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3 years ago

If y varies directly with x, and y = 10 when x = 4, write the direct linear variation equation

2 answers:

4 0

The answer is c. I chose the answer c because y=5/2x(I think you forgot to put the x in the question) filled in with the numbers are true while a, b, and d aren't true if filled with 10 and 4.

igomit [66]3 years ago

4 0

Answer:

$y=\frac{5}{2}x$

Step-by-step explanation:

Given,

y varies directly with x,

I.e. $y\propto x$

$\implies y = kx ----(1)$

Where,

k = constant of proportionality,

We have,

y = 10 when x = 4

From equation (1),

$10=4x\implies x = \frac{10}{4}=\frac{5}{2}$

Again from equation (1),

$y=\frac{5}{2}x$

Which is the required direct linear variation equation.

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Assume that military aircraft use ejection seats designed for men weighing between 141.8 lb and 218 lb. If women's weights are

Mariulka [41]

Answer:

$P(141.8$

And we can find this probability with this difference and using the normal standard table:

$P(-0.639$

Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(173.6,49.8)$

Where $\mu=173.6$ and $\sigma=49.8$

We are interested on this probability

$P(141.8$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(141.8$

And we can find this probability with this difference and using the normal standard table:

$P(-0.639$

Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women

8 0

3 years ago

The area of a rectangular wall of a barn is 252 square feet. Its length is 10 feet longer than twice its width. Find the length

valentinak56 [21]

Answer: Length = 28 feet and width = 9 feet

Step-by-step explanation:

Let x = width of the wall.

Then, Length of the wall = 10+2x

Since , Area of rectangle = length x width

Then, as per given,

$252= (10+2x)x\\\\\Rightarrow\ 252=10x+2x^2\\\\\Rightarrow\ 2x^2+10x-252=0\\\\\Rightarrow\ x^2+5x-126=0\\\\\Rightarrow\ x^2+14x-9x-126=0\\\\\Rightarrow\ (x+14)-9(x+14)=0\\\\\Rightarrow\ (x+14)(x-9)=0\\\\\Rightarrow\ x=-14 \ or \ x= 9$