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zaharov [31]
2 years ago
8

The density of apple juice is 1.04 grams per cm3. The density of fruit syrup is 1.6 grams per cms The density of sparkling water

is 0.99 grams per cm3. 35 cm of apple juice are mixed with 25 cm3 of fruit syrup and 270 cm3 of sparkling water to make a drink with a volume of 330 cm3. Work out the density of the drink. Give your answer correct to 3 decimal places.
Mathematics
1 answer:
natulia [17]2 years ago
3 0

Answer:

Density = 1.042  grams /cm^3

Step-by-step explanation:

Work out the mass of each of three in a unit volume (cm^3)

Givens

  • Apple Juice = 1.04 grams / cm^3
  • Fruit Syrup = 1.6 grams / cm^3
  • Sparkling water = 0.99 grams / cm^3

Mixture

35 cm^3 Apple Juice = 1.04 grams / cm^3 * 35 cm^3 = 36.4 grams

25 cm^3 Fruit = 1.6 grams/cm^3 * 25 cm^3 =                  40    grams

270 cm^3 water = 0.99 * 270                                        267.3 grams

Total Mixture

  • Volume = 25 + 35 + 270 = 330 cm^3
  • Mass =  36.4 + 40 + 267.3 = 343.7 grams

Density

Density = mass / volume = 343.7 / 330 = 1.0415

Answer

1.042 grams / cm^3  

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Cheese costs $4.40 per pound. Find the cost per kilogram. (1kg = 2.2lb)
MakcuM [25]

Answer:

The cost is $9.70 per kilogram.

Step-by-step explanation:

This can be solved by a rule of three.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

In this problem, the measures are the weight of the cheese and the price. As the weight increases, so does the price. It means that this is a direct rule of three.

Solution:

The problem states that cheese costs $4.40 per pound. Each kg has 2.2 pounds. How many kg are there in 1 pound. So:

1 pound - xkg

2.2 pound - 1 kg

2.2x = 1

x = \frac{1}{2.2}

x = 0.45kg

Since cheese costs $4.40 per pound, and each pound has 0.45kg, cheese costs $4.40 per 0.45kg. How much does is cost for 1kg?

$4.40 - 0.45kg

$x - 1kg

0.45x = 4.40

x = \frac{4.40}{0.45}

x = 9.70

The cost is $9.70 per kilogram.

6 0
2 years ago
Heidi is saving for a new bike. She has already saved $57. If Heidi earns
PtichkaEL [24]

Answer:

8 hours

Step-by-step explanation:

57 + 9h = 129

9h = 72

h = 8

7 0
2 years ago
Read 2 more answers
A cell phone company charges a $10 flat fee plus $0.05 per minute for minutes up to 600. For minutes over 600, the company
mash [69]

Answer:

In both the cases, the given total amount is given as:

T  = 10 + 0.05 m     (when minutes talked m   < 600)

T   =  40   +   0.15 k           (when minutes talked  k   > 600)

Step-by-step explanation:

Here, the flat fee by the phone company = $10

The charge for each minute for  first 600 minutes = $0.05

The per minute cost after 600 minutes  = $0.15

Let us assume the number of minutes talked = m

<u>Case 1:</u><u> when the minutes talked is less than 600 minutes.</u>

Total Charges = Flat Fee  +  0.05 x ( the minutes talked)

or, T   = $10 + m ($0.05)

or T  = 10 + 0.05 m     (when m  < 600)

<u>Case 2:</u><u> when the minutes talked is more than 600 minutes.</u>

Let us assume the minutes talked over 600 = k minutes

Total Charges = Flat Fee  + Charges for 600 minutes  +  0.15 x ( the minutes talked over 600)

or, T   = $10 + 600 ($0.05)  + k($0.15)

or T   =  10 + $30     +   0.15 k            (when k   > 600)

⇒  T   =  40   +   0.15 k            (when k   > 600)

Hence, in both the cases, the given total amount is given as:

T  = 10 + 0.05 m     (when m  < 600)

T   =    T   =  40   +   0.15 k            (when k   > 600)

7 0
2 years ago
If the tax rate on homes in Topeka, Kansas is 2.4 percent of their value and Bonnie owns a $100,000 house, how much will the rea
Ksivusya [100]

Answer:

  $200

Step-by-step explanation:

The annual tax bill is ...

  2.4% × $100,000 = $2,400

On a monthly basis, that is ...

  $2400/(12 mo) = $200/mo

Taxes will add $200 per month to Bonnie's mortgage payment.

3 0
2 years ago
Evaluate the expression. P(9, 3) · P(5, 4)
boyakko [2]

Answer:

P(9,3) *P(5,4)

And if we use the permutation formula given by:

nPx = \frac{n!}{(n-x)!}

And replacing we got:

\frac{9!}{6!} \frac{5!}{4!}= 504*5 = 2520

Step-by-step explanation:

For this problem we want to find the following expressionÑ

P(9,3) *P(5,4)

And if we use the permutation formula given by:

nPx = \frac{n!}{(n-x)!}

And replacing we got:

\frac{9!}{6!} \frac{5!}{4!}= 504*5 = 2520

6 0
2 years ago
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