(1 point) from a group of 8 men and 6 women a committee consisting of 4 men and 4 women is to be formed. how many different committees are possible if (a) 2 of the men refuse to serve together? answer: (a) 2 of the women refuse to serve together? answer: (a) 1 man and 1 woman refuse to serve together? answer:

Answer:

[tex]x = 15 $^{\circ}$ ; z = 74$^{\circ}$[/tex]

Step-by-step explanation:

First, combine all like terms. Like terms are terms that have the same amount of the same variables:

[tex]m$\angle$(5x - 1) + m$\angle$(7x + 1) = 180$^{\circ}$\\\\[/tex]

[tex]m$\angle$(5x + 7x) + (1 - 1) = 180$^{\circ}$[/tex]

[tex]12x + 0 = 180$^{\circ}$[/tex]

Next, isolate the variable, x. Divide 12 from both sides of the equation:

[tex]12x = 180\\\frac{12x}{12} = \frac{180}{12}\\ x = \frac{180}{12}\\ x = 15 $^{\circ}$[/tex]

Next, plug in 15 for x in one of the given expressions. If you choose the right one (7x + 1), you will solve using the straight angle theorem. If you choose the bottom one (5x - 1), you will solve using the vertical angle postulate. Both will give you the same answer for x.

Firstly, if you want to solve using the straight angle theorem. The straight angle theorem is defined that all straight angles are 180 degrees. Solve using the straight angle theorem. Set both angle measurements equal to 180°:

[tex](z) + (7x + 1) = 180[/tex]

Plug in 15 for x and solve for the parenthesis:

[tex]z + 7(15) + 1 = 180 $^{\circ}$\\[/tex]

First, multiply 7 with 15:

[tex]z + (7 * 15) + 1 = 180 $^{\circ}$\\z +105 + 1 = 180$^{\circ}$\\[/tex]

Next, simplify by combining like terms:

[tex]z + (105 + 1) = 180 $^{\circ}$\\z + 106 = 180$^{\circ}$[/tex]

Next, isolate the variable, z, by subtracting 106 from both sides of the equation:

[tex]z + 106 = 180 $^{\circ}$\\z + 106 (-106) = 180 (-106)\\z = 180 - 106\\z = 74$^{\circ}$[/tex]

Your answer:

[tex]x = 15 $^{\circ}$ ; z = 74$^{\circ}$[/tex]

~

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The length of each side of the given square is 3.306 yards.

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.

It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.

In geometry, a square is a flat shape with four equal sides and four right angles (90°).

A square is a unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).

So, we have the area of the square as:

1.21 yards²

Area formula of square: A = s²

Now, calculate to find the length of the square as follows:

A = s²

1.21 = s²

s = 4/1.21

s = 3.306

Therefore, the length of each side of the given square is 3.306 yards.

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The locations on the function's graph that are most near the specified point f(x) = x2, (0,9) are approximately 3 units to the right and left, respectively, or (sqr8.5, 8.5).

The initial estimate would be rough to the right and left by around 3 units, or (sqr8.5, 8.5), rounded to the nearest decimal place.

Visually, it is most likely just below y=9 and just below x=3. Additionally, roughly (-3, 9) slightly lower than 3 and 9

Connect the parabola's nearest point to the point at (0,9). Where the two intersect, its slope is the negative inverse of the parabola's slope. The derivative's slope is 2x for the equation f(x) = x2. -1/2x is its inverse negative. The line from (0,9) to the parabola's nearest point has a slope that is perpendicular to the tangent to the parabola at that location.

Get the equation of the line joining (0,9) and the nearest point (x,y) on the parabola using the point-slope formula: 8.5 or y=-1/2 + 9 = (-1/2x)(x)

The closest point's y coordinate is that. The square root of 8.5, including both positive and negative square roots, is the closest point's x coordinate (-sqr8.5, 8.5)

Sqr8.5 =[tex]\sqrt{8.5}[/tex], or approximately 2.91 or -2.91

The process entails finding the equation for the line connecting (0,9) with the parabola's nearest point and then setting the two equations equal. Set the line equation to y=(-1/2x), the parabola equation. The parabola equation is y=[tex]x^{2}[/tex] and the line equation is x + 9.

Equalize them, then find x using the square of the result. The closest point is at x,y. There are two places that are equally far from (0,9), both of which are as close as they can be to 3 at (3,9). (0,9). At the parabola point, that line is not perpendicular to the tangent line (3,9). The line must be perpendicular to the tangent line, which is the slope of the parabola, in order to be closest.

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1. The equation of the straight line is y = -x -1.

2. The equation of the point-gradient form is 3x -y - 10.

3. The equation of the straight line that is parallel to the line y = x-2 and goes through the point (0,1) is y = x + 1.

What is a straight line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things. In daily language, a line segment with two points designating its endpoints is also referred to as a "line."

Here, we have

1. The slope-intercept form of the equation of a line is:

y = mx + b

We are fortunate to be given the y-intercept, the point(0,-1) therefore, the value, b, in the slope-intercept form is -1:

y = mx - 1

Substitute the other point(-1,0) into the equation and then solve for the value of m:

0 = -m - 1

m = -1

y = -x -1

Hence, the equation of the straight line is y = -x -1.

2. We know that the equation of a line passing through the point (x₀, y₀  ) whose slope is m is (y -  y₀) = m(x -x₀)

The equation of a line passing through the point(2,-4) and the slope is 3.

(y+4) = 3(x-2)

y + 4 = 3x - 6

3x -y - 10

Hence, the equation of the point-gradient form is 3x -y - 10.

3. Consider the given equation: y = x-2

Since, the line is parallel to given line. so slope will be same.

slope = 1

We know that the second line will also have a slope of 1, and we are given the point (0,1). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

1 = b

Now, we put the value of b in the equation and we get

y = x + 1

Hence, the equation of the straight line that is parallel to the line y = x-2 and goes through the point (0,1) is y = x + 1.

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A biconditional statement is a statement that may be stated in the form “p if and only if q.” This implies “if p, then q” and “if q, then p.”

A biconditional statement is one that can be expressed as "p if and only if q," which implies "if p, then q" and "if q, then p."

For example, "If the polygon is a square, then it has four equal sides and four right angles," and "If a polygon has four equal sides and four right angles, then it is a square," are two examples of biconditional statements.

A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form.

Two line segments are congruent if and only if they are of the same length.

Therefore, the biconditional statement is a statement that may be stated in the form “p if and only if q.” This implies “if p, then q” and “if q, then p.”

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All of the following statements are true:

a. Effective listening is vital to success in selling.

b. visual aids play a part in the listening process.

c. people can talk approximately twice as fast as they can listen.

d. you should listen closely to everything you hear.

e. listening refers to the process of trying to detect sounds.

Listening is the act of paying attention to sounds that are happening around you. It involves both hearing the sounds and interpreting what they mean. Good listening skills are important for many reasons, including being able to communicate effectively with others and understand instructions. To listen effectively, you need to be able to focus on the speaker and try to understand their perspective, rather than just waiting for your turn to talk.

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The given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).

A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image).

We can picture what would happen if you turned the form across the line to graph a reflection.

So, we have a triangle with coordinates:

(8, 2), (3, 4), (2, 7)

Now, we will reflect it according to the rule:

(x, y)→(−x, y)

Then, the coordinates will be:

(-8, 2), (-3, 4), (-2, 7)
(Refer to the graph attached below)

Therefore, the given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).

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The correct option for the graph shown are-

The question's line traverses the origin and (4,-12).

The line's rate of change is;

m = -12 - 0 / 4 - 0

m = -3

The slope of the line or its rate of change is -3.

The line's equation is provided by;

y - 0 = -3(x - 0)

y = -3x

This relationship is linear as a result.

The relationship is proportionate if we take any value of x because there will only ever be one value of y.

Therefore, the following claims are accurate:

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Answer:

The value of x should be x = 40.

Step-by-step explanation:

Step-by-step explanation:

Bro it is just 180- 41 - 93

you do the calculation

The data does contradict with the prior evidence

To determine whether the data presented here are significantly inconsistent with previous assumptions, a statistical test was performed to verify that the observed relationship between tendon length and cranial volume was significantly greater than the expected relationship. You have to decide if they are different.

To do this, fit a line to the data using linear regression analysis and test the hypothesis that the slope of the line is equal to 20 cm3/mm. If the p-value for this hypothesis test is less than 0.05, you can conclude that the data are inconsistent with previous assumptions at the 0.05 significance level.

It is crucial to realize that this analysis assumes that the relationship between tendon length and cranial volume is linear.

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The 95% confidence interval estimate of the population mean is 98.10< μ < 98.30.

Given that

sample mean = ~x = 95.2

sample standard deviation = s = 0.7

sample size = n = 175

Degrees of freedom = d.f = n - 1 = 175 - 1 = 174

αt /2,d.f = 1.974.

The explanation for step 1

At 95% confidence level

 α= 1-0.95% =1-0.95 =0.05

α /2=0.05/ 2= 0.025

αt /2,d.f = t0.025,174 = 1.974

αt /2,d.f = 1.974

The explanation of Step 2

Margin of error = E = t/2,df x (s /Vn )    =  1.974 x ( 0.7/ V175)   = 0.10

Margin of error = E = 0.10

The 95% confidence interval estimate of the population mean is,

~x- E < μ < ~x + E

98.2 - 0.10< μ < 98.2 + 0.10

98.10< μ < 98.30

Margin of error = E = 0.10

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Answer:  l +d ≤ 14

Step-by-step explanation:

Answer:

13.3 ft

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\\\end{minipage}}[/tex]  [tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

The surface area of a square-based pyramid is made up of:

Given:

Find the area of the square base and the area of one of the triangles by substituting the given values into the formulas:

[tex]\textsf{Area of the square base} = 5^2 = 25\; \sf ft^2[/tex]

[tex]\textsf{Area of one of the side triangles} = \dfrac{1}{2} \cdot 5 \cdot l= 2.5l \; \sf ft^2[/tex]

Substitute these values along with the given total surface area into the formula and solve for l:

[tex]\begin{aligned}\textsf{Total Surface Area}&=\sf square+4\;triangles\\\implies 158&=25+4\left(2.5l)\\158&=25+10l\\133&=10l\\l&=\dfrac{133}{10}\\l&=13.3\; \sf ft\end{aligned}[/tex]

Therefore, the missing length is 13.3 feet.

Answer:

  0 < x < 4.5

Step-by-step explanation:

You want the reasonable domain of V(x) = (8.5 -2x)(11 -2x).

The equation describes volume (V) and cut length (x), so both need to be positive. Volume will be positive when ...

  8.5 -2x > 0

  4.25 > x

The reasonable domain is 0 < x < 4.5.

Answer:

5x + 10× - 30= 180 degree

15x =150

x= 10

From the base of the wall, the bottom of the ladder is 10.6 feet away

information given in the question

hypotenuse = 16 foot long ladder

opposite = 12 foot high wall

adjacent =  How far away from the base of the wall is the bottom of the ladder = ?

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

16² = 12² + x²

256 = 144 + x²

256 - 144 = x²

x² = 112

x = √112

x = 10.583

the ladder is  10.6 feet away from the base of the wall

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In mathematics, linear programming is a technique for maximizing operations under certain restrictions.

Using the mathematical modeling technique of linear programming, a linear function is maximized or minimized depending on the restrictions it is subjected to. This method has proved helpful for directing quantitative judgments in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.

In mathematics, linear programming is a technique for maximizing operations under certain restrictions. Maximizing or minimizing the numerical value is the primary goal of linear programming. It comprises of linear functions that are subject to restrictions in the form of inequalities or linear equations.

Therefore, the correct answer is option A. this is a binding constraint, so there is no slack or surplus.

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As per the given confidence interval, the interval notation is 2.576

Confidence interval:

Is statistics, an estimate of an interval in statistics that may contain a population parameter is known as confidence interval.

Given,

Here we have to calculate a 99% confidence interval for the difference in the proportions of those older than 30 and those 30 or younger that believe alcoholic beverage commercials targeted teenagers and young adults. let the 30 or younger age group be population 1 and let the older than 30 age group be population.

And we need to find the write your answer using interval notation and round the interval endpoints to three decimal places.

While we looking into the given question,

We have identified the following things,

Confidence interval = 99%

When we convert this into decimal, then we get the value as 0.99

Then the z score of the given data is calculated as

=> 2.576

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The value of the double integral ∫∫[tex]\frac{y^{2} }{x^{2} +y^{2} }[/tex] dA is 131.95.

We know that in polar coordinates, the circle become r = 4 and r = 16. These are the limits on the radius. Clearly the limits on the angle are

0 ≤ θ ≤ 2π.

Therefore we get,

∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = ∫ ∫ r²sin²θ / r² dr dθ

                  = ∫ sin²θ dθ ∫ r dr

                  = [ [tex]\frac{1}{2}[/tex]θ - [tex]\frac{1}{4}[/tex]sin(2θ)]₀²ⁿ[ [tex]\frac{1}{2}[/tex] r²]₄¹⁰

                  = [tex]\frac{1}{4}[/tex] (2π)(10² - 4²)

                  = 42π

∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = 131.95.

What is Polar coordinates?

When each point on a plane of a two-dimensional coordinate system is decided by a distance from a reference point and an angle is taken from a reference direction, it is known as the polar coordinate system.

Polar coordinates are useful in calculating the equations of motion from a lot of mechanical systems. Polar coordinate means the magnitude and direction of a vector.

Polar coordinate system of locating points in a plane with reference to a fixed point O and a ray from the origin usually chosen to be the positive x-axis.

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According to the Central Limit Theorem, the mean of the sampling distribution of means will be equal to The mean of the Original Population.

Central Limit theorem:

The central limit theorem (CLT) is a statistical concept that states that the sample mean distribution of a random variable assumes an approximately normal or normal distribution when the sample size is large enough. Simply put, the theorem states that the mean sampling distribution approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

For example:

An investor wants to estimate the return on the ABC stock market index, which consists of 100,000 shares. Due to the large size of the index, the investor cannot analyze each stock individually and instead chooses to use a random his sample to obtain an estimate of the index's total his return. Investors select a sample of stocks. Each sample contains at least 30 strains. Samples should be random and previously selected samples should be replaced by subsequent samples to avoid bias.

If the average return of the first sample was 7.5%, the average return of the next sample could be 7.8%. Due to the nature of random sampling, each sample will produce different results. As you increase the sample size for each selected sample, the sample means begin to form their own distribution.

The distribution of the sample mean approaches a normal distribution as the value of n increases. The average return of the index example stocks estimates the return of the entire index of 100,000 shares, and the average returns follow a normal distribution.

According to the central limit theorem, if a large sample is chosen from an unknown population with mean μ and standard deviation σ, the sampling distribution of the sample mean follows a normal distribution.

The mean and standard deviation of this sampling distribution are:

                        μₐ = μ

                      σₐ = σ/√n

This standard deviation of the sampling distribution of the mean is called the standard error.

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Answer:

  20%

Step-by-step explanation:

You want to know the percentage change from 1120 to a final number that is 100 less, 130 more, and 254 less.

The percentage change is given by ...

  percent change = change/(original amount) × 100%

Here, the total amount of change is the sum of the given changes:

  -100 +130 -254 = -224

Then the percentage change is ...

  -224/1120 × 100% = -20%

The percent decrease is 20%.

<95141404393>

Answer: h = 92

Step-by-step explanation:

148 - 180 = 32

32 + 56 = 88

88 - 180 = 92

Answer:

60?

Step-by-step explanation:

15/0.25

Answer:

Jeff took 60 total shots.

Answer:

slope of original line; m = -3/-4

                                         =3/4

slope of parallel line = 3/4

slope of perpendicular line = m1*m2=-1

                                               =(3/4)*m2=-1

                                               =-4/3

equation passes through point (4,-3) is : 3x + 4y = -12

The best attendance is at School W, according to a The highest average attendance is at School W, according to b.

According to a, the school with the least amount of volatility in its data will be the most reliable.

It's only the least inconsistent among its own data; consistent doesn't necessarily indicate the best. Because variance indicates how dispersed the data is, the school with the lowest variance is the most reliable.

For an explanation of how each school's deviations were determined, see photo 1.

Take each school's mean as b. Whichever is higher in value is the school with the highest average.

For the computations of the means for each school, see photo 1. (Since the mean is used to determine variance, we will start with this step.)

These are the justifications for our secondary school selection. Our top consideration while selecting a secondary school is: A Journey Like when we looked at elementary schools, I want my kids to attend a secondary school that they can walk to. Due to this factor, we are left with only two institutions to choose from when ranking schools on the application form.

You might not have much work experience for interviewers to talk about as a recent graduate or candidate for an entry-level employment. Similar insights into your career aspirations and personal interests can be gained from selecting a college or university.

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Answer: T  = 1

Step-by-step explanation:

As 6/9 is equivalent to 2/3, then 1/1.5 is similar to 10/15, which is also 2/3

Answer:

t = 1

Step-by-step explanation:

Given equation,

→ (6/9) = (t/1.5)

Now the value of t will be,

→ (6/9) = (t/1.5)

→ (t/1.5) = (6/9)

→ t = (6/9) × 1.5

→ t = (6 × 1.5)/9

→ t = 9/9

→ [ t = 1 ]

Hence, the value of t is 1.

Answer: I believe that this statement is very true. People shouldn’t be pushing others down when instead they could be pushing themselves up, improving them to be better.

Step-by-step explanation:

Answer:

THAT VERY RIGHT INSTEAD OF PEOPLE HELPING THEMSELVES THEY SPEND THEIR TIME CRITICIZING OTHERS KUDO TO U

A random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm is 0.0749.

In the given question,

18-year-old American males stated that the sample mean waist circumference was 86.3 cm.

The populations mean waist size is 85 cm.

The population standard deviation is 15 cm.

We have to find, a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm.

H(0): μ = 85

H(A): μ > 85

Sample mean(X) = 86.3

Standard deviation(σ) = 15

Standard error of mean =σ/√n

Standard error of mean (SE) = 15/√277

SE = 15/16.6433

SE = 0.9013

z = (X- μ)/SE

z=(86.3-85)/0.9013

z = 1.4424

P(z > 1.4424) = 0.0749

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The right question is;

The National Health Statistics Reports dated Oct. 22, 2008 stated that for a sample size of 277. 18-year-old American males stated that the sample mean waist circumference was 86.3 cm.

Suppose that the population mean waist size is 85 cm and that the population standard deviation is 15 cm. how likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm? (Round your answers to four decimal places.)

Answer: x+6

Step-by-step explanation:

5x-3(x-2)-x .......................... Question

5x-3x+6-x ........................... Distribute

1x+6 ..................................... Combine like terms

x+6 ...................................... Multiply by 1

Answer: x+6

Step-by-step explanation:

5x-3(x-2)-x

5x -3x +6 -x

x + 6