a student council consists of three freshmen, four sophomores, four juniors and five seniors. a committee of five members of the council is randomly chosen. how many possible committees contain at least one member of each class? [

The missing sides and angles are listed below:

Triangle A: x = 27.061

Triangle B: θ = 70.562°

Triangle C: θ = 51.756

In this problem we find three triangles, a right triangle (Triangle a)) and two non-right triangles (Triangles b) and c)), whose missing angles and sides.

Triangle A

The missing side is determined by following trigonometric function:

x = 43 · sin 39°

x = 27.061

Triangle B

The missing angle is determined by sine law:

2.2 / sin 42° = 3.1 / sin θ

sin θ = 0.943

θ = 70.562°

Triangle C

The missing side is determine by cosine law:

4.1² = 5.2² + 3.6² - 2 · 5.2 · 3.6 · cos θ

16.81 = 40 - 37.44 · cos θ

37.44 · cos θ = 23.19

cos θ = 0.619

θ = 51.756

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The recommended time for cleaning and sanitizing a cutting board depends on various factors, such as the type of food being prepared and the risk of contamination.

However, a general guideline suggests that a cutting board should be cleaned and sanitized if it has been used for the same task for more than 4 hours.

Food safety guidelines emphasize the importance of preventing cross-contamination in the kitchen. Cutting boards, especially those used for cutting raw meats, poultry, and seafood, can harbor harmful bacteria that can contaminate other foods if not properly cleaned and sanitized.

The 4-hour guideline is based on the understanding that bacteria can multiply rapidly at room temperature and can reach levels that may pose a health risk. To minimize this risk, it is recommended to clean and sanitize cutting boards after approximately 4 hours of continuous use for the same task.

It's important to note that the 4-hour guideline is a general recommendation and may vary depending on the specific circumstances. Factors such as the type of food being prepared, the level of contamination, and the sanitation practices in place should be considered. Additionally, cutting boards should be cleaned and sanitized immediately if visible signs of contamination or soiling are present, regardless of the time duration.

To ensure food safety, it is always advisable to follow specific guidelines and regulations provided by local health authorities or food safety organizations. These guidelines take into account the specific risks associated with different types of food and provide detailed recommendations for cleaning and sanitizing cutting boards.

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Answer:

480

Step-by-step explanation:

Using the formula s=n/2(a+l), where a is the first term, l is the last term, n is the number of terms, and s is the sum of the terms, we can substitute the given values and solve for s:

s = 15/2(2 + 30)

s = 15/2(32)

s = 15/64

s = 480

Therefore, the value of s is 480.

Answer:

Step-by-step explanation:

[tex]s = \frac{n}{2}(a+l) \\s = \frac{15}{2} (2+30)\\s = \frac{15}{2} X 32\\s = 15 X 16\\s = 240[/tex]

Answer:

Answer

Step-by-step explanation:

To solve the inequality 1/6(2-x) - 1/3(2-x) > 2, we can simplify it step by step as follows:

1/6(2-x) - 1/3(2-x) > 2

(2-x)/6 - 2(2-x)/6 > 2

[2(2-x) - (2-x)]/6 > 2

(4-2x)/6 > 2

4-2x > 12

-2x > 8

x < -4

Therefore, the solution for x is x < -4.

We need to first determine the equation of the portion of the plane that lies in the first octant. The area of the surface is 1262.5 square units.

The first octant is the region of space where all three coordinates (x, y, and z) are positive. Therefore, we need to find the values of x, y, and z that satisfy the equation 5x + 13y + z = 65 and are all positive.

To do this, we can use the fact that the plane intersects each of the coordinate axes (x, y, and z) when the other two coordinates are equal to 0.

When z = 0 and y = 0, we get:
5x = 65
x = 13

When z = 0 and x = 0, we get:
13y = 65
y = 5

When x = 0 and y = 0, we get:
z = 65

Therefore, the portion of the plane that lies in the first octant is the triangle with vertices at (13, 0, 0), (0, 5, 0), and (0, 0, 65).

To find the area of this triangle, we can use the formula:
Area = 1/2 * base * height

The base of the triangle is the distance between the points (13, 0, 0) and (0, 5, 0), which is the same as the length of the projection of this line segment onto the xy-plane. We can find this length using the Pythagorean theorem:
base = sqrt((13-0)^2 + (0-5)^2) = sqrt(169 + 25) = sqrt(194)

The height of the triangle is the distance between the point (0, 0, 0) and the plane, which is given by the equation z = (65 - 5x - 13y)/1. Plugging in the coordinates of any of the three vertices of the triangle gives:
z = (65 - 0 - 0)/1 = 65

Therefore, the height of the triangle is 65.

Plugging these values into the formula for the area, we get:
Area = 1/2 * sqrt(194) * 65 = 1262.5

So the area of the surface is 1262.5 square units.

To find the area of the surface, we need to consider the part of the plane 5x + 13y + z = 65 that lies in the first octant. In the first octant, all values of x, y, and z are non-negative.

We can find the points where the plane intersects each of the three axes by setting two variables to 0 and solving for the third variable:

1. x-axis: Set y = 0 and z = 0:
  5x = 65
  x = 13

2. y-axis: Set x = 0 and z = 0:
  13y = 65
  y = 5

3. z-axis: Set x = 0 and y = 0:
  z = 65

Now we have three points on the plane in the first octant: (13, 0, 0), (0, 5, 0), and (0, 0, 65). These points form a triangle. To find the area of this triangle, we can use the formula:

Area = (1/2) * base * height

Since we have a right triangle, we can use the distance between the points on the x and y axes as the base and height:

Base = 13 (x-axis distance)
Height = 5 (y-axis distance)

Area = (1/2) * 13 * 5 = 32.5 square units.

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Answer:

0, -2 for the slope and y intercept

hooe this helps

Answer:

The slope is -5/6 and the y intercept is -2.

Step-by-step explanation:

One way to solve is rewriting the standard form ax+by=c to slope intercept form y=mx+b

5x+6y=-12

6y=-12-5x

Divide both sides by 6.

6y/6 = (-12-5x)/6

y=-2-(5/6)x

The slope is -5/6 and the y intercept is -2.

There are 2,646 different ways to form the committee with 5 teachers and 5 students.

There are 7 teachers to choose from, and we need to select 5 of them. This can be done in C(7,5) ways:

C(7,5) = 7! / (5!2!) = 76 / 21 = 21

There are 9 students to choose from, and we need to select 5 of them. This can be done in C(9,5) ways:

C(9,5) = 9! / (5!4!) = 9876 / 4321 = 126

To find the total number of ways to form the committee, we multiply the number of ways to select 5 teachers by the number of ways to select 5 students:

21 × 126 = 2,646

Therefore, there are 2,646 different ways to form the committee with 5 teachers and 5 students.

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The correct answer is B. The derivative is 2x - 49.

To find the derivative of the function (x - 50 + (x + 1)), we can apply the product rule, which states that the derivative of the product of two functions is the first function times the derivative of the second function, plus the second function times the derivative of the first function.

Let's break down the given function into its components:

f(x) = (x - 50) + (x + 1)

To differentiate this function, we can consider each term separately:

Term 1: (x - 50)

Term 2: (x + 1)

Now, applying the product rule, we differentiate each term and combine the results:

Derivative of Term 1 = 1  (since the derivative of x is 1)

Derivative of Term 2 = 1  (since the derivative of x is 1)

Using the product rule, the derivative of the function is:

f'(x) = (x - 50) * 1 + (x + 1) * 1

f'(x) = x - 50 + x + 1

f'(x) = 2x - 49

Therefore, the correct answer is B. The derivative is 2x - 49.

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The equivalent value of the expression is x = 65

Given data ,

The equation is represented by the letter A , where

By substituting the values in the equation, we obtain the value of A as

5x + 1 + 5x - 1 - 650 = 0

Taking the similar terms of the expression:

10x - 650 = 0

Adding 650 to both sides:

10x = 650

Dividing both sides by 10:

x = 65

Hence , the expression is x = 65

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The largest integer that is a divisor of (n 1)(n 3)(n 57)(n 9 ) for all positive even integers $n$ is the largest prime factor of $n_9$.

The given expression consists of five consecutive odd numbers: $(n_1), (n_3), (n_5), (n_7), (n_9)$. When we multiply these consecutive odd numbers, all their prime factors cancel out except for the largest prime factor, which is the prime factor of the largest odd number.

Since we are considering even numbers, the largest odd number in this case is $n_9$. Therefore, the largest prime factor of the expression is the largest prime factor of $n_9$.

To find the largest prime factor of a number, we can start dividing it by the smallest prime numbers (2, 3, 5, etc.) and keep dividing until we can't divide anymore. The result will be the largest prime factor.

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Seven faces, fifteen edges and ten vertices.

Answer:

7 faces

15 edges

10 vertices

The z-score of 1.6 corresponds to a probability of 0.0548 or 5.48%. Therefore, the probability that the force acting on the column is greater than 17 kips is 5.48%.

To answer this question, we need to use the concept of deviation. The deviation measures the distance of a data point from the mean. In this case, the mean force acting on the column is 15.0 kips, and the standard deviation is 1.25 kips.
We can use the normal distribution formula to calculate the probability that the force will be within a certain range. Since we are interested in the probability that the force is greater than a certain value, we need to calculate the z-score corresponding to that value. The z-score is the number of standard deviations that the value is from the mean.
To calculate the z-score, we use the formula:
z = (x - mu) / sigma
where x is the value we are interested in, mu is the mean, and sigma is the standard deviation. In this case, we want to find the probability that the force is greater than a certain value, say 17 kips.
z = (17 - 15) / 1.25

= 1.6
In summary, the deviation of a data point from the mean is an important concept when calculating probabilities using the normal distribution. By calculating the z-score, we can determine the probability that a data point falls within a certain range. In this case, the probability that the force acting on the column is greater than 17 kips is 5.48%.

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The value of a is of a = -1/3 and the equation of f(x) in factored form is f(x) = -1/3(x + 5)(x - 9)

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

The roots for this problem are given as follows:

Hence the function in factored form is defined as follows:

f(x) = a(x + 5)(x - 9)

When x = -2, f(x) = 11, hence the leading coefficient a is given as follows:

11 = a(3)(-11)

-33a = 11

33a = -11

a = -1/3.

Hence the equation is:

f(x) = -1/3(x + 5)(x - 9).

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The distribution of the number of coin tosses required until a tail is observed is geometric, not binomial. Its mean is 2 and variance is 2. so none of the answer options is correct and option is D).

The distribution of x, the number of tosses required until a tail is observed, is a geometric distribution.

It is not a binomial distribution because the trials are not independent (the probability of getting a tail increases with each additional toss). The mean of a geometric distribution with probability of success p is 1/p, so in this case the mean is 1/0.5 = 2.

The variance of a geometric distribution with probability of success p is (1-p)/p², so in this case the variance is (1-0.5)/0.5² = 2. Therefore, none of the answer choices is correct. So, the correct option is D).

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The Volume of the candle is approximately 147.66 cubic inches.

To find the volume of the candle, we need to use the formula for the volume of a cylinder, which is:

V = πr^2h

where r is the radius of the circular base, h is the height of the cylinder, and π is approximately equal to 3.14.

In this case, we are given that the height of the candle (h) is 7.5 inches and the diameter (d) is 5 inches. To find the radius (r), we need to divide the diameter by 2:

r = d/2 = 5/2 = 2.5 inches

Now we can substitute these values into the formula and simplify:

V = πr^2h

V = π(2.5)^2(7.5)

V = π(6.25)(7.5)

V = 147.66 cubic inches (rounded to two decimal places)

Therefore, the volume of the candle is approximately 147.66 cubic inches.

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Mr. Smith can bake 3/5 of the total number of cupcakes he needs in an hour.

Since Mr. Smith can bake 1/5 of the total number of cupcakes he needs in 1/3 hour, we can say that he can bake 3/5 of the total number of cupcakes he needs in an hour, since 1 hour is 3 times as long as 1/3 hour.

To see why this is true, we can think about it in terms of rates.

If Mr. Smith can bake 1/5 of the cupcakes he needs in 1/3 hour, then he can bake (1/5)/(1/3) = 3/5 of the cupcakes he needs in an hour, since dividing by 1/3 is the same as multiplying by 3.

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Answer:

the graph plotting changes, the numbers decreases

We find that the approximation converges to 9.74679419, accurate to eight decimal places. So, the square root of 95, approximated using Newton's method, is 9.74679419.

Newton's method is a way to approximate the roots of a function. In this case, we want to approximate the square root of 95 correct to eight decimal places. To use Newton's method, we start with an initial guess and then apply the following formula repeatedly:
x1 = x0 - f(x0) / f'(x0)
where x0 is our initial guess, f(x) is the function we are trying to find the root of (in this case, f(x) = x^2 - 95), and f'(x) is the derivative of f(x) (which is 2x).
Let's start with an initial guess of 10:
x1 = 10 - (10^2 - 95) / (2 * 10) = 5.75
We can continue this process, plugging in our new guess into the formula each time, until we reach a value that is accurate to eight decimal places. After a few iterations, we get:
x8 = 9.74679434
This is our final answer, correct to eight decimal places.
Using Newton's method, we can approximate the square root of a number, such as 95, to eight decimal places. Newton's method is an iterative process that starts with an initial guess and refines the guess using the formula:
x1 = x0 - f(x0)/f'(x0)
For square root approximation, f(x) = x^2 - a, where a is the number we want to find the square root of (95 in this case), and f'(x) = 2x.
Let's start with an initial guess x0 = 9 (since 9^2 = 81 is close to 95). We can then perform the following iterations:
1. x1 = 9 - (9^2 - 95)/(2*9) ≈ 9.72222222
2. x2 = 9.72222222 - (9.72222222^2 - 95)/(2*9.72222222) ≈ 9.74679424
3. x3 = 9.74679424 - (9.74679424^2 - 95)/(2*9.74679424) ≈ 9.74679419
Continuing this process, we find that the approximation converges to 9.74679419, accurate to eight decimal places. So, the square root of 95, approximated using Newton's method, is 9.74679419.

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The quotient of the polynomial long division is determined as 4x²  +  11x  +  15. The remainder = -13

The quotient of the polynomial long division is calculated as follows;

                 2x²  +  5.5x + 7.5

               -------------------------------------

( 2x - 6) √ (2x³ - x² - 18x + 32)

               - (2x³  - 12x²)

              ------------------------------------

                         11x² - 18x + 32

                     -  (11x² - 33x )

             -----------------------------------------

                                 15x  + 32

                              - (15x + 45)

                   ----------------------------------------

                                       -13

The quotient of the polynomial long division is determined as;

2x²  +  5.5x + 7.5 = 20x² +  55x²  + 75 = 4x²  +  11x  +  15

The remainder = -13

So (2x³ - x² - 18x + 32) / ( 2x - 6)  =  4x²  +  11x  +  15 [ -13 /  ( 2x - 6) ]

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The complete question is below:

(2x³ - x² - 18x + 32) / ( 2x - 6) . Find the quotient and remainder of this polynomial division.

Answer:

x = 10 and y = 11

Step-by-step explanation:

2x + 3y = 53      (call this equation '1')

3x - y = 19      (call this '2')

multiply '2' by 3:

9x - 3y = 57          (call this '3')

add '1' and '3':

(2 + 9)x  + (3 + -3)y = 53 + 57

11x = 110

x = 10.

now sub that value of x into '1':

2(10) + 3y = 53

20 + 3y = 53

3y = 53 -20

3y = 33

y = 11

no sub both x = 10 and y =11 into '2' to see if everything adds up:

3x - y = 19

3(10) - 11 = 30 - 11 = 19.

so x = 10 and y =11

The expression tan²θ-Sin²θ = tan²θsin²θ is proven that the left hand side is equal to the right hand side.

To prove the expression, tan²θ-Sin²θ = tan²θsin²θ, start from the left-hand side and use the trigonometric identity tan²θ = sin²θ/cos²θ and the Pythagorean identity sin²θ + cos²θ = 1.

Starting from the left-hand side:

tan²θ - sin²θ = (sin²θ/cos²θ) - sin²θ

= sin²θ (1/cos²θ - 1)

= sin²θ ((1-cos²θ)/cos²θ)

= sin²θ (sin²θ/cos²θ)

= tan²θ sin²θ

Thus, it is shown that the left-hand side is equal to the right-hand side: tan²θ - sin²θ = tan²θ sin²θ.

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[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =2.2 \end{cases}\implies A=\cfrac{(2.2)(8)^2}{2}\implies A=70.4~m^2[/tex]

Answer:

5 units down

Step-by-step explanation:

Hope this helped, all you are doing is a translation.

Edit* If there is no down option do -5

Answer:

It would take 6 workers 16 days to complete the job.

This is because the number of workers and the number of days are inversely proportional. This means that if the number of workers increases, the number of days will decrease, and vice versa.

In this case, the number of workers has decreased from 8 to 6. This means that the number of days will increase from 12 to 16.

Here is the formula for calculating the number of days it would take 6 workers to complete the job:

Number of days = (Number of workers x Number of days) / (New number of workers)

Plugging in the values, we get the following:

Number of days = (8 x 12) / 6 = 16

Therefore, it would take 6 workers 16 days to complete the job.

Step-by-step explanation:

Answer:

It will take 6 workers 16 days

Step-by-step explanation:

8 workers at 12 days = 96 work days

We have 6 workers

96/6 = 16 days

It will take 6 workers 16 days

It represents exponential growth. As x increases, the value of f(x) will increase at an accelerating rate, reflecting the steady growth rate of 8.5% each year in the US credit card debt.

The given equation, f(x) = 86(1.085)^x, represents the US credit card debt in billions of dollars over time. To determine whether this equation shows exponential growth or exponential decay, we need to analyze the properties of the function.

Exponential growth is characterized by an increasing value over time. In this case, if the value of f(x) is increasing as x increases, then it indicates exponential growth.

Let's examine the equation: f(x) = 86(1.085)^x.

The base of the exponential term, 1.085, is greater than 1. This implies that the value of f(x) will grow exponentially as x increases. Each time x increases by 1, the term (1.085)^x will be multiplied by 1.085, causing the function to grow even further. This multiplication by a constant greater than 1 ensures exponential growth.

Additionally, the initial value, 86 billion, further supports the idea of growth. As x increases, the exponential term will cause the function to increase rapidly, reflecting the compounding effect of the growth rate.

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To ensure generalizability, the sample should be representative, meaning that it should accurately reflect the characteristics of the population being studied.

The size of the sample, whether small or large, is not as important as the representativeness of the sample. A small or large sample that is not representative can lead to inaccurate conclusions about the population.

Therefore, it is important to carefully select a sample that is diverse and includes a range of characteristics that are relevant to the research question. By having a representative sample, researchers can increase the external validity of their findings and make more accurate generalizations about the population as a whole.

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The sample proportion (360 out of 1200) can be used to estimate the population proportion, and statistical tests such as a one-sample proportion test or a Z-test can be applied to evaluate the hypotheses and determine the significance of the results.

The null and alternative hypotheses that should be used in this scenario are as follows:

Null Hypothesis (H₀): The proportion of families interested in the program is still 20% or less.

Alternative Hypothesis (H₁): The proportion of families interested in the program has increased, i.e., it is greater than 20%.

Symbolically, we can represent the hypotheses as:

H₀: p ≤ 0.20 (proportion is 20% or less)

H₁: p > 0.20 (proportion is greater than 20%)

In this case, "p" represents the population proportion of families in New Jersey interested in the renewable energy program.

To determine if there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis, a hypothesis test can be conducted using appropriate statistical methods.

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Answer:

D. 23% decrease

Step-by-step explanation:

To find the percentage of increase or decrease, we can use the following formula:

Percentage change = ((New value - Old value) / Old value) * 100

Let's calculate the percentage change in the price of the television:

Old value = 398

New value = 306.46

Percentage change = ((306.46 - 398) / 398) * 100

Percentage change = (-91.54 / 398) * 100

Percentage change ≈ -22.98%

The percentage change is approximately -22.98%.

Since the value decreased, the correct answer is:

D. 23% decrease

91.54 decrease

91.54/398 ~ 0.23 ~ %23

the answer must have been D

Answer: g(f(3)) = 21.5

Step-by-step explanation:

     g(f(3)) is asking us to substitute 3 into f(x) and then substitute that into g(x).

Given:

   f(x) = x +[tex]\frac{1}{2}[/tex]  

Substiute 3 into f(x) for x:

   f(3) = 3 +[tex]\frac{1}{2}[/tex]  

     f(3) = 3.5

Given:

     g(x) = 2x² –  3

Substiute f(3) = 3.5 into g(x) for x:

      g(f(3)) = 2(3.5)² –  3

     g(f(3)) = 24.5 –  3

     g(f(3)) = 21.5

The P-value for the hypothesis test H₀: p = 0.9 against H₁: p ≠ 0.9, at α = 0.056, is less than 0.056.

What is hypothesis test?

A hypothesis test is a statistical procedure used to make inferences or draw conclusions about a population based on sample data. It involves formulating two competing hypotheses, the null hypothesis (H₀)

In this hypothesis test, we are interested in determining if the proportion (p) of customers who are satisfied or very satisfied with a corporation's products and services is different from 0.9.

The null hypothesis (H₀) states that the proportion is equal to 0.9, while the alternative hypothesis (H₁) states that the proportion is not equal to 0.9.

To test these hypotheses, we use a binomial proportion test. From the given information, we have a sample of 1000 customers, and 850 of them are satisfied or very satisfied.

Using the sample proportion calculated as 850/1000 = 0.85, we can calculate the test statistic, which follows an approximately standard normal distribution under the null hypothesis.

Since the P-value is less than 0.056, we reject the null hypothesis and conclude that there is evidence to suggest that the proportion of satisfied or very satisfied customers is different from 0.9.

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