Suppose that two teams play a series of games that end when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. Find the expected number of games that are played when i = 2. Also show that this number is maximized when p= 21.

Step-by-step explanation:

this is the correct answer for the question

Answer: x=4, y=-6

Step-by-step explanation:

Answer:

[tex]x = 5600 + 5600 * 0.042 * 1[/tex]

Step-by-step explanation:

Given

[tex]P = 5600[/tex] -- Principal

[tex]R = 4.2\%[/tex] -- Rate

[tex]T = 1[/tex] -- Time

Required

The amount (x) to be paid

This is calculated as:

[tex]x = P + I[/tex]

Where:

[tex]I = PRT[/tex]

So, we have:

[tex]x = 5600 + 5600 * 4.2\% * 1[/tex]

Express percentage as decimal

[tex]x = 5600 + 5600 * 0.042 * 1[/tex]

(c) is correct

Answer:4778.3 cm^3

Step-by-step explanation: The formula for volume of a cone is V=1/3h pi r^2. By plugging in the height and the radius we get our answer.

Answer:

4778.4 :)

Step-by-step explanation:

Answer:

[tex]44[/tex]

Step-by-step explanation:

The dimensions of the garden is 12 by 8. If we have a walkway that surrounds the garden, the dimensions of the walkway is 2. Since it surrounds the rectangle all sides add 2 to each of the dimensions so now the dimensions of the garden and walkway is 14×10.

The area of the garden is 96 square ft.

The area of the garden and walkway is 140 so let subtract the area of the garden from the total area of both the garden and walkway.

[tex]140 - 96 = 44[/tex]

The area is 44.

Answer:

120 square feet

Step-by-step explanation:

(8+2*2)

(18+2*2) - 8*18 = 120 square feet.

Using a linear approximation, the estimated cube root of 217 is  6.00925.

Given that the number is,

The cube root of 217

Now, for the cube root of 217 using a linear approximation, use differentials.

So, the derivative of the function [tex]f(x) = x^{(1/3)[/tex] at a known point.

Taking the derivative of [tex]f(x) = x^{(1/3)[/tex], we get:

[tex]f'(x) = (\dfrac{1}{3} )x^{-2/3[/tex]

Now, we can choose a point near 217 to evaluate the linear approximation.

Let's use x = 216, which is a perfect cube.

Substituting x = 216 into the derivative, we get:

[tex]f'(216) = (\dfrac{1}{3} )(216)^{-2/3[/tex]

            [tex]= 0.00925[/tex]

Next, use the linear approximation formula:

Δy ≈ f'(a)Δx

Since our known point is a = 216 and we want to estimate the cube root of 217,

since 217 - 216 = 1

Hence, Δx = 1

Δy ≈ f'(216)

Δx ≈ 0.00925 × 1

      ≈ 0.00925

Finally, add this linear approximation to the known value at the known point to get our estimate:

Estimated cube root of 217 ;

f(216) + Δy = 6 + 0.00925

                 = 6.00925

Therefore, the estimated cube root of 217 is 6.00925.

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Answer:

The cost of 16 onions is $ 1.20.

Step-by-step explanation:

To determine what is the cost, in dollars, of 16 onions if 3 onions weigh 1.5 lb and the price of onions is 33 cents per kilogram, the following calculation must be performed:

1.5 pounds = 0.68 kilos

0.68 / 3 = 0.22666 kilos each onion

16 x 0.22666 = 3.626 kilos

0.33 x 3.626 = 1.20

Therefore, the cost of 16 onions is $ 1.20.

Answer:

DL/dt = 529 miles/h

Step-by-step explanation:

The radio station (point A) the point just up the radio station ( point B), and the variable position of the plane ( at specif t  point C) shape a right triangle wich hypothenuse L is:

L²  =  d² + x²

d is the constant distance between the plane and the ground

Then differentiation with respect to time on both sides of the equation

2*L*dL/dt  = 2*d* Dd/dt  + 2*x*dx/dt

But   Dd/dt  =  0

L*dL/dt  =  x*dx/dt

x =  5 miles       dx/dt  =  570 m/h        L  = √ d² + x²    L  √ (5)² + (2)²

L = √29      L  = 5.39 m

5.39 *DL/dt  =  5*570 m/h

DL/dt  =   5*570/5.39   miles/h

DL/dt  =  528.76  miles/h

DL/dt = 529 miles/h

Answer:

sin A = 4/5

cos A = 3/5

Step-by-step explanation:

SOHCAHTOA

cot A = 1/tan A

tan A = opp/adj

cot A = 1/tan A = adj/opp

cot A = 3/4

adj = 3; opp = 4

adj^2 + opp^2 = hyp^2

3^2 + 4^2 = hyp^2

9 + 16 = hyp^2

hyp = 5

sin A = opp/hyp

sin A = 4/5

cos A = adj/hyp

cos A = 3/5

Answer:

sin A = 4/5

cos A = 3/5

Answer:

[tex]x = 77[/tex]

Step-by-step explanation:

Given

[tex]First \to Second[/tex]

[tex]35 \to x[/tex]

[tex]20 \to 44[/tex]

[tex]20 \to 44[/tex]

Required

Find x by SSS

Represent the triangle sides as a ratio

[tex]35 : x = 20 : 44[/tex]

Express as fraction

[tex]\frac{x}{35} = \frac{44}{20}[/tex]

Multiply by 35

[tex]x = \frac{44}{20} * 35[/tex]

[tex]x = \frac{44 * 35}{20}[/tex]

[tex]x = \frac{1540}{20}[/tex]

[tex]x = 77[/tex]

Answer:

ccccccccccccccccccccccccccc

Step-by-step explanation:

Answer:

x = -2; y = 1

Step-by-step explanation:

See picture below.

We are told matrices B is the inverse of matrix A.

The product of a matrix and its inverse is the identity matrix.

Answer:

34n=306

Step-by-step explanation:

Use inverse operation to find it, 306÷34= 9, check again 34(9)=306, so it's correct!

Answer:

Step-by-step explanation:

(0, -1)  & (3 ,1)

[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{1-[-1]}{3-0}\\\\=\frac{1+1}{3}\\\\=\frac{2}{3}[/tex]

Answer:

C $13,220

Step-by-step explanation:

Answer:

6/11, 11/2, 5.77, 5.772

Step-by-step explanation:

Answer:

Following are the response to the given points:

Step-by-step explanation:

For question 5.11:

For point a:

For all the particular circumstances, it was not an appropriate sampling strategy as each normal distribution acquired is at a minimum of 30(5) = 150 or 2.5 hours for a time. Its point is not absolutely fair if it exhibits any spike change for roughly 10 minutes.

For point b:

The problem would be that the process can transition to an in the state in less than half an hour and return to in the state. Thus, each subgroup is a biased selection of the whole element created over the last [tex]2 \frac{1}{2}[/tex] hours. Another sampling approach is a group.

For question 5.12:

This production method creates 500 pieces each day. A sampling section is selected every half an hour, and the average of five dimensions can be seen in a [tex]\bar{x}[/tex]line graph when 5 parts were achieved.

This is not an appropriate sampling method if the assigned reason leads to a sluggish, prolonged uplift. The difficulty would be that gradual or longer upward drift in the procedure takes or less half an hour then returns to a controlled state. Suppose that a shift of both the detectable size will last hours [tex]2 \frac{1}{2}[/tex] . An alternative type of analysis should be a random sample of five consecutive pieces created every [tex]2 \frac{1}{2}[/tex] hour.

Answer:

y - 1 =  -1/4(x+5)

Step-by-step explanation:

Answer:

B: Ones.

Step-by-step explanation:

Because this number is 4.09, and the decimal is right next to the 4, that means that it is in the ones place. Decimals are always adjacent on the right to the ones place.

Answer:

4

Step-by-step explanation:

The mean is the average of a data set. It can be found by adding up all of the values in a data set and then dividing it by the number of values in the data set.

The values in this data set;

[tex]7,5,5,3,2,2[/tex]

The number of values in this data set,

[tex]6[/tex]

Find the mean;

[tex]\frac{sum\ of\ vlaues}{number\ of\ values}[/tex]

[tex]=\frac{7+5+5+3+2+2}{6}\\\\=\frac{24}{6}\\\\=4[/tex]

Answer:

5,5,6,6,13

Step-by-step explanation:

Mode means most often.  The 5 numbers has 2 modes 5 and 6

This means that 4 of the numbers must be 5,5,6,6

Median means the middle number must be 6

5,5,6,6,x is the only way to to get the middle number to be 6

We need to average to 7

(5+5+6+6+x) /5 = 7

(5+5+6+6+x) /5  *5= 7*5

(5+5+6+6+x) =35

22+x = 35

x = 35-22

x = 13

The other number is 13

Answer:

Question 1: x = 6

Question 2: Correct!

Question 3: x = 11

Question 4: Correct!

Step-by-step explanation:

Question 1:

Angle 22x - 2 DOESN'T equal 50 degrees. Only Alternate Interior Angles will equal each other. These two angles are Same Side Interior Angles, meaning if you added them together, they would equal 180 degrees.

Knowing that adding 22x - 2 and 50 will equals 180 degrees, here's how we solve for x:

First, subtract 50 from 180 to find what angle 22x - 2 will equal:

180 - 50 = 130

130 = 22x - 2

Now use basic algebra to solve for x:

130 = 22x - 2

(add 2 to both sides)

132 = 22x

(divide both sides by 22)

x = 6

Question 3:

Angle 5x + 15 DOESN'T equal 9x + 11. They make up a line, which is 180 degrees, so they are supplementary angles.

With that in mind, to solve for x, add the two equations and set it equal to 180:

5x + 15 + (9x + 11) = 180

Now use basic algebra to solve for x:

5x + 15 + 9x + 11 = 180

(add like terms)

14x + 26 = 180

(subtract 26 from both sides)

14x = 154

(divide 14 from both sides)

x = 11

Hope it helps (●'◡'●)

Answer: D

Step-by-step explanation:

Try to draw the X and Y axis: When you shift the function to left it translates as going to the left of the X axis. So what you want is that every value of X on the parent function to correspond to the same x value minus four.

You can apply the same logic to get the + 6

(1) Recall that

sin(x - y) = sin(x) cos(y) - cos(x) sin(y)

sin²(x) + cos²(x) = 1

Given that α lies in the third quadrant, and β lies in the fourth quadrant, we expect to have

• sin(α) < 0 and cos(α) < 0

• sin(β) < 0 and cos(β) > 0

Solve for cos(α) and sin(β) :

cos(α) = -√(1 - sin²(α)) = -3/5

sin(β) = -√(1 - cos²(β)) = -5/13

Then

sin(α - β) = sin(α) cos(β) - cos(α) sin(β) =  (-4/5) (12/13) - (-3/5) (-5/13)

==>   sin(α - β) = -63/65

(2) In the second identity listed above, multiplying through both sides by 1/cos²(x) gives another identity,

sin²(x)/cos²(x) + cos²(x)/cos²(x) = 1/cos²(x)

==>   tan²(x) + 1 = sec²(x)

Rewrite the equation as

3 sec²(x) tan(x) = 4 tan(x)

3 (tan²(x) + 1) tan(x) = 4 tan(x)

3 tan³(x) + 3 tan(x) = 4 tan(x)

3 tan³(x) - tan(x) = 0

tan(x) (3 tan²(x) - 1) = 0

Solve for x :

tan(x) = 0   or   3 tan²(x) - 1 = 0

tan(x) = 0   or   tan²(x) = 1/3

tan(x) = 0   or   tan(x) = ±√(1/3)

x = arctan(0) + nπ   or   x = arctan(1/√3) + nπ   or   x = arctan(-1/√3) + nπ

x = nπ   or   x = π/6 + nπ   or   x = -π/6 + nπ

where n is any integer. In the interval [0, 2π), we get the solutions

x = 0, π/6, 5π/6, π, 7π/6, 11π/6

(3) You only need to rewrite the first term:

[tex]\dfrac{\sin(x)}{1-\cos(x)} \times \dfrac{1+\cos(x)}{1+\cos(x)} = \dfrac{\sin(x)(1+\cos(x))}{1-\cos^2(x)} = \dfrac{\sin(x)(1+\cos(x)}{\sin^2(x)} = \dfrac{1+\cos(x)}{\sin(x)}[/tex]

Then

[tex]\dfrac{\sin(x)}{1-\cos(x)}+\dfrac{1-\cos(x)}{\sin(x)} = \dfrac{1+\cos(x)+1-\cos(x)}{\sin(x)}=\dfrac2{\sin(x)}[/tex]

1km = 0.621371miles

195 km= ?

cross multiplication

= 121.167 miles

25 miles= 1hour

121.167miles = ?hours

121.167=25x

divide by 25x both sides

=4.84 hours

approx 5hours

She must ride for 5 hours if she wants to bike 195 km.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

Given that cyclist rides at an average speed of 25 miles per hour.

Since 1 km = 0.621371 miles

So 195 km = 121.167 miles

The speed of the cyclist (s)  = 24 miles per hour.

Distance covered by the rider = 195 km

Distance covered by the rider (d) = 121.167 miles

By using the formula,  time taken by a body, we calculate the time,

⇒ t = d/s

Substitute the value of d and s in above the equation

⇒ t = 121.167/ 24

Apply the division operation,

⇒ t = 5

Hence, she must ride for 5 hours if she wants to bike 195 km.

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9514 1404 393

Answer:

Step-by-step explanation:

a) The starting height is h(0) = 7.5 feet, the constant in the quadratic function.

The irrigation system is positioned 7.5 feet above the ground

__

b) The axis of symmetry for quadratic ax^2 +bx +c is x = -b/(2a). For this quadratic, that is x=-10/(2(-1)) = 5. This is the horizontal distance to the point of maximum height. The maximum height is ...

  h(5) = (-5 +10)(5) +7.5 = 32.5 . . . feet

The spray reaches a maximum height of 32.5 feet at a horizontal distance of 5 feet from the sprinkler head.

__

c) The maximum distance will be √32.5 + 5 ≈ 10.7 ft.

The spray reaches the ground at about 10.7 feet away.

Answer:

7.5

32.5

5

maximum

10.7

Step-by-step explanation:

The power consumed in the lamp marked 100W - 110V is 15.68W

The power consumed in the lamp marked 100W - 220V is 62.73W

Given:

First lamp rating

Power (P) = 100W

Voltage (V) = 110V

Second lamp rating

Power (P) = 100W

Voltage (V) = 220V

Source

Voltage = 220V

i. Get the resistance of each lamp.

Remember that power (P) of each of the lamps is given by the quotient of the square of their voltage ratings (V) and their resistances (R). i.e

P = [tex]\frac{V^2}{R}[/tex]

Make R subject of the formula

⇒ R = [tex]\frac{V^2}{P}[/tex]             ------------------(i)

For first lamp, let the resistance be R₁. Now substitute R = R₁, V = 110V and P = 100W into equation (i)

R₁ = [tex]\frac{110^2}{100}[/tex]

R₁ = 121Ω

For second lamp, let the resistance be R₂. Now substitute R = R₂, V = 220V and P = 100W into equation (i)

R₂ = [tex]\frac{220^2}{100}[/tex]

R₂ = 484Ω

ii. Get the equivalent resistance of the resistances of the lamps.

Since the lamps are connected in series, their equivalent resistance (R) is the sum of their individual resistances. i.e

R = R₁ + R₂

R  = 121 + 484

R = 605Ω

iii. Get the current flowing through each of the lamps.

Since the lamps are connected in series, then the same current flows through them. This current (I) is produced by the source voltage (V = 220V) of the line and their equivalent resistance (R = 605Ω). i.e

V = IR [From Ohm's law]

I = [tex]\frac{V}{R}[/tex]

I = [tex]\frac{220}{605}[/tex]

I = 0.36A

iv. Get the power consumed by each lamp.

From Ohm's law, the power consumed is given by;

P = I²R

Where;

I = current flowing through the lamp

R = resistance of the lamp.

For the first lamp, power consumed is given by;

P = I²R           [Where I = 0.36 and R = 121Ω]

P = (0.36)² x 121

P = 15.68W

For the second lamp, power consumed is given by;

P = I²R           [Where I = 0.36 and R = 484Ω]

P = (0.36)² x 484

P = 62.73W

Therefore;

The power consumed in the lamp marked 100W - 110V is 15.68W

The power consumed in the lamp marked 100W - 220V is 62.73W