The demand function for a certain make of replacement cartridges for a water purifier is given by the equation p=−0. 01x2−0. 1x+21 where p is the unit price in dollars and xis the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the market price is set at $9/cartridge. (Round your answer to two decimal places. )

The given equation x/4 - y = -2(x/y) can be expressed in a verbal sentence as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.

How to express the mathematical equation in the form of a verbal sentence?    

To express the mathematical equation in the form of a verbal sentence, we have to express the operations by using sentences.

Let's take an example,

                   x + y = 4.

Then the verbal form will be the sum of two numbers is 4.

Hence, the given expression can be expressed as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.

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Answer:

Step-by-step explanation:

COP = Constant of Proportionality. • y varies directly to x. > If 10 miles varies directly to 5 minutes,. – then 10 = y and 5 = x. • Unit Rate (1, r). > (x, y).

The absolute equation in the graph is f(x) = |x - 3| + 5

From the question, we can see that the lines on the graph has a sharp v-shape

Graphs that have this form are absolute value graphs

The general form of an absolute value equation is expressed as

y = |x - h| + k

From the above form, we have

Vertex = (h, k)

By definition, the vertex of a function is either the maximum point or the minimum point

On the given graph, the minimum point is (3, 5)

So, we have the following representation

(h, k) = (3, 5)

Substitute (h, k) = (3, 5) in the above equation

So, we have:

y = |x - 3| + 5

Hence, the function represented by the graph has an equation of f(x) = |x - 3| + 5

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The complete statement will be;

⇒ angle R + angle A + angle T = 180°

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle RAT is shown in figure.

Now,

We know that;

The sum of all interior angles in a triangle is 180 degree.

Hence, In ΔRAT;

⇒ ∠R + ∠A + ∠T = 180°

Thus, The complete statement will be;

⇒ angle R + angle A + angle T = 180°

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The probability of not spinning a 3 is 8/9

From the question, the given parameters are:

Number of sections = 9

Sections = Number 1 to 9

The probability of spinning a 3 = 1/9

The above probability can be represented as

P(3) = 1/3

The probability that the number 3 is not spun is the complement of the  probability of spinning a 3

This is calculated as

P(3) + P(Not 3) = 1

Substitute the known values in the above equation So, we have the following equation

1/9 + P(Not 3) = 1

Evaluate the like terms

P(not 3) = 8/9

Hence, the probability is 8/9

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A yield sign measures 24 inches on each of its three sides ( equilateral )then the area of the sign is 249.4

Given,

24 inches on each of its three side. (See in attached picture)

Consider ADB,

As it is an equilateral triangle, BD = BC/2 = 12 inches

By Pythagoras theorem,

AB^2 = BD^2 + AD^2

24^2 = 12^2 + AD^2

24^2 – 12^2 = AD^2

576-144 = AD^2

432= AD^2

20.78= AD

Area = ½ (base * height)

       = ½ (24*20.78)

       = 249.4

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The actual roots ordered from least to greatest is -45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45

Rational roots are roots of a quadratic equation which can be expressed as a ratio or are elements of rational numbers.

Since we have that the possible rational roots are  ±1, ±3, ±5, ±9, ±15, and ±45.

We list the actual roots as follows

+1, -1, +3, -3, +5, -5, +9, -9, +15, - 15, +45 and -45

Since we require the actual roots from least to greatest knowing that the largest negative number is the least and tha largest positive number is the greatest, rearranging, we have

-45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45

So, the actual roots are -45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45

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The percentage of the profit gain by karen on a pack of 8 bottles  is 220%.

Karen buys a pack of bottles of water. = 8

Karen sells all 8 bottles of water for rupees =  50p each

=  50p/100 each

= 0.5 rupees

Total rupees for 8 bottles = 8 x 0.5 = 4

The pack costs  = 1.25

Profit % = (Profit / C.P.) × 100

Profit = SP - CP

=  4 - 1.25

= 2.75

then using these values in equation we get :

profit = [tex]\frac{4 - 1.25}{1.25} * 100[/tex]

profit = (2.75/1.25 )x 100

profit = 2.2 x 100 = 220

profit = 220%

The percentage of the profit gain by karen on a pack of 8 bottles  is 220%.

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In regards to the question above, the solution for the equation is x=-2(1+2x)/x^2-4.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. Equations come in two varieties: identities and conditional equations.

How to solve this:

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

collecting like terms

2/x^2-4 -1/x+2 -3/x-2=0

Divides through by:

x^2-42 -1(x-2) -3(x+2)/x^2-4=0

Remove bracket: 2-x+2-3x-6/x^2-4

Lastly, collecting like terms:

2+2-6-x-3x/x^2-4-2-4x/x^2-4

=-2(1+2x)/x^2-4

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Answer: f = 12m

Step-by-step explanation:

Starting at mile 5 we notice it's 60. But now at mile 7, we notice its 84. This means that we increase by 12 for each mile. Ergo, the answer should be f = 12m.

Answer:

[tex]6x^{3}t^{3}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{\left(3xt\right)^3}{9x^2t}[/tex]

[tex]\textsf{Apply exponent rule} \quad (ab)^c=a^c \cdot b^c:[/tex]

[tex]\implies \dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{3^3x^3t^3}{9x^2t}[/tex]

[tex]\implies \dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{27x^3t^3}{9x^2t}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{bd}:[/tex]

[tex]\implies \dfrac{2x^3t^327x^3t^3}{xt^29x^2t}[/tex]

Collect like terms:

[tex]\implies \dfrac{2 \cdot 27x^3x^3t^3t^3}{9x^2xt^2t}[/tex]

Multiply the numbers 2 and 27:

[tex]\implies \dfrac{54x^3x^3t^3t^3}{9x^2xt^2t}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \dfrac{54x^{3+3}t^{3+3}}{9x^{2+1}t^{2+1}}[/tex]

[tex]\implies \dfrac{54x^6t^6}{9x^3t^3}[/tex]

Separate like terms:

[tex]\implies \dfrac{54}{9} \cdot \dfrac{x^6}{x^3}\cdot \dfrac{t^6}{t^3}[/tex]

Divide the numbers 54 and 9:

[tex]\implies 6 \cdot \dfrac{x^6}{x^3}\cdot \dfrac{t^6}{t^3}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies 6 \cdot x^{6-3}\cdot t^{6-3}[/tex]

[tex]\implies 6 \cdot x^{3}\cdot t^{3}[/tex]

[tex]\implies 6x^{3}t^{3}[/tex]

17576000 courses can be given unique catalog numbers.

There are three numbers and three English letters.

Each of three numbers can be chosen from 0 to 9, so the ways to choose each number is  = 10

So the total number to choose three numbers = 10*10*10 = 1000

Each of letters can be chosen from A to Z.

Number of choice for the each letter = 26

So, the outcomes of letter combination = 26*26*26 = 17576

Hence the total possible catalog numbers = 1000*17576 = 17576000

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Dimensions of the area enclosed is l = 800 ,b = 800 and the maximum area = 6,40,000 square yards.

Given:

Liana has 3200 yards of fencing to enclose a rectangular area.

Let l and b be the length and breadth.

we know that:

perimeter of rectangle = 2(l+b)

2l + 2b = 3200

l+b = 1600

b = 1600 - l

Area of rectangle A = lb

= l*1600-l

= 1600 l - l^2

Apply derivative:

dA/dl = 1600 - 2l

1600 - 2l = 0

1600 = 2l

l = 1600/2

l = 800

l+b = 1600

b = 1600 - 800

= 800

Area = 800*800

= 6,40,000

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The probability distribution of all possible values of the sample mean is called the sampling distribution of the mean.

What is meant by the sampling distribution of the mean?

Why is sampling essential and what does it mean?

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The value is 350.

From the question, we have

Dan uses the equation g(x)=5x+50 to model the balance of his savings account after saving for x weeks.

g(x)=5x+50

substituting the value x = 60, we get

g(60)=5*60+50

=300+50

=350

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer:

[tex]x^2+3x-10[/tex]

Step-by-step explanation:

To expand you must do this:

[tex]x*x+(-2x)+(5x)-10\\x^2-2x+5x-10\\x^2+3x-10[/tex]

Answer: calculate these equations

Step-by-step explanation: if you have times the square of the expression following b plus b times that same expression not squared plus c equal to 0, you have an equation that is quadratic in form. If we substitute what is in the ( ) with a variable like t, then the original equation will become a quadratic equation.

This is completely Randomized experiment design .

Randomized block design is an experiment design in which the experimental units are categorized into groups, which are called blocks.

In the given question, we see that Estelle's cornfield is divided into 666 regions. She is curious about whether a new pesticide is effective because she uses pesticides and assigns each of the 666 regions at random.Now, the experiment units, i.e., 666, are not split into groups before random assignment. The entire region is randomly assigned to a pesticide. A randomised block design assigns some of each block to different treatment and control groups.

So , this is a completely randomized block design.

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The number of ways voters could rank their first 5 choices out of 10 is 30240.

Given,

Number of students sought the nomination for president of the student body = 10 students

We have to find the number of ways voters could rank their first 5 choices.

Permutation;

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.

Here we have to use permutation formula;-

ⁿPr = n! /  (n - r)!

Here,

n is the number of students = 10

r is the choices = 5

Then,

ⁿPr = n! /  (n - r)!

¹⁰P₅ = 10! / (10 - 5)!

¹⁰P₅ = 10! / 5!

¹⁰P₅ = 10 x 9 x 8 x 7 x 6

¹⁰P₅ = 30240

That is,

The number of ways voters could rank their first 5 choices out of 10 is 30240.

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Answer:

6x - 3

Step-by-step explanation:

3 ( 2x - 1  )

= 3 ( 2x ) - 3 ( 1 )

= 6x - 3

Answer:

x=1/2 or 0.5 or just 6x-3

Step-by-step explanation:

3(2x-1)

distribute.

6x-3

get 6x alone

6x=3

divide

x=3/6

x=1/2 or 0.5

If the p-value is less than or equal to the selected significance level, the null hypothesis is rejected; otherwise, it is not. In other words, if p, reject[tex]H_{0}[/tex]; if p>, do not reject [tex]H_{0}[/tex].

In null hypothesis testing, this criterion, also known as (alpha), is frequently set to 05. If there is less than a 5% chance that the null hypothesis would be accepted and a result as spectacular as the effects that result would occur, the null hypothesis is rejected. When this happens, the result is said to be statistically significant.

The null hypothesis would be rejected if a statistical test was conducted with a threshold of relevance = 0.1, 0.05, & 0.01.

If the P value is smaller than alpha, the preset level of statistical significance, the alternative hypothesis is considered instead of the null hypothesis.

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Answer:

600ml

Step-by-step explanation:

Answer:

Carmen will have her loan paid back in 20 months

The value of the square root of 60 subtracted from 17 is D. 9.3

It's important to note that a square root simply means the number that you can multiply by itself in order to get the original number.

In this case, the information given regarding the numbers is illustrate below:

= 17 - ✓60

= 17 - 7.7

= 9.3

Therefore, the value is.9.3

The correct option is D.

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A) The equation is 22 + (d * 1/2) = 30

B) The plant that still have to grow 8 cm more

C) d = 16 days, d represents the number of days

Step-by-step explanation:

Given:

Initial height (basil plant at buying) = 22cm

Plant grows on everyday = 1/2cm

A) Given:

Total  height (to be grown) = 30 cm.

The equation is,

Initial height+ ( number of days * plant grows on everyday) =  Total height

22 + (d * 1/2) = 30  →  equation 1

B) The plant that still have to grow = Total height - Initial height

= 30 - 22

= 8 cm

C) Solving the value d using equation 1:

22 = 30 - (d * 1/2)

    44 = 60 - d 

      d = 16 days

Hence, A) The equation is 22 + (d * 1/2) = 30.

B) The plant that still have to grow 8 cm more.

C) d = 16 days, d represents the number of days.

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AREA OF A SQUARE= LENGTH* LENGTH

16900= L²

TAKE THE SQUARE ROOTS OF BOTH SIDES

√16900 =√L²

L= 130

THEREFORE THE LENGTH OF THE FIELD IS 130cm.