You would like to make a nutritious meal of eggs, edamame, and elbow macaroni. The meal should provide at least 40 g of carbohydrates, at least 20 g of protein, and no more than 50 g of fat. An egg (one serving) contains 2 g of carbohydrates, 17 g of protein, and 14 g of fat. A serving of edamame contains 12 g of carbohydrates, 12 g of protein, and 6 g of fat. A serving of elbow macaroni contains 43 g of carbohydrates, 8 g of protein, and 1 g of fat. An egg costs $2, a serving of edamame costs $5, and a serving of elbow macaroni costs $3. Formulate a linear optimization model that could be used to determine the number of servings of egg, edamame, and elbow macaroni that should be in the meal in order to meet the nutrition requirements at minimal cost. (You don’t need to find the optimal solution to the model you formulate) ======== In your response please - define decision variables with NUN (Name, Unit, Notation) (e.g. Let E be the number of eggs in the meal) Then provide the mathematical model for the LP problem. - objective function - constraints

Answer:

3.5

Step-by-step explanation:

21  (pages) divided by 6 (minutes) = 3.5 per minute

The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.

The given function is,

y = 1/2 x + 2.

Also, the domain of the function is {-4, -2, 0}.

Since, the domain of the functions defines the values of x,

And range defines the value of y in function.

The value of y at x = -4

y = 1/2(-4) + 2 = -2 + 2 = 0

At x = -2,

y = 1/2(-2) + 2 = -1 + 2 = 1

At x= 0,

y = 1/2 (0) + 2 = 2

The values of y are 0, 1 and 2.

Hence, the range of the function is {0, 1, 2}.

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Given:

m∠YXV = 3x + 48

m∠WUX = x + 62

Using the corresponding angle theorem, since X is the midpoint of UV and Y is the midpoint VW, m∠YXV is congruent to m∠WUX.

Thus, we have:

m∠YXV = m∠WUX

3x + 48 = x + 62

Solve for x.

Subtract x from both sides:

3x - x + 48 = x - x + 62

2x + 48 = 62

Subtract 48 from both sides:

2x + 48 - 48 = 62 - 48

2x = 14

Divide both sides by 2:

To find m∠WUX, where x = 7, we have:

m∠WUX = x + 62

= 7 + 62

= 69º

ANSWER:

m∠WUX = 69º

The time JBLM will you be the closest to Mt. Rainier will be 5.12 minutes.

A measurement of the distance between two places along a line or line segment.

The plane's flight route follows the line.

y = -125/135x = -25/27x

The direction of the perpendicular line passing across Mt. Rainier is,

y = 27/25(x -56) -40

In standard form, these two equations are,

25x +27y = 0

27x -25y = 2512

The coordinates at the closest approach are the answers to these two equations:

(x, y) = (33912/677, 31400/677)

The Pythagorean theorem (distance formula) states that the distance d from the origin to this point is as follows:-

d = 1256√(2/677) km

The airplane's speed can be used to convert this distance to time:

1256√(2/677) X 60/800 =  94.2√(2/677) ≈ 5.120019 mins

So, 5.12 minutes after leaving JBLM, Mt. Rainier will be the nearest.

The attached graph shows the geometry of the problem.

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Let a be the amount of 40% solution and b be the amount of pure alcohol that you will use.

You want to end up with a volume of 660 mL, so

a + b = 660

For each mL of solution used, the 40% solution would contribute 0.4 mL of alcohol, and the pure alcohol will contribute 1 mL of alcohol. In the desired solution, you want a concentration of 80% alcohol, so that it contains 0.8 • 660 mL = 528 mL of alcohol, and

0.4a + b = 528

Solve the system of equations above. Subtracting the second from the first eliminates b and lets us solve for a :

(a + b) - (0.4a + b) = 660 - 528

0.6a = 132

a = 220

Then

220 + b = 660

b = 440

So you will need 220 mL of the 40% solution and 440 mL of pure alcohol.

Step-by-step explanation:

Scale Factor (Dilation) The scale factor in the dilation of a mathematical object determines how much larger or smaller the image will be (compared to the original object). When the absolute value of the scale factor is greater than one, an expansion occurs. Hope this helps :)

Answer:

X>-3

Step-by-step explanation:

Hope I helped

Do u want the steps ?

Answer: x > -3

Step-by-step explanation: -5(4x + 7) <25

                                              -20x - 35 < 25

                                              -20x -35 + 35 < 25 + 35

                                              -20x/20 < 60/20

                                              x > -3

Answer:

(1,2)

Step-by-step explanation:

x+4y = 9

2x -4y= -6

Add the equations together

x+4y = 9

2x -4y= -6

-------------------

3x +0y = 3

3x=3

Divide by 3

3x/3 = 3/3

x=1

Now find y

x+4y = 9

1 +4y =9

Subtract 1 from each side

4y = 8

Divide by 4

4y/4 = 8/4

y =2

Answer:

This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.

Step-by-step explanation:

x < 3 or x > 5

This means, x is less than 3, but greater than 5.

Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.

Answer: \(14\ ft\)

Step-by-step explanation:

Given

Length of rectangle is \(6\ ft\)

Perimeter must be greater than 40 ft

Suppose l and w be the length and width of the rectangle

\(\Rightarrow \text{Perimeter P=}2(l+w)\\\Rightarrow P\geq 40\\\Rightarrow 2(l+w)\geq40\\\Rightarrow l+w\geq20\\\Rightarrow w\geq20-6\\\Rightarrow w\geq14\ ft\)

So, the smallest width can be \(14\ ft\)

The steps to create a bar graph are explained below.

To match the two-way table to the segmented bar graph, we need to create a segmented bar graph that represents the data in the table. The table shows the percentage of students in each grade who voted for each mascot option.

Here is how we can match the two-way table to the segmented bar graph:

By creating a segmented bar graph that represents the data in the two-way table, we can visually compare the percentage of students who voted for each mascot option across different grade levels.

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Taking into account the scientific notation, the result of the sum is 2.56197×10¹⁹.

Scientific notation is a quick way to represent a number using powers of base ten.

The numbers are written as a product:

a×10ⁿ

where:

You want to add the following two numbers in scientific notation:

When the numbers to be added do not have the same base 10 exponent, the base 10 power with the highest exponent must be found. In this case, the highest exponent is 19.

Then all the values ​​are expressed as a function of the base 10 exponent with the highest exponent. In this case: 3.197×10¹⁷= 0.03197×10¹⁹

Taking the quantities to the same exponent, all you have to do is add what was previously called the number "a". In this case:

2.53×10¹⁹ + 0.03197×10¹⁹= (2.53 + 0.03197)×10¹⁹= 2.56197×10¹⁹

Finally, the result of the sum is 2.56197×10¹⁹.

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Answer:

Step-by-step explanation:

We are given that T is the midpoint of LM, J is the midpoint of MO, and P is the midpoint of LO. This means that LT = TM, JO = OM, and LP = PO.

We can use this information to find the lengths of the sides of triangle LMO. Since T is the midpoint of LM, we have LT = TM = 9. Similarly, since J is the midpoint of MO, we have JO = OM = 12. Finally, since P is the midpoint of LO, we have LP = PO = (LO)/2 = 32/2 = 16.

Now, we can use the Pythagorean theorem to find the length of the third side, LM:

LM^2 = LT^2 + TM^2

LM^2 = 9^2 + 16^2

LM^2 = 337

LM = sqrt(337)

Therefore, the perimeter of triangle LMO is:

LM + MO + LO = sqrt(337) + 2(12) + 32

Perimeter = sqrt(337) + 56

To find the perimeter of triangle TJP, we need to find the lengths of the sides TJ, JP, and TP. Since T and J are midpoints of their respective sides, we know that TJ = 2(LT) = 18 and JP = 2(JO) = 24. To find TP, we can use the Pythagorean theorem:

TP^2 = TJ^2 + JP^2

TP^2 = 18^2 + 24^2

TP^2 = 900

TP = 30

Therefore, the perimeter of triangle TJP is:

TJ + JP + TP = 18 + 24 + 30

Perimeter = 72

Therefore, the perimeter of triangle TJP is 72.

Answer:

120 miles

Step-by-step explanation:

2.7 times 2 is 4.5, so 60 times 2 is 120 (you're basically doubling both.)

For the present problem, we can use the following strategy to calculate:

There will be 4 selection of fruits: For the first, you have 5 possibilities to pick an apple, because there are 5 in the bag. For the second round, there will be only 4 possibilities, because it is the total of apples less the one you already picked. Using this way to think, it will be 3 possibilities for the third and 2 for the last selection of fruit. From this, we can say that there are 120 ways to select 4 apples. But because the order you select them will not affect the result, you can exchange them among themselves, the calculation becomes:

It means the answer is D. 5

Answer:

76

Step-by-step explanation:

Answer:

494 divided by 6.5 =76

Step-by-step explanation:

Answer:

3/10 in fractions, 0.3 in decimals.

Step-by-step explanation:

I dont know how to explain for decimal, but for fractions, just divide by 10, and you will get 3, and since 10 can fit in 100 10 times, you just put 3/10 which means 30/100. for decimals, just move the percent two parts backwards, and it should be 0.3 or .30. hopefully it helped (for fraction).

Angles of similar triangles are always congruent a: 63, b: 88, c: 29 and x = 53.75

Based on the information available, there are numerous equations for calculating the area of a triangle. As indicated in the calculator above, please use the Triangle formula for additional information and equations for calculating the area of a triangle as well as determining the sides of a triangle using whatever information is available.

find the ratio between the two triangles:

40 on the left corresponds to 50 on the right = 40/50 = 43/x

to find x:

40x = 43 × 50

40x = 215

x = 215/40

x = 53.75

"angles of similar triangles are always congruent."

a: 63

b: 88

c: 29

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Full question:

Given a pair of similar triangles, find the missing length x and the missing angles A, B, and C.

We have a dataset that is:

50 60 80

90 50 70

40 50 80

We have to identify the mode of this dataset.

The mode is the value in the dataset that has the highest frequency. We can have more than one mode if there is more than one value with the maximum frequency.

To find the mode it is usually helpful to count the frequency for each element.

We can do it as:

50: III

60: I

80: II

90: I

70: I

40: I

As "50" has the highest frequency, with a value of 3, it is the mode of the dataset

Answer: the mode is 50.

Answer:

1st box: -1/2

2nd box: 2/1 or just 2

Step-by-step explanation:

1st box: parallel slopes have the EXACT same slope as the original

2nd box: perpendicular slopes are the negative reciprocal of the original

Answer:

96 cm²

Step-by-step explanation:

From the question,

s = (2πr∅/360)+2r................. Equation 1

Where s = Perimeter of a sector, r = radius, ∅ = angle subtend by the sector at the center of the circle.

Given: s = 40 cm, r = 8 cm

Constant : π = 3.14.

Substitute into equation 1 and solve for ∅

40 = (2×8×3.14×∅/360)+(2×8)

40 = (50.24∅/360)+16

40-16 = 50.24∅/360

50.24∅/360 = 24

50.24∅ = 24×360

50.24∅ = 8640

∅ = 8640/50.24

∅ = 171.97°

Area of a sector (A') = ∅πr²/360

A' = 171.97×3.14×8²/360

A' = 95.997

A' ≈ 96 cm²

Answer:

1 and two-thirds yards

Step-by-step explanation:

5⅓ = 3⅔ + y. Subtract 3⅔ from both sides.

It may be useful to use improper fractions.

16/3 – 11/3 = y

5/3 = y

5/3 is equivalent to 1⅔

Answer:

First one

Step-by-step explanation:

The solution is : x = 19 is the extraneous solution Li Juan obtained.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Here, we have,

The given equation is 13 - 2w = w + 6.

We need to solve the equation by squaring both sides of the equation.

Now,  13 - 2w = w + 6 squaring both sides of the equation.

That is, (13-2w)²= 169 - 52w + 4w²

(w+6)²= w²+ 12w + 36

Setting them equal, we get

169 - 52w + 4w² = w² + 12w + 36

⇒3w²- 64w + 133 = 0

Now, using the quadratic formula, we get

x = (64±√(64² - 4×3×133))/6

⇒x = (64±√2500)/6.

⇒x = (64±√50)/6.

⇒x = 19 or 14/6 = 7/3.

Solving the original equation, we get

7 = 3w⇒w = 7/3

Therefore, x = 19 is the extraneous solution Li Juan obtained.

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complete question:

Li Juan solves the equation below by first squaring both sides of the equation.

13 - 2w = w + 6

What extraneous solution does Li Juan obtain?

Answer:

∆K = 98°

∆M = 82°

∆G = 118°

∆H = 62°

Step-by-step explanation:

∆K & ∆G is by corresponding angle

and

∆M & ∆H is by linear pairs

Answer:

Step-by-step explanation:

the insterrest will be $650 after 4 years

The value of the angle x is 30 degrees

To determine the value of the variable x, we need to know the triangle sum theorem.

The triangle sum theorem is a theorem in mathematics stating that the sum total of the interior angles in a triangle is equivalent to 180 degrees.

We should also note that angle at right angle is 90 degrees

Then, we have the angles written as;

90 degrees

2x degrees

x degrees

Equate the angles , we have;

2x + x + 90 = 180

collect the like terms, we have;

2x + x = 180 - 90

add or subtract the like terms, we have;

3x = 90

divide by the coefficient

x = 30

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The earnings from the sales of the palm baskest is 20x, where x is the number of palm baskets, the cost of making x palm baskets is 4x. Then, the total income for this kind of baskets is:

20x - 4x = 16x

The earnings from the sales of the pine straw baskest is 17y, where y is the number baskets, the cost of making x pine straw baskets is 3y. Then, the total income for this kind of baskets is:

17y - 3y = 14y

The objective function is:

f(x,y) = 16x + 14y

They have $100 to spend on supplies. Then, based on the costs to make the baskets you can write:

4x + 3y ≤ 100

The learners agree that they will each make at least 14 items. Then, you have:

x + y ≤ 14

By using the previous inequalities, you can solve for x and y as follow:

4x + 3y ≤ 100 solving for x

4x ≤ -3y + 100

x ≤ -3/4 y + 25

x + y ≤ 14 solving for y

y ≤ -x + 14