INEQUALITY:

PetSmart.com sold the following varieties of dog food in June 2003.

aivan3 [116]

Let x be the number of bags of Nature's Recipe Venison Meal & Rice Canine 20 percent protein, y be the number of bags of Nutro Max Natural Dog Food 27 percent protein and z be the number of bags of PetSmart Premier Oven Baked Lamb 25 percent protein a dog breeder buys. He wants to make 300 pounds of a mix. Then

20x+17.5y+30z=300.

Now

in 20x pounds of Nature's Recipe Venison Meal & Rice Canine 20 percent protein is 0.2·20x=4x pounds of protein;
in 17.5y pounds of Nutro Max Natural Dog Food 27 percent protein is 0.27·17.5y=4.725y pounds of protein;
in 30z pounds of PetSmart Premier Oven Baked Lamb 25 percent protein is 0.25·30z=7.5z pounds of protein;
in 300 pounds of mix containing 22 percent protein is 0.22·300=66 pounds of protein.

Then 4x+4.725y+7.5z=66.

You get a system

$\left\{\begin{array}{l}20x+17.5y+30z=300\\4x+4.725y+7.5z=66.\end{array}\right.$

From the first equation $z=10-\dfrac{2}{3}x-\dfrac{7}{12}y.$ Substitute it into the second equation:

$4x+4.725y+7.5(10-\dfrac{2}{3}x-\dfrac{7}{12}y)=66.$

Simplify it:

$-x+\dfrac{7}{20}y=-9,\\ \\ 20x-7y=180.$

y must be divided by 20, then

y=0, x=9, z=10-6=4;
y=20, x=16, z is not a whole number;
y=40, x=23, z is not a whole number;
y=60, x=30, z=10-20-35<0;
thus, all other possible z will be <0.

Answer: 9 bags with 1st mix, 0 bags with 2nd mix and 4 bags with 3rd mix.

5 0

3 years ago

A teacher places n seats to form the back row of a classroom layout. Each successive row contains two fewer seats than the prece

Alex_Xolod [135]

Answer:

The number of seat when n is odd $S_n=\frac{n^2+2n+1}{4}$

The number of seat when n is even $S_n=\frac{n^2+2n}{4}$

Step-by-step explanation:

Given that, each successive row contains two fewer seats than the preceding row.

Formula:

The sum n terms of an A.P series is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$=\frac{n}{2}[a+l]$

a = first term of the series.

d= common difference.

n= number of term

l= last term

$n^{th}$ term of a A.P series is

$T_n=a+(n-1)d$

n is odd:

n,n-2,n-4,........,5,3,1

Or we can write 1,3,5,.....,n-4,n-2,n

Here a= 1 and d = second term- first term = 3-1=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=1 and d=2

$n=1+(t-1)2$

⇒(t-1)2=n-1

$\Rightarrow t-1=\frac{n-1}{2}$

$\Rightarrow t = \frac{n-1}{2}+1$

$\Rightarrow t = \frac{n-1+2}{2}$

$\Rightarrow t = \frac{n+1}{2}$

Last term l= n,, the number of term $=\frac{ n+1}2$ , First term = 1

Total number of seat

$S_n=\frac{\frac{n+1}{2}}{2}[1+n}]$

$=\frac{{n+1}}{4}[1+n}]$

$=\frac{(1+n)^2}{4}$

$=\frac{n^2+2n+1}{4}$

n is even:

n,n-2,n-4,.......,4,2

Or we can write

2,4,.......,n-4,n-2,n

Here a= 2 and d = second term- first term = 4-2=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=2 and d=2

$n=2+(t-1)2$

⇒(t-1)2=n-2

$\Rightarrow t-1=\frac{n-2}{2}$

$\Rightarrow t = \frac{n-2}{2}+1$

$\Rightarrow t = \frac{n-2+2}{2}$

$\Rightarrow t = \frac{n}{2}$

Last term l= n, the number of term $=\frac n2$ , First term = 2

Total number of seat

$S_n=\frac{\frac{n}{2}}{2}[2+n}]$

$=\frac{{n}}{4}[2+n}]$

$=\frac{n(2+n)}{4}$

$=\frac{n^2+2n}{4}$

4 0

3 years ago

The average of two numbers is 10.What is the sum of the two numbers?

geniusboy [140]

The sum of the numbers is 20 10+10=20 20/2=10

5 0

2 years ago

Read 2 more answers

Cindy's age, x, is 3 times her age 6 years ago.

Ugo [173]

The algebraic expression for the statement Cindy's age, x, is 3 times her age 6 years ago is 3(x-6).

The given statement is Cindy's age, x, is 3 times her age 6 years ago.

We need to represent the given statement as the algebraic expression.

<h3>What is an algebraic expression?</h3>

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.

6 years ago Cindy's age(x) is x-6.

3 times Cindy's age=3(x-6)

Therefore, the algebraic expression for the statement Cindy's age, x, is 3 times her age 6 years ago is 3(x-6).

To learn more about the algebraic expression visit:

brainly.com/question/953809.

#SPJ1

3 0

1 year ago

So answer this ok WHO HATES JIJI on ST MATH

hoa [83]

Answer:

me

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers