Four times the difference of a number and 16.

Answer:

Solution is:

z  (max) = 687.5

x₁   =  0

x₂   = 16

x₃   = 21

Step-by-step explanation:

From the problem statement we have:

Resources:      machine time ( 183 h)      labor (250  h)   steel  185 (pounds)

Unit

Spoons                          4                                     4                          3

forks                               4                                     9                          2

knives5                          5                                     5                          4

Profit $                           9                                    20                       17.5

Objective function z =  9*x₁  +  20*x₂  + 17.5 *x₃   to maximize

Subject to:

Availability of machine time  :  183 h

4*x₁  +  4*x₂ +   5*x₃ ≤  183

Availability of labor  :  250 h

4*x₁  +  9*x₂  +  5*x₃  ≤  250

Availability of steel  :  185 pounds

3*x₁  +  2*x₂  +  4*x₃  ≤  185

Requirement:

x₂ ≥ 16

General constraints:

x₁  ≥ 0             x₃      ≥  0 all integers

After 6 iteration the solution using AtomZmath on-line solver

z  (max) = 687.5

x₁   =  0

x₂   = 16

x₃   = 21

Resources used:

Machine time: 16* 4 + 21*5  =  64  +  105  = 169

remains   183 - 169  = 14 h

Labor:  16*9  +  21* 5  =  144  +  105  =  249

remains   250 -  249  =  1 h

Steel :  16*2  +  21*4  =  32  + 84  =  116

remains   185  -  116  = 69 pounds.

If it is decided that 20 units of forks are to be made then

we will need   4*4 = 16   h of machine time

                         9*4 =  36 h  of labor

                         2*4 = 8 pounds of steel

We can get that from abandom to make one unit of x₃ ??

No because as we said we need 36 hours  of  labor ( we still have 1 we need 35 more hours ) if we make 20 x₃ insted of 21 we get only 5 hours.

z we got is maximum

Answer:boy

Step-by-step explanation:boy

Mr. Smith exercises for between 10 and 40 minutes on 77.45 percent of the days in a year.

Given that his exercising time follows a normal distribution with a mean of 30 minutes and a standard deviation of 10 minutes.

Here we have to find the percentage of days in a year that Mr. Smith exercises for between 10 and 40 minutes,

First, we need to standardize the values of 10 and 40 minutes using the formula,

⇒ z = (x - μ) / σ

where x is the value we want to standardize,

μ is the mean,

And σ is the standard deviation.

For x = 10:

⇒ z = (10 - 30) / 10

       = -2

For x = 40:

⇒ z = (40 - 30) / 10

      = 1

Now, we need to find the probability of Mr. Smith exercising between -2 and 1 standard deviations from the mean.

We can use a standard normal distribution table or a calculator to find this probability.

Using a standard normal distribution table,

we can find the probability of z being between -2 and 1 is about 0.7745. This means that on approximately 77.45% of the days in a year, Mr. Smith exercises for between 10 and 40 minutes.

Therefore,

Mr. Smith exercises for between 10 and 40 minutes on approximately 77.45% of the days in a year.

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ2

Answer:

Yes, there are exactly 2 ways to solve this triangle.

Step-by-step explanation:

Well we know that to find out a trigonometric ratio we are given an angle and a side, and we have to solve for the other side. In this case only 2 of the legs are given, hypotenuse is neither given nor asked. So we have to use the ratio that doesn't have hypotenuse included. Tangent is the only such ration. Now we can use either Tan(51) or Tan(39) to solve for the "x".

These would be the functions to solve for x:

1.)     Tan(51) = [tex]\frac{x}{10}[/tex]

2.)    Tan (39) = [tex]\frac{10}{x}[/tex]

Hope this helps!

Answer:

{16,20,24,28}

Step-by-step explanation:

___________

Answer:

-4, 3

Step-by-step explanation:

To find x intercepts, set y equal to 0;

0 = 5(x+4)(x-3); when x = -4 or x = 3, y will be zero (these are the x intercepts),

Answer:

I think is b

Step-by-step explanation:

sorry if it is not right

Answer:

43% of the students prefer biology

Step-by-step explanation:

Among girls:

39 of the students are girls.

21 of the girls like biology best.

Boys:

100 - 39 = 61 are boys.

16 prefer physics

11 out of the 34 who prefer chemistry are girls, so 34 - 11 = 23 are boys.

61 - (16 + 23) = 22 prefer biology.

What percentage of the students prefer biology?

21 boys and 22 boys, that is, 43 students out of 100. So

43*100%/100 = 43%

43% of the students prefer biology

Answer:

Yes the square of the total spin of two electrons is conserved ( s^2)

Step-by-step explanation:

using the Hamiltonian operator H = A · (σ1 × σ2)

S = ( S1 + S2 )

S^2 = S²₁ + S²₂ + 2S₂ . S₂ ( apply the equation of time evolution )

Attached below is the detailed solution

Answer:

x² + 3x - 10

Step-by-step explanation:

( x + 5 ) ( x - 2 )

→ Expand

x² + 5x - 2x - 10

→ Simplify

x² + 3x - 10

Answer:

5/52.

Step-by-step explanation:

Prob(Jack of hearts) = 1/52 - as there is only 1 jack hearts in pack.

Prob(Ace drawn) = 4/52 as there are 4 aces.

Answer:

C. (10x - 2) units

Step-by-step explanation:

Perimeter of a rectangle:

The perimeter of a rectangle of length l and width w is given by:

[tex]P = 2(l + w)[/tex]

A rectangle has a length of (3x - 4) units and a width of (2x + 3) units.

This means that [tex]l = 3x - 4, w = 2x + 3[/tex]

What is the perimeter of the rectangle in terms of x?

[tex]P = 2(l + w) = 2(3x - 4 + 2x + 3) = 2(5x - 1) = 10x - 2[/tex]

The correct answer is given by option C.

Answer:

10

Step-by-step explanation:

Angles 8x - 12 and 6x + 8 are adjacent angles.

Adjacent angles are equal.

8x - 12 = 6x + 8

8x - 6x = 8 + 12

2x = 20

x = 20 / 2

x = 10

Answer:

8x-12=6x+8

[corresponding angle]

8x-6x=12+8.

x=20/2

x=10

Answer:

(2x + 3)(x - 2)

Step-by-step explanation:

use FOIL

First, Outside, Inside, Last

2x x x = 2x²

2x x -2 = -4x

3 x x = 3x

3 x -2 = -6

2x² - 4x + 3x - 6

Answer:

Step-by-step explanation:

(21+13/74-18x3)x10=17

rad3/ 2=0.86

ad 281^r2-160^2=231

2^10-2^9=512

ultima= 4

Given:

The diagram of a circle.

[tex]m\angle BPV=124^\circ ,m\angle VPE=30^\circ ,m\angle EPF=76^\circ, m\angle FPD=48^\circ[/tex].

To find:

The measure of arc BEF.

Solution:

The measure of central angle is equal to the measure of corresponding arc.

So, in the given figure,

[tex]n(arcBV)=124^\circ ,m(arcVE)=30^\circ ,m(arcEF)=76^\circ, m(arcFD)=48^\circ[/tex]

Now,

[tex]m(arcBEF)=m(arcBV)+m(arcVE)+m(arcEF)[/tex]

[tex]m(arcBEF)=124^\circ +30^\circ+76^\circ[/tex]

[tex]m(arcBEF)=230^\circ[/tex]

Therefore, the measure of arc BEF is 230 degrees.

Answer:

108: 4x3^3, 3^2x12, 6^2x3

96: 2^5x3, 2^3x122^4x6

Step-by-step explanation:

Answer:

you can do 2^12=4096

there are 4096 different ways nick can answer the question

Answer: 1/12 or 8.3%

Step-by-step explanation:

probability of a 2 on the cube: 1/6

probability of tails on the quarter: 1/2

1/6*1/2=1/12

1/12 or 8.33333% (round to 8.3%)

Answer:

do you go gca too

Step-by-step explanation:

The best way to sample the population so that she can conduct a survey is to conduct a random sampling

From the question, we have the population to be:

Population = 5000

In order to conduct a survey, Tasha must carry out a random sampling by using the following steps

The above is called a random sampling technique

Read more about random sampling at:

https://brainly.com/question/14470673

#SPJ2

Answer:

$10.67

Step-by-step explanation:

If you made 20,800 a year, your hourly wage would be $10.67

Answer:

The hourly wage is $56.98

Step-by-step explanation:

20,800/365 equals 56.98

Answer:

Square pyramid

Step-by-step explanation:

Answer: in photo

Step-by-step explanation:

Photo

Answer:

its 40

Step-by-step explanation:

1x20 = 20

and 2x20=40

Answer:

C) 40

Step-by-step explanation:

Ratio of blue to white marbles: 1:2 = 20:40