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musickatia [10]
3 years ago
9

Find the area of a square with side length x when x is equal to the given value. Are the area of a square and the length of its

side directly proportional? Justify your answer. x=10 in.
Mathematics
1 answer:
anyanavicka [17]3 years ago
7 0

Step-by-step explanation:

The formula for calculating the area of a square is expressed as;

A = x² where;

x is the length of one side of the square

Given

x = 10in

A = 10²

A = 10 * 10

A = 100in²

Area of the square with side length 10in is 100in²

From the equation A = x², we can see that as the value of x increases, the value of the area also increases and vice versa. This means that the area of the square is directky proportional to its length. Hence we can say YES, the area of a square and the length of its side directly proportional

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The time between telephone calls to a cable television service call center follows an exponential distribution with a mean of 1.
Ulleksa [173]

Answer:

0.52763 is the probability that the time between the next two calls will be 54 seconds or​ less.

0.19285 is the probability that the time between the next two calls will be greater than 118.5 ​seconds.

Step-by-step explanation:

We are given the following information in the question:

The time between telephone calls to a cable television service call center follows an exponential distribution with a mean of 1.2 minutes.

The distribution function can be written as:

f(x) = \lambda e^{-\lambda x}\\\text{where lambda is the parameter}\\\\\text{Mean} = \mu = \displaystyle\frac{1}{\lambda}\\\\\Rightarrow 1.2 = \frac{1}{\lambda}\\\\\lambda = 0.84 \\f(x) = 0.84 e^{0.84 x}

The probability for exponential distribution is given as:

P( x \leq a) = 1 - e^{\frac{-a}{\mu}}\\\\P(a \leq x \leq b) = e^{\frac{-a}{\mu} -\frac{-b}{\mu}}

a) P( time between the next two calls will be 54 seconds or​ less)

P( x \leq 0.9)\\= 1 - e^{\frac{\frac{-54}{60}}{1.2}} = 0.52763

0.52763 is the probability that the time between the next two calls will be 54 seconds or​ less.

b) P(time between the next two calls will be greater than 118.5 ​seconds)

p( x > \frac{118.5}{60}) = P(x > 1.975)\\\\ = 1 - P(x \leq 1.975) \\\\= 1 -1+ e^{\frac{-1.975}{1.2}}\\\\= 0.19285

0.19285 is the probability that the time between the next two calls will be greater than 118.5 ​seconds.

6 0
4 years ago
Find the value of X
kap26 [50]

Answer:

x = 27

Step-by-step explanation:

We can say that sum of all interior angles adds up to: 180°, therefore;

(3x - 17) + (2x - 5) + (x + 40) = 180°

=> now add like terms together:

=> 3x + 2x + x = 6x

=> -17 + (-5) + 40 = 18

Therefore;

6x + 18 = 180°

6x = 180 - 18

6x = 162

x = 162/6

<u>x = 27</u>

Hope this helps!

7 0
3 years ago
On a chapter test, Josh completed the problem listed below by applying the properties of exponents in the order listed below. He
likoan [24]

Answer:

The Ansewer is B.

I got it rigth.

Step-by-step explanation:

B) Josh misapplied the division property of exponents in Step 1.

5 0
3 years ago
What is constant rate of change for a piece of cheese if 1.24 cost 11.25
Vikki [24]
<span>$9.07/p,,,,,,,.............</span>
8 0
3 years ago
Read 2 more answers
What is the y-intercept of a line that has a slope of –3 and passes through point (–5, 4)? –17 , –11 , 7 , 19
Ilia_Sergeevich [38]

Answer:

-11

Step-by-step explanation:

There is enough information to put the equation in point slope form.

y-y_1=m(x-x_1)

We are given the point of (-5,4) and the slope of -3.

y-y_1=m(x-x_1)\rightarrow \boxed{y-4=-3(x+5)}

Now, we can take the point slope equation and convert it into slope intercept form.

y-4=-3(x+5)\\\\\left \{ {{-3*x=-3x} \atop {-3*5=-15}} \right.\\\\ y-4=-3x-15\\\\y-4+4=-3x-15+4\\\\\boxed{y=-3x-11}

The y-intercept should be -11.

4 0
3 years ago
Read 2 more answers
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