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VashaNatasha [74]
3 years ago
14

6. If two quantities vary directly, which must be true of a graph showing the relationship between them?

Mathematics
1 answer:
larisa86 [58]3 years ago
6 0

Answer:

The points of the graph form a straight line, and the line must pass

through the origin ⇒ answer d

Step-by-step explanation:

* Lets explain the meaning of vary directly

- Direct variation is a relationship between two variables

- Two variable quantities have a constant ratio

- One of them equal the other multiplied by a constant

- If y varies directly with x, the y = kx, where k is the constant

 of variation

- The equation y = kx is represented graphically by a line

- If the value of x = 0 then the value of y must be equal zero, then <u><em>the </em></u>

<em>  </em><u><em>line which represented the direct variation must be passes through </em></u>

<em>   </em><u><em>the origin</em></u>

* Lets look to the answer to find the correct statement

a. The graph is a curve ⇒ Not true ⇒The graph must be line

b. The graph increases from left to right ⇒ Not true ⇒ maybe if the

    graph is a line there is no mention about the type of the graph

c. The points on the graph are connected ⇒ Not true ⇒ there is no

    mention about the type of the graph

d. <u><em>The points of the graph form a straight line, and the line must pass</em></u>

<em>     </em><u><em>through the origin</em></u> ⇒ <em>True</em> ⇒ as we said above

* <em>The answer is statement d</em>

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Dominick weighs 30 pounds more than his sister. Together they weigh 330 pounds. How much does Dominick weigh?
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Domik weights 30 pounds more than his sister

Together they weigh 330 pounds

Let "x" represent the weight of Dominik's sister, then his weight can be expressed as "x+30"

And their total weight can be calculated as:

x+(x+30)=330

From this expression you can calculate the value of x:

\begin{gathered} 2x+30=330 \\ 2x+30-30=330-30 \\ 2x=300 \\ \frac{2x}{2}=\frac{300}{2} \\ x=150 \end{gathered}

x=150 pounds

x+30=150+30=180 pounds

Dominik weights 180pounds and his sister 150 pounds

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Step-by-step explanation:

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In a study of speed​ dating, female subjects were asked to rate the attractiveness of their male​ dates, and a sample of the res
Blizzard [7]

Answer:

hello the data is missing but it is included in the explanation below

missing data = 9, 6, 2, 1, 2, 5, 5, 1, 2, 6, 8, 10, 6, 6, 1, 5, 1, 3, 4, 4, 4, 5, 10, 9, 1, 6

Answer :

A) range = 9 , variance = 8.3015,  standard deviation = 2.8812

B)  The results cannot be a representative of the variation of attractiveness among the population of adult males

Step-by-step explanation:

A ) calculate the Range, variance and standard deviation

The given data = 9, 6, 2, 1, 2, 5, 5, 1, 2, 6, 8, 10, 6, 6, 1, 5, 1, 3, 4, 4, 4, 5, 10, 9, 1, 6

i) Range = difference between largest and smallest values

              = 10 -1 = 9

ii) variance = summation of ; (xi − x)^2/n-1

                   = 207.5385/26−1   ≈ 8.3015

iii) standard deviation = \sqrt{variance}

                                    = \sqrt{8.3015} = 2.8812

B) The results cannot be a representative of the variation of attractiveness among the population of adult males

     

5 0
3 years ago
A famous monument is 300 ft tall. When it casts​ 210-ft shadow, a nearby tree casts a shadow that is 27 ft long. About how tall
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Answer:

38.57 feets

Step-by-step explanation:

Given that:

Height of monument, h = 300ft

Shadow of monument, s = 210 ft

Shadow of tree, s = 27ft

Height of tree, = x

Using the relation :

Height / shadow = height / shadow

Monument = tree

300 / 210 = h / 27

Cross multiply

300 * 27 = 210 * h

8100 = 210h

h = 8100 / 210

h = 38.57 feets

3 0
3 years ago
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