Free response: 3 questions, 52 points, 30 minutes
1. blinko is a game in which three dice are rolled. to win the game, a player must
roll triples – that is, three of the same number. you roll the dice 20 times.
a. verify that the situation is binomial. (8points)
b. out of 20 rolls, what is the probability you win exactly 4 times? show your
work using the formula for binomial probability. (6 points)
c. what is the probability that you win at least 3 times? (6 points)
d. what is the mean number of wins in 20 rolls of the dice?

The equation of the ellipse with center (1, -3), and a semi major axis of 4, and a semi minor axis of 3 is; (x - 1)²/4² + (y + 3)²/3²

The standard form equation of an ellipse can be presented as follows;

(x - h)²/a² + (y - k)²/b² = 1

Where;

(h, k) = The coordinates of the center of the ellipse.

The length of the semi major axis = a

Length of the semi minor axis = b

The center of the specified ellipse is; (h, k) = (1, -3)

The semi major axis = 4

The length of the semi minor axis = 3

The equation of the ellipse is therefore;

(x - 1)²/4² + (y - (-3))²/3² = 1

(x - 1)²/4² + (y + 3)²/3² = 1

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Answer: 720

Step-by-step explanation: 1800 x 40%

Answer:

720 math books

Step-by-step explanation:

1800×40%= 720

there are 720 math books

The salesman's actual profit earnings after suffering a 5% loss due to damages when assembling the computer is $14,820.

Let's first calculate the original cost price of the computer to the salesman. We know that the salesman sold the computer for $15,600 and made a profit of 25%, which means that the selling price is 125% of the cost price.

Let the cost price of the computer be x.

Selling price = 125% of cost price

$15,600 = 1.25x

Solving for x, we get:

x = $12,480

So, the salesman's cost price of the computer was $12,480.

Now, the salesman suffered a loss of 5% due to damages when assembling the computer.

Loss = 5% of cost price

Loss = 5% of $12,480

Loss = $624

So, the actual earnings of the salesman after the loss is: $15,600 - $624 = $14,820.

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This expression is not a polynomial, and it doesn't have a type or degree.

The expression zx^3/9-x^3 can be simplified as:

zx^3/(9-x^3)

This expression is not a polynomial because it contains a variable (x) in the denominator, which makes it a rational expression.

A polynomial is an expression of one or more terms involving only constants and variables raised to positive integer powers, with no variables in the denominators.

Therefore, this expression is not a polynomial, and it doesn't have a type or degree.

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0 J. When the child carries the box at a constant speed, the net force on the box is zero because there is no acceleration. Therefore, the work done by the child on the box is zero. So, the correct option is 0 J.

To determine the amount of work done by the child while walking across the floor at a constant speed, we need to consider the following terms: work, force, and displacement.

Work is the amount of energy transferred when a force is applied over a certain distance. It is calculated as:

Work = Force x Distance x cos(θ)

where Force is the applied force, Distance is the displacement, and θ is the angle between the force and displacement vectors.

When the child carries the box with a constant speed across the room, the force applied is equal to the gravitational force acting on the box (i.e., the weight of the box). However, since the force and displacement are in different directions (the force is acting vertically, while the displacement is horizontal), the angle between the force and displacement is 90 degrees.

Now, we know that cos(90°) = 0. Thus,

Work = Force x Distance x cos(90°) = Force x Distance x 0 = 0 J

So, the work done by the child on the box while walking across the floor at constant speed is 0 J.

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The area of the first triangle is 0 square feet.

To find the area of the first triangle with the given side lengths of 1 ft, 3 ft, and 4 ft, you can use Heron's formula.

Calculate the semi-perimeter (s) of the triangle:
s = (a + b + c) / 2
where a, b, and c are the side lengths of the triangle.
s = (1 + 3 + 4) / 2 = 8 / 2 = 4 ft

Apply Heron's formula to find the area (A) of the triangle:
A = √(s * (s - a) * (s - b) * (s - c))
A = √(4 * (4 - 1) * (4 - 3) * (4 - 4))
A = √(4 * 3 * 1 * 0)
A = √0 = 0

The area of the first triangle is 0 square feet. This means that the given side lengths do not form a valid triangle, as two sides' lengths (1 ft and 3 ft) do not add up to be greater than the length of the third side (4 ft).

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Answer:

43.96 cm

Step-by-step explanation:

Given

Radius ( r ) = 7 cm

To find : Circumference of Circle

Formula

Circumference of Circle = 2πr

Note

The Value of π = 3.14

Circumference of Circle

= 2πr

= 2 × 3.14 × 7

= 43.96 cm

Answer:

Not Rounded: 43.9822971503

Rounded: 44

Step-by-step explanation:

r= radius

2[tex]\pi[/tex]r

2[tex]\pi[/tex](7)

= 43.9822971503

The population increased by a percentage of 5%.

The population of Sanibel, Florida in 2016 can be determined using the given population model P = 6191 * 1.05^t, where t represents the number of years since 2016. To find the population in 2016, we set t to 0 since there are 0 years since 2016.

Step 1: Set t to 0 in the equation:
P = 6191 * 1.05^0

Step 2: Calculate the population P:
P = 6191 * 1
P = 6191

So, the population in Sanibel, Florida in 2016 was 6,191.

Regarding the percent population increase each year, the given model uses an exponential growth formula with a constant factor of 1.05. The factor (1.05) represents a 5% increase in the population each year.

In summary, the population in Sanibel, Florida in 2016 was 6,191, and the population increases by 5% each year. This exponential growth model demonstrates how the population continues to grow at a steady rate, contributing to the overall population increase in the area.

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Answer:

x=81

Step-by-step explanation:

Rewrite log_3 (x)=4 in exponential form using the definition of a logarithm. If x and b are positive real numbers and b≠1, then log_b(x)=y is equivalent to b^y=x.

Rewrite the equation as x=3^4

Raise 3 to the power of 4 

x=81

Answer:

1024

Step-by-step explanation:

I hope everything I wrote is clear, I really need to sharpen my pencil oof

The overall limit is undefined as the the second limit is undefined

The given limit is of the indeterminate form 0/0 and hence we can apply l'Hôpital's Rule to evaluate it.

Applying l'Hôpital's Rule, we get:

lim sin(3x) / (3x) = lim [cos(3x) * 3] / 3 = cos(3x)

Now, we need to evaluate lim (3x)/(1 - cos(x)) as x approaches 0.

Again, this limit is of the indeterminate form 0/0, so we can apply l'Hôpital's Rule once again:

lim (3x)/(1 - cos(x)) = lim (3)/(sin(x)) = 3/0 (which is undefined)

Since the second limit is undefined, the overall limit is also undefined.

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Answer:

(8/√2)^2 = 64/2 = 32 square inches

The height of the trapezoid is 9 yards. Therefore, the correct answer is option b. 9 yd.

To find the height of the trapezoid with the given area and base lengths, we will use the formula for the area of a trapezoid:

Area = (1/2) * (base1 + base2) * height

Here, the area is given as 126 square yards, base1 is 17 yards, and base2 is 11 yards. We need to find the height.

1. Substitute the given values into the formula:

126 = (1/2) * (17 + 11) * height

2. Simplify the equation:

126 = (1/2) * 28 * height

3. To isolate the height, divide both sides by (1/2) * 28:

height = 126 / ((1/2) * 28)

4. Calculate the result:

height = 126 / 14

height = 9

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a) The graph of the given lines is as attached

b) The area of the enclosed triangle is: 8 square units

The general form of expression of linear equations in slope intercept form is expressed as:

y = mx + c

where:

m is slope

c is y-intercept

We are given the equations as:

y = x + 5

y = 5

x = 4

The graph of these three linear equations is as shown in the attached file

2) The area of the given triangle enclosed by the three lines is gotten from the formula:

A = ¹/₂ * b * h

where:

A is area

b is base

h is height

Thus:

A = ¹/₂ * 4 * 4

A = 8 square units

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Step-by-step explanation:

First start with the graph of    y = | x|

  then shift it RIGHT one unit

         | x -1 |

  then shift it DOWN one unit

  y=   |x-1| -1

Answer: To find the vertex of the graph of the equation Y=3x^2+6x+1, we can use the formula:

x = -b/2a

where a = 3 and b = 6, which are the coefficients of the x^2 and x terms, respectively.

x = -6/(2 x 3) = -1

Substituting x = -1 into the equation, we get:

Y = 3(-1)^2 + 6(-1) + 1 = -2

Therefore, the vertex of the graph is (-1, -2), so the answer is A. (-1,-2).

Step-by-step explanation:

discount amount= CP-Disount percentage

or,480=CP-25/100

or480×100+25 =CP

48025 is the original price of shirt

Answer: 1.3

Step-by-step explanation:

The interest accrued after one month at a rate of 15.5% on a principal amount of $1,000 is $12.92.

To use the formula I=Prt to calculate the interest accrued after one month at a rate of 15.5%, we need to know the principal amount (P) and the time period (t) in years.

Assuming that the principal amount is $1,000, and the time period is one month, which is equivalent to 1/12 of a year, we can calculate the interest as follows:

[tex]I = Prt[/tex]

[tex]I[/tex] [tex]= 1000 x 0.155 x (1/12)[/tex]

[tex]I = $12.92[/tex]

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For Camden the equation is c = 18 + 11t and for Violet the equation is v = 39 + 8t. After 2 days, Camden will be on page 40 and Violet will be on page 55.

Let's represent the situation with two equations, one for Camden (c) and one for Violet (v), using the given information and the variable t for the number of days.

Camden:
At the beginning of the month, Camden was on page 18 and will read 11 pages per day. So, his equation will be:
c = 18 + 11t

Violet:
At the beginning of the month, Violet was on page 39 and will read 8 pages per day. So, her equation will be:
v = 39 + 8t

Now, we need to determine who is farther along in the book after 2 days. To do this, we will substitute t = 2 into both equations.

Camden's equation (c):
c = 18 + 11(2)
c = 18 + 22
c = 40

Violet's equation (v):
v = 39 + 8(2)
v = 39 + 16
v = 55

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Unfortunately, this integral doesn't have a simple closed-form solution. However, you can use numerical methods or software like Wolfram Alpha or a graphing calculator to approximate the value of the integral.

We have:

y = t and ds = sqrt(9t^4 + 1) dt

So, the line integral becomes:

∫C y^3 ds = ∫0^5 (t^3)(sqrt(9t^4 + 1)) dt

Using the substitution u = 9t^4 + 1, we get du/dt = 36t^3, which means dt = du/36t^3. Also, when t = 0, u = 1 and when t = 5, u = 1126.

Substituting these values and simplifying, we get:

∫C y^3 ds = (1/36) ∫1^1126 (u-1/4)(1/2) du
= (1/72) [(u-1)^2 u^(1/2)]_1^1126
= (1/72) [(1125)^2 (1126^(1/2)) - (1)^2 (1^(1/2))]

= 3555.89 (approx)

Therefore, the line integral is approximately equal to 3555.89.
To evaluate the line integral along the curve C with the given parameterization x = t^3 and y = t for 0 ≤ t ≤ 5, we need to find the integral of y^3ds. First, we need to find the derivative of the parameterization with respect to t:

dx/dt = 3t^2
dy/dt = 1

Now, we can find the differential arc length ds, which is given by the formula:

ds = √((dx/dt)^2 + (dy/dt)^2) dt

ds = √((3t^2)^2 + (1)^2) dt
ds = √(9t^4 + 1) dt

Next, substitute the parameterization of y in terms of t (y = t) into the integral:

∫(y^3 ds) = ∫(t^3 √(9t^4 + 1)) dt, with limits 0 to 5.

Now, evaluate the integral:

∫(t^3 √(9t^4 + 1)) dt from 0 to 5.

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If you let z be a random variable with a standard normal distribution, the indicated probability is 0.0793. So, the probability P(z ≥ 1.41) = 0.0793

To find the probability P(z ≥ 1.41) for a standard normal distribution, you can use a Z-table or calculator to find the area to the right of z = 1.41.

Using a Z-table or calculator, you will find the value of P(z ≥ 1.41) is approximately 0.0793. So, the probability P(z ≥ 1.41) = 0.0793. Remember to round your answer to four decimal places.

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The maximum area of the quadrilateral is achieved when it is a square with a side length of 50cm, resulting in an area of 2500cm².

This is because a square has equal sides and equal angles,

resulting in the most efficient use of the perimeter to enclose the maximum area.

To see why, consider a rectangle with a perimeter of 200cm.

If the rectangle is long and thin, with one side much longer than the others,

then it will have a smaller area than a square with the same perimeter.

This is because the longer sides of the rectangle will be less effective at enclosing area than the shorter sides.

Hence, The maximum area of a quadrilateral with a minimum perimeter of 200cm is achieved when the quadrilateral is a square.

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The measure of ∠4 is 151°.

The equation that can be used to solve for the value of x is: 3x - 8 = 151°

The value of x is 53.

(a) The measure of ∠4 is found as follows:

∠2 + ∠4 = 180° ( sum of angles on a straight line)

However, ∠2 = 29°

29° + ∠4 = 180°

∠4 = 180° - 29°

∠4 = 151°

(b) The equation that can be used to solve for the value of x is found as follows:

∠3 = ∠4 ( vertical angles are equal)

Substituting for ∠3 = 3x - 8 and ∠4 = 151°,

3x - 8 = 151°

(c) The value of x is detremined as follows:

3x - 8 = 151°

3x = 159°

x = 53

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The equation that can be used to compute the number of pieces of jewellery is ($120 + $15q)/q = $20 .

Average cost is total cost divided by the quantity of jewellery sold.

Average cost = total cost / quantity

Total cost is the sum of fixed cost and variable cost.

Total cost = fixed cost + variable cost

The fixed cost is the cost of renting the stall. The variable cost is the cost of the materials.

Total cost = $120 + ($15 x q)

T = $120 + $15q

Average cost = ($120 + $15q)/q = $20

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The equation of demand of candle sticks can be modeled by

y = 14 - 0.02x while the revenue function will be xy = 14x - 0.02x².

Here we are given the information that

200 candles are sold for $10 and,

250 candles are sold for $9

Let the Price be y while the Quantity sold be x

Hence, by one unit decrease in price P, the quantity sold is increased by 50 units.

Here the slope of the function will be

(10 - 9)/(200 - 250)

= - 1/50

= - 0,02

Now we will use the formula of the equation of a straight line

(y - y₁) = m(x - x₁)

where, m is the slope and x₁ , y₁ are some point on line

Hence we get

(y - 10) = -0.02(x - 200)

or, y - 10 = -0.02x + 4

or, y = 14 - 0.02x

The revenue function will be xy = 14x - 0.02x²

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Correct Question

A candlemaker prices one set of scented candles at $10 and sells an average of 200 sets each week. he finds that when he reduces the price by $1, he then sells 50 more candle sets each week. a function can be used to model the relationship between the candlemaker's weekly revenue, r(x), after one-dollar decrease in price. this situation can be modeled by the equation y =

The value of m is 11, and the divisibility test states that n is divisible by 11 if and only if the alternating sum of its two-digit chunks is divisible by 11.

Let's consider the given divisibility test proposed by Lizzie. The process involves breaking a positive integer, n, into two-digit chunks and finding the alternating sum of these chunks. The alternating sum is obtained by adding the first number, subtracting the second, adding the third, and so on.

To find the value of m that makes this a divisibility test, we need to analyze the properties of this test. Let's assume that n is divisible by m.

When n is divisible by m, each two-digit chunk in n will also be divisible by m. This means that the alternating sum of these chunks will also be by m since adding or subtracting multiples of m will not change its divisibility.

Conversely, if the alternating sum of the two-digit chunks is divisible by m, it implies that each chunk is divisible by m. Therefore, if the chunks are divisible by m, the original number n will also be divisible by m.

Hence, this process indeed serves as a divisibility test for m, where n is divisible by m if and only if the result of the alternating sum of the two-digit chunks is divisible by m.

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The speed of the boat is 21 km/h and the speed of the stream is 2 km/h.

Answer:

It's fascinating to observe how the volume of different shapes can vary based on their measurements. For instance, a cylinder with a height of 6 centimeters and radius r1 has a volume of 302 cubic centimeters. Do you require further assistance?

As for the new set of instructions, please consider the following statements:

6. Sometimes true. The period of the function is determined by the formula T= 2π/b, where b is the coefficient of x in the argument of the sine function. In this case, b = π/5, so T= 10.

7. Always true. The maximum height of the object is equal to the amplitude of the function plus the vertical shift, which is 55 centimeters.

8. Sometimes true. The minimum height of the function occurs when the sine function has a value of -1, which happens at x= h-5. So, if h= 0, then x= -5, which means the statement is sometimes true depending on the value of h.

9. Always true. The midline of the function is determined by the vertical shift, which is 55 in this case.

10. Always true. The amplitude of the function is given by A= |b|, where b is the coefficient of x in the argument of the sine function. In this case, A= 42π/5, which simplifies to 84.

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