How do you start this
Please setup the following minimization problem and then solve it. [That is, you want to Minimize the Objective function Subject to the Constraints.]
A company is creating a meal replacement bar. They plan to incorporate peanut butter, oats, and dried cranberries as the primary ingredients. The nutritional content of 10 grams of each is listed below, along with the cost, in cents, of each ingredient.
Find the amount of each ingredient they should use to minimize the cost of producing a bar containing a minimum of 15g of each ingredient, at least 10g of protein and at most 14g of fat.

Answer:

Step-by-step explanation:

To determine whether y is a function of x in the equation x+4y=8, we can solve for y in terms of x:

x + 4y = 8

4y = 8 - x

y = (8 - x)/4

Copy

Since every value of x corresponds to exactly one value of y, y is a function of x.

Answer:

y = 67.19

Step-by-step explanation:

y/5.6 = 12

=> y = 12(5.6)

=> y = 67.19

The simplified form of 13¹/3 + 2¹/3 - 10/2 is a fraction 64/6 that can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2 the final answer is 32/3.

Given

13¹/3+2¹/3-10/2​

Required simplified it =?

First, we have simplified both constants separately

13¹/3 = (3 * 13 + 1) / 3 = 40/3

2¹/3 = (3 * 2 + 1) / 3 = 7/3

now the expression become = 40/3 + 7/3 - 10/2

now taking LCM of 3 and 2 which is 6.

                                                = 80/6 + 14/6 - 30/6

 now we have to simplify this fraction by dividing by 2 = 64/6

Therefore, the simplified form of 13¹/3 + 2¹/3 - 10/2 is 32/3.

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Answer: Let's call the number of good oranges in the first basket "x" and the number of good oranges in the second basket "y". We know that:

x + y = 22 (since the sum of the number of oranges in the two baskets is 22)

xy = 120 (since their product is 120)

We want to find the number of good oranges in the basket with more oranges, assuming that 5 of them are bad. Without loss of generality, we can assume that x ≤ y, so the basket with more oranges is the second basket.

If 5 of the oranges in the second basket are bad, then the total number of oranges in the second basket is y + 5. Since x + y = 22, we know that x = 22 - y. Substituting this into the equation xy = 120, we get:

(22 - y)y = 120

Expanding and rearranging, we get a quadratic equation:

y^2 - 22y + 120 = 0

We can solve this equation by factoring or using the quadratic formula:

(y - 10)(y - 12) = 0

The solutions are y = 10 and y = 12. Since we assumed that x ≤ y, the number of good oranges in the first basket is x = 22 - y. So we have:

y = 10: x = 22 - y = 12

y = 12: x = 22 - y = 10

Therefore, the number of good oranges in the basket with more oranges is 12 (since y = 12 is the larger of the two solutions), and there are 12 - 5 = 7 good oranges in that basket.

Answer:

45 degrees

Step-by-step explanation:

The 4 angles of a quadrilateral will add to 360.

We know 1 of them (angle B) is 90 degrees.

We can set up an equation to solve the others.

2x+3x+x+90 = 360

Now solve for x.

Start by combining the x terms together.

6x+90 = 360

6x = 360-90

6x = 270

(6x/6) = 270/6

x = 45 degrees

Check back to see if that makes sense and if the equation equals 360 when x is 45:

2x+3x+x+90 = 360

2(45)+3(45)+45+90=360.

Answer:

B. making an inference.

Step-by-step explanation:

The drama teacher's decision to add another performance time on Saturday is a result of making an inference based on the information that 80% of last year's sold-out plays occurred during weekend performances. By observing this pattern, the drama teacher infers that adding another performance on Saturday will likely attract a larger audience and increase the chances of having a sold-out show.

Answer:

1,000

Step-by-step explanation:

There are 52 weeks per year, therefor

52,000÷52= 1000

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

The car's total cost, including the purchase price and tax, is $26,416. The tax paid on the car is $1,016.

a. To calculate the amount of tax paid, you can multiply the purchase price of the car by the sales tax rate, which is 4% or 0.04.

Tax amount = Purchase price * Sales tax rate

Tax amount = $25,400 * 0.04

Tax amount = $1,016

Therefore, the tax paid on the car is $1,016.

b. To determine the car's total cost, you need to add the purchase price and the tax amount.

Total cost = Purchase price + Tax amount

Total cost = $25,400 + $1,016

Total cost = $26,416

Therefore, the car's total cost, including the purchase price and tax, is $26,416.

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Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

Answer:

I totally get why you are asking , how do I solve this.  there is so much implied about this

Step-by-step explanation:

1st you have to recognize that ∠ACB ( in my drawing ) has that same angle as the arc from A to B  ,  so that's implied.   next you have to recognize that the triangle formed by ACB with the 124 degree angle at C is an isosceles and therefore has identical angles at A and B  so that's  180 = 124 + 2A  , so A = 28° and so does B , then , b/c we know that small angle... you also have to know, that the line AC is perpendicular to AD.  that they from a right angle and there for... you now know , that ∠BAD is the other part of that 90 or 90= 28 + ∠BAD so  ∠BAD = 62°

I went through that kinda fast, there was several "leaps" of using logic to get to the correct answer , using things you know from prior understanding about angles , circles  and geometry,  you are putting all of the parts together here.  :/  kinda daunting in some ways.

The relation which are function are (1) and (2).

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

To test the whether the given relation is function or not we can

Use the vertical line test to determine whether or not a graph represents a function.

If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function.

If the vertical line touches the graph at more than one point, then the graph is not a function.

From above,

Graph (1), (2) passes the vertical line test and are the function. But the graph (3) and (4) is not a function.

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Answer:

2 students play both

Step-by-step explanation:n(u)=28

n(b)=7,n(b)=5,n(who play neither sport)=18

HERE,

n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)

28=7+5-n(BnB)+18

28=30-n(BnB)

n(BnB)=30-28

 =2 answer

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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The graph of the translated function is g ( x ) = ( x + 5 )² + 2

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x²

On simplifying , we get

The function is translated 5 units to the horizontal left direction:

And , when the function is translated 2 units in the vertical upward direction:

So , the translated function is

g ( x ) = ( x + 5 )² + 2

Now , the vertex of the function g ( x ) = ( x + 5 )² + 2 is (-5, 2)

Hence , the graph of the function is plotted and g ( x ) = ( x + 5 )² + 2

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Answer:

515$

Step-by-step explanation:

Because 20$=1 month

1 year=12 months

12 months=240$

2 years=24 months

20x24=480+35$ for the hotspot in the first place=415

Answer:

Point O represents the center of the circle

Step-by-step explanation:

HOPE IT HELPS. PLEASE MARK IT AS BRAINLIEST

Answer:

Step-by-step explanation:

To find the volume of the solid formed by rotating the region about the x-axis, we can use the method of disks.

At a given value of x, the distance between the curve y = 9 + x^2 and the x-axis is 9 + x^2. Thus, the area of the disk at x is A(x) = π(9 + x^2)^2. The limits of integration are 0 and 1, since the region is bounded by the lines x = 0 and x = 1.

Therefore, the volume of the solid is given by:

V = ∫(0 to 1) π(9 + x^2)^2 dx

Using integration techniques (such as substitution), we can evaluate this integral to get:

V = (112π/5) cubic units (rounded to 3 decimal places)

Therefore, the volume of the solid formed by rotating the region about the x-axis is (112π/5) cubic units

The solution to the equation 12m + 100 = 700m is given as follows:

m = 0.1453.

The equation in the context of this problem is defined as follows:

12m + 100 = 700m

The variable for which we want to obtain the solution is given as follows:

m.

To obtain the solution, we isolate the variable m, applying inverse operations, as follows:

12m + 100 = 700m

700m - 12m = 100 -> subtraction is the inverse of addition.

688m = 100

m = 100/688 -> division is the inverse of multiplication.

m = 0.1453.

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For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.

The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.

The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).

The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.

So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.

Correct option is D.

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Complete question is:

What are the domain and range of the function f(x)=-x+3-2?

A) domain: -3 -2

B) domain: -3 -3 range: y<-2

C) domain: x>-3 range:y>-2

D) domain : x>-3 range: y ≤ 2

Answer:

2.5

Step-by-step explanation:

please mark brainliest

Example:

f(x) = (x - 1)2, f(x) = 8x , f(x) = x2 - x , f(x) = 7. Summary: From the given functions, f(x) = 7 is the even function.

Step-by-step explanation:

The bisection method is a root-finding algorithm that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. To apply the bisection method to the equation x^3 - x - 9 = 0, you need to find two initial values a and b such that f(a) and f(b) have opposite signs. This means that there is at least one root of the equation in the interval [a, b].

Let’s take a = 2 and b = 3 as our initial interval. We can see that f(2) = 2^3 - 2 - 9 = -1 and f(3) = 3^3 - 3 - 9 = 18, so f(a) and f(b) have opposite signs.

Now we can apply the bisection method as follows:

Calculate the midpoint c = (a + b)/2 = (2 + 3)/2 = 2.5.

Evaluate f© = 2.5^3 - 2.5 - 9 ≈ 5.625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

Calculate the new midpoint c = (a + b)/2 = (2 + 2.5)/2 = 2.25.

Evaluate f© ≈ 1.765625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

We can continue this process until we reach the desired level of accuracy.

Answer:

Step-by-step explanation:

This number line says that  we can take all values of x that are less than or equal to 2. That is, the solution is

                                  \(x\leq 2\)

NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)

Answer:

All figures in Group 1 appear to have at

least one square face

Step-by-step explanation:

Let us examine each statement and see whether they are true or not.

The first statement is not true. Only one of the figures (square pyramid) has at least one triangular face. It has 4 triangular faces, actually.

The second statement is not true. Only one of the figures is a rectangular prism. The remaining two are triangular pyramid and triangular prism respectively.

The third statement is not true also. Only 1 figure is a triangular prism.

The fourth statement is correct. In group 1, all the figures has at least one square face.

Answer:

9:30 PM (C) You're welcome

Step-by-step explanation:

Answer:

√x³=√(x²·x)=x√x

√xy³z=√(x·y²·y·z)=y√xyz

√18x²y=√(3²·2·x²·y)=3x√2y

√32x⁴y²=√(2⁴·2·x⁴·y²)=2²x²y√2=4x²y√2

2√16x⁷y³z⁴=2√(2⁴·x⁶·x·y²·y·z⁴)=2³x³yz²√xy=8x³yz²√xy

-3√180x⁵y=-3√(3²·2²·5·x⁴·x·y)=-3(3)(2)x²√5xy=-18x²√5xy

5√108xyz²=5√(2²·3²·3·x·y·z²)=5(2)(3)z√3xy=30z√3xy

3x√xy¹⁰z⁷=3x√x·y¹⁰·z⁶·z)=3xy⁵z³√xz

x²√x³y²=x²√(x²·x·y²)=x²·x·y√x=x³y√x

The minimum amount that Mr. Khumalo can be charged for the cash deposit is R99.12.

To calculate the minimum amount charged for a cash deposit over the counter at Standard Bank, we'll use the given information.

The deposit charge includes an initial fee of R10.39, and an additional fee of K1.95 per R100 or part thereof, with a minimum charge of R16.00.

First, we calculate the additional fee based on the deposit amount:

Additional fee = (Deposit amount / 100) x K1.95

For Mr. Khumalo's deposit of R4,550.00:

Additional fee = (4,550.00 / 100) x 1.95

Additional fee = 88.725

Next, we compare the additional fee to the minimum charge of R16.00:

If the additional fee is less than the minimum charge, the minimum charge applies. Otherwise, the additional fee is charged.

Since the additional fee of R88.725 is greater than the minimum charge of R16.00, the additional fee will be charged.

Finally, we add the initial fee and the additional fee to get the total charge:

Total charge = Initial fee + Additional fee

Total charge = R10.39 + R88.725

Total charge = R99.115

Therefore, the minimum amount that Mr. Khumalo can be charged for the cash deposit is R99.12.

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