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Aleks [24]
3 years ago
13

5/16 ÷ 5/12

Mathematics
1 answer:
harkovskaia [24]3 years ago
4 0

Answer:

1.) 3/4

2.) 44/5 or 8 4/5

3.) 17/6 or 2 5/6

Step-by-step explanation:

1.) 5/16 ÷ 5/12

To divide a fraction by another fraction, reciprocate (put the numerator to denominator and vice versa) the divisor then change the sign to multiplication:

5/16 × 12/5

5 × 12 / 16 × 5

Cancel out 5 since both numerator and denominator has it:

12 / 16

Divide both by 4:

12 ÷ 4 / 16 ÷ 4

3/4

2.) 3 1/5 • 2 3/4

You have to convert the fractions first to improper fractions by multiplying the denominator to the whole number then adding the numerator to the product:

3 1/5 = 3×5 + 1 = 16/5

2 3/4 = 2 × 4 + 3 = 11/4

Now you can multiply the numerator to numerator then denominator to denominator:

Since 16 is a factor of 4, you can cancel it out, which leaves 4:

16 / 5 × 11/4

4 × 11 / 5 × 1

44/ 5

3.) 6 3/8 ÷ 2 1/4

Convert to improper fraction:

6 3/8 = 6× 8 + 3 = 51/8

2 1/4 = 4 × 2 + 1 = 9/4

(51 × 4)/ (9×8)

51 × 1/ 9× 2

51 / 18

Divide by 3:

17/6

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A certain car rental location charges a daily fee as well as a mileage charge. On one trip a businessman rented a car for the da
nikklg [1K]

Answer:

x\approx 267\ miles

Step-by-step explanation:

<u>Linear Modeling</u>

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

f(x)=mx+b

For the problem at hand, we must pick the adequate variables according to the data provided.

The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:

c = the charge for renting a car in dollars

x = the distance driven by the businessman in miles

Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:

c = mx+b

We must find the values of m and b with the data provided. Substituting the first point:

79 = 150m+b

Substituting the second point:

63.70 = 65m+b

Both equations form the following system:

\left\{\begin{matrix}150m+b=79\\ 65m+b=63.70 \end{matrix}\right.

Subtracting both equations:

150m-65m=79-63.70

Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:

85m=15.3

Solving:

m=15.3/85=0.18

From the first equation

79 = 150m+b

Solving for b:

b=79-150m=79-150(0.18) = 52.

The model for the problem is:

c=0.18x+52

Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100

100=0.18x+52

Solve for x:

0.18x+52=100

0.18x=100-52=48

x=48/0.18=266.67

Rounding to the closest integer:

\boxed{x\approx 267\ miles}

7 0
3 years ago
7m + 3mn when m = 8 and n = 14
Kazeer [188]

Answer:

392

Step-by-step explanation:

m = 8 and n = 14

Substituting the values of m and n in the question, we get :

7m + 3mn

=( 7 x 8) +(3 x 8 x 14)

= 56 + 336

= 392

8 0
3 years ago
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iris [78.8K]

Answer:

8

Step-by-step explanation:

4 0
2 years ago
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How many 6-ounces cups can be filled from 4 gallons of juice
solmaris [256]
1 gallon = 128 oz
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Please help me! thank you so much
Luda [366]

The Correct Answer Is f(x)=2.5x+5

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