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Mrac [35]
3 years ago
14

on monday, roger drove to work in 20 minutes. on tuesday, he averaged 15 miles per hour more, and it took him 6 minutes less to

get to work. how far in miles does he travel to work?
Mathematics
1 answer:
ch4aika [34]3 years ago
7 0
Let the distance to his office be x, then
On monday, speed = x/20 miles per minutes = 3x miles per hour
On tuesday, speed = (3x + 15) miles per hour
Time = distance / speed
(20 - 6)/60 hours = x/(3x + 15) hours
7/30 = x/(3x + 15)
7(3x + 15) = 30x
21x + 105 = 30x
30x - 21x = 105
9x = 105
x = 105/9 = 11.7 miles

Therfore he travels an average of 11.7 miles to work.
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A random sample of 64 students at a university showed an average age of 20 years and a sample standard deviation of 4 years. The
adelina 88 [10]

Answer:

The 90%  confidence level is  19.15<  L  <   20.85

Step-by-step explanation:

From the question we are told that

     The sample size is  n =  64

     The mean age is  \= x  =  20  \ years

      The standard deviation  is   \sigma  =  4 \ years

 

Generally  the degree of freedom for this data set is mathematically represented as

        df  = n -  1

substituting values

        df  = 64 -  1

        df  = 63

Given that the level of confidence is  90%  the significance level is mathematically evaluated as

          \alpha  =  100 - 90

         \alpha  =10 %  

         \alpha   = 0.10

Now   \frac{\alpha }{2}  =  \frac{0.10}{2}  = 0.05

Since we are considering a on tail experiment

The  critical value for half of  this significance level at the calculated  degree of freedom is obtained from the critical value table as

           t_{df, \frac{ \alpha}{2}   } = t_{63,  0.05   } =  1.669

   The margin for error is mathematically represented as

          MOE  =  t_{df ,  \frac{\alpha }{2} } *  \frac{\sigma}{\sqrt{n} }

substituting values  

          MOE  = 1.699  *   \frac{4 }{\sqrt{64} }

         MOE  = 0.85

he 90% confidence interval for the true average age of all students in the university is evaluated as follows

           \= x - MOE  <  L  <  \= x  + E

substituting values  

         20  - 0. 85 <  L  <   20  + 0.85

         19.15<  L  <   20.85

4 0
3 years ago
Complete the table:
Dafna11 [192]

Answer:

d. 0

Step-by-step explanation:

The table can be interpreted as:

\theta = 0

Required

Find sin(\theta)

sin(\theta)

Substitute: \theta = 0

\sin(\theta) = \sin(0)

Using a calculator

\sin(0) = 0

Hence:

\sin(\theta) = 0

3 0
3 years ago
5(2/5) how to solve it?
mina [271]

Answer:

2

Step-by-step explanation:

Solve. Technically, there are two methods. You can first multiply, or first divide.

Essentially the question is:

(5 * 2)/5

or

2 * (5/5)

Solve. Remember to follow PEMDAS. First solve the parenthesis, then simplify:

(5 * 2)/5 = (10)/5 = 2

2 * (5/5) = 2 * 1 = 2

2 is your answer.

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5 0
3 years ago
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Given the function, check all transformations that occurred from the graph of the function y=x^2
Hatshy [7]

Answer: left 7 units, up 4 units, and vertical compression

Step-by-step explanation:

Given

The function is y=x^2

First shift it to the left by 7 units, so the function becomes

y=(x+7)^2

Now compress it to make it one-third

y=\dfrac{1}{3}(x+7)^2

Now, sift the graph upward by 4 units

y=\dfrac{1}{3}(x+7)^2+4

Thus , the conditions are left 7 units, up 4 units, and vertical compression.

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3 years ago
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Elden [556K]
Answer
I’m pretty sure it’s c
Explanation
4 0
2 years ago
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