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Sav [38]
2 years ago
14

Mason and Dallas are in a canoe race. Mason paddles 7/8 mile in 1/4 hour. Dallas paddles 9/5 miles in 1/3 hour. Who paddles fast

er? Find each speed in miles per hour.
Mathematics
1 answer:
brilliants [131]2 years ago
8 0

Answer: See explanation

Step-by-step explanation:

Mason paddles 7/8 mile in 1/4 hour.

Speed = Distance/Time

= (7/8)/(1/4)

= (7/8) × (4/1)

= 7/2

= 3.5 miles per hour

Dallas paddles 9/5 miles in 1/3 hour.

Speed = Distance/Time

= (9/5)/(1/3)

= (9/5) × (3/1)

= 27/5

= 5.4 miles per hour.

From the speed calculated, we can see that Dallas paddles faster

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The art museum is 8 1/2 miles from Alison's house. Alison has ridden her bike 2/3 of the way there so far. How far how she gone?
ozzi
Alison is 2/3 of the way to the museum, so the answer is about 2/3 of 9, or 6 miles.  Let's calculate it:

  2                              17 miles
---- * (8 1/2 miles) = --------------     She has ridden (17/3) miles, which is 5 2/3 
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2 years ago
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The Bay Area Online Institute (BAOI) has set a guideline of 60 hours for the time it should take to complete an independent stud
yarga [219]

Answer:

 At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

Step-by-step explanation:

From the question we are told that

   The  population mean is \mu  =  60 \ hr

    The sample size is  n  =  16

    The  sample mean is  \= x  =  68 \ hr

     The  standard deviation is  \sigma  =  20 \ hr

The  null hypothesis is  H_o  :  \mu  =  60

The  alternative H_a :  \mu >  60

Here we would assume the level of significance of this test to be  

         \alpha  =  5\%  =  0.05

Next we will obtain the critical value of the level of significance from the normal distribution table, the value is    Z_{0.05} =  1.645

  Generally the test statistics  is mathematically represented as

           t =  \frac{ \= x  - \mu}{  \frac{ \sigma }{\sqrt{n} } }

substituting values

           t =  \frac{  68  - 60 }{  \frac{ 20 }{\sqrt{16} } }

          t = 1.6

Looking at the value of t and  Z_{\alpha } we see that t< Z_{\alpha } hence we fail to reject the null hypothesis

   This means that there no sufficient evidence to conclude that it takes more than 60 hours to complete the course

So

   At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

6 0
2 years ago
Use exponential form to evaluate log8(2)
maks197457 [2]
<span>Logarithm form is another way to express a number in exponential (exp.) form. log 8 (2) is the same as 8 (x) = 2 or in words, eight with exp. x equals two. If we take that equation and cube both sides, or raise each side to the power of 3, [8 (x)] with exp. 3 = 2 with exp. 3. This simplifies to 8 (3x) = 8. By definition, 8 is the same as 8 with exp. 1. So the equation is now 8 (3x) = 8 (1). This means 3x = 1. We can simplify to x = 1/3.</span>
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2 years ago
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Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travel
alexira [117]

Answer:

the correct choice is A. At the gas station

Step-by-step explanation:

Lucy starts at home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at the post office.

Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.

From the given data:

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The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.

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Answer:

(a) = 40%

(b) = 28%

(c) Expected value = $222,500

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Step-by-step explanation:

This is a normal distribution with a = 210,000 and b =235,000

(a) The probability that he will get at least $225,000 for the house is:

P(X\geq 225,000) =1 -\frac{225,000-a}{b-a} =1-\frac{225,000-210,000}{235,000-210,000} \\P(X\geq 225,000) =0.4= 40\%

(b)The probability he will get less than $217,000 is:

P(X\leq 217,000) =\frac{217,000-a}{b-a} =\frac{217,000-210,000}{235,000-210,000} \\P(X\leq 217,000) =0.28= 28\%

(c) The expected value (E) and the standard deviation (S) are:

E=\frac{a+b}{2}=\frac{210,000+235,000}{2}\\ E=\$222,500\\S=\frac{b-a}{\sqrt{12}}=\frac{235,000-210,000}{\sqrt{12}}\\S=\$7,216.88

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