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arsen [322]
2 years ago
10

The sum of two numbers is 23. Twice one number increased by 6 is the same as 4 times the other number decreased by 2. What is th

e largest of the two numbers?
Mathematics
1 answer:
Crank2 years ago
8 0

Answer:

One number is 4.2, the other is 18.8

Step-by-step explanation:

1.)  x+y=23

    (x+6y)x2=4

2.) (x+6y)x2=4   =   2x+12y=4

3.)Use elimination/substitution to solve

     2x+12y=4  =   x+6y=2  =  x=2-6y

     2-6y+y=23

4.)Solve for y

     2-5y=23 -> -5y=21 -> y=4.2.

5.)Solve for x

    x+4.2=23

    x=18.8

I may be wrong so let me know if I am

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Answer:

P(2 quarters) = 19/ (13*16) = 19/208  = 0.0913

Step-by-step explanation:

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P(2 quarters) = P( 1st quarter)* P(2nd quarter)

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A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measurin
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Answer:

The standard deviation of weight for this species of cockroaches is 4.62.

Step-by-step explanation:

Given : A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams.

To find : What is the approximate standard deviation of weight for this species of cockroaches?

Solution :

We have given,

Mean \mu=50

The sample mean x=55

A lab assistant reports that 14% of the cockroaches weigh more than 55 grams.

i.e. P(X>55)=14%=0.14

The total probability needs to sum up to 1,

P(X\leq 55)=1-P(X>55)

P(X\leq 55)=1-0.14

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The z-score value of 0.86 using z-score table is z=1.08.

Applying z-score formula,

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Where, \sigma is standard deviation

Substitute the values,

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

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\sigma=\frac{5}{1.08}

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The standard deviation of weight for this species of cockroaches is 4.62.

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