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Digiron [165]
3 years ago
15

Jack is growing Red wiggler worms to help make compost. He measured the lengths of two young worms. The 10- day old worm is 10/1

2 inch long. The 20-day old worm is 1 4/6 inches long. About how much longer is the 20- day old worm than the 10-day old worm? Explain how you found your estimate.
Mathematics
1 answer:
Lilit [14]3 years ago
3 0

Answer:

The 20-day old worm is \frac{5}{6} inches more longer than the 10-day old worm.

Step-by-step explanation:

Jack is growing Red wiggler worms to help make compost. He measured the lengths of two young worms. The 10- day old worm is \frac{10}{12} inch long. The 20-day old worm is 1\frac{4}{6} inches long.  

Therefore, the 10-day old worm is \frac{10}{12} i.e \frac{5}{6} inches long.

And the 20-day old worm is 1\frac{4}{6} i.e. \frac{10}{6} = \frac{5}{3} inches long

Therefore, the 20-day old worm is (\frac{5}{3} - \frac{5}{6}) = \frac{5}{6} inches more longer than the 10-day old worm. (Answer)

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Answer:

a) there are 7,854,000 number of ways the random selections can be arranged

b) the required probability is 0.0445

Step-by-step explanation:

Given that;

you have 12 pair of long pants, 6 pair of short pant and 17 t-shirt which in total;

Total = 12 + 6 + 17 = 35

a) number of ways a random selection of 9 pair of long pants, 4 pair of short pants and 13 t-shirts can be arranged;

⇒ [ 12   ×    [ 6     ×    [ 17

     9 ]          4 ]           13 ]

= (12! / (9! 3!)) (6! / (4! 2!)) (17! / (13! 4!))

= (220) (15) (2380)

= 7,854,000

Therefore there are 7,854,000 number of ways the random selections can be arranged

b)

Number of ways of selecting 25 item from 35 items;

⇒ [ 35        

    25 ]

=

(35! / (25! 10!) = 183.579,396

now number of ways to select 10 pair of long pants, 3 pairs of short pantts and 12 t-shirt;

⇒ [ 12   ×    [ 6     ×    [ 17

     10 ]         3 ]           12 ]

= (12! / (10! 2!)) (6! / (3! 3!)) (17! / (12! 5!))

= (66) (20) (6188)

= 8,168,160

So, Required probability = 8,168,160 / 183,579,396

= 0.0445

So the required probability is 0.0445

5 0
3 years ago
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Answer:

z=9.7

Step-by-step explanation:

3z + 8 - 2 = -35

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divide 3 from both sides

z=9.7

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3 years ago
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3 years ago
Write an equation that goes through (8,1) and is perpendicular to 2y + 4x =12
Serggg [28]

Answer:

2y -x + 6 = 0

Step-by-step explanation:

Here a equation and a point is given to us and we are interested in finding a equation which is perpendicular to the given equation and passes through the given point .

The given equation is ,

\sf \longrightarrow 2y + 4x = 12 \\

\sf \longrightarrow 4x + 2y = 12

Firstly convert this into slope intercept form , to find out the slope of the line.

\sf \longrightarrow 2y = -4x +12\\

\sf \longrightarrow y =\dfrac{-4x+12}{2}\\

\sf \longrightarrow y =\dfrac{-4x}{2}+\dfrac{12}{2}\\

\sf \longrightarrow \red{ y = -2x + 6 }

Now on comparing it to slope intercept form which is y = mx + c , we have ,

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And as we know that the product of slopes of two perpendicular lines is -1 . So the slope of the perpendicular line will be negative reciprocal of the slope of the given line. Therefore ,

\sf \longrightarrow m_{\perp}=\dfrac{-1}{-2}=\red{\dfrac{1}{2}}

Now we may use the point slope form of the line to find out the equation of the line using the given point . The point slope form is,

\sf \longrightarrow y - y_1 = m(x - x_1)

Now on substituting the respective values we have,

\sf \longrightarrow y - 1 = \dfrac{1}{2}(x-8)\\

\sf \longrightarrow 2(y-1 )= x -8 \\

\sf \longrightarrow 2y -2=x-8\\

\sf \longrightarrow \underline{\boxed{\bf 2y - x + 6=0}}

5 0
3 years ago
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