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vladimir1956 [14]
3 years ago
14

Suppose that w and t vary inversely and that t = 5/12

Mathematics
1 answer:
Svetlanka [38]3 years ago
8 0

Answer:

Option B. t=5/3w ;1/3

Step-by-step explanation:

We are told that w varies Inversely with t thus generally speaking w∝\frac{1}{t}  since they are inverted, <u>otherwise</u> if they were proportionally varied then w∝t. This means that there is a constant value ( a ) for which w is inversely proportional to t and can be mathematically expressed as:

w=\frac{a}{t}        Eqn. (1)

Now since we are given the values of w=4 and t=\frac{5}{12}, we can plug them in Eqn. (1) and find our constant of proportionality a as follow:

w=\frac{a}{t}\\ \\a=wt\\\\a=(4)(\frac{5}{12} )\\\\a=\frac{5}{3}

Now that we have our constant we can find the new t value for the second value of w=5 as follow:

w=\frac{a}{t} \\\\t=\frac{a}{w}\\ \\t=\frac{\frac{5}{3} }{5}\\\\t=\frac{5}{15}\\ \\t=\frac{1}{3}\\

Therefore based on the options give, we can see that Option B. is correct since

t=\frac{5}{3w} and for w=5, then t=\frac{1}{3}

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zhenek [66]

Answer:

There is a strong positive relationship between sales of firewood and cough drops.

Step-by-step explanation:

Correlation Coefficient

  • Correlation is a technique that help us to find or define a relationship between two variables.
  • It is a measure of linear relationship between two quantities.
  • Values between 0 and 0.3 tells about a weak positive linear relationship, values between 0.3 and 0.7 shows a moderate positive correlation and a correlation of 0.7 and 1.0 states a strong positive linear relationship.

Thus, a coefficient correlation of 0.85 between weekly sales of firewood and cough drops over a 1-year period suggest that there is a strong positive relationship between sales of firewood and cough drops.

Thus, as the sale of firewood increase there is an increase in the sale of cough drops.

3 0
3 years ago
Which expression is equivalent to: −20+(−60)+(−90)? A: 20+60+90 B: −(20−60)+(−90) C: −20−(60−90) D: −20+(−90)+(−60)
Marina86 [1]

-140

Step-by-step explanation:

8 0
3 years ago
What is (11 5/8 - 2 1/16) - 4 3/4 ? ​
Vitek1552 [10]

Answer:

4.8125 or 4 13/16

Step-by-step explanation:

(11 10/16 - 2 1/16) - 4 12/16

(9 9/16) - 4 12/16

4 .8125 or 4 13/16

3 0
3 years ago
Which of the following equations could be th equation to represent the given graph? Make sure you explain your answer thoroughly
Alex17521 [72]

Answer:

Option (C) is correct.

Step-by-step explanation:

The given options of the possible equation for the graph are as follows:

(A) y=2\left(\frac{3}{2}\right)^x \\\\(B) y=-2\left(\frac{3}{2}\right)^{-x} \\\\(C) y=2\left(\frac{2}{3}\right)^x \\\\(D) y=-2\left(\frac{2}{3}\right)^{-x} \\\\

The given graph is decreasing and at x=0, y=2.

So, first checking the value of the given options for x=0

(A) y=2\left(\frac{3}{2}\right)^0=2\times 1= 2 \\\\(B) y=--2\left(\frac{3}{2}\right)^{-0}= -2\times 1= -2 \; (not\; possible) \\\\(C) y=2\left(\frac{2}{3}\right)^0= 2\times 1= 2 \\\\(D) y=2\left(\frac{2}{3}\right)^{-0} = -2\times 1= -2 \; (not\; possible)

As, for x=0, y=2, so options (C) and (D) are not possible, so rejected.

Now, checking the nature (increasing or decreasing) of the given equation by differentiating it.

For option (A),

\frac{dy}{dx}=2\left(\frac{3}{2}\right)^{x}\times \ln\left(\frac{3}{2}\right)

As \ln \left(\frac{3}{2}\right)=\ln(1.5)>0 \;and\; \left(\frac{3}{2}\right)^{x} >0

So, \frac{dy}{dx}>0

Therefore, the function in option (A) is increasing function.

Similarly, for option (C),

\frac{dy}{dx}=2\left(\frac{2}{3}\right)^{x}\times \ln\left(\frac{2}{3}\right)

As \ln \left(\frac{2}{3}\right)=\ln(0.67)0

So, \frac{dy}{dx}

Therefore, the function in option (C) is decreasing function.

As the given graph is decreasing, so, (C)  representsy=2\left(\frac{2}{3}\right)^x the given graph.

Hence, option (C) is correct.

6 0
3 years ago
Find the total surface area of the net below.
Solnce55 [7]

Total surface area of the triangular prism is  81.6 square m.

Step-by-step explanation:

  • b = 3 m
  • h = 2.6 m
  • p = 3+ 2.6 +2.6=  8.2
  • H = 9 m
  • SA = bh + pH

    = 3 × 2.6 + 8.2 ×9

    = 7.8 + 73.8

    = 81.6

  • Therefore,
  • SA = 81.6 square m
  • Total surface area of the triangular prism is  81.6 square m.
8 0
3 years ago
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