Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf. She writes the expression (x−5)(50−2x) to represent her profit based on the price per scarf, x . Enter Sofie's average change in profit for two different sections of the graph.

Hello,

Answer:

We can start by rationalizing the denominators of each fraction.

For the first fraction, we multiply the numerator and denominator by the conjugate of the denominator, which is √4 - √5:

1/√4+√5 = 1/√4+√5 × (√4 - √5)/(√4 - √5)

= (√4 - √5)/(4 - 5)

= (√4 - √5)/(-1)

For the second fraction, we multiply the numerator and denominator by √5 - √6:

1/√5+√6 = 1/√5+√6 × (√5 - √6)/(√5 - √6)

= (√5 - √6)/(5 - 6)

= (√5 - √6)/(-1)

We can do the same for the remaining fractions:

1/√6+√7 = (√6 - √7)/(-1)

1/√7+√8 = (√7 - √8)/(-1)

1/√8+√9 = (√8 - √9)/(-1)

Now we can simplify the expression:

1/√4+√5 + 1/√5+√6 + 1/√6+√7 + 1/√7+√8 + 1/√8+√9

= (√4 - √5)/(-1) + (√5 - √6)/(-1) + (√6 - √7)/(-1) + (√7 - √8)/(-1) + (√8 - √9)/(-1)

= (√4 - √5 + √5 - √6 + √6 - √7 + √7 - √8 + √8 - √9)/(-1)

= (√4 - √9)/(-1)

= √9 - √4

= 3 - 2

= 1

Therefore, the expression simplifies to 1, which is equal to the right-hand side of the equation.

Good luck

The below calculation allows us to determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.

To create a fruit punch that is entirely fruit juice, we must calculate the ratio of fruit juice to total punch. To do this, we will use the following formula:

Fruit Juice Ratio = (Fruit Juice / (Fruit Juice + Punch)) x 100

For example, if we have 10 ounces of fruit juice and 10 ounces of fruit punch, the ratio of fruit juice to total punch is 50%. Therefore, we need to mix 50% fruit juice with 50% punch to create a fruit punch that is entirely fruit juice.

To calculate this for any given amount of fruit juice and punch, we simply plug the numbers into the formula. For instance, if we have 20 ounces of fruit juice and 60 ounces of punch, the ratio of fruit juice to total punch is 25%. Therefore, we need to mix 25% fruit juice with 75% punch to create a fruit punch that is entirely fruit juice.

By using this formula, we can easily determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.

We can use the formula Fruit Juice Ratio = (Fruit Juice / (Fruit Juice + Punch)) x 100 to calculate the ratio of fruit juice to total punch. This allows us to determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.

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Answer:

*diameter=radius ×2

6cm×2=12cm

*diameter=10 ×2=30cm

*radius=diameter÷2

140cm÷2=70cm

*radius

250cm÷2=125cm

*diameter

2.5m×2=5m

*radius

3.6m÷2=1.8m

The radius of the cylinder will be equal to 112.8 cm.

The capacity of an object is measured by its volume. For instance, a cup's volume is said to be 100 ml if it can hold 100 ml of water in its brim. The amount of space occupied by a three-dimensional object can also be used to define volume.

Given that a graduated cylinder that is 24 cm tall can hold 1 L of water. The radius of the cylinder will be calculated as:-

Volume = 1 L

Volume = 1000000 cm³

πr²l =  1000000 cm³

r² = ( 1000000 / π x 25 )

r² = 12732.4

r = √12732.4

r = 112.8 cm

Therefore, the radius of the cylinder will be 112.8 cm.

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The width of the rectangle is 7.2 cm because if you divide 93.6 cm by 13 cm you will get 7.2 cm.

Brainliest please that would be nice of you(:

Step-by-step explanation:

To determine the missing values in the Venn diagram, we can use the information from the problem to set up a system of equations. Let's assign variables to each section of the diagram:

X = number of students who play tennis only

Y = number of students who play soccer only

Z = number of students who play volleyball only

W = number of students who play tennis and soccer only

y = number of students who play tennis and volleyball only

Using the information from the problem, we can set up the following equations:

X + W + 3 = 21 (21 students play tennis)

Y + W + 4 = 16 (16 students play soccer)

Z + y + 5 = 19 (19 students play volleyball)

W + 3 = 3 (3 students play soccer and tennis)

y + 5 = 5 (5 students play volleyball and tennis)

Solving for one variable in terms of the others, we can substitute into the other equations:

X = 21 - W - 3

Y = 16 - W - 4

Z = 19 - y - 5

Substituting into the equation for W, we find:

W + 3 = 3

W = 0

Substituting W = 0 into the equations for X and Y:

X = 21 - 0 - 3 = 18

Y = 16 - 0 - 4 = 12

Finally, we can substitute X, Y, and W into the equation for Z to find:

Z = 19 - y - 5

Z = 19 - 5 - 5 = 9

So the missing values in the Venn diagram are:

Soccer: 12 students

Volleyball: 9 students

Tennis: 18 students

Soccer & Tennis: 0 students

Volleyball & Tennis: 5 students

Volleyball & Soccer: 4 students

Note that the number of students who play none of the three sports is not explicitly stated in the problem, but it can be calculated as:

13 = total number of students - (X + Y + Z + W + y)

13 = total number of students - (18 + 12 + 9 + 0 + 5)

13 = total number of students - 44

So there are 57 total middle school students

The equation by substituting first equation in the second equation:

[tex]n^2 - c^2 =0[/tex]

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

The  equation for both triangles have :

[tex]c^2 = a^2 + b^2\\n^2 = a^2 + b^2[/tex]

To write the equation by substituting first equation in the second equation.

Now consider,

[tex]c^2 = a^2 + b^2-------(1)\\n^2 = a^2 + b^2-------(2)[/tex]

Now, Plug the value of equation(2) in (1), we get

[tex]n^2 = c^2[/tex]

[tex]n^2 - c^2 =0[/tex]

Hence, the equation by substituting first equation in the second equation:

[tex]n^2 - c^2 =0[/tex]

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The given expression [tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]is equivalent to (x - y)/18y².

Given is the expression as -

[tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]

The given expression is -

[tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]

We can solve further as -

{(x² - xy)/9y²} x {3y/2x}

{x(x - y)/9y²} x {3y/2x}

(x - y)/18y²

Therefore, the given expression [tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]is equivalent to (x - y)/18y².

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The average daily rate is calculated by dividing the total rooms revenue by the total number of rooms sold. In this case, the average daily rate is (option) $114.63.

The average daily rate is a measure of the average amount of money that a hotel is able to generate per room per day. It is calculated by dividing the total rooms revenue by the total number of rooms sold. In this case, the total rooms' revenue was $75,884 and the total number of rooms sold was 662, which gives us an average daily rate of $114.63. This is a useful measure for hotels to gauge the performance of their business and to set pricing accordingly. It also helps hotels identify opportunities for increasing revenue, such as offering discounts or promotions to attract more customers.

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The correct similarity of the triangles are JMK ~ LMK ~ JLM (option D)

Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles and equal scale factors. Equal scale factors mean that the lengths of their corresponding sides have a matching ratio.

Given that, there are 3 right triangles in the drawing given. They are all similar. we need to identify the correct similarity,

So, from the figure, if we separate each triangle,

We will get,

Triangles JLM, JMK and LMK

If we check,

They are showing true similarity by their figure (refer to diagram attached)

Hence, the correct similarity of the triangles are JMK ~ LMK ~ JLM (correct option is D)

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On solving the provided question, we can say that the equation, we have is [tex]t^2 +5t +6.[/tex]

Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol. In this case, 2x4=2.

the equation, we have is V = P/I

[tex]V = \frac{t^3 +9t^2 +26t +24}{t + 4}[/tex]

on dividing

the answer will be [tex]x^3+9x^2+26x +24=t^2 + 5t + 6[/tex]

x = -4

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No, it is not possible to obtain a negative value for the ss, variance, or standard deviation. They represent the amount of spread in data, and the values are always positive or zero.

Sum of squares (SS) measures the deviation of each data point from the mean of the set, squared. The formula for SS is:

SS = Σ (X - μ)^2

Variance is the average of the sum of squares, and it is calculated by dividing the SS by the degrees of freedom (n-1), where n is the number of data points in the set:

Variance = SS / (n - 1)

Standard deviation is the square root of variance and it is a measure of how far each data point is from the mean of the set:

Standard deviation = √Variance

Since both variance and standard deviation are based on the sum of squares, which is always non-negative, variance and standard deviation are also always non-negative.

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A stem-and-leaf display is a statistical tool used for organizing and displaying data.

It is especially useful for analyzing small data sets and can be used for a variety of purposes. With stem-and-leaf displays, individual data points can be easily observed and analyzed, which is particularly useful for answering multiple-choice questions.

Additionally, stem-and-leaf displays can be used to analyze qualitative data by observing patterns and relationships between data points. By determining the central tendency and dispersion of the data, a stem-and-leaf display can help to provide a clearer understanding of the data set as a whole.

Furthermore, the shape of the data can be analyzed through the use of a stem-and-leaf display, which can be helpful in identifying outliers and skewness. In conclusion, stem-and-leaf displays are a useful tool for organizing and analyzing data and can provide valuable insights into data sets.

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See the attached image for the plotted graph

The graph of a function f in mathematics is the collection of ordered pairs where f(x)=y.

These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

4x -4y = 24

x - y= 6

y= x-6

Slope= 1, pass through (6,0), (0, -6)

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The ordered pair that lies on the inverse of the function is (6, -3)

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

g(x)=−(x+1)3−2.

Rewrite as

g(x) = −(x + 1)³ − 2

Next, we test the options

Set x = -3

So, we have the following representation

g(-3) = −(-3 + 1)³ − 2

Evaluate the expression

g(-3) = 6

As an ordered pair, we have (6, -3)

So, the ordered pair of the inverse is (6, -3)

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Option A is the correct option

So, the approximate form of the expression for all values of t is 0.75.

The expression 3(1.25)/5 can be simplified to

3/5 * 1.25

= 0.75.

=3(0.25)

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

Term is defined as a constant, a single variable, or a mixture of variables and constants multiplied or divided. Algebra Expression Example: 3x + 9, 5x + 10

To simplify simply is to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

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Answer:

Step-by-step explanation:

1. B

2.D

3.2

4.A,C,D

Answer:

1=b

Step-by-step explanation:

go to the comments for other answers

The Histogram shows the distribution of the students’ balance-scale readings is Histogram II.

The distribution of numerical data is roughly shown by a histogram. Karl Pearson was the one who initially coined the phrase. The first stage in creating a histogram is to "bin" (or "bucket") the range of values, or split it into a series of intervals, and then count the number of values that fall into each interval.

The bins are often defined as a series of discrete intervals that don't overlap. The bins (intervals) must be close together and frequently, but not always, have the same size.

When the mean and median are equal, a histogram is said to be symmetrical. A symmetric histogram will be split into two equal halves if we draw a line through its centre. The two parts will be exact replicas of one another. 

Therefore, The Histogram shows the distribution of the students’ balance-scale readings is Histogram II.

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The salt is in the tank (a) after t minutes is 20 minutes and (b) after 20 minutes there are 150 kg of salt.

        S(t) = C(t) * 1000

        dS(t)/dt = (C(0) - C(t)) * 10

         where C(0) is the initial concentration of salt in the

         brine (15 kg / 1000 liters = 0.015 kg/liter).

        C(20) = C(0) - (S(20) / 1000 - S(0)) / 10

                  = 0.015 - (S(20) / 1000) / 10

        S(20) = C(20) * 1000

        S(20) = (0.015 - S(20) / 1000 / 10) * 1000

        S(20) = 15 - S(20) / 10

        S(20) = 150

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The distance the defender had to run to get to the spot where Beckham caught the ball is 34.6 yards.

Let's call the distance the defender had to run to get to the spot where Beckham caught the ball "d".

Since the defender was running aslant towards Beckham, we can use the Pythagorean theorem to find the distance he had to run. The theorem states that in a right triangle, the sum of the squares of the two smaller sides is equal to the square of the hypotenuse (the longest side).

If we call the sideline 40 yards, we can set up the equation as follows:

d² + 20² = 40²

Expanding and simplifying:

d² + 400 = 1600

d² = 1600 - 400 = 1200

d = √(1200)

= √(300 * 4)

= √(300) * √(4)

= √(300) * 2

= 10 √(3) * 2

= 20 √3

Rounding to the nearest tenth, we have:

d ≈ 34.6 yards

So, the defender had to run approximately 34.6 yards to get to the spot where Beckham caught the ball.

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The probability that Juan will choose a kind of plant his mother would want is 6/30, which is equal to 0.2 or 20%

To calculate the probability that Juan will choose a kind of plant his mother would want, out of 30 plants, six of them are a kind that his mother would want, first divide the number of plants his mother would want (6) by the total number of plants (30). This will give you a decimal, 0.2. To turn this decimal into a percent, multiply it by 100. This will give you 20%, or a 20% chance of Juan choosing a kind of plant his mother would want. To summarize, therefore, the probability that Juan will choose a kind of plant his mother would want is 0.2 or 20%.

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It takes Ermias and Manuel 3.43 hours to paint the room if they are working together. To find the time it takes for Ermias and Manuel to paint the room together, we can use the formula: 1/rate = time.

The rate is the combined painting rate of both workers, which is equal to the sum of their individual painting rates.

Let's call the time it takes for Ermias and Manuel to paint the room together "T". The combined painting rate of both workers is then 1/T.

The individual painting rates of Ermias and Manuel are 1/8 hours per room and 1/6 hours per room, respectively. Therefore, their combined painting rate is 1/8 + 1/6 = 6/48 + 8/48 = 14/48 hours per room.

Now we can use the formula 1/rate = time to find T:

1/ (14/48) = T

48/14 = T

T = 3.43 hours

So it takes Ermias and Manuel 3.43 hours to paint the room if they are working together.

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Answer:

Reflection , Reflection

Step-by-step explanation:

when the triangle reflects off the x axis and then reflects along the y axis.

The triangles are similar by the SAS(side–angle–side) criteria for triangle similarities.

The SAS(side–angle–side) criterion for triangle similarity states that If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.

Observing the triangles, if the ratio of side lengths 24 and 120 is equal to that of 14 and (14 + 56), then the angles inscribed by the two sides are in both triangles are equal.

24 : 120 = 24/120

24 : 120 = 1/5

24 : 120 = 1: 5

14 : 70 = 14/70

14 : 70 = 1/5

14 : 70 = 1 : 5

In conclusion, the triangles are similar by the SAS(side–angle–side) criteria for triangle similarities

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Answer:

1.) 160

2.) 40

3.) 200

Step-by-step explanation:

Hoped this helped! =)

294 cm² is  the lateral area of the drawing .

Describe Area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies. Area is the amount of surface a two-dimensional shape can cover, measured in square units. The SI unit of area is the square meter (m2), which is a derived unit.

the lateral surface are square of each side .

                    = 7 cm

          lateral area =  6 * (7)²  = 294 cm²

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The nth term in the given AP is given by aₙ = 125000n - 124990 and the nth term in the given GP is given by aₙ = 5×4ⁿ/2

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.

Given that, an arithmetic sequence has a common difference of 125,000. A geometric sequence has a common ratio of 4. In both sequences, a(1) = 10.  We asked to compare the sequences,

The formula for AP =

aₙ = a + (n-1)d, d = common difference, a = first term, n = number of terms and aₙ = nth term

The formula for GP =

aₙ = arⁿ⁻¹, r = common ratio, a = first term, n = number of terms and aₙ = nth term

The common difference and first term are, 125000 and 10 respectively,

aₙ = 10 + (n-1)125000

aₙ = 10+1245000n-125000

aₙ = 125000n - 124990

Therefore, nth term in the given AP is given by aₙ = 125000n - 124990

The common ratio and the first term are, 4 and 10 respectively,

aₙ = 10×4ⁿ⁻¹

aₙ = 10×4ⁿ / 4

aₙ = 5×4ⁿ/2

Therefore, nth term in the given GP is given by aₙ = 5×4ⁿ/2

In the AP, nth term will be multiplied to 125000 and the product will be subtracted from 124990, and GP nth term will increase by product of 2.5 and 4ⁿ,

Hence, the nth term in the given AP is given by aₙ = 125000n - 124990 and the nth term in the given GP is given by aₙ = 5×4ⁿ/2

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