B. You are given nine stones which look and feel identical. One of them contains a valuable gem worth $250,000 and is actually slightly heavier than the other eight (but not enough to detect by lifting by hand). If you identify the gemstone it is yours to keep. You have a balance scale, (see diagram) which you can use exactly two times. Once you have used the scale twice you never get another opportunity. How can you be certain to find the stone contains the gem. (If you guess at any point you lose your chance to win the gem stone.)​

Answer: C. Stratification

Step-by-step explanation: There are diverse samping techniques employed for statistical purposes depending on the tipe and nature of data available or other factors. When a data population is sampled in sects such that the entire data is divided into a equals groups at a fixed intervals based on a certain criteria, it is called stratified sampling. Here, data is divided into strata, with each stratum containing a fixed amount of samples with each partition taking place at regular interval. In the scenario stratification process is employed by sampling at a fixed and regular interval, however, the random nature of the data is not violated.

Answer:If an N-gon (polygon with N sides) has perimeter P, then each of the  

N sides has length P/N.  If we connect two adjacent vertices to the  

center, the angle between these two lines is 360/N degrees, or 2*pi/N  

radians.  (Do you understand radian measure well enough to follow me  

this far?)

The two lines I just drew, plus the side of the polygon between them,  

form an isosceles triangle.  Adding the altitude of the isosceles  

triangle makes two right triangles, and we can use one of them to  

derive the equation

 sin(theta/2) =  s/(2R)

where theta is the apex angle (which I said is 2*pi/N radians), R is  

the length of the lines to the center (the radius of the circumscribed  

circle), and s is the length of the side (which I said is P/N).

Putting those values into the equation, we have

 sin(pi/N) = P/(2NR)

so that

 P = 2NR sin(pi/N)

gives the perimeter of the N-gon with circumradius R.

Can we see a connection between this formula and the perimeter of a  

circle?  The perimeter of the circumcircle is 2*pi*R.  As we increase  

N, the perimeter of the polygon should get closer and closer to this  

value.  Comparing the two, we see

 2NR*sin(pi/N) approaches 2*pi*R

 N*sin(pi/N)   approaches pi

You can check this out with a calculator, using big numbers for N such  

as your teacher's N=1000.  If you calculate the sine of an angle in  

degrees rather than radians, the formula will look like

 N*sin(180/N) --> pi

Step-by-step explanation:

Answer:

Step-by-step explanation: x can be 3, -3, i, or -i.

Explanation:

If you can't find the factoring by looking at this, simplify the equation.

let

x

2

=

y

to make things easier to see

Now we have

y

2

−

8

y

−

9

=

0

See it now?

We can factor into

(

y

−

9

)

(

y

+

1

)

Now substitute back in

x

2

for

y

.

(

x

2

−

9

)

(

x

2

+

1

)

Since

(

x

2

−

9

)

is a difference of two squares,

(

x

−

3

)

(

x

+

3

)

Now we have

(

x

−

3

)

(

x

+

3

)

(

x

2

+

1

)

x can be 3, -3 for the first two parts

x

2

+

1

=

0

can become

x

2

=

−

1

Taking the positive and negative root means

x

=

±

√

−

1

Thus

x

=

±

i

in addition to 3 and -3.

Answer:

you combine like terms and that will get you your answer

Step-by-step explanation:

2x+x

2y+3y

15+2

to get your answer

Answer:

-320000

Step-by-step explanation:

Given

Lost Land = 80,000 acres yearly

Duration 4 years

Required

The total change

Represent the total change with y;

y is calculated as thus;

[tex]y = Lost\ Land * Duration[/tex]

[tex]y = -80,000 acres * 4[/tex]

[tex]y = -320000\ acres[/tex]

Hence, a total of 320000 acres were lost during the period

Answer:

750

Step-by-step explanation:

Answers:

A.   6 Large taxis = 42 seats 9 Small taxis = 36 seats = 78  seats in total

  B.  6 Large taxis =  $498 + 9 Small taxis = $450     498+450= $948

    C.  5 Large taxis and 10 Small taxis

Step-by-step explanation:

A.   6 Large taxis = 42 seats 9 Small taxis = 36 seats = 78  seats in total

If I did 8 small taxis the total number of seats would be 74, so I did one small taxi more to make it fair. There would be seats for everyone but 3 seats extra

  B.  6 Large taxis =  $498 + 9 Small taxis = $450     498+450=948

    C.  5 Large taxis and 10 Small taxis

While the more small taxis there are, the more cheaper it is for Max but the less seats there would be for 75 people, So I did 1 more small taxi and 1 less large taxi.

The total number of seats now is 75 seats which is perfect amount for 75 people

So the total cheaper cost would $915 while still maintaining a fair amount of seats which is 75

I think its 1/6

I'm not sure tho

u take the bottom and subtract it by the top then multiply

Answer:

I think its 1/6

You will end up taking the bottom number and subtract it by the top number then multiply to get your final

Step-by-step explanation:

Answer:

don't give up try and you will find the answers

Answer:

AB = 38.6metres

Step-by-step explanation:

Given the right angled triangle ABC with hypotenuse AB and ∠CAB to be 75°, the opposite side of the triangle will be the side facing the angle ∠CAB directly and this is side BC. The adjacent side of the triangle will be side CA.

To get the length of the hypotenuse AB, we will use the trigonometry identity SOH, CAH, TOA.

According to CAH;

Cos∠CAB = adjacent/hypotenuse = CA/AB

Substituting CA = 10 metres and ∠CAB = 75° into the equation;

Cos75° = 10/AB

AB = 10/cos75°

AB = 10/0.2588

AB = 38.6metres

Hence the length of the hypotenuse AB is 38.6metres.

Answer:

38.6 m

Step-by-step explanation:

Answer:

Option (2)

Step-by-step explanation:

From the picture attached,

Angle 1 and angle 2 are the angles made between two lines intersecting each other at a point and a third line is perpendicular to one of them.

Therefore, both the angles are equal in measure.

Rest all the options are not applicable to show the relation between these angles.

Option (2) will be the correct option.

Answer:

what's the question though ?

In the book Business Research Methods, Donald R. Cooper and C. William Emory (1995) discuss a manager who wishes to compare the effectiveness of two methods for training new salespeople. The authors describe ...

Answer:

18

Step-by-step explanation:

We can create a ratio of the amount of students who picked green over the total amount of students.

9 students picked the green pattern, and a total of 50 students were surveyed. This means the ratio is [tex]\frac{9}{50}[/tex].

To turn [tex]\frac{9}{50}[/tex] into a percentage, we must divide it's numerator by it's denominator and multiply by 100.

[tex]8\div50=0.18\\\\0.18\cdot100=18[/tex]

So the green bar's height will be 18.

Hope this helped!

Answer: 37.9 ft

Step-by-step explanation:

concept to know: trigonometric relation (sine, cosine, tangent)

In this case, we use cosine (adjacent/hypotenuse)

   cos (65)=16/x

16/ cos(65)=x

               x=37.9 ft (rounded)

Answer:

x = 0

y = 3

Step-by-step explanation:

Step 1: Write systems of equations

9x - 2y = -6

5x + 4y = 12

Step 2: Rewrite 1st equation

9x = 2y - 6

x = 2/9y - 2/3

Step 3: Substitute

5(2/9y - 2/3) + 4y = 12

Step 4: Solve for y

10/9y - 10/3 + 4y = 12

46/9y - 10/3 = 12

46/9y = 46/3

y = 3

Step 5: Plug in y to find x

5x + 4(3) = 12

5x + 12 = 12

5x = 0

x = 0

Answer:

Equation of the circle   (x-3)²+(y-5)²=(6.4)²

                             x² -6x +9 +y² -10y +25 = 40.96

Step-by-step explanation:

Step(i):-

Given endpoints of diameter P(−2, 1) and Q(8, 9)

Centre of circle = midpoint of diameter

                   Centre = [tex](\frac{-2+8}{2} ,\frac{1+9}{2} )[/tex]

               Centre (h, k) = (3 , 5)

Step(ii):-

The distance of two end points

PQ = [tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

[tex]PQ= \sqrt{(8+2 )^{2} +(8 )^{2} }[/tex]

PQ = √164 = 12.8

Diameter    d = 2r

                 radius r = d/2

                Radius r = 6.4

Final answer:-

Equation of the circle  

                    (x-h)²+(y-k)² = r²

                   (x-3)²+(y-5)²=(6.4)²

x² -6x +9 +y² -10y +25 = 40.96

x² -6x  +y² -10y  = 40.96-34

x² -6x  +y² -10y -7= 0

Answer:

$1.50 per card

Step-by-step explanation:

Knowns:

$10 to spends, Wants to buy $7 book and two equal priced cards.

10 = 7 + 2x

Subtract 7 from both sides to find out how much money Dave has after he buys his book.

3 = 2x

Divide each side by 2 to find out how much he cana spend on each card

x = 1.50

i hope this helps!

-TheBusinessMan

Answer:

the answer is 28

Step-by-step explanation:

This is simple

if 5 people need 2 gallons we can use that to figure out how many gallons 75 people need.

75 divided by 5 is 15. so if 5 fits into 75 15 times that means that 75 people need 15 times 2 gallons or 30 gallons of fruit punch.

But the problem ask how much "additional" fruit punch so we subtract 2 from 30 to get 28 additional gallons of fruit punch

Answer:

Step-by-step explanation:

Given the vectors based on the number line as RS = 7y +3, ST = 5y +8, and RT = 83, the equation RS+ST = RT will be used to get the unknown.

Substituting the given equation into the expression we will have;

7y +3+5y +8 = 83

collect like terms'

7y+5y+3+8 = 83

12y + 11 = 83

12y = 83-11

12y = 72

y = 72/12

y = 6

b) Substitute y = 6 into RS and ST

Given RS = 7y+3

RS = 7(6)+3

RS = 42+3

RS = 45

For ST;

ST = 5y+8

ST = 5(6)+8

ST = 30+8

ST = 38

Answer:

0 Is Integer ,

rational and a

whole number.

Hope it helps.

Answer:

(-3,-4)

Step-by-step explanation:

● (-1,-8) => (0,-11)

Notice that to move from -1 to 0 in the x-axis we should go one unit to the right wich means adding 1.

● -1 + 1 = 0

Notice that to move from -8 to -11 in the y-axis we should go 3 units down wich means substracting 3.

● -8-3 = -11

Let's do the same for the second point.

● (-4,-1) => ?

Add 1 to -4

● -4+1 = -3

We moved 1 unit to the right by adding 1

Substract 3 from -1

● -1-3 = -4

We moved down 3 units by substracting 3

So the image of (-4,-1) is (-3,-4)

Answer:

The inequality is

88<x<93

Step-by-step explanation:

The average of Shondra's test scores in physics is between 88 and 93.

Let me give out the meaning of some inequality symbols

<= Less than or equal to

>= Greater than or equal to

< Less than

> Greater than

Let the average score be x

In this case , the average score is between 88 and 93

The inequality is

88<x<93

==============================================

Work Shown:

F = future value

P = present value = 280

r = rate of inflation in decimal form = 0.08

t = elapsed time in years = 2

---------

F = P*(1+r)^t

F = 280*(1+0.08)^2

F = 326.592

F = 326.59

Answer:

The side length of the square is 3 meters.

The side length of the triangle is 4 meters.

Step-by-step explanation:

This is basically a systems of equations word problem.

To solve this, we have to create two different equations. Let's assume [tex]s[/tex] is the side length of the square and [tex]t[/tex] is the side length of the triangle.

We can make the equation [tex]4s=3t[/tex], since the perimeters are the same. (A square has 4 sides, a triangle has 3 - multiplying by the side length of each will get perimeter)

We also know that the side length of the triangle is 1 meter longer than the side length of the square, so the equation here becomes [tex]t = s+1[/tex].

Now, let's substitute the second equation ([tex]t = s+1[/tex]) into the first ([tex]4s=3t[/tex]).

[tex]4s = 3(s+1)[/tex]

Apply the distributive property:

[tex]4s = 3s+3[/tex]

Subtract 3s from both sides:

[tex]s=3[/tex]

So the side length of the square is 3. We can now plug it into the equation [tex]t = s + 1[/tex] to find the side length of the triangle.

[tex]t = 3+1\\\\t=4[/tex]

Hope this helped!

Answer:

We can solve this using ratio and proportion. Let x be the number of hits the baseball player will have in the next 28 games.

4 : 8 = x : 28

(4)(28) = (x)(8)

112 = 8x

112/8 = 8x/8

14 = x

Step-by-step explanation:

Answer:

14 hits

Step-by-step explanation:

We can use a ratio to solve

4hits            x hits

------------ = -------------

8 games      28 games

Using cross products

4 * 28 = 8x

Divide each side by 8

112/8 = x

14 = x

14 hits

Answer:

The equation that represents the perimeter of the rectangle is:

[tex]\text{Perimeter} = \frac{2}{3} \times [4l-27][/tex]

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

Perimeter = 2 × [l + w]

It is provided that the width of a rectangle is 9 less than one-third it's length.

That is:

[tex]w = \frac{1}{3}l-9[/tex]

The perimeter is given as 45.

The equation that represents the perimeter of the rectangle is:

[tex]\text{Perimeter} = 2 \times [l + \frac{1}{3}l-9]\\\\\text{Perimeter} = 2 \times [\frac{3l+l-27}{3}]\\\\\text{Perimeter} = 2 \times [\frac{4l-27}{3}]\\\\\text{Perimeter} = \frac{2}{3} \times [4l-27][/tex]

Thus, the equation that represents the perimeter of the rectangle is:

[tex]\text{Perimeter} = \frac{2}{3} \times [4l-27][/tex]

Answer:

m = slope= 5/3

Step-by-step explanation:

[tex](-6, -2) = (x_1,y_1) \\ (-1.5, 5.5) (x_2 ,y_2) \\ \frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 -x _1} [/tex]

[tex] \frac{y - ( - 2)}{x - ( - 6)} = \frac{5.5 - ( -2 )}{ - 1.5 - ( - 6)} \\ \frac{y + 2}{x + 6} = \frac{5.5 + 2}{ - 1.5 + 6} [/tex]

[tex] \frac{y + 2}{x + 6} = \frac{7.5}{4.5} \\ 4.5(y + 2) = 7.5(x + 6)[/tex]

[tex]4.5y + 9 = 7.5x + 45 \\ 4.5y = 7.5x + 45 - 9 \\ 4.5y = 7.5x + 36[/tex]

Divide through by 4.5

[tex] \frac{4.5y}{4.5} = \frac{7.5x}{4.5} + \frac{36}{4.5} \\ y = \frac{5}{3} x + 8 \\ [/tex]

Answer:

-4

Step-by-step explanation:

5x+4=-16: minus 4 from both sides

5x=-20: Divide by 5 to solve for x

x=-4

Answer:

9x - 24 ÷ 6

Step-by-step explanation:

Quotient means that one number will be divided by another, so the division sign will be involved in the expression.

9 times x minus 24 translates to 9x - 24.

Now, put it all together.

9x - 24 ÷ 6 will be the expression.

Hope that helps.