From the 10 male and 7 female sales representatives for an insurance company a team of 3 men and 3 women will be selected to attend a national conference on insurance fraud. In how many ways can the team of 6 be selected?

The coordinates which divide the segment with endpoint (-1,-2) and (8,4) in the ratio 2 to 1 are (5,2)

What is section formula?

Section formula is used to find the ratio in which a line segment is divided by a point internally or externally. The section formula can be given as

\((\frac{mx_{2}+nx_{1} }{m+n} ,\)\(\frac{my_{2}+ny_{1} }{m+n})\) where \((x_{1},y_{1} ),(x_{2},y_{2} )\) are the endpoints of the segment and this points are divided in the ratio \(m:n\)

We are given the coordinates as (-1,-2) and (8,4)

This segment is divided in ratio 2:1

We use section formula to find the coordinates

the x- coordinates can be given as

\(x=\frac{2(8)+1(-1)}{2+1}\)

\(x=\frac{16-1}{3}\\\)

\(x=\frac{15}{3}\)

\(x=5\)

Similarly the y coordinate can be given as

\(y=\frac{2(4)+1(-2)}{2+1}\)

\(y=\frac{8-2}{3}\)

\(y=\frac{6}{3}\)

\(y=2\)

Hence the coordinates which divide the segment with endpoint (-1,-2) and (8,4) in the ratio 2 to 1 are (5,2)

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Answer:

C

Step-by-step explanation:

Answer: The probability is 0.083

Step-by-step explanation:

First, let's find the individual probabilities:

The probability that the outcome of the red number cube is even:

This will be equal to the quotient between the number of outcomes that are even (3) and the total number of outcomes for this dice (6)

Then the probability is:

p = 3/6 = 1/2.

The probability that the outcome of the blue number cube is a 5.

Similar to the above case, here the probability will be the quotient between the number of outcomes that are 5 (only one) and the total number of outcomes.

q = 1/6

And the joint probability will be equal to the product of the individual probabilities, then he probability that the outcome of the red number cube is even and the outcome of the blue number cube is a 5 is equal to:

P = p*q = (1/2)*(1/6) = 1/12 = 0.083

Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

To solve the problem we must know about quadratic equations.

A quadratic equation is an equation that can be written in the form of

ax²+bx+c.

Where a is the leading coefficient, and

c is the constant.

The breadth of the rectangle is 200 ft, while the length is 210 ft.

Given to us

Area of the parking lot = Area of the rectangle

42,000 ft² = Length x Breadth

Solving for L,

\(42,000 = L \times B\\\\ L = \dfrac{42,000}{B}\)

Perimeter of the parking lot = Perimeter of the rectangle

820 ft. = 2(Length + Breadth)

820 ft. = 2(L+ B)

\(2(L+ B) = 820\\\\ (L+B) = \dfrac{820}{2}\\\\ (L+B) = 410\)

Substituting the value of L,

\((L+B) = 410\\\\ (\dfrac{42,000}{B}) +B = 410\\\\ 42000 + B^2 = 410B\\\\ B^2 -410B +42000 = 0\)

Solving the quadratic Expression,

\(B^2 -410B +42000 = 0\\\\ (B-210)(B-200)=0\)

Equation the factors against zero,

B-210=0

B = 210

B-200=0

B = 200

Hence, the breadth of the rectangle is 200ft, while the length is 210 ft.

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Answer:

210ft

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

(a) The differential equation is not in exact form.

(b) The integrating factor for the given differential equation is μ(t) = e^(-t).

(c)  The solution is  y = -e^(2t) + Ce^t, where C is a constant of integration.

(a) A differential equation is said to be in exact form if it can be written as M(x, y) dx + N(x, y) dy = 0, where the partial derivatives of M and N with respect to y and x, respectively, are equal, i.e., ∂M/∂y = ∂N/∂x. In the given differential equation, t dy/dt + (1 – t)y = e^2t, the partial derivatives of (1 – t)y with respect to y and t are -t and (1 - t), respectively, which are not equal. Therefore, the given differential equation is not in exact form.

(b) To transform the given differential equation into an exact form, we can find an integrating factor, denoted by μ(t), which is a function of t only. The integrating factor is obtained by dividing an expression involving the partial derivatives of the given equation with respect to y and t. In this case, we have ∂M/∂y - ∂N/∂x = -t - (1 - t) = -1. Thus, the integrating factor is μ(t) = e^(-∫1 dt) = e^(-t).

(c) Multiplying the given differential equation by the integrating factor e^(-t), we obtain e^(-t)(t dy/dt + (1 – t)y) = e^(-t)e^(2t). Simplifying this equation, we have e^(-t) d(ty) = e^(t). Integrating both sides with respect to t, we get ∫e^(-t) d(ty) = ∫e^(t) dt. The left-hand side can be evaluated as -e^(-t)y + C_1, where C_1 is the constant of integration. The right-hand side evaluates to e^t + C_2, where C_2 is another constant of integration. Combining these results, we have -e^(-t)y + C_1 = e^t + C_2. Rearranging the equation, we obtain y = -e^(2t) + Ce^t, where C = C_1 - C_2 is a constant of integration. This is the solution to the given differential equation.

In summary, the given differential equation is not in exact form. By finding an integrating factor of μ(t) = e^(-t), we transform the equation into an exact form. The solution to the transformed equation is y = -e^(2t) + Ce^t, where C is a constant of integration.

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To find the probability that more than 35 minutes will pass without a student appearing at the drop-in center, we can use the exponential distribution formula. Given that the rate of arrivals is one every 25 minutes, we can calculate P(X ≥ 35), where X represents the length of time between successive arrivals.

The exponential distribution probability density function (pdf) is given by:

f(x) = λ * e^(-λx)

Where λ is the rate parameter. In this case, the rate parameter is 1/25 since the rate is one student every 25 minutes.

To find the probability P(X ≥ 35), we need to calculate the integral of the pdf from 35 to infinity:

P(X ≥ 35) = ∫[35, ∞] (1/25) * e^(-(1/25)x) dx

To evaluate this integral, we can use integration techniques or a calculator. The result is:

P(X ≥ 35) ≈ 0.264

Therefore, the probability that more than 35 minutes will pass without a student appearing at the drop-in center is approximately 0.264, rounded to 3 decimal places.

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Answer: $4.45

Step-by-step explanation: you will get $4.45

Answer:

it should be 445%

Step-by-step explanation:

Temperature of refrigerators - Cannot determine. Horsepower of race car engines - Ratio. Marital status of school board members - Nominal. Ratings of television programs - Ordinal. Ages of children enrolled in a daycare - Interval

The level of measurement for the temperature of refrigerators cannot be determined based on the given information. The temperature could potentially be measured on a nominal scale if the refrigerators were categorized into different temperature ranges. However, without further context, it is not possible to determine the specific level of measurement.

The horsepower of race car engines can be measured on a ratio scale. Ratio scales have a meaningful zero point and allow for meaningful comparisons of values, such as determining that one engine has twice the horsepower of another.

The marital status of school board members can be measured on a nominal scale. Nominal scales are used for categorical data without any inherent order or ranking. Marital status categories, such as "married," "single," "divorced," etc., can be assigned to school board members.

The ratings of television programs, such as "poor," "fair," "good," and "excellent," can be measured on an ordinal scale. Ordinal scales represent data with ordered categories or ranks, but the differences between categories may not be equal or measurable.

The ages of children enrolled in a daycare can be measured on an interval scale. Interval scales have equal intervals between values, allowing for meaningful differences and comparisons. Age, measured in years or months, can be represented on an interval scale.

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Person A would save the most money because they had a coupon that was worth more than their portion of the purchase price.

To determine who would save the most money if each person paid an equal amount, we need to calculate how much each person paid and then compare the amounts saved by each person. For instance, let's consider an example with four people who want to split the cost of a $60 purchase equally. Each person would pay $60 / 4 = $15.

If person A has a $20 coupon, then they would save $20, and their net cost would be $15 - $20 = -$5. Person B has a $15 coupon, so they would save $15, and their net cost would be $15 - $15 = $0. Person C has a $10 coupon, so they would save $10, and their net cost would be $15 - $10 = $5. Person D has a $5 coupon, so they would save $5, and their net cost would be $15 - $5 = $10.

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DEFINITIONS and APPLICATION:
1A short answer is a concise response that directly addresses the question or prompt. It typically consists of a few sentences or a paragraph and is focused on providing a specific answer without unnecessary details or elaboration.

Example: When asked "What is the capital of France?", a short answer would be "Paris."

A 100-word response refers to providing a written explanation or description within a specific word limit of 100 words. This limitation requires the writer to be concise and selective with their information while still conveying a comprehensive understanding of the topic.

Example: If asked to describe the water cycle in 100 words, a response could include information about evaporation, condensation, precipitation, and how water moves between the Earth's surface, atmosphere, and bodies of water.

A conclusion is the final part of a written piece that summarizes the main points and provides a closing statement. It serves to wrap up the information discussed in the body of the text and leave a lasting impression on the reader.

Example: In an essay about the benefits of exercise, the conclusion may restate the key advantages, such as improved physical and mental health, increased energy levels, and reduced risk of chronic diseases, while also encouraging the reader to prioritize regular physical activity.

4. Application: In the context of these concepts, application refers to the practical use or implementation of a particular idea, theory, or skill in real-life situations. It involves taking what has been learned and using it to solve problems, make decisions, or accomplish specific tasks.

Example: If learning about the Pythagorean theorem, applying it would involve using the formula to find the length of the hypotenuse in a right triangle when given the lengths of the other two sides.

These are four of the eight concepts related to definitions and applications. Remember to provide clear explanations, relevant examples, and use a step-by-step approach when addressing each concept.

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Answer:

La suma de los tres ángulos interiores de un triángulo es 180°. Uno de los ángulos mide 90° porque es un triángulo rectángulo.

Answer:

La suma de los ángulos interiores de un triángulo es 180°.

Answer:

u need 78 feet of the three foot wide fencing

Thee volume of the cone has a value of 1, 739. 60 cubic feet

The formula for calculating the volume of a cone is expressed as;

V = πr²h/3

Where;

From the information given, we have the values as;

Diameter = 19

But radius = Diameter/2

Now, radius = 18. 7/2 = 9.35 ft

Substitute the values into the formula

Volume = 3. 142( 9.35)² × 19/3

Find the value of the square

Volume = 3. 142(87. 42) × 6. 3

Multiply the values

Volume = 1, 739. 60 cubic feet

Hence, the value is 1, 739. 60 cubic feet

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The standard deviation of the sampling distribution of sample means, based on samples of the amounts of weight lost by 72 people on this diet, is approximately 0.695 pounds.

To calculate the standard deviation of the sampling distribution of sample means, we need to use the formula for the standard deviation of a sample mean. This formula states that the standard deviation of the sampling distribution (σ) is equal to the standard deviation of the population (σ) divided by the square root of the sample size (n).

Given that the population standard deviation (σ) is 5.9 pounds and the sample size (n) is 72, we can plug these values into the formula:

Standard Deviation of the Sampling Distribution (σ) = σ / √n

σ = 5.9 pounds

n = 72

Substituting these values, we get:

Standard Deviation of the Sampling Distribution (σ) = 5.9 / √72

To find the standard deviation of the sampling distribution, we need to evaluate the square root of 72. Using a calculator or mathematical software, we find that √72 is approximately 8.49.

Now, let's calculate the standard deviation of the sampling distribution:

Standard Deviation of the Sampling Distribution (σ) = 5.9 / 8.49 ≈ 0.695 pounds (rounded to two decimal places)

Therefore, the standard deviation of the sampling distribution of sample means, based on samples of the amounts of weight lost by 72 people on this diet, is approximately 0.695 pounds.

This value represents the average amount of variation or dispersion in the means of different samples taken from the population. It indicates how much the sample means are likely to deviate from the population mean.

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Answer:

Domain: \(x\)

Number of pieces of candy: Discrete variable.

Domain of the function: \(Dom\{y\} = \mathbb{N}_{O}\)

Step-by-step explanation:

Let \(y = 150\cdot x\). From Function Theory, we know that domain represents the set of values of the independent function, defined by the variable \(x\) in this case, whereas the range represents the set of values associated with the domain, defined by the variable \(y\) in this case.

Since \(x\) represents the number of pieces of candy, this variable has a discrete nature.

In addition, this linear function has a domain represented by the set of natural number and the zero element.

Answer:

Two angles are complementary angles if the sum of their measures is 908.

Each angle is the complement of the other. Two angles are supplementary

angles if the sum of their measures is 1808. Each angle is the supplement of

the other.

Complementary angles and supplementary angles can be adjacent angles

or nonadjacent angles. Adjacent angles are two angles that share a common

vertex and side, but have no common interior points.

Step-by-step explanation:

it easy

Ludolph van Ceulen, a Dutch mathematician, calculated an impressive 35 digits of pi during his lifetime.

1. Van Ceulen used a geometrical approach called the method of polygons to approximate the value of pi.

This method involves inscribing and circumscribing polygons around a circle, then finding the perimeters of those polygons.
2. As the number of sides of the polygons increases, the perimeters of the inscribed and circumscribed polygons get closer and closer to the circumference of the circle.

The ratio of the circumference to the diameter of the circle is pi.
3. To improve the accuracy of his approximation, Van Ceulen increased the number of sides of the polygons.

He started with a polygon with a smaller number of sides and then successively doubled the number of sides.
4. For each set of polygons, Van Ceulen calculated the perimeters using trigonometric formulas and algebraic manipulations.

This process is quite labor-intensive and time-consuming, especially considering the mathematical tools available at the time.
5. By comparing the perimeters of the inscribed and circumscribed polygons, Van Ceulen was able to narrow down the range of possible values for pi.
6. Eventually, he reached a point where the polygons had so many sides that their perimeters were almost indistinguishable from the circumference of the circle.

At this stage, he determined pi to an accuracy of 35 digits.
It's important to note that Van Ceulen's achievement was remarkable for his time, as he completed these calculations by hand, without the aid of modern computers or calculators.

His dedication to the task led to a significant advancement in our understanding of pi.

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The regular dodecagon is a polygon with 12 sides of equal length and 12 angles of equal measure.

        Area = 3 × side length × apothem,

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So we see that r = 0. Therefore, the equation of the circle is just:

(x - 2)^2 + (y - 9)^2 = 0

Company revenue quadratic function.

Angel

The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?

To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:

r(x) = a(x - h)^2 + k

where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

We can use the given revenue values to set up a system of three equations:

2.7 = a(0 - h)^2 + k

3.4 = a(1 - h)^2 + k

2.7 = a(6 - h)^2 + k

Subtracting the first equation from the second, and the first equation from the third, we get:

0.7 = a(1 - h)^2

0 = a(6 - h)^2

Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:

6 - h = 10

which gives us h = -4.

Substituting h = -4 into the first equation, we get:

2.7 = a(0 - (-4))^2 + k

2.7 = 16a + k

Substituting the revenue value for 2005, we get:

3.9 = a(3 - (-4))^2 + k

3.9 = 49a + k

Solving for a and k, we get:

a = -0.1

k = 4.3

Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:

r(x) = -0.1(x + 4)^2 + 4.3

The vertex of this function is at (-4, 4.3).

Angel

What is the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101?

We can notice that the sequence alternates between adding an odd number and subtracting an even number. The first term is 3, which is odd, so the sequence starts by adding an odd number. The second term is -4, which is even, so the sequence then subtracts an even number. This pattern continues, so the sum of the sequence can be written as:

3 - 4 + 5 - 6 + ... + 101

We can group the terms into pairs:

(3 - 4) + (5 - 6) + ... + (99 - 100) + 101

Each pair of terms adds up to -1, so we can simplify the expression to:

-1 -1 -1 ... -1 + 101

where there are 50 pairs of -1's. The sum of 50 -1's is -50, so the sum of the sequence is:

-50 + 101 = 51

Therefore, the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.

Angel

What is 12 7/8 - 56/17?

To subtract mixed numbers like 12 7/8, we first need to convert it to an improper fraction. We can do this by multiplying the whole number by the denominator of the fraction, and adding the result to the numerator. This gives us:

12 7/8 = (12 × 8 + 7)/8 = 103/8

Now we can subtract 56/17 from 103/8. To do this, we need to find a common denominator for the two fractions. The least common multiple of 8 and 17 is 136, so we can rewrite the fractions with this denominator:

103/8 = (103/8) × (17/17) = 1751/136

56/17 = (56/17) × (8/8) = 448/136

Now we can subtract the two fractions:

1751/136 - 448/136 = (1751 - 448)/136 = 1303/136

We can simplify this fraction by finding a common factor to divide both the numerator and denominator. Since both 1303 and 136 are relatively prime, we cannot simplify it any further. Therefore, the final answer is:

12 7/8 - 56/17 = 1303/136

Angel

A circle in the xy-plane has a diameter with endpoints (2,4) and (2,14). An equation of this circle is (x-2)^2+(y-9)^2=r^2 ,where r is a positive constant. What is the value of r?

The center of the circle is the midpoint of the diameter, which is at (2, (4+14)/2) = (2, 9). We can substitute this center point into the equation of the circle to get:

(x - 2)^2 + (y - 9)^2 = r^2

(2 - 2)^2 + (9 - 9)^2 = r^2

0 + 0 = r^2

So we see that r = 0. Therefore, the equation of the circle is just:

(x - 2)^2 + (y - 9)^2 = 0

This describes a single point in the xy-plane, which is the center of the circle. Note that this point is already on the given diameter, so it makes sense that the radius is zero.

Answer:

\(equation \: for \: pythagorean \: theorem \: is \: \\ {3.8}^{2} + {6.8}^{2} = {x}^{2} \)

Answer:

Step-by-step explanation:

see attached

Answer:

-3=b

Step-by-step explanation:

Hey there!

In order to find the value for b, we must first combine all like terms

-11-6b+3=16+2b

-8-6b=16+2b

-24=8b

Now we simplified the equation to a point where we can find the value of b in one step

-24/8 = 8b/8

-3=b

Answer:

-3

Step-by-step explanation:

Bring to the right of = the Number with b and to the left the other.

Remember to change sign of Number when you switch

So

\( - 11 + 3 - 16 = 2b + 6b\)

Do addition

\( - 24 = 8b\)

Find b

\(b = - 24 \div 8\)

b= -3

Answer:

x=1

Step-by-step explanation:

We wanna have the same amount on both sides

There are 3 circles on the left and 7 circles on the right. There are also 4 triangles. Turn into numbers...

4x+3=7

4x=7-3

x=1

We can check by substituting one

7=7

w is no more than 7 is different

Answer:

W is no more than 7

Step-by-step explanation:

W is greater than or equal to -7 is (W>_-7)

W is no more than 7 is (W<_7)

W is no less than -7 is (W>_7)

W is at least -7 is (W>_7)

Out of all of these, w is no more than 7 is the only different expression

Answer:

There are no possible solutions for this question.

Step-by-step explanation:

Answer:

There are no possible solutions

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

5+5+7+7

Answer:

24 feet

Step-by-step explanation:

7 times 2 is 14

5 times 2 is 12

14 plus 12 is 24

The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

k=1.66666666667

3:5 or y+9-x=17

Step-by-step explanation:

idrk, this SHOULD be the correct answer