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qwelly [4]
3 years ago
14

Jerry is a judge. He hears 5 cases in 2 3/8 hours. How many cases does he hear per hour

Mathematics
1 answer:
Serggg [28]3 years ago
4 0

Answer:

Jerry does 2.11 cases per hour (Rounded to 2 decimal places). As we cannot do 0.11 cases. We can say Jerry does 2 cases per hour.

Step-by-step explanation:

to find the number of cases per hour, we have to divide the number of cases by number of hours taken for those cases,

Number of cases per hour = \frac{5cases}{2\frac{3}{8} hours}

                                             =\frac{5}{\frac{19}{8} } \\ cases per hour

                                             =\frac{5*8}{19} cases per hour

                                             =\frac{40}{19} cases per hour

                                              =2.11 cases per hour (Rounded to 2 decimal places)

As we cannot do 0.11 cases. We can say Jerry does 2 cases per hour.

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The answer is 55 6/9, but when simplified, it is 55 1/3

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125

Step-by-step explanation:

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A television screen's width is 1.778 times its height. If its
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Answer:

Let a, b, and c be the height, width, and the diagonal of the screen respectively

Since they form a triangle and the angle between a and b is 90 degrees, according to the Pythagorean Theorem a^2 + b^2 = c^2

Let's assume that the aspect ratio is 16:9. Therefore b/a = 16/9

Now we have a system of two equations with two unknowns. We need to express everything in terms of a single unknown, so let's express a in terms of b.

Since, b/a = 16/9, by cross multiplying 16a = 9b. Therefore a=9b/16.

Now we can subsitute 9b/16 for a in the first equation

a^2+b^2=c^2 becomes (9b/16)^2 + b^2 = c^2

Squaring the nominator and the denominator of the fraction yields

81b^2/256 + b^2 = c^2

To perform the addition, we need to express b^2 as a fraction with denominator 256 which is 256b^2/256, Now we have

81b^2/256 + 256b^2/256 = c^2

Adding fractions with the same denominators is now easy and produces

337b^2/256 = c^2

Cross multiply to get

337b^2 = 256c^2

Divide both sides by 337 to get b^2

b^2=256c^2/337

Take the square root of both sides to get b

b = sqrt(256c^2/337)

Lots of complicated Pythagorean responses. This is much simpler to answer with Trigonometry.

TLDR; just multiply the diagonal by the following two coefficients, and add the bezel width, to get the width and height:

w = diag x 0.872 + 2 x bw

h = diag x 0.49 + 2 x bw

(Where diag is the diagonal size of the screen and bw is the bezel width)

Thats all you need to know to do this.

Now here’s the Teig behind it:

First, calculate the angle of the diagonal relative to the base, using tangent, which yields ::

a = tan(9/16)

This will give you an angle of 0.512 radians (or roughly 30 degrees).

Next, calculate the ratio of the height relative to the hypotenuse (the diagonal length) using arc-sine, which yields the relative proportion of opposite length over the hypotenuse for a given angle:

h = asin(0.512)

The result will be roughly h = 0.49, or 49% of the diagonal.

Finally, get the ratio of eidth to hypotenuse using arc-cosine:

w = acos(0.512)

The result is roughly w = 0.872, or 87.2% of the diagonal.

that’s all the math! Enjoy!

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Answer:

Step-by-step explanation:

try https://www.mathpapa.com/calc.html?q=y%3D2x+1 for faster answers next time

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