Write the following set using roster notation. Do not include repeats.
C is the set of colors in a U.S. flag.

Answer:

The answer is below

Step-by-step explanation:

a) Food I contains 3 g of carbohydrate and food II 5 g of carbohydrate. x is the number of ounce of food I while y is the number of ounce of food II.

Therefore, the amount of carbohydrate in food 1 is 3x while that of food II is 5y. Since the blend contains  exactly 73 g of carbohydrate, the total number of carbohydrate in both food I and food II is 73 g. Hence:

3x + 5y = 73                    (1)

Food I contains 2 g of protein and food II 3 g of carbohydrate. Therefore, the amount of protein in food 1 is 2x while that of food II is 3y. Since the blend contains  exactly 46 g of protein, the total number of protein in both food I and food II is 46 g. Hence:

2x + 3y = 46                   (2)

Using geogebra to Sketch the graphs of both equations.

b) The point of intersection is gotten from the graph, this gives x = 11, y = 8.

The point of intersection shows the amount of food I and food II that give the required amount of protein and carbohydrate.

11 ounce of food I and 8 ounce of food II would produce the required amount of protein and carbohydrate

Step-by-step explanation:

z=y+16

y=y

:.z+y=5x where z=y+16

2y+16=5x

x=(2y+16)/5

.:z+y+x=180

y+16+y+(2y+16)/5=180

12y+80+16=900

y=67

z=16+67=83

x=30

Answer:

12 boxes an hour

Step-by-step explanation:

If Adsila made 9 boxes an hour for 6 hours,she made 54 boxes (9*6=54). Take how many she made away from the total (126-54=72). If Carlos made 72 boxes in 6 hours, divide 72 by 6 to get 12 (72/6=12). Carlos made 12 boxes an hour.

Answer:

Probability that the measure of a segment is greater than 3 = 0.6

Step-by-step explanation:

From the given attachment,

AB ≅ BC, AC ≅ CD and AD = 12

Therefore, AC ≅ CD = [tex]\frac{1}{2}(\text{AD})[/tex]

                                  = 6 units

Since AC ≅ CD

AB + BC ≅ CD

2(AB) = 6

AB = 3 units

Now we have measurements of the segments as,

AB = BC = 3 units

AC = CD = 6 units

AD = 12 units

Total number of segments = 5

Length of segments more than 3 = 3

Probability to pick a segment measuring greater than 3,

= [tex]\frac{\text{Total number of segments measuring greater than 3}}{Total number of segments}[/tex]

= [tex]\frac{3}{5}[/tex]

= 0.6

Answer:

LCM = 20

Step-by-step explanation:

You need to make everything into 20. Luckily, 4X5 is 20 and vise versa.

Answer:

All real numbers

Step-by-step explanation:

Solution set of -2(x +3) = -2x -6 is all x ∈R (real numbers).

" Equation is defined as when two algebraic expression which are related with the sign of equality."

According to the question,

Given,

-2(x + 3) = -2x - 6

Open the brackets of the equation we get,

-2(x) + (-2)(3) = -2x - 6

⇒ -2x - 6 = -2x - 6

Add 6 on both the sides of the equation we get,

-2x = -2x

Divide by -2 of the equation both sides

x = x                                 _____(1)

Add (-x) both the sides we get,

0 = 0                                 _____(2)

From (1) and (2) we conclude ,

Solution is true for all  the real values of x.

Hence, solution set of -2(x +3) = -2x -6 is all x ∈R (real numbers).

Learn more about equation here

https://brainly.com/question/10413253

#SPJ2

Answer:

x=-6

For PA:  78-29=49

For AQ:  48+3=51

Step-by-step explanation:

The line is from left to right PAQ

It says PQ is 100 which is the whole line

PA +AQ is PQ so that means:

-13x-29-8x+3=100

-21x-26=100

-21x=126

x=-6

Plug in the x values to PA and AQ

For PA:  78-29=49

For AQ:  48+3=51

Answer:

(-1,-4)

Step-by-step explanation:

(-5,-3) if we're moving four units right on the x axis, it would be a bigger number near the center.  Think of it as adding -5 and 4, which would get you -1 for x (-1,x)

Now to get y, we would basically do the same thing except if it's going down, it would be a negative.  We would add both -1 and -3 together to get -4, hence the answer, (-1,-4)

I suggest drawing a graph and doing it yourself, it'll really help you.

Answer: 93

Step-by-step explanation:

To solve this problem, we need to use the order of operations, or PEMDAS.

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

For multiply/divide and add/subtract, you don't necessarily go in that specific order. You go from left to right, depending on what comes first. For example, if division comes before multiply, you would divide first, then multiply. Same goes for add/subtract.

9²+3×(9-5)²/4                          [solve parenthesis]

9²+3×(4)²/4                              [solve exponent]

81+3×16/4                                [solve multiply or divide, whichever comes first]

81+12                                        [solve add or subtract, whichever comes first]

93

Now, we know that 93 is our final answer.

Answer:

Sam can do more work.

Step-by-step explanation:

2/3 equals out to just over half of his work done. 0.66666667.

3/4 equals out to almost all of her work done. 0.75.

*hope this helps*

Answer:

Sam can do more work:)

Step-by-step explanation:

Answer:

Associative property is the math strategy Josiah used

Answer:

n - 6 = 5 * ( n + 2 ) ; n = -4

Step-by-step explanation:

For this problem, we will use the words to create an equation.  The left hand side of the equation will be the difference of a number and 6 and the right hand side of the equation will be 5 times the sum of the number and 2.  Hence, we can build the equation:

n - 6 = 5 * ( n + 2 )

If we wanted, we can solve the equation for the number, n.

n - 6 = 5 * ( n + 2 )

n - 6 = 5 * n + 5 * 2

n - 6 = 5n + 10

-16 = 4n

-4 = n

Thus, we have found the missing number to be negative four.

Cheers.

Answer:

b) 8.

Step-by-step explanation:

The tens digit must be 2, 4, 6 or 8.

The units digit must be 0 or 5 ( as the 2 digit number must be divisible by 5).

So they are:

20, 25, 40, 45, 60, 65 , 80 and 85.

Answer:The tens digit must be 2, 4, 6 or 8.

The units digit must be 0 or 5 ( as the 2 digit number must be divisible by 5).

So they are:

20, 25, 40, 45, 60, 65 , 80 and 85.

Step-by-step explanation:

Answer: (x,y) —> (x+4, y-3)

it could also be T 4, -3 (x,y)

Step-by-step explanation:

If you move something right 4, x+4. Moving something down 3 is y-3.

the general form is always (x,y) —> (x + (whatever)), y + (whatever))

Or T whatever, whatever (x,y)

The first (whatever) is applied to x, second is for y.

hopes this helps

Answer:

22

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

6 + 24 ÷ 3 x 4 ÷ 2

Step 2: Divide

6 + 8 x 4 ÷ 2

Step 3: Multiply

6 + 32 ÷ 2

Step 4: Divide

6 + 16

Step 5: Add

22

Answer:

The possible number of combination to select two positions from 9 people is 72.

Answer:

49

Step-by-step explanation:

7x7=49

Answer:

49

Step-by-step explanation:

7x7=49

Answer:

it will take a programmer about 16.67 times to work before they are fired

Step-by-step explanation:

From the information given;

The transistion matrix for this study can be computed as:

       P          M         X

P     0.7      0.2        0.1

M     0        0.95     0.05

X      0        0            1

where;

The probability that the programmer remains a programmer = [tex](P *P)[/tex]

The probability that the programmer turns out to be a manager = [tex](P*M)[/tex]

The probability that the programmer is being fired = [tex](P*X)[/tex]

Thus, the required number of years prior to the moment being fired for an employee y(P), for programmer and y(M) for manager is represented by ;

[tex]y(P)=1+0.7y(P)+0.2y(M)[/tex]

[tex]y(M)=1+ 0.95y(M).[/tex]

[tex]0.05y(M)=1[/tex]

y(M) = [tex]\dfrac{1}{0.05}[/tex]

y(M) =20

y(P)=1+0.7y(P)+0.2y(M)

y(P) - 0.7y(P) = 1 + 0.2y(M)

0.3y(P) = 1 + 0.2(20)=1+4

0.3y(P) = 1 + 4

0.3y(P) =  5

[tex]y(P)=\dfrac{5}{0.3}[/tex]

[tex]y(P)=16.67[/tex]

Therefore, it will take a programmer about 16.67 times to work before they are fired

Answer:

y=2x-5

Step-by-step explanation:

y is double x minus 5

2x+5

Step-by-step explanation:

let the number be x

According to the question

2x+5

hope it whould help

Answer:

8.1

Step-by-step explanation:

the answer the problem is 8.1

Answer:

10%

Step-by-step explanation:

convert fraction (ratio) 9/90 Answer : 10%

Answer:

The test statistics is  [tex]t  =  -1.727[/tex]

Step-by-step explanation:

From the question we are told that

The data given is  

   330 620 1870 2410 4620 6396 7822 81028309 12882 14419 16092 18384 20916 23812 25814

 The population mean is  [tex]\mu  =  14400[/tex]

    The  sample  size is  n =  16

  The  null hypothesis is  [tex]\mu \le  14400[/tex]

    The  alternative hypothesis is  [tex]H_a  :  \mu > 14400[/tex]

The sample mean is mathematically evaluated as

  [tex]\= x  =  \frac{\sum x_i}{n}[/tex]

So

   [tex]\= x  =  \frac{330+ 620+ 1870 +2410+ 4620+ 6396+ 7822+ 8102+8309+ 12882+ 14419+ 16092+ 18384 +20916+ 23812+ 25814 }{16}[/tex]

=>  [tex]\= x = 10799.9[/tex]

The  standard deviation is mathematically represented as

      [tex]\sigma =\sqrt{\frac{ \sum (x_i - \=x)^2}{n}} [/tex]

So

[tex]\sigma =\sqrt{\frac{(330- 10799.9)^2 + (620- 10799.9)^2+ (1870- 10799.9)^2 +(2410- 10799.9)^2 + (4620- 10799.9)^2 +(6396- 10799.9)^2 +(7822- 10799.9)^2 }{16}}  \ ..[/tex]

   [tex]..\sqrt{ \frac{(8102 - 10799.9)^2 +(8309 - 10799.9)^2 + (12882 - 10799.9)^2 + (14419 - 10799.9)^2 + (16092 - 10799.9)^2 + (18384 - 10799.9)^2 +(20916 - 10799.9)^2  }{16}} \ ...[/tex]

  [tex]\ ... \sqrt{\frac{(23812 - 10799.9)^2 +(25814 - 10799.9)^2 }{16}}[/tex]

=>  [tex]\sigma  =  8340[/tex]

  Generally the test statistic is mathematically represented as

  [tex]t =  \frac{10799.9- 14400}{ \frac{8340}{\sqrt{16} } }[/tex]

[tex]t  =  -1.727[/tex]

From the z-table  the p-value is  

     [tex]p-value  = P(Z > t) =  P(Z >  -1.727) =  0.95792[/tex]

 From the values obtained we see that

        [tex]p-value  >  \alpha[/tex]  so we fail to reject the null hypothesis

Which implies that the claim of the NarStor is wrong

Answer:

Add the similar elements

[tex]x+3x=4x\\-50-23+5=-68\\\\4x=-68[/tex]

Step-by-step explanation: Further steps

Divide both sides by 4

[tex]\frac{4x}{4}=\frac{-68}{4}[/tex]

Simplify

[tex]x=-17[/tex]

Answer:

combine like

Step-by-step explanation:

Answer:

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Step-by-step explanation:

2x- 6 is 5x + 3

your answwr

Answer:

(-3 , -7)

Step-by-step explanation: