Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?

Answer:

60 degrees

Step-by-step explanation:

since its a vertically opposite angle so angle 1 will equal angle 3

Answer:

60

Step-by-step explanation:

Answer:

0.8 miles

Step-by-step explanation:

Answer:

5.2 miles

Step-by-step explanation:

Airport to Arcadia is one leg of right triangle = x

Airport to Stafford is leg2 of right triangle  = 7.6

9.2 miles is hypotenuse of right triangle

Pythagorean theorem:

x^2 + 7.6^2 = 9.2^2

x = ~ 5.2 miles

Answer:

(15squrt3)/2

Step-by-step explanation:

cos30=x/15

Answer:

964.

Step-by-step explanation:

The first digit after the decimal point is 6 so we round up the 3.

The value of x in the right angle triangle is approximately 45 degrees.

The angle of the right angle triangle can be found as follows:

Therefore, let's find the hypotenuse side using Pythagoras theorem,

6² + 6² = c²

c² = 72

c = √72

c = 8.48528137424

c = 8.5 cm

Hence,

sin x = opposite / hypotenuse

sin x = 6 / 8.5

sin x = 0.70588235294

x = sin⁻¹ 0.70588235294

x = 44.9006818301

x = 45°

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Answer: 60

Step-by-step explanation:

See

Hence

m<COB=60°

Step-by-step explanation:

the extreme values (minimum, maximum) of a function are the zero points of the first derivation of the function.

so,

f'(x) = 2x + b

and then

2x + b = 0

we know, x = 20 for the minimum

2×20 + b = 0

40 + b = 0

b = -40

therefore, the actual function is

f(x) = x² - 40x + 164

the target format is

f(x) = (x - h)² + k = x² - 2hx + h² + k

so,

-40x = -2hx

-40 = -2h

h = 20

and

h² + k = 164

20² + k = 164

400 + k = 164

k = -236

The resulting ordered pair if the value of the independent variable is –2 will be B. (-2, -4).

From the information given, it was stated that we should calculate the resulting ordered pair if the value of the independent variable is –2.

Therefore, in this case, x = -2. Therefore, we will play it into the equation. This will be:

f(x)=2x³ +3x²

= 2(-2)³ + 3(-2)²

= -16 + 12

= -4

Therefore, the ordered pair will be (-2, -4).

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Answer:

x = 31.

Step-by-step explanation:

93 = x + 62  (External Angle Theorem).

x = 93 - 62

= 31

Answer:

Number of terms = 4 (there are four terms)

coefficients = the coefficient of ab = 4

✓✓✓ ✓✓✓ ✓ b = -5

✓✓✓ ✓✓✓ ✓ m = 1

constant terms = 3

Hope it helped!!

Number of terms, Coefficients, Constant terms are 4,2 and 1

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

3 + 4ab - 5b + m

Number of terms here are

=4

Coefficients we have

=2

Constant terms

=1

Therefore, the answer to this algebra will be 4,2 and 1

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Answer:

x=7

Step-by-step explanation:

x(x-2) (x+4) =385

distribute the x and solve

The value of x is 8 in.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

Length = x + 4

Width = x

Height = x - 2

The volume of the rectangular prism = 385 in³

The volume of the rectangular prism = length x width x height

Now,

length x width x height = 385

(x + 4) x (x - 2) = 385

(x + 4) (x² - 2x) = 385

x³ - 2x² + 4x² - 8x = 385

x³ + 2x² - 8x = 385

This is a cubic polynomial.

f(x) = x³ + 2x² - 8x - 385

f(x) = a³ + bx² + cx + d = 0

Using the calculator we get,

Roots:

x = -3.20181 + 5.96339 i (rejected)

x = -3.20181 - 5.96339 i (rejected)

x = 8.40362 = 8

Thus,

The value of x is 8 in.

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The integer representing the change in the number of DVDs sold is -10000.

Given, The number of DVDs shipped to an online retailer was 10,000 less than the previous year.  

We have to Use an integer to describe the change in the number of DVDs sold.

Now, let the number of DVDs shipped to an online retailer in the previous year be x.

Then, according to the given information, DVDs shipped to the online retailer this year will become x – 10000

So, now, the change in the number of DVDs sold = DVDs sold this year – DVDs sold last year

= x – 10000 – x

= 0 – 10000

= - 10000

Hence, the integer representing the change in the number of DVDs sold is -10000.

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Answer:

[tex]A=41\pi\: \text{units}^2\approxA\approx128.8053\:\text{units}^2[/tex]

Step-by-step explanation:

I assume you mean [tex]r=3+8\sin\theta[/tex]:

Use the formula [tex]\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta[/tex] where [tex]a[/tex] and [tex]b[/tex] are the lower and upper bounds and [tex]r(\theta)[/tex] is the equation of the polar curve.

Since the graph is symmetrical about the line [tex]\displaystyle \theta=\frac{\pi}{2}[/tex], let the bounds of integration be [tex]\displaystyle \biggr(-\frac{\pi}{2},\frac{\pi}{2}\biggr)[/tex] to find half the area of the curve, and then find twice of that area:

[tex]\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta\\\\A=2\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{1}{2} {(3+8\sin\theta)^2} \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\sin^2\theta \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\biggr(\frac{1-\cos2\theta}{2} \biggr) \, d\theta\\\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (9+48\sin\theta+32-32\cos2\theta) \, d\theta[/tex]

[tex]\displaystyle A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (41+48\sin\theta-32\cos2\theta) \, d\theta\\\\A=41\theta-48\cos\theta-16\sin2\theta\biggr|^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\[/tex]

[tex]A=\biggr[41\biggr(\frac{\pi}{2}\biggr)-48\cos\biggr(\frac{\pi}{2}\biggr)-16\sin2\biggr(\frac{\pi}{2}\biggr)\biggr]-\biggr[41\biggr(-\frac{\pi}{2}\biggr)-48\cos\biggr(-\frac{\pi}{2}\biggr)-16\sin2\biggr(-\frac{\pi}{2}\biggr)\biggr]\\\\A=\biggr[\frac{41\pi}{2}-24\sqrt{2}\biggr]-\biggr[-\frac{41\pi}{2}+24\sqrt{2}\biggr]\\ \\A=41\pi\\\\A\approx128.8053[/tex]

Thus, the area of the curve is 41π square units. See below for a graph of the curve and its shaded area.

Answer:

32 1/3

Step-by-step explanation:

Answer:

The answer is [tex]31\frac{9}{10}[/tex].

Step-by-step explanation:

Make sure to follow this formula

[tex]2(lw)+(lh)+(wh)[/tex]

[tex]2(1.3x1.5)+(1.3x5)+(1.5x5) \\= 2(1.95+6.5+7.5)\\=31.9=31\frac{9}{10}[/tex]

After the reflection over the line x = 0, the coordinates will be:

J' = (2, 1)

K' = (0, 4) = K

For any point (x, y), if we apply a reflection across the line x = 0, the image after the reflection will be (-x, y).

So it only changes the sign of the x-component.

In the graph, we can see that J = (-2, 1). So after the reflection, we will have:

J' = (2, 1).

And we also can see that K = (0, 4), then after the reflection, we have:

K' = (-0, 4) = (0, 4) = K

So point K does not change under that reflection.

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Answer:

2.96 cm to the nearest hundredth.

Step-by-step explanation:

V = 3.14 r^2 h

226 = 3.14 * r^2 * 8.2

r^2 = 226 / (3.14*8.2)

r^2 = 8.7774

r =  2.96 cm to the nearest hundredth.

The trigonometric ratios of the right triangle with the given value tan A = 9 / 40 are

sin A = 9 / 41

cos A = 40 / 41

Trigonometric ratios are used to solve for the sides and angles of a right angle triangle.

Therefore,

sin A = opposite / hypotenuse

cos A = adjacent / hypotenuse

tan A = opposite / adjacent

Using Pythagoras theorem, let find the hypotenuse side

c² = 40² + 9²

c = √1681

c = 41

Therefore,

sin A = 9 / 41

cos A = 40 / 41

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Answer:

8 cm

Step-by-step explanation:

because when it's reduced we multiply the side length by 1/3 * 6 = 2cm and the volume will equal v = a^3 = 2^3 = 8cm

Answer:

8cm

Step-by-step explanation:

step1: 6/3=2

volume of a cube =x*x*

v

:=8cm

v=2×2×2

vvv v

A pyramid is a polyhedron built by connecting a polygonal base and a point known as the top. The ratio of the height of pyramid A to pyramid B is 0.064.

A pyramid is a polyhedron built by connecting a polygonal base and a point known as the top. A lateral face is formed by the base edge and top of each triangle.

The volume of a pyramid is given by the formula,

Volume of the pyramid = (Length×Width×Height)/3

                                       = (Area of base ×Height)/3

If the area of the base of the two pyramids is the same, then the ratio of the volume of the two pyramids will be,

[tex]\dfrac{\text{Volume of Pyramid A}}{\text{Volume of Pyramid B}} = \dfrac{60\rm\ mm^3}{937.5\rm\ mm^3}\\\\\\\dfrac{3 \times \text{(Area of base})_a \times h_a}{3 \times \text{(Area of base})_b \times h_b}= \dfrac{60}{937.5}\\\\\\\dfrac{h_a}{h_b} = 0.064[/tex]

Hence, the ratio of the height of pyramid A to pyramid B is 0.064.

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Answer:

hope this will help you........

Answer:

Given the equations, I plotted 2 lines.

Line 1               Line 2

 x  |  y                x  |  y  

 0  | 101             0  |  -5

  1  |  101             1  |  -6

Answer: The mode of the data in the line plot is the data with the highest number of marks

The mode of the data is 8

How to determine the mode?

From the line plot, we have the following frequency table:

Number        Frequency

5                       2 marks6                       4 marks.

7                        3 marks

8                        6 marks

9                         2 marks

10                         4 marks

11                         2 marks

The number with the highest mark is 9

Hence, the mode of the data is 8

Step-by-step explanation:

Answer:

13 x 3 ft

Step-by-step explanation:

RECTANGULAR deck

L x W = 39 ft^2

(w+10)  x w = 39

w^2 + 10w - 39 = 0

(w-3)(w+13) = 0        w = 3    or  -13 (throw out)

w = 3    then l = 10 +3 = 13

Answer:

25

Step-by-step explanation:

Please refer to the picture;

By using partial products to multiply, 52 × 6 is 312

From the question, we are to use partial products to multiply 52 × 6

The partial multiplication is shown below

5 2

× 6

300       6 × 5 tens (That is, 6 × 5 × 10 = 300)

+ 12       6 × 2 ones (That is, 6 × 2 × 1 = 12)

312  

Hence, by using partial products to multiply, 52 × 6 is 312

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