A certain game consists of rolling a single fair die. If a four or five comes​ up, you win 10 ​dollars; otherwise, you lose 5 dollars. Find the expected winnings for this game. Is this a fair​ game?

Answer:

-3x^3 + x^2 + 4x +6

Answer is C

Step-by-step explanation:

Answer: -3x^3 + x^2 + 4x +6

Answer is C

Step-by-step explanation:

Answer:

[tex]c = \frac{2}{0.42} [/tex]

Step-by-step explanation:

AB = c

[tex] \frac{a}{sin \: A} = \frac{c}{sin \: C} \\ \frac{2}{sin \: 25} = \frac{c}{sin \: 90} \\ \frac{2}{0.42} = \frac{c}{1} \\ 0.42 \: c = 2 \\ c = \frac{2}{0.42} [/tex]

Answer:

4.73

Step-by-step explanation:

​

​

Answer:

[tex]x=30\\y=68\\z=82[/tex]

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

[tex]y+z=5x[/tex]

The third angle is 14 more than the second

[tex]z=y+14[/tex]

And remember that the sum of these three angles must be equal to 180.

[tex]x+y+z=180[/tex]

Let's take these equations

[tex]y+z=5x\\z=y+14\\x+y+z=180[/tex]

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

[tex]x+y+z=180\\x+(y+z)=180\\x+(5x)=180[/tex]

Distribute the + sign

[tex]x+5x=180[/tex]

Combine like terms;

[tex]6x=180[/tex]

Divide by 6.

[tex]x=\frac{180}{6}\\ x=30[/tex]

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example [tex]z=y+14[/tex]

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

[tex]x+y+z=180\\30+y+(y+14)=180[/tex]

Distribute the + sign and Combine like terms;

[tex]30+y+y+14=180\\44+2y=180\\[/tex]

Subtract 44 to isolate 2y.

[tex]2y=180-44\\2y=136[/tex]

Now divide by 2.

[tex]y=\frac{136}{2}\\ y=68[/tex]

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

[tex]x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82[/tex]

Answer:

(19/23)(18/22)(17/21) or 969/1771

Step-by-step explanation:

You add up the total number of cans, giving you 6+4+5+8 = 23 cans total. From there, you only have 4 cans of grape juice. That means 19 of these cans aren't grape, meaning you are checking the probability of choosing these three times in a row.

The probability of selecting the first can and it not being grape is 19/23. Then, when you select another can in succession, without replacing the cans, you now only have 22 cans left, meaning 18 also will not be grape, so it will be a 18/22 chance. Then, selecting your third can, 21 cans are left, and 17 of them are not grape since you have not yet chosen one, giving you 17/21. You multiply them together.

Hopefully I reduced the fraction properly (or even did this question properly)

Answer:

2/13

Step-by-step explanation:

In a regular deck of cards, there are a total of 52 cards. Of these, there are 4 8's and 4 jacks, making a total of 8 "desirable" outcomes. Therefore, the probability is 8/52=2/13. Hope this helps!

Answer:

1 lb 8 oz

Step-by-step explanation:

The weight gain was the difference between the current weight and the beginning weight:  20 lb 2 oz less 18 lb 10 oz.  Since 10 oz is less than 2 oz, we must 'borrow" 1 lb, or 16 oz, to be able to perform the subtraction.  Thus, 20 lb 2 oz becomes 19 lb + 16 oz + 2 oz, or 19 lb 18 oz.

Then the indicated subtraction comes out to 1 lb 8 oz, which represents the baby's weight gain over the past month.

Answer:

The central angle measure of the sector is 150º.

Step-by-step explanation:

A sector of a circle is the portion of a circle enclosed by two radii and an arc.

When you know the central angle the area of a sector is given by

                                              [tex]A=\pi r^2(\frac{C}{360} )[/tex]

where

r is the radius of the circle of which the sector is part.

C is the central angle in degrees.

We know that the area of the sector is [tex]60\pi \:cm^2[/tex] and the radius is 12 cm. Applying the above formula and solving for the central angle we get that

[tex]60\pi =\pi (12)^2(\frac{C}{360}) \\\\\pi \left(12\right)^2\left(\frac{C}{360}\right)=60\pi \\\\\frac{\pi 12^2\cdot \frac{C}{360}}{144\pi }=\frac{60\pi }{144\pi }\\\\\frac{C}{360}=\frac{5}{12}\\\\C=150[/tex]

Answer:5pi/6

Step-by-step explanation:

Answer:

1440 feet

Step-by-step explanation:

15 × 12 × 8 = 1440

Answer:

1128cm

Step-by-step explanation:

The diagram of the problem is annotated and attached.

In the diagram, we are required to find the distance between Aliaa and the far corner, b.

In Triangle ABC

[tex]\angle A+\angle B+\angle C=180^\circ\\53^\circ+100^\circ+\angle C=180^\circ\\\angle C=180^\circ-153^\circ\\\angle C=27^\circ[/tex]

Using Law of Sines

[tex]\dfrac{b}{sin B} =\dfrac{c}{sin C} \\\dfrac{b}{sin 100} =\dfrac{520}{sin 27}\\b=(520 X sin 100)\div sin 27\\b=1127.997\\b\approx 1128$ cm (to the nearest centimeter.)[/tex]

Therefore, Aliaa should hit the ball a distance of 1128cm so that it lands perfectly in the far corner of the court.

Answer:

Step-by-step explanation:

I only know that number 2 is 56.

The exact values of [tex]cos\theta[/tex], [tex]tan\theta[/tex], and [tex]cosec\theta[/tex] are [tex]\frac{\sqrt{33} }{7}[/tex], [tex]\frac{4}{\sqrt{33} }[/tex] and [tex]\frac{7}{4}[/tex] respectively.

The sine (sin) of an acute angle in a right angled triangle is the ratio between the side opposite the angle and the hypotenuse of the triangle.

In a right triangle, the cosine of an angle is the length of the adjacent side (A) divided by the length of the hypotenuse (H).

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In a right angled triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the side opposite the angle.

According to the given question.

We have a right angle triangle ABC.

In which

AB = 7

AC = 4

Now by Pythagoras Theorem

[tex]AB^{2} =AC^{2} +BC^{2}[/tex]

⇒ [tex](7)^{2} = (4)^{2} + BC^{2}[/tex]

⇒ [tex]49 = 16 +(BC)^{2}[/tex]

⇒ [tex]49 - 16=BC^{2}[/tex]

⇒ [tex]BC^{2} = 33[/tex]

⇒ [tex]BC=\sqrt{33}[/tex]

In the right angle triangle

Hypotenuse, AC = 7

The side BC is the adjacent side w.r.t angle θ.

And, Side BC is the opposite side w.r.t angle θ.

Therefore,

[tex]tan\theta=\frac{4 }{\sqrt{33} }[/tex]

[tex]cos\theta= \frac{\sqrt{33} }{7}[/tex]

[tex]sin\theta= \frac{4}{7}[/tex]

[tex]cosec\theta=\frac{1}{sin\theta} =\frac{1}{\frac{4}{7} } =\frac{7}{4}[/tex]

Hence, the exact values of [tex]cos\theta[/tex], [tex]tan\theta[/tex], and [tex]cosec\theta[/tex] are [tex]\frac{\sqrt{33} }{7}[/tex], [tex]\frac{4}{\sqrt{33} }[/tex] and [tex]\frac{7}{4}[/tex] respectively.

Find out more information about cosine, tangent and cosecant of an angle here:

https://brainly.com/question/1832081

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Answer:

y/2 + 5 = -3

y/2 = -8

y = -16

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

  9

Step-by-step explanation:

The median is the average of the base lengths. Where "b" is the length of the other base, we have ...

  36 = (44 +b)/2

  b = 72 -44 = 28

We are told this is the same as 2x+10, so we have ...

  28 = 2x +10

  18 = 2x . . . . . subtract 10

  9 = x . . . . . . . divide by 2

The value of x is 9.

Answer:

The illustration is approximately 226 times larder than the actual pollen grain.

Step-by-step explanation:

First of all, we have to write out the size of the actual pollen grain in a manner that is easy for us to work with.

This will be

[tex](\frac{3}{10}) ^{3}=0.027cm[/tex] wide

The original width of the pollen is 0.027 cm.

Next,

We can take the width of the illustration to be 6.10 cm  wide.

After this,

To get the magnification factor, we will have to use the formula

Magnification = illustrated size/ actual size

This will be the magnification = [tex]6.10/0.027[/tex] = 255.92 times

Hence, the illustration is approximately 226 times larder than the actual pollen grain.

Answer:16/15 or 1 1/15

Step-by-step explanation:

4/5 ➗ 3/4

4/5 x 4/3

(4 x 4) ➗ (5 x 3)

16 ➗ 15=16/15 or 1 1/15

Answer:

~ Surface Area 1 = 9 * Surface Area 2 ~

Step-by-step explanation:

Let us look through this problem step by step;

1. The formula to determine the surface area of a sphere is 4πr^2

2. Here we can see that the difference between the two radii of the spheres is that one is 3 times greater than the other

3. So if you were to think about it, in this surface area formula if the radii is squared, the difference between the two surface areas would also be squared. That means that the difference between the surface areas is 3^2, or 9 times the other.

4. This would mean the scale factor to be that one of the spheres surface area is 9 times the other ( Surface Area 1 = 9 * Surface Area 2)

Answer:

we are given

length =3 yards and 16 inches

now, we can change it in inches

we know that

1 yard =36 inches

so, we get

length =3*36 inches and 16 inches

length=124 inches

now, we will check each option

option-A:

we can see that this is also 124 inches

so, this is TRUE

option-B:

4 yd 4 in

we can change into inches

we know that

1 yard =36 inches

4 yd 4 in=4*36 inches +4 inch

4 yd 4 in=144 in

this is not equal to 124 in

so, this is FALSE

option-C:

3 yd 1 1/2 in

we know that

1 yard =36 inches

3 yd 1 1/2 in =

3 yd 1 1/2 in =

this is not same as 124 in

so, this is FALSE

option-D:

2 yd 52 in

we know that

1 yard =36 inches

2 yd 52 in

2 yd 52 in

so, this is same

so, this is TRUE

option-E:

10 ft 4 in

we know that

1 feet =12 inches

so,

10 ft 4 in=12*10 +4 in

10 ft 4 in=124 in

this is same

so, this is TRUE

Step-by-step explanation:

So yes 124 is the same as 3 yards and 16 inches

Hope this helps!!!

Work Shown:

1 foot = 12 inches

3 feet = 36 inches (multiply both sides by 3)

1 yard = 3 feet

1 yard = 36 inches (replace "3 ft" with "36 in")

3 yards = 108 inches (multiply both sides by 3)

3 yards, 16 inches = 3 yards + 16 inches

3 yards, 16 inches = 108 inches + 16 inches

3 yards, 16 inches = 124 inches

Answer:

Measure of first angle: 42 degrees,

Measure of second angle: 138 degrees

Step-by-step explanation:

Let us say x ⇒ measure of the smaller angle, y ⇒ measure of the larger angle

1. Now given that the measure of the larger angle is 12° more than 3 times the smaller angle: y = 12 + 3x

2. If these angles are supplementary, we could formulate another equation were the two angles add to 180°: x + y = 180

3. In this situation it is convenient to apply substitution as to solve for x, y:

1. x + ( 12 + 3x ) = 180

2. x + 12 + 3x = 180

3. 4x + 12 + 180

4. 4x = 168

5. x = 42 degrees

4. Now substitute this value of x into the first equation y = 12 + 3x, and to solve for y as well:

1. y = 12 + 3 ( 42 )

2. y = 12 + 126

3. y = 138 degrees

Here we need to find two angles given that the angles are supplementary and one is 12° larger than the other.

the two angles are 84° and 96°.

We should start by defining what supplementary angles are.

Two angles a and b are supplementary if:

a + b = 180°.

Now, we also know that one of the angles is 12° larger than the other, so we can write:

a = b + 12°

Now that we have that equation, we can replace it in the first one, so we get:

a + b = 180°

(b + 12°) + b = 180°

Now we can solve this for b.

2*b + 12° = 180°

2*b = 180° - 12°  = 168°

b = 168°/2 = 84°

To find the value of a, we can use the equation:

a = b + 12°

a = 84° + 12° = 96°.

Then the two angles are:

84° and 96°.

If you want to learn more, you can read:

https://brainly.com/question/18164299

Answer:

The answer is D.

Step-by-step explanation:

In $1 there are 4 quarters. Having $2 you would multiply 4 by 2 to get how many quarters there are in $2

Answer:

The answer is D.  

Step-by-step explanation:

In $1 there are 4 quarters. Having $2 you would multiply 4 by 2 to get how many quarters there are in $2

Answer:

x=11.429

Step-by-step explanation:

10x+4x-15=145

14X=160

x=11.429

Answer:

11.43

Step-by-step explanation:

Combine like terms 10x and 4x to get 14x.your new equation is 14x-15=145 add 15 on both sides and then you get 14x=160. 160/14 = 11.43 rounded to the nearest hundredth

Answer:

5

Step-by-step explanation:

The probability of tails is 1/2, so the expected value is (1/2) (10) = 5.

Answer:

5

Step-by-step explanation:

Probability of land a tail when the coin is tossed once is 1/2 because a coin has two sides and contains one head

Then when it is tossed 10 times, the no of time a tail appears is. 1/2 * 10 =5

Answer:D or k(x)

Step-by-step explanation: Ik because I cheated like the rest of you, your welcome.

Answer:

Factor out the greatest common factor

Step-by-step explanation:

The first step when factoring any polynomial is to factor out the GCF. The GCF is the greatest common factor for all the terms of the polynomial. By factoring out the GCF first, the coefficients and constant term of the polynomial will be reduced.

Answer:

  1/16, 1/16

Step-by-step explanation:

Perhaps you want to complete the square. You do that by adding the square of half the x-coefficient:

  ((1/2)/2)^2 = (1/4)^2 = 1/16

The number to complete the square is 1/16. It is added to both sides of the equation to give ...

  x^2 +1/2x +1/16 = 2 +1/16

_____

Written as a square, the equation is ...

  (x +1/4)^2 = 33/16

Answer:

Paasche's Index=  168.63= 169

Step-by-step explanation:

Products

Base-Period                                                    Current Period

    Quantities    Mean Shipping                    Quantities    Mean Shipping

     (Year 1)         Cost per Unit ($)                  (Year 5)  Cost per Unit ($)

A         1,500         10.50                         4000                 15.90

B         5,000      16.25                            3000                 33.00

C         6,500        12.20                          8000                  18.40

D          2,500      20.00                         3000                   35.50

Paasche's Index= ∑ pn.qn/∑po.qn* 100

Where pn is the price of the current year and qn is the quantity of the current year and po. is the price of the base year and qo. is the quantity of the base year.

Paasche's Index is the percentage ratio of the aggregate of given period prices weighted by the quantities sold or consumed in the given period to the aggregate of the base period prices weighted by the given period quantities.

Multiplying the current year prices with the current year quantities and the base year price with the current year quantities we get.

Product               pn.qn                      po.qn

A                         15.90* 4000         10.50* 4000

                          = 63600                    =42000

B                       33.00*3000           16.25 * 3000  

                           = 99000                    = 48750

C                      18.40* 8000          12.20 *8000

                            =147200                 =97600

D                     35.50* 3000        20.00*3000  

                          =106500              60,000        

∑                          416300                  248350      

Paasche's Index= ∑ pn.qn/∑po.qn= 416300/ 248350 *100  =  1.676=1.68= 168.63= 169

Answer: trinomial

Step-by-step explanation:

i answered it

Answer:

The answer is 35%

Step-by-step explanation:

How much is 42 out of 120 written as a percentage? Convert fraction (ratio) 42 / 120 Answer: 35%