Luke melts 200 grams of dark chocolate that contains 60% cocoa and mixes it with 200 grams of milk chocolate that contains 30% cocoa.

a) So x = 5 is the critical point, and the vertex is at (5, -3).

b) the y-intercept is (0, -3).

c) y = 2/3 * (x - 5) - 3 for x >= 5

y = -2/3 * (x - 5) - 3 for x < 5

d) The slopes of the two pieces are 2/3 and -2/3 respectively.

(a) To find the vertex, set the derivative of the equation to 0 and solve for x:

dy/dx = 2/3 * d/dx |x-5| = 2/3 * sign(x-5) = 0, where sign(x-5) = 1 if x > 5, sign(x-5) = -1 if x < 5, sign(x-5) = 0 if x = 5.

So x = 5 is the critical point, and the vertex is at (5, -3).

(b) The axis intercepts are the points where the graph crosses the x-axis and y-axis.

The x-intercepts occur when y = 0:

2/3 * |x-5| - 3 = 0

2/3 * |x-5| = 3

|x-5| = 9/2

x = 5 +/- 9/2 = 5 + 9/2 = 7 or x = 5 - 9/2 = 2.5

So the x-intercepts are (7, 0) and (2.5, 0).

The y-intercept occurs when x = 0:

y = 2/3 * |0-5| - 3 = -3.

So the y-intercept is (0, -3).

(c) The graph is a piecewise linear function with two pieces:

y = 2/3 * (x - 5) - 3 for x >= 5

y = -2/3 * (x - 5) - 3 for x < 5

(d) The slopes of the two pieces are 2/3 and -2/3 respectively. These slopes are related because the graph is symmetrical about the vertical line x = 5, with the two pieces being reflections of each other across the line.

Learn more on calculations based on graphs here https://brainly.com/question/27166136

#SPJ1

The average rate of change of f(x) over the interval is 3

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

The graph

We have the interval to be

x=-1 to x=1.

From the graph, we have

f(-1) = -3

f(1) = 3

The average rate is then calculated as

Average rate = [f(1) - f(-1)]/[1 + 1]

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

Average rate = (3 + 3)/2

Evaluate

Average rate = 3

Hence, the average rate is 3

Read more about average rate at

brainly.com/question/17131025

#SPJ1

The side lengths of an equiangular octagon are 1, 2, 3, 4, 1, 2, 3, and 4 in clockwise order so area of octagon is 11 + 12√2 square units.

The sides of octagon are 1, 2, 3, 4, 1, 2, 3, 4 as shown in the figure,

The area of the octagon = area of the rectangle - the area of the four right isosceles triangular corners.

A = (lxb) - 1/2[√2×√2 + √8×√8]x2

A = [(3+√2+√8)(1+√2+√8)] -1/2[√2×√2 + √8×√8 + √2×√2 + √8×√8]

A = 3 + 12√2 +7

A = 11 + 12√2

Therefore, The area of the octagon is 11 + 12√2 square units.

A closed two-dimensional shape having eight sides, eight vertices, and eight internal angles is known as an octagon. An octagon is referred to as a regular octagon if all of its sides and internal angles are of equal length; otherwise, it is referred to as an irregular octagon. The next sections also discuss the various octagon types, such as convex and concave octagons.

Learn more about Area of octagon:

https://brainly.com/question/860089

#SPJ4

As a result, 315 pupils attended the school play.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The first equation in the system is given by the total number of attendees:

c + a = 330

The second equation is given by the number of children being 21 times the number of adults:

c = 21a

We can use substitution to find the value of a and then find the value of c. Substituting the second equation into the first equation, we get:

21a + a = 330

Combining the two terms on the left-hand side, we have:

22a = 330

Dividing both sides by 22, we have:

a = 15

So there were 15 adults in attendance at the school play. To find the number of children, we can use the second equation:

c = 21a = 21 * 15 = 315

So there were 315 children in attendance at the school play.

To know more about equation,

https://brainly.com/question/2228446

#SPJ4

In the video, the presenter used Tableau to help interpret the large p-value of the variable spec. feats in the multiple linear regression model.

The presenter first used a scatter plot to visualize the relationship between size and spec. feats and included a regression line to represent the linear relationship between the two variables.

The presenter then used Tableau's Trend Lines tab to calculate the p-value of the spec. feats by providing the regression equation and data points.

This allowed the presenter to determine the p-value of the spec. feats were too large to be significant and thus concluded that spec. feats did not have a significant linear relationship with size.

For more questions like Tableau click the link below:

https://brainly.com/question/25531734

#SPJ4

The candle that will burn out first is the yellow candle rather than the blue candle.

Blue candle:

1/4 inch per hour or 0.25 inches per hour

8 / 0.25 = 32 hours to completely burn out

Yellow candle:

1/2 inch per hour or 0.5 inches per hour

12 / 0.5 = 24 hours

If the blue candle is lit 6 hours before the yellow candle then:

Blue candle: 32 - 6 = 26 hours left

Yellow candle: 24 hours left

This means the yellow candle will burn out first.

Learn more about time in https://brainly.com/question/28050940

#SPJ1

The simplified expression is 4a⁵ * b³.

Exponents are a way to represent repeated multiplication. The exponent of a number represents the number of times the base is multiplied by itself. For example, 2^3 means 2 multiplied by itself 3 times, or 2 * 2 * 2 = 8.

In general, if the base number is b and the exponent is n, then b^n represents b multiplied by itself n times. This can be written as b * b * ... * b (n times). The exponent can be any positive integer or zero, and the base can be any real number.

Exponents have several properties, including the following:

b^0 = 1 for any non-zero base b.

b^1 = b for any base b.

b^n * b^m = b^(n + m) for any base b and positive integers n and m.

(b^n)^m = b^(n * m) for any base b and positive integers n and m.

b^(-n) = 1 / b^n for any base b and positive integer n.

These properties help simplify and manipulate expressions with exponents.

We can simplify the expression using the properties of exponents and radicals as follows:

^3√32a¹⁰b⁶

= ^3√(2⁵ * 2¹ * a¹⁰ * b⁶) [since 32 = 2⁵ and 2¹]

= ^3√(2⁶ * a¹⁰ * b⁶) [using the property of exponents: a^m * a^n = a^(m+n)]

= 2^2 * ^3√(a¹⁰ *b⁶) [since 2⁶  = 2² * 2⁴]

= 2² * a⁵ * b³ [since (^3√(x))³ = x, and since a^m * b^m = (ab)^m]

= 4a⁵ * b³.

So, the simplified expression is 4a⁵ * b³.

To  know more about expression visit:

https://brainly.com/question/27148036

#SPJ1

1:3

simplify the ratio and you would get 1:3

The center of the ellipse will be (3, 0). And the lengths of the major and minor axes will be 4.4721 and 2, respectively.

Ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.

The equation of the ellipse is given below.

5x² + y² − 30x + 40 = 0

Convert the ellipse into standard form. Then we have

5x² + y² − 30x + 40 = 0

5[x² − 6x] + y² + 40 = 0

5[x² − 6x + 9] − 45 + y² + 40 = 0

5(x − 3)² + y² = 5

(x − 3)² + y² / 5 = 1

The equation center of the ellipse is (3, 0). Then the major axis is given as,

Major axis = 2 √5

Major axis = 4.4721

Then the minor axis is given as,

Minor axis = 2 x 1

Minor axis = 2

The center of the ellipse will be (3, 0). And the lengths of the major and minor axes will be 4.4721 and 2, respectively.

More about the ellipse link is given below.

https://brainly.com/question/19507943

#SPJ1

The correct equation is given below.

5x² + y² − 30x + 40 = 0.

Answer:

b) 20

Step-by-step explanation:

In supplementary angles, the sum of two angles add up to 180°

  3x + 40 + 80 = 180

          3x + 120 = 180

Subtract 120 from both sides,

                    3x = 180 - 120

                   3x = 60

Divide both sides by 3

                     x = 60 ÷ 3

                      [tex]\boxed{\bf x = 20^\circ}[/tex]

The volume of the prism is 360cm³

A prism is a solid shape that is bound on all its sides by plane faces. There are two types of faces in a prism. The top and bottom faces are identical and are called bases. A prism is named after the shape of these bases.

The volume of a prism is expressed as base area x height

The height = 10cm

base area = ½b×h

= ½ × 6× 12

= 36cm²

therefore;

volume = 36 × 10 = 360cm³

therefore the volume of the shape is 360cm³

learn more about volume of prism from

https://brainly.com/question/23766958

#SPJ1

It's not fully accurate to say that. In many tropical and subtropical coastal places around the world, where warm, moist air from the ocean mixes with the land and creates high humidity and frequent rainfall, a hot, humid coastal tropical atmosphere prevails. This climate is not specific to the Indian or Pacific Oceans.

The majority of tropical regions are renowned for their year-round high temperatures and heavy precipitation. Tropical regions are humid because of the heavy rainfall and hot because of the high temperature.

The tropical wet climate, often referred to as the tropical monsoon climate, dominates a section of the southwest lowlands that border the Malabar Coast, the Western Ghats, and southern Assam. It is the driest climate. Lakshadweep and the Andaman and Nicobar Islands, two of India's island territories, are also impacted by severe weather.

To know more about Tropical visit:

https://brainly.com/question/9339571

#SPJ1

Answer:

(-4,3)

x = -4 and y = 3

Step-by-step explanation:

Set the two equation equal to each other and solve for x.

x + 7 = [tex]\frac{3}{4}[/tex] x + 6  Multiply all the way through by 4 to clear the fraction

4(x + 7) = 4( [tex]\frac{3}{4}[/tex] x + 6)  Distribute the 4

4x + 4(7) = 4([tex]\frac{3}{4}[/tex]x) + 4(6)

4x + 28 = 3x + 24             [tex]\frac{4}{1}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{12}{4}[/tex] = 3   ([tex]\frac{4}{1}[/tex] is another name for 4)  subtract 3x from both sides

4x - 3x + 28 = 3x - 3x + 24

x + 28 = 24  subtract 28 from both sides

x + 28 - 28 = 24 - 28

x = -4

Substitute -4 for x in either of the two original equations and solve for y.

y = x + 7

y = -4 + 7

y = 3

Check

Substitute in -4 for x and 3 for y and see if we get true statements.

y = x + 7

3 = -4 + 7

3 = 3 checks

y = [tex]\frac{3}{4}[/tex] x + 6

3 = [tex]\frac{3}{4}[/tex] [tex](\frac{-4}{1})[/tex] + 6

3 = -3 + 6

3 = 3 cfhecks

The answers for questions G, H, K, and L are the same as questions C, D, K, and L, respectively, because the speed (65mi/h) remains constant.

A. 65 miles in one hour: If a car is traveling at 65 miles per hour (mi/h), then in one hour it will travel 65 miles.

B. 340,800 feet in one hour, 65 miles is equal to 5,280 x 65 = 340,800 feet.

C. 5,680 feet in one minute, 340,800 feet ÷ 60 = 5,680 feet in one minute.

D. 94.67 feet in one second, 5,680 feet ÷ 60 = 94.67 feet in one second.

E. 42 miles in one hour: If a car is traveling at 42 miles per hour, then in one hour it will travel 42 miles.

F. 221,760 feet in one hour, 42 miles is equal to 5,280 x 42 = 221,760 feet.

G. 5,680 feet in one minute.

H. 94.67 feet in one second.

I. x miles in one hour.

J. 5,280 x x feet in one hour:

K. (5,280 x x) ÷ 60 feet in one minute.

L. ((5,280 x x) ÷ 60) ÷ 60 feet in one second.

To learn more about constant please click on below link

https://brainly.com/question/14159361

#SPJ4

There are 5,280 feet in a mile. Round answers to the nearest unit.

A. How many miles does a car traveling at 65mi/h go in one hour?

B. How many feet does a car traveling at 65mi/h go in one hour?

C. How many feet does a car traveling at 65mi/h go in one minute?

D. How many feet does a car traveling at 65mi/h go in one second?

E. How many miles does a car traveling at 42mi/h go in one hour?

F. How many feet does a car traveling at 42mi/h go in one hour?

G. How many feet does a car traveling at 65mi/h go in one minute?

H. How many feet does a car traveling at 65mi/h go in one second?

i. How many miles does a car traveling at x mi/h go in one hour?

J. How many feet does a car traveling at x mi/h go in one hour?

K. How many feet does a car traveling at x mi/h go in one minute?

L. How many feet does a car traveling at x mi/h go in one second?

The a1 of the sequence is  28715.

The sum of a geometric series can be found using the formula:

S = a / (1 - r)

where:

S is the sum of the series

a is the first term of the series

r is the common ratio, which is the ratio of any term to its preceding term

For a1;

Sn= a1 - anr/ r - 1

Where;

Sn = 21825

n = 125

r = 15

Thus;

2185 = a1 - (125 * 15)/15 -1

2185 * 14 = a1 - 1875

-30590 = a1 - 1875

a1 = 30590 + 1875

a1 = 28715 as we cans see

Learn more about geometric sequence:https://brainly.com/question/13008517

#SPJ1

A line spectrum refers to a type of spectrum where light is emitted at specific, discrete frequencies. A continuous spectrum, on the other hand, refers to a type of spectrum where light is emitted at all frequencies within a given range.

A line spectrum refers to a type of spectrum where light is emitted at specific, discrete frequencies. The light is emitted in a pattern of individual lines, hence the name "line spectrum." Hot gases or plasmas often produce this type of spectrum, and the lines represent specific energies of electrons in the gas.

An example of a line spectrum is the Hydrogen spectrum, which consists of a series of distinct lines of different colours that correspond to different energies of the electrons in a hydrogen atom.

A continuous spectrum, on the other hand, refers to a type of spectrum where light is emitted at all frequencies within a given range. The light is emitted in a smooth, continuous manner, hence the name "continuous spectrum." This type of spectrum is often produced by hot solid objects, such as the sun, and it represents a continuous range of energies.

An example of a continuous spectrum is the spectrum of light emitted by the sun, which spans a wide range of frequencies and has a smooth, continuous appearance.

To know more about Hydrogen spectrum, here

https://brainly.com/question/7586240

#SPJ4

Answer: To find the least common denominator (LCD) of fractions with variables, you need to determine the smallest number that all the denominators will divide into evenly.

One method to find the LCD is to multiply all the denominators together and simplify the expression. For example, if the denominators are x and y, the LCD would be xy. Another method is to find the greatest common factor (GCF) of all the denominators, and then divide each denominator by the GCF to obtain the LCD.

In either case, it may be necessary to factor the denominators to determine the GCF and simplify the expression for the LCD.

Step-by-step explanation:

The area of the shape is x²+2x +1 and the perimeter is 4x +7

The area is the region covered by shape or figure whereas perimeter is the distance covered by outer boundary of the shape. The unit of area is given by square unit or unit2 and unit of perimeter is same as the unit.

The area of the shape is :

The shape is sub divided into 4 with different areas x, x , x², and 1

Therefore the area of the shape = x²+x+x+1 = x²+2x+1

The perimeter is obtained by adding all the sides

x+x+x+x+1+1+1+1+1+1+1 = 4x+7

therefore the perimeter of the shape is 4x+ 7

learn more about area and perimeter from

https://brainly.com/question/25292087

#SPJ1

The measure of the missing angle a is 155 degrees.

The sum of angles on a straight line is equal to 180 degrees.

From the diagram;

Since the sum of angles on a straight line is equal to 180 degrees.

Supplement angle to a  + angle a = 180

25° + a = 180°

Solve for a by subtracting 25° from both sides.

25° - 25° + a = 180° - 25°

a = 180° - 25°

a = 155°

Therefore, the measure of angle a is 155°.

Learn more about supplementary angles here: https://brainly.com/question/18164299

#SPJ1

Money will the group have at the end of 10 years are $82,719.58.

Money is a kind of trade that is utilized in business dealings and other types of economic activity. All economic agents within a particular nation or geopolitical region accept it as a form of asset that is used to store purchasing power and is accepted as payment. It functions as a store of value, a unit of account, and a medium of exchange. Because it allows people to buy and sell goods and services, is crucial.

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] is the formula for computing the amount after compound interest.

Where P is the principal amount, which is $50,000, A is the amount due after 10 years, r is the interest rate, which is 6%, n is the number of times the interest is compounded each year, which is 12, and t is the number of years, which is 10.

Putting the values in the formula,

[tex]A=50,000(1+\frac{0.06}{12})^{(12\times 10)}[/tex]

[tex]A=50,000(1.005)^{120}[/tex]

A=50,000(1.71958)

A=82,719.58

To learn more about money

brainly.com/question/30279568

#SPJ1

Answer:

The interest amount Karen needs to pay each month is $1000 * .0025 = $2.5.

So, she needs to pay $1100 - $1000 = $100 in interest.

Therefore, Karen will have to pay for 100 / 2.5 = 40 months.

Rounding to the nearest month, Karen will have to pay for 40 months.

Answer: Shows base 2 exponents

Step-by-step explanation: When there are no folds, the paper is at 2^0 which is one piece. The after one fold is 2^1 which is 2 and doubles after. This represents exponents with base 2.

The solution is Option A.

The inequality equation is x ≥ 1.4 ( 50 )

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

The number of tablets XYZ Tech sold last week = 50 tablets

The number of tablets XYZ Tech needs to sell this week = 40 % more

So , number of tablets XYZ Tech needs to sell this week = 50 +( 40/100 )50

On simplifying the equation , we get

The number of tablets XYZ Tech needs to sell this week = 50 ( 1 + 0.4 )

The number of tablets XYZ Tech needs to sell this week = 1.4 ( 50 )

Now , they have to sell at least 40 % more

So , the inequality equation is x ≥ 1.4 ( 50 )

Hence , the inequality equation is x ≥ 1.4 ( 50 )

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

Answer:

204000$ is the new selling price

I think

Answer:

2040000

Step-by-step explanation:

15%of 240 000 is 36 000

240 000 - 36 000 = 204000

The population of a town increased by 1.5% per year from 1995 to 2015. The town's population at the beginning of 1995 was 16112. The 1-year growth factor for the town's population is 1.49%.

The population of a town increased by 1.5% per year from 1995 to 2015.

So, rate of growth is 1.5%.

The town's population at the beginning of 1995 was 16112.

So, initial population is 16112.

And we have to calculate 1 year growth factor.

So, we will use the formula i.e.

x(t) = [tex]x_{o}[/tex] × (1 + r) t

Here, Initially the Population is [tex]x_{o}[/tex] =16112

Growth Rate (%) (r) = 1.5

Number of years (t)= 1

So, we get=

x(t)=16112 × (1+1.5) 1

x(t)=16353.67

To calculate growth factor = (Final population- Initial population/ Initial population) *100

= (16353.67-16112/16112) *100

=1.49%

Here is more information on growth rate: brainly.com/question/2639972

#SPJ4

The simplified  form for the  given problem (5 √(3) + √(15)) × (3 √(5) + √(15))  is 45√(45).To solve the equation we are using the distributive property.

The  property which states that the product of a number and the sum of two numbers is equal to the sum of the products of the number and each of the two numbers being added. Using this principle, the problem can be broken down into two separate products, (5 √(3) × 3 √(5)) and (5 √(3) × √(15)) + (√(15) × 3 √(5)).  

The first part of the problem can be simplified by combining 5 and 3, which is 15. This leaves 15 √(15). The second part of the problem can be simplified by combining 3 and 5, which is 15. This leaves 15 √(15). Adding the two parts together results in 30 √(15). The √(15) can be multiplied by itself, which is 15. Multiplying 30 by 15 results in 45 √(45). The √(45) cannot be simplified any further, so the final answer is 45√(45).

To know more about  distributive property refer to  the link  brainly.com/question/6276874

#SPJ4

The total area of all three circular lights is 115.395 square inches

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

Using the above as a guide, we have the following:

The total area of all three circular lights = 3 * 38.465 square inches.

Evaluate

The total area of all three circular lights = 115.395 square inches.

Hence, the area is 115.395 square inches

Read more about area at

https://brainly.com/question/22972014

#SPJ1

Hello!

Answer:

The slope of the line that runs through the two points (-3,1) and (-17,2) is

[tex]m= - \frac{1}{14}[/tex]

Step-by-step explanation:

Use the formula of slope to find [tex]m[/tex]

Hope this helps!