(5 pts) interpolation is used to determine values beyond a given set of data points. a) true b) false

There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

The average velocity from 4 to 8 seconds is given as follows:

v = [position at 8 seconds - position at 4 seconds]/4.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

The change in the distance from 4 to 8 seconds is given as follows:

position at 8 seconds - position at 4 seconds

The change in the time from 4 to 8 seconds is given as follows:

8 - 4 = 4 seconds.

Hence the velocity is of:

v = [position at 8 seconds - position at 4 seconds]/4.

The problem is incomplete, hence the general procedure to obtain the average velocity was presented.

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a = 1st zero or root of the quadratic

b = 2nd zero or root of the quadratic

[tex]x^2-8x+k=0\implies (x-a)(x-b)=0\implies x= \begin{cases} a\\ b \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -ax-bx=-8x\implies -a-b=-8\implies -b=a-8\implies b=8-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{3a+4b=29}\qquad \implies \qquad \stackrel{\textit{substituting from above}}{3a+4(8-a)~~ = ~~29}\implies 3a+32-4a=29 \\\\\\ -a+32=29\implies 32=a+29\implies \boxed{3=a}\hspace{5em}\stackrel{ 8~~ - ~~3 }{\boxed{b=5}}[/tex]

[tex]~\dotfill\\\\ (x-3)(x-5)=0\implies x^2-8x+\stackrel{ \textit{\LARGE k} }{15}=0[/tex]

Answer:

Kurram is elder by 19 months

a. If you can play the game for free, the expected value is zero since there is no cost and no prize for winning.

b. To calculate the expected value when it costs $3 to play, we need to first find the probability of winning.

There are 8 possible outcomes on the spinner, and only one of them results in a win, so the probability of winning is 1/8. The probability of losing is 7/8.

The expected value is the sum of the product of each outcome and its probability. Let X be the amount won. Then:

E(X) = (1/8)($100) + (7/8)(-$3)

= $12.50 - $2.63

= $9.87

So the expected value when it costs $3 to play is $9.87. Since the expected value is positive, you can expect to make a profit in the long run.

However, this does not mean that you will win every time you play, as the outcome of each individual game is still random.

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The expressions, in terms of t, for each vehicle so that the vehicles start separated and meet at 10 seconds is:

Tractor's position = Vt * t

Scooter's position = Vs * t

Let's assume that the starting point for both the tractor and the scooter is at "0". We can then write the expressions for their positions in terms of time "t" as follows:

For the tractor:

Tractor's speed = Vt

Tractor's position = Vt * t

For the scooter:

Scooter's speed = Vs

Scooter's position = Vs * t

Now, as both the vehicles meet at 10 seconds, we can write the equation:

Vt * 10 = Vs * 10

The above equation represents the position of both the vehicles at 10 seconds. If we assume the speed of the tractor and the scooter to be constant, then the equation gives us the relationship between their speeds.

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The unshaded area is 11.5 times bigger than the shaded area.

The area of the circle is given by:

A_circle = πr^2

where;

n this case, r = 10 cm, so:

A_circle = π(10 cm)^2 = 100π cm^2

The area of the semicircle is given by:

A_semicircle = (1/2)πr^2

where;

In this case, the diameter of the semicircle is 8 cm, so the radius is 4 cm:

A_semicircle = (1/2)π(4 cm)^2 = 8π cm^2

To find the area of the shaded region, we need to subtract the area of the semicircle from the area of the circle:

A_shaded = A_circle - A_semicircle

= 100π cm^2 - 8π cm^2

= 92π cm^2

The unshaded area is the area of the circle minus the area of the shaded region:

A_unshaded = A_circle - A_shaded

= 100π cm^2 - 92π cm^2

= 8π cm^2

So the unshaded area is 8π cm^2 and the shaded area is 92π cm^2.

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The line of the best fit of the scatter plot is added as an attachment

The missing graph is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The graph

A good line of best fit would have equal number of points on either sides

To plot the graph, we draw a line that divides the points on the graph evenly

This line when drawn on the scattered points divided the points approximately evenly

Hence, the line of the best fit is attached

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Step-by-step explanation:

h represents the number of hours

15 represents the initial price for bike rentals

0.75h represents that for every hour, the price of bike rentals increases by 0.75

We can use the sine ratio to solve this problem and the value of x would be 8.604.

What are trigonometric ratios?

Trigonometric ratios are ratios of the side lengths of a right triangle with respect to its acute angles.

Sine (sin) ratio: The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In the given figure, we have given the hypotenuse of the triangle, and  an angle is given which is opposite to 35 degree, so we can use the sine ratio to find the value of x

sin35°= x/15

To solve for x, we can use the following steps:

Multiply both sides of the equation by 15 to isolate x:

sin 35° = x/15

15 * sin 35° = x

Use a calculator to approximate sin 35°:

sin 35° ≈ 0.5736

Substitute the approximation into the equation and solve for x:

x = 15 * 0.5736

x ≈ 8.604

Therefore, x is approximately equal to 8.604.

Hence, we can use the sine ratio to solve this problem and the value of x would be 8.604.

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The mean difference between the skier's practice times and the qualifying time is given as follows:

-2.01 seconds.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

The observations for this problem are given as follows:

1.25, -5.38, -0.92, 2.19, -6.74, -2.46.

The sum of these six observations is of:

1.25 - 5.38 - 0.92 + 2.19 - 6.74 - 2.46 = -12.06.

Hence the mean is of:

Mean = -12.06/6

Mean = -2.01 seconds.

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Answer:

Step-by-step explanation:

Part A:

The actual length of the dining room is 120 inches and the percent error is -5%, which means that Rihana's measurement was too short. To find the length she measured, we need to add 5% to the actual length:

120 inches * (1 + (-5%)/100) = 120 inches * (1 - 0.05) = 120 inches * 0.95 = 114 inches

So Rihana measured the length of her dining room as 114 inches.

Part B:

To find the length that Rihana measured, we used the formula for calculating percent error:

measured length = actual length * (1 + (percent error)/100)

Since the percent error was negative (-5%), this means that Rihana's measurement was too short, so we subtracted the percent error from 100%. To do this, we added the negative percent error to 100%:

100% + (-5%) = 100% - 5% = 95%

So the measured length was 120 inches * 95% = 114 inches.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

The length of the dining room measured by Rihana with a -5%  percent error  is 114 inches.

What is a percent error?

The percent error is the distinction between the estimated value and the actual value in relation to the actual value. In other words, the relative error is multiplied by 100 to calculate the percent error.

A) Given the percent error as -5%.

The actual length = 120inches

Now error in measurement = 5% of 120 inches = 6 inches.

Since there is a negative sign in percent error, the measured value is 6 inches less than actual value.

Therefore the measured value = 120 - 6 = 114 inches.

B) We are given the actual length as 120 inches.

There is a -5% error in the measured value.

This means that the measured value is (5% of 120) inches less than actual value. It is identified as less because of the negative sign.

So the measured value is = 120 - 0.05*120 = 114 inches.

Therefore the length of the dining room measured by Rihana with a -5%  percent error is 114 inches.

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A graph of the system of linear equations y = -2x + 2 and y = -2x + 1 is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the given system of equations has no solution because both lines have the same slope and are parallel.

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Answer:

30%

Step-by-step explanation:

100-70=30

Any value of x that is less than or equal to -2 will make the inequality true.

What is Number line?

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every point on a number line is presumed to be a real number, and every real number is assumed to be a point.

To solve the inequality 3x - 1 <= -7, we can start by adding 1 to both sides to isolate the variable:

3x - 1 + 1 <= -7 + 1

Simplifying, we get:

3x <= -6

Next, we can divide both sides by 3 to solve for x:

3x/3 <= -6/3

Simplifying, we get:

x <= -2

This tells us that any value of x that is less than or equal to -2 will make the inequality true. We can represent this on a number line by shading all values less than or equal to -2

The circle at -2 indicates that -2 is included in the solution set, and the arrow pointing to the left indicates that all values less than -2 are also included in the solution set. Therefore, the number line that shows all of the values of x that make the inequality 3x - 1 <= -7 true is the one with all values less than or equal to -2 shaded.

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The inequality that matches the region is [tex]y\geq -3[/tex].

What is linear inequality?

When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression. Different types of linear inequalities can be represented in a number of different ways.

The graph of the region shows a positive region which represents the value as a greater or increasing order.

The sign '>' represents the greater region.

So, the required answer is [tex]y\geq -3[/tex].

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The value of t* would use for this interval is 1.699 to compute a 90% confidence interval.

It is given that the confidence = 90% or 0.9

also, the sample size (n) = 30

The degrees of freedom is the sample size decreased by 1:

df = n - 1

df   = 30 - 1

df = 29

The critical value t* can then be found in the row with df = 29 and in the column with c = 90% (or upper tail probability p = 0.05) using table B.

t* = 1.699

The image attached is t* table

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Answer:

The length of the unknown side of the triangle is

[tex]5 \sqrt{5} [/tex]

Answer:

1.) -12

2.) 28

3.) 40

Step-by-step explanation:

The elevation of an object is the height or depth of the object relative to the sea level. If the object is above sea level, its elevation will be positive. However, if the object is below sea level, its elevation will be negative. Therefore, we can conclude that the elevation of the fish is -12 m because it is below sea level.

The measure of arc FE in the figure is 100 degrees

From the question, we have the following parameters that can be used in our computation:

The circle and the intersecting chords

The value of arc FE represented by x is then calculated as

80 = 1/2(x + 60)

Cross multiply the equation

This gives

x + 60 = 160

Subtract 60 from both sides

x = 100

Hence, the measure of x is 100 degrees

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The system that is represented in the graph include:

y > x² – 2x – 3

y > 3x + 4

The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this case, a graph consists of vertices connected by edges.

The graph shows a dashed upward opening parabola with a vertex at negative 1 comma negative 4, with shading inside the parabola. It also shows a dashed line passing through the points negative 2 comma negative 1 and 0 comma 3, with shading above the line.

This depicts y > x² – 2x – 3 and y > 3x + 4.

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Which system is represented in the graph?

y ≥ x2 – 2x – 3

y ≤ 3x + 4

y < x2 –2x – 3

y > 3x + 4

y < x2 – 2x – 3

y > 3x + 4

y > x2 – 2x – 3

y > 3x + 4

The width of the rectangle is 4*m⁷*n³

Remember that for a rectangle of length L and width W the area is given by the formula:

A = W*L

Here we know that:

A = 20*m¹⁰*n⁴

L = 5*m³*n

Then we can write:

20*m¹⁰*n⁴ = (5*m³*n)*W

Now we can solve that for W.

(20/5)*(m¹⁰/m³)*(n⁴/n) = W

4*m¹⁰⁻³*n⁴⁻¹ = W

4*m⁷*n³ = W

That is the width.

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You did not make enough money to buy the television with a total earnings of $458

To write an expression for total earnings, we can use the given rates of pay and multiply them by the unit rates of the activites and then add them together.

So the expression for total earnings (E) is:

E = 10x + 8y + 20z

Where

Using the given parameters in the question, the total earnings (E) in the last 4 weeks is

E = ($10 x 9) + ($8 x 26) + ($20 x 8)

Evaluate

E = $90 + $208 + $160

E = $458

$458 is less than the cost of television ($540)

This means that you did not make enough money

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Complete Question

You earn $10 for each lawn you mow. You earn $8 per hour working part time at an ice cream shop. You earn $20 cach day you deliver newspapers.

In the last four weeks, you mowed 9 lawns, worked 26 hours at the ice cream shop, and delivered newspapers 8 days.

Did you make enough to buy the television? Explain...

The television price is $540

According to the given information Congruent diagonals is not a property of parallelogram.

A kite's opposing forces aren't always parallel, just like not every kite is just a parallelogram. Trapezoids are quadrilaterals having a single pair of parallel sides. The parallel sides make up the bases. If somehow the foundation angles are equal, the trapezoid is said to be an isosceles trapezoid.

Since a diamond has four slanted, equal-length sides, it is an example of a rhombus. They are also both parallelograms since a parallelogram is indeed a rhombus and a diamond is one as well.

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The value of 33.4 meters to centimeters is 3340 centimeters

Conversion of units is described as the  conversion between different units of measurement for the same quantity, and it is done mostly through multiplicative conversion factors.

It also involves multiple steps of multiplication or division by a numerical factor or, a conversion factor.

From the information given, we have to convert meters to centimeters

Note that;

100 centimeter = 1 meter

Then x centimeters = 33.4 meters

cross multiply

x = 100(33.4)

multiply the values

x = 3340 centimeters

Hence, the value is 3340 centimeters

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The difference of the fractions 8/2 and 3/5 is given as follows:

17/5.

The difference operation for this problem is defined as follows:

8/2 - 3/5.

8 is divisible by 2, with a quotient of 4, hence the subtraction can be simplified as follows:

4 - 3/5.

With a common denominator of 5, we have that 4 x 5 = 20, hence:

20/5 - 3/5.

As the fractions now have a common denominator, we can subtract the numerators while keeping the denominator constant, thus the subtraction is given as follows:

(20 - 3)/5 = 17/5.

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The total amount y collected from x students is y = 10x.

The graph is given below.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The club is charging $10 per student that attends.

This means,

Number of students = x

The total amount y collected from x students.

y = 10x

The graph is given below.

Thus,

y = 10x is the total amount y collected from x students is

The graph is given below.

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Answer: 123 students

32 % of 384 is 122.88. Since a percent of a person can't walk to school, we should round up. This means 123 students in the eighth grade walk to school each day.

I hope this helps and good luck <3!!