Cocoa plant type 1 yielded 155 bushels per acre last year at a research farm. This year,

find three consecutive odd integers such that the sum of the smallest number and middle number is 27 less than 3 times the large

katrin2010 [14]

A generic odd number can be written as

$2k+1,\quad k \in \mathbb{Z}$

Since there is an odd number every two numbers, three consecutive odd numbers will be

$2k+1,\quad 2k+3,\quad 2k+5$

Now let's make up the equations: the sum of the first two is

$(2k+1)+(2k+3)$

And 27 less than 3 times the largest is

$3(2k+5)-27$

These two must be the same, so we have

$(2k+1)+(2k+3)=3(2k+5)-27 \iff 4k+4 = 6k+30-27 \iff 4k+4=6k+3$

Subtracting 4k and 3 from both sides gives

$1=2k \iff k=\dfrac{1}{2}$

Which means that the problem has no solution.

To confirm this hypothesis, we can observe that, on the left hand side, we have the sum of two odd numbers, which is even

On the right hand side, we have an odd number, multiplied by 3 (still odd), take away 27 (still odd).

So, the left hand side is even, and the right hand side is odd. They can't be the same number.

7 0

4 years ago

I’ll give you 15 point just help

Maru [420]

Answer:

Step-by-step explanation:

y - 4 = -2/3(x - 3)

y - 4 = -2/3x + 2

y = -2/3x + 6

4 0

3 years ago

Most ATM’s require a 4-digit code using the digits 0-9 how many 4-digit codes can you use

Zolol [24]

10000 digits can be used for 4 digit A.T.M code.

Solution:

Given that A.T.M required 4 digit codes using the digits 0 to 9.

Need to determine how many four digit code can be used.

We are assuming that number starting with 0 are also valid ATM codes that means 0789 , 0089 , 0006 and 0000 are also valid A.T.M codes.

Now we have four places to be filled by 0 to 9 that is 10 numbers

Also need to keep in mind that repetition is allowed in this case means if 9 is selected at thousands place than also it is available for hundreds, ones or tens place .

First digit can be selected in 10 ways that is from 0 to 9.

After selecting first digit, second digit can be selected in 10 ways that is 0 to 9 and same holds true for third and fourth digit.

So number of ways in which four digit number is created = 10 x 10 x 10 x 10 = 10000 ways

Hence 10000 digits can be used for 4 digit A.T.M code.

7 0

3 years ago

The sum of the ages of Rudy and his father is 58 years. The difference in their ages is 32 years. How old is each ?

Anestetic [448]

Answer:

Rudy is 13 years old. Her father is 45 years old.

Step-by-step explanation:

It's very simple actually!

All you need to do is subtract 32:

58 - 32 = 26

Then divide:

26 ÷ 2 = 13

13 is Rudy's age. Let's find her father's age!

We then add 32 back to 13:

32 + 13 = 45

And there you have it!

Hope this helped! :)

7 0

3 years ago

The radius of a circle is 14 meters. What is the circle circumference

seropon [69]

Step-by-step explanation:

HERE,

redius of a circle (r)=14 meters.

we know that,

$\boxed{\red{\sf{circle~ circumference=2\times \pi \times r }}}$

According to the question, 

circle circumference=

$\tt{2\times \pi \times 14 }$

$\tt{2 \times \dfrac{22}{7} \times 14 }$

$\tt{2 \times \dfrac{22}{\cancel{7}} \times \cancel{14}}$

$\tt{2\times 22 \times 2 }$

$\tt{ 88~meters }$

so, the circumference of that circle is 88 meters.

5 0

3 years ago