Each unit of food A contains 120 milligrams of sodium, 1 gram of fat, and 5 grams of protein. Each unit of food B contains 60 milligrams of sodium, 1 gram of fat, and 4 grams of protein. Suppose that a meal consisting of these two types of food is required to have at most 480 milligrams of sodium and at most 6 grams of fat. Find the combination of these two foods that meets the requirements and has the greatest amount of protein. 1) Define your variables. 2) Create an organizational chart of information. 3) Create an objective equation (what is to be maximized or minimized). 4) Write constraint inequalities. Don't forget the non-negative restrictions if applicable. 5) Graph the constraints in order to identify the feasible region. 6) Find the vertices of the feasible region. 7) Test all vertices in the objective equation to identify the point of optimization. 8) Write the complete solution with clear and concise language.

Step-by-step explanation:

5x + 2y = 6

m = -a/b

m = -5/2

Option → A

Answer:

a= im not sure sorry

h= horizontal shift

k= vertical shift

Step-by-step explanation:

a = the vertical stretch or compression factor

h = is the x-translation, that is it moves the graph right or left

k = The 'k' is the "vertical shift".

If positive, moves graph up k units.

If negative, moves graph down k units.

The number of words he still need to write in one of his writing sessions would be = 95 minutes.

A graduate is an individual that has completed studies in an institution for a number of years and is being issued a certificate afterwards.

The number of words committed for a day by Nick = 500 words.

He writes 120 words = 30 mins

The total number of words remaining = 500 - 120 = 380 words.

Therefore the time it will take to finish the remaining 380 words in the day = X mins.

If 30 mins= 120 words

X mins = 380 words.

Make X mins the subject of formula;

X mins = 380× 30/120

X mins = 11,400/120

X mins= 95 minutes.

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Answer:

128.125

Step-by-step explanation:

64%=64/100

64/100 = 82 cars

1 = 82÷64/100

=82×100/64

=41×25/8

=1025/8

=128.125

Answer:

y = -1/6x - 1/2

Step-by-step explanation:

y = -1/6x + b

-1 = -1/6(3) + b

-1 = -1/2 + b

-1/2 = b

Answer:

Step-by-step explanation:

The system is not given to give exact answer.

Possible solution is:

A. (2,7), because this point is true for both equations

B. (4, -6), because this point lies only on one of the two lines

C. (4, -6), because this point makes both equations true

D. (2,7), because the lines intersect the x-axis at these points

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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The temperature in the late afternoon is -3°F.

According to the question,

We have the following information:

When Liz woke up in the morning, it was 6°F. By the late afternoon, the temperature had dropped 9°F.

Now, we can easily find the temperature in late afternoon.

To find this, we will have to subtract 9 from 6 because the temperature has dropped from 6.

(Please note that the temperature given here is in ° F. However, it is to be noted that the two most commonly used units of temperature are °F and °C.)

So, we have the following expression:

6-9

-3°F

Hence, the temperature in the late afternoon is -3°F.

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Answer:

\( x = \sqrt {40}\)

Step-by-step explanation:

Given is an isosceles triangle, dotted line is the bisector of top angle which is also perpendicular bisector of the base of the triangle. Hence, by Pythagoras theorem:

\( {x}^{2} = {6}^{2} + ({ \frac{4}{2} })^{2} \\ = 36 + 4 \\ = 40 \\ \therefore \: x = \sqrt{40} \\ \)

Answer:

D. x = sqrt(52).

Step-by-step explanation:

Since the line measuring 6 units bisects the top angle, there are two right angles. We can use the Pythagorean Theorem to solve for x.

a^2 + b^2 = x^2

4^2 + 6^2 = x^2

16 + 36 = x^2

52 = x^2

x = sqrt(52)

x = sqrt(2 * 2 * 13)

x = 2sqrt(13)

x = 7.211102551.

Hope this helps!

Answer:

\(\frac{79}{100}\)

Step-by-step explanation:

Question:

Write as a fraction in lowest terms:

Answer:

a = 79

b = 99

To rewrite the integral ∫(2x)\(e^{4x^{2} }\)dx using integration by parts, we'll consider the function f(x) = (2x) and g'(x) = \(e^{4x^{2} }\).

Integration by parts states that ∫u dv = uv - ∫v du, where u and v are functions of x.

Let's assign:

u = (2x) => du = 2 dx

dv = \(e^{4x^{2} }\) dx => v = ∫\(e^{4x^{2} }\) dx

To evaluate the integral of v, we need to use a technique called the error function (erf). The integral cannot be expressed in terms of elementary functions. Hence, we'll express the integral as follows:

∫\(e^{4x^{2} }\) dx = √(π/4) × erf(2x)

Now, we can rewrite the integral using integration by parts:

∫(2x)\(e^{4x^{2} }\) dx = uv - ∫v du

= (2x) × (√(π/4) × erf(2x)) - ∫√(π/4) × erf(2x) × 2 dx

= (2x) × (√(π/4) × erf(2x)) - 2√(π/4) × ∫erf(2x) dx

The integral ∫erf(2x) dx can be further simplified using substitution. Let's assign z = 2x, which implies dz = 2 dx. Substituting these values, we get:

∫erf(2x) dx = ∫erf(z) (dz/2) = (1/2) ∫erf(z) dz

Therefore, the final expression becomes:

∫(2x)\(e^{4x^{2} }\) dx = (2x) × (√(π/4) × erf(2x)) - √(π/2) × ∫erf(z) dz

Please note that the integral involving the error function cannot be expressed in terms of elementary functions and requires numerical or tabulated methods for evaluation.

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Answer:

First, we can find the least common denominator for 8 and 3 which is 24.

5/8 = 15/24

1/3 = 8/24  

Then we can divide 15/24 by 8/24 which is 2 1/4.

If we then do 16 divided by 2 1/4 we get 7 1/9

Answer = 7 1/9

Step-by-step explanation:

The statement is false. The arc length of the curve defined by x = 4(3 + y)² on the interval [1, 4] is not approximately 131 units.

To find the arc length of a curve, we use the formula ∫ √(1 + (dx/dy)²) dy, where the integral is taken over the given interval.

In this case, the equation x = 4(3 + y)² represents a parabolic curve. By differentiating x with respect to y and substituting it into the arc length formula, we can calculate the exact arc length over the interval [1, 4].

However, it is clear that the arc length of the curve defined by x = 4(3 + y)² cannot be approximately 131 units, as this would require a specific calculation using the precise integral formula mentioned above.

Therefore, the statement is false, and without further calculations, we cannot determine the exact arc length of the given curve on the interval [1, 4].

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Answer:

1. Equation: x/-9=-16

solution: x=144

2. Equation:15*x=-75

solution: x=-5

3.Equation:0.75n=36

solution: n=48

Step-by-step explanation:

No, because the product of the slopes is not -1.

===================================================

Explanation:

Let's find the slope of line DE.

\(D = (x_1,y_1) = (1,-2) \text{ and } E = (x_2,y_2) = (3,4)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{4 - (-2)}{3 - 1}\\\\m = \frac{4 + 2}{3 - 1}\\\\m = \frac{6}{2}\\\\m = 3\\\\\)

The slope of line DE is 3.

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

Use similar steps to find the slope of line FG.

\(F = (x_1,y_1) = (-1,2) \text{ and } G = (x_2,y_2) = (4,0)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{0 - 2}{4 - (-1)}\\\\m = \frac{0 - 2}{4 + 1}\\\\m = -\frac{2}{5}\\\\\)

Line FG has a slope of -2/5

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

Now multiply the two slopes together

3*(-2/5) = -6/5 = -1.2

The product of the slopes is not -1, so the lines are not perpendicular.

This confirms why choice C is the answer.

Answer:

79

Step-by-step explanation:

To find probabilities using the standard normal distribution curve, we convert the given values to z-scores. The formula to calculate the z-score is: z = (x - μ) / σ

Probability that a randomly selected dog weighs less than 65 pounds:

z = (65 - 58) / 17.2 ≈ 0.40698. By referring to the standard normal distribution table or using a calculator, we find that the probability corresponding to a z-score of 0.41 is approximately 0.6591. Probability that a randomly selected dog weighs between 45 and 70 pounds: z1 = (45 - 58) / 17.2 ≈ -0.7558. z2 = (70 - 58) / 17.2 ≈ 0.6977. Using the standard normal distribution table or calculator, we find that the probability corresponding to a z-score of -0.76 is approximately 0.2236, and the probability corresponding to a z-score of 0.70 is approximately 0.7577. To find the probability between these two values, we subtract the smaller probability from the larger probability: 0.7577 - 0.2236 ≈ 0.5341.Therefore, the probability that a randomly selected dog weighs between 45 and 70 pounds is approximately 0.5341. Probability that a randomly selected dog weighs more than 80 pounds: z = (80 - 58) / 17.2 ≈ 1.2791. Using the standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 1.28 is approximately 0.8997. Probability that a randomly selected dog weighs less than 50 pounds: z = (50 - 58) / 17.2 ≈ -0.4651. Using the standard normal distribution table or calculator, we find that the probability corresponding to a z-score of -0.47 is approximately 0.319.Therefore, the probability that a randomly selected dog weighs less than 50 pounds is approximately 0.3192.Probability that a randomly selected dog weighs between 60 and 70 pounds: z1 = (60 - 58) / 17.2 ≈ 0.1163. z2 = (70 - 58) / 17.2 ≈ 0.6977. Using the standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 0.12 is approximately 0.4515, and the probability corresponding to a z-score of 0.70 is approximately 0.7577. To find the probability between these two values, we subtract the smaller probability from the larger probability: 0.7577 - 0.4515 ≈ 0.3062. Probability that a randomly selected dog weighs more than 90 pounds: z = (90 - 58) / 17.2 ≈ 1.8605. Using the standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 1.86 is approximately 0.9693.Probability that a randomly selected dog weighs less than 40 pounds: z = (40 - 58) / 17.2 ≈ -1.0523.Hence the   z-score of -1.05 is approximately 0.1474.

Using the standard normal distribution table or calculator, we find that the probability corresponding to a z-score of -1.05 is approximately 0.1474.

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Answer:

The volume of prism A is the same as the volume of prism B.

Step-by-step explanation:

Given

See attachment for prisms

Required

Compare the volume of both

First, we calculate the volume of both prisms.

Prism A is a rectangular prism.

So, its volume is:

\(V_A = Length * Base * Height\)

Where

\(Length \to a\)

\(Base \to b\)

\(Height \to h\)

So:

\(V_A = abh\)

For Prism B, we have:

\(Volume = Base\ Area * Height\)

Where

\(Base\ Area = Length * Base\)

and

\(Length = a\)

\(Base = b\)

So:

\(Base\ Area = a * b\)

\(Base\ Area = a b\)

The volume is then calculated as:

\(Volume = Base\ Area * Height\)

\(V_B = ab * Height\)

Where

\(Height \to h\)

So:

\(V_B = ab * h\)

\(V_B = abh\)

By comparison:

\(V_A = V_B = abh\)

Answer:

Te conozco y sé qué

Como Nuevo de fabrica el otro

Answer:

x=1

Step-by-step explanation:

10(x-1) =0

We want to use the distributive property.

10x -10 =0

Add 10 to each side.

10x-10+10 = 10

10x = 10

Divide each side by 10.

10x/10 = 10/10

x = 1

The hourly growth rate parameter in this continuous exponential growth model is approximately 4.88008%.

the hourly growth rate parameter (r) in a continuous exponential growth model, we can use the formula:

r = (1 / t) × ln(N / N0)

Where:

t is the time interval (in this case, 2.5 hours)

N is the final population size (2591 bacteria)

N0 is the initial population size (2300 bacteria)

ln is the natural logarithm function

Substituting the given values into the formula, we have:

r = (1 / 2.5) × ln(2591 / 2300)

Using a calculator, we can calculate the natural logarithm and perform the division:

r ≈ (1 / 2.5) × 0.122002

r ≈ 0.0488008

To express the growth rate as a percentage, we multiply by 100

r ≈ 4.88008%

Therefore, the hourly growth rate parameter in this continuous exponential growth model is approximately 4.88008%.

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The question is incomplete the complete question is :

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 2300 bacteria selected from this population reached the size of 2591 bacteria in two and a half hours. Find the hourly growth rate parameter Note: This is a continuous exponential growth model. wite your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth

Given points, point A = (2, -5) and point B = (-3, -7).We need to find the translation vector that takes B to A.For any two points A(x1, y1) and B(x2, y2) in a coordinate plane, the translation vector that takes B to A is given by:

Translation Vector = [x1 - x2, y1 - y2]

Here, x1 = 2, y1 = -5, x2 = -3, and y2 = -7

Translation Vector = [x1 - x2, y1 - y2]= [2 - (-3), -5 - (-7)]= [2 + 3, -5 + 7]= [5, 2]

Therefore,

the coordinates of the translation vector that takes B to A are (5, 2).

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Answer:

\(3 \times 2 = 6 \\ \\ \\ \\ \\ \)

Answer:

3×2/9=6/9

2/3=2/3

LHS=RHS

is your answer

Step-by-step explanation:

heres a picture too :)

Answer:

4

Step-by-step explanation:

Answer:

f(x) = (x+5)²-26

Step-by-step explanation:

x² + 10x + 25 = 1 + 25

(x+5)² = 26

f(x) = (x+5)²-26

Answer:

is there a picture I can look at?

Answer: Line

Step-by-step explanation:

Answer:

x=40.375

Step-by-step explanation:

Since HYV and AYB are similar, we know that the sides in each of the triangles with have the same ratio to each of their corresponding sides.

For example, YV/YB=YH/YA.

Now we have to find the ratio of the sides which can be done using the lengths of segments YB and YV. YB=16 YV=16+22=38 38/16=2.375

2.375 is our ratio.

Next we are going to find the length of YH so we can determine x.

YA=17 YH=17*2.375=40.375

The length of side YH=40.375 which is equal to x.

Franklin wrote his autobiography for a number of reasons: to "remember" and relive his life, perhaps more perfectly, as he said at the beginning; to provide some genealogical anecdotes to his son; to bow before his friends To their flattery, he owes society an account of his life.

Benjamin Franklin was an American polymath author, scientist, inventor, statesman, diplomat, printer, publisher, forger, and political philosopher. Among the leading intellectuals of the time, Franklin was one of the founding fathers of the United States, the drafter and signer of the American Declaration of Independence, and the first postmaster of the United States.

As a scientist, he was an important figure in American Enlightenment history and physics as he studied electricity and mapped and named the Gulf Stream. As an inventor, he is known for the lightning bolt, bifocal glasses, and the Franklin stove, among others. He founded many civic organizations, including the Library Company, Philadelphia's First Fire Department, and the University of Pennsylvania. Franklin earned the title of "First American" for his early and tireless efforts to unify the colonies and for his work in London as a writer and spokesperson for several colonies. As the first United States Ambassador to France, he exemplified America's rise to power.

Franklin defined the American spirit as the combination of practical values ​​of economy, industry, education, community spirit, self-government, and opposition to political and religious authoritarianism with the values ​​of science and tolerance. clarification. In the words of historian Henry Steele Commager, "In Franklin it was possible to combine the virtues of faultless Puritanism, the lightness of Enlightenment without enthusiasm." Franklin has been called "the most able and influential American inventor in this type of society". America will become.

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Answer: \(\frac{1}{27}\)

Step-by-step explanation:

Anything to the third power means it is multiplied by itself 3 times.

   --> \((\frac{1}{3})^{3} =(\frac{1}{3})(\frac{1}{3})(\frac{1}{3})=\frac{1}{27}\)