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-Dominant- [34]
3 years ago
5

Sally travels to work each day. she travels 12 km east from home to main road. sally then travels 9 km north on the main road to

work. if the council was to put a direct road from sally's house to work, how much shorter would her journey be?
a. 6 km
b. 7.94 km
c. 11.06 km
d. 15 km
Mathematics
1 answer:
marshall27 [118]3 years ago
7 0
This way Sally travels 12+9=21 kilometers.
If there was a direct way she could go to work, that way would have been 15 km (because her way to work forms a right-angled triangle).
Therefore her journey would be 21-15=6 km shorter. Choice A.
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Answer:

Step-by-step explanation

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This problem has been solved!See the answerA municipal bond service has three rating categories (A, B, and C). Suppose that in t
mariarad [96]

Answer:

a. \frac{35}{51}

b. \frac{51}{100}

c. \frac{1}{5}

Step-by-step explanation:

Suppose cities represented by C', suburbs represented by S and rural represented by R,

Let x be the total number of bonds issued throughout the US,

According to the question,

n(A) = 70% of x = 0.7x,

n(B) = 10% of x = 0.1x,

n(C) = 20% of x = 0.2x,

n(A∩C') = 50% of n(A) = 0.5 × 0.7x = 0.35x,

n(A∩S) = 20% of n(A) = 0.2 × 0.7x = 0.14x,

n(A∩R) = 30% of n(A) = 0.3 × 0.7x = 0.21x,

n(B∩C') = 40% of n(B) = 0.4 × 0.1x = 0.04x,

n(B∩S) = 30% of n(B) = 0.3 × 0.1x = 0.03x,

n(B∩R) = 30% of n(B) = 0.3 × 0.1x = 0.03x,

n(C∩C') = 60% of n(C) = 0.6 × 0.2x = 0.12x,

n(C∩S) = 15% of n(C) = 0.15 × 0.2x = 0.03x,

n(C∩R) = 25% of n(C) = 0.25 × 0.2x = 0.05x,

n(C') = n(A∩C')  + n(B∩C')  + n(C∩C')  = 0.35x + 0.04x + 0.12x = 0.51x

n(S) = n(A∩S) + n(B∩S) + n(C∩S) = 0.14x + 0.03x + 0.03x = 0.20x

a. The probability that it will receive an A rating, if a new municipal bond is to be issued by a city,

P(\frac{A}{C'})=\frac{P(A\cap C')}{P(C')}=\frac{0.35x/x}{0.51x/x}=\frac{0.35}{0.51}=\frac{35}{51}

b. The proportion of municipal bonds are issued by cities = \frac{n(C')}{x}

=\frac{0.51x}{x}

=\frac{51}{100}

c. The proportion of municipal bonds are issued by suburbs = \frac{n(S)}{x}

=\frac{0.20x}{x}

=\frac{20}{100}

=\frac{1}{5}

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2 years ago
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Which ordered pair is a solution of the equation? y=8x+3y=8x+3
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Multiply the first equation by 4 (so that both equations will have 8x terms) and then subtract:  

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8x +3y = 68

------------

0 -23y = -92  

Now divide both sides by -23:  

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Find x by plugging y=4 into either equation:  

8x +3(4) = 68

8x = 68 - 12

8x = 56

x = 7  

So the answer is ordered pair is (7,4)

3 0
3 years ago
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