1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SpyIntel [72]
3 years ago
12

Ethan builds two different kinds of chairs, rockers and swivels. It takes him 3 hours to build a rocker and requires 2 oz of sta

in. It takes him 2 hours to build a swivel chair and requires 8 oz of stain. Ethan has 56 oz of stain available and he can only work up to 24 hours. He makes $12 profit on each rocker and $10 profit on each swivel chair. 1. Since there cannot be negative chairs, create two constraints to represent this. 2.Create a constraint for the hours it takes to build the chairs. 3. Create a constraint for the stain it takes for the chairs. PLEASE HELP
Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
8 0

Answer:

(1) x\geq 0\; \text {and}\;y\geq 0

(2) 3x + 2y\leq 24

(3) x+4y\leq 28

Step-by-step explanation:

Let x and y be the numbers of rockers and swivels made by Ethan.

(1) Since the number of chairs can't be negative. So,

x\geq0 and y\geq 0 are the two constraints.

(2) He can work a maximum of 24 hours.

The time required to make 1 rocker chair and 1 swivels chair are 3 hr and 2 hr respectively.

So, the time required to make x rocker chair = 3x hr

and the time required to make y swivel chair = 2y hr.

The total time required is  3x + 2y hr which can't be more than the available time, 24 hr.

So, the required constraint is

3x + 2y\leq 24

(3) Similarly,

As 1 rocker chair requires 2 oz strain and 1 swivel chair required 8 ox strain.

So, to make x rocker chair 2x oz required and make y swivel chair 8y oz required which can't be more than the available oz, 56.

So, the required constraint is

2x + 8y\leq 56

\Rightarrow x+4y\leq 28.

You might be interested in
How can you find 5% of any number using mental math?
Kryger [21]

Answer:

Step-by-step explanation:

I'm not sure my way is going to be any quicker or better. Let's take an example.

Suppose you start with 456

Put a decimal at the end of the 6.   You get 456.

Shift the decimal to the left one place           45.6

Divide by 2

22.8 (done mentally)

Note: dividing by 2 is easier than dividing by 5. Or multiplying by 5 for that matter.

Check the result.

456 * 5/100 =2280 / 100.

Shift a decimal 2 places to the left.

22.80 which agrees with your result.

8 0
3 years ago
Read 2 more answers
(-11x^2 +6) - (14x^2 +2)
Nataly [62]

Answer:

−1(5−2)(5+2)

Step-by-step explanation:

Eliminate redundant parentheses

(−11²+6)−1(14² +2)

Distribute

−11² + 6 -- 1(14² +2)

−11² + 6 - 14² − 2

8 0
2 years ago
) The manager of a local Gap store estimates that on average the probability of a customer entering the store and will purchase
xeze [42]

Answer: 1. 0.0256

2. 0.4096

Step-by-step explanation:

Binomial probability formula , to find the probability of getting x successes:

P(x)=^nC_xp^x(1-p)^{n-x} , where n= Total number of trials

p= Probability of getting success in each trial.

Let x be the number of customers will make purchase.

As per given , we have

p= 0.20

n= 4

1. The probability that 3 of the next 4 customers will make a purchase will be:-

P(x=3)=^4C_3(0.20)^3(1-0.20)^{4-3}

P(x=3)=(4)(0.20)^3(0.80)^{1}\ \ [\because\ ^nC_{n-1}=n]

P(x=3)=(4)(0.008)(0.80)=0.0256

Hence, the probability that 3 of the next 4 customers will make a purchase = 0.0256

2. The probability that none of the next 4 customers will make a purchase will be :

P(x=0)=^4C_0(0.20)^0(1-0.20)^{4-0}

P(x=0)=(1)(0.80)^{4}\ \ [\because\ ^nC_{0}=1]

P(x=0)=0.4096

Hence, the probability that none of the next 4 customers will make a purchase= 0.4096

5 0
3 years ago
Construct a triangle with side lengths 6,6 and 6. what are the angle measures of a triangle
Ann [662]

Answer:

60 degrees

Step-by-step explanation:

Hello! The side lengths of this triangle are all the same, so this is an equilateral triangle. These types of triangles have equal angles. A triangle equals 180 degrees so divide that by three. Each angle in this triangle is 60 degrees. Hope this helps :)

6 0
3 years ago
Read 2 more answers
If one letter is chosen at random from the word assists, what is the probability that the letter chosen will be an "s"?
OLEGan [10]

Answer:

4/7 or 57%

There are 7 letters in the word "assists" and 4 of them are "s"

4 divided by 7 will give you the percentage

7 0
3 years ago
Other questions:
  • Comparison of Ani and Ina 3 money: 5. The amount of their money is Rp.400,000.00. The difference in money is both
    7·1 answer
  • Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Fi
    11·1 answer
  • Rewrite the equation from intercept form to standard form:
    10·2 answers
  • Lisa's favorite chocolate candies are wrapped in the shape of a triangular prism with shiny gold paper as shown below. If all si
    9·1 answer
  • Melissa made a school banner that is 3 yards long in a 11 over 12 yards wide what is the area of the banner
    6·2 answers
  • Corrine's chocolate cake recipe calls for 1 3/4 cups of flour. She has 5 pound bag of flour, and there are 4 cups to each pound.
    9·2 answers
  • Pls answer this correct ;( don't answer it nonsenses. :) Thanks!
    14·1 answer
  • One more i need help with plz answer I need it done by today
    5·2 answers
  • Four over seven equals twelve over g<br> A. 21<br> B. 15<br> C. 24<br> D. 3
    12·2 answers
  • Find the radius of a circle with an area of 1,124 sq feet.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!