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erastova [34]
3 years ago
12

The value of y varies directly with x, and y = 343 when x = 49. Find y when x = 8

Mathematics
1 answer:
Ivan3 years ago
5 0

\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad  y=kx\impliedby  \begin{array}{llll} k=constant\ of\\ \qquad  variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=343\\ x=49 \end{cases}\implies 343=k49\implies \cfrac{343}{49}=k \\\\\\ 7=k\qquad therefore\qquad \boxed{y=7x} \\\\\\ \textit{when x = 8, what is \underline{y}?}\qquad y=7(8)\implies y=56

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An airplane is landing at Memphis International Airport. The airplane is currently flying at a height of 13,000 feet. The airpla
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A teacher was interested in knowing the amount of physical activity that his students were engaged in daily. He randomly sampled
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The standard error of the mean is 4.5.

Step-by-step explanation:

As we don't know the standard deviation of the population, we can estimate the standard error of the mean from the standard deviation of the sample as:

\sigma_{\bar{x}}\approx\frac{s}{\sqrt{n}}

The sample is [30mins, 40 mins, 60 mins, 80 mins, 20 mins, 85 mins]. The size of the sample is n=6.

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\bar{x}=\frac{1}n} \sum x_i =\frac{30+40+60+80+20+85}{6}=52.5

The standard deviation of the sample is calculated as:

s=\sqrt{\frac{1}{n-1}\sum (x_i-\bar x)^2} \\\\ s=\sqrt{\frac{1}{5}\cdot ((30-52.5)^2+(40-52.5)^2+(60-52.5)^2+(80-52.5)^2+(20-52.5)^2+(85-52.5)^2}\\\\s=\sqrt{\frac{1}{5} *3587.5}=\sqrt{717.5}=26.8

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6 0
3 years ago
The distance of planet Mercury from the Sun is approximately 5.8 ⋅ 10^7 kilometers, and the distance of Earth from the Sun is 1.
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Answer:

The answer is 9.2 * 10^7

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6 0
2 years ago
Read 2 more answers
Graph the feasibility region represented by the given inequalities and find the maximum profit if P = 4x + 5y. x ≥ 5 y ≤ 10 2x -
Brilliant_brown [7]

First, graph the three inequalities:  x ≥ 5  ,  y ≤ 10  ,  2x - y  ≤ 8

Next, look for the 3 intersections (vertices) of the lines: (5, 2)  ,  (5, 10)   ,  (9, 10)

Finally, input the vertex coordinates into P = 4x + 5y and look for the biggest #.

(5, 2):  4(5) + 5(2)  = 20 + 10  = 30

(5, 10): 4(5) + 5(10)  = 20 + 50  = 70

(9, 10): 4(9) + 5(10)  = 36 + 50  = 86

Answer: maximum profit = 86


8 0
3 years ago
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