Suppose you are the treasurer of the drama club.The cost of scripts for the spring musical is $254. The cost of props and costumes is $400. You must also pay $1.20 per ticket to the play's director. You charge $4.00 per ticket and you also expect to make $150 on refreshments. How many tickets will the drama club need to sell to break even?

The sample space contains three types of animals; 5 salamanders, 3 crayfish, and 12 minnows.

So population of sample space would be, n(S) = Salamanders + Crayfish + Minnows.

n(S) = 5 + 3 + 12 = 20.

She wants to randomly select an animal and check if it is Salamander or not.

population of favourable outcomes would be, n(salamander) = 5.

Now the probability for selecting a salamander would be :-

[tex]P(salamander) = \frac{n(salamander)}{n(S)} \\\\ P(salamander) = \frac{5}{20} \\\\ P(salamander) = \frac{1}{4} \;or\; 0.25 \;or\; 25\%[/tex]

we know that
Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another. 
In this problem to prove circle 1 and circle 2 are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.

we have that
 

step 1
Move the center of the circle 1 onto the center of the circle 2
the transformation has the following rule
(x,y)--------> (x+6,y-4)
so
(-4,5)------> (-4+6,5-4)-----> (2,1)
so
center circle 1 is now equal to center circle 2 
The circles are now concentric (they have the same center)

step 2
A dilation is needed to increase the size of circle 1 to coincide with circle 2

scale factor=radius circle 2/radius circle 1-----> 6/2----> 3

radius circle 1 will be=2*scale factor-----> 2*3-----> 6 cm
radius circle 1 is now equal to radius circle 2 

A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar

the answer is

The probability that the average mosquito count in a randomly chosen square meter of the pond is more than 68 mosquitoes is approximately 59.87%.

To find the probability that the average count of mosquitoes in a randomly chosen square meter of the pond is more than 68 mosquitoes per square meter, we can use the normal distribution properties.

Given:

We need to find P(X > 68). To do this, we convert the raw score to a Z-score using the formula:

Z = (X - μ) / σ

Substitute the given values:

Z = (68 - 70) / 8 = -2 / 8 = -0.25

Next, we need to find the probability corresponding to Z > -0.25 using the standard normal distribution table.

Looking up Z = -0.25, we find the cumulative probability (P(Z < -0.25)) is approximately 0.4013.

To find P(Z > -0.25):

P(Z > -0.25) = 1 - P(Z < -0.25) = 1 - 0.4013 = 0.5987

Therefore, the probability that the average mosquito count in a randomly chosen square meter is more than 68 mosquitoes per square meter is approximately 0.5987 or 59.87%.

Answer:

Angela's board is a rectangle.

Step-by-step explanation:

As we know rectangle follow two properties.

1). All angles of a rectangle are right angle.

2). Opposite sides of a rectangle are equal in measure.

Since all angles of a rectangle are 90°. Therefore, right angle triangle formed by length, width and diagonal will follow Pythagoras theorem.

For Angela

20² + 21² = 841 = 29²

Therefore Angela's board is a rectangle.

For Bradley

9² + 9² = 162 ≈ 9²

So Bradley's board is not a rectangle.

For Carlton

25² + 30² = 1525 ≠ 35²

Carlton's board is not a rectangle.

For Della

10² + 12² = 244 ≠ 15²

Della's board is not a rectangle.

Therefore, Angela's board is a rectangle.

The best point estimate for the true mean weight of all packages received by a parcel service, given a sample mean of 20.6 pounds and a standard deviation of 3.2 pounds, is 20.6 pounds.

In this problem, we are given that a sample of 41 packages were randomly selected. This sample provided a mean weight of 20.6 pounds and a standard deviation of 3.2 pounds. It is asked what the best point estimate for a confidence interval estimating the true mean weight of all packages is.

The best estimate of the true mean weight (µ) of all packages would be the mean of the sample that was taken, assuming that the sample was randomly selected and is representative of the entire population. This is due to the fact that in statistics, the sample mean is the best point estimate of the population mean.

Therefore, the best point estimate for the true mean weight of all the packages received by the parcel service is 20.6 pounds.

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The correct minimum number of students required to guarantee that at least three answer sheets must be identical is 5.

To solve this problem, we can use the pigeonhole principle. The pigeonhole principle states that if you have more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon.

In this scenario, each question can be thought of as a pigeonhole, with the possible answers (a, b, c, d) as the pigeons. Since there are four possible answers for each question, we have four pigeonholes for each of the ten questions.

Now, let's consider the number of students (pigeons) and the number of unique answer sheets (pigeonholes). We want to find the minimum number of students such that at least three of them have identical answer sheets.

For two students, there are [tex]\(4^{10}\)[/tex] possible combinations of answers for the ten questions. For three students, the number of possible combinations of answers is [tex]\(4^{10} \times 4^{10}\)[/tex]. In general, for [tex]\(n\)[/tex] students, the number of possible combinations is [tex]\(4^{10} \times 4^{10} \times \ldots \times 4^{10}\) (\(n\) times)[/tex].

We need to find the smallest [tex]\(n\)[/tex] such that the number of combinations exceeds the number of ways to distribute the answer sheets without having three identical ones.

The number of ways to distribute the answer sheets without having three identical is given by the sum of the combinations of choosing 1, 2, ...,[tex]\(n-1\)[/tex] students out of [tex]\(n\)[/tex] to have unique answer sheets, and then multiplying by [tex]\(4^{10}\)[/tex] for each unique combination. This is because we are allowing for the possibility that some students have the same answer sheets, but not more than two.

The sum is given by:

[tex]\[ \binom{n}{1} \times 4^{10} + \binom{n}{2} \times 4^{10} + \ldots + \binom{n}{n-1} \times 4^{10} \][/tex]

We want to find the smallest [tex]\(n\)[/tex] such that:

[tex]\[ \binom{n}{1} \times 4^{10} + \binom{n}{2} \times 4^{10} + \ldots + \binom{n}{n-1} \times 4^{10} < 4^{10n} \][/tex]

For [tex]\(n = 4\)[/tex], we have:

[tex]\[ \binom{4}{1} \times 4^{10} + \binom{4}{2} \times 4^{10} + \binom{4}{3} \times 4^{10} = 4 \times 4^{10} + 6 \times 4^{10} + 4 \times 4^{10} = 14 \times 4^{10} \][/tex]

For [tex]\(n = 5\)[/tex], we have:

[tex]\[ \binom{5}{1} \times 4^{10} + \binom{5}{2} \times 4^{10} + \binom{5}{3} \times 4^{10} + \binom{5}{4} \times 4^{10} \][/tex]

[tex]\[ = 5 \times 4^{10} + 10 \times 4^{10} + 10 \times 4^{10} + 5 \times 4^{10} = 30 \times 4^{10} \][/tex]

Now, we compare [tex]\(30 \times 4^{10}\) with \(4^{10 \times 5}\)[/tex]. Since [tex]\(4^{10 \times 5}\)[/tex] is much larger than[tex]\(30 \times 4^{10}\)[/tex], we can see that for [tex]\(n = 5\)[/tex], the number of possible combinations exceeds the number of ways to distribute the answer sheets without having three identical ones.

Therefore, the minimum number of students required to guarantee that at least three answer sheets must be identical is 5.

Answer:

x-9,y+4,92

Step-by-step explanation:

Area and volume are both used to determine the amount of space.

While area is used for two-dimensional shapes, volume is used for three-dimensional shapes.

The difference between the given parameters are:

For instance:

[tex]\mathbf{Length = b -a}[/tex]

[tex]\mathbf{Area = ab}[/tex]

[tex]\mathbf{Volume= abc}[/tex]

Read more about lengths, areas and volumes at:

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Answer: 40 pi

Step-by-step explanation:

Final answer:

The quantity with units of (kg*m²)/(s²*c) is closely related to the energy concept in physics, specifically within the framework of Einstein's mass-energy equivalence formula, E = mc², albeit with an added factor of the speed of light in the denominator.

Explanation:

The quantity with units of (kg*m^2)/(s^2*c) is related to the concept of mass-energy equivalence, as seen in Albert Einstein's famous equation, E = mc².

In this equation, E represents energy in joules, m represents mass in kilograms, and c represents the speed of light in meters per second.

The units of c² are m²/s², making the units of energy (when mass is given in kilograms) equivalent to kg*m²/s², or joules.

However, the specific units you mentioned, (kg*m²)/(s²*c), seem to incorporate an additional factor of the speed of light in the denominator, suggesting a possible deviation or specific application within the broader context of relativistic physics or energy conversions where the factor of c is explicitly considered.

To find the total bill including the service charge, multiply the original meal cost by 15% to calculate the service charge. Then, add this to the original meal cost to get the total of £75.21.

The question involves Mathematics as it requires calculating the total bill including the service charge which is essentially calculating a percentage of the original amount. To determine the total amount to be paid, one must first calculate the 15% service charge on the £65.40 meal and add it to the original amount. The service charge is calculated by converting the percentage to a decimal and multiplying it by the meal cost: 0.15 × £65.40.

Let's do the calculation:

The total bill after adding the 15% service charge to the £65.40 meal cost is £75.21.