What’s the slope of 10,6 and 4, 1.2

The definition of the set E gives you a natural choice for the limits in the integral:

[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x \int_{x-y}^{x+y} y \, dz \, dy \, dx[/tex]

Computing the integral, we get

[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x y ((x+y)-(x-y)) \, dy \, dx = 2 \int_0^6 \int_0^x y^2 \, dy \, dx[/tex]

[tex]\displaystyle \iiint_E y \, dV = 2 \int_0^6 \frac13 (x^3 - 0^3) \, dx = \frac23 \int_0^6 x^3 \, dx[/tex]

[tex]\displaystyle \iiint_E y \, dV = \frac23 \cdot \frac14 (6^4 - 0^4) = \boxed{216}[/tex]

The evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216

Triple integral integrates the integrand over three dimensions.

Given that:

E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y}

Evaluating the integral:

[tex]I = \int \int \int _E y \: dV[/tex]

[tex]I = \mathlarger{\int_0^6 (\int_0^x (\int_{x-y}^{x+y} y\: dz)dy)dx}\\\\I = \int_0^6 (\int_0^x [yz]_{z=(x-y)}^{z=(x+y)}dy)dx\\\\I = \int_0^6 (\int_0^x y( (x+y) - (x-y)) \: dy)dx\\\\ I = \int_0^6 (\int_0^x y(2y) \: dy)dx\\\\I =2 \int_0^6 \left [\dfrac{y^3}{3}\right ]_{y=0}^{y=x} dx\\\\I = 2 \int_0^6 (x^3/3) dx\\\\I = \dfrac{2}{3} \left[\dfrac{x^4}{4} \right]_{x=0}^{x=6} = \dfrac{2}{3} \times \dfrac{6^4}{4} =216[/tex]

Thus, the evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216

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Answer:

Mia sold 72 tickets, Jade sold 80 tickets, and Amelia sold 144 tickets.

Step-by-step explanation:

You can solve this question by coming up with equations for each friend and then substituting them into the equation M + J + A = 296

Jade sells 8 more tickets than Mia, so Jade's equation for how many tickets she sold is the amount of tickets that Mia sold + 8:

J = M + 8

Amelia sells twice as many tickets as Mia, so her equation is the amount of tickets Mia sold * 2:

A = 2 * M

Now we can substitute these equations into the overall one.

M + (M + 8) + (2M) = 296

Now we can combine like terms and solve for M.

2M + 8 + 2M = 296

4M + 8 = 296

4M = 288

M = 72

We now have the amount of tickets Mia sold, so we can insert this number into the equations for Amelia and Jade.

J = M + 8

J = 72 + 8

J = 80

A = M * 2

A = 72 * 2

A = 144

So Mia sold 72 tickets, Jade sold 80 tickets, and Amelia sold 144 tickets.

The solution is Mia sold 72 tickets, Jade sold 80 tickets, and Amelia sold 144 tickets

What is Equation?

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 number of tickets sold by Mia , Jade and Amelia be M , J and A respectively

Total number of tickets = 296

So , M + J + A = 296   be equation (1)

Now , Jade sells 8 more tickets then Mia

So , J = M + 8   be equation (2)

Subtracting 8 on both sides , we get

M = J - 8   equation (3)

Now , Amelia sells twice as many tickets as Mia

So , A = 2M   be equation (4)

Substituting the value of J and A in equation (1) , we get

M + ( M + 8 ) + 2 M = 296

4M + 8 = 296

Subtracting 8 from both sides , we get

4M = 288

Divide by 4 on both sides , we get

M = 72

The number of tickets sold by Mia = 72

Substituting the value of M in equation (2) and equation (4) , we get

J = M + 8

J = 80

The number of tickets sold by Jade = 80

A = 2M

A = 144

The number of tickets sold by Amelia = 144

Hence , The number of tickets sold by Mia is 72 tickets, Jade is 80 tickets, and Amelia is 144 tickets

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Answer:

y=-6x

Step-by-step explanation:

Slope intercept form is y=mx+b where b is the y intercept and m is the slope. In this particular example, the y intercept is at (0,0), the origin, so b=0. y=mx+0 or just y=mx. Now, to determine the slope, we must look at the graph. It appears the graph intersects the point (-10, 60) as well as the point (0,0). Other than just calculating it quickly in your head, the way to get slope from that is y1-y2/x1-x2. Setting that up, 60-0/-10-0, which is 60/-10, which is equal to -6. Put that into the equation and you get y=-6x

The total amount of money Kelly earned for the month is $1,736

Given:

Kelly

Worth of goods sold = $21,700

commission = 8%

Total earned = 8% of $21,700

= 8/100 × 21,700

= 0.08 × 21,700

= $1,736

Approximately, $1,736.00

Therefore, the amount of money Kelly earned for this month is $1,736

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Answer:

3/2 is the slope and (0,5) is the y-intercept

Step-by-step explanation:

We need slope-intercept form for this question, so we simplify the equation into:

-2y=-10-3x which is just

y=5+3/2x =

y=3/2x+5

When we compare this to y=mx+b, we see that 3/2 is the slope and (0,5) is the y-intercept.

Answer: The slope is [tex]\frac{3}{2}[/tex] and the y-intercept is 5.

Step-by-step explanation:

The equation is 3x - 2y = -10

We need to turn 3x - 2y = -10 into slope intercept form.

y = mx + b → slope-intercept form

3x - 2y = -10

-3x           -3x

-2y = -3x - 10

Divide the whole equation by -2

y = [tex]\frac{3}{2}[/tex]x + 5

The slope of the equation is [tex]\frac{3}{2}[/tex] and the y-intercept is -2.

Step-by-step explanation:

RV = QV but also = PV = 26

because RVQ and RVP are both isoceles triangles.

TR = QR/2 = 24/2 = 12

because T is the middle point of RQ.

Answer:

4 better inbox

Step-by-step explanation:

Answer:

[tex]\huge\boxed{f(x)=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x}[/tex]

Step-by-step explanation:

[tex]f(x)=a(x+3)(x-0)(x-7)=ax(x+3)(x-7)\\\\=ax\bigg((x)(x)+(x)(-7)+(3)(x)+(3)(-7)\bigg)\\\\=ax(x^2-7x+3x-21)=ax(x^2-4x-21)\\\\=(ax)(x^2)+(ax)(-4x)+(ax)(-21)\\\\=ax^3-4ax^2-21ax\qquad(*)\\\\f(-8)=-5[/tex]

[tex]\text{substitute}\ x=-8\\\\f(-8)=(a)(-8)^3-(4a)(-8)^2-(21)(-8)a=-512a-(4a)(64)+168a\\\\=-512a-256a+168a=-600a\\\\f(-8)=-5\\\\\text{therefore}\\\\-600a=-5\qquad|\text{divide both sides by (-600)}\\\\a=\dfrac{-5}{-600}\\\\a=\dfrac{1}{120}[/tex]

[tex]\text{Substitute to}\ (*):\\\\f(x)=\dfrac{1}{120}x^3-4\cdot\dfrac{1}{120}x^2-21\cdot\dfrac{1}{120}x=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x[/tex]

The distance between (12,5) and (3,4) approximated to the 1 decimal place is 9.1.

To find the distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we will use the distance formula:

Distance = [tex]\(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]

In this case, [tex]\((x_1, y_1) = (12, 5)\)[/tex] and [tex]\((x_2, y_2) = (3, 4)\)[/tex].

Substituting these values:

Distance = [tex]\(\sqrt{(3 - 12)^2 + (4 - 5)^2}\)[/tex]

Distance = [tex]\(\sqrt{(-9)^2 + (-1)^2}\)[/tex]

Distance = [tex]\(\sqrt{81 + 1}\)[/tex]

Distance = [tex]\(\sqrt{82}\)[/tex]

Now, approximate value of [tex]\(\sqrt{82}\)[/tex] to 1 decimal place:

[tex]\(\sqrt{82} \approx 9.1\)[/tex]

So, the correct response is 9.1.

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Based on the information given, the number of tokens that will be bought if a child has $20 will be 70.

Since a child can buy 21 tokens for $6, the cost of one token will be:

= $6 / 21 = $0.2857143

Therefore, if a child has $20, the number of tokens that will be gotten will be:

= $20 / $0.2857143

= 70

Therefore, 70 tokens will be bought.

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Answer:

Working out 20% of 30

If you are using a calculator, simply enter 20÷100×30 which will give you 6 as the answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

what is 20% of 30? how would you calculate it?

30 : 100 * 20 = 6

or

30 * 0.20 = 6

Answer:

40 students earned a B on this paper.

40%×80=32 people who chose action as their fav.

Answer:

b.$120

Step-by-step explanation:

Party Favors rounded= 40

Dollars rounded= 3

40x3= 120

On the list of facts, the second fact says "A quarter of the nuts are walnuts.".

A quarter of 956 is => 239 <= .

the regular price is "x", which of course is the 100%, but we also know that $459 is 32% off that, hmmmmm well 100% - 32% = 68%, so $459 is really 68% of "x", because $459 is whatever "x" is minus 32%.

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 459&68 \end{array}\implies \cfrac{x}{459}=\cfrac{100}{68}\implies \cfrac{x}{459}=\cfrac{25}{17} \\\\\\ 17x = 11475\implies x = \cfrac{11475}{17}\implies x = 675[/tex]

Answer:

Step-by-step explanation:

Yes, but like they say in Vegas, you're trying to make your point the hard way.

8 * (8 - 4)              So the distributive property is means remove the brackets.

8*8 - 4*8               What you have done is multiply the numbers on either side of the - sign by 8. It is a good practice NOT to destroy the minus sign just yet.

64 - 32

32                          The answer is 32. That's how the distributive property works

With this question only It might be easier to do what is inside the brackets first. That's making your point the easy way.

8*(8-4) = 8* 4 = 32

A scale drawing is a method of drawing that requires either increasing or decreasing the dimensions of a given object. So then, the actual width of the office floor is: 115.2 feet.

A representative factor is a factor the can be used to either increase or decrease the dimensions of an object. It is sometimes referred to as a scale factor.

In the given question, the scale factor is given as:

[tex]\frac{ 1 }{4}[/tex] inch = 4.5 feet

Given that the width in the scale drawing of the office floor is 6.4 inches, let the actual width be represented by x.

So then;

[tex]\frac{ 1 }{4}[/tex] inch = 4.5 feet

6.4 inches = x

x = [tex]\frac{6.4 *4.5}{\frac{1}{4} }[/tex]

  = [tex]\frac{28.8}{0.25}[/tex]

x = 115.2

Therefore, the actual width of the office floor is 115.2 feet.

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Answer:

115.2                                                                /\

Step-by-step explanation:                         /     \

What the person above me said.             /         \

182.00 miles per hour

y = 182x will be the equation to represent one way you can find how many miles Emily's plane flew each hour.

A formula that expresses the connection between two words on each side of an indication. A calculation with an integer multiple is referred to as an equation. Algebra is widely used in equations. In performing calculations but unsure of the precise amount, algebra is utilized.

The information that is provided is

the air travel time is 12 hours

The destination miles will include  2,184 miles​

Assuming the values of x and y

x = number of hours n

y = distance covered

The equation that will be made will be:

y = (2184 / 12)x

y = 182x

Therefore, the equation will be y = 182x.

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Answer:

[tex]y < 3x - 4[/tex]

Step-by-step explanation:

We can tell right away, that the line has a positive slope, since it goes upwards and to the right. To find the slope exactly, we will use rise/run. We will count the units from the first given point until we reach the next point.

So we can tell that the slope is 3/1 or just 3.

Also, since the line crosses the y-axis at -4, this will be the y-intercept.

Next, since the line is dotted, we know that the inequality sign will either be the "greater than" sign, or the "lesser than" sign. In this case, since the shaded area is below the line, we will use the "lesser than" sign.

So all together, we have y < 3x - 4.

Hope this helps you :)

Answer:

15 years old

Step-by-step explanation:

You would have to create a equation. 2x+3=33, 2x=30, x=15.

Answer: The answer is A. Six 10% and total 100% (I hope ya'll understand what I'm saying)

Answer:

it is A

Step-by-step explanation:

just finished

The relationships between the two medians and an altitude marked on

ΔABC can be used to determine the true statements.

The true statements are;

Reasons:

A median line is a line that extends from the vertex to the midpoint of the

opposite side, bisecting the opposite side.

In the figure, we have;

The median of ΔABC are; JC, and BI

The point of intersection is the point K

The altitude is a perpendicular line from a vertex to the opposite side

known as the base of the triangle.

The given altitude of ΔABC is; AH

Therefore, the statements that are true are;

A. AH is an altitude

C. JC is a median

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Answer:

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

The exponent of 1 can be ignored. This means we're simplifying ...

  [tex]\left(\left(\dfrac{3}{4}\right)^{-2}+\dfrac{1}{\left(\dfrac{3}{4}\right)}\right)^{3/4}=\left(\dfrac{16}{9}+\dfrac{4}{3}\right)^{3/4}=\left(\dfrac{28}{9}\right)^{3/4}\\\\=\left(\dfrac{28\cdot9}{3^4}\right)^{3/4}=\boxed{\dfrac{252^{3/4}}{27}}\qquad\text{rational exponent form}\\\\=\boxed{\dfrac{\sqrt[4]{252^3}}{27}=\dfrac{\sqrt[4]{16003008}}{27}}\qquad\text{radical form}[/tex]

Answer:

0.267

Step-by-step explanation:

the answer is 0.267

The table shows the results for spinning the spinner 80 times. The relative frequency for the event​ "spin a 3​" is 0.32.

Relative frequency is the ratio of the considered sub-group's count to the total count. (so its frequency of the considered subgroup relative to the total frequency).

In the problem given,

The table shows the results for spinning the spinner 80 times.

Number of Outcomes of "Spin a 3"=16

Total Number of Trials =50

Therefore,

The relative frequency for the event​ "spin a 3​" = 16/50

                                                                             = 0.32

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Check the picture below.

Answer:

Step-by-step explanation:

Recall that a proportional relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity is constant. ... When ratios between quantities are not constant, a relationship may be linear but not proportional and the graph does not pass through the origin.

There are 123 Asians, 25 Africans, 21 Europeans and 8 Americans in the village.

To determine the number of Asians, Africans, Europeans, and Americans in the village, the following calculation must be performed:

Therefore, there are 123 Asians, 25 Africans, 21 Europeans and 8 Americans in the village.

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