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algol [13]
3 years ago
8

B) David and Andrew are traveling to a Mathematics conference. David travels 110 miles in the same time that Andrew travels 140

miles. Andrew travels 15 miles per hour faster than David. Find the average rate of each person.
Mathematics
1 answer:
nasty-shy [4]3 years ago
3 0

Answer:

David's average speed is 55 mph and Andrew's average speed is 70 mph

Step-by-step explanation:

Let David's speed be s.

Average speed is given as:

speed = distance / time

They both spent the same time, t.

David's speed is:

s = 110 / t

=> t = 110 / s

Andrew travels 15 mph faster than David.

Andrew's speed is:

(15 + s) = 140 / t

=> t = 140 / (15 + s)

Therefore, since they spent the same time:

110 / s = 140 / (15 + s)

Cross multiply:

110(15 + s) = 140s

1650 + 110s = 140s

1650 = 140s - 110s

30s = 1650

s = 1650 / 30

s = 55 mph

Andrew's speed is:

15 + 55 = 70 mph

Therefore, David's average speed is 55 mph and Andrew's average speed is 70 mph.

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74% of freshmen entering public high schools in 2006 graduated with their class in 2010. A random sample of 81 freshmen is selec
Assoli18 [71]

Answer: Probability that the proportion of students who graduated is greater than 0.743 is P = 0.4755

Step-by-step explanation:

Given that,

Probability of freshmen entering public high schools in 2006 graduated with their class in 2010, p = 0.74

Random sample of freshman, n = 81

Utilizing central limit theorem,

P(\hat{p}

So,

(P(\hat{p}>0.743) = P(Z>0.743 - \frac{0.74}{\sqrt{\frac{0.74(1-0.74)}{81} }  } )

= P( Z > 0.0616)

= 0.4755 ⇒ probability that the proportion of students who graduated is greater than 0.743.

7 0
3 years ago
Sum of cubes: (a b)(a2 – ab b2) = a3 b3 Difference of cubes: (a – b)(a2 ab b2) = a3 – b3 Which products result in a sum or diffe
valentina_108 [34]

By comparing all the options with the formula of sum of cubes and difference of cubes we get that  (x+4)\left(x^{2}-4 x+16\right)  is sum of cubes

<h3>What is formula of sum of cubes and difference of cubes?</h3>

Formula of sum of cubes and difference of cubes are following

(a+b)(a^2 -ab +b^2) = a^3+ b^3 \\\\\\(a - b)(a^2+ ab+ b^2) = a^3 - b^3

(a)

(x-4) \left(x^{2}+4 x-16\right)\\=(x-4) \left(x^{2}+4 x-4^2\right)\\\\

by comparison with formula we can say that this is neither sum or nor difference of cubes.

(b)

(x-1)\left(x^{2}-x+1\right)\\=(x-1)\left(x^{2}-x+1^2\right)

by comparison with formula we can say that this is neither sum nor difference of cubes.

(c)

(x+1)(x-1)=x^{2}-1^{2}\\

we can say that this is neither sum  nor difference of cube as it's difference of squares.

(d)

(x+4)\left(x^{2}-4 x+16\right)\\\\(x+4)\left(x^{2}-4 x+4^2\right)

by comparison with formula this is equal to

x^{3}+4^{3}\\

Hence this is sum of cubes

(e)

(x+4)\left(x^{2}+4 x+16\right)\\(x+4)\left(x^{2}+4 x+4^2\right)

by comparison with formula we can say that this is neither sum  nor difference of cubes.

By comparing all the options with the formula of sum of cubes and difference of cubes we get that  (x+4)\left(x^{2}-4 x+16\right) is sum of cubes

To know more about cubes visit: brainly.com/question/107100

8 0
2 years ago
How much dollars is in 14 quarters and 5 nickels​
marishachu [46]

Answer:

$4.25

Step-by-step explanation:

4 quarters is 1 dollar

1 nickel is 5 cent

14 divided by 4 = 3.5

3.5 + 5 times 5 =  $4.25

8 0
3 years ago
Read 2 more answers
50 POINTS !!
Anna35 [415]

Answer:

Step-by-step explanation:

Hope this helps u!!

7 0
2 years ago
Your friend has owned a dog for 35 weeks. This is five weeks less than twice as long as he has owned a cat. How long has your fr
pashok25 [27]

Answer:

20 weeks

Step-by-step explanation:

35+5=40

40/2=20

6 0
3 years ago
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