Two chemical plants, one at Macon and one at Jonestown, produce two types of fertilizer, low phosphorus (LP) and high phosphorus (HP). At each plant, the fertilizer is produced in a single production run, so the two types are produced in fixed proportions. The Macon plant produces 1 ton of LP and 3 tons of HP in a single operation, and it charges $600 for what is produced in one operation, whereas one operation of the Jonestown plant produces 1 ton of LP and 1 ton of HP, and it charges $1,000 for what it produces in one operation. If a customer needs at least 100 tons of LP and 180 tons of HP, how many production runs from each plant should be ordered to minimize the cost.

Answer:

y = 16

Step-by-step explanation:

Given that,

y varies inversely with x i.e.

[tex]y=\dfrac{k}{x}[/tex]

Where

k is a constant of proportionality

Put y = 48 and x = 6 in the above equation to find k.

So,

[tex]k=48\times 6\\\\k=288[/tex]

Now put k = 288 and x = 18 in the above equation to find y.

[tex]y=\dfrac{288}{18}\\\\y=16[/tex]

So, the value of y is equal to 16 when x = 18.

Answer:

16

Step-by-step explanation:

Answer:

(x-7)(x+4)

Step-by-step explanation:

PLATO

Answer:

36

Step-by-step explanation:

Ken = 6 yo

6 *3 = 18

Richard = 18 yo

8 * 2 = 36

Micah = 36

The age of Micah is 36 years.

A subfield of mathematics known as arithmetic operations deals with the study and application of numbers to all other subfields of mathematics. Operations like addition, subtraction, multiplication, and division make up the bulk of it.

These fundamental mathematical operations  (+, -, ×, and ÷) that we use every day.

Given age of Ken = 6 years

let age of Micah be m and age of Richard be r

acc. to condition

Micah is twice as old as Richard

m = 2r

Richard is three times as old as Ken

r = 3 ken

r = 3 x 6

r = 18

Richard age is 18 years.

m =2r

m = 2 x 18

m = 36 years

Hence age of Micah is 36 years.

Learn more about arithmetic operation;

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Answer/Step-by-step explanation:

✔️Using trigonometric ratio, find b:

Reference angle = 45

opposite = 8

Hypotenuse = b

Thus,

Sin(45) = 8/b

b = 8/sin(45)

b = 8/(1/√2) (sin 45 = 1/√2)

b = 8 × √2/1

b = 8√2

✔️Find a using trigonometric ratio:

Reference angle = 60°

Hypotenuse = b = 8√2

Adjacent = a

Therefore,

Cos(60) = a/8√2

8√2*cos(60) = a

8√2*½ = a

4√2 = a

a = 4√2

✔️Find c using Pythagorean Theorem:

c² = b² - a²

c² = (8√2)² - (4√2)²

c² = 128 - 32

c² = 96

c = √96

c = √(16*6)

c = 4√6

Answer:

Answer:

Step-by-step explanation:

Wait where is the picture

Answer:

  3x - 4 = -2x + 3

3x + 2x = 3 + 4

       5x = 7

        x = 5/7

Step-by-step explanation:

1. move the same term to one side

2. the rest are simply solving equation

Answer:

s [tex]\leq[/tex] 14

Step-by-step explanation:

divide both sides by 7

Answer: For the first part, the answers are 4, 9, 11, 13, and 14. I have no idea how to do the 2nd part though. Sorry.

Step-by-step explanation: Divide 98 by 7. This gives you 14. However, s can be equal to or less than 14, giving you multiple answers which are 4, 9, 11, 13, and 14. Hopefully this helps.

Answer:

When x = 1, y = -2

Step-by-step explanation:

The equation of this line is y = x - 3, so when x = 1, y would equal 1 - 3 or -2.

Answer:

x=1, then y= -2

Answer:

(f o h)(-5)=-33

Step-by-step explanation:

Let f(x) = 4x - 1, h(x) = - X-3.

(f o h)=4(-x-3)-1

(f o h)=-4x-12-1

(f o h)=-4x-13

(f o h)(-5)=-4(-(-5))-13

(f o h)(-5)=-20-13

(f o h)(-5)=-33

Answer:

15.

a)

i)43/9= 4 7/9

ii)17/4= 4 1/4

b)

i)3 9/11=  42/11 - 11 times 3=33, 33+9=42

ii)5 6/12= 66/12 - 12 times 6=60, 60+6=66

Answer:

m = -2

Step-by-step explanation:

5m - 2 = -12

Isolate m.

5m = -12 + 2

5m = -10

m = -10/5

m = -2

Answer:

how to make change for 50 cent.

Step-by-step explanation:

1. 3 dimes and 4 nickels

3 x 10 = 30. 4 x 5 = 20.

30 + 20 = 50

2. 2 quarters

25 + 25 = 50

3. 1 quarter and 2 dimes and 1 nickel

25 + 20 + 5 = 50

4. 5 nickels and 1 quarter

5 + 5 + 5 + 5 +5 + 25

Answer: 14 boys

Step-by-step explanation:

ratio 2:3

7 divided by 21 = 3, so 7 times 2 equals 14

Answer:

14

Step-by-step explanation:

Divide 21 by 3, you get 7. Multiply 7 by 2, you get 14.

Answer:

Positive 2 or Negative 4

Step-by-step explanation:

If this is on a number line

Answer:

it would be 7 divided by 10, so .7 i think?

Step-by-step explanation:

Answer:

7/10

Step-by-step explanation:

7/10 bc if there are 7 mangos and 10 friends then 10 (the number of friends ) is the amout in all and 7 (the amout of mangos ) is the fraction of the whole that willl be passed out

The sum of an interior angle and an exterior angle is 180°. Then the 130° is not an exterior angle of the triangle.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

The two angles of a triangle have measures of 55° and 65°. Then the third angle (x) will be

w + 55° + 65° = 180°

                  w = 180° - 120°

                  w = 60°

Let the exterior angle be x, y, and z.

The sum of an interior angle and an exterior angle is 180°. Then we have

[tex]\rm x = 180^o - 55^o = 125^o \\\\y = 180^o - 65^o = 115^o \\\\z = 180^o - 60^o = 120^o[/tex]

More about the triangle link is given below.

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Answer:

Heat and sound energy

Step-by-step explanation:

It starts off as potential energy, which is then converted to kinetic energy and by impact it'll develop a sound and heat energy.

Sound waves generates heat, and if some glass fell on the floor you can heat the shatter from the sound waves. The same goes for a book.

Answer:

2

Step-by-step explanation:

Its quite obvious

It would take 0.5 seconds for the ball to hit the ground.

To solve this problem, we are to use one of newton equations. Let us use:

s = ut + (1/2)gt²

Where u is the initial velocity = 88 ft/s, s is the height = 48 feet and g is the acceleration due to gravity = 32 ft/s²

Hence:

48 = 88t + 0.5*32*t²

16t² + 88t - 48 = 0

t = -6 or 0.5

Since the time cannot be negative, hence t = 0.5 seconds

It would take 0.5 seconds for the ball to hit the ground.

Find out more on Newton law at: https://brainly.com/question/25545050

Answer:

70 feet total

Step-by-step explanation:

Answer:

4,000

Step-by-step explanation:

50•80=4,000

Answer:

2.64575

Step-by-step explanation:

Answer: it would be 0.6

Step-by-step explanation: why?, because, you must divided 60,000 by 100,000. To get the kilometer 0.6 I hope this helps :), I also took the test!.

Answer:

0.6

Step-by-step explanation:

the answer above is correct

Answer:

29 and 31

Step-by-step explanation:

What integer is -1 away from 30? 29. What integer is +1 away from 30? 31. 29 and 31

x =76° is the answer

Step-by-step explanation:

because being alternate angle.

Answer:

Measure the line of x only from scale and how much it came its the answer

Step-by-step explanation:

X+76=180

x=180-76

Therefore,x=104.

Hope it will help you be happy!

Answer:

i might not be correct but 33?

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

trust me i just did it. it was very hard but i got it.

Answer:

In general for a point we have (in, out)

The domain is the set of all the 'in's and the range is the set of all the 'out's

Domain: {2, 8, 1, 7} or {1, 2, 7, 8} in order

Range: {5, 3, 9} or {3, 5, 9}

Sets do not contain duplicates so 5 appears only once.

Answer:

This measure is just 0.17 standard deviations from the mean, so we should not be surprised.

Step-by-step explanation:

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If the z-score is lower than -2, or higher than 2.5, the score of X is considered unusual.

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

Let xS – xL represent the sampling distribution.

Mean s 6, means L 4. So

[tex]\mu = 6 - 4 = 2[/tex]

Standard deviation s is 2.5, for L is 1.5. So

[tex]\sigma = \sqrt{2.5^2+1.5^2} = 2.915[/tex]

Should we be surprised if the sample mean housebroken age for the small breed dogs is at least 2.5 months more than the sample mean housebroken age for the large breed dogs? Explain your answer.

We have to find the z-score for X = 2.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.5 - 2}{2.915}[/tex]

[tex]Z = 0.17[/tex]

This measure is just 0.17 standard deviations from the mean, so we should not be surprised.