Last Wednesday, students could choose ham or turkey sandwiches for lunch. The cafeteria made 120 sandwiches in all, 30% of which were turkey. How many ham sandwiches did the cafeteria make?
A. 84
B. 36
C. 60
D. 72

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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If a student is ranked in the 85th percentile on their college entrance exams, it means that they scored better than 85% of the other students who took the same exam.

In other words, only 15% of the students who took the exam scored higher than this student. This is a good achievement and suggests that the student is likely to be competitive in the college application process.

A percentile is a statistical metric that shows the proportion of a dataset's values that are equal to or lower than a given value. For instance, the dataset's 75th percentile implies that 75% of the values are equal to or lower than that number.

In the case of the request for the "percentile 100 words," it appears to be a misunderstanding or an incomplete query. In order to produce a useful response, the term "percentile" often needs more details, such as the dataset or the particular value of interest. Could you please elaborate on your point or make your inquiry more clear?

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Answer:

Answer:

Most poison dart frogs are brightly colored, displaying aposematic patterns to warn potential predators. Their bright coloration is associated with their toxicity and levels of alkaloids. ... Poison dart frogs are an example of an aposematic organism.

Hostas for Full Sun

In general, yellow or gold hostas tolerate partially sunny location without losing their vibrant yellow color. About two hours of daily sun exposure will keep these yellow or golden beauties looking their best. Aim for morning sun to avoid burned leaves.

hope this helps

Step-by-step explanation:

Hope this is the right answer Have a good day!

have a good day

To find the equation of the line, we need to determine its slope (m) and y-intercept (b). We can use the two given points on the line to find the slope:

m = (y2 - y1) / (x2 - x1)

m = (-3 - 5) / (8 - 8)

m = -8/0

The slope is undefined because the line is vertical and has no horizontal run.

Since the line is vertical, it is of the form x = c, where c is the x-coordinate of any point on the line. From the given points, we can see that the x-coordinate of every point along the line is 8.

Therefore, the equation of the line is x = 8.

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Based on the information, the equation of the line is x = 8.

To find the equation of the line, we need to determine its slope (m) and y-intercept (b). We can use the two given points on the line to find the slope:

m = (y₂ - y₁) / (x₂ - x₁)

m = (-3 - 5) / (8 - 8)

m = -8/0

The slope is undefined because the line is vertical and has no horizontal run. Since the line is vertical, it is of the form x = c, where c is the x-coordinate of any point on the line. From the given points, we can see that the x-coordinate of every point along the line is 8.

Therefore, the equation of the line is x = 8.

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Answer:

  0, 5, 10

Step-by-step explanation:

You can solve the inequality to determine what values to select.

  28 -7x ≤ -4(-7x -7) . . . . . . given

  28 -7x ≤ 28x +28 . . . . . . eliminate parentheses*

  -7x ≤ 28x . . . . . . . . . . . . . subtract 28 from both sides

  0 ≤ 35x . . . . . . . . . . . . . . add 7x to both sides

  0 ≤ x . . . . . . . . . . . . . . . . . divide by 35

So, all values that are 0 or greater will make the inequality true:

  0, 5, 10

_____

* Parentheses are eliminated using the distributive property. The factor outside parentheses multiplies each of the terms inside. Pay attention to signs.

  -4(-7x -7) = (-4)(-7x) +(-4)(-7) = 28x +28

False. A line graph typically shows the relationship between two variables.

It is a useful visualization tool for displaying trends or patterns in data over time or across different categories. The x-axis represents the independent variable or the variable being manipulated or controlled, while the y-axis represents the dependent variable or the variable being measured or observed. Each point on the line graph represents the value of the dependent variable corresponding to a specific value of the independent variable.

However, a line graph cannot directly represent the relationship between three variables.

Therefore, the given statement is false. A line graph typically shows the relationship between two variables.

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Complete question is below

A line graph shows the relationship between three variables true or false

Answer:

5/x

Step-by-step explanation:

11-6/x=5/x

The probability is approximately a 3.51% chance that an elite athlete has a maximum oxygen uptake of at least 73.3 ml/kg.

To find the probability that an elite athlete has a maximum oxygen uptake of at least 73.3 ml/kg, we need to use the concept of z-scores and the standard normal distribution.

Step 1: Calculate the z-score
The z-score measures how many standard deviations a particular value is away from the mean. In this case, we want to find the z-score for 73.3 ml/kg using the formula:

z = (x - μ) / σ

where x is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.

In this case:
x = 73.3
μ = 62.5
σ = 7.2

Substituting these values into the formula:
z = (73.3 - 62.5) / 7.2

Step 2: Look up the z-score
Once we have the z-score, we can use a standard normal distribution table or a calculator to find the probability associated with that z-score. The probability corresponds to the area under the normal distribution curve to the right of the z-score.

In this case, we want to find the probability of an elite athlete having a maximum oxygen uptake of at least 73.3 ml/kg, which means we want to find the probability to the right of the z-score.

Step 3: Calculate the probability
Using a standard normal distribution table or a calculator, we find that the z-score of 73.3 ml/kg is approximately 1.826.

The probability to the right of this z-score can be calculated by subtracting the cumulative probability from 1.

P(Z > 1.826) = 1 - P(Z < 1.826)

From the standard normal distribution table, the cumulative probability associated with a z-score of 1.826 is approximately 0.9649.

So, the probability that an elite athlete has a maximum oxygen uptake of at least 73.3 ml/kg is:

P(Z > 1.826) = 1 - 0.9649 = 0.0351

Therefore, the probability is approximately 0.0351 or 3.51%.

In conclusion, there is approximately a 3.51% chance that an elite athlete has a maximum oxygen uptake of at least 73.3 ml/kg.

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The turning point of the quadratic function g(x) is (-7, 12), which is choice (1).

In mathematics, a graph is a collection of vertices (also known as nodes) and edges that connect those vertices. The edges represent relationships between the vertices. Graphs can be used to model many different types of systems, including social networks, transportation networks, computer networks, and more.

A graph can be represented visually by drawing points or circles to represent the vertices, and lines or curves to represent the edges. The vertices and edges can also be labeled with numbers or other symbols to give them more meaning.

There are many different types of graphs, including directed graphs (also known as digraphs), undirected graphs, weighted graphs, and more. Directed graphs have edges that have a specific direction, while undirected graphs have edges that go both ways. Weighted graphs have edges with weights, which can represent things like distance, cost, or strength.

Graph theory is the branch of mathematics that studies graphs and their properties. It has many applications in computer science, operations research, physics, and other fields.

If the quadratic function f(x) has a turning point at (-3, 7), then the vertex of the parabola is at (-3, 7).

Now consider the quadratic function g(x) = f(x+4) + 5. To find the turning point of g(x), we need to rewrite g(x) in the form of f(x) by making a substitution. Let y = x + 4, then x = y - 4. We can substitute x = y - 4 into the expression for g(x) to get:

g(y-4) = f(y) + 5

So the graph of g(y-4) is the same as the graph of f(y), but shifted 4 units to the left and 5 units up.

The vertex of f(x) is (-3, 7), so the vertex of f(y) is (-3, 7) after making the substitution y = x + 4. Therefore, the vertex of g(y-4) = f(y) + 5 is obtained by shifting the vertex of f(y) 4 units to the left and 5 units up. This gives:

(-3 - 4, 7 + 5) = (-7, 12)

So the turning point of the quadratic function g(x) is (-7, 12), which is choice (1).

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Answer: 5x + 6y = -8

Step-by-step explanation: i believe this is the answer but i might be wrong, let me know. hope I helped!

The  required general solution for the given equation is

y(x) = \(e^{(-x/2)(C1 sin(\sqrt{(7/2)x} )}\) + C2 cos(√(7/2)x)) + \(e^{(-x/2)(C3 sin(\sqrt{(21/2)x }\)+ C4 cos(√(21/2)x))

here

C1, C2, C3 and C4 = constants determined by initial conditions.

It is given to us

y = sin(x) is a solution of y⁴ + 2y"' + 11y" +2y' + 10y = 0, by the method of undetermined coefficient we can calculate the general solution.

we evaluate the differential equation by considering that

y = \(e\sqrt{(rx)}\). We get r⁴ + 2r³ + 11r² + 2r + 10 = 0.

After factorizing the equation as

(r² + r + 2)(r² + r + 5) = 0.

The  evaluated roots of this equation are

r = -1/2 ± i√(7/2) and r = -1/2 ± i√(21/2).

We know that sin(x) is a solution of the differential equation,

Therefore, y = A sin(x) + B cos(x) is also a solution.

Now implementing the roots that we have derived, the general solution is

y(x) = \(e ^{(-x/2)(C1 sin(\sqrt{(7/2)x\)+ C2 cos(√(7/2)x)) + \(e ^{(-x/2)(C3 sin\sqrt{((21/2)x)} }\)+ C4 cos(√(21/2)x))

The  required general solution for the given equation is

y(x) = \(e^{(-x/2)(C1 sin(\sqrt{(7/2)x} )}\) + C2 cos(√(7/2)x)) + \(e^{(-x/2)(C3 sin(\sqrt{(21/2)x }\)+ C4 cos(√(21/2)x))

here

C1, C2, C3 and C4 = constants determined by initial conditions.

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Answer:

13

Step-by-step explanation:

Writing linear equations given two points can be a useful skill when graphing linear equations.

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Answer:

14

Step-by-step explanation:

The given piecewise-defined function is:

It is required to graph the function.

To do this, graph each piece with respect to the corresponding domain.

Graph g(x)=2 over x<-1:

Notice that an open circle is at x=-1 since it is not included in the interval x<-1.

Graph g(x)=3 for x=-1. This is just a point:

Finally, graph g(x)=-1 for x>-1:

There is an open circle at x=-1 since it is not included in the interval x>-1.

Thus, the required graph of the piecewise-defined function is shown below:

Alex can make a total of 180 different sandwiches by choosing one kind of meat from 10 options and two kinds of cheese from 9 options.

To determine the number of different sandwiches Alex can make, we need to consider the combinations of meat and cheese. Since Alex can choose one kind of meat from 10 options, there are 10 choices for the meat component of the sandwich. For the cheese component, Alex can choose two kinds of cheese from 9 options.

To calculate the total number of combinations, we can use the formula for combinations without repetition. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices. In this case, n is 9 (number of cheese options) and r is 2 (number of cheese choices). Thus, the number of combinations of two kinds of cheese is \(9C2\)= 9! / (2!(9-2)!) = 36.

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Answer:

The answer is 9 (D).

Step-by-step explanation:

Hope this helps!

The best integer for you to pick in this game is 1. By choosing the number 1, you ensure that regardless of the number I generate, your number will always be the smallest possible.

This means that you minimize the potential loss in the game. Since my number is randomly generated, there is an equal chance for it to be any number between 1 and 100. By selecting 1, you guarantee that you will never have to pay more than 1, regardless of the outcome. Choosing any number larger than 1 would increase the risk of having to pay a larger amount if my number happens to be higher. Therefore, by selecting 1, you make the most strategic move to minimize your potential losses and improve your overall chances in the game.

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The amount of money in Lucia's account after 5 years will be $1,105.5.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. Then the amount of money after 5 years will be given as,

A = $600 × (1 + 0.13)⁵

A = $600 × (1.13)⁵

A = $600 × 1.84

A = $1,105.5

The amount of money in Lucia's account after 5 years will be $1,105.5.

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9514 1404 393

Answer:

  2a(a^3 +a^3 b^2 +a b^2 +b^3)/(a^2 +b^2)

Step-by-step explanation:

Division is the same as multiplication by the inverse. Multiplication and division proceed left-to-right. So, we can rewrite the expression as ...

  \(\dfrac{a^3+a^3b^2+ab^2+b^3}{2a(a-b)^2}\times\dfrac{a^2-b^2}{a+2b}\times\dfrac{a^2+ab-2b^2}{a+b}\times\dfrac{4a^2}{a^2+b^2}\\\\=\dfrac{(a^3+a^3b^2+ab^2+b^3)(a-b)(a+b)(a+2b)(a-b)(4a^2)}{2a(a-b)^2(a+2b)(a+b)(a^2+b^2)}\\\\=\dfrac{4a^2}{2a}\cdot\dfrac{(a-b)^2}{(a-b)^2}\cdot\dfrac{a+2b}{a+2b}\cdot\dfrac{a^3+a^3b^2+ab^2+b^3}{a^2+b^2}\\\\=\boxed{\dfrac{2a(a^3+a^3b^2+ab^2+b^3)}{a^2+b^2}}\)

Answer:

The answer is -4 as the correct slope for Find the slope:

(-1, 5), (2, -7)

Step-by-step explanation:

The statement "Integration by parts can only be used when there is a polynomial or exponential" is false. Integration by parts is a technique in calculus that can be applied to a wide range of functions beyond polynomials and exponentials.

Integration by parts is a method used to evaluate integrals that involve the product of two functions. It is based on the product rule for differentiation. While it is commonly used with polynomials and exponentials due to their simple derivative and antiderivative properties, integration by parts can be used with other types of functions as well.

The technique of integration by parts can be applied to functions that are differentiable or have well-defined antiderivatives. It involves selecting one function to differentiate and another function to integrate. The choice of functions depends on their properties and simplification of the resulting integral.

Functions such as trigonometric functions, logarithmic functions, inverse trigonometric functions, and more can also be integrated using the integration by parts method. Therefore, integration by parts is not limited to only polynomials or exponentials, but can be applied to a wide range of functions in calculus.

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Answer:

-3(-1)=

Step-by-step explanation:

Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees

Trigonometry identities are expressed as a function of cosine, sine and tangent.

Given the trigonometry expression shown

4cos2θ+9=−14cosθ

Equate to zero

4cos2θ+9 + 14cosθ = 0

According to trig identity

cos2θ = 2cos²θ - 1

Substitute to have:

4(2cos²θ - 1)+9 + 14cosθ = 0

Expand

8cos²θ - 4 + 9 + 14cosθ = 0

8cos²θ+ 14cosθ + 5 = 0

let P = cosθ to have;

8P² + 14P + 5 = 0

Factorize the result

8P² + 10P + 4P + 5 = 0

2P(4P+5)+1(4P+5)=0
(2P+1) = 0 and 4P+5 = 0
2P = -1 and P = -5/4

P = -1/2 and -5/4

Recall that P = cosθ

If P = -1/2

cosθ = -1/2

θ = -60

Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees

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The expected total prize money is $2p/q.

Given that,

You participate as a participant in a game show and respond to questions. You receive $1 for each correct response, and you are disqualified if you first provide two consecutive inaccurate answers. You can answer properly with probability p or wrongly with probability q. Each question stands alone.

Let,

The probability of correctly answering a question is = p

The probability of incorrectly answering a question is = q

The number of failures after which you are eliminated is = 2

Let r = 2 =  No. of failures and

Let q = The probability of failure in a single question

Now, the number of questions that you will attempt will follow a negative binomial distribution whose parameters are r and q.

The expected value of a negative binomial distribution is given by

E[X] = r/q

So, the expected number of questions that you will attempt is = r/q = 2/q

Out of 2/q questions, the expected number of correct questions is = 2p/q

So, the expected total prize money is $2p/q.

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The accompanying tables of Laplace transforms and properties of Laplace transforms are used to find the Laplace transform of the given function. Note that an appropriate trigonometric identity may be necessary.

The Laplace transform of the given function is as follows. the Laplace transform of the given function is frac{2}{s^2 + 4}.

Laplace Transform of given function

In order to find the Laplace transform of the given function, use the formula of Laplace Transform below:

f(t) = sin(at)The Laplace Transform of sin(at) is given as:

{L}[sin(at)]

= \frac{a}{s^2 + a^2}

Substituting the values of a and t in the above equation, we get:

Laplace Transform of the given function

{L}[sin(2t)]

= \frac{2}{s^2 + 4} Therefore, the Laplace transform of the given function is frac{2}{s^2 + 4}.

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