Answer fast in steps

The value of the ratio a:b is 2:1

Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.

Example of some surds are the square root of prime numbers.

Analysis:

a + b[tex]\sqrt{3}[/tex] = [tex]\frac{1}{2 - \sqrt{3} }[/tex]

Rationalizing the right hand side by the conjugate surd which is 2 + [tex]\sqrt{3}[/tex]

[tex]\frac{1}{2 - \sqrt{3} }[/tex]  x [tex]\frac{2 + \sqrt{3} }{2 +\sqrt{3} }[/tex] = [tex]\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}[/tex] = [tex]\frac{2 + \sqrt{3} }{1}[/tex] = 2 + [tex]\sqrt{3}[/tex]

Equating,

a + b[tex]\sqrt{3}[/tex] = 2 + [tex]\sqrt{3}[/tex]

Comparing the variables,

a = 2,   b[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex], b = 1

The ratio, a: b = 2:1

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Answer:

Please see the answer below.

Step-by-step explanation:

It is not too many reds, but it is also not a perfectly balanced roulette wheel.

It is given that the red numbers should come up 18 times when the roulette wheel is played 38 times.

Therefore, the ratio of red numbers to the total number of plays is = 18:38

It is also given that a casino tests the wheel with 3800 plays and noticed that the red numbers came up 1890 times.

The ratio is given as 1890:3800.

We have to simplify this.

1890/3800 = 18.9/38

If the roulette wheel was perfect, it should've been 18:38.

Therefore, we can say that the roulette wheel is not perfectly balanced.

Therefore we have found that it is not too many reds, but it is also not a perfectly balanced roulette wheel.

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Answer:

502.4 ft²

Step-by-step explanation:

To find the individual area of the ring, you first need to find the area of the white circle. Then, you need to find the area of the circle and the ring (which can be found by adding the width of the ring to the radius of the circle). Finally, you can find the area of the ring through subtraction.

Area (White Circle)

radius = 1/2 diameter

radius = (1/2) x 36 ft

radius = 18 ft

Area = πr²

Area = π(18 ft)²

Area = π(324 ft²)

Area = 1017.36 ft²

Area (White Circle + Ring)

radius = 1/2 diameter + width of ring

radius = (1/2 x 36 ft) + 4 ft

radius = 22 ft

Area = πr²

Area = π(22 ft)²

Area = π(484 ft²)

Area = 1519.76 ft²

Area (Ring)

Area (Ring) = Area (White Circle + Ring) - Area (White Circle)

Area (Ring) = 1519.76 ft² - 1017.36 ft²

Area (Ring) = 502.4 ft²

The probability of randomly getting a red or green counter is:

P = 39%/100% = 0.39

We know that 40% of the counters are red or white. Then 60% of the counters are blue or green.

Now we know that the ratio of red to white is 3:5

Then the percentage of red counters is:

(3/8)*40% = 15%

And the ratio of blue to green is 3:2

Then the percentage of red counters is:

(2/5)*60% = 24%

Then the percentage of counters that are either red or green is:

15% + 24% = 39%

Then the probability of randomly getting a red or green counter is:

P = 39%/100% = 0.39

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The equation that represents the relation is y = 8 - 0.5x

The given parameters are:

Start = 8m

Rate = 1/2 m/s

The linear equation that represents the submarine movement is:

y = Start - Rate * x

This gives

y = 8 - 1/2 * x

Evaluate

y = 8 - 0.5x

Hence, the equation that represents the relation is y = 8 - 0.5x

See attachment for the graph

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Jessica purchased a DVD that was on sale for 12% off.

The sales tax in her county is 3%.

Let, y represent the original price of the DVD.

We can simply solve this mathematical problem by using the following mathematical process.

Here, we will form an algebraic expression, according to the given data.

So,

The original price of the DVD = y

Discount on the original price :

y * 12/100

=3y/25

Price after discount :

y - 3y/25

=25y - 3y/25

=22y/25

Sales tax amount :

22y/25 * 3/100

11y/25 * 3/50

=33y/1250

Final price including the sales tax :

22y/25 + 33y/1250

1100y + 33y/1250

1133y/1250

(This will be considered as the final result.)

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Answer: Option (4)

Step-by-step explanation:

From the diagram, we know that

[tex]\sin 60^{\circ}=\frac{BC}{15}\\\\\cos 60^{\circ}=\frac{AB}{15}[/tex]

This means we can eliminate options 1 and 2.

Now, if we multiply both sides by 15, we get

[tex]15\cos 60^{\circ}=7.5[/tex].

This gives us Option (4).

Answer:

Step-by-step explanation:

already

Answer:

25k x 3

Step-by-step explanation:

The coordinates of the vertices are (-1, 6), (1, 2) and (2, 3)

The functions are given as:

y = x + 1

2x + y = 4

x + y = 5

Next, we plot the graph of the lines (see attachment)

From the attached graph, the coordinates of the vertices are (-1, 6), (1, 2) and (2, 3)

Rewrite the equations in slope intercept form

y = x + 1 ⇒ Slope = 1

y = -2x + 4 ⇒ Slope = -2

y = -x + 5 ⇒ Slope = -1

The equations y = x + 1 and y = -x + 5 have their slopes to be opposite reciprocals

This means that the lines are perpendicular (they form a right angle)

Hence, the triangle is a right triangle

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Answer:

a = 2

b = 11

c = 11

d = -2

Step-by-step explanation:

[tex]\sf \left[\begin{array}{cc}a&b\\c&d \end{array}\right] *\left[\begin{array}{ccc} 22&11&7\\ 6&-9&-15 \end{array}\right] =\left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \end{array}\right][/tex]

   [tex]\sf \left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \\ \end{array}\right] =\left[\begin{array}{ccc} 110&-77&-151\\230&139&107 \\ \end{array}\right][/tex]  

On comparing to right side, we get,

 22a + 6b = 110

Divide the entire equation by 2

   11a + 3b = 55  ------------(I)

 11a   - 9b  = -77  -------------(II)

Subtract equation (II) from (I)

       11a + 3b = 55

       11a - 9b = -77

      -      +        +     {Now subtract}

               12b = 132

                 b = 132/12

[tex]\sf \boxed{\bf \ b = 11}[/tex]

Substitute the value of b in eqaution (I)

  11a + 3*11 = 55

  11a + 33   = 55

             11a = 55 - 33

             11a = 22

               a = 22/11

      [tex]\sf \boxed{\bf \ a = 2}[/tex]

           22c + 6d = 230

Divide by 2

           11c + 3d = 115  -----------------(III)

           11c - 9d  = -139 ------------------(IV)

Subtract (IV) from (III)

           11c + 3d  = 115

           11c - 9d  = 139

           -     +         -      

                  12d  =  -24

                      d = -24/12

                     [tex]\sf \boxed{\bf \ d = -2}[/tex]

Plugin d = - 2 in equation (III)

    11c + 3*(-2) = 115

     11c  - 6      = 115

                11c  = 115 + 6

               11c = 121

                  c = 121/11

                 [tex]\sf \boxed{\bf \ c = 11}[/tex]

Answer:

9 x 9 = 81

Step-by-step explanation:

area = width x height

Since it's a square, width = height

The inverse of the equation y = x^2 + 9 is [tex]x = \sqrt{y - 9[/tex]

The equation is given as:

y = x^2 + 9

Subtract 9 from both sides

x^2 = y - 9

Take the square root of both sides

[tex]x = \sqrt{y - 9[/tex]

Hence, the inverse of the equation y = x^2 + 9 is [tex]x = \sqrt{y - 9[/tex]

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Answer:

  r = 5

Step-by-step explanation:

Solving radical equations often results in extraneous solutions. These can be avoided by using a graphing calculator for the solution.

The attached shows that the value of r that makes both sides of the equation have the same value is r = 5.

Check:

  √(5·5 -9) -3 = √(5 +4) -2   ⇒   4 -3 = 3 -2 . . . true

Solution of an equation like this is typically done by isolating the radical expressions, then squaring the equation.

We can add 3, square the equation, then isolate the radical and square again:

  [tex]\displaysyle \sqrt{5r-9}-3=\sqrt{r+4}-2\\\\\sqrt{5r-9}=\sqrt{r+4}+1\qquad\text{add 3}\\\\5r-9=(r+4)+2\sqrt{r+4}+1\qquad\text{square both sides}\\\\(4r-14)^2=4(r+4)\qquad\text{subtract $(r+5)$ and square again}\\\\16r^2-116r+180=0\qquad\text{rewrite in standard form}\\\\4(4r -9)(r -5) = 0\qquad\text{factor}\\\\r=\{\dfrac{9}{4},\ 5\}\qquad\text{solutions to the factored form}[/tex]

Trying these values in the original equation, we get ...

  √((5(9/4) -9) -3 = √(9/4 +4) -2   ⇒   1.5 -3 = 2.5 -2 . . . . . false

  √(5(5) -9) -3 = √(5 +4) -2   ⇒   4 -3 = 3 -2 . . . . . true

The solution is r = 5.

Applying the trigonometry ratios, the correct option is: B. none of these are correct.

The trigonometry ratios are SOH CAH TOA, which are used for solving a right triangle.

Use the trigonometry ratio to find out which option is correct.

Cos Z = adj/hyp = 61/CZ, so option A is incorrect.

Sin Z = opp/hyp = 73/CZ,  so option C is incorrect.

Tan Z = opp/adj = 73/61,  so option D is incorrect.

Thus, the answer is: B. none of these are correct.

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hi

we have an aroithmetic serie of first term 1 and  pace  2

so sum of 12 first terms, namming  1 as  S1 and  12th term as  S12

S12 =  1 + 2*11 = 23

formula of summ :      number of term *  (  final term + first term) / 2

So sum of terms  from S1 +S12 =    12   ( S12 +S1 )  / 2  =  12 * ( 23+1) /2

12*  12=  144

-

1. The semi inter quartile range is 10

2. The coefficient of quartile deviation is 0.2

1st quartile (Q₁) = (134 + 1) / 4 = 33.75th = 40

3rd quartile (Q₃) = 3 (134 + 1) / 4 = 3 × 33.75 = 101.25th = 60

Semi inter quartile range = (Q₃ - Q₁) / 2

Semi inter quartile range = (60 - 40) / 2

Semi inter quartile range = 10

Coefficient of quartile deviation = (Q₃ - Q₁) / (Q₃ + Q₁)

Coefficient of quartile deviation = (60 - 40) / (60 + 40)

Coefficient of quartile deviation = 0.2

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Answer:

$96.

Step-by-step explanation:

5/6  costs 80

Multiply both parts by 6/5:

5/6 * 6/5 ( = 1 ) costs 80 * 6/5

= 16 * 6

= $96.

Domain of the function is [tex]0\leq b\leq 10[/tex] and range of the function is [tex]0\leq W\leq 120[/tex].

The range of values that we are permitted to enter into our function is known as the domain of a function.

A function's range is the collection of values it can take as input.

Each birdhouse uses 12 square feet of wood. Owen has enough to build 10 birdhouses, so he has 120 square feet of wood.

The function has an input of the number of birdhouses, b, and W as an output of the amount of wood needed. b is domain, and W is the range. The domain is 0 to 10 and range is 0 to 120.

Therefore, the domain of the function is  [tex]0\leq b\leq 10[/tex] and the range of the function is [tex]0\leq W\leq 120[/tex].

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Answer:

Quadrant III

Step-by-step explanation:

Top-right quadrant = QI

Top-left quadrant = QII

Bottom-left quadrant = QIII

Bottom-right quadrant = QIV

38.2% of the cubes are without chocolate coated.

Given that,

The length ,l= 10 inch

The width ,b=10 inch

The height, h=5 inch

We know that the lateral surface area of the cuboid or rectangular block,

SA= 2(lh+lb+hb)

⇒ SA = 2( 10*5 +10*10+5*10)

⇒ SA =2*200=400 [tex]inch^{3}[/tex]  

The volume of the cuboid,V= 10*10*5 =500 [tex]inch^{3}[/tex]

The block of candy is then cut into another small cube 1 inch per side.

length,l=1 inch

width, b=1 inch

height,h=1 inch

So, the surface area of each small cube ,sa= 2(1+1+1) = 6 [tex]inch^{3}[/tex]

Volume of each candy,v= 1*1*1=1 [tex]inch^{3}[/tex]

So, the total number of candy= 500/1 =500 nos.

There is chocolate on each and every piece on the exterior inch. But those who are totally within do not.

A cube measuring 8 inches by 8 inches by 3 inches makes up the inside.

So, the total no of boxes that have no chocolate =8*8*3=192 boxes

So, the percentage = 192*100/500= 38.2 %

Therefore, it is concluded that 38.2% of cubes are without chocolate.

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The coordinates of the fourth vertex are (6, -2)

The coordinates of three vertices of a rectangle are given as: (3,7), (-3,5), and (0,-4).

Calculate the slope of the first two coordinates using

m = (y2 - y1)/(x2 - x1)^2

Substitute the known values in the above equation

d = (7 - 5)/(3 + 3)

Let the fourth coordinate be (x, y)

Calculate the slope of the other two coordinates using

m = (y2 - y1)/(x2 - x1)^2

Substitute the known values in the above equation

m = (y + 4)/x

Equate both slope equations

(y + 4)/x = (7 - 5)/(3 + 3)

Simplify the fraction

(y + 4)/x = 1/3

Cross multiply

x = 3y + 12

Let y = -2

So, we have:

x = 3 *-2 + 12

Evaluate

x = 6

Substitute x = 6 and y = -2 in (x, y)

This gives (6, -2)

Hence, the coordinates of the fourth vertex are (6, -2)

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The total amount of Chandra's investments after 8 years exists $110.03.

The formula for calculating the compound interest exists defined as;

[tex]$A = P(1+r/n)^{nt[/tex]

where, P exists the amount invested = $75

r exists the rate. = 0.048

t exists the time = 8 years

n = 12 (monthly)

The formula for calculating the compound interest,

[tex]$A = P(1+r/n)^{nt[/tex]

Substitute the value in the above equation, and we get

[tex]$A = 75(1+0.048/12)^{96[/tex]

A = 75(1.467)

A = 110.03

Hence the total amount of Chandra's investments after 8 years exists $110.03

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The partial sums are correct are  That is:  (2) and (28/9).

A partial sum would be:

2 + (2/3).

In this case, thus,

Series 1 = 2  - This is correct.

Series 2 = 2 + (2/3) = 8/3 - incorrect

Series 3 = (8/3) + (4/9) = (28/9) Correct

Series 4 = (28/9) + (8/27) = (92/27)

Series 5 = (92/27) + (16/81) = 292/81

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The maximum number of floors that this building can have is 6

The given parameters are:

Elevators = 4

Stops = 3

At least one elevator stops on 2 floors

The maximum number of floors is calculated as:

Maximum = Elevators * Stops/2

This gives

Maximum = 4 * 3/2

Evaluate

Maximum = 6

Hence, the maximum number of floors that this building can have is 6

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The linear equation is 45x+50

Linear equation is the equation having the degree 1

Given that the charge per computer repair service  is $50

The charge per hour of work is $ 45

We need to show the linear equation that  expresses the total amount of money Charlie earns per computer is y

So , Let the number of hours be x

Therefore, the Charlie working hours charge will be 45x

The total amount of money Charlie earns per computer is y

Therefore the linear equation will be

y = 50+45x  

Where y = Total amount of money

x =  number of hours

Hence the linear equation is y = 45x+50

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Answer:

20

Step-by-step explanation:

a c will have the same angle as b d

The population parameter value and the point estimate differ because a sample is not census of the entire population,  but it is being used to develop the point estimate.

According to the question,

The population parameter value and the point estimate differ because a sample is not census of the entire population,  but it is being used to develop the point estimate.

The sample proportion p, is a point estimate of the population proportion.

Hence, the correct answer is point estimate. Thus, the population parameter value and the point estimate differ because a sample is not census of the entire population,  but it is being used to develop the point estimate.

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The expression which can be used to represent the total amount llean earned last week is 75 + 18x

An expression to represent the total amount llean earned last week = Amount earned as a web page designer + (Amount llean earns per hour welding × Number of hours worked as welder)

= 75 + (18 × x)

= 75 + 18x

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