Based on the graph above, estimate to one decimal place the average rate of change from

Answer:

The origin is the point (0,0)

(2,-2)  Start at the origin and move 2 unit right along the x axis, from there move down 2 units.  Place a point at that location.

(-2, 1.5) Start at the origin and move 2 units left along the x axis, from there move up 1.5 space and place a point.

(-1, 2/4)  Start at the origin and move left 1 unit along the x axis, from there move up 1/2 a unit and place a point.  2/4 is the same as 1/2

Step-by-step explanation:

Population: The customers of Jerry's Barbershop. Time is taken to cut hair: Minutes. Amount of money spent: Currency (e.g. dollars).

Stage of life: Categorical (Child, Teen, or Adult)

A population is a discrete group of people, animals, or things that can be recognized by at least one common trait for the purposes of data collection and analysis in statistics and other fields of mathematics.

As per the given information, the required solution would be as:

Population: The customers of Jerry's Barbershop.

Variables and their units are, as follows:

Time taken to cut hair: Minutes

Amount of money spent: Currency (e.g. dollars)

Stage of life: Categorical (Child, Teen, or Adult)

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The function that has the average rate of change of -4 over the  interval [-2, 2] is (D) p(x).

What is the Average Rate of Change?

Here, average rate of change of the function must be calculated over the interval [-2, 2].

(A) The average rate of change of the function m(x):

Here, a = -2, m(a) = -12, and b = 2, m(b) = 4

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{m(b)-m(a)}{b-a}\\\implies A(x)=\frac{4-(-12)}{2-(-2)} \\\implies A(x)=4[/tex]

(B) The average rate of change of the function q(x):

Here, a = -2, q(a) = -4, and b = 2, q(b) = -12

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{q(b)-q(a)}{b-a}\\\implies A(x)=\frac{-12-(-4)}{2-(-2)} \\\implies A(x)=-2[/tex]

(C) The average rate of change of the function n(x):

Here, a = -2, n(a) = -6, and b = 2, n(b) = 6

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{n(b)-n(a)}{b-a}\\\implies A(x)=\frac{6-(-6)}{2-(-2)} \\\implies A(x)=3[/tex]

(D) The average rate of change of the function p(x):

Here, a = -2, p(a) = 12, and b = 2, p(b) = -4

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{m(b)-m(a)}{b-a}\\\implies A(x)=\frac{-4-12}{2-(-2)} \\\implies A(x)=-4[/tex]

Therefore, the function that has the average rate of change of -4 over the  interval [-2, 2] is (D) p(x).

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The distance Derick walked from 12 pm to 4.45 pm is 16.625 miles

The distance is solved form the concept of speed which is defined as the ratio of distance with time

The formula for speed is

= distance covered / time taken

The time taken in the journey is

= from 12 pm to 4:45 pm = 4 hours 45 minutes = 4.75 hours

distance covered

= speed * time consumed

= 3.5 mph * 4.75 hours

= 16.625 miles

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Answer:

B

Step-by-step explanation:

All that they were asking for is what is given to you, so B would be right

1. KEA's brand image is centered around affordability, simplicity, and modern design.

2. IKEA has a strong commitment to sustainability, with initiatives that include reducing waste, using sustainable materials in its products, and investing in renewable energy.

3. Sustainability is an increasingly important issue for consumers, and many businesses use it as a marketing tactic to appeal to environmentally-conscious consumers. l IKEA is one such company, and its commitment to sustainability is reflected in its long-term goals and initiatives, as well as its focus on sustainable product design and operations.

The company's "Democratic Design" philosophy reflects this, emphasizing the importance of quality, sustainability, and affordability in its products.

The company has set ambitious goals to become more environmentally friendly, such as producing as much renewable energy as it consumes by 2020 and becoming climate positive (i.e., reducing its net greenhouse gas emissions) by 2030.

In recent years, Gen Z has been a major driving force behind holding retailers accountable for their environmental impact, and IKEA has responded to this by continuing to focus on sustainability and transparency in its operations.

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The mean of the number of hours of sleep for this sample is 7.4, the standard deviation is 1.759186 and the variance is. 3.0947.

Standard deviation, denoted by the symbol σ, describes the square root of the mean of the squares of all the values of a series derived from the arithmetic mean which is also called the root-mean-square deviation. 0 is the smallest value of standard deviation since it cannot be negative. When the elements in a series are more isolated from the mean, then the standard deviation is also large

Mean [tex]& =\frac{\text { Sum of all data }}{\text { Total number data }} \\[/tex]

[tex]& =\frac{6+5+10+5+6+9+9+5+9+5+8+7+8+6+9+8+9+6+10+8}{20} \\& =\frac{148}{20} \\\end{aligned}$$[/tex]

= 7.4

Thus, the mean of the number of hours of sleep for the above sample is 7.4.

To find: the variance and standard deviation for the above sample.

Standard Deviation=[tex]\sqrt{\frac{\sum f_i\left(x_i-\mu\right)^2}{n-1}} \\[/tex]

[tex]& \sigma \quad=\sqrt{\left\{\begin{array}{l}(6-7.4)^2+(5-7.4)^2+(10-7.4)^2+(5-7.4)^2+(6-7.4)^2 \\+(9-7.4)^2+(9-7.4)^2+(5-7.4)^2+(9-7.4)^2+(5-7.4)^2 \\+(8-7.4)^2+(7-7.4)^2+(8-7.4)^2+(6-7.4)^2+(9-7.4)^2 \\+(8-7.4)^2+(9-7.4)^2+(6-7.4)^2+(10-7.4)^2+(8-7.4)^2\end{array}\right\}} \[/tex]

[tex]& \sigma=\sqrt{\frac{\left\{4(6-7.4)^2+4(5-7.4)^2+2(10-7.4)^2+5(9-7.4)^2+4(8-7.4)^2+(7-7.4)^2\right\}}{19}} \\& \sigma=\sqrt{\frac{\left\{4(-1.4)^2+4(-2.4)^2+2(2.6)^2+5(1.6)^2+4(0.6)^2+(-0.4)^2\right\}}{19}} \\& \sigma=\sqrt{\frac{58.8}{19}} \\& \sigma=\sqrt{3.0947} \\[/tex]

[tex]& \sigma \quad=1.759186 \\[/tex]

Variance = 3.0947

Therefore, the mean of the number of hours of sleep for this sample is 7.4, the standard deviation is 1.759186 and the variance is. 3.0947.

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Answer:

12 feet

Step-by-step explanation:

This example can be solved using a proportion. The ratio between the height of the girl and her shadow is equal to the ratio of the height of the tree and its shadow.

Ratio of girl height to shadow length: [tex]\frac{3}{7}[/tex]

Ratio of the tree height and its shadow: [tex]\frac{x}{28}[/tex]

The proportion can be written: [tex]\frac{3}{7}=\frac{x}{28}[/tex]

The relationship between the denominators happens to be obvious, so this can be solved easily. 7 times 4 is 28, and since the ratios are equal, 3 times 4 must be X.

[tex]3\times4=12\\x=12[/tex]

The tree is 12 feet tall!

The simplified form of the expression (x² + 7x) / (9 - x²) is x(x + 7) / ( 3 + x )( 3 - x ).

Given the expression in the question;

(x² + 7x) / (9 - x²)

To simplify, first factor out x form x² + 7x

(x × x + 7 × x) / (9 - x²)

Factor out x

x (x + 7) / (9 - x²)

Next, simplify the denominator

x (x + 7) / (9 - x²)

Rewrite 9 as 3²

x (x + 7) / (3² - x²)

Now, since both terms are perfect squares

a² - b² = (a + b)(a - b)

Hence,

x(x + 7) / ( 3 + x )( 3 - x )

Therefore, the simplified form is x(x + 7) / ( 3 + x )( 3 - x ).

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The first investment is $22500 and second investment is $34000.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Two investments totaling $56,500 produce an annual income of $2480.

let the two investments be x and y.

So, x + y = 56500.........(1)

and, One investment yields 8 % per year, while the other yields 2 % per year then

0.08x+0.02y=2480.......(2)

Solving equation (1) and (2) we get

0.08(56500-y)+0.02y=2480

4520-0.08y+0.02*y=2480

-0.06y=-2040

y= 34000

and, x=56500-y =22500

Hence, the investments were $22500and $34000.

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Answer:

x = -3 & 3

Step-by-step explanation:

∣5xI = 15

divide both sides by 5:

(∣5xI)/5 = 15/5

∣xI = 3

I-3I = 3 AND I3I = 3

so:

x = -3 & 3

After using the distribution, the value of P(X(1) < 20, X(2) > 10) is 0.18.

The distribution of random variables x(1) and X(2) have given below:

We have to determine P(X(1) < 20, X(2) > 10).

We have to determine the joint probability.

From the table we can see that the value of x(1) is less than 20 is (5, 10) and x(2) greater than the (10, 20).

P(X(1) < 20, X(2) > 10) = P(5, 10) + P(10, 20)

From the table

P(X(1) < 20, X(2) > 10) = 0.06 + 0.12

P(X(1) < 20, X(2) > 10) = 0.18

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The complete question is:

Random variables x(1) and X(2) have the following distribution:

Find P(X(1) < 20, X(2) > 10) (write up to second decimal place)

The amount of money that Yolanda invested in the stock is x = $1600

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

To solve this problem we will only formulate two equations:

(a) The sum of the amount to invest in stocks and bonds will be $6000:

x + y = 6000

(b) The percentage of stocks 6% and bonds 11% for a profit of $580.

0.06x + 0.11y = 580

x + y = 6000 ----⇒ x = 6000 - y

0.06(6000 - y) + 0.11y = 580

360 - 0.06y + 0.11y = 580

0.05y = 220

y = $4400

x = 6000 - 4400

x = $1600

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Answer:

The product of (-12 + 4i) and its conjugate is (-12 - 4i).

The conjugate of (-12 + 4i) is (-12 - 4i).

Completing the square is a strategy that is sometimes required to complete a quadratic equation, the steps and provide an example as to how it can be used are:

Writing a quadratic expression so that it contains the perfect square is known as "completing the square" in algebra. In plain English, the act of "completing the square" can be described as taking the quadratic equation "ax2 + bx + c = 0" and changing it to "a(x + p)2 + q = 0."

Example: expression is x2 - 7x.

A = 1; B = -7 when the above expression is compared to ax2 + bx + c.

The term that needs to be added, according to the formula, to convert the given expression into a perfect square trinomial is (b/2a)2 = (-7/2(1))2 = 49/4.

The term that needs to be added to make the given expression a perfect square trinomial, then, from both approaches, is 49/4.

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The inequalities are :

x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27

|x - 6| ≥ 2  ⇒x- 6 ≥ 2 and 6 - x ≤ 2

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two integers on a number line.

The occurrence of an unfair and/or uneven distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different individuals and in various settings, the word "inequality" may indicate different things.

Inequality is a connection between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

The inequalities are :

x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27

|x - 6| ≥ 2  ⇒x- 6 ≥ 2 and 6 - x ≤ 2

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To make a tree diagram, start by writing out the given information and drawing a box around it. Then draw two branches off of the box representing the two possible outcomes of selecting a student, male or female. Then draw two more branches off of each of the first two branches, representing the two possible outcomes of receiving aid.

Then draw two more branches off of each of the second two branches, representing the two possible outcomes of receiving federal aid. This will create a tree diagram that looks like this (see the image).

From the tree diagram, we can calculate the probability of selecting a student from the given information as follows:

P(selecting a student) = P(selecting a male) + P(selecting a female) = (of male students/total students) + (of female students/total students) = (of male students + of female students)/total students =

Therefore, the probability of selecting a student from the given information is .

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The stem-and-leaf plot of the given data is attached.

A stem-and-leaf plot refers to a device used to present quantitative data in a graphical format to help in visualizing the shape of a distribution. It is a table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

From the given options, the statements that describe the percentages distributed, distribution skewness and whether there are any gaps are:

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The distance between the cities on the map is given by the equations

a) The distance of 50km = ( 1/3 ) cm

b) The distance of 280km = ( 1 13/15 ) cm

c) The distance of 142 1/2 km = ( 19/20 ) cm

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the distance on the map be represented as A

Now , the equation will be

The scale on the map is given by 1/2 cm = 75 km

So , 1 km = ( 1/2 ) / 75 cm

1 km = ( 1/150 ) cm

a)

when the distance = 50 km

The distance on the map = 50 x ( 1/150 ) cm

The distance on the map = ( 1/3 ) cm

b)

when the distance = 280 km

The distance on the map = 280 x ( 1/150 ) cm

The distance on the map = ( 1 13/15 ) cm

c)

when the distance = 142 1/2 km

The distance on the map = 142 1/2 x ( 1/150 ) cm

The distance on the map = ( 19/20 ) cm

Hence , the equation is solved

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The average rate of change of the function f(x) on the interval [4,9] is equal to 23.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function f(x) over the interval [4, 9]:

a = 4; f(a) = 97

b = 9; f(b) = 212

Substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (212 - 97)/(9 - 4)

Average rate of change = 115/5

Average rate of change = 23.

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Answer:

B. the area is d x pi its the solution

Answer:

Chair: $2.50

Table: $8.50

Step-by-step explanation:

First, let's create equations with the information given to us:

x= cost of a chair

y= cost of a table

5x + 3y = $38

2x + 12y = $107

The next step is to solve for x in terms of y. To do this, I will be using the equation 5x + 3y = $38.

5x + 3y = $38   [Subtract 3y from both sides]

5x = -3y + 38   [Divide by 5]

x =(-3/5)y + 38/5

Now that we have found the value of x in terms of y, we will plug it into the equation 2x + 12y = $107.

2x + 12y = $107

2 ((-3/5)y + 38/5) + 12y = 107   [Distribute]

(-6/5)y + 76/5 + 12y = 107   [Combine like terms]

(54/5)y + 76/5 = 107   [Subtract 76/5 from both sides]

(54/5)y = 459/5   [Multiply both sides by 5/54]

y = 17/2 or 8.5

So, the cost of a table is $8.50.

Now that we have found the price of the table, let's plug it into the equation  5x + 3y = $38 to find the price of the chair.

5x + 3y = $38

5x + 3 ( 17/2 ) = 38   [Distribute]

5x + 51/2 = 38   [Subtract 51/2 from both sides]

5x = 25/2   [Divide both sides by 5]

x = 5/2 or 2.5

So, the cost of a chair is $2.50.

So, the chair costs $2.50 while the table costs $8.50.

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Answer:To convert this to miles per hour, we need to first convert the distance to miles. We know that 1 mi = 5280 ft, so 98 ft = 98 / 5280 mi = 0.0184 mi.

Now we can use the formula speed = distance / time again, but this time using miles and hours as the units. So, speed = 0.0184 mi / (11.5 s / 3600 s/hr) = 0.0184 mi / 0.003194 hr = 5.8 mi/hr.

Step-by-step explanation:

Answer:

5.81 mph

Step-by-step explanation:

We want to first convert the number of feet to miles and then divide by the number of hours. Since we know that 5280 feet is one mile, we essentially want to find how many "groups" of 5280 are in some distance and that's the number of miles. We can do this by dividing.

[tex]\frac{98}{5280}\approx0.018561[/tex]

Now we want to find how many hours 11.5 seconds is. It's basically the same process as we divide this by the number of seconds in an hour 3600.

11.5/3600 = 0.00319

Now divide the distance over the time and this gives us approximately: 5.81 mph

The domain of the table below is {-3, 6, 12}

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

The table of values

The domain of a function is the set of the input values

This means that the domain is

Domain =  {-3, 6, 12}

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The smaller of the triangle’s two acute angles is 65 degrees

Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.

Given:

Angles in a triangle

[tex]sin (4x-5)^\circ= cos (3x+4)^\cir[/tex]

Since, sin [tex]\theta[/tex]= cos(90 - [tex]\theta[/tex]),

cos(90 - (4x - 5 )) = cos(3x +4)

cos(85 - 4x) = cos (3x+4)

Cancel out the cosine functions to have:

85- 4x = 3x+ 4

81 = 7x

x= 11.57

Hence, the smaller of two acute angles is 11.57 degrees

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Answer:

27

Step-by-step explanation:

Answer:

x < -2 or x > 5

Step-by-step explanation:

We want to write the compound inequality.

There is an open circle at -2 and a line going to the left.

x < -2

There is an open circle at 5 and a line going to the right.

x > 5

We use an or since they are not connected.

x < -2 or x > 5

97.75 - 85 = 12.75

This means the amount of tax was $12.75.

If we divide the amount of tax by the original price of the shirt, it gives us the percent of the tax:

      12.75 ÷ 85 = 0.15 = 15%

Sales tax is 15%.

The key in the calculation is to divide by the original price of the shirt.

For the hours is she going to do studying per day is 10 hours.

The Lagrangian method is a mathematical technique used to find the maximum or minimum value of a function subject to constraints. It is used in optimization problems where the objective is to maximize or minimize a function, but there are some constraints that limit the possible values of the inputs.

The Lagrangian method works by combining the objective function and the constraints into a single function, called the Lagrangian, which is then optimized. The Lagrangian is defined as the original objective function minus the product of the constraints and a set of Lagrange multipliers, which represent the trade-off between the objective and the constraints.

To maximize Julie's utility subject to the constraint of 15 hours of waking time, we need to find the optimal level of s (study time) that satisfies the constraint and maximizes the utility function.

We can start by using the Lagrangian method to find the optimal solution. The Lagrangian is given by:

L(s,λ) = S^(1/3)I^(2/3) + λ(15 - s - I)

Where λ is the Lagrange multiplier, representing the marginal rate of substitution between s and I. To find the optimal solution, we need to find the values of s and λ that satisfy the first-order conditions:

∂L/∂s = (1/3)S^(-2/3)I^(2/3) - λ = 0

∂L/∂λ = 15 - s - I = 0

Solving the first-order conditions for s and λ, we get:

s = (15 * (2/3)) / (1 + (2/3)) = 10 hours

I = 15 - s = 5 hours

So, Julie will spend 10 hours per day studying.

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