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Using proportions, it is found that the expression that can be used to find the number of inches in 6 feet is given by:

6 feet = 6 x 12 inches = 72 inches.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the rule of three is given as follows:

1 foot - 12 inches.

6 feet - x inches.

Applying cross multiplication:

6 feet = 6 x 12 inches = 72 inches.

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Given:

Product A requires 7 board feet of wood and 4 lbs of wicker.

Product B requires 5 board feet of wood and 5 lbs of wicker.

Product C requires 4 board feet of wood and 3 lbs of wicker.

Available wood = 3000 board feet

Available wicker = 1400 lbs

Profit margin of A = $35 per unit

Profit margin of B = $42 per unit

Profit margin of C = $20 per unit

To find:

The linear programming problem for given situation.

Solution:

Let the number of units produced of products A, B and C are x, y and z respectively.

                                Product A       Product B           Product C      Total

Board feet of wood       7                       5                       4               3000

wicker                            4                       5                        3               1400

Objective function: Maximize [tex]z=35x+42y+20z[/tex]

s.t.,

Board feet of wood  : [tex]7x+5y+4x\leq 3000[/tex]

Wicker : [tex]4x+5y+3x\leq 1400[/tex]

Number of units  cannot be negative. So, [tex]x,y,z\geq 0[/tex].

Therefore, the required LPP is

Maximize [tex]z=35x+42y+20z[/tex]

s.t.,

[tex]7x+5y+4x\leq 3000[/tex]

[tex]4x+5y+3x\leq 1400[/tex]

[tex]x,y,z\geq 0[/tex]

Answer:

D, F

Step-by-step explanation:

rational numbers

real numbers

Answer:

68y-42

Step-by-step explanation:

Answer:

68 y-42

Step-by-step explanation:

Answer:

I'm pretty sure its b

Step-by-step explanation:

I plotted each one to make a polynomial graph and b was the one that had the x-intercepts at -6, 1, and 4.

hope this helped a little :))

Answer:

How to Easily Calculate the Serving Size in Recipes

Weigh the Food. Before you can accurately divide your recipe into servings, you need to know how much it weighs in total. ...

Divide the Recipe into Servings. ...

Calculate Calories. ...

Save the Information.

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

A deck of card:

Number of hearts = 13

Diamond = 13

Spade = 13

Club = 13

Each of heart, club diamond and spade has is numbered from (2,3,4,5,6,7,8,9,10,Ace, queen, Jack, king)

Hence, a club, diamond, spade and heart has one of each of the above numbers.

a. List the sample points in the event a jack is selected.

Jack : ( heart, club, diamond, spade)

B.) club is selected :

Cub : (Ace, 2, 3,4,5,6,7,8,9,10,king,queen,jack)

C)

Jack : ( heart, club, diamond, spade)

Queen : (heart, club, diamond, spade)

King : (heart, club, diamond, spade)

D) probability = required outcome / Total possible outcomes

P(jack selected) = 4 /52 = 1/13

P(club selected). = 13/52 = 1/4

P(face card selected) = 12 / 52 = 3/13

Answer:

50.1

The area of the composite figure is 50.1

Trust me

Answer:

A

Step-by-step explanation:

Answer:

medians in the triangle

Step-by-step explanation:

just took the test

Answer:

a

   This data does not  support the Minister of Commerce or Amnesty

International

b

Another issue that is  important when evaluating this data is the judicial system of the Turgistan

Step-by-step explanation:

From the question we are told that

  The  sample size is  n  =  500

 The  number of political  prisoners is  k  =  90

  The  level of significance is  [tex]\alpha = 0.05[/tex]

        The null hypothesis  is  [tex]H_o  :  p =  \frac{1}{3} =  0.33[/tex]

        The alternative hypothesis is  [tex]H_a : p \ne  0.33[/tex]

Generally the sample proportion is mathematically represented as

      [tex]\^ p  =  \frac{k}{n}[/tex]

=>   [tex]\^ p  =  \frac{90}{500}[/tex]

=>   [tex]\^ p  =  0.18[/tex]

 Generally the test statistics is mathematically represented as

    [tex]z =  \frac{\^ p  -  p}{\sqrt{\frac{p (1- p)}{n} } }[/tex]

=>  [tex]z =  \frac{0.18  -  0.40}{\sqrt{\frac{0.33 (1- 0.33)}{500} } }[/tex]      

=>  [tex]z = -7.1429 [/tex]

Generally the p-value is mathematically represented as

      [tex]p-value  =  2 *  P( Z  >  -7.1429)[/tex]

From the normally distribution table

    The  probability of [tex]P( Z  >  -7.1429)  =  0[/tex]

=>     [tex]p-value  =  2 * 0[/tex]

=>     [tex]p-value  =  0[/tex]  

From the value obtained we see that the [tex]p-value  <  \alpha[/tex] hence the decision rule is

  Reject the null hypothesis

The conclusion is  

  There is no sufficient evidence to conclude that  this data does support the Minister of Commerce or Amnesty International

jj

Answer:

b

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

Answer:  A) The equation will be     x + 4x + x + 10 = 82   B) Paul's age is 12, Rebecca's age is 48  and Gemma's age is 22.

Step-by-step explanation:

We will represent Paul's age by    the equation  p= x  where p is Paul

We will represent Rebecca's age by the equation  r = 4x  Where r is Rebecca

We will represent Gemma's age by the equation g = x + 10  where g is also Gemma's age.

We given that the sum of their ages is 82 years so meaning that  x + 4x + x + 10  has to equal 82.

A) The equation will be     x + 4x + x + 10 = 82  

Solve for the x equation to find Paul age because his age is x.

B)  (x) + (4x) + (x+10) = 82   combine like terms on the left side

    6x + 10 = 82

           -10    -10

   6x = 72

   x= 12  

Paul age is 12.  

r= 4(12)

r = 48

Rebecca's age is 48.

g= 12 +10

g= 22

Gemma's age is 22.  

7

The digit in ten thousandths place is 7 as it is the fourth digit to the right of decimal point.

Answer:

8

Step-by-step explanation:

9= one hundred thousands

8= ten thousands

3= one thousands

4= one hundreds

7= tens

1= ones

Answer:

(0, 7)

Step-by-step explanation:

y = mx + c

c is the y-intercept - where the line crosses the y-axis

Answer:

r(q(2)) = 11

Step-by-step explanation:

given r(x) = x^2 + 2, and q(x) = -2x + 1.

Here is the equation to the composite function:

r(q(x)) = (-2x+1)^2 + 2 = 4x^2-4x+3 .

Then just substitute the input and solve:

r(q(2)) = 4(2)^2- 4(2) + 3 = 16 - 8 + 3 = 16 - 5 = 11

______________________________

Or if you don't like this, first find the answer to q(2) = -2(2) + 1 = -3

Then substitute this value into the second equation r(x).

r(x) → r(-3) = (-3)^2 + 2 = 9 + 2 = 11

Answer:

9 dollars or B

Step-by-step explanation:

16.50 (hourly wage) x 6 (hours worked) = 99 dollars

$99/11 deliveries= 9 dollars per delivery.

Answer:

$1.12

Step-by-step explanation:

When you multiply 8/7 of 56, you get 64.

This shows that you will need 64 paperclips to make 56 inches worth of paper clips. If each paper clip costs two cents, you need to multiply 56 paperclips by 2 cents. 56x0.02=1.12 so it will cost you 1 dollar and twelve cents

Answer:

2 mi per hour

Step-by-step explanation:

1/3*6=

6/3= 2

2 mi per hour

Answer:

2mph

Step-by-step explanation:

If a person walks 1/3 of a mile every 1/6 of an hour you divide to solve.

[tex]\frac{\frac{1}{3}}{\frac{1}{6}}[/tex] To solve you flip the bottom and multiply:

[tex]\frac{1}{3} *\frac{6}{1}[/tex] = [tex]\frac{6}{3} = 2[/tex]

The person is walking 2mph

Answer:

rwqrqwrq

Step-by-step explanation:

Answer:

2 hours 50 minutes

Step-by-step explanation:

subtract 3:48 from 6:38

and you get 2 hours 50 minutes.

Answer:

One hundred million, two hundred, 4 thousand one, hundred eighty

The word form of 100204180 is One hundred million, two hundred, 4 thousand one, hundred eighty.

Given,

100204180 .

Now,

To write the numerical from in the word form,

100204180 = One hundred million, two hundred, 4 thousand one, hundred eighty.

Thus the number is of the range of hundred million.

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Answer:

Step-by-step explanation:

Total energy of the sandwich = 628kcal

Mass of fat contained = 36grams

Convert gram to kcal

1gram = 9kcal

36 grams = x

x = 36×9

x = 324kcal

Hence the fat contains 324kcal

%fat contained = fat(in kcal)/total calorie × 100%

%fat contained = 324/628 × 100%

%fat contained = 1/2 × 100%

%fat contained = 50%

Hence approximately 50% of the total energy is contributed by fat.

Answer:

600 ×1200=720,000

720,000×12=8,640,000

8,640,000×1%=8,640,000÷100%=86,400

86,400 per year

Answer:

Step-by-step explanation:

Answer:

f(-3)= 18

Step-by-step explanation:

step 1: sub -3 in the equation f(x).

f(x)= -2x+12

f(-3)= -2×-3+12

step2: simplify to solve for f(-3).

=6+12

=18

Answer: I got this answer wrong but I go two right look at the step by step explanation

Hopefully that helped a little

Step-by-step explanation:

The expression (x + 5) is a factor of given function f(x) So the remainder of the function will be zero.

Remainder theorem:

The given function,

[tex]f(x) = x^3+3x^2-25x-75[/tex]

Equate (x + 5) is equal to 0.

x + 5 = 0

x = -5

Substitute x = -5 in given equation.

[tex]f(x) = x^3+3x^2-25x-75\\\\f(-5) = -5^3+3(-5)^2-25(-5)-75\\\\f(-5) = 0[/tex]

Since f(-5) = 0. thus, (x + 5) is a factor of given function f(x).

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