The 8th grade class of City Middle School has decided to hold a raffle to raise money to fund a trophy cabinet as their legacy to the school. A local business leader with a condominium on St. Simons Island has donated a week’s vacation at his condominium to the winner—a prize worth $1200. The students plan to sell 2500 tickets for $1 each.



1) Suppose you buy 1 ticket. What is the probability that the ticket you buy is the winning ticket? (Assume that all 2500 tickets are sold. )


2) After thinking about the prize, you decide the prize is worth a bigger investment. So you buy 5 tickets. What is the probability that you have a winning ticket now?


3) Suppose 4 of your friends suggest that each of you buy 5 tickets, with the agreement that if any of the 25 tickets is selected, you’ll share the prize. What is the probability of having a winning ticket now?


4) At the last minute, another business leader offers 2 consolation prizes of a week-end at Hard Labor Creek State Park, worth around $400 each. Have your chances of holding a winning ticket changed? Explain your reasoning. Suppose that the same raffle is held every year. What would your average net winnings be, assuming that you and your 4 friends buy 5 $1 tickets each year?

Answer:

\( \huge{ \boxed{ \tt{1 }}}\)

❁ Question : Simplify :

❁ Solution :

First , Use power law of indices.

Remember : If \( \sf{ {a}^{m} }\) is an algebraic term , then

\( \sf{( {a}^{m} ) ^{n} } = {a}^{m \times n} = {a}^{mn} \) , where m and n are positive integers.

➝ \( \sf{ {x}^{a(b - c)} \times {x}^{b(c - a)} \times {x}^{c(a - b)}} \)

➝ \( \sf{ {x}^{ab - ac} \times {x}^{bc - ba} \times {x}^{ca - cb}} \)

Now , Use product law of indices :

Remember : If \( \sf{ {a}^{m} }\) and \( \sf{ {a}^{n}} \) are the two algebraic terms , where m and n are the positive integers then \( \sf{ {a}^{m} \times {a}^{n} = {a}^{m + n}} \)

➝ \( \sf{ {x}^{ab - ac + bc - ba + ca - cb}} \)

Since two opposites adds up to zero , remove them :

➝ \( \sf{ {x} \: ^{ \cancel{ab} \: - \cancel{ac} \: + \cancel{bc} \: - \cancel{ba} \: + \cancel{ca} \: - \cancel{cb} } }\)

➝ \( \sf{ {x}^{0} }\)

Use Law of zero index

Remember : If \( \sf{ {a}^{0}} \) is an algebraic term , where a ≠ 0 , then \( \sf{ {a}^{0} = 1}\)

➝ \( \boxed{ \sf{1}}\)

And we're done !

Hope I helped ! ♡

♪ Have a wonderful day / night ツ

~~

Answer:

Step-by-step explanation:

We know that Jonathan bought the desk for $24, so the cost of the desk before any profit is $24.

After the 525% profit, the cost of the desk will be increased by 525% of $24, which is:

525% of $24 = (525/100) x $24 = $126

So the cost of the desk after the 525% profit is:

C = $24 + $126 = $150

Therefore, Jonathan sold the desk for $150.

Answer:

$25.20

Step-by-step explanation:

First, take the 50% off the sales price:

($48)*(-0.50) = -$24.

($48 - $24) = $24 sale price.

Tax on $24 is ($24)*(0.05) = $1.20

Add the price and sales tax:

$24 + $1.20 = $25.20

Answer:

.5

Step-by-step explanation:

this is the answer I got out of my calculator. so your answer is going to be your second choice.

The question number 33 have the measure of the unknown angle m∠CAF = 32°.

We are given the angle m∠EBG = 19°, and it is observed that m∠EBG and m∠EAF are the same, so;

m∠EBG = m∠EAF = 19°

Since m∠CAE = 51°, then unknown angle;

m∠CAF = m∠CAE - m∠EAF

m∠CAF = 51° - 19°

m∠CAF = 32°

Therefore, the unknown angle m∠CAF is equal to 32°.

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Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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Answer: 700

Step-by-step explanation:

175 * 4 = 700

Answer:

700

Step-by-step explanation:

To solve this problem you multiply 175 by 100 and then divide the total by 25 as follows: (175 x 100) / 25

When we put that into our calculator, we get the following answer:

700

Thus, the output of the loop is non-deterministic.

Let us consider the loop and the conditions given:

While the condition `x ≠ 0` holds, the loop will continue.

Within the loop, there are two possible paths: `y:=y1` or `y:=y2`.

Since the path to take is non-deterministic, there are two possible outputs:

Either y will be assigned a value of y1 or y2.

Here, it is impossible to determine which assignment will be executed; there is no way to know if x will be decremented once or twice.

This demonstrates that the behavior is non-deterministic, and the possible outputs are `[y1,y2]`.

Thus, the output of the loop is non-deterministic.

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Answer:

x^2+6x+9

Step-by-step explanation:

x^2 +6x

Take the coefficient of x

6

Divide by 2

6/2 = 3

Square it

3^2 = 9

Add 9 to each side

x^2+6x+9

Answer:

1.4 estimated to the nearest tenth

Answer:

3840

Step-by-step explanation:

thbyrtjnbyj

To find the average amount that Sarah saved per month over the last six months, we need to add up the total amount saved and divide by the number of months.

Total amount saved = $135.00 + $144.00 + $104.00 + $80.00 + $90.00 + $160.00 = $713.00

Number of months = 6

Average amount saved per month = Total amount saved / Number of months = $713.00 / 6 = $118.83

Therefore, the correct answer is d. $118.83.

It is important to note that when working with numbers and calculations, accuracy is crucial. In this case, rounding off the answer to the nearest cent would result in a different answer.

Additionally, checking the calculations multiple times to ensure accuracy is always recommended.

Overall, tracking and analyzing expenses and savings is important for financial planning and achieving financial goals. By keeping track of how much she saved each month,

Sarah can make informed decisions about her spending and saving habits and adjust accordingly to reach her vacation savings goal.

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The figure that is not equivalent to 2¾ is 2¼ × 2½. That is option B.

Simplification is a process that is used to make a fraction appear in its simplest forms.

The fraction given is = 2¾

The simplification of the fraction= 2^3/4 = 2

But simplification of 2¼ × 2½ is equal to;

2¼= 0.5

2½= 1

Therefore 2¾ is not equivalent to 2¼ × 2½ when simplified.

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Answer:The midpoint can be any middle part of a line, and the perpendicular Bisector is can only be 90 degrees.

Answer:

Nnnnnnnnnnnn

Step-by-step explanation:

L bozo

Answer:

The answer is

Equation: y+-3=-8

Solution: y= -5

Step-by-step explanation:

Hope this helps!

There are 35 possible designs for the printed circuit board with four different components placed on it, assuming each of the seven locations can hold only one component.

To calculate the number of possible designs for the printed circuit board with seven locations for component placement, we can use the combination formula.

The number of combinations of r items from a set of n items is given by the formula:

nCr = n!/r!(n-r)!

In this case, we want to find the number of combinations of four components from seven locations. Thus, we can calculate it as follows:

7C4 = 7!/4!(7-4)! = (7x6x5)/(3x2x1) = 35

Therefore, there are 35 possible designs for the printed circuit board with four different components placed on it, assuming each of the seven locations can hold only one component.

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Answer: quantifies the economic devastation of natural and man-made disasters

Within-groups design compares the same subjects across time. In this design, participants are measured or observed on multiple occasions, such as before and after an intervention or at different time points.

The purpose of the within-groups design is to examine changes within individuals over time, allowing researchers to assess the impact of an intervention or the natural progression of a phenomenon within the same group of subjects.

By comparing the same subjects across time, within-groups designs help to control for individual differences and increase the internal validity of the study.

This design allows researchers to evaluate the effectiveness of an intervention by assessing changes within individuals and determining if those changes are statistically significant.

It also allows for a more precise assessment of the impact of an intervention or the stability of a phenomenon over time.

Within-groups designs are commonly used in fields such as psychology, education, and medicine to study changes in behavior, cognition, or health outcomes.

They provide valuable insights into individual responses to interventions or the natural course of development or disease progression within a specific group of subjects.

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The remaining credit after 50 minutes of calls is given as follows:

$22.38.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For 17 minutes, the amount of credit decays by $2.85, hence the slope m is given as follows:

m = -2.85/17

m = -0.1676.

50 minutes is seven minutes after 43 minutes, hence the amount remaining is given as follows:

23.55 - 7 x 0.1676 = $22.38.

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The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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False because descriptive statistics doesn't make any prediction, but inferential statistics make predictions about a population based on a sample of data taken from the population.

Descriptive statistics are informational coefficients that summarize a given data set, but they can't make predictions about the population based on a sample of data for the example is chart or graph.

It has differences from Inferential statistics which allow you to test a hypothesis or prediction from the data. The prediction is made by collecting the sample of data which is taken from the population such as calculating the z-score or ANOVA test.

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Answer:

y = 1/2x + 2

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,2) (2,3)

We see the y increase by 1 and the x increase by 2, so the slope is

m = 1/2

Y-intercept is located at (0,2)

So, the equation of the line is y = 1/2x + 2

Another possible vertex of the square is determined as (2, 1).

option B is the correct answer.

The vertex of a figure is the point of intersection of two sides of the shape.

The perimeter of the square is given as 12 units, the length of each side of the square is calculated as follows;

P = 12 units

a side length = 12 units / 4 = 3 units

To determine another possible vertex of the square, the length between the points must be equal to 3.

Let's consider point A;

A = (1, 2)

given vertex = (-1, 1)

distance between the points = √ (-1 -1)² + (1 - 2)² = √5

Let's consider point B;

B = (2, 1)

given vertex = (-1, 1)

distance between the points = √ (-1 -2)² + (1 - 1)² = √9 = 3

Thus, point B is another possible vertex of the square.

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To use Lagrange multipliers to find the shortest distance from the point (7, 0, −8) to the plane x y z = 1, we need to set up the following optimization problem:

Minimize the distance function D(x, y, z) = √((x-7)^2 + y^2 + (z+8)^2) subject to the constraint f(x, y, z) = x y z - 1 = 0.

Using Lagrange multipliers, we set up the following system of equations:

∇D(x, y, z) = λ∇f(x, y, z)
f(x, y, z) = 0

Taking the partial derivatives, we have:

∇D(x, y, z) = (x-7, y, z+8)
∇f(x, y, z) = (y z, x z, x y)

Setting these equal to each other and solving for x, y, z, and λ, we get:

x-7 = λ y z
y = λ x z
z+8 = λ x y
x y z = 1

Multiplying the first three equations together and using the fourth equation, we get:

(x-7)yz = λxzy = (z+8)xy
(x-7)yz = (z+8)xy
xz - 7z = yz + 8xy
xz - yz = 8xy + 7z
z(x-y) = 8xy + 7z
z = (8xy)/(y-x)

Substituting this into the equation x y z = 1, we get:

x y (8xy)/(y-x) = 1
8x^2 y - xy^2 = x^2 y - xy^2
7x^2 y = 0
x = 0 or y = 0

If x = 0, then we have yz = 1, and substituting into the equation z = (8xy)/(y-x), we get z = -8, which is not on the plane x y z = 1.

If y = 0, then we have xz = 1, and substituting into the equation z = (8xy)/(y-x), we get z = -1/8.

Therefore, the point on the plane x y z = 1 closest to the point (7, 0, −8) is (0, 0, -1/8), and the shortest distance is:

D(0, 0, -1/8) = √((0-7)^2 + 0^2 + (-1/8+8)^2) = √(49 + 63/64) ≈ 7.98.

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Answer:

Options A, B, C and D

Step-by-step explanation:

This question is not complete; here is the complete question.

Tori bought 24 candy bars for 69 cents each. She used partial products to find the total cost in cents. Which are NOT possible partial products for 24 × 69?

A. 24

B. 36

C. 180

D. 240

E. 1656

Cost of one candy = 69 cents  

Since, cost of 24 candies = Cost of one candy × Number of candies

                                          = 69 × 24

For partial product,

69 × 24 = (60 + 9)(20 + 4)

             = 60(20 + 4) + 9(20 + 4)

             = 60×20 + 60×4 + 9×20 + 9×4

             = 1200 + 240 + 180 + 36

             = 1656

Therefore, Options A, B, C and D are not possible partial products.

Answer:

33 / the second one

Step-by-step explanation:

5 x 5 = 25

4 x 2 = 8

25 + 8 = 33

Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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The dimensions of the field should be 125m by 100m to enclose the maximum area.

To solve this problem, we can use the fact that the area of a rectangle is given by A = lw, where l and w are the length and width of the rectangle, respectively. Since the field is to be subdivided into four congruent plots, we can express the width in terms of the length as w = (1/4)(l).

We can then use the fact that the total length of fencing available is 6000m to set up an equation for the perimeter of the rectangle, which is given by P = 2l + 5w. Substituting w with (1/4)(l), we get P = 2l + 5((1/4)(l)) = (9/2)l.

Solving for l in terms of P, we get l = (2/9)P. Substituting this expression for l into the equation for the area, we get A = (1/4)(l)(w) = (1/4)(l)((1/4)(l)) = (1/16)l^2.

We can now express the area in terms of P as A = (1/16)((2/9)P)^2 = (4/81)(P^2). To find the maximum area, we can take the derivative of A with respect to P and set it equal to zero, which gives dA/dP = (8/81)P = 0. This implies that P = 0 or P = 81/8. Since P cannot be zero, we have P = 81/8.

Substituting this value of P back into the equation for l, we get l = (2/9)(81/8) = 18.75. Finally, substituting l and w = (1/4)(l) into the equation for A, we get A = (1/16)(18.75)(4.6875) = 117.1875. Therefore, the dimensions of the field should be 125m by 100m to enclose the maximum area.

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The rate of change of angle of elevation between the radar station and airplane is

                       \(\displaystyle \frac{-10}{109} \left(\frac{rad}{min}\right)\)

The airplane is flying at the speed of 200 mph

The airplane is at an altitude of 3 miles over the radar station

The distance travelled by the airplane after 3 mins

      distance = speed x time

                     = 200 mi/hr x 3 min

Since the speed is hour let us convert it to mins

                     = 200 x 3 x 1/60

                     = 600 / 60

                    = 10 miles

So , let us assume that the airplane is exactly at the top of the radar station at an altitude of 3 miles

Then the elevation angle of the between radar station and airplane can be find by

                              tan θ = O / A
where O is the opposite side to the angle of elevation

          A is the adjacent side to the angle of elevation.

But we need the find the rate of change of angle of elevation , so let us differentiate on both side with respect to time

                                \(\displaystyle sec^{2}\theta\frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{A^{2}}\)

                                        \(\displaystyle \frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{sec^{2}\theta A^{2}}\)

                                       \(\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{sec^{2}(10)^{2}}\)

The altitude is gonna be a constant , thus the derivative of altitude will be zero whereas , the the distance travelled by airplane is changing with respect to time.

                                   \(\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{\frac{109}{100}(10)^{2}}\)

We had found the value of sec²θ = (hyp/adj)²

                                    \(\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \frac{rad}{hr}\)

Now , let us convert in terms of rad/min

                                   \(\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \left(\frac{1}{60}\right)\)

                                  \(\displaystyle \frac{d\theta}{dt} = \frac{-10}{109} \left(\frac{rad}{min}\right)\)    

Therefore , the rate of change of angle of elevation is -10/109 (rad/min)    

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