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lora16 [44]
3 years ago
5

Five students wrote a mathematics test. The average mark was 68. If the marks for four of the students were 75, 62, 84 and 53, t

he mark of the fifth student was
Mathematics
1 answer:
konstantin123 [22]3 years ago
4 0

Answer:

66

Step-by-step explanation:

Use the formula for the mean of a set of numbers:

                  sum of the numbers

average = --------------------------------

                     count of numbers

Here we know that the average mark was 68, so we can write:

               

                           75 + 62 + 84 + 53 + x

average = 68 = ----------------------------------

                                           5

or                            274 + x

                  68 = -------------------

                                    5

Solving for x, we multiply both sides by 5:     340 = 274 + x.

Subtracting 274 from both sides effectively isolates x:

 340 = 274 + x

- 274    -274

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

  66      =    x

The fifth student's mark was 66.

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Step-by-step explanation:

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lakkis [162]

Answer:

hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to

Answer:  v = 5v + 4u + 1.5sin(3t),

  • 0
  • 1
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Step-by-step explanation:

u" - 5u' - 4u = 1.5sin(3t)        where u'(1) = 2.5   u(1) = 1

v represents the "velocity function"   i.e   v = u'(t)

As v = u'(t)

<em>u' = v</em>

since <em>u' = v </em>

v' = u"

v'  = 5u' + 4u + 1.5sin(3t)   ( given that u" - 5u' - 4u = 1.5sin(3t) )

    = 5v + 4u + 1.5sin(3t)  ( noting that v = u' )

so v' = 5v + 4u + 1.5sin(3t)

d/dt \left[\begin{array}{ccc}u&\\v&\\\end{array}\right]= \left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right]  \left[\begin{array}{ccc}u&\\v&\\\end{array}\right] + \left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right]

Given that u(1) = 1 and u'(1) = 2.5

since v = u'

v(1) = 2.5

note: the initial value for the vector valued function is given as

\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right]  = \left[\begin{array}{ccc}1\\2.5\\\end{array}\right]

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3.  (30 * 12.5)/2 = 187.5

4. 187.5 + 245.31 + 312.5 = 745.31

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