to get the total cost under Plan B:

$0.20\times 3500+0.10\times 3300$

$=700+330$

$=1030.$

Hence, the cost of Plan B = $1,030.

Therefore, (1) The total cost under Plan A is $92 and the total cost under Plan B is $515.

(2) The total cost under Plan A is $92 and the total cost under Plan B is $1,030.

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3 years ago

A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x,

tatiyna

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

7 0

3 years ago