Marshall pours 1/2 gallon of lemonade into 8 glasses. He pours the same amount of lemonade into each glass. How much lemonade, in gallons, does Marshall pour into each glass?

Based on the explanation that is provided below, Holly's conclusion is based on inductive reasoning.

Inductive reasoning can be described as reasoning whose conclusion is based on a pattern of observations.

On the other hand, deductive reasoning refers to reasoning whose conclusion is based on a fact.

As Holly notices that every Saturday, her neighbor mows his lawn, this shows a pattern of observations.

This, therefore, implies that Holly's conclusion is based on inductive reasoning.

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Solve for [tex]z=f(x,y)[/tex] in the plane equation.

[tex]4x + 5y + z = 7 \implies f(x,y) = z = 7 - 4x - 5y[/tex]

Let [tex]E[/tex] be the set of points in the plane [tex]z=0[/tex] bounded by the ellipse [tex]\frac{x^2}{25}+\frac{y^2}{100}=1[/tex], i.e.

[tex]E = \left\{(x,y) ~:~ \dfrac{x^2}{25} + \dfrac{y^2}{100} \le 1\right\}[/tex]

Then the area of the plane bounded by the elliptic cylinder is

[tex]\displaystyle \iint_E dA = \iint_E \sqrt{1 + \left(\dfrac{\partial f}{\partial x}\right)^2 + \left(\frac{\partial f}{\partial y}\right)^2} \, dx \, dy \\\\ ~~~~~~~~ = \iint_E \sqrt{1 + (-4)^2 + (-5)^2} \, dx\, dy \\\\ ~~~~~~~~ = \sqrt{42} \iint_E dx \, dy[/tex]

which is simply √42 times the area of the ellipse in the plane [tex]z=0[/tex]. This ellipse has a minor axis of length 5 and a major axis of length 10, so its area is π•5•10 = 50π, and so the area of the plane in question is 50√42 π.

To confirm this result: In polar coordinates, with

[tex]\begin{cases}x(r,\theta) = 5r\cos(\theta) \\ y(r,\theta) = 10r\sin(\theta) \\ \frac{x^2}{25}+\frac{y^2}{100}=r^2\end{cases}[/tex]

the area element is

[tex]dA = \begin{vmatrix}\frac{\partial x}{\partial r}&\frac{\partial x}{\partial\theta} \\ \frac{\partial y}{\partial r} & \frac{\partial x}{\partial\theta}\end{vmatrix} \, dr \, d\theta \\\\ ~~~~~~~~ = \begin{vmatrix}5\cos(\theta)&-5r\sin(\theta)\\10\sin(\theta)&10r\cos(\theta)\end{vmatrix} \, dr \, d\theta \\\\ ~~~~~~~~ = \left(50r\cos^2(\theta)+50r\sin^2(\theta)\right)\,dr\,d\theta \\\\ ~~~~~~~~ = 50r \, dr \, d\theta[/tex]

The ellipse can be parameterized by

[tex]E = \left\{(r,\theta) ~:~ 0\le\theta\le2\pi \text{ and } 0\le r\le1\right\}[/tex]

so that the integral for the area of the ellipse in the plane [tex]z=0[/tex] is

[tex]\displaystyle \iint_E dA = \int_0^{2\pi} \int_0^1 50r \, dr \, d\theta \\\\ ~~~~~~~~ = 100\pi \int_0^1 r \, dr \\\\ ~~~~~~~~ = 100\pi\left(\frac12-0\right) = 50\pi[/tex]

By evaluating in x = 8 we can see that the value of g(8) is 45.

Here we have the function:

g(x) = (1/3)*(2x - 1)^2

We want to get the value of g(8), this means that we need to evaluate the function in x = 8.

To do this, we just need to replace the variable "x" in the equation by the number 8.

We will get:

g(8) = (1/3)*(2*8 - 1)^2 = (1/3)*(15)^2 = 3*15 = 45

g(8) = 45

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Answer:

Y-intercept is -1

Step-by-step explanation:

Slope-intercept form:

y=mx+b

b=y-intercept

m=slope

y=3x-1

b=-1

Hope this helps!

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She makes 12 earrings and 8 bracelets of each type of jewelry. (option 3 is correct.)

Jenny sells earrings and bracelets on Etsy

The cost of a pair of earrings = $5

The cost of bracelets = $12.

If Jenny made 20 pieces on Saturday for the cost of $156.

Each type of jewelry made by Jenny is

Let she made X pair of earrings

Y  number of bracelet

Then the linear equation will be

$5X +$12Y = $156

by using the given values in option we get the answer

X = 12

Y = 8

She makes 12 earrings and 8 bracelets of each type of jewelry. (option 3 is correct.)

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Answer:

Your initial inequality should be 5x < 30

Step-by-step explanation:

I saw it on a answer similar to yours but it said "have at least 10$ of your money left"

The percentage of Americans over the age of 65 has increased while the percentage of Americans under the age of 18 has decreased .

The United Stats of America is one of the countries that is known to have a very good health care system. This implies that, there has ben a very huge improvement in the health care of the population of the United States.

As a result of this improvement in the healthcare of the people of the United States, the percentage of Americans over the age of 65 has increased while the percentage of Americans under the age of 18 has decreased .

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According to the given statement the weight of each tire in pounds:

For 800 grams = 1.76 pounds.

For 700 grams = 1.54 pounds.

For dry substances, it's crucial to convert to weight. While most recipes

meant for home chefs express the components by volume, most recipes in industrial kitchens express essential ingredients by weight.

A conversion factor is indeed a number that is used to multiply or divide one set of units into another. If a conversion is necessary, it must be carried out with the right conversion factor to produce a value that is identical. That example in the case, when translating between inches and feet, 12 inches equals one foot.

800 grams must be converted to pounds.

(1 pound =453.592 x= 800)

800 must be divided by 453.592 to get the number 1.763699. To round it up: 1.76

We now repeat this for 700.

1,5432 when 700 is divided by 453.592. Rounding that down, we get: 1.54

The given statement the weight of each tire in pounds:

For 800 grams = 1.76 pounds.

For 700 grams = 1.54 pounds

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Answer:

O Scatterplot C

Step-by-step explanation:

Sales Revenue

(Millions of $)

1.5

4

6

8

10

11

Customer Satisfaction

(Scale: 1-100)

78

75

62

50

35

15

Examine the scatterplots provided in this graphic.

Which one correctly displays these data?

The simple interest rate on the account is 13%

Here Sunil deposited $400 for one and a half years, and the interest he gets is $78. He deposits in at the simple rate of interest.

We know that the simple interest formula is

     Simple interest = Principle × time × rate/ 100

It is given that,

            simple interest = $78

            time = 1 [tex]\frac{1}{2}[/tex] year = 3/2 year

            Principle = $400

Let the rate of interest be r

So we have

     78 =( 400 × 3/2 × r )/100

     r =( 78 × 2×100) / (400 × 3)

     r = 39%

Therefore the simple interest rate on the account is 13%.

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Answer:

something

Step-by-step explanation:

something

The equation of the line is x - 3y = 12 which is parallel to the line x - 3y = 3 and passes through (-3, -5).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The equation of the line is:

x - 3y = 3

Parallel to the above line:

x - 3y = c

Plug x = -3 and y = -5

-3 + 15 = c

c = 12

x - 3y = 12

Thus, the equation of the line is x - 3y = 12 which is parallel to the line x - 3y = 3 and passes through (-3, -5).

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Answer:

24

Step-by-step explanation:

4 x 6 = 24

The three consecutive numbers are 58, 59 and 60.

Consecutive numbers are the numbers that follow each other continuously in a sequence from smallest number to largest number.

Let the first number = x

Let the second number = y

And Let the third number = z

As given in the question that the sum of the first and third number is 118, So we can write mathematically as

x + z = 118

The first and third numbers  are 58 and 60 and their sum is 118.

The second number automatically will be 59.

So, the three consecutive numbers are 58, 59 and 60.

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We get the value of f ( - 1 ) as - 5 for the function f (x) = x + 4 x³.

We are given a function:

f (x) = x + 4 x³

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

We need to find the value of f ( - 1 )

We will do this by substituting the value of x as - 1

Put x = -1, we get that:

f ( x = -1 ) = ( - 1 ) + 4 ( - 1 )³

f ( - 1 ) = - 1  + 4 ( - 1 )

f ( - 1 ) = - 1 - 4

Simplifying the function:

f ( - 1 ) = - 5

Therefore, we get the value of f ( - 1 ) as - 5 for the function f (x) = x + 4 x³.

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Existence and value - Are the accounts for the AR really there, and can they be collected.

Money owed to a business in the near future is represented by the asset account known as accounts receivable on the balance sheet. When a business permits a customer to pay for its products or services on credit, accounts receivable are generated. Similar to accounts receivable, accounts payable tracks money that is due as opposed to money that will be collected. The ratio of accounts receivable to sales outstanding or days sales outstanding can be used to determine how strong an organization's AR is. To determine when the AR will really be received, a turnover ratio study might be performed.

Existence is an audit affirmation that the auditor must examine to ensure that all accounts receivable are present.

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Answer:

x = 16

Step-by-step explanation:

Simplify: (-12c⁵) (3c⁴)=36c⁹.

Given that

To find

So, according to the question

We have,

To convert it in simplest form we have to use mathematically operations of powers.

           = (-12c⁵) (3c⁴)

Now, separate the numerical and variable parts from equation

           = (-12 ×3) c⁵× c⁴

Now, from using the mathematically operations of powers, to add powers, and multiply 12 with 3.

∵ [tex]a^m\times a^n = a^{m+n}[/tex]

∴[tex]c^5\times c^4 = c^{5+4}[/tex]

           = (-36) c⁵⁺⁴

          = (-36) c⁹

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Answer: 24c

Step-by-step explanation:

c = cost

6x4=24

24 times the amount it costs per hour c

24c

Answer:

The intercept is - 1.

Hope this helps :)

Step-by-step explanation:

In the function y = - x - 1 the initial value which is the y-intercept is - 1, and the line intercepted at -1 on the y-axis. Also, the line on the graph also intercepted at - 1 on the x-axis too. So the interceptes is - 1.

A = { 0,6,7} is the complement of the set given.

What is the set in math?

What is sets and its types?

Given  U = { 0,1 , 2 , 3, 4,5,6,7 }

Let set  A  = { x/x < 6  and  x ∈ NI}

   A = { 1,2,3 ,4,5}

∴ AC = Complement of A = { 0,6,7}

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Answer:

2,689

Step-by-step explanation:

you got the first two right it's the last that is wrong

you need to do 2,407-(-282) the two negative make it a positive so add them together and you get 2,689.

The least to greatest will  [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 ) .

( - 1 ) ^ 5 , 3 ^ ( - 6 ) , 3 ^ 6 , 5 ^ 1 , 10 ^ 0 , 0.1

Simplifying each of them

( - 1 )  ^ 5 = - 1

3 ^ ( - 6 ) = 0.001

3 ^ 6 = 729

5 ^ 1 = 5

10 ^ 0 = 1

0.1   = 0.1

Least to greatest = - 1 < 0.001 < 0.1 < 1 < 5 < 729

                            = [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 )

Hence , least to greatest will  [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 ) .

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There are 5 11 pointer questions and 15 3 pointer questions

We are given that total points of the test is 100

The test contains questions of two markings 3 points and 11 points

It is given that the total number of questions is 20

Let the number of three pointer questions be 'x' and the number of 11 pointer questions be 'y'

Thus total number of questions=x + y =20

Now the total sum of all the points comes to 100

Therefore,

3x+11y =100

x + y =20

x= 20-y

Now putting the value of x in the other question,

3(20-y) +11y =100

60-3y +11y=100

8y=100-60

8y=40

y=5

Thus x=20-y=20-5=15

Thus there are 5 11 pointer questions and 15 3 pointer questions

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Thus, the equation of the line of reflection,

x=2 and x=4

When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula.

It is given that,

A=(7,6)

A'=(-1,6),

B=(5,5)

and B'=(1,5),

As, the mid point of vertices of figure to the corresponding vertices of  reflected figure should lie on reflected line.

Since, Δ ABC is reflected to Δ A'B'C' through this line,

Let, Q be the mid point of  line AA', using section formula

Coordinate of Q = ((7-(-1))/2 , (6-6)/2 )

                       Q = (4,0)

and R be the mid point of line BB', using section formula

Coordinate of R = Q = ((5-1)/2 , (5-5)/2 )

                       Q = (2,0)

Q and R lies on the line of the reflection,

Thus, the equation of the line of reflection,

x=2 and x=4

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The inequalities are matched with their correct graph respectively as follows:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

In Geometry, if the leading coefficient of a quadratic equation is greater than (>) zero, the parabolic curve would open upward while the parabolic curve would open downward when the leading coefficient of a quadratic equation is less than (<) zero.

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Complete Question:

Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)

1. A = {(x, y): y > x^2}

2. B = {(x, y): y ≥ x^2+ 3}

3. C = {(x, y): y ≤ 3x^2 + 2}

4. D = {(x, y): y ≥ 2x^2- 5x + 1}

6. x^2- 3x ≥ 0

7. x^2- 3x + 2 ≤ 0

8. {(x, y): y ≤ 1 - x^2}

9. {(x, y): y ≥ -1}

Answer:

the answer is simple you just p times a

and d

Step-by-step explanation:

:]

Answer:

hope this help you

Step-by-step explanation:

p times x and d

Answer:

(4r - 3)(r + 1)(r - 1)

Step-by-step explanation:

In order to factor the polynomial [tex]\sf 4r^3 - 3r^2 - 4r + 3[/tex], we can use various factoring methods.
In this case, we can use grouping.

Let's break down the expression and factor it step by step:

Group the terms in pairs:

(4r^3 - 3r^2) +(-4r + 3)

Factor out the greatest common factor from each group:

[tex]\sf r^2(4r - 3) - 1(4r - 3)[/tex]

Notice that both groups have a common factor of (4r - 3): and keeping remaining in bracket

[tex]\sf (4r -3)(r^2-1)[/tex]

Now, the expression r² - 1 can be factored further using the difference of squares:

(r + 1)(r - 1)

So, the fully factored form of the polynomial 4r³ - 3r² - 4r + 3 is:

(4r - 3)(r + 1)(r - 1)

The values of a and b are:

a = 5 + √7

b = 5 - √7

Given data

x2 − 10x + 26 = 8

Transform the equation to standard quadratic equation by equating to zero

x2 − 10x + 26 = 8

x2 − 10x + 26 - 8 = 0

x2 − 10x + 18 = 0

x2 − 10x + 18 + 5^2 - 5^2 = 0

x2 − 10x + 25 = 25 - 18

(x-5) (x-5) = 7

(x-5)^2 = 7

(x-5) = √7

x = 5 + √7

x = 5 - √7

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