A museum opened at 8:00 a.m. In the first hour, 200 people purchased admission tickets. In the second hour, 30% more people purchased admission tickets than in the first hour. Each admission ticket cost $8.50.

\( {16x}^{2} - 4x - 4x + 1 \\ = 4x(4x - 1) - 1(4x - 1) \\ = (4x - 1)(4x -1 )\)

Answer:

1x +3= T

Step-by-step explanation:

x is the number of miles driven times 1

add 3 to the total charge per miles

Answer:

Well let's say you went 15 miles around town that would be 15.00 in total for the 15 miles then you add the 3.00 to you answer and you get 18.00 ! Hope this helped!!

Step-by-step explanation:

The gradient of the stream is 1 meter per kilometre, which means that the stream drops 1 meter for every kilometre travelled. This is a relatively gentle slope and suggests that the stream is not flowing rapidly or eroding its bed very quickly.

The gradient of a stream is a measure of its steepness and is calculated by dividing the change in elevation by the distance travelled. In this case, the stream drops 15 meters in 15 kilometres, which means that the gradient can be calculated as follows:
Gradient = Change in elevation ÷ Distance travelled
Gradient = 15 meters ÷ 15 kilometers
Since we need to express the gradient in terms of meters per kilometre, we can simplify the above equation as follows:
Gradient = (15 meters ÷ 15,000 meters) × 1,000
Gradient = 1 meter per kilometer
Therefore,  understanding the gradient of a stream is important for a range of activities, including flood control, erosion management, and habitat restoration. By monitoring changes in the gradient over time, scientists and engineers can gain insights into the health and behaviour of streams and develop strategies to protect them.

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Answer:

63 sandwiches

Step-by-step explanation:

Pete and his friend Danny volunteered to bring sandwiches for lunch at a homeless shelter

They brought 7 loaves of bread

Each loaves have 18 slices

They used 2 slices each to make the sandwich

The first step is to calculate the total number of slices

Sinces 7 loaves of bread are used and each of them contain 18 slices then, the total number of slices can be calculated as follows

= 7 ×18

= 126 slices

Therefore since 2 slices of bread is used to make one sandwich then, the number of sandwiches that was made can be calculated as follows

= 126/2

= 63

Hence 63 sandwiches were made for the shelter

It is assumed you are looking for the inequalities that the problem dictates.

Number of seats is at most 2500:

At least 1000 tickets must be priced at $15:

Total sales need to exceed $10,000:

So there is a system of 3 inequalities you need to solve.

Let me know if you need additional guidance on solving the system.

a. P(G1 and Gy) = The probability of drawing a green card first (G1) and a yellow card second (Gy).

The probability of drawing a green card first is 6/11 (since there are 6 green cards out of 11 total cards remaining after the first draw).

After drawing a green card, there will be 5 green cards remaining and 5 yellow cards remaining out of a total of 10 cards. So, the probability of drawing a yellow card second is 5/10.

To find the probability of both events occurring, we multiply the individual probabilities:

P(G1 and Gy) = (6/11) * (5/10) = 30/110 = 3/11

b. P(At least 1 green) = The probability of drawing at least one green card.

To calculate this probability, we can find the complement of drawing no green cards.

The probability of not drawing a green card on the first draw is 5/11 (since there are 5 yellow cards out of 11 total cards remaining).

The probability of not drawing a green card on the second draw, given that a yellow card was drawn first, is 4/10 (since there are 4 yellow cards remaining out of 10 cards).

To find the probability of drawing no green cards, we multiply the probabilities:

P(No green) = (5/11) * (4/10) = 20/110 = 2/11

The probability of drawing at least one green card is the complement of drawing no green cards:

P(At least 1 green) = 1 - P(No green) = 1 - (2/11) = 9/11

c. P(G2G1) = The probability of drawing a green card second (G2) given that a green card was drawn first (G1).

After drawing a green card first, there will be 5 green cards remaining and 5 yellow cards remaining out of a total of 10 cards.

The probability of drawing a green card second is 5/10.

P(G2G1) = 5/10 = 1/2

d. Are G1 and G2 independent?

To check if G1 and G2 are independent, we need to compare the joint probability of both events (drawing a green card first and drawing a green card second) to the product of their individual probabilities.

P(G1 and G2) = (6/11) * (5/10) = 30/110 = 3/11

P(G1) = 6/11

P(G2) = 5/10 = 1/2

If P(G1 and G2) = P(G1) * P(G2), then G1 and G2 are independent.

In this case, (3/11) does not equal (6/11) * (1/2), so G1 and G2 are not independent.

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n = - 3

How is the given equation  \(5^{n} =\frac{1}{125}\)   solved to find n ?

Converting the fraction to negative exponential form,

\(5^{n} ={125}^{-1} \\\\5^{n} ={(5^{3})}^{-1} \\\\\text{We know } (a^{n} )^{m} =a^{nm} \\\\\text{Applying this exponent power rule in the above expression},\\\\5^{n} = 5^{-3} \\\\\text{As the corresponding exponents are equal}\\\\n= -3\)

What are laws of exponents?

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The area of the square is 25ft² and the perimeter is 20ft.

It's important to note that the area of a square is calculated as:

= Side ²

The perimeter is calculated as:

= 4 × Side

From the information given, the side is 5ft. The area will be:.

= 5 × 5

= 25ft²

The perimeter will be:

= 4 × Sode

= 4 × 5ft.

= 20 feet

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The average of the first five numbers 7, 8, 9, 10 in the set is 10.

Let's begin by finding the sum of the 15 consecutive numbers. We know that the average of these numbers is 15, so we can use this information to find their sum.

The formula for the average (or arithmetic mean) of a set of numbers is:

average = (sum of numbers) / (number of numbers)

In this case, we know the average is 15 and there are 15 numbers, so we can rearrange the formula to solve for the sum:

sum of numbers = average x number of numbers

sum of numbers = 15 x 15

sum of numbers = 225

So the sum of the 15 consecutive numbers is 225.

To find the average of the first five numbers in this set, we need to know what those five numbers are. Let's call the first number in the set "x". Then the next four consecutive numbers would be x+1, x+2, x+3, and x+4.

The average of these five numbers can be found using the same formula as before:

average = (sum of numbers) / (number of numbers)

In this case, we want to find the average of five numbers, so we can plug in:

average = (x + (x+1) + (x+2) + (x+3) + (x+4)) / 5

We can simplify this expression by combining like terms:

average = (5x + 10) / 5

average = x + 2

So the average of the first five consecutive numbers in this set is x + 2. We don't know what x is, but we can use some algebra to solve for it.

We know that the sum of all 15 consecutive numbers is 225:

x + (x+1) + (x+2) + ... + (x+14) = 225

We can simplify this expression by combining like terms:

15x + (1+2+...+14) = 225

15x + 105 = 225

15x = 120

x = 8

So the first number in the set is 8, and the first five consecutive numbers are:

8, 9, 10, 11, 12

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Answer:

f(x) = x2 – 10x + 21

Step-by-step explanation:

I got it because you substract and add the last part

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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Answer:

Step-by-step explanation:

Smallest number:7-3-1=3

Largest number: 7x3x1=21

The highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.

In mathematics, a base is the number of digits or distinct symbols used to represent numbers in a positional numeral system. For example, in the decimal system (which we commonly use), the base is 10 because we use 10 distinct digits from 0 to 9.

Now, let's consider the number 1000. In order to find the lowest base in which this could be a valid number, we need to break down 1000 into its constituent digits. Since 1000 has 4 digits, we can represent it as:

1000 = 1 x base^3 + 0 x base^2 + 0 x base^1 + 0 x base^0

where base is the number system we are using. Now, we need to find the lowest value of base that makes this equation valid.

We can see that if we set base = 2, then the equation becomes:

1000 = 1 x 2^9 + 0 x 2^8 + 0 x 2^7 + 0 x 2^6 + 0 x 2^5 + 0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0

Here, we have used the binary system, which has a base of 2. As we can see, the highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.

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Problem: Maryland transportation authority decided to setup toll booths on either side of the Fort McHenry tunnel due to increased traffic. After studying the traffic patterns, MTA found that peak traffic occurs in the evenings on Friday and Saturday.

On average, 4796 vehicles per hour pass through the tunnel each way during peak times. The vehicles need to go through the toll booths. MTA would like to keep the average time spent at each toll booth to less than 2 minutes. How many lanes should MTA open if they do not want to have more than 10 vehicles waiting in line (on average)?Solution:We are given that:- Average number of vehicles that passes through the tunnel each way during peak time = 4796 per hour- Vehicles need to go through the toll booth.- Maximum allowable average time at each toll booth is 2 minutes.- MTA does not want more than 10 vehicles waiting in line at a time.We need to find out how many lanes MTA should open in order to fulfill the above criteria.

We can calculate the number of cars waiting in the line, using the formula:- L = Wq / λ - µWhere,- L is the number of cars in the system (waiting in line or being serviced),- Wq is the average waiting time in the queue,- λ is the arrival rate of the vehicles (i.e., the number of vehicles arriving per minute),- µ is the service rate (i.e., the number of vehicles that can be served per minute).So, first let’s calculate the number of vehicles arriving per minute.- λ = (4796 vehicles / hour) / (60 minutes / hour) = 79.9333 vehicles / minuteNow let’s calculate the number of lanes (number of toll booths) we need, assuming that we have only one toll booth and the average waiting time is less than 2 minutes.

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There are 130 positive integers less than 1000 that are divisible by 7 but not by 11.

The rule used to find the number of positive integers less than 1000 that are divisible by 7 but not by 11 is the inclusion-exclusion principle. This principle states that if we want to find the number of elements that belong to at least one of two sets, we can add the sizes of the sets together and then subtract the size of the intersection of the sets. In this case, we first find the number of positive integers less than 1000 that are divisible by 7 (which is 142), then the number that are divisible by 11 (which is 90), and finally the number that are divisible by both (which is 12). Using the inclusion-exclusion principle, we can find the number of positive integers less than 1000 that are divisible by 7 but not by 11 by subtracting the number that are divisible by both from the number that are divisible by 7: 142 - 12 = 130. Therefore, there are 130 positive integers less than 1000 that are divisible by 7 but not by 11.
To find the number of positive integers less than 1000 that are divisible by 7 but not by 11, you can use the Inclusion-Exclusion Principle.

First, find the number of integers divisible by 7: there are 999/7 = 142.71, so 142 integers are divisible by 7.

Next, find the number of integers divisible by both 7 and 11 (i.e., divisible by their LCM, which is 77): there are 999/77 = 12.97, so 12 integers are divisible by 77.

Now, apply the Inclusion-Exclusion Principle: Subtract the number of integers divisible by both 7 and 11 from the number of integers divisible by 7: 142 - 12 = 130.

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To make logistic regression work in this case, we would need to formulate the hypothesis and apply it to the given training examples.
The hypothesis for logistic regression can be written as follows:
hθ(x) = g(θ^T * x)
Where:
- hθ(x) is the predicted probability that the house is expensive (class 1) given the features x.
- θ is the vector of coefficients that we want to estimate.
- x is the vector of features, in this case, the depth and frontage of the house.

The function g(z) is the sigmoid function, which maps any real-valued number to a value between 0 and 1. It is defined as follows:
g(z) = 1 / (1 + e^(-z))

To apply this hypothesis to the training examples, we would calculate the predicted probabilities for each example and compare them to the actual class labels. We can then use a cost function, such as the cross-entropy loss function, to measure the error between the predicted probabilities and the actual class labels. The goal is to find the values of θ that minimize this error.
By using an optimization algorithm, such as gradient descent, we can iteratively update the values of θ to minimize the cost function and find the optimal parameters for our logistic regression model.
Overall, the full hypothesis for logistic regression in this case is:
hθ(x) = g(θ₀ + θ₁ * depth + θ₂ * frontage)

Where θ₀, θ₁, and θ₂ are the coefficients that we need to estimate.

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Lucas can make a maximum of 3 biscuits using the available ingredients.

To determine the greatest number of biscuits Lucas can make, we need to compare the available quantities of ingredients to the required quantities for each biscuit.

Let's compare the ingredients:

1. Butter:

Lucas has 900 g of butter, and each biscuit requires 225 g.

Therefore, Lucas can make 900 g / 225 g = 4 biscuits with the available butter.

2. Caster Sugar:

Lucas has 1000 g of caster sugar, and each biscuit requires 110 g.

Therefore, Lucas can make 1000 g / 110 g = 9 biscuits with the available caster sugar.

3. Plain Flour:

Lucas has 1000 g of plain flour, and each biscuit requires 275 g.

Therefore, Lucas can make 1000 g / 275 g = 3.6363 (approximately 3) biscuits with the available plain flour.

4. Chocolate Chips:

Lucas has 225 g of chocolate chips, and each biscuit requires 75 g.

Therefore, Lucas can make 225 g / 75 g = 3 biscuits with the available chocolate chips.

Now, let's find the minimum number of biscuits Lucas can make based on the available quantities of each ingredient:

- Butter: 4 biscuits

- Caster Sugar: 9 biscuits

- Plain Flour: 3 biscuits

- Chocolate Chips: 3 biscuits

To find the greatest number of biscuits Lucas can make, we need to consider the ingredient with the lowest quantity, which is the plain flour at 3 biscuits. Therefore, Lucas can make a maximum of 3 biscuits using the available quantities of all the ingredients.

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Answer: there is one apple in the frig and two in the bowl how many are there in all

Step-by-step explanation:

a) The 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b) The 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

To calculate the confidence intervals for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± margin of error

The margin of error can be calculated using the formula:

Margin of Error = critical value * standard error

where the critical value is determined based on the desired confidence level and the standard error is calculated as:

Standard Error = \(\sqrt{((p * (1 - p)) / n)}\)

Given that the sample proportion (p) is 0.81 and the sample size (n) is 500, we can calculate the confidence intervals.

a. 90% Confidence Interval:

To find the critical value for a 90% confidence interval, we need to determine the z-score associated with the desired confidence level. The z-score can be found using a standard normal distribution table or calculator. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = \(1.645 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0323

Confidence Interval = 0.81 ± 0.0323

≈ (0.7777, 0.8423)

Therefore, the 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b. 95% Confidence Interval:

For a 95% confidence level, the critical value is approximately 1.96.

Margin of Error = \(1.96 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0363

Confidence Interval = 0.81 ± 0.0363

≈ (0.7737, 0.8463)

Thus, the 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

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Answer:

5*5*5 - 12 / 3 = 121

Step-by-step explanation:

5^3 = 5 * 5 * 5 = 25 * 5 = 125

12/3 = 4

We evaluate exponents first: 5^3 = 125

Then division: 12/3 = 4

Then subtraction: 125 - 4 = 121

A regular polygon with interior angles that measure 140 degrees has 9 sides. All interior angles are congruent, meaning they have the same degree measure.

To find the number of sides in a regular polygon with a given interior angle measure, we can use the formula:

n = 360 / (180 - x)

where n is the number of sides and x is the measure of each interior angle in degrees.

This formula is derived from the fact that the sum of the interior angles in a polygon with n sides is given by the formula (n-2) * 180. In a regular polygon, each interior angle measures (Sum of interior angles / n). If we substitute the formula for the sum of interior angles into the formula for the measure of each interior angle, we get:

x = (n-2) * 180 / n

Solving for n:

n = 360 / (180 - x)

So, when we plug in the given interior angle measure of 140 degrees, we get:

n = 360 / (180 - 140)

n = 360 / 40

n = 9

Therefore, a regular polygon with interior angles that measure 140 degrees has 9 sides.

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How many sides does a regular polygon have if each interior angle measures 140?

Answer:

The sum of the interior angles of any quadrilateral is 360°.

Answer:

Step-by-step explanation:

A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles and the sum of all the angles is 360°.

I'll give you an example with the square, it has 4 right angles, so the sum is 360 ° as in all quadrilaterals.

The probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct is 0.9925 (or 99.25%).

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

We can use the central limit theorem to approximate the distribution of the sample mean. According to the central limit theorem, if the sample size is sufficiently large, the distribution of the sample mean will be approximately normal with a mean of 30,641 and a standard deviation of sqrt(variance/sample size).

So, we have:

mean = 30,641

variance = 14,561,860

sample size = 242

standard deviation = sqrt(variance/sample size) = sqrt(14,561,860/242) = 635.14

Now, we need to calculate the z-score corresponding to a sample mean of 31,358 miles:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

= (31,358 - 30,641) / (635.14 / sqrt(242))

= 2.43

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 2.43. The probability is approximately 0.9925.

Therefore, the probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct is 0.9925 (or 99.25%).

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Answer:50

Step-by-step explanation:

In the event that your credit card is stolen in the United States, federal law limits the liability of cardholders to $50, regardless of the amount charged on the card by the unauthorized user.

Answer:

$50

Step-by-step explanation:

It depends in what country you live. In the United States, you will be charged up to $50 but in others countries you would be refunded for the amount of money you had on that card

66.67%.

Divide the two; 400/600. Then, multiply by 100 to get a percentage.

Answer:

04x=24

Step-by-step explanation:

04x=24

divide both sides by 4 to let x stand alone

04x÷4=24÷4

x=6

Therefore, the compound inequality for the diameter of the washers is: 3.150 ≤ d ≤ 3.240.

In mathematics, an inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or equal to the other. The symbols used to represent inequalities are:

">" which means "greater than"

"<" which means "less than"

"≥" which means "greater than or equal to"

"≤" which means "less than or equal to"

Inequalities can be solved by applying algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides of the inequality by the same number. The solution to an inequality is a range of values that satisfy the inequality.

Here,

The formula for the circumference of a circle in terms of its diameter is:

C = πd

where π (pi) is approximately 3.14.

We are given that the acceptable range for the circumference of the washer is 9.9 ≤ C ≤ 10.2 centimeters. Substituting C = 3.14d into this inequality, we get:

9.9 ≤ 3.14d ≤ 10.2

Dividing all sides of the inequality by 3.14, we obtain:

3.15 ≤ d ≤ 3.24

Rounding to three decimal places, the corresponding interval for the diameters of the washers is:

3.150 ≤ d ≤ 3.240

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Answer:

The initial velocity of the runner was 4 m/s, and the runner stopped after 8 seconds.

Step-by-step explanation:

Answer:

1600

Step-by-step explanation:

We can setup a ratio in terms of words per minute.

Mr. Brown can type 80 words in 2 minutes, so our ratio looks like this:

40:2

In order to find how many words he can type in 40 minutes, we must set the minutes side of our ratio to 40. In order to do that, we must multiply our minutes side by a factor that makes it equal 40, and then multiply the words side by the same factor. We can divide 40 by 2 to figure out the factor, which is 20. Since the factor is 20, we must multiply it by the words side to figure out how many words he types in 40 minutes, which is 20 · 80 = 1600 words.

All the possible values of a must be less than 3.75 excluding values from 3 and below

Inequalities are expressions that are not separated by an equal sign

Since we are not given the required inequality expression, Let us assume the equation below:

10 - 5a > -a

Add 5a to both sides

15 - 5a + 5a > -a + 5a

15 > 4a

4a<15

a < 15/4

a<3.75

Since the value of a is less than 3.75, hence all the possible values of a must be less than 3.75 excluding values from 3 and below.

NB: The inequality expression was assumed, the same concept can be applied to any other expression

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