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vredina [299]
3 years ago
10

You are considering renting a car from two different rental companies. Proxy car rental company charges. $0.32 per mile plus an

$18 surcharge. YourPal rental company charges $0.36 per mile plus a $12 surcharge.
For what distance is the price the same for both companies?
Mathematics
1 answer:
mash [69]3 years ago
6 0
Let y = total charge for a car rental and x = miles driven
Proxy car equation: y = 0.32x + 18
YourPal equation: y = 0.36x + 12

Set equations right sides equal to each other... meaning their cost, y, are equal
0.32x + 18 = 0.36x + 12
18 = 0.04x + 12  (subtract 0.32x from both sides of the equation)
6 = 0.04x            (subtract 12 from both sides of the equation)
150 = x               (divide both sides of the equation by 0.04)
ANSWER: 150 miles
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Determine each of the following.
castortr0y [4]

Answer:

(a) \{1,2,3,4,5,6,7,8,9,10\}

(b) 10

(c) \{\}

(d) 0

(e) 1024

Step-by-step explanation:

(a)

A = {x ∈ Z | 0 < x, x² ≤ 100}

We need to find all the elements of given set.

The given conditions are

0                ... (1)

x^2\leq 100

Taking square root on both sides.

-\sqrt{100}\leq x\leq \sqrt{100}

-10\leq x\leq 10             .... (2)

Using (1) and (2) we get

0

Since x ∈ Z,

A=\{1,2,3,4,5,6,7,8,9,10\}

(b)

We need to find the value of  | {x ∈ Z | 0 < x, x² ≤ 100}| or |A|. It means have to find the number of elements in set A.

|A|=10

| {x ∈ Z | 0 < x, x² ≤ 100}| = 10

(c)

B = {x ∈ Z | x > 10, x² ≤ 100}

We need to find all the elements of given set.

The given conditions are

x>10                ... (3)

x^2\leq 100

It means

-10\leq x\leq 10             .... (4)

Inequality (3) and (4) have no common solution, so B is null set or empty set.

B=\{\}

(d)

We need to find the value of |{x ∈ Z | x > 10, x² ≤ 100}| or |B|. It means have to find the number of elements in set B.

|B|=0

|{x ∈ Z | x > 10, x² ≤ 100}| = 0

(e)

We need to find the value of | P(A) |. P(A) is the power set of set A.

Number of elements of a power set is

N=2^n

where, n is the number of elements of set A.

We know that the number of elements of set is 10. So the value of |P(A)| is

|P(A)|=2^{10}

|P(A)|=1024

Therefore |P(A)|=1024.

7 0
3 years ago
Last week, Gina's art teacher mixed 9 pints of red paint with 6 pints of white paint to make pink. Gina mixed 4 pints of red pai
cricket20 [7]
No, in order to do the correct ratio she would have needed to add 4.5 pints to 3 pints because if you divide 9:6 by 2 it is 4.5:3 not 4:3
6 0
3 years ago
Arnie decides to make 3 cups of dark orange paint and 3 cups of light orange paint.
dimulka [17.4K]

The question is an illustration of equivalent ratios.

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1 cup of dark orange requires

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Yellow =1oz

To make 3 cups, we simply multiply by 3, because 3 \times 1 = 3

So, we have:

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Yellow =1oz \times 3 = 3oz

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To make 3 cups, we simply multiply by 1.5, because 2 \times 1.5 = 3

So, we have:

Red = 3oz \times 1.5 = 4.5oz

Yellow = 13oz \times 1.5 = 19.5oz

Hence:

  • 3 cups of dark orange require 3 ounces of yellow  paint
  • 3 cups of light orange require 19.5 ounces of yellow paint

Read more about equivalent ratios at:

brainly.com/question/18441891

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Type the correct answer in each box.
Fittoniya [83]

the answer would be 2.5

8 0
3 years ago
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A window in the shape of a parallelogram has the dimensions given.
devlian [24]

Answer:

A. 20ft

Step-by-step explanation:

5 0
3 years ago
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