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3 years ago

7. GEOGRAPHY The discharge of a river

Mathematics

1 answer:

Rama09 [41]3 years ago

8 0

Answer:

10 m

Step-by-step explanation:

Given:

The discharge of water is equal to the product of of its width, its average depth and its speed.

Let $D$ be discharge of water, $w$ be its width, $h$ be its average depth and $v$ be its speed.

So, $D=vwh$

As per question,

$D=3198\textrm{ }m^{3},w=533\textrm{ m},v=0.6\textrm{ }m/s$

Plug in the above values and solve for $h$ .

$3198=0.6\times 533\times h\\3198=319.8h\\h=\frac{3198}{319.8}=10\textrm{ m}$

Therefore, the average depth of the Mississippi river is 10 m.

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Answer:

$Mean = 68.9$

$s^2 =18.1$ --- Variance

Step-by-step explanation:

Given

$\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

$x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5$

For 59 - 66

$x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5$

For 67 - 74

$x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5$

For 75 - 82

$x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5$

For 83 - 90

$x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5$

So, the table becomes:

$\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

The mean is then calculated as:

$Mean = \frac{\sum fx}{\sum f}$

$Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}$

$Mean = \frac{2547.5}{37}$

$Mean = 68.9$ -- approximated

Solving (b): The sample variance:

This is calculated as:

$s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}$

So, we have:

$s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}$

$s^2 =\frac{652.8}{36}$

$s^2 =18.1$ -- approximated

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2 years ago

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sdas [7]

Answer:1) 32. 2). 3) 21. 4) 4

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2 years ago

Given f(x) = -x + 5, find f(-3). Answer:

user100 [1]

Hey there!

Find f(-3) :

Answer :

f(-3) = 8 ✅

Explanation :

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>> Substitute -3 for x in f(x) :

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f(-3) = 3 + 5

f(-3) = 8

Therefore, your answer is f(-3) = 8

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