You spin each spinner once. You get $50 if you spin a 2 and a vowel. You get $25 if you spin a 2 and a consonant. You get $5 if you spin a 1 and a vowel. Everything else earns $0. What is the expected value of this game?
$8.75
$12.50
$80
$10.25​

Using polar/cylindrical coordinates, we take

x = r cos(t )

y = r sin(t )

z = z

so that

dV = dx dy dz = r dr dt dz

The solid is given by the set

D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}

or in cylindrical coordinates,

D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}

Then the volume of the solid is

[tex]\displaystyle \iiint_D \mathrm dV = \iiint_Dr\,\mathrm dr\,\mathrm dt\,\mathrm dz \\\\ = \int_0^{2\pi} \int_0^1 \int_0^{4-2r\cos(t)-r\sin(t)} r\,\mathrm dz\,\mathrm dr\,\mathrm d t \\\\ = \int_0^{2\pi}\int_0^1 (4r-2r^2\cos(t)-r^2\sin(t))\,\mathrm dr\,\mathrm dt \\\\ = \int_0^{2\pi} \left(2 - \frac23 \cos(t) - \frac13 \sin(t)\right) \,\mathrm dt \\\\ = \boxed{4\pi}[/tex]

The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.

The volume of the solid in polar coordinates can be calculated by the double integral in polar coordinates.

[tex]V = \iint_R f(x,y) \,dA.\\[/tex]

Similarly, by polar coordinates,

x = r cost

y = r sint

z = z

we get, dV = dx dy dz = r dr dt dz

The solid is given

D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}

or in polar coordinates,

D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}

The volume of the solid is

[tex]\rm \int \int\int\ dV = \int \int\int\ rdr dt dz\\ \rm = \int\limits^{2\pi}_0\int\limits^1_0 \int\limits^{4-2rcost-rsint}_0 rdr dt dz\\\rm =\int\limits^{2\pi}_0\int\limits^1_0 {4r-2r^{2} cost-r^{2} sint} dr dt\\\rm =\int\limits^{2\pi}_0( 2-2/3cost-1/3sint) dt\\\rm =4\pi[/tex]

Hence, The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.

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Answer:

f(-3)= 10(-3)^2 - 5(-3) - 3

       =90 + 15 -3

f(-3) = 102

Step-by-step explanation:

Step-by-step explanation:

es 1

6/9+2/3+10/2(5)=

6+6+45/9=

57/9

es 2

-3/6-2/4-10/5(2)=

-6-6-24/12=

36/12=3

es 3

15/8-3/2+8/9=

135-108+64/72=

91/72

Answer:

the answer is infinity....

well you see I'm supposed to answer this with 20 character so my bad for the long response, but I'd go with C

Answer:

B.) Progressive

Step-by-step explanation:

Its schedule of marginal tax rates imposes a higher income tax rate on people with higher incomes, and a lower income tax rate on people with lower incomes. The percentage rate increases at intervals as taxable income increases.

Answer:

ST = 2x

Step-by-step explanation:

if not please elaborate on the question.

Answer:

D`

Step-by-step explanation:

The answer would be D because 40 is twice as much as 20. We also double the number of hours. So instead of having the ratio of 20:1 we have the ratio 40:2 (Miles : Hours)

lolol lfeofviponvfnfuibouigb

Answer:

153

Step-by-step explanation:

The formula is 3 mL of A to 5 mL of B.

Let's say the chemist uses just the numbers in the formula.

Add 3 mL of A to 5 mL of B.

3 mL + 5 mL = 8 mL

The chemist ends up with 8 mL of the drug.

He really want 408 mL.

408 mL is how many times greater than 8 mL?

408/8 = 51

He needs to use 51 times the numbers in the formula.

51 * 3 mL of A + 51 * 5 mL of B =

= 153 mL of A + 255 mL of B

= 408 mL of the drug

Answer: 153

Answer:

sorry bro I even don't know coz I am class 7

Answer:

it will look like this 4(a+3)-2/3

Step-by-step explanation:

look since the equation "a+3" replaced for the place of "x" in f(x), you replace it on the equation "4x- 2/3" and just solve

Answer:

Step-by-step explanation:

Id..k how to help u sorry

Answer is

2, 4, 6, 8

Answer:

40 calories per 10 min

Step-by-step explanation:

Because 30 divided by 3 is 10 and 120 divided by 3 is 40

Answer:

x-525000+0

Step-by-step explanation:

No of hours

[tex]\\ \sf\longmapsto 4(1)[/tex]

[tex]\\ \sf\longmapsto 4 hours[/tex]

None of the above

Answer:

Find the GCF of all the terms in the polynomial.

Express each term as a product of the GCF and another factor.

Use the distributive property to factor out the GCF.

Step-by-step explanation:

Answer:

[tex]13x + 7 = 9x - 33 + 4x \\ 7 + 33 = 13x - 13x \\ \\ 40 = 0 \\ \\ no[/tex]

The least-squares regression line equation gives the line that approximate the relationship between the variables in the fuel efficiency data

The fuel efficiency when the speed is 60 mph is approximately 38.55 mpg.

Reason:

The given least-squares regression line equation is presented as follows;

ln(Fuel Efficiency) = 1.437 + 0.541 × ln(speed)

Required:

The value of the fuel efficiency for a speed of 60 mph.

Solution:

The general form of the least-squares regression line equation is [tex]\hat y[/tex] = a + b·x

Where, in the current question, we have;

[tex]\hat y[/tex] = The predicted value = ln(Fuel Efficiency)

a = The y-intercept = 1.437

b = The slope = 0.541

x = The input value = ln(speed)

When the speed = 60 mph, we have;

ln(Fuel Efficiency) = 1.437 + 0.541 × ln(60) = 3.65204040816

Therefore;

[tex]Fuel \ Efficiency = e^{(1.437 + 0.541 \times ln(60))} \approx 38.55[/tex]

The fuel efficiency when the speed is 60 mph ≈ 38.55 miles per gallon

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Answer:

the person above me is correct.

Step-by-step explanation:

Answer:

[tex]x+4[/tex]

Step-by-step explanation:

This question is essentially asking: [tex]p(x)^2*(x-3)=x^3+5x^2-8x-48[/tex]. Find [tex]p(x)[/tex].

The left hand side can be factored into [tex](x-3)(x+4)^2[/tex] by the rational root theorem and polynomial division.

We can then divide both sides of the equation to get [tex]p(x)^2=(x+4)^2[/tex].

Finally, we take the square root of both sides to obtain [tex]p(x)=x+4[/tex].

So, the answer is [tex]\boxed{x+4}[/tex]

Answer:

A. 6.6 ft

Step-by-step explanation:

Answer:

−101430

Step-by-step explanation:

Pictomath lol

Answer:

This cinder block has gravitational potential energy.

This cinder block has 15 484 joules of potential energy

Step-by-step explanation:

PE = mass*gravity*height and g= 9.8 m/s^2

PE = 79 * 9.8 * 20

PE = 15 484

Answer:

true

Step-by-step explanation:

England claimed the colonies, so they ruled over them.