The diameter of the base of a water bottle is 3 1/2 inches. What is the length on inches of the diameter of 6 of these water bottles?

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]

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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The time taken to finish the race is 3.49 hours

Speed is defined as. The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

Given,

The total distance = 500 miles

The speed = 143.187 mph

We know, Speed = Distance / Time

Time = Distance / Speed

Substitute the values

Time = [tex]\frac{500}{143.187}=3.49[/tex] hours

Hence, the time taken to finish the race is 3.49 hours

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The required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978

Explain the divisibility test of 11.

For a number to be divisible by 11, the difference between the sum of its odd digits (1st, 3rd, 5th...) and the sum of its even digits (2nd, 4th...) must be divisible by 11.

Calculation for the positive five-digit integer of the form ab,cba to be divisible by 11

Required 5 digit number is of the form, ab,cba

Using the divisibility test of 11, we get

(b + b) - (a + c + a) to be divisible by 11

i.e. 2b - (2a + c) to be divisible by 11

Replacing ab,cba using the greatest numbers, such as 7, 8 and 9 and checking its divisibility with 11

78,987 = 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO

87,978 = 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES

79,897 = 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO

97,879 = 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO

89,798 = 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO

98,789 = 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO

Thus, a positive 5-digit number is 87,978

Hence, the required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978

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Answer:

x = 16

Step-by-step explanation:

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: 24c

Step-by-step explanation:

c = cost

6x4=24

24 times the amount it costs per hour c

24c

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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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!

Please mark as brainliest if correct!

Answer:

The Correct answer is 21.78 meters

Step-by-step explanation:

Simply divide 326.7 ÷ 15 and it will leave you with 21.78

A scatter plot is also referred to as scatter chart, scatter diagram or scattergram and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.

A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the polynomial function is given by:

y = -0.4908x² + 5.8845x + 1.3572

For the number of students that are absent 10 days after the outbreak, we have:

y = -0.4908(10)² + 5.8845(10) + 1.3572

y = -0.4908(100) + 58.845 + 1.3572

y = -49.08 + 58.845 + 1.3572

y = 11.12 ≈ 11 students.

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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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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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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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Answer: c

Step-by-step explanation: it is a rational number because it repeats

Answer:

B: All real numbers

Step-by-step explanation:

Check the attached image for explanation.

Answer:

Step-by-step explanation

Mikhail is 37

Gabrielle is 30

37+30= 67

The area of the frame is D. 252 in².

It should be noted that the frame 2 inches wide surrounds a painting that is 18 inches wide and 14 inches tall.

The area will be:

= Length × Width

= 18 × 14

= 252 in²

The area is 252 inches².

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Answer:

2.1

Step-by-step explanation:

A function that has been transformed by the given transformations is y = -f(x - 3) + 2

The transformation are given as:

Let the equation of the parent function be

y = f(x)

So, we have the following transformations

Shifted right 3 units

The transformation rule is

(x, y) = (x - 3, y)

So, we have:

y = f(x - 3)

Shifted up 2 units

The transformation rule is

(x, y) = (x, y + 2)

So, we have:

y = f(x - 3) + 2

Reflected about the x-axis

The transformation rule is

(x, y) = (x, -y)

So, we have:

y = -f(x - 3) + 2

Hence, a function that has been transformed by the given transformations is y = -f(x - 3) + 2

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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: 6[tex]a^{2}[/tex]+a-12

Step-by-step explanation:

First, you want to distribute (2a+3)(3a-4) ---> 2a(3a-4) + 3a(3a-4)

That will get you 6[tex]a^{2}[/tex]-8a+9a-12

Next, you will want to combine like terms to get 6[tex]a^{2}[/tex]+a-12

Since you cannot simplify that any further, 6[tex]a^{2}[/tex]+a-12 is your answer.

(Refer to the table given below)

So,

Then,

Therefore,

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Answer:

Step-by-step explanation:

5 x 2 = 10

Pretty sure this is right but I'm not 100 percent sure!

Answer: 10P ==> A

Step-by-step explanation:

5 · P · 2= 5 · 2 · P      ==> Commutative property of multiplication

5 · 2 · P=

10 · P=10P ==> A

Answer: BC=14

Subtract AC by AB. Just learned this in Geomatry.

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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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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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.