The cost per guest of catering an event of no more than 150 people is modeled by the function () = 45 + 15. The number of guests is modeled by the function () = 150 − , where x represents the number of guests fewer than 150 that attend. Evaluate ( ∙ )() and interpret what it means in the context of the problem. Show all work

personal experience based .

maths gives us a way to understanding patterns ,define relationships , and predict the future.

One of my friends wanted to host a dinner party at her house, and she asked me to help her plan the menu. She told me that she was expecting around 10 guests, and she wanted to make sure that she had enough food for everyone. The difficult part was that she had a limited budget and wanted to keep the cost of ingredients low.

Mathematical approach:

To help my friend plan the menu, I used math to estimate the amount of food we needed to buy. I researched online to find the average portion sizes for the dishes we were planning to serve and calculated the total amount of ingredients needed based on the number of guests. Then, I compared the cost of the ingredients at different grocery stores to find the best deals and estimated the total cost of the meal.

Outcome:

By using math, we were able to plan a menu that was within my friend's budget and had enough food for all the guests. We were also able to find the best deals on ingredients, which helped us save money.

Approach for next time:

Next time, I would try to involve my friend more in the mathematical calculations to make sure she understands how to plan a meal within her budget. I would also consider making a list of alternative dishes that we could serve in case we were unable to find a certain ingredient or if it was too expensive.

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There will be 16 small circular bubbles.

A circle is a shape formed by all points in a plane that are at a particular distance from the centre. It is the curve sketched out by a point moving in a plane so that its distance from a given point remains constant. The radius is the distance between any two points on a circle and the centre.

The area of a circle is given by the formula A = πr², where A is the area and r is the radius.

The area of the large bubble is A = π(8cm)² = 64π cm².

The area of a small bubble is A = π(2cm)² = 4π cm².

Let's assume that the number of small bubbles is n. Then, the total area of the small bubbles is n times the area of a single small bubble:

n(4π) = 4nπ cm²

According to the problem, the area of the large bubble is equal to the sum of the areas of the small bubbles:

64π = 4nπ

Dividing both sides by 4π, we get:

n = 16

Therefore, there are 16 small bubbles.

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Answer:

All you need to do now is plug the numbers in and use the right units.

Step-by-step explanation:

Angle A is the right angle, so the trigonometric ratio we get is sin(LA) = 8/17, cos(LA) = 15/17, tan(LA) = 8/15, sin(LB) = 15/17, cos(LB) = 8/17, tan(LB) = 15/8

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios. (sec). A branch of mathematics called trigonometry in geometry works with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.

The right triangle with sides that are 8, 15, and 17 in length needs to be labeled as follows in order to use trigonometry ratios.

       B

      /|

   17/ |

    /  |

   /___|__

  A    C  15

where the right angle A is. The chart can then be filled out as follows:

angle   opp     adj     hyp     sin     cos     tan

LA      8       15      17      8/17    15/17   8/15

LB      15      8       17      15/17   8/17    15/8

The tangent is opposite/adjacent, the sine is adjacent/hypotenuse, and the cosine is opposite/hypotenuse.

The trigonometry ratios for the right triangle with sides that are 8, 15, and 17 in length are as follows.

sin(LA) = 8/17

cos(LA) = 15/17

tan(LA) = 8/15

sin(LB) = 15/17

cos(LB) = 8/17

tan(LB) = 15/8

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The axis of symmetry for f(x) is x = 1 and h(x) is x=3.

The axis of symmetry is an imaginary straight line that divides a shape into two identical parts, thereby creating one part as the mirror image of the other part. When folded along the axis of the symmetry, the two parts get superimposed. The straight line is called the line of symmetry/the mirror line. This line can be vertical, horizontal, or slanting.

Assuming that f(x) and h(x) are quadratic functions, here's how to find the axis of symmetry for each function:

f(x) = 2x² - 4x + 1

To find the axis of symmetry for f(x), we first identify the coefficients a, b, and c:

a = 2, b = -4, c = 1

Then, we use the formula:

x = -b / (2a) = -(-4) / (2 * 2) = 1

Therefore, the axis of symmetry for f(x) is x = 1. This means that the graph of f(x) is symmetric with respect to the vertical line x = 1.

h(x) = -x² + 6x - 5

To find the axis of symmetry for h(x), we first identify the coefficients a, b, and c:

a = -1, b = 6, c = -5

Then, we use the formula:

x = -b / (2a) = -6 / (2 * -1) = 3

Therefore, the axis of symmetry for h(x) is x = 3. This means that the graph of h(x) is symmetric with respect to the vertical line x = 3.

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The complete question would be:

Two functions are given below: f(x)=2x² - 4x + 1 and h(x)=-x² + 6x - 5. State the axis of symmetry for each function and explain how to find it.

Answer:

average rate of change = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the average rate of change of h(x) in the interval a ≤  x ≤ b , is

[tex]\frac{h(b)-h(a)}{b-a}[/tex]

here the interval is - 2 ≤ x ≤ 2 , then

h(b) = f(2) = [tex]\frac{1}{8}[/tex] (2)³ - 2² = [tex]\frac{1}{8}[/tex] (8) - 4 = 1 - 4 = - 3

h(a) = h(- 2) = [tex]\frac{1}{8}[/tex] (- 2)³ - (- 2)² = [tex]\frac{1}{8}[/tex] (- 8) - 4 = - 1 - 4 = - 5

then average rate of change

= [tex]\frac{-3-(-5)}{2-(-2)}[/tex]

= [tex]\frac{-3+5}{2+2}[/tex]

= [tex]\frac{2}{4}[/tex]

= [tex]\frac{1}{2}[/tex]

The probabilities of Brian and leo  being assigned a window seat on each flight are 1/9

The probability that Brian is assigned a window seat on the flight to his grandmother's house is:

50/150 = 1/3

The probability that LEO is assigned a window seat on the flight home from his grandmother's house is also:

50 window seats/ 150 seats = 1/3

The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is:

50 window seats/150 seats  *  49 window seats/  149 seats  = 1/9

Take note that Brian and Leo's chances of getting a window seat on each flight are independent, so we can simply multiply the odds to determine the likelihood of both happening.

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Answer:

(H)

Step-by-step explanation:

Recall that [tex]V-E+F=2[/tex].

Setting [tex]V=F=4[/tex] yields [tex]E=6[\tex].

The point-slope form of the equation that represents the data set is y - 56 = -5(x - 6), or y = -5x + 86.

We are given two points: (6,56) and (12,26) from the data set. We can use the point-slope form of a linear equation to find an equation that represents the data set.

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

To find the slope, we use the two given points:

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

m = (26 - 56) / (12 - 6)

m = -30 / 6

m = -5

Now that we have the slope, we can use one of the given points, say (6, 56), to write the point-slope equation:

y - y1 = m(x - x1)

y - 56 = -5(x - 6)

y - 56 = -5x + 30

y = -5x + 86

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Consider the equation |x-4| = 5. This equation has two solutions since the distance of x from 4 on the number line can be 5 units in either direction, giving x = 9 or x = -1.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

An absolute value equation is of the form |x| = a, where "a" is a positive number. The absolute value of a number is always non-negative, so the equation |x| = a has two possible solutions, x = a and x = -a.

However, there are three possible cases for how many solutions an absolute value equation could have:

One solution: This occurs when a=0. The only solution is x=0 because |0|=0.

Two solutions: This occurs when a > 0. The two possible solutions are x = a and x = -a, since |a| = a and |-a| = a. For example, the equation |x-3| = 2 has two solutions: x-3 = 2 or x-3 = -2, which gives x = 5 or x = 1.

No solutions: This occurs when a < 0. Since the absolute value of a number is always non-negative, an absolute value equation with a negative number on the right-hand side has no solutions. For example, the equation |x-3| = -2 has no solutions since -2 is negative.

The difference in the number of solutions is due to the nature of absolute values. The absolute value of a number represents the distance of the number from zero on the number line, so an absolute value equation can have two solutions when the distance is equal to a positive number, one solution when the distance is equal to zero, and no solution when the distance is less than zero.

For example, consider the equation |x-4| = 5. This equation has two solutions since the distance of x from 4 on the number line can be 5 units in either direction, giving x = 9 or x = -1.

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Answer: Absolute value equations are important in situations where values cannot be negative, like measuring distance. For example, if you forget which floor your friend lives on and he tells you he's on the fourth floor, and you say you're two floors away, you could be on either the second or sixth floor. Absolute value inequalities are important in determining margins of error or tolerance, especially in manufacturing.

Step-by-step explanation:

When solving an absolute value equation, three possible scenarios could occur. The first scenario is when the absolute value expression equals a positive number. In this case, there will be two solutions, one positive and one negative. The second scenario is when the absolute value expression equals zero. In this case, there will be only one solution, which is zero. The third and final scenario is when the absolute value expression equals a negative number. In this case, there are no solutions, as the absolute value of any number is always non-negative.

The reason there are differences in the number of solutions for each case is due to the nature of absolute value. Absolute value always returns a non-negative value, regardless of the sign of the number inside the absolute value expression. Therefore, when the absolute value expression is positive, there are two possible solutions, one positive and one negative. When the expression equals zero, there is only one solution, which is zero. And when the expression is negative, there are no solutions, as there cannot be a negative absolute value.

Answer: 30.4

Step-by-step explanation:

Answer:

x≥ -2

Step-by-step explanation:

−2x + 1 ≥ 5

       -1     -1

-2x ≥ 4

x≥ -2

Answer:

Using the formula for compound interest: A = P(1 + r/n)^(nt) where: A = the balance after the investment period P = the principal amount (the initial deposit) r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = the time the money is invested (in years) We can plug in the values given in the problem: P = $1856 r = 0.0242 (2.42% expressed as a decimal) n = 4 (quarterly compounding) t = 6/12 (6 months expressed as a fraction of a year) A = $1856(1 + 0.0242/4)^(4 * 6/12) A = $1856(1.00605)^2 A = $1931.

[tex] \:\:\:\:\: \:\:\:\:\:\:\star\longrightarrow \sf y = x^{x}{}^{²}\\[/tex]

Taking the logarithm on both sides -

[tex] \:\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf log y = log x^{x}{}^{²}\\[/tex]

[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf log y = x^2 log x\\[/tex]

[tex]\:\:\: \boxed{\sf\pink{\:\:\: loga^b = blog a }}\\[/tex]

Differentiating with respect to x-

[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \dfrac{d}{dx} logy = \dfrac{d}{dx} x^2 log x \\[/tex]

[tex] \:\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf \dfrac{1}{y} \times \dfrac{dy}{dx} = x^2 \dfrac{d}{dx} log x + logx \dfrac{d}{dx} x^2\\[/tex]

[tex] \:\:\:\:\boxed{\sf\pink{\dfrac{d}{dx} logx = \dfrac{1}{x}}} \\[/tex]

[tex] \:\:\:\:\boxed{\sf\pink{\sf\dfrac{d}{dx}\bigg[f(x)\:g(x)\bigg] = f(x) \dfrac{d}{dx} g(x) + g(x) \dfrac{d}{dx} f(x)}}\\[/tex]

[tex] \:\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf \dfrac{d}{dx} = y \bigg[ x^2 \times \dfrac{1}{x} + logx \times 2x \bigg]\\[/tex]

[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \dfrac{dy}{dx} = y \bigg[ \cancel{x}\: x \times \dfrac{1}{\cancel{x}} + 2x\:logx \bigg]\\[/tex]

[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \underline{\dfrac{dy}{dx} = y \bigg[ x + 2x\:logx \bigg]}\\[/tex]

[tex] \:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf \underline{\dfrac{dy}{dx} = \boxed{\sf x^{x}{}^{²}\bigg[ x + 2x\:logx \bigg]}}\\[/tex]

the gcf of 3, 15, and 35 is 1.

Answer: 1

Step-by-step explanation:

GCF means greatest common factor.

And the greatest common factor of 3, 15 and 35 would be 1 since

no other number is common between them.

3 * 1 = 3

15 * 1 = 15

35 * 1 =35

Answer:

[tex]\frac{24}{5}[/tex]

Step-by-step explanation:

We Know

The test has 6 questions.

Each question has 5 answers.

What would be the probability of getting at least one question wrong?

Each question can only have one correct answer, so the probability of getting a wrong answer for each question is [tex]\frac{4}{5}[/tex]

There are 6 questions on the test, so we take

[tex]\frac{4}{5}[/tex] x 6 = [tex]\frac{24}{5}[/tex]

So, the probability of getting at least one question wrong is [tex]\frac{24}{5}[/tex]

The margin of safety in dollars is $113100

The margin of safety is the value of sales or sales in units that are in excess of the break-even sales or units. The break-even point is where the firm is neither making a profit nor a loss and its total revenue is equal to its total expenses.

The margin of safety can be calculated by deducting the break-even sales value from the budgeted/actual sales value.

The margin of safety in dollars = budgeted/actual sales value - break-even sales value

Margin of safety in dollars = (87 * 13000) - (87 * 11700) = $113100

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The ratio of the height of the smaller prism to the height of the larger prism is 1:sqrt(27).

what is prism?

A prism is a geometric solid that has two parallel and congruent polygonal bases, and the sides connecting the bases are parallelograms. These parallelograms are typically rectangles, but they can also be squares or rhombuses. A prism can be named based on the shape of its base, such as a rectangular prism, triangular prism, hexagonal prism, etc.

Since the prisms are similar, their corresponding sides are proportional. In particular, the ratio of the heights of the prisms is the same as the ratio of their volumes.

Let the height of the smaller prism be h1 and the height of the larger prism be h2. Let the volume of the smaller prism be V1 = 15 cm^3 and the volume of the larger prism be V2 = 405 cm^3. Then:

V1/V2 = (h1^2 * 5) / (h2^2 * 5)

V1/V2 = h1^2 / h2^2

sqrt(V1/V2) = h1 / h2

Substituting the given values, we get:

sqrt(15/405) = h1 / h2

sqrt(1/27) = h1 / h2

1/sqrt(27) = h1 / h2

Therefore, the ratio of the height of the smaller prism to the height of the larger prism is 1:sqrt(27), or approximately 1:5.2.

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Answer: 1/3

Step-by-step explanation: To do complex equations like this try using a calculator

The True statement is parallelogram DEFG is the pre-image because it is not the result of the transformation.

What is Transformation?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

Parallelogram DEFG is transformed to parallelogram VSTU.

It changes from parallelogram DEFG to parallelogram VSTU.

According to how it is said, DFEG is the initial parallelogram or pre-image that is changed to create VSTU, VSTU is changed from DEFG.

The following is an accurate statement concerning the transformation:

As the parallelogram DEFG is not the outcome of the transformation, it is the pre-image.

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The correct Question attached here are as follow:

(Q). Parallelogram DEFG is transformed to parallelogram VSTU. Which statement about the transformation is true?

16.5 I relllllllly hope this helps

Given: D = 8 1/2 in.

We know that the diameter of a circle is twice the radius. Therefore, we can find the radius by dividing the diameter by 2:

radius (r) = D/2 = 8 1/2 / 2 = 4 1/4 in.

To find the circumference (C) of the circle, we can use the formula:

C = 2πr

where π (pi) is a constant approximately equal to 3.14.

Substituting the value of r, we get:

C = 2π(4 1/4) = 2π(17/4) = 8.5π

Therefore, the radius is 4 1/4 in. and the circumference is 8.5π in.

Answer:

[tex]625 \: {in}^{3} [/tex]

Step-by-step explanation:

This figure is formed from a cube and a rectangular prism

First, we can find the volume of the cube:

(l (side length) = 5 in)

[tex]v(cube) = {l}^{3 } = {5}^{3} = 125 \: {in}^{3} [/tex]

Now, let's find the volume of the rectangular prism:

(h = 5 in; a (base area) = 20 × 5 = 100 in^2)

[tex]v(prism) = a(base) \times h[/tex]

[tex]v(prism) = 100 \times 5 = 500 \: {in}^{3} [/tex]

In order to find the total volume of this figure, we have to add these two volumes together:

[tex]v(total) = v(cube) + v(prism)[/tex]

[tex]v(total) = 125 + 500 = 625 \: {in}^{3} [/tex]

The experimental probability that the card selected was a K or 6 is [tex]3/20[/tex].

The answer is "three over twenty."

The frequency of K and 6 in the table are 8 and 7 respectively. Therefore, the total number of times a K or 6 was drawn is [tex]8 + 7 = 15[/tex].

The total number of draws was 100, so the probability of drawing a K or 6 on any one draw is:

Probability of K or 6 =[tex](Frequency of K + Frequency of 6) / Total number of draws[/tex]

[tex]= (8 + 7) / 100\\= 15 / 100\\= 3 / 20[/tex]

So the experimental probability that the card selected was a K or 6 is [tex]3/20[/tex].

Therefore, the answer is "three over twenty."

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Answer:

A + B + C = 68

Step-by-step explanation:

A : B = 1 : 2

B : C = 3 : 4

Find the LCM of 2 and 3. LCM = 6

Multiply A : B by 3 and B : C by 2      

[tex]\dfrac{A}{B}=\dfrac{1}{2}=\dfrac{1*3}{2*3}=\dfrac{3}{6}\\\\\\\dfrac{B}{C }=\dfrac{3}{4}=\dfrac{3*2}{4*2}=\dfrac{6}{8}[/tex]

A : B = 3 : 6    &   B : C = 6 :8

A : B : C = 3 : 6 : 8

A = 3x

B = 6x

C = 8x

It is given that C is 32.

         8x = 32

Divide both sides by 8

          x = 32÷ 8

          x = 4

A = 3*4 = 12

B = 6 * 4 = 24

Sum of three numbers = 12 + 24  + 32

                                      = 68

The estimated number of students on the A honor roll who are 8th graders is 126.

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It involves using letters and other symbols to represent numbers and quantities in equations and formulas.

The main goal of algebra is to find the value of an unknown quantity, called a variable, by using known quantities and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions can be solved using various techniques, including simplification, factoring, and solving equations.

The total number of students on the A honor roll is given by adding the number of students in each grade:

Total = 15 (6th grade) + 11 (7th grade) + 14 (8th grade) = 40

To find the proportion of students who are in 8th grade, we can divide the number of 8th graders by the total number of students:

Proportion of 8th graders = 14/40 = 0.35

To estimate the number of students on the A honor roll who are 8th graders, we can multiply the proportion of 8th graders by the total number of students on the A honor roll:

Estimated number of 8th graders = 0.35 x 360 = 126

Therefore, the estimated number of students on the A honor roll who are 8th graders is 126.

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Farmers Products Inc. should disclose a contingent liability in its 2016 financial statements for the lawsuit filed against them due to a collision caused by one of their delivery truck drivers.

Based on the information provided, it appears that as of the date of the financial statements (March 3, 2017), Farmers Products would need to disclose a contingent liability related to the lawsuit filed against them by the other driver.

A contingent liability is a potential liability that may arise from past events but the outcome is uncertain and will depend on future events. In this case, the lawsuit filed against Farmers Products by the other driver represents a potential liability that may result in damages being awarded against the company.

Under accounting standards, a contingent liability should be disclosed in the notes to the financial statements if it is probable that a liability has been incurred and the amount of the liability can be reasonably estimated. In this case, it is probable that Farmers Products may be liable for damages resulting from the accident and the estimated damages fall within a reasonable range of $6,000 to $10,000.

Therefore, in the notes to its 2016 financial statements, Farmers Products should disclose the existence of the lawsuit and the potential liability that may result. The disclosure should also include an estimate of the potential damages, if any, and any other relevant information about the lawsuit.

The question is incomplete; please see below for the whole question -

On December 4, 2016, Dan Johnson, a Farmers Products Inc. delivery truck driver, ran a stop sign and collided with another vehicle. On January 8, 2017, the driver of the other car filed a lawsuit against Farmers Products for vehicle damages. Damage to this vehicle was estimated to be between $6,000 and $10,000, with no value within that range being more likely than any other. Farmers Products' 2016 financial statements were released on March 3, 2017.

1. Prepare the disclosures and/or journal entries that Farmers Products should include in its financial statements for the fiscal year ending December 31, 2016.2. How would the disclosures and/or journal entries alter if Farmers Products employed IFRS versus US GAAP?

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The statement that is NOT true is: "The y-intercept of the line of best fit means that it cost $9,994 to build the house."

Hi! Based on the given information and without a visual of the graph, I will provide a general answer using the terms provided. Please note that an accurate response may require additional information or context.

The slope of the line of best fit indicates the rate of change in the value of the house over time, and a positive slope signifies that the value has increased. However, the y-intercept of the line of best fit does not necessarily mean that it cost $9,994 to build the house.

The y-intercept represents the estimated value of the house when the independent variable (usually time) is zero, but it does not account for factors like construction costs, inflation, or changes in the real estate market.

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