this and the notation , help!:__)

Answer:

Step-by-step explanation:

just here for the points

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

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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Answer:

7% of cars traveled east.

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

[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]

Answer:

13

Step-by-step explanation:

5^2+8^2= c^2

25+64=c^2

89=c^2

c=9.4

9.4^2+9^2=c^2

c=170

c=13

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."--

An equation using x as the number of pages in the book that has 6 chapters with the same number of pages and an introduction with 8 pages is 6x + 8 = 194.

An equation is a mathematical statement that defines that two or more mathematical or algebraic expressions are equal or equivalent.

Equations use the equal symbol (=) while mathematical expressions just combine variables with numbers, constants, and values using mathematical operands.

The number of chapters in the book = 6

The number of pages of the introduction = 8 pages

The total number of pages of the whole book = 194

Let the number of pages in each chapter = x

6x + 8 = 194

6x = 186 (194 - 8)

x = 31

Thus, we can evaluate the equation to show that x is 31.

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Write an equation using x to show the number of pages in each chapter of the book.

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: 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

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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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:

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 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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To determine if the point (5,1) is part of the line y = 7-2x, we need to substitute x=5 and y=1 into the equation of the line and check if it is a true statement:

y = 7 - 2x

1 = 7 - 2(5)

1 = 7 - 10

1 = -3

Since -3 is not equal to 1, the point (5,1) is not part of the line y = 7-2x.

Answer: the answer is 24

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=192\pi \\ r=2 \end{cases}\implies 192\pi =\cfrac{\pi 2^2 h}{3} \\\\\\ 192\pi =\cfrac{4\pi h}{3}\implies \cfrac{ 3}{4\pi }\cdot 192\pi=h\implies 144=h \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=192\pi \\ r=3 \end{cases}\implies 192\pi =\cfrac{\pi 3^2 h}{3} \\\\\\ 192\pi =3\pi h\implies \cfrac{192\pi }{3\pi }=h\implies 64=h \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=192\pi \\ r=4 \end{cases}\implies 192\pi =\cfrac{\pi 4^2 h}{3} \\\\\\ 192\pi =\cfrac{16\pi h}{3}\implies \cfrac{ 3}{16\pi }\cdot 192\pi=h\implies 36=h[/tex]

[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 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?"

The percentage change in the number of websites from 1991 to 1992 is 900%.

Given that,

In 1991 there was 1 website.

In 1992 there were 10 websites.

The formula to find the percentage change is,

Percent change = (New value - old value) / old value

Here,

New number of websites = 10

Old number of websites = 1

Percentage change = (10 - 1) / 1 = 9 = 900%

Hence the percentage change in the number of websites is 900%.

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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

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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Step-by-step explanation:

Maximum area enclosed will be a square enclosure

  since the river is one side , the other three sides of the square will be

       1440 / 3 = 480 ft long

Square with sides 480 ft

area =480 x 480 = 230 400 ft^2

Answer:

If Sarah received 10 points for each of the four targets she hit, her total point gain from hitting targets would be:

4 targets x 10 points = 40 points

If Sarah loses 105 points for taking too long, her total loss is -105 points (due to the negative change in her score).

As a result, the total change in Sarah's score may be determined by adding her point gain from hitting targets to her point loss from taking too long:

Total difference = 40 points minus 105 points

-65 points total change

As a result, Sarah's score dropped by 65 points after completing the following level of her video game.

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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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: 344

Step-by-step explanation:

Well I dont know