If the figure is a regular polygon find the value of x

The fraction that represents the point M is 2 3/10

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

The number line

Such that

M is between 2 1/5 and 2 1/2

This means that

M is between 2.2 and 2.5

By the positiining of the points, we have

M = 2.2 + 0.1

Evaluate

M = 2.3

As a fraction, we have

M = 2 3/10

Hence, the fraction is 2 3/10

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So, the unit vector that points in the direction of the vector −4i+7j can be written as (-4/√65)i + (7/√65)j.

To find a unit vector that points in the direction of the vector −4i+7j, follow these steps:

1. Find the magnitude of the given vector: The magnitude of a vector (a, b) can be calculated using the formula √(a^2 + b^2). In this case, the vector is (-4, 7).

Magnitude = √((-4)^2 + (7)^2) = √(16 + 49) = √65

2. Divide each component of the vector by its magnitude to find the unit vector: A unit vector has a magnitude of 1. To obtain the unit vector, divide each component of the original vector by the magnitude calculated in Step 1.

Unit vector = (-4/√65)i + (7/√65)j , So, the unit vector that points in the direction of the vector −4i+7j can be written as (-4/√65)i + (7/√65)j.

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Answer:

7% of cars traveled east.

Assuming that the probability of a student trying out for a fall sport is 1/6, we would need to randomly select approximately 123 students to get 20 students who were trying out for a spring sport.

To calculate this, we can use the binomial distribution, which models the probability of obtaining k successes in n independent trials, each with a probability of success p. In this case, the trials are the random selections of students, and the success is a student who is trying out for a spring sport. The probability of success is 5/6 (since 1/6 are trying out for a fall sport), and we want to find the smallest n such that the probability of obtaining at least 20 successes is greater than or equal to 0.95 (or 95%).

Using a calculator or software, we can find that:

where X ~ Binomial(n, 5/6).

Therefore, we need to solve for n in the inequality:

where "binom.dist" is the binomial cumulative distribution function with the "TRUE" argument for a cumulative probability.

Solving for n, we get:

Therefore, we would need to randomly select approximately 123 students to get 20 students who were trying out for a spring sport.

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We can see from the table and the graph that the relationship is proportional. Also, the line passes through the origin

A relationship between two variables is said to be proportionate if it causes both of the variables' values to rise or fall by the same amount.

To know if the relationship is proportional we have to look at the table so that we can be able to see the movement of the values and thus know whether or not we can classify what we see as a proportional relationship.

If the relationship is proportional, then the increase would be by fixed amounts as shown in the graph.

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According to the information, the answer is (C) 375 square feet, which is the closest option to 300 square feet.

Let's start by drawing a rectangle and labeling its dimensions. Since the perimeter is 80 feet and the minimum side length is 180 inches, we can set up the following equations:

Simplifying the perimeter equation, we get:

Solving for one variable in terms of the other, we get:

Substituting into the area equation:

To find the maximum area, we need to find the vertex of the parabolic equation[tex]A = -W^{2} + 60W + 800[/tex]. The x-coordinate of the vertex is given by x = -b/2a, where a = -1 and b = 60:

So the width of the pen is 30 feet, and the length is:

[tex]L = 40 - W = 40 - 30 = 10 feet[/tex]

Therefore, the area of the pen is:

[tex]A = LW = 10 x 30 = 300 square feet[/tex]

Since the pen has a height of 10 feet, we can also calculate the volume of the pen:

[tex]V = LH = 10 x 10 x 30 = 3,000 cubic feet[/tex]

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Answer: B

Step-by-step explanation:

Put the numbers in order from smallest to largest

the first smallest is your first dot at 13

That means D is out because that first dot is at 12

The last dot is 37 which means A is out because thats at 36

C is out because that at 38

B is your answer based on range, to figure out the box part, break up the numbers into quartiles(4 even groups). The middle numbers take the average or 27 and 27 so 27 is you middle box number

the left box is the average of 18 and 20 which is 19

the right box is the average of 31 and 33 which is 32

Answer:

Step-by-step explanation:

just here for the points

The depth of the water if the speed of the tsunami is 10 m/s is approximately 0.34 meters, or 34 centimeters, given by the equation d = s / (3v).

Speed is the rate at which an object moves through a distance per unit of time. It is often expressed in meters per second (m/s) or kilometers per hour (km/h).

An equation is a mathematical statement that shows that two expressions are equal. It usually contains variables, constants, and mathematical operations, and can be solved to find the value of the variables.

According to the given information:

The equation relating the speed of a tsunami and the depth of the water is s = 3vd, where s is the speed of the wave (in m/s), v is the velocity of gravity (which is approximately 9.8 m/s²), and d is the depth of the water (in meters).

We can rearrange the equation to solve for d, which gives us:

d = s / (3v)

Plugging in the given values, we get:

d = 10 m/s / (3 × 9.8 m/s²)

Simplifying, we get:

d = 10 / 29.4

Therefore, the depth of the water is approximately 0.34 meters, or 34 centimeters.

So, if the speed of the tsunami is 10 m/s, the depth of the water is approximately 0.34 meters.

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Answer:

C

Step-by-step explanation:

The value of cos Θ /2 and tan Θ /2 can be found to be:

We are given that  90° < Θ < 180°,  which means that theta would be in the second quadrant.

We can therefore use half - angle formulas to find cos Θ /2 and tan Θ /2.

To find cos Θ /2, we have:

cos(Θ/2) = ±√((1 + cos(Θ))/2)

cos(Θ/2) = ±√((1 - √(4/13))/2)

cos(Θ/2) = √((1 - √(4/13))/2)

To find tan Θ /2, we have:

tan(Θ/2) = ±√((1 - cos(Θ))/(1 + cos(Θ)))

tan(Θ/2) = ±√((1 + √(4/13))/(1 - √(4/13)))

tan(Θ/2) = √((1 + √(4/13))/(1 - √(4/13)))

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The full question is:

Suppose that tan Θ = - 3/2 and 90 °< Θ < 180 °.

Find the exact values of cos Θ /2 and tan Θ /2

Super Fast Food typically has more wait time, because although its box is wider than Fast Chicken's, its median is lower, indicating a shorter typical wait time.

The median is a measure of central tendency that represents the value at which half of the data falls below and half falls above.

A higher median indicates that the data is more dispersed, and thus there is likely to be more wait time at that drive-thru.

The median wait time for Fast Chicken in this case is 12.5 minutes, while the median wait time for Super Fast Food is 12 minutes. As a result, Fast Chicken typically has a longer wait time.

Thus, its upper whisker (ending at 27) is longer than Fast Chicken's (ending at 20), indicating that some customers had to wait much longer at Super Fast Food.

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Answer:

Let x be the weight of a bag of almonds (in grams) and y be the weight of a bag of peanuts (in grams).

From the first statement, we have the equation:

4x + 3y = 750

From the second statement, we have:

3x + 5y = 14y

Simplifying the second equation, we get:

3x - 9y = 0

Now we have two equations:

4x + 3y = 750

3x - 9y = 0

We can use elimination to solve for one variable. Multiplying the second equation by 4, we get:

12x - 36y = 0

Adding this to the first equation, we get:

16x = 750

x = 46.875

Now we can substitute this value of x back into one of the equations to solve for y. Using the second equation, we get:

3(46.875) + 5y = 14y

140.625 = 9y

y = 15.625

Therefore, each bag of almonds weighs approximately 46.875 grams, and each bag of peanuts weighs approximately 15.625 grams.

Answer:  -6

Step-by-step explanation:

f(5) means plug in 5 for x

f(5) = -5 - 1

    =-6

Confidence interval (3,4) will provides the most precise estimation.

To determine which of the three confidence intervals provides the most precise estimation, we need to calculate the width of each interval. The width of a confidence interval is determined by the confidence level, the standard deviation of the population, and the sample size.

Assuming all three intervals have the same confidence level and population standard deviation, the interval with the smallest width will be the most precise.

Therefore, we can calculate the width of each interval as follows:

Interval (3,4): Width = 4 - 3 = 1

Interval (2,5): Width = 5 - 2 = 3

Interval (2.5,4.5): Width = 4.5 - 2.5 = 2

From the calculations, we can see that the interval (3,4) has the smallest width, and thus provides the most precise estimation.

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Answer:

  210°

Step-by-step explanation:

You want the angle in standard position to the point (-√3, -1).

The angle θ in standard position to a point (x, y) can be found from ...

  tan(θ) = y/x

  θ = arctan(y/x)

The arctangent function gives an angle between -90° and +90°, so will give the value of the reference angle in this case. To find the angle in quadrant III, we must add 180° to the reference angle.

  θ = arctan(-1/-√3) + 180° = 210°

The angle shown is 210°.

__

Additional comment

If you draw a vertical line from the point to the x-axis, you have a right triangle with side lengths 1 and √3. You know from your memory of special right triangles that this is a 30°-60°-90° triangle, whose smallest angle is 30°. This is the reference angle, so the angle of interest is 180° +30° = 210°.

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{8}}} \implies \cfrac{7 +3}{2} \implies \cfrac{ 10 }{ 2 } \implies 5[/tex]

The area of enclosed region is 18 square units by equation of curve y= 5x²  and y =x² +9 with application of integration.

Dr.Jones  decides to build a fence as represented by the given two equations,

y =5x² ___(1)

and y= x² + 9 ___(2)

To find the point of intersection of the two equations we equate (1) and (2) as,

5x² = y = x² -9

⇒ 5x² = x² -9

⇒ 9 -4x²  = 0 ___(3)

⇒ 4x² = 9

⇒ x² = 9/4

Taking square roots on both the sides we get,

⇒ x = ± 3/2

Thus the interval in which value of x ( as length of fence) lies is (-3/2 , 3/2).

Therefore, we can calculate the area enclosed region by  equation (1) and (2) with the formula of integration,

Area= integration of equation (3) in interval (-3/2,3/2) = [tex]\int\limits^a_b {9-4x^2} \, dx[/tex]  

where, a =3/2 and b =-3/2

=[ 9*(3/2) - (4/3)*(3/2)³] - [ 9*(-3/2) - (4/3)(-3/2)³ ] sqaure units

= 18 square units

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The given question is incomplete, the complete question is

"Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a mathematician, she suggests building fences described by y=5x^2 and y=x^2+9. Farmer Jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. What is the area of the enclosed region?"

Answer: 344

Step-by-step explanation:

Well I dont know

Answer: 536.6 cm²

Step-by-step explanation:

Area for 3 rectangles = bh*3

=(10)(15)(3) = 450

Area for 2 triangles = 1/2 bh *2

= 1/2 10*8.66*2

=86.6

Total area = 86.6+450=536.6

Answer:

24

Step-by-step explanation:

If two angles are supplementary, they add up to 180.

Let's say m∠A = a and m∠B = b.

[tex]a=5(b+7.2)[/tex]

[tex]a= 5b + 36[/tex]

[tex]a-5b = 36[/tex]

We also still have [tex]a+b=180[/tex]

[tex]a-5b=36\\a+b=180[/tex]

Subtract,

[tex]-6b=-144[/tex]

[tex]b=24[/tex]

The circumference of a circle is 14π cm. Then, the area of the circle is 49π square centimeters.

The circumference of a circle is the distance around the outer edge of the circle. It is the perimeter or the boundary of the circle. It is calculated by multiplying the diameter or radius of the circle by the mathematical constant pi (π), which is approximately equal to 3.14159.

The formula for the circumference of circle will be C = 2πr, where C is circumference and r is radius. We are given that the circumference of the circle is 14π cm, so we can write;

14π = 2πr

Dividing both sides by 2π, we get;

r = 7

Now we can use the formula for the area of a circle, A = πr², to find the area of the circle;

A = π(7)²

A = 49π

Therefore, the area of the circle will be 49π square centimeters.

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--The given question is incomplete, the complete question is

"The circumference of a circle is 14π cm. What is the area, in square centimeters? Express your answer in terms of π."--

The product of 7/8 and 1/8 is 7/64. This can be obtained by multiplying the numerators together to get 7, and multiplying the denominators together to get 64.

To multiply two fractions, we simply multiply their numerators together and then multiply their denominators together. So, 7/8 x 1/8 would be

(7 x 1) / (8 x 8) = 7/64

Therefore, 7/8 x 1/8 equals 7/64.

In words, we can say that 7/8 represents 7 parts out of 8, while 1/8 represents 1 part out of 8.

To find the result of multiplying these fractions, we multiply the parts together: 7 x 1 = 7. Then, we multiply the total number of parts, which is

8 x 8 = 64.

So, the result is 7/64, which means that 7/8 x 1/8 represents 7 parts out of 64.

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Answer: Therefore, the scale length of the model car is 4.32 cm.

Step-by-step explanation:

If the scale of the model car is 1:100, this means that every 1 unit on the model represents 100 units in real life. Let's use x to represent the scale length in cm.

Since the car is 4.32m long in real life, and 1m = 100cm, the length of the car in cm is:

4.32m x 100cm/m = 432cm

According to the scale, 1 unit on the model car represents 100 units in real life. Therefore:

1 unit on the model car = 100 units in real life = 100cm

So we can set up a proportion:

1 unit on the model car / x cm = 100 units in real life / 432 cm

Simplifying this expression, we get:

1 / x = 100 / 432

Cross-multiplying, we get:

x = 432 / 100

x = 4.32 cm

The vertical asymptotes of the function are -5 and 3, and the horizontal asymptote is 1.

The asymptotes of the function, f(x) = (x² + 5x) / (x² + 2x - 15), is calculated as follows;

For vertical asymptotes;

x² + 2x - 15 = 0

(x + 5)(x - 3) = 0

x = -5 or 3, this is the vertical asymptotes.

The horizontal asymptotes is calculated as;

divide the numerator and denominator by x²;

f(x) = (x² + 5x) / (x² + 2x - 15)

= (1 + 5/x) / (1 + 2/x - 15/x²)

As x approaches infinity, both 5/x and 2/x become very small, and 15/x² becomes even smaller.

The limit of the function:

f(x) → 1 / 1 = 1

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[tex]1~~,~~\stackrel{1-13}{-12}~~,~~\stackrel{-12-13}{-25}~~,~~...\hspace{5em}\stackrel{\textit{common difference}}{-13} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=1\\ d=-13\\ n=96 \end{cases} \\\\\\ a_{96}=1+(96-1)(-13)\implies a_{96}=1+(-1235)\implies \boxed{a_{96}=-1234}[/tex]

The correct point on the graph would be (1, 14). This point represents the population of stingrays in the enclosure after 1 year.

In the given inequality, the population of stingrays in the enclosure is expected to at least double every year, which means the population grows exponentially.

The graph of an exponential function appears as an upward curve, and the point that represents the initial population of 7 stingrays would be the one located closest to the y-axis, which is point (0, 7).

Since the population of stingrays is expected to double every year, after one year it would be 7 x 2 = 14.

Thus, the point (2, 28) would represent the population of stingrays after 2 years, and so on.

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If sin(θ) = 4/5 then the value of cos(90-θ) is 4/5 by trigonometric identity cos(90-θ) = sin(θ)

We can use the trigonometric identity cos(90-θ) = sin(θ) to find the value of cos(90-θ), since we know the value of sin(θ):

cos(90-θ) = sin(θ)

Substituting the given value of sin(θ) = 4/5, we get:

cos(90-θ) = sin(θ) = 4/5

cos(90-θ) = 4/5.

Hence, if sin(θ) = 4/5 then the value of cos(90-θ) is 4/5 by trigonometric identity cos(90-θ) = sin(θ)

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