The probability that a randomly selected person at a show has seen the band play live before is 30%. A "superfan" is defined as someone who has seen the band play live at least 10 times. The probability that a person at a show is a "superfan" is 20%. Two people are selected at random. What is the probability that both people have both seen the band perform live before, and are superfans?

The equation of circle for both the parts will be as,

(a)  (x-3)² +(y-2)²= 4

(b)   x²+y² = 1

What is circle?

A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.

Main Body:

(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.

Circle centered at (h, k) with radius r:

(x -h)² +(y -k)² = r²

The given circle is ...

(x -2)² +(y -2)² =2²

(x -2)² +(y -2)² = 4

__

(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:

x²+y² = 1

Hence the equation of circle is such.

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Step-by-step explanation:

Good luck with your friend and like you

The difference quotient of \(f(x) = x^2 - 6x + 5\) is is 2x - 6 + h.

To find the difference quotient for the function \(f(x) = x^2 - 6x + 5\), we need to evaluate

(f(x + h) - f(x)) / h, where h is not equal to 0.

First, let's find f(x + h):

\(f(x + h) = (x + h)^2 - 6(x + h) + 5\)

\(= x^2 + 2hx + h^2 - 6x - 6h + 5\)

\(= x^2 - 6x + 5 + 2hx - 6h + h^2\)

Now, we can substitute the values of f(x + h) and f(x) into the difference quotient:

\((f(x + h) - f(x)) / h = ((x^2 - 6x + 5 + 2hx - 6h + h^2) - (x^2 - 6x + 5)) / h\)

= (2hx - 6h + h^2) / h

= 2x - 6 + h

Therefore, the difference quotient of \(f(x) = x^2 - 6x + 5\) is 2x - 6 + h.

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Answer:

117

Step-by-step explanation:

1,100 - 160 = 940

940 ÷ 8 = 117.5

you round down to 117

Answer:

D. Subtract 4 from both sides

Explanation:

I just learned about quadratic equations in school. The first step of solving quadratic equations is to make sure it is in standard form and equal to 0.

Standard form:

ax^2 + bx + c = 0

The answer would be 1.03! hopes this helps!

Answer:

1.03

Step-by-step explanation:

i did the assignment on edg 2020/2021

Answer: 1/2

Step-by-step explanation:

The probabilities must add to 1, so:

\(P(x < 9) +P(X=9)+P(X > 9)=1\\\\\frac{1}{6}+P(X=9)+\frac{1}{3}=1\\\\P(X=9)=\boxed{\frac{1}{2}}\)

Answer:

48

Step-by-step explanation:

Answer:

26.5

Step-by-step explanation:

Complimentary angles are 90 degrees

90-63.5=26.5

The approximate value of the expression sec 4π / 13 is 1.76

Radian is a unit of measurement of angles equal to about 57.3° . equivalent to angle subtended at the center of a circle by a arc equal to length of radius

To Change Radian into degree, we multiple the angle with 180/π

The given Expression is

sec 4π / 13

Changing radian into Degree ,

=> 4π / 13 × 180 / π

=> 720 / 13

=> 55.38

Therefore , sec 55.38° is 1.7603

rounding off to two decimal places is 1.76

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A recipe says it produces the best summer drink. The recipe calls for 12 cup of lemonade for every 112 cups of iced tea. If 16 cups of the summer drink are made

then 8 cups of lemonade are needed.

What is unitary method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams.

5 ice-creams cost is $125.

Step 1: Let's find the cost of 1 ice cream.

In order to do that, divide the total cost of ice-creams by the total number of ice-creams.

The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-

creams = 125/5 = 25.

Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams.

The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75.

Finally, we have the cost of 3 ice-creams i.e. $75.

lemonade: tea : total

1                 1    1+1=2

We need a total of 16 and divide it

= 16/2 = 8

Then the composition will be

lemonade:    tea:        total

1*8 = 8      1*8 = 8      2*8 = 16

Hence, 8 cups of lemonade are needed.

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If the total weight of the coins is 800 kg, then there are 64 coins in total.

Without the total weight of the coins we cannot determine the total number of coins. However if the total weight of the coins is 800 kg, then we can use the following formula to determine the total number of coins:

Total number of coins = Total weight of coins / Average weight of one coin

The average weight of one coin can be calculated by taking the average of the minimum and maximum weights given in the question:

Average weight of one coin = (8 kg + 17 kg) / 2 = 12.5 kg

Now, we can plug in the values into the formula:

Total number of coins = 800 kg / 12.5 kg = 64 coins

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Answer:

No they are not equivalent.

Step-by-step explanation:

2(x - 2) + 3

First distribute the 2. It goes to both the x and also to the - 2

= 2x - 4 + 3

Add - 4 + 3

= 2x - 1

This is not equal to 2x - 7

Consider the angles are = 60,2x,3x

As we know the sum of the interior angle of a triangle is 180

60+2x+3x= 180

5x= 120

x= 24°

Angles are 2x= 2(24)= 48°

and 3x= 72°

The measure of smaller angle is 48°

The volume of a cone with a diameter of 8 cm and a height of 6 cm is

100.48 cm³.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, The height of the cone is 6 cm.

Also given the diameter of the base 2r = 8 cm hence r = 4 cm.

Therefore, The volume of this cone is,

= (1/3)π(4)²×6 cm³.

= 32π cm³.

= 100.48 cm³

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Answer:

200.96

Step-by-step explanation:

2(3.14)2^2 + 2(3.14)2*14

8*3.14 = 25.12

56*3.14 = 175.84

175.84 + 25.12 = 200.96

The probability that the first "4" will be the 8th digit generated on the TI-83 calculator is approximately 0.048, as calculated using the geometric probability formula. (option c)

To explain this calculation, we can consider the probability of generating a "4" on a single trial. Since the student is randomly generating 1-digit numbers, there are a total of 10 possible outcomes (0 to 9), and only one of these outcomes is a "4". Therefore, the probability of generating a "4" on any given trial is 1/10 or 0.1.

Since the student is generating digits one at a time, we can model the situation as a geometric distribution. The probability that the first success (i.e., the first "4") occurs on the kth trial is given by the geometric probability formula: P(X=k) = (1-p)^(k-1) * p, where p is the probability of success and k is the number of trials.

In this case, we want to find the probability that the first "4" occurs on the 8th trial. So we plug in p=0.1 and k=8 into the formula: P(X=8) = (1-0.1)^(8-1) * 0.1 = 0.9^7 * 0.1 ≈ 0.0478.

Therefore, the probability that the first "4" will be the 8th digit generated is approximately 0.048, which corresponds to option (c) in the given choices.

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The complete compound inequality is 9 <= 1.5x <= 12

From the given figure, we have'

Height = x

Base = 3

The area of a triangle is

Area = 0.5 * Base * Height

So, we have

A = 0.5 * 3 * x

Evaluate

A = 1.5x

The compound inequality is given as

9 <= A <= 12

Substitute A = 1.5x in 9 <= A <= 12

9 <= 1.5x <= 12

Hence, the complete compound inequality is 9 <= 1.5x <= 12

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Answer:

56

Step-by-step explanation:

a + 89 + b

Let a= 12 and b = -45

12 + 89 - 45

101-45

56

Investment B provides a higher value in comparison to Investment A.

Given that Investment A: A monthly investment of $200 starting now and lasting for 40 years at a 9% annual interest rate, compounded monthly.

Investment B: A monthly investment of $400 starting in 20 years and lasting for 20 years at a 9% annual interest rate, compounded monthly.

To Find Investment A (The present value of annuity due)

PVAD=PMT*(((1-(1+r)^-n)/r)*(1+r))

Here, PMT=$200,

r=0.75%

= (9/12)% monthly interest rate,

n=40*12

months=480P

VAD=$200*(((1-(1+0.75%)^-480)/(0.75%))*(1+0.75%))

= $67,933.50

Investment B (The present value of annuity)

PVA= PMT*(((1-(1+r)^-n)/r))

Here, PMT=$400,

r=0.75%

= (9/12)% monthly interest rate,

n=20*12

=240 months

PVA=$400*(((1-(1+0.75%)^-240)/(0.75%)))

= $69,354.54

∴ Investment B provides a higher value in comparison to Investment A.

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To compare the values - 1.4 and - 1.1 using a number line, the correct expression for the comparison will be the less than sign, Hence, expressed as - 1.4 < -1.1

On a number line, negative values decreases as we move to the left of the number line ; Hence, values which are situated to the leftmost part are lesser than those to their right.

The value - 1.4 tends more to the left than the value - 1.1 ; therefore, - 1.4 is less than - 1.1

Therefore, the correct expression which shows the relation is - 1.4 < - 1.1

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Answer:

4x-5y+45=0.

Step-by-step explanation:

1) formula is:

\(\frac{x-X_A}{X_B-X_A} =\frac{y-Y_A}{Y_B-Y_A};\)

2) if point A is (0;9) and point B is (5;13), then:

\(\frac{x}{5} =\frac{y-9}{13-9}; \ => \frac{x}{5} =\frac{y-9}{4}; \ => \ 4x-5y+45=0.\)

The correct option is A. The volume is 6.77 cubic units

The function and interval given are f(x) = (x - 1)^-1/4 and the x-axis on the interval (1, 6].

We want to find the volume of the solid of revolution when the region is rotated about the x-axis.

Let's consider the graph of the function: graph{(x-1)^(-1/4) [-10, 10, -5, 5]}

To set up the integral to find the volume of the solid of revolution, we can use the disk method.

We need to integrate the area of each disk perpendicular to the x-axis from x = 1 to x = 6.

The area of a disk is given by the formula: A = πr²

where r is the radius of the disk and is equal to f(x) in this case.

Therefore, the area of a disk is: A = πf(x)²

Let's substitute f(x) into this formula and integrate from x = 1 to x = 6 to get the volume of the solid.

We have The integral that should be used to find the volume of the solid is given as:

V = ∫₁⁶ πf(x)² dx

We substitute f(x) = (x - 1)^(-1/4) into this expression and integrate to get the volume.

We have: V = ∫₁⁶ π(x - 1)^(-1/2) dx

Let u = x - 1, so that du/dx = 1 and dx = du.

When x = 1, u = 0, and when x = 6, u = 5.

Therefore, we have: V = ∫₀⁵ πu^(-1/2) du= 2π[u^(1/2)]₀⁵= 2π(√5 - 1) ≈ 6.77 cubic units.

The volume of the solid of revolution when the region is rotated about the x-axis is approximately 6.77 cubic units.

Thus, the correct option is A. The volume is 6.77 cubic units.

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       Rate at which the car is moving is 27 miles per gallon.

   If we plot gallons of gas remaining in the tank at x-axis and miles driven on y-axis, points will form a linear graph.

After driving 45 miles, 15 gallons of the gas remaining in the tank will  represent a point (15, 45).

Similarly, after 153 miles gas,11 gallons of the gas remaining in the tank will form a point (11, 153).

Slope of the line joining these points will represent the rate.

Therefore, slope of the line = \(\frac{y_2-y_1}{x_2-x_1}\)

                                              = \(\frac{153-45}{15-11}\)

                                              = 27 miles per gallon

    Hence, rate at which the car is moving is 27 miles per gallon.

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the volume of the cylinder is 572.27 cm³

Given:

radius of the cylinder = 4.5cm

height = 9cm

To get the volume of the cylinder, we will use the formula:

To the nearest hundredth, the volume of the cylinder is 572.27 cm³

Answer:

u = 1/6

Step-by-step explanation:

1 (12u - 2 )= 0

3

3×1 (12u-2) =0×3

3

12u -2 =0

12u = 2

12 12

u = 1

6

Answer:

-21.6

Step-by-step explanation:

-5.4    

x  4               4x 4=16 so you carry the one to 5x4= 20 + 1 that was carried

--------           keep it negative

-21.6