A restaurant advertises that its burritos weigh 250 g 250 g250, start text, space, g, end text. A consumer advocacy group doubts this claim, and they obtain a random sample of these burritos to test if the mean weight is significantly lower than 250 g 250 g250, start text, space, g, end text.

Answers

Answer 1

Answer: C) H0 : μ = 250 , Ha: μ < 250

Step-by-step explanation:

The questions is incomplete. The correct question is

A restaurant advertises that its burritos weigh 250 g. A consumer advocacy group doubts this claim, and they obtain a random sample of these burritos to test if the mean weight is significantly lower than 250 g. Let u be the mean weight of the burritos at this restaurant and ĉ be the mean weight of the burritos in the sample. Which of the following is an appropriate set of hypotheses for their significance test? Choose 1 answer:

A) H0 : x = 250 , Ha : x < 250

B) H0 : x = 250 , Ha : x > 250

C) H0 : μ = 250 , Ha: μ < 250

C) H0 : μ = 250 , Ha: μ > 250

Solution:

The null hypothesis is the hypothesis that is assumed to be true. The restaurant advertises that its burritos weigh 250. This is the null hypothesis. 250 is the population mean,μ . Thus, the null hypothesis is

H0 : μ = 250

The alternative hypothesis is what the researcher expects or predicts. The consumer advocacy group tests if the mean weight is significantly lower than 250g. This is the alternative hypothesis. It is expressed as

H0 : μ < 250

Answer 2

Answer:

Yes, because 0.002 < 0.01

Step-by-step explanation:


Related Questions

plz help !!!!!! 30 points
The distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the graph: A graph titled Motion of Ant is shown. The graph shows time in seconds on the x-axis and the Distance from Hole in centimeters on the y-axis. The scale on the x-axis is shown from 0 to 7 at increments of 1, and the scale on the y-axis is shown from 0 to 24 at increments of 4. The graph has 3 straight lines. The first line is labeled A and joins ordered pairs 0, 0 and 2, 16. The second line is labeled B and joins ordered pairs 2, 16 and 4, 16. The third line is labeled C and joins ordered pairs 4, 16 and 6, 0.

Part A: Is the graph linear or nonlinear? Explain your answer. (2 points)

Part B: In which segments is the graph increasing, decreasing, and constant? (3 points)

Part C: In your own words, describe the motion of the ant, as shown on the graph. (5 points)

plz help !!!!!! 30 points The distance, y, in centimeters, of an ant from a hole in the tree for a certain

Answers

Part A. It is non linear because it can't make straight line.

Part B. In the graph

A is increasing,

B is Constant,

C is decreasing,

Part C. A is Increasing by the (0 to 16) because it is in upward and B is constant because it is (16 to 16) it is in same level then C is decreasing by the (16 to 0) because it is in downward.

I hope you understand....

Thanks....

Make me as brainliest....

what are the three different types of proofs in geometry

Answers

Direct proofs, Indirect proofs and Coordinate proofs are the three different types of proofs in geometry.

The three different types of proofs in geometry are: direct proofs, indirect proofs, and coordinate proofs.

1. Direct Proofs: In a direct proof, you start with given facts or established theorems and use logical reasoning to derive a conclusion. You follow a step-by-step process using definitions, postulates, and previously proven theorems.

2. Indirect Proofs: In an indirect proof, also known as proof by contradiction, you assume that the statement you want to prove is false, and then show that this assumption leads to a contradiction, which means the original statement must be true.

3. Coordinate Proofs: A coordinate proof involves assigning coordinates to geometric figures and using algebraic techniques, such as the distance formula or the slope formula, to prove geometric properties. This type of proof is particularly useful when working with figures in the coordinate plane.

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solve for B please help

solve for B please help

Answers

Answer:

0.54

Step-by-step explanation:

sin 105 / 2 = sin 15 / b

b = sin 15 / 0.48296

b = 0.54

About 0.5 units. This is a trigonometry problem

witch is grater 18/24 or 55%

Answers

Answer:

i would say 18/24

Step-by-step explanation:

What is the suface area of a rectangular prism that measures 2cm × 5cm × 8cm?​

Answers

Answer: 132 hope that helps

Step-by-step explanation

Fastest way to do it A=2(wl+hl+hw)=2·(5·2+8·2+8·5)=132

Answer:

132 \(cm^{2}\)

Step-by-step explanation:

A rectangular prism has 6 sides in total. We need to find the area of each side and add the areas together to find the total surface area.

Each side has an opposite that's parallel and on the opposite side of the prism, so there are 3 different sides whose areas are to be multiplied by 2.

First: let this side be SIDE A:  5 x 8 = 40 \(cm^{2}\)

Second, let this side be SIDE B:  8 x 2 = 16 \(cm^{2}\)

And thirdly, let this side be SIDE C:  2 x 5 = 10 \(cm^{2}\)

These are the areas of 3 of the the sides of the prism. The other 3 are identical.

Now to find the Total SA, we add all of them together,

SA   =    2 x (SIDE A) + 2 x (SIDE B) + 2 x (SIDE C).

       =    (2 x 40) + (2 x 16) + (2 x 10)

       =    80 + 32 + 20

SA   =    132 \(cm^{2}\)

2. Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i and .

Review Andrew’s work, identify the error and correct all work from that point forward that is affected by this error. Include at least one sentence explaining his error. Use proper mathematical vocabulary, appropriately
(x-3)(x+2+2i)(x+2-2i)=0
(x-3)(x^2+4x+8)=0
x^3+x^2-4x-24=0)

Answers

Using the Factor Theorem, Andrew's error was at the application of the minus signal to the complex roots, and the polynomial of degree 3 is of f(x) = x³ - 7x² + 20x - 24.

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

For this problem, the roots are given as follows:

\(x_1 = 3\).\(x_2 = 2 + 2i\).\(x_3 = 2 - 2i\).

Hence the polynomial is given as follows, considering leading coefficient a = 1:

\(f(x) = (x - 3)(x - 2 - 2i)(x - 2 + 2i)\)

His error was at the application of the minus signal to the complex roots.

Then:

f(x) = (x - 3)[(x - 2)² - (2i)²]

f(x) = (x - 3)(x² - 4x + 4 + 4)

f(x) = (x - 3)(x² - 4x + 8)

f(x) = x³ - 7x² + 20x - 24.

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let p be the projection matrix corresponding to a subspace s of r m. show that (a) p 2 = p. (b) p t = p

Answers

To prove the properties of the projection matrix, we'll assume that p is the projection matrix corresponding to a subspace S of \(R^{m}\).

(a) p² = p

To show that p² = p, we need to demonstrate that applying the projection matrix p twice is equivalent to applying it once.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, if we apply the projection matrix p again to p(x), we have:

p(p(x)) = projection of p(x) onto S

Since p(x) is already the projection of x onto S, applying the projection matrix p once more won't change the result. Hence, we can write:

p(p(x)) = p(x)

This equation holds for any vector x in \(R^{m}\), meaning that p² = p.

(b) \(p^{T}\) = p

To prove that \(p^{T}\) = p, we need to show that the transpose of the projection matrix p is equal to p.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, let's compute the transpose of p(x):

\((p(x))^{T}\) = \((projection of x onto S)^T\)

The transpose of a projection onto a subspace doesn't change the result because it only affects the column vectors of the projection matrix. The transpose of p(x) is still the projection of x onto S. Hence, we can write:

\((p(x))^T\) = p(x)

Since this equation holds for any vector x in \(R^{m}\), we can conclude that \(p^T\) = p.

Therefore, we have shown that (a) p² = p and (b) \(p^T\) = p, proving the properties of the projection matrix corresponding to a subspace S of \(R^{m}\).

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384.75 as a fraction

Answers

Answer:

1539/4 (improper fraction) or 384 3/4 (simplified fraction)

Step-by-step explanation:

To find the improper fraction, write 384.75 as a fraction:

384.75/1

Then, since you have 2 decimal places after the ., multiply the entire fraction by 100:

38475/100

Next, find the GCF, which is 25, and simplify this fraction to find the final improper fraction:

1539/4

To find the simplified fraction, we already have the whole number, 384, so we have to convert 0.75 to a fraction which is 3/4, because 0.75 is 3/4 of 100:

384 3/4

Hope this helps :)

need help!! also this is 17 points so yeah :)

need help!! also this is 17 points so yeah :)

Answers

You have to split the 2 rectangles off then add them together.
12*7 = 84
12*(12-(3+3)) = 72
84+72 = 156
The area is 156 square feet

in exercises 59-62, find the component form of the sum of u and v with direction angles

Answers

The component form of the sum of u and v with direction angles is u + v = (10√2 - 50)i + 10√2 j.

We are given the magnitudes and direction angles of vectors u and v. We need to find the component form of their sum.

Let's first convert the given magnitudes and direction angles to their corresponding components. For vector u:

|u| = 20, θu = 45°

The x-component of u is given by:

ux = |u| cos(θu) = 20 cos(45°) = 10√2

The y-component of u is given by:

uy = |u| sin(θu) = 20 sin(45°) = 10√2

Therefore, the component form of vector u is:

u = 10√2 i + 10√2 j

Similarly, for vector v:

|v| = 50, θv = 180°

The x-component of v is given by:

vx = |v| cos(θv) = -50 cos(180°) = -50

The y-component of v is given by:

vy = |v| sin(θv) = 50 sin(180°) = 0

Therefore, the component form of vector v is:

v = -50 i + 0 j

The component form of the sum of u and v is given by the sum of their x- and y-components:

u + v = (10√2 - 50) i + (10√2 + 0) j

Simplifying, we get:

u + v = (10√2 - 50) i + 10√2 j

Therefore, the component form of the sum of u and v is:

u + v = (10√2 - 50) i + 10√2 j

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The question is -

Find the component form of the sum of u and v with the given magnitudes and direction angles θu and θv.

| | u | | = 20 , θu = 45° | | v | | = 50 , θv = 180°.

Please help , I do not understand this at all

Please help , I do not understand this at all

Answers

The frequency of the sine function is given as follows:

F = 0.5/π Hz.

How to obtain the frequency of a sine function?

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.

For the function y = sin(x), we have that B = 1, hence the period is given as follows:

P = 2π/B

P = 2π.

The frequency is one divided by the period, hence:

F = 1/P

F = 1/2π

F = 0.5/π Hz.

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Answer:

\(F=\dfrac{1}{2\pi}\; \sf Hz\)

Step-by-step explanation:

The frequency of a sinusoidal wave refers to the rate at which the wave completes one full cycle, typically measured in Hertz (Hz), where 1 Hz signifies one complete oscillation of the wave in one second.

The period of a sinusoidal wave is the amount of time it takes for the wave to complete one complete oscillation.

The frequency (F) of a sinusoidal wave can be determined from its period (P) using the formula:

\(\boxed{F=\dfrac{1}{P}}\)

The sine function y = sin(x) completes one full cycle over the interval [0, 2π]. Therefore, its period is P = 2π.

To calculate the frequency (F), substitute P = 2π into the frequency formula:

\(F=\dfrac{1}{P}=\dfrac{1}{2\pi}\; \sf Hz\)

The straight line L1 passes through the points with coordinates (6, 5) and (10, 3)
The straight line L2 passes through the origin and has gradient -3
The lines L1 and L2 intersect at point P
Find the coordinates of P.

Answers

Answer:

The coordinates of point p are:

x = -3.2

y = 9.6

Step-by-step explanation:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Then if we know that L1 passes through the points (6, 5) and (10, 3) the slope of this line will be:

a = (3 - 5)/(10 - 6) = -0.5

Then this line will be something like:

y = -0.5*x + b

To find the value of b we can just replace the values of one of the points in the above equation. For example if we use the point (6, 5), this means that:

x = 6

y = 5

Then we get:

5 = -0.5*6 + b

5 = -3 + b

5 + 3 = b

8 = b

Then the equation for line L1 is:

y = -0.5*x + 8

Now, for line L2 we know that it has a gradient -3 (for linear equations, the gradient is the same as the slope)

Then line L2 has a slope equal to -3

y = -3*x + b

And we know that this line passes through the origin, (0, 0)

Then if we replace the values of that point in our equation, we get:

0 = -3*0 + b

0 = b

Then line L2 is:

y = -3*x

Then our two lines are:

y = -0.5*x + 8

y = -3*x

Now we want to find the point where these lines intersect. The lines will intersect in one point that belongs to both lines, then we can use the relation:

-0.5*x + 8 = y = -3*x

-0.5*x + 8 = -3*x

now we can solve this for x.

-0.5*x + 8 = -3*x

8 = -3*x + 0.5*x

8 = -2.5*x

8/-2.5 = x = -3.2

Now we need to evaluate one of the lines on this value, i will use line L2

y = -3*(-3.2) = 9.6

Then we can conclude that the lines do intersect in the point:

x = -3.2

y = 9.6

this point is written as: (-3.2, 9.6)

The distance from the Sun to Mercury is approximately 57910000 km.
Assuming Mercury has a circular** orbit around the Sun, find the distance Mercury travels in orbiting the Sun through an angle of 2.65 radians.

Answers

Mercury travels a distance of 153 461 500 kilometers on its orbit.

How much distance did Mercury travel on its orbit?

The statement indicates that Mercury has a circular orbit and indicates the central angle covered by translation. The distance traveled is found by definition of circular arc:

s = (2.65 rad) · (57 910 000 km)

s = 153 461 500 km

Please notice that the radius of translation is the distance from the Sun to Mercury.

Mercury travels a distance of 153 461 500 kilometers on its orbit.

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What is 1/4 0.75 1/3 0.5 greatest to least

Answers

Answer:

1/4 = 1 ÷ 4 = 0.251/3 = 1 ÷ 3 ≈ 0.330.750.5

0.75 → 0.5 → 1/3(0.33) → 1/4(0.25)

hope this helps! feel free to clarify
What is 1/4 0.75 1/3 0.5 greatest to least

The number below is not correctly written in scientific notation.

0.0038 × 105
What is the new exponent for the power of 10 after rewriting the number correctly in scientific notation?

3.8 × 10?

Write the new exponent value in the blank below.

Answers

Answer: use a picture math thing

Step-by-step explanation:0.0038 x 105=0.399 so move the decimal point over 1 then it should look like 0.038 x 10.5=0.399 then repeat.

Which equation represents a line which is perpendicular to the line
7x + 3y = -18?

Answers

Answer:

c y=6x+4

Step-by-step explanation:

c y=6x+4
Hope this helps you

write an exponential function to model the situation. find the amount after the specified time. $1,000 principal, 3.6% compounded monthly for 10 years

Answers

We can model this problem by an exponential growth:

\(A=P(1+\frac{r}{n})^{nt}\)

where A is the amount accumulated, P is the principal, r is the interest rate, n is the number of times per year and t is the time. By substituting our given data, we get

\(\begin{gathered} A=1000(1+\frac{0.036}{12})^{12t} \\ A=1000(1+0.003)^{12t} \end{gathered}\)

therefore, the model is

\(A=1000(1.003)^{12t}\)

Now, by substituting t=10 years, we have

\(A=1000(1.003)^{120}\)

then, the amount will be

\(A=1432.55\text{ dollars}\)

state the domain and range for the following relation. then determine whether the relation represents a function.

Answers

The domain and range need to be determined for a given relation, and it will be determined whether the relation represents a function.

To determine the domain and range of a relation, we need to examine the set of inputs (domain) and the set of corresponding outputs (range). The domain is the set of all possible input values for which the relation is defined, while the range is the set of all possible output values that result from the given inputs.

In the context of determining whether the relation represents a function, we need to ensure that each input value from the domain corresponds to a unique output value. If there is any input value that produces multiple output values, the relation is not a function.

To determine the domain, we examine the set of all valid input values. This can be based on restrictions or limitations stated in the problem or the nature of the relation itself. The range, on the other hand, is determined by observing the set of all output values that result from the given inputs.

Once the domain and range are determined, we can check if each input in the domain corresponds to a unique output in the range. If every input has a unique output, the relation represents a function. If there is any input that maps to multiple outputs, the relation does not represent a function.

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The probability of a teenager in a locality owning a bike is 0.33, of owning a car is 0.16 and of owning both is 0.11. If a teenager is chosen random from the locality, what is the probability that the teenager owns a bike or a car? a)0.34 b)0.36 c)0.38 d)0.40

Answers

Answer:

C) 0.38

Explanation:

Given the below;

p(owning a bike) = 0.33

p(owning a car) = 0.16

p(owning both) = 0.11

We'll use the below formula to determine the probability of owning a bike or a car;

\(\begin{gathered} p(\text{ owning a bike or a car) = }p(\text{ owning a bike) + p(owning a car) - p(owning both)} \\ \end{gathered}\)

Substituting the given values, we'll have;

\(\begin{gathered} p(\text{ owning a bike or a car) = }0.33+0.16-0.11 \\ =0.38 \end{gathered}\)

Determine the lateral area of a triangular prism with a height of 12 centimeters (cm)
and whose base is a right triangle with side lengths of 6 cm, 8 cm, and 10 cm.

plsss helppp

Answers

The lateral area of the triangular prism is 288 cm².

How to determine the lateral area of the triangular prism

From the question, we have the following parameters that can be used in our computation:

Height = 12 cm

Base = 6 cm, 8 cm and 10 cm

The lateral area of the triangular prism is calculated as

Area = Sum of base lengths * Height

Substitute the known values in the above equation, so, we have the following representation

Area = (6 + 8 + 10) * 12

Evaluate

Area = 288

Hence, the area is 288 square cm

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Select the correct answer.
Simplify the following expression.
6- .6-
OA. 60
B. 6-H
C. 6
D. 6-
Reset
Next

Select the correct answer.Simplify the following expression.6- .6-OA. 60B. 6-HC. 6D. 6-ResetNext

Answers

Answer:

its D

Step-by-step explanation:

rewriting in exponential form is 6 - 67/28

Answer:

Step-by-step explanation:

i think the answern is a but im not sure.

Cash price 550 000 installment 4500 per month repayment term 240 months determine the total amount if the installment option is used?

Answers

if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

To determine the total amount if the installment option is used, we need to calculate the total repayment over the 240-month term.

The installment amount per month is $4,500, and the repayment term is 240 months.

Total repayment = Installment amount per month * Repayment term

Total repayment = $4,500 * 240

Total repayment = $1,080,000

Therefore, if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

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1.Which quadrant will the terminal ray falls for an angle of rotation equal to 1.2 radians.

A.) QIV
B.)QII
C.)QI
D.)QIII

1.Which quadrant will the terminal ray falls for an angle of rotation equal to 1.2 radians.A.) QIVB.)QIIC.)QID.)QIII

Answers

Answer:

D.) QIII

Step-by-step explanation:

Because 1.2 radians is in between 7π/6 and 5π/4

Consider the plate dealt with in Example 8.1. Plot has a function of the angle of inclination of the plate as the hot side is tilted both upward and downward over the range +90°. Note that you must make do with discontinuous formulæ in different ranges of 0.

Answers

The question refers to the plot of the plate's function of the angle of inclination. When the hot side is tilted both upward and downward over the range of +90°, the discontinuous formulas must be used in different ranges of 0.

It refers to the plot of the function of the angle of inclination of a plate. It is a graph that shows the relationship between the angle of inclination and the plate's function. A plate is tilted on its hot side both upward and downward over a range of +90°. The graph shows that different discontinuous formulas are needed for different ranges of 0. A discontinuous formula refers to a formula that consists of two or more parts, each with a different equation. The two or more parts of a discontinuous formula have different ranges, such that each range requires a different equation. These formulas are used in cases where the same equation cannot be applied throughout the entire range.

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I’ll give the Brainliest to who answers this question with a reasonable explanation.

What is the ratio of circumference to diameter for the circle with a 7.2 cm circumference?

A) 22.61 cm/7.2 cm

B) 20.10 cm/7.2 cm

C) 7.2 cm/20.10 cm

D) 7.2 cm/22.61 cm

Thank you!

Ill give the Brainliest to who answers this question with a reasonable explanation.What is the ratio

Answers

Answer:

I

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

So it’s asking for the ratio for a diameter of 7.2 so if you look at the table 22.61 is the one next to it. So it’s A because it says circumference to diameter not diameter to circumference

what is the slope of the linear regression prediction equation if a person with 12 years of schooling earns $27,000 per year and a person with 13 years of schooling earns $28,600 per year?

Answers

The slope of the linear regression prediction equation is 1,600, which means that for each additional year of

schooling, the expected increase in salary is 1,600.

The slope of the linear regression prediction equation can be calculated by using the formula:

slope = (y2 - y1) / (x2 - x1)

where y2 is the second data point (in this case, 28,600),

y1 is the first data point (in this case, 27,000),

x2 is the second value of the independent variable (in this case, 13 years of schooling), and

x1 is the first value of the independent variable (in this case, 12 years of schooling).

Plugging in the values, we get:

slope = (28,600 - 27,000) / (13 - 12)

slope = 1,600 / 1

slope = 1,600

Therefore, the slope of the linear regression prediction equation is 1,600, which means that for each additional year of

schooling, the expected increase in salary is 1,600.

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How much bigger is the largest bowl than the smallest bowl?

How much bigger is the largest bowl than the smallest bowl?

Answers

Answer:

5/8

Step-by-step explanation:

The biggest bowl Mr. Ramsey bought is 7/8, and the smallest is 2/8.

Thus, 7/8 - 2/8 = 5/8 quarts.

Answer:

5/8

Step-by-step explanation:

We see that the largest bowl size is 7/8, and that the lowest size is 2/8, from the data from the x plot.

Since these are similar fractions with the same denominator, we can subtract them. 7/8-2/8=5/8.

I really need help!!!!!!​

I really need help!!!!!!

Answers

Answer:

y = 1.50x + 4 ;

Step-by-step explanation:

Given that bike rental cost $4 plus $1.50 per hour

From the information given, the change in y per unit change in x is the value of the slope ;

Therefore, Given that total cost = y and x) number of hours

Change in cost per change in number of hours) 1.50 = slope ; intercept = constant = $4

The equation, in slope intercept form :

y = mx + c

y = 1.50x + 4

a = 2, b = 3, c = 4 and d = 12
20 - 2b/ a (2b/a is supposed to be a fraction)

Answers

The expression when evaluated is 17

How to evaluate the expression

From the question, we have the following parameters that can be used in our computation:

a = 2, b = 3, c = 4 and d = 12

Also, we have

20 - 2b/a

Substitute the known values in the above equation, so, we have the following representation

20 - 2b/a = 20 - 2 * 3/2

Evaluate

20 - 2b/a = 17

Hence, the solution is 17

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Set up the objective function and the constraints, but do not solve. Jack has a casserole and salad dinner. Each serving of casserole contains 300 calories, 5 milligrams of vitamins, and 9 grams of protein. Each serving of salad contains 45 calories, 9 milligrams of vitamins, and 1 gram of protein. Jack wants to consume at least 25 milligrams of vitamins and 27 grams of protein but keep the calories at a minimum. How many servings of each food should he eat? (Let x represent the number of servings of casserole, y the number of servings of salad, and C the number of calories.) C= subject to vitamins protein x≥0,y≥0 e z=5x+3y, sul 3x+y≥60 4x+3y≥120 2x+4y≥80 x≥0,y≥0

Answers

The objective function is to minimize the number of calories, subject to the constraints that the total vitamins should be at least 25 milligrams and the total protein should be at least 27 grams.

The objective function is to minimize the number of calories, denoted as C. The constraints are as follows:

- The total vitamins consumed, represented by the variable z, should be at least 25 milligrams: z ≥ 25.

- The total protein consumed, also represented by z, should be at least 27 grams: z ≥ 27.

- The number of servings of casserole, x, and salad, y, should be greater than or equal to 0: x ≥ 0, y ≥ 0.

- The total calories, C, is a linear combination of the calories from casserole (300x) and salad (45y): C = 300x + 45y.

- Additional constraints are given:

  - 3x + y ≥ 60 (ensuring minimum vitamins)

  - 4x + 3y ≥ 120 (ensuring minimum protein)

  - 2x + 4y ≥ 80 (ensuring a balanced diet)

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