Contestants in a game show are each given three pairs of numbers (for example, 2 and 3, 5 and 6, and 6 and 1). a person in the audience is randomly picked and asked to roll two dice, one white and one red. the white die gives the first number in the pair, and the red die gives the second number. the probability that each player has of winning is .

The volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16 is 24.74 cubic units.

Find the volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16

From the sphere and cylinder, the cylindrical coordinate will be

[tex]z = \pm \sqrt{16 - r^2}[/tex]

And the radius of the cylinder is |r| < 1 and the 0 ≤ θ ≤ 2π.

Then the volume will be given as

[tex]\rm V = \int _0^{2\pi} \int _0^1 \int _{- \sqrt{16 - r^2}}^{\sqrt{16-r^2}} \left ( r \ dz \ dr \ d\theta \right ) \\\\\\V = 2\pi \int_0^1 \left ( 2r\sqrt{16-r^2} \right ) \ dr\\\\\\V = 4\pi \left [ -\dfrac{1}{3} (16 - r^2)^{3/2} \right ]\\\\\\V = \dfrac{4\pi}{3} \left ( 16^{3/2} - 15^{3/2} \right )\\\\\\V = 24.74[/tex]

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Answer:

The correct answer is A

Step-by-step explanation:

The books sold are 30,000, so that is our total sale for January. His sales are decreasing by an average of 500 books per month, which means he is losing sales so it is a negative value, and we multiply that by x (number of months) since the question has not stated the number of months. Therefore, the equation would be f(x) = 30,000 - 500x

Hope this is of help!

Using the normal distribution, it is found that there is a 0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 2.8, \sigma = 0.7[/tex].

The probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters is one subtracted by the p-value of Z when X = 4, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{4 - 2.8}{0.7}[/tex]

Z = 1.71

Z = 1.71 has a p-value of 0.9564.

1 - 0.9564 = 0.0436.

0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.

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Answer:

x = 3, y = 3

Step-by-step explanation:

x = -5x -18

5x + 18 = -x

6x + 18 = 0

6x = 18

x = 3

The statement third, “This is voluntary response bias. The result overestimates true support for firing the coach” is correct.

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

We have:

A local baseball team is struggling this season, and many fans of the team believe it may be time to replace the head coach.

Number of votes V(n) = 2367

After the value of V(n) 79% of those who responded felt the coach should be fired.

Based on the data given, we can say this is referred to as voluntary response bias. The outcome exaggerates the level of support for firing the coach.

Thus, the statement third “This is voluntary response bias. The result overestimates true support for firing the coach” is correct.

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Answer:

10 lbs

Step-by-step explanation:

25 is to 5    as   x is to 2

25/5 = x/2

2 * 25/5 = x = 10 lbs

The algebraic expression of a polynomial with a degree of 4 is 9x⁴ – x³ – x/5

For a polynomial to have a degree of 4, the following must be true:

Using the above highlight, the algebraic expression of a polynomial with a degree of 4 is 9x⁴ – x³ – x/5

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The statements which are correct include the following:

The table given shows that:

This therefore results in the conclusion that option 1,3 and 4 are

the most appropriate options.

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Answer:

pls refer to given attachemnt

Answer:

See below ~

Step-by-step explanation:

Things to Find

Volume of Toy

Volume of Circumscribing Cube

Difference in Volume

Slant height of cone

Surface Area of Toy

Answer:

The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps.

Answer:

I don't know

Step-by-step explanation:

You didn't give a picture to see the rectangle.

Answer:

original weight= mass/weight

62kg/7

Step-by-step explanation:

8.85 original weight

Answer:

-90=-100+x

-90+100=x

x=10

hence 10 is that value whose satisfy this equation

Step-by-step explanation:

Answer: f(y) x g(y) = 1

Step-by-step explanation:

[tex]\frac{2y^3-y^2+2y-1}{y^3-y^2+y-1}\cdot \frac{2y^2-3y+1}{4y^2-4y+1}\\\\= \frac{4y^5-8y^4+9y^3-9y^2+5y-1}{4y^5-8y^4+9y^3-9y^2+5y-1} \\\\= \frac{(y-1)(2y-1)(2y-1)(y^2+1)}{(y-1)(2y-1)(2y-1)(y^2+1)} \\\\= 1[/tex]

Answer:

60

Step-by-step explanation:

AT = ½bh

AT = (6(20)) / 2

AT = 60

Answer:

The answer is 60

Step-by-step explanation:

^^

Happy to help :D

Answer:

½ (a + b) h

Step-by-step explanation:

Answer:

n = 1

Step-by-step explanation:

1 x 2 = 2
2 + 1 = 3
3 < 4

hope this helps

Answer: x = 6.56

Step-by-step explanation: -0.4x - 0.5 + x = 3.63

-0.4x^2 - 0.5 = 3.63

-0.4x^2 = 4.13

0.63x = 4.13

x = 6.56

Step-by-step explanation:

I always try to find the easiest way to solve this kind of questions.

The easiest percentage to calculate with is number 10.

first step , divide the whole amount of the money by ten.

as a result we get 40,000

second step, we were asked to calculate a20% so we will double the 10 percent

and the answer goes to 80,000.

Answer:

Step-by-step explanation: umm i think 6000000 i don't know it might be right because i guess you need to add

Step-by-step explanation:

[tex]Another example , when a straight wire is moved up and down rapidly between the two poles of a horseshoe magnet , then an electric current is produced in the wire. This is also an example of electromagnetic induction .

The total amount that Penny has budgeted for her trip to Egypt is £5351.62.

The exchange rate is the rate at which one currency is exchanged for another currency.  The total amount that was budgeted by Penny is the sum of the different compoments that she compiled for the trip.

Cost of international phone card in Egyptian pound = 41.38 x 5.3841 =£222.79

Cost of passport in Egyptian pound = 65 x 5.3841  = £349.97

Total cost =  3,241.77 + £222.79 + 494.25 +  £349.97+ 398.26 £ + 644.48 = £5351.62

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Answer:

5000 multiplied by 0.05 multiplied by 4

Step-by-step explanation:

you should get 1000. :D next you add 1000 to the orginal 5000 to get 6000!

Answer:

A

Step-by-step explanation:

if it is at least -27 it will be greater than or equal to -27

Answer:

5/6

Step-by-step explanation:

The factors of 24 that are on a die are: 1,2,3,4 and 6. This only leaves 5 that isn't a factor of 24. Therefore, since there are 5 possibilities out of the 6 total numbers, the probability of rolling factors of 24 is 5/6.

x = 50.5°

In order to solve, get to know about the sine rule:

[tex]\bf Sine \ Rule = \dfrac{A}{sinA} = \dfrac{B}{sinB}= \dfrac{C}{sinC}[/tex]

[tex]\sf \dfrac{BD}{sin(50)} = \dfrac{5.6}{sin(78)}[/tex]

[tex]\sf BD = \dfrac{5.6(sin(50))}{sin(78)}[/tex]

[tex]\sf BD = 4.385686657 \ cm[/tex]

Then find angle D = 180° - 78° = 102°

[tex]\sf \dfrac{4.385686657}{sinC} = \dfrac{9.3}{sin(102)}[/tex]

[tex]\sf C = sin^{-1}(\dfrac{4.385686657sin(102)}{9.3} )[/tex]

[tex]\sf C = 27.37 ^{\circ \:}[/tex]

[tex]\sf B + C + D = 180^\circ[/tex]

[tex]\sf x + 27.37^\circ + 102^\circ = 180^\circ[/tex]

[tex]\sf x = 180^\circ - 102^\circ - 27.37^\circ[/tex]

[tex]\sf x = 50.53^\circ[/tex]

[tex]\sf x = 50.5^\circ \ \ \ (rounded \ to \ nearest \ 3 \ significant \ figure)[/tex]

Answer:

x = 50.5° (3 sf)

Step-by-step explanation:

Sine Rule for side lengths

[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Find BD:

[tex]\implies \sf \dfrac{BD}{\sin BAD}=\dfrac{AB}{\sin BDA}[/tex]

[tex]\implies \sf \dfrac{BD}{\sin 50^{\circ}}=\dfrac{5.6}{\sin 78^{\circ}}[/tex]

[tex]\implies \sf BD=\dfrac{5.6\:sin 50^{\circ}}{\sin 78^{\circ}}[/tex]

[tex]\implies \sf BD=4.385686657...cm[/tex]

Angles on a straight line sum to 180°

⇒ ∠ADB + ∠BDC = 180°

⇒ 78° + ∠BDC = 180°

⇒ ∠BDC = 102°

Sine Rule for angles

[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Find ∠BCD:

[tex]\implies \sf \dfrac{\sin BCD}{BD}=\dfrac{\sin BDC}{BC}[/tex]

[tex]\implies \sf \dfrac{\sin BCD}{4.385...}=\dfrac{\sin 102^{\circ}}{9.3}[/tex]

[tex]\implies \sf BCD=\sin^{-1}\left(\dfrac{4.385...\sin 102^{\circ}}{9.3}\right)[/tex]

[tex]\implies \sf BCD=27.46935172...^{\circ}[/tex]

The interior angles of a triangle sum to 180°

⇒ ∠CBD + ∠BDC + ∠BCD = 180°

⇒ x + 102° + 27.469...° = 180°

⇒ x = 50.53064828...°

⇒ x = 50.5° (3 sf)