Question 2 Mohammed and Mira are getting married. They are looking for a catering service for their wedding day. The cost of hiring a catering service to serve food is depends on the number of persons (pax). It costs RM120/pax for 30 persons or less, RM105/pax for 31 to 60 persons, and RM95/pax for 61 to 100 persons. For more than 100 persons, the cost is at RM80/pax. a) Construct the piecewise function for the problem. b) Graph the piecewise functions. c) If they pay RM9025 for the catering service, how many persons that they invite to their wedding? (8 Marks)​

The equation in standard form of the eclipse is expressed as:

D. x²/9 + y²/8 = 1.

The standard form equation for an ellipse with center at the origin, a vertex at (a, 0), and a focus at (c, 0) is:

x²/a² + y²/b² = 1, where c² = a² - b².

In this case, the center is at the origin, a vertex is at (3, 0), and a focus is at (1, 0).

Since the center is at the origin, we know that a vertex is located a distance of a units to the right and left of the center, so a = 3.

Since the focus is located a distance of c units to the right and left of the center, we know that c = 1.

Using c² = a² - b², we can solve for b²:

1² = 3² - b²

b² = 8

So the equation in standard form is:

x²/9 + y²/8 = 1.

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Michio's answer not correct. He made a mistake when he was trying to convert the equation to logarithmic form. The right answer is  2.57

Looking at the equation 2(3)ˣ = 34, the best way to convert to logarithm is by isolating x.

we divide  2(3)ˣ = 34 by 2 on both side.

= (3)ˣ = 17

In logarithm form 3 becomes the base of the log

x = log₃(17)

x= 2.578

The answer above is based on the information seen in the picture.

Michio wanted to find the value of x in the equation 2(3)ˣ = 34. He first converted the equation to log₃2x = 17. Next, he wrote 2x = 3¹⁷ and used a calculator to find x = 64,570,081.5. Was his answer correct? If not, what was his mistake and what is the right answer? Justify your answer.

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The equation of p(x) in vertex form is p(x) = 3(x + 1)² - 3.

Option C is the correct answer.

Since, Polynomial is an equation written as the sum of terms of the form kxⁿ.

where k and n are positive integers.

We have,

From the table,

From p(x) = 24 to p(x) = -3 the value of p(x) is decreasing and from p(x) = -3 to p(x) = 24 it is increasing.

So,

The vertex is (- 1, -3).

The vertex form of p(x).

p(x) = a ( x - h)² + k

Where (h, k) is the vertex.

Now,

(-1, -3) = (h, k)

Make (- 2, 0) = (x, p(x))

0 = a (- 2 + 1)² + (-3)

0 = a x 1 - 3

a = 3

Thus, The vertex equation of p(x).

p(x) = 3(x + 1)² - 3

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The population proportion of items manufactured that are defective is estimated to be between 0.137 and 0.037 with a 95% confidence level.

The sample proportion, denoted as ^p, is the proportion of a certain characteristic or outcome in a sample. It is calculated by dividing the number of individuals in the sample that exhibit the characteristic or outcome of interest by the total number of individuals in the sample.

It is an estimate of the population proportion, denoted as p, which represents the proportion of the same characteristic or outcome in the entire population.

Here we have

The sample proportion (^) of defective items is not provided in the question.

Hence, let's assume that the sample proportion (^) of defective items is 0.05 (i.e., 5% as specified in the question).

The sample size is 50, and the sample proportion (^) is 0.05.

The question is asking for the population proportion of items manufactured that are defective (P).

Use the sample proportion (^) and the sample size to calculate the margin of error and construct a confidence interval.

Assuming a 95% confidence level, we can use the following formula to calculate the margin of error:

Margin of error = 1.96 × √(^×(1⁻^)/n)

Substituting the values, we get:

Margin of error = 1.96 × √(0.05 × (1 - 0.05)/50) = 0.087

To construct the confidence interval, we add and subtract the margin of error from the sample proportion:

Confidence interval = ^ ± margin of error

Confidence interval = 0.05 ± 0.087

Confidence interval = (0.137, 0.037)

Therefore,

The population proportion of items manufactured that are defective is estimated to be between 0.137 and 0.037 with a 95% confidence level.

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Answer:

$74.66

Step-by-step explanation:

Plot the points on the graphing calculator (x = length of HDMI cord, y = cost). Then generate a linear regression model:

y = 3.68x + 1.06 (approximately)

x = 20, so y = 74.66

$74.66 is the correct answer.

Answer: 97.5

Step-by-step explanation:

Just do base times height divided by 2, which I'm assuming is 13x15 , that'd be 195. 195 divided by 2 is 97.5

The option that is not a run-on sentence is this: According to data collected throughout film history, the average length for a feature film is between 80 and 100 minutes, although some far exceed the standard running time.

A run-on sentence is a sentence that continues without using appropriate punctuation to join independent clauses. In the sentence above, the comma is used in the right place to join the independent clause, so we may not refer to this as a run-on sentence.

The other three options continue on end without appropriate punctuation to break off the independent clauses.

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The height of the traffic barrel is 42.97 inches.

The surface area of a cylinder is derived with A = 2πr² + 2πrh. A = surface area, r = radius and h = height.

Since diameter is given as 18 inches, we can get radius by dividing the diameter by 2:

r = 18 / 2

r = 9 inches.

Substituting these values, we get:

2,939.04 = 2π(9²) + 2π(9)h

2,939.04 = 162π + 18πh

2,939.04 - 162π = 18πh

h = (2,939.04 - 162π) / (18π)

h = 42.9736382161

h = 42.97 inches

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The solution of the equation is x = -1.

Given is an equation we need to solve it,

3x/4 + 3 - 2x = -1/4 + x/2 +5

Multiplying the equation by 4 both the sides,

3x + 12 - 8x = -1 + 2x + 20

Combining the like terms,

3x - 8x - 2x = 20 - 1 - 12

3x - 10x = 7

-7x = 7

x = -1

Hence the solution of the equation is x = -1.

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Answer: p > 6.5

Step-by-step explanation:

Let p = the time, in hours, that Harry plans to practice soccer.

Since we don't know the hours Harry will plan to practice soccer, we will replace it with p, and Harry wants to practice more than his older brother, so we put the greater than symbol.

Hope this helped!

The volume of the clay used to make the vase is 36 in³

To determine the volume of clay that was used for the vase, we need to consider that;

The formula for the volume of a rectangular prism is expressed as;

Volume = lwh

Such that;

For the bigger prism, we have;

Volume = 3 × 3 × 5

Multiply the values

Volume = 45 in³

For the hole, we have;

Volume = 4 × 3/2 × 3/2

Multiply the values

Volume = 9 in³

Then, the volume of clay used for the vase = 45 - 9 = 36 in³

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Answer:

f(x) = x²-8x+15

g(x) = x -3

h(x) = f(x) ÷ g(x)

= x²-8x+15 ÷ x-3

x-3√x²- 8x +15 | x-5

x² - 3x

-5x + 15

- 5x + 15

-----------

h(x) = x-5

The logarithm expression In(9/x) can be expanded as In(9) - In(x)

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

In(9/x)

Using the logarithmic identity log a/b = log a - log b, we can expand ln(9/x) as follows:

ln(9/x) = ln(9) - ln(x)

Therefore, ln(9/x) can be expressed as the difference of two natural logarithms: ln(9) and ln(x).

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The complete statement is, if 8 = m/4, then m - 12 = 20.

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols. It involves solving equations and inequalities, manipulating expressions, and working with mathematical formulas to describe and analyze relationships between variables. Algebraic equations and expressions are used to represent and solve problems in a wide range of fields, including science, engineering, economics, and finance. Algebra is an essential tool for problem-solving and critical thinking, and it provides the foundation for more advanced mathematical concepts such as calculus, statistics, and linear algebra.

The main goal of algebra is to find unknown values or variables, typically represented by letters such as x, y, or z. Algebraic equations involve a variety of mathematical operations, including addition, subtraction, multiplication, and division. These equations may also include exponents, logarithms, and other advanced mathematical concepts.

To solve the problem, we can use algebraic manipulation.

Given 8 = m/4, we can solve for m by multiplying both sides by 4:

8 × 4 = m

32 = m

Now we can substitute m = 32 into the expression m - 12 to find:

m - 12 = 32 - 12 = 20

Therefore, if 8 = m/4, then m - 12 = 20.

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The complete question is:

Complete the statement: if 8= m/4, then m-12=

Answer: 29

Step-by-step explanation:

<F is 29 degrees because 180-58=122 and 180-122= 58, so then you divide 58 by 2 to get 29 for each x. The x's are each equal to 29.

Answer:

29 degrees

Step-by-step explanation:

The problem shows angle HGE as 58 degrees.

Segment HF is 180 degrees so we can subtract 58 from 180 to get 122 degrees for angle g

Now, the sum of all angles in a triangle is 180.

So, there are 3 angles in the triangle:

g(we know this is 122)

e

f

the graph denotes that the measures of angle e and f are the same because they are the same variable.

Lets subtract 122 from 180 to get 58.

So, angle e and f together combine to make 58 degrees.

But we also know that e and f have the same measure.

So, to find the measure of f, simply divide 58/2 to get 29 degrees.

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The percentage of sugar price per pound less than 64 cents is 50%

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

Mean = 64

Standard deviation = 2

For sugar price per pound that are less than 64 cents, we have

z = (64 - 64)/2

z = 0

This is then represented as

Probability = (z < 0)

Using a graphing calculator, we have

Probability =  0.5

Express as percentage

Probability =  50%

Hence, the probability is 50%

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Answer:

  (a)  (-5,20) and (4,11)

Step-by-step explanation:

You want the solutions to the system of equations ...

Using the second equation to substitute for y in the firs equation, we have ...

  x +x² -5 = 15

  x² +x -20 = 0 . . . . . subtract 15, put in standard form

  (x +5)(x -4) = 0 . . . . . factor

A product is zero only when one or more factors is zero. The values of x that make the factors zero are ...

  x = -5  and  x = 4

The corresponding values of y are ...

  y = 15 -x

  y = 15 -{-5, 4} = {20, 11}

The solutions are (x, y) = (-5, 20) and (4, 11).

The surface area of the triangular prism is given as follows:

S = 549.15 m².

The surface area of a prism is given by the sum of the areas of all the parts that compose the prism.

The prism for this problem is composed as follows:

Hence the surface area is obtained as follows:

S = 15 x 13 + 15 x 15.81 + 2 x 0.5 x 9 x 13

S = 549.15 m².

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The triangular prism's surface area is given as follows:

S = 549.15 m².

The total area of all the prism's component components determines the prism's surface area.

The following is the structure of the prism for this issue:

rectangle with 15 and 13 meter sides.

rectangle with measurements of 15 and 15.81 meters.

two right triangles with 9 and 13 meter sides. So, the following is how the surface area is determined:

S is equal to 15 x 13 plus 15 x 15.81 and 2 x 0.5 x 9 x 13

S = 549.15 m².

An equivalent fraction to 1 whole and 7/8 is 15/8.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. It is, in other words, a "top-heavy" fraction since the fraction represents a value greater than one full unit.

1 whole and 7/8 can be written as a mixed number, which is a combination of a whole number and a fraction:

1 whole and 7/8 = 1 + 7/8

To find an equivalent fraction, we can convert the mixed number to an improper fraction by multiplying the whole number by the denominator of the fraction, and then adding the numerator. The result is the numerator of the improper fraction, and the denominator stays the same:

1 + 7/8 = (1 × 8 + 7)/8 = 15/8

Therefore, an equivalent fraction to 1 whole and 7/8 is 15/8.

For instance, the improper fraction 7/4 results from the numerator's (7), which is greater than the denominator (4).

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[tex]x=\textit{gallons of solution at 10\%}\\\\ ~~~~~~ 10\%~of~x\implies \cfrac{10}{100}(x)\implies 0.10 (x) \\\\\\ y=\textit{gallons of solution at 60\%}\\\\ ~~~~~~ 60\%~of~y\implies \cfrac{60}{100}(y)\implies 0.6 (y) \\\\\\ \textit{150 gallons of solution at 50\%}\\\\ ~~~~~~ 50\%~of~150\implies \cfrac{50}{100}(150)\implies 75 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{lcccl} &\stackrel{gallons}{quantity}&\stackrel{\textit{\% of gallons that is}}{\textit{fertilizer only}}&\stackrel{\textit{gallons of}}{\textit{fertilizer only}}\\ \cline{2-4}&\\ \textit{Sol'n of 10\%}&x&0.10&0.10x\\ \textit{Sol'n of 60\%}&y&0.60&0.60y\\ \cline{2-4}&\\ mixture&150&0.5&75 \end{array} \\\\\\ \begin{cases} x + y = 150\\\\ 0.10x+0.60y=75 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=150}\implies y=150-x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 2nd equation}}{0.10x+0.60y=75}\implies \stackrel{\textit{substituting on the 2nd equation from above}}{0.10x+0.60(150-x)=75} \\\\\\ 0.10x+90-0.60x=75\implies 90-0.50x=75\implies 90=0.50x+75 \\\\\\ 15=0.50x\implies \cfrac{15}{0.50}=x\implies \boxed{30=x}\hspace{5em}\stackrel{ 150~~ - ~~30 }{\boxed{y=120}}[/tex]

Answer:

cot(65 deg)

Step-by-step explanation:

cot(x) is the complimentary func. of tan(x) with the relation:

tan x = cot (90 - x) and

cot x = tan (90 - x)

Answer:

x=7

(x)(x+1)=(4)(4+10)

Step-by-step explanation:

Expanding the right-hand side of the equation, we get:

(x)(x+1) = (4)(14)

Simplifying, we get:

x^2 + x = 56

Moving all terms to the left-hand side, we get:

x^2 + x - 56 = 0

Now we can factor this quadratic equation:

(x + 8)(x - 7) = 0

So the solutions are x = -8 or x = 7.

Answer: X=7

Step-by-step explanation:

To Solve this problem we have to remember a formula regarding secants in circles it states (A+B)*B=(C+D)*D, I have attached said Theorem. This is Exactly what your problem is asking.

So First

B = 4

A = 10

D = x

C = 1

(A+B)*B=(C+D)*D

(10+4)*4=(1+x)*x

14*4=x²+x

-x²-x+56=0

Using Quadratic Formula

X = 7, X = -8

Since you cant have - side length X= -8 is Extraneous

Thus Final solution is X = 7

Answer: I did not do the math, I just tell people how to do it

Hope I helped.

Step-by-step explanation:

Multiply the number of triangles you created by 180.

Answer:

Let's use "K" to represent Kevin's current age, and "M" to represent his mother's current age.

According to the problem, if you triple Kevin's age, the result is 1 less than his mother's age:

3K = M - 1

We can simplify this equation by adding 1 to both sides:

3K + 1 = M

This equation tells us that if we add 1 to three times Kevin's age, we get his mother's age. We can use this equation to solve for Kevin's age if we know his mother's age, or we can use it to solve for his mother's age if we know Kevin's age.

The measure of angle ∠4 is 29°, the equation is 3x = 159 and the value of x is 53

Given that, we have

∠2 = 29°

(a)

Angles 2 and 4 are vertical angles

So, we have

∠4 = 29°

(b) and (c)

We have

∠3 = (3x - 8)°

Angles 3 and 4 are angles on a straight line

So, we have the equation to be

3x - 8 + 29 = 180

Solving for x, we have

3x = 159

Divide by 3

x = 53

This means that the equation is 3x = 159 and the value of x is 53

In this section, we have the following side lengths

Lengths = 6, 8 and 10

This means that

Side lengths = 6 and 8

Hypotenuse = 10

Next, we create the right angle using the given lengths of the legs and the hypotenuse

Here, we have

R = 13

r = 8

The exact area is calculated as

A = π(R² - r²)

So, we have

A = π(13² - 8²)

Evaluate

A = 105π

For the approximate area, we have

A = 105 * 22/7

A = 330

This means that the exact area of the brick path is 105π square meters and the approximate area is 330 square meters

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Answer:

3

Step-by-step explanation:

The inverse function returns the original value for which a function gave the output.

This means if there is a function f(x) and at x = a, f(a) = k then f⁻¹(k) = a

This may be difficult to grasp with variables but essentially returning to the specific question
if f(3) = 17

then

f⁻¹(17) = 3

And that is the answer

The amount of time it takes the horse to complete a full cycle of motion is known as the period of the motion and can be calculated as follows:

T = 2π/ω.

Let's assume that a straightforward harmonic motion can be used to simulate the horse's movements. The simple harmonic motion equation is:

y = A sin(ωt + φ)

where:

The deviation from equilibrium is represented by the number y.

The maximum displacement's amplitude is A.

The angular frequency is equal to two times the frequency ω.

It's time t

The phase angle is φ

The equation can be written as follows, assuming that the horse is moving vertically and that its highest point corresponds to y = 0.

y = A sin(ωt)

where is the angular frequency and A is the motion's amplitude.

On a graph, where the horizontal axis denotes time and the vertical axis denotes displacement, we can draw this function as a sine wave. The

amount of time it takes the horse to complete a full cycle of motion is known as the period of the motion and can be calculated as follows:

T = 2π/ω

We need to know the duration of the horse's motion in order to predict when Ivan will have another chance to make a flawless shot. It's challenging to determine the period precisely in the absence of more details.

You can name the graph of the carousel equation θ = A cos(ωt) as follows:

The time, t, is displayed on the x-axis as seconds.

The angular position from the midline, θ, expressed in degrees, is shown on the y-axis.

The horizontal axis at θ = 0 degrees is the midline.

The largest angle of departure from the midline, or the distance between the wave's crest (highest point) or trough (lowest point), is known as the amplitude, or A.

The interval between two consecutive wave crests or troughs is known as the period, or T, which is the length of time it takes for one full cycle of motion.

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According to the information, Hannah donated b/50 books in total.

First, we need to find the average number of books donated by each student. We can do this by dividing the total number of books donated by the number of students:

Hannah donated 3 times this amount, so we can multiply the average by 3 to find how many books she donated:

Simplifying this expression, we get:

Therefore, Hannah donated b/50 books in total.

Note: This question is in Spanish. Here is the question in English:

Hannah's school organized a book donation. There are 150 students in her school who donated a total of b books. Hannah donated 3 times the average number of books donated by each student. How many books did Hannah donate?

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Answer:

[tex]\large\boxed{\tt Area = Length \times Width}[/tex]

[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]

[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked for the area of a 2D Rectangle.}[/tex]

[tex]\large\underline{\textsf{What is Area?}}[/tex]

[tex]\textsf{Area for 2D shapes is how much space is inside between edges. Consider edges}[/tex]

[tex]\textsf{as the sides of a shape.}[/tex]

[tex]\underline{\textsf{How are we able to find Area?}}[/tex]

[tex]\textsf{Many shapes require different formulas to find the area. Some have the same}[/tex]

[tex]\textsf{formulas however it depends on how many sides the shape has, and the number of}[/tex]

[tex]\textsf{dimensions shown in the shape. For a Rectangle it's simple. Because a Rectangle}[/tex]

[tex]\textsf{has 2 Dimensions (Length and Width), to find the area we should multiply}[/tex]

[tex]\textsf{the dimensions together, hence resulting in the amount of space inside the shape.}[/tex]

[tex]\large\underline{\textsf{Formula;}}[/tex]

[tex]\large\boxed{\tt Area = Length \times Width}[/tex]

[tex]\large\underline{\textsf{Plug in Values;}}[/tex]

[tex]\textsf{The Length and Width aren't mentioned in the question, but it doesn't matter}[/tex]

[tex]\textsf{since we're still going to get the same answer no matter which place they're in.}[/tex]

[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]

[tex]\large\underline{\textsf{Solving for the Area;}}[/tex]

[tex]\textsf{We have our formula, now multiply the dimensions together.}[/tex]

[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]

Answer:

Step-by-step explanation:

To calculate the mean (average) weekly earnings of workers in the occupations listed for 2010, we need to add up the earnings for each occupation and divide by the total number of occupations.

Forestry, logging and support: $971

Manufacturing: $977

Transportation and warehousing: $900

Construction: $1071

Retail trade: $501

Total earnings: $4,420

Total number of occupations: 5

Mean weekly earnings: $4,420 ÷ 5 = $884

Therefore, the mean (average) weekly earnings of workers in the occupations listed for 2010 is $884.