Suppose that y is directly proportional to x, and y = 150 when x = 15. What is the constant of proportionality?

Mathematics

1 answer:

galina1969 [7]3 years ago

3 0

Answer: The required constant of proportionality is 10.

Step-by-step explanation: Given that y is directly proportional to x, and y = 150 when x = 15.

We are to find the constant of proportionality.

According to the given information, we can write

$y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~~~~~~~[\textup{where k is the constsnt of propotionality}].$

When y = 150 and x = 15, we get from the above equation that

$y=kx\\\\\Rightarrow 150=k\times15\\\\\Rightarrow k=\dfrac{150}{15}\\\\\Rightarrow k=10.$

Thus, the required constant of proportionality is 10.

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How do you solve this

lys-0071 [83]

2x^2 + 14x = -12

Step 1: Subtract -12 from both sides.

2x^2 + 14x - (-12) = -12 - (-12)

2x^2 + 14x + 12 = 0

Step 2: Factor the left side of the equation.

2(x + 1)(x + 6) = 0

Step 3: Set Factors equal to 0.

x + 1 = 0 or x + 6 = 0

x = -1 or x = -6

Answer:
x = -1 or x = -6

Hope this helps. : )

5 0

4 years ago

for the data values below construct a 95 confidence interval if the sample mean is known to be 12898 and the standard deviation

Volgvan

Answer:

A 95% confidence interval for the population mean is [3315.13, 22480.87] .

Step-by-step explanation:

We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$