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Kobotan [32]
3 years ago
12

The newest model of smart car is supposed to get excellent gas mileage. a thorough study showed that gas mileage (measured in mi

les per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. what is the probability that, if driven normally, the car will get 100 miles per gallon or better
Mathematics
1 answer:
DaniilM [7]3 years ago
3 0
AMERICAN POLICE CANT HANDLE THAT
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Use spherical coordinates. Find the volume of the solid that lies within the sphere x^2 + y^2 + z^2 = 81, above the xy-plane, an
Natasha_Volkova [10]

Answer:

The volume of the solid is 243\sqrt{2} \ \pi

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0  ≤ ρ²   ≤   81

0  ≤ ρ   ≤  9

The intersection that takes place in the sphere and the cone is:

x^2 +y^2 ( \sqrt{x^2 +y^2 })^2  = 81

2(x^2 + y^2) =81

x^2 +y^2 = \dfrac{81}{2}

Thus; the region bounded is: 0 ≤ θ ≤ 2π

This implies that:

z = \sqrt{x^2+y^2}

ρcosФ = ρsinФ

tanФ = 1

Ф = π/4

Similarly; in the X-Y plane;

z = 0

ρcosФ = 0

cosФ = 0

Ф = π/2

So here; \dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}

Thus, volume: V  = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4}  \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho   ^2 \ sin \phi \ d\rho \   d \theta \  d \phi

V  = \int \limits^{\pi/2}_{\pi/4} \ sin \phi  \ d \phi  \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho   ^2 d\rho

V = \bigg [-cos \phi  \bigg]^{\pi/2}_{\pi/4}  \bigg [\theta  \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3}  \bigg ]^{9}_{0}

V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ]

V = 243\sqrt{2} \ \pi

4 0
3 years ago
Sketch the image of quadrilateral PQRS under the following dilations:
kramer

Answer:

dam this been up for a long time

Step-by-step explanation:

its just too hard sorry man

7 0
3 years ago
Cottage cheese is being sold in different size containers. The sizes and prices are given below: 4 - 5 ounce containers for $5.
Karolina [17]

Division is the process of finding the number of times a number is multiplied by itself. The 16-ounce container is the better buy.

<h3>What is Division?</h3>

The division is the process of finding the number of times a number is multiplied by itself.

The prices of the different size containers are given to us,

4-5 ounce containers for $5. 00

1-12 ounce container for $3. 24

1-16 ounce container for $4. 19

Now, find the cost of the cheese per ounce when we buy the minimum cheese and when we but the maximum amount of cheese.

1.   For the first Container, 4-5 ounce containers for $5.00

If we buy 4 ounces of cheese, then the cost of each ounce of cheese will be $1.25 for each ounce, while if we buy the maximum amount of cheese therefore 5 ounces for $5 then the cost of each ounce of cheese will be $1.

2.  For, the second container, 1-12 ounce container for $3.24

If we buy 1 ounce of cheese, then the cost of each ounce of cheese will be $3.24 for each ounce, while if we buy the maximum amount of cheese therefore 5 ounces for $5 then the cost of each ounce of cheese will be $0.27.

3.  For, the third container, 1-16 ounce container for $4.19.

If we buy 1 ounce of cheese, then the cost of each ounce of cheese will be $4.19 for each ounce, while if we buy the maximum amount of cheese therefore 16 ounces for $4.19 then the cost of each ounce of cheese will be $0.26.

Thus, if we buy the maximum amount of cheese from each of the boxes, the third box will be the cheapest.

Hence, The 16-ounce container is the better buy.

Learn more about Division:

brainly.com/question/369266

3 0
2 years ago
I've tried solving this but I'm stuck -8=2/x
USPshnik [31]

Answer:

-0.25

Step-by-step explanation:

-8= 2/x

multiply both sides by x -> -8x =2

divide both sides by -8 -> x=2/-8

Ans= -1/4 = -0.25

5 0
3 years ago
Read 2 more answers
What’s the equation of a line passing through the two points (-3,3) and (0,-1)
kirill [66]

Answer:

y = -4/3x - 1

Step-by-step explanation:

3 0
3 years ago
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