A contestant on a game show must choose 2 of 16 boxes. Once a box is chosen, it is removed from the game. Of the 16 boxes, 3 contain money, 5 contain traveling prizes, and 8 are empty. What is the probability that both boxes are empty?

Answer:

D

Step-by-step explanation:

u are correct

Answer:

The Pythagorean identity [tex]\sin^2\theta+\cos^2\theta=1[/tex] comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle [tex]\theta[/tex], we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.

The Pythagorean theorem states that in all right triangles, the following must be true:

[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle.

Therefore, we have the following equation:

[tex](\sin\theta)^2+(\cos\theta)^2=1^2,\\\boxed{\sin^2\theta+\cos^2\theta=1}[/tex]

The Pythagorean identity  comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle , we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.

The Pythagorean theorem states that in all right triangles, the following must be true:

, where  is the hypotenuse of the triangle and  and  are two legs of the triangle.

Therefore, we have the following equation:

Answer:

96 squared units

Step-by-step explanation:

Please find attached the diagram used in answering this question

The surface area is equal to the area of each shape

Area of a triangle = Area of a triangle = 1/2 x ( base x height)

1/2 x 2 x 3= 3

there are 4 triangles, area of both triangles = 3x4 = 12

Area of rectangle = length x width

Area of middle rectangle = 6 x 7 = 42

Area of two side rectangles = (3 +3) x 7 = 42

surface area = 42 + 42 + 12 = 96

Answer:

1.0

2.undefined

Step-by-step explanation:

Answer:1) 0, 2) is undefined

Step-by-step explanation:

Answer:

32 just multiply by four

Answer:

If it is:

1,089-4,445= -3,356

but if it is the other way:

4,445-1,089= 3,356

Hope it helped!

Answer:

Its a Subtraction problem

4445-1089

=3356

Answer:

The question is not biased

The sample is biased because it does not represent the population of customers at the lawn and garden store

Step-by-step explanation:

I just took the test :)

The question is not biased. The sample is biased because it does not represent the population of customers at the lawn and garden store.

Randomization allows a sample or small groups with similar characteristics to determine a probability or to hypothesize an event, that is why this type of sample is important in an experiment, that is, to carry it out in a random way.

For the 250 random customers who bought perennial flowers. The question is not biased. The sample is biased because it does not represent the population of customers at the lawn and garden store.

To know more about randomization follow

https://brainly.com/question/13219833

#SPJ2

Answer:

32º

Step-by-step explanation:

Solve for sin(x). Then use inverse sine to get your angle measurement. From there, convert radians to degrees by multiplying by 180/π.

sin (x) = opp/hyp = 8/15

sin-1(8/15) = x = 0.56253 radians

0.56253 radians * 180/π = 32.23º

Round this to 32º

rectangle = 3 x 2 = 6 cm2

cirrel = pier2 = 3.14 x 7 x 7 = 3.14 x 49 = 153.86 cm2

153.86 - 6 = 147.86cm2

Answer:they are supplementary

Step-by-step explanation:

Answer:

6/4

Step-by-step explanation:

Answer:

Exact Form:

3/2

Decimal Form:

1.5

Mixed Number Form:

1 1/2

Step-by-step explanation:

Answer:

x = 10.5

Step-by-step explanation:

[tex]cos 65 =\frac {adjacent}{hypotenuse} \\\\0.4226 = \frac{x}{25}\\\\0.4226 \times 25 = x \\\\x = 10.565[/tex]

Answer:

Step-by-step explanation:

take 65 degree as reference angle

using cos rule

cos 65=adjacent/hypotenuse

0.42=x/25

0.42*25=x

10.5=x

Answer:

Solution given:

[tex]4\frac{2}{3}÷7[/tex]

=[tex] \frac{4*3+2}{3}×\frac{1}{7}[/tex]

=[tex]\frac{14}{3*7}[/tex]

=[tex]\frac{2}{3}[/tex] is a required answer.

Answer:

2.65

Step-by-step explanation:

Multiply each payout by its probability, then add those products.

See the attached image.

The first column has the payouts.  The second column has the probabilities. The third column has the results of multiplying a payout by its probability.

The sum of the entries in the third column is 2.65

The expected value is $3.1 if the payout probability distribution is payout ($)| 0 4 6 8 10 probability 0.45 0.3 0.1 0.1 0.05

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

From the table we can find the expected value:

Multiply payout to probability such that:

= 0×0.45 = 0

= 4×0.3 = 1.2

And so on

Now sum all values(refer to the attached table)

= 0+1.2+0.6+0.8+0.5

= $3.1

Thus, the expected value is $3.1 if the payout probability distribution is payout ($)| 0 4 6 8 10 probability 0.45 0.3 0.1 0.1 0.05

Learn more about the probability here:

brainly.com/question/11234923

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Answe545r:

45454

Step-by-step explanation:

Answer:

x=5, y=4. (5, 4).

Step-by-step explanation:

y=2x-6

y=5x-21

--------------

2x-6=5x-21

2x-5x-6=-21

-3x-6=-21

-3x=-21+6

-3x=-15

3x=15

x=15/3

x=5

y=2(5)-6

y=10-6

y=4

Answer:

d= 8.3 units

➴➵➶➴➵➶➴➵➶

[tex]Given:[/tex]

[tex]L=7[/tex]

[tex]B=4[/tex]

[tex]H=2[/tex]

[tex]d=\sqrt{L^2+B^2+H^2}[/tex]

[tex]d=\sqrt{7^2+4^2+2^2}[/tex]

[tex]d=\sqrt{49+16+4}[/tex]

[tex]d=\sqrt{69}[/tex]

[tex]d=8.3~units[/tex] ✔︎

•❅────✧❅✦❅✧────❅•

hope it helps...

have a great day!!!

Answer:

she gets paid 6,521 a month

Step-by-step explanation:

just divide 78,252 by 12

Explanation:

Divide the given value by 12 to get the answer. This is the salary before taxes and such. The net salary is after taxes are taken away.

Answer:

(0, 3)

Step-by-step explanation:

y= 3 when x=0

Answer:

Number of rack made from total wood = 5 rack

Step-by-step explanation:

Given:

Length of wood Zendaya has = 5/6 yard

Length of each rack = 1/6 yard

Find:

Number of rack made from total wood

Computation:

Number of rack made from total wood = Length of wood Zendaya has / Length of each rack

Number of rack made from total wood = [5/6] / [1/6]

Number of rack made from total wood = [5/6][6/1]

Number of rack made from total wood = 5 rack

Answer:

D 45

Step-by-step explanation:

90/2 = 45

135/3 = 45

180/4 = 45

Answer:

you have 48

Step-by-step explanation:

15x2=30

9x2=18

18+30=48

Given:

The first four terms of a sequence are:

8, 5, 2, -1

To find:

The function that defines the given sequence.

Solution:

We have,

8, 5, 2, -1

The differences between two consecutive terms are:

[tex]5-8=-3[/tex]

[tex]2-5=-3[/tex]

[tex]-1-2=-3[/tex]

The given sequence has a common difference -3. It means the given sequence is an arithmetic sequence with first term 8 and common difference -3.

The nth terms of an arithmetic sequence is:

[tex]f(n)=a+(n-1)d[/tex], for [tex]n\geq 1[/tex]

Where, a is the first term and d is the common difference.

Putting [tex]a=8,d=-3[/tex], we get

[tex]f(n)=8+(n-1)(-3)[/tex]

[tex]f(n)=8-3(n-1)[/tex]

[tex]f(n)=-3(n-1)+8[/tex], for [tex]n\geq 1[/tex]

Therefore, the correct option is A.

Answer:

the unknown number of fish is 26

Step-by-step explanation:

I figured this out by subtracting 68 - 47 = x.

x = 26

Answer:

Unknow fishes = 26

Step-by-step explanation:

We are given that 42 and x fishes sum up to 68 fishes, so we can say;

42 + x = 68

x = 68 - 42

x = 26

Therefore the number of unknown fishes = 26

Hope this helps!

Answer:

[tex] \displaystyle \theta = \frac{3\pi}{4},\frac{11\pi}{12}, \frac{7\pi}{4}, \frac{23\pi}{12} [/tex]

Step-by-step explanation:

we would like to solve the following trigonometric equation on interval of [0,2π)

[tex] \displaystyle \cos \left(2 \theta + \frac{\pi}{3} \right ) = \frac{ \sqrt{3} }{2} [/tex]

remember that,

[tex] \displaystyle \cos(t) = \cos(2\pi - t) [/tex]

so the equation has two solutions

[tex] \begin{cases} \displaystyle \cos \left(2 \theta + \frac{\pi}{3} \right ) = \frac{ \sqrt{3} }{2} \\ \cos \left(2\pi - (2 \theta + \frac{\pi}{3} )\right ) = \frac{ \sqrt{3} }{2} \end{cases}[/tex]

take inverse trig both sides which yields:

[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} \\ 2\pi - 2 \theta - \frac{\pi}{3} = \frac{\pi}{6} \end{cases}[/tex]

simplify the second equation:

[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} \\ \frac{5\pi}{3} - 2 \theta = \frac{\pi}{6} \end{cases}[/tex]

add period of 2kπ:

[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} + 2k\pi \\ \frac{5\pi}{3} - 2 \theta = \frac{\pi}{6} + 2k\pi\end{cases} [/tex]

By making theta subject of the equation we acquire:

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + k\pi \\ \theta = \frac{3\pi}{4} - k\pi\end{cases} [/tex]

since [tex]k\in\mathbb{Z}[/tex] we get:

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + k\pi \\ \theta = \frac{3\pi}{4} + k\pi\end{cases} [/tex]

as we want to Solve the trigonometric equation on the interval of [0,2π) we get

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} \\ \theta = \frac{3\pi}{4} \end{cases} \text{and} \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + \pi \\ \theta = \frac{3\pi}{4} + \pi\end{cases} [/tex]

by simplifying we acquire:

[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} \\ \theta = \frac{3\pi}{4} \end{cases} \text{and} \begin{cases} \displaystyle \theta = \frac{23\pi}{12} \\ \theta = \frac{7\pi}{4} \end{cases} [/tex]

and we are done!

hence,

[tex] \displaystyle \theta = \frac{3\pi}{4},\frac{11\pi}{12}, \frac{7\pi}{4}, \frac{23\pi}{12} [/tex]