Of 5,000 high school students surveyed, 85% said they would be willing to pay $5.00 to see a play at their school. How many of the 520 students at Fair Oaks High would be willing to pay $5.00 to see a play at their school?

The probability of winning the lottery after at least n trials, we can use the formula: P(X≤ n) = 1 - (1-p)^n

Where X is the number of trials needed to win the lottery, p is the probability of winning the lottery in each trial, and n is the minimum number of trials we are considering.

To understand the above formula, we need to consider the probability of winning the lottery in each trial. Let's assume that the probability of winning the lottery in each trial is p. Therefore, the probability of not winning with the same ticket is 1-p in each trial.

Now, let's consider the random variable X, which represents the number of trials needed to win the lottery. If we want to calculate the probability of winning the lottery after at least n trials, we need to find the probability of winning in the first n trials, plus the probability of winning in the (n+1)th trial or any subsequent trial.

The probability of winning in the first n trials can be calculated using the binomial distribution formula, which is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where k is the number of trials in which we win the lottery.

However, we are interested in finding the probability of winning after at least n trials, which means that we need to consider all possible values of k greater than or equal to n. Therefore, we can use the cumulative distribution function (CDF) of the binomial distribution to calculate the probability of winning after at least n trials, which is:

P(X≥ n) = 1 - Σ P(X=k) for k=0 to n-1

This formula calculates the probability of winning the lottery in the first n-1 trials and subtracts it from 1 to get the probability of winning in the nth trial or any subsequent trial.

However, we are interested in the probability of winning after at least n trials, not just in the nth trial or any subsequent trial. Therefore, we can rewrite the above formula as:

P(X≤n) = 1 - P(X>n-1)

Which gives us the probability of winning the lottery after at least n trials, using the complement rule of probability.

Finally, substituting the binomial distribution formula in the above formula, we get:

P(X≤n) = 1 - (1-p)^n

This formula gives us the probability of winning the lottery after at least n trials, based on the probability of winning the lottery in each trial and the minimum number of trials we are considering.

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So, the closest total balance Sue will have in the two accounts at the end of 5 years is approximately $2,028.80.

The initial deposit of $600 in Account A will accumulate interest at a flat rate of 7.5% over five years resulting in the final amount valued at $825.

For Account B, which utilizes an alternative principal and compounded interest formula, the deposit starts at $900 with a time duration of 5 years while calculated annually at a percentage rate of 6%.

After computing these figures utilizing the specialized formula provided, the overall total balance would be approximately worth $1203.80 rounded to its nearest full cent.

By adding together the calculated balances for both accounts, Sue's closest estimated combined balance value after 5 years summed up to approximately $2,028.80.

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Sue opened two different savings accounts.

Account A: $600 deposit at a 7.5% simple interest

Account B: $900 deposit at a rate of 6% compounded annually

Sue does not deposit additional money into the accounts and she doesn't withdraw any money from the accounts after her initial deposit

If Sue does not deposit additional money into the accounts and she doesn't withdraw any money from the accounts, which is closest to the total balance she will have in the two accounts at the end of 5 years

The correct point-slope equation for the line that passes through the point (-4,-2) and is parallel to the line given by y = 5x + 44 is: A. y + 2 = 5(x + 4)

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since the line is parallel to y = 5x + 44, the slope is equal to 5.

At data point (-4, -2) and a slope of 5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-2) = 5(x - (-4))  

y + 2 = 5(x + 4)

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The possible prices of the charm is $4 and $8, based on stated depiction of their prices.

Firstly, the multiple of 4 that lead to 12 are 3. The multiples 1, 2 and 3 wil result in 4, 8 and 12. Since the total cost is 12, so it is not possible that 3 times of 4 can be among answers.

Now, possible cost of each sea shell charm can be multiple of 1 and 2. Hence, the possible price of each sea shell charm wil be $4 and $8.

Validating the answer as follows -

Total cost = sum of cost of each sea shell charm

12 = 4 + 8

12 = 12

Since LHS is same as RHS, the estimated possible cost is true.

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Answer:

The mode is 2.

Step-by-step explanation:

Two people voted for 0 pets and two people voted for four pets.

The number, 2 showed more than the rest of the numbers, if the number of people were to be on the bottom the graph would be impossible because of the two graphs with the number 1.

It is a useful tool for marketers and managers to plan product launches, allocate resources, and estimate potential market share.

The Bass forecasting model is a popular approach used in marketing and management to forecast the adoption of new products or services by consumers. It is based on the assumption that the adoption of a new product is driven by two factors: innovation and imitation.

The coefficient of innovation (p) represents the likelihood of adoption due to a potential adopter's intrinsic motivation or independent decision-making process to adopt the product, while the coefficient of imitation (q) represents the likelihood of adoption due to a potential adopter being influenced by someone who has already adopted the product.

The coefficient of imitation captures the network effect of adoption, where early adopters serve as opinion leaders and influence others to adopt the product. As more people adopt the product, the likelihood of adoption for potential adopters increases due to social influence and perceived social norms. This creates a positive feedback loop, leading to an S-shaped adoption curve over time.

The Bass model combines the coefficients of innovation and imitation to forecast the cumulative number of adopters over time. It is a useful tool for marketers and managers to plan product launches, allocate resources, and estimate potential market share.

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The assumption of the independent samples t-test that the populations from which the samples are drawn have equal variability is known as the homogeneity of variances or homoscedasticity.

The assumption of homogeneity of variances, also known as homoscedasticity, in the independent samples t-test states that the populations from which the samples are drawn have equal variability or spread. In other words, the standard deviations of the two populations being compared should be roughly the same.

This assumption is important because it affects the accuracy of the t-test in determining whether there is a significant difference between the means of the two groups. Violation of this assumption can lead to inaccurate results and affect the validity of the t-test. If the assumption is not met, alternative tests, such as Welch's t-test or non-parametric tests, may be more appropriate.

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Answer:

x=15

Step-by-step explanation:

5x+17+36=128

5x+53=128

5x=75

x=15

Answer:  kg⋅m/s2,

Step-by-step explanation:

I hope you do well on your test Good luck!!!

To determine if it is possible for Sean to have purchased 15 hamburgers and 17 slices of pizza for the baseball team, we can calculate the total cost of the order using the given information.

The regular price of 15 hamburgers is 15 x $5.00 = $75.00

The regular price of 17 slices of pizza is 17 x $4.00 = $68.00

If Sean received a 50% discount on each slice of pizza when ordered with a hamburger, then he would have saved 50% x $4.00 = $2.00 on each slice of pizza. Since he ordered 17 slices of pizza and 15 hamburgers, he would have received the discount on 15 slices of pizza, resulting in a total discount of 15 x $2.00 = $30.00.

Therefore, the total cost of Sean's order would be $75.00 + $68.00 - $30.00 = $113.00.

Since the total cost of Sean's order is $124.00, it is not possible for him to have purchased 15 hamburgers and 17 slices of pizza for the baseball team.

Therefore, the answer is C. It is not possible because the total cost for 15 hamburgers and 17 slices of pizza would have been $113.00.

The answer is O 0.260.

To find the probability of rolling two 5's when 8 fair six-sided dice are thrown, we can use the binomial probability formula. The probability of rolling a 5 on one die is 1/6, and the probability of not rolling a 5 on one die is 5/6. We want to find the probability of getting exactly two 5's, which can happen in different ways. We can roll a 5 on the first die and another 5 on the second die, or we can roll a 5 on the second die and another 5 on the third die, and so on. Therefore, the probability of getting exactly two 5's is:

P(X = 2) = (8 choose 2) * (1/6)^2 * (5/6)^6

where (8 choose 2) is the number of ways to choose 2 dice out of 8, which is equal to 28. Using a calculator, we get:

P(X = 2) ≈ 0.260

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The mean of the given probability distribution is μ = 3.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

To find the mean of a probability distribution, we need to multiply each outcome by its probability, and then sum up those values. So, using the given probabilities and outcomes:

Mean (μ) = (0 x 0.02) + (1 x 0.16) + (2 x 0.21) + (3 x 0.11) + (4 x 0.41) + (5 x 0.09)

Mean (μ) = 0 + 0.16 + 0.42 + 0.33 + 1.64 + 0.45

Mean (μ) = 3

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This means we are 90% confident that upper bound of the true proportion of masks of this type whose lenses would pop out at 250° is between 0.1338 and 0.3055.

To construct a 90% upper confidence limit for the true proportion of masks with lenses popping out at 250°F, follow these steps:

1. Calculate the sample proportion (p'):
Upper bound = p' + zα/2 * √(p'(1-p')/n)

where p' is the sample proportion (12/60 = 0.2), zα/2 is the critical value for a 90% confidence interval (1.645), and n is the sample size (60).

p' = Number of masks with lenses popping out / Total number of masks tested
p' = 12/60 = 0.2

2. Determine the sample size (n) and the complement of the sample proportion (q'= 1 - p'):
n = 60
q' = 1 - 0.2 = 0.8

3. Determine the Z-score for a 90% confidence level:
For a 90% confidence level, the corresponding Z-score is 1.645 (using a Z-table or calculator).

4. Calculate the margin of error (E):
E = Z * sqrt(p' * q' / n)
E = 1.645 * sqrt(0.2 * 0.8 / 60)
E ≈ 0.0812

5. Calculate the upper confidence limit (UCL):
UCL = p' + E
UCL = 0.2 + 0.0812
UCL ≈ 0.2812

Rounding to four decimal places, the 90% upper confidence limit is (0.1338, 0.3055). This means we are 90% confident that the true proportion of masks of this type whose lenses would pop out at 250° is between 0.1338 and 0.3055. Note that this upper bound is slightly different from the given answer of 0.2662, which may be due to rounding or calculation errors.
Therefore, the 90% upper confidence limit for the true proportion of masks with lenses popping out at 250°F is approximately (0.1338, 0.2812).

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The value of w in the equation (Wx24) - (2,400 divided by 80) =1,602 is 68

From the question, we have the following parameters that can be used in our computation:

(Wx24) - (2,400 divided by 80) =1,602

Evaluate the brackets

So, we have

(Wx24) - 30 =1,602

Next, we evaluate the like terms

(Wx24) =1,632

Divide by 24

W = 68

Hence, the value of W is 68

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Answer:

Step-by-step explanation:

To complete the sequence, we need to find the missing numbers that fit the pattern.

Looking at the given numbers, we can see that each number is obtained by adding a constant value to the previous number.

To find this constant value, we can calculate the differences between consecutive numbers in the sequence:

8 - 0 = 8

15 - 8 = 7

24 - 15 = 9

So the constant difference between consecutive terms in the sequence is not the same. Therefore, we can assume that this is not an arithmetic sequence.

However, we can observe that the sequence follows a pattern of adding increasing odd numbers to the previous term:

0 + 1 = 1

1 + 7 = 8

8 + 7 = 15

15 + 9 = 24

So the missing numbers in the sequence are 1 and 33.

Therefore, the completed sequence is:

0, 1, 8, 15, 24, 33.

The required, we need 740 feet of fencing to enclose the rectangular area of the Tarbosaurus enclosure.

To enclose the rectangular area needed for the Tarbosaurus, we need to calculate the perimeter of the rectangle, which is the sum of the lengths of all four sides. Since we are given the length and width of the rectangle, we can use the formula:

Perimeter = 2(length + width)

Substituting the given values, we get:

Perimeter = 2(300ft + 70ft)

Perimeter = 2(370ft)

Perimeter = 740ft

Therefore, we need 740 feet of fencing to enclose the rectangular area of the Tarbosaurus enclosure. Since the park can provide up to 800 feet of fencing, we have enough fencing to enclose the area.

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The value of x is given as follows:

x = 90.

The value of x is obtained applying the two secant segment theorem, which means that the following equation will hold true:

a(x + a) = b(b + c)

(a secant is a segment that crosses the circumference of the circle twice, and the product has to be equal for each).

Hence, replacing the values of a, b and c, we can obtain the value of x as follows:

11(11 + x) = 24.2(24.2 + 21.7)

121 + 11x = 1110.78

x = (1110.78 - 121)/11

x = 90.

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The mathematical statement is an inequality that can be written as:

26  > k

Here we have the following mathematical statement:

"26 is more than k"

This type of statement is what we know as an inequality, this is a comparation between two values.

Here, the statement says that the number 26 is a number larger than k, which is a variable.

This statement will be written as:

26 > k

Where the symbol ">" means that the thing in the left is larger than the thing in the right,

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If A is an m×n matrix, then both ATA and AAT are defined.

If A is an m×n matrix, then both ATA and AAT are defined.

The matrix ATA is the product of the transpose of A and A itself. It is a square matrix of size n×n.

The matrix AAT is the product of A and the transpose of A. It is a square matrix of size m×m.

Both ATA and AAT are important and commonly used in linear algebra and statistics. The matrix ATA arises in the context of least squares regression, while AAT arises in the context of principal component analysis (PCA) and singular value decomposition (SVD).

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Answer:

Which statement BEST defines a circle? A) A circle is the set of all points in a plane equidistant from each other. B) A circle is the set of all points in a plane equidistant from a given arc. C) A circle is the set of all points in a plane equidistant from a given point. D) A circle is the set of all points in a plane equidistant from a given segment.

Step-by-step explanation:

pls mark brainliest, i tried my best...

a) To find the score of a student who scored in the 80th percentile on the Quantitative Reasoning section, we need to find the z-score corresponding to the 80th percentile and then use it to find the raw score.

Using the standard normal distribution table or calculator, we find that the z-score corresponding to the 80th percentile is approximately 0.84.

Using the formula for converting a z-score to a raw score:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation, we can solve for x:

0.84 = (x - 153) / 7.67

x - 153 = 0.84 * 7.67

x = 153 + 0.84 * 7.67

x = 159.19 (rounded to two decimal places)

Therefore, the score of a student who scored in the 80th percentile on the Quantitative Reasoning section is 159.19.

b) To find the score of a student who scored worse than 70% of the test takers in the Verbal Reasoning section, we need to find the z-score corresponding to the 70th percentile and then use it to find the raw score. Using the standard normal distribution table or calculator, we find that the z-score corresponding to the 70th percentile is approximately -0.52 (since we are looking for scores worse than 70%, we need to use the negative z-score).

Using the formula for converting a z-score to a raw score:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation, we can solve for x:

-0.52 = (x - 151) / 7

x - 151 = -0.52 * 7

x = 151 - 0.52 * 7

x = 147.64 (rounded to two decimal places)

Therefore, the score of a student who scored worse than 70% of the test takers in the Verbal Reasoning section is 147.64.

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Answer: 3 sq. m

Step-by-step explanation:

assuming you are solving for the large, solid triangle, you can subtract the whole minus the part

to solve for the whole, (3 + 1) [base] x 2 [height] / 2 = 4

to solve for the dotted part, 1 [base] x 2 [height] / 2 = 1

whole - part, or 4 - 1, equals 3

The value of x from the relation is x= a/b √(y²a² - b²).

We have,

y=√x²b²- a²b² ÷ a²

Now, we have to find the value of x

y=√x²b²- a²b² ÷ a²

ya² = √x²b² - a²b²

ya² = √b²(x²- a²)

ya²= b √ x² - a²

ya²/b = √x²-a²

Now, taking square on both side we get

y²[tex]a^4[/tex] / b² = x² - a²

x² = y²[tex]a^4[/tex] / b² - a²

x² = (y²[tex]a^4[/tex] - a²b²)/ b²

x= √(y²[tex]a^4[/tex] - a²b²)/ b²

x= a/b √(y²a² - b²)

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The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)

Here, we have,

to determine the correct representations

From the question, we have the following expression that can be used in our computation:

–3(2x – 5) < 5(2 – x)

Divide bot sides of the inequality by -1

So, we have the following representation

3(2x – 5) > -5(2 – x)

Next, we open the brackets

This gives

6x – 15 > -10 + 5x

Hence, the representation is 6x – 15 > -10 + 5x

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Complete question

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

(a) 6x – 15 > -10 + 5x

(b) 6x – 15 < -10 + 5x

(c) 3(2x – 5) > -5(2 – x)

(d) 3(2x – 5) < -5(2 – x)

Answer:

The scale factor is 20.

Explanation:

The scale factor is the ratio of the corresponding side lengths (or areas or volumes) of the two similar figures. In this case, we are given the areas of the front sides of the toy building and the real building, and we want to find the scale factor between them.

Let x be the scale factor. Then, the area of the front side of the real building is x^2 times the area of the front side of the toy building. We can set up the equation:

x^2 * 1 square foot = 400 square feet

Solving for x, we get:

x^2 = 400

x = sqrt(400)

x = 20

Therefore, the scale factor between the toy building and the real building is 20.

Answer:

4/6 because the bag holds six tiles total so 4 of the 6 are numbered so you would have 4/6 of a chance of picking a numbered tile.

Step-by-step explanation:

4/6 because the bag holds six tiles total so 4 of the 6 are numbered so you would have 4/6 of a chance of picking a numbered tile.

Answer:

4/6

Step-by-step explanation:

4/6 because the bag holds six tiles total so 4 of the 6 are numbered so you would have 4/6 of a chance of picking a numbered tile.

The probability of getting three 7's in a row on a roulette wheel is given by the relation P ( A ) = 0.00000247

Given data ,

The type of roulette wheel being used affects the likelihood of landing on a given number, such 7, on a typical roulette wheel. There are typically 37 slots on ordinary roulette wheels, numbered 0 to 36, with a total of 18 red, 18 black, and one green number (zero).

Given that there is only one 7 among the 37 potential outcomes of a regular roulette wheel, the likelihood of landing a 7 on a single spin is 1 in 37.

So , the probability of getting three 7's in a row on a roulette wheel is given by the relation P ( A ) = ( 1/37 ) x ( 1/37 ) x ( 1/37 )

P ( A ) = 0.00000247

Hence , the probability is 0.00000247

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In this case, the city planner is using a camera to record the number of cars passing through the intersection at different hours of the day and on different days of the week. This allows the planner to gather information on traffic patterns and congestion without directly influencing the traffic flow. The data collected will help the city planner identify trends and potential areas of improvement for traffic management and infrastructure planning.

The city planner is conducting a quantitative investigation using observational research methods. They are collecting numerical data through the use of a camera to record the number of cars that pass through the intersection at various times and days. This type of investigation involves the collection and analysis of data in a systematic and objective manner. The data collected will allow the city planner to identify patterns and trends in traffic congestion at the intersection, which can then be used to inform future decision-making and planning. Additionally, the use of observational research methods ensures that the data collected is reliable and unbiased, as it is based on direct observations of traffic flow rather than self-reported information from drivers or other subjective sources. Overall, the city planner's investigation is an important step in improving traffic flow and reducing congestion in the area.
The city planner's investigation can be best described as an observational study. In this type of investigation, the researcher collects data by observing and recording the occurrence of specific events or behaviors without interfering or manipulating the subjects or environment. In this case, the city planner is using a camera to record the number of cars passing through the intersection at different hours of the day and on different days of the week. This allows the planner to gather information on traffic patterns and congestion without directly influencing the traffic flow. The data collected will help the city planner identify trends and potential areas of improvement for traffic management and infrastructure planning.

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Answer:

You are going to spend $3.48 in total.

Step-by-step explanation:

You need to add the two numbers together.

1.49+1.99=$3.48

You are going to spend $3.48 in total. (I'm assuming we aren't supposed to include tax)

The true population means the weight of the residents in the town is between 147.6 and 160.4 pounds.

Use the formula for the confidence interval:

[tex]CI = \bar X \pm z*(\sigma/\sqrt{n})[/tex]

where:

X= sample mean = 154 pounds

σ = population standard deviation = 39 pounds

n = sample size = 149

z = z-score corresponding to the confidence level of 95%, which is 1.96 (from a standard normal distribution table)

Substituting the values, we get:

[tex]CI = 154 \pm 1.96*(39/\sqrt{149})\\CI = 154 \pm 6.4[/tex]

Rounding to the nearest tenth, we get:

CI = (147.6, 160.4)

Therefore, we can say with 95% confidence that the true population means the weight of the residents in the town is between 147.6 and 160.4 pounds.

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