The system of equations is graphed on the coordinate plane.

y=−12x−2

y=−32x+2

permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.

The factorial function (symbol: !) just means to multiply a series of descending natural numbers.

a) The number of four people committees that can be selected from a group of 16 people is:

no. of committees are possible = 16!/ 4!

(16x15x14x13)/(1x2x3x4)=1820

b)Given that

One person is the chair, and the rest are general members

n! / (n − r)!

where n is the number of things to choose from,

Pick a chairman:: 16 ways

Pick 3 others:: 15C3 = 455 ways

Ans: 16×455 = 7200

c)

Each committee has a chair, a secretary, a refreshment person and a cleanup person.

The number of combinations of assignments within each committee is: 4x3x2x1=24.

The total number of committees with each committee member’s responsibility is: 1820x24=43680.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Greetings from Brasil...

Comparing the distances AB and A'B ', we notice that AB = 3 and A'B' '= 9.

We can say that:

AB · X = A'B'

3 · X = 9

3X = 9

X = 9 ÷ 3

X = 3

Thus, figure B is 3x larger than figure A

scale factor = 3x larger

Answer:

x=3

Step-by-step explanation:

AB = 3 and A'B' '= 9.

hope this helps

You can suggest that managers should avoid the quick-fix mentality that makes management by best-seller so tempting by implementing the following strategies:

1. Understand the Unique Nature of Your Business: Managers should take the time to understand the unique nature of their business. They should realize that what worked for another company may not work for their own company.

2. Avoid Short-Term Solutions: Managers should avoid short-term solutions that provide quick results. They should focus on long-term solutions that will benefit the organization in the long run.

3. Develop a Comprehensive Strategy: Managers should develop a comprehensive strategy that includes long-term goals and objectives. They should also have a plan in place to achieve those goals.

4. Invest in Employee Development: Managers should invest in employee development by providing training and development opportunities. This will help to build a strong workforce that is capable of handling complex challenges.

5. Encourage Collaboration: Managers should encourage collaboration among team members. This will help to create a culture of teamwork and cooperation.

6. Monitor Progress: Managers should monitor progress and adjust strategies as necessary. This will help to ensure that the organization is on track to achieving its goals.

By following these strategies, managers can avoid the quick-fix mentality that makes management by best-seller so tempting. They can focus on long-term solutions that will benefit the organization in the long run.

Hope this helped you...

Answer:

Step-by-step explanation:

To find the volume of the solid of revolution, we can use the formula for the volume of a solid of revolution:

V = π∫[a,b] (f(x))^2 dx

where f(x) is the distance between the x-axis and the upper half of the ellipse at x, a and b are the limits of integration.

The upper half of the ellipse can be written as y = b√(1 - x^2/a^2). Thus, the distance between the x-axis and the ellipse at x is given by f(x) = b√(1 - x^2/a^2). Substituting this into the formula for the volume of a solid of revolution, we get:

V = π∫[-a,a] (b√(1 - x^2/a^2))^2 dx

= 2πb^2∫[0,a] (1 - x^2/a^2) dx (because the integrand is even)

= 2πb^2 [x - x^3/(3a^2)]|[0,a]

= 2πb^2 [a - a^3/(3a^2)]

= (4π*b^2*a^2)/3

Therefore, the volume of the solid of revolution is (4π*b^2*a^2)/3, which is the volume of a prolate spheroid.

The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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A leading question is worded in a way that will influence the response of the question.

A leading question is worded in such a way that it has the tendency to lead the person being asked the question to a specific answer. A leading question can be said to be a question that is worded or constructed in a way that assumes a particular answer and in turn, encourages a particular response from the person being asked the question. A leading question may involve asking a question that presumes the answer, such as, "You believe that it is important to support animal rights, don't you?". Such a question may encourage the respondent to say yes even if they do not believe that supporting animal rights is important. This is because the question has already led them to the desired response. Another example of a leading question may involve asking a question that is framed in a way that encourages a particular response. For instance, asking "How many times do you watch television each day?" may lead to a different response compared to asking "Do you watch television often?".

Therefore, a leading question is worded in a way that will influence the response to the question. By doing so, the person asking the question is likely to obtain the response they are seeking. The answer to this question is option B. A leading question is worded in a way that will influence the response of the question.

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The area of the pentagon is 1,453 squared centimeters.

Given information-

The length of the apothem of a regular pentagon is 20 cm.

The measure of the perimeter of a regular pentagon is 145.3 cm.

The length of the apothem of a rectangular pentagon is 20 cm.

The measure of the perimeter of a rectangular pentagon is 145.3 cm.

Pentagon is the closed shaped polygon which has 5 sides. When these 5 sides are equal in length then the pentagon is called teh regular pentagon. When four of the sides of pentagon make a rectangle then the pentagon is called the rectangular pentagon.

Area of regular pentagon is half of the product of its apothem and perimeter. It can be given as,

\(A=\dfrac{1}{2} \times 20\times 145.3\\A=1453\)

Thus the area of the pentagon is 1,453 squared centimeters.

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tan 35 = (height - 5)/100

0.7002 = (height-5)/100

0.7002 x 100 = height - 5

70.02 = height - 5

height = 70.02 + 5

height = 75.02 feet

height = approx. 75 feet

The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in

(4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in

(6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Answer:

-42

Step-by-step explanation:

The predecessor of -41 is -42.

The inequality value of y in -5+y>or=7 is y >or = 12

Inequality is a statementof an order relationship. Greater than, greater than or equal to, less than, or less than or equal to,between two numbers or algebraic expressions.

-5+y>or equal to 7 is an example of inequality expression

adding 5 to both sides,

-5+5+y>or=7+5

then y>or = 12

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As a result, f(x) changes at a rate of 1/2 on average over the range [0, 1/2].

A function is a mathematical formula that relates every element in one set, known as the domain, to a single element in another set, known as the range. The most prevalent way to represent a function is as f(x), where f(x) stands for the output or dependent variable and "x" stands for the input or independent variable. There is a value of f(x) in the range for each value of x in the domain. Consider the function f(x) = 2x + 1 as an illustration. This function's range and scope possibilities are both limited to the real numbers.

given

We must determine the slope of the secant line that goes through the interval's endpoints in order to determine the average rate of change of a function over the interval. Since the range in this instance is [0, 1/2], we must determine the slope of the secant line that connects (0, f(0)) and (1/2, f(1/2)).

Let's first assess the function at the interval's endpoints:

f(0) = 0² + 2(0) + 1 = 1

f(1/2) = (1/2)² + 2(1/2) + 1

= 5/4

Next, we can calculate the slope of the secant line using the slope formula:

slope is equal to (f(1/2)-f(0)) / (1/2 - 0)

= ((5/4)-1) / (1/2)

= (1/4) / (1/2)

= 1/2.

As a result, f(x) changes at a rate of 1/2 on average over the range [0, 1/2].

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Answer:

The 3rd quartile

Step-by-step explanation:

The median to referred to as the 2nd quartile which is in the middle. To the right of the median is the 3rd quartile. Hope this helps! :)

Answer:

The answer to your problem is, subtraction property of equality

Step-by-step explanation:

Given information, If x + 5 = 15

By subtraction property of equality:

Subtract 5 from both sides we have;

then; x = 10

Thus the answer to your problem is, subtraction property of equality

Answer:

(3,1)

Step-by-step explanation:

There are 12 different ways to vote for Jenny.

Jenny has been given a list of 4 bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list.

How many different ways can someone vote?The sequence matters and repetitions are not permitted when choosing two options out of four.

Therefore, we may use the permutation formula P(n, r) = n! / (n - r)! to find the number of possible methods of voting. Here, r = 2 and n = 4 respectively.P(4, 2) = 4! / (4 - 2)! = 4! / 2! = 24 / 2 = 12

There are twelve ways to support Jenny.

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Let's open the brackets

Now, let's solve by isolating like terms.

Since all of the like variables and constants are isolated, we can easily solve by solving the constants and the variables.

Hence, the missing variable value is 22.

\(BrainiacUser1357\)

A particular solution and the fundamental solution of a nonhomogeneous differential equation cannot be the same.

1. Nonhomogeneous differential equation: A differential equation that has a non-zero term independent of the dependent variable (the function you are trying to find). It can be represented as L(y) = f(x), where L is the differential operator, y is the dependent variable, and f(x) is a non-zero function of the independent variable x.

2. Particular solution: A specific solution to a nonhomogeneous differential equation that satisfies both the differential equation and the initial or boundary conditions. It represents a single instance of the infinite possible solutions.

3. Fundamental solution: A set of linearly independent solutions to the corresponding homogeneous differential equation, i.e., the equation with the non-zero term set to zero (L(y) = 0). These solutions form a basis to construct the complementary function, which, when added to the particular solution, provides the general solution of the nonhomogeneous differential equation.

Since the fundamental solution refers to solutions of the homogeneous equation, and the particular solution is a specific solution to the nonhomogeneous equation, they cannot be the same. The general solution to the nonhomogeneous differential equation is obtained by combining the complementary function derived from the fundamental solutions and the particular solution.

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It would be less expensive to join Gym A for b. Less than 12 months.

The total cost C for Gym A can be represented by the equation,

C = 50 + 79n

where n represents the number of months of membership.

The total cost C for Gym B can be represented by the equation,

C = 250 + 63n

where n represents the number of months of membership.

To find the conditions under which joining Gym A would be less expensive, we need to set up an inequality. Since we want to compare the costs for the two gyms, we will set the inequality of Gym A's cost less than Gym B's cost. This can be written as

50 + 79n < 250 + 63n

This can be simplified and solved:

16n < 200

n < 12.5

Therefore, if Delilah is planning to be a member of a gym for less than 12 months, then joining Gym A will be less expensive. If she is planning to be a member for more than 12 months, then joining Gym B will be less expensive. Hence, the answer is option b. Less than 12 months.

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The car's speed is 60 km/hour.

Let's denote the distance from the starting point to the destination by D, and let's denote the car's speed by S.

Using the formula speed = distance / time.

S = d  / t = (D - 200) / 1  ---- (1)

S = d / t = (D - 80) / 3  ----- (2)

We can simplify equation (2) by multiplying both sides by 3:

Expanding the right-hand side:

3S = D - 80

From equation 1 and 2:

3 (D - 200) = D - 80

3D - 600 = D - 80

3D - D = 600 - 80

2D = 520

D = 260

Therefore, the distance from the starting point to the destination is 260 km.

Using equation (1), we can find the car's speed:

S = 260 - 200 / 1

S = 60 m/s

Therefore, the car's speed is 60 km/hour.

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The complete question is:

A car is 200km from its destination after 1 hour and 80km from its destination after 3 hours. At what rate is the car traveling per hour?

The measure of each new angle is 26°

Answer:

Step-by-step explanation:

I realize that the time is passed.... but FYI

BD is Geometric Mean

That's mean BD² = 6 × 5 = 30 ⇒ BD = √30

x² = BD² + 6² = 30 + 36 = 66 ⇒ x = √66

y = √55

Answer: 66

Step-by-step explanation:

ΔADC and ΔABD are similar (AAA)

Therefore the cooresponging sides are in proportion: AD/AC = AB/AD

D its aswer

Step-by-step explanation:

Answer: No solution (please give me the brainiest this took so long)

Step-by-step explanation:

step 1: distribute

7+5(+3)=8+4(+2)

7+5+15=8+4(+2)

step 2: combine like terms

7+5+15=8+4(+2)

12+15=8+4(+2)

step 3: distribute again

12+15=8+4(+2)

12+15=8+4+8

step 4: combine like terms

12+15=8+4+8

12+15=12+8

step 5: subtract 15 from both sides of the equation

12+15=12+8

12+15−15=12+8−15

step 6: simplify

subtract the numbers

12+15−15=12+8−15

12=12+8−15

subtract the numbers

12=12+8−15

12=12−7

step 7: subtract 12a from both sides of the equation

12=12−7

12−12=12−7−12

step 8: simplify

combine like terms

12−12=12−7−12

0=12−7−12

combine like terms

0=12−7−12

0=−7

The input is a contradiction: it has no solutions

A mathematical quantity having both direction and magnitude is called a vector.

A vector is a mathematical quantity that has both direction and magnitude. It is often represented graphically as an arrow, where the length of the arrow corresponds to the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Vectors are used in many areas of mathematics and science, including physics, engineering, and computer science. Some common operations performed on vectors include addition, subtraction, dot product, and cross product.

Vectors can also be expressed in various coordinate systems, such as Cartesian, polar, and spherical coordinates, depending on the context and application.

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Answer:

4−2x<−3

Step-by-step explanation:

check:

now --- 4°

after 1 hr --- 2°

after 2 hrs--- 0°

after 3 hrs--- -2°

after 4 hrs--- -4°

so between 3 and 4 hrs it will reach -3°

4-2x < -3

-2x < -7

x > 3 1/2

The required answers are:

a. The standard error of the mean (SEM) is approximately 0.79 (to 2 decimals).

b. At a 95% confidence level, the margin of error (ME) is approximately 1.55 (to 2 decimals).

a. The standard error of the mean (SEM) is calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population standard deviation is 5 and the sample size is 40.

Standard error of the mean (SEM) = \(population- standard -deviation / \sqrt {sample -size\)

\(= 5 / \sqrt40\)

≈ 0.79 (to 2 decimals)

b. The margin of error (ME) at a 95% confidence level can be calculated by multiplying the critical value for a 95% confidence interval by the standard error of the mean. The critical value for a 95% confidence interval corresponds to a z-score of 1.96.

Margin of error (ME) = critical value * standard error of the mean

= 1.96 * 0.79

≈ 1.55 (to 2 decimals)

Therefore, at a 95% confidence level, the margin of error is approximately 1.55.

Therefore, the required answers are:

a. The standard error of the mean (SEM) is approximately 0.79 (to 2 decimals).

b. At a 95% confidence level, the margin of error (ME) is approximately 1.55 (to 2 decimals).

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Approximately 95.44% of the time, the car will stop at a distance between 120 feet and 140 feet.

To calculate the percentage of the time the car stops at a distance between 120 feet and 140 feet, we need to find the probability within that range in the given normal distribution.

The Z-score formula can help us calculate the probability in a normal distribution:

Z = (X - μ) / σ

In this case, we want to calculate the probability between 120 feet and 140 feet, which means X = 120 and X = 140.

Calculating the Z-scores for these values:

Z1 = (120 - 130) / 5 = -2

Z2 = (140 - 130) / 5 = 2

Now, we can use a Z-table or a calculator to find the probabilities corresponding to these Z-scores. Since the normal distribution is symmetric, the probability between -2 and 2 is the same as the probability between 2 and -2.

Using a standard normal distribution table or calculator, the probability of a Z-score between -2 and 2 is approximately 0.9544.

Therefore, approximately 95.44% of the time, the car will stop at a distance between 120 feet and 140 feet.

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