10.
Find the length of the arc on a circle of radius r intercepted by a central angle 0.
r=20 cm,
e
1/4 radian

Answers

Answer 1

Answer:

Length of arc = 5 cm (Approx)

Step-by-step explanation:

Given:

Radius of circle = 20 cm

Angle = 1/4 radian

Find:

Length of arc

Computation:

Angle in degree = 1/4 radian × 180°π

Angle in degree = 1/4 × 180°  / 22/7

Angle in degree = 14.31° Approx

Length of arc = (Ф / 360)2πr

Length of arc = (14.31 /360)2(22/7)(20)

Length of arc = 4.997 cm

Length of arc = 5 cm (Approx)


Related Questions

For the following systems of equations, match each diagram on the left with its solution on the right.

Answers

Answer:

1. (2,1)

2. (6,-1)

3.(-2,3)

Answer:

1. (2,1)

2.  (6,-1)

3. (-2,3)

Step-by-step explanation:

Each of the answer is consistent system because the lines intersect at one point, which is one solution.

Many websites have ads whose appearance is based onprobability. Advertisers pay the website based on the number of timesthe ad appears.a. The probability that an ad appears when a particular website isloaded is 0.2. The website gets 2000 hits a day. About how manytimes does the ad appear?b. The probability that an ad appears when a particular website isloaded is 0.05. About how many hits must the website have for thead to appear 1000 times?

Answers

Answer:

A. How many times the ad appear:

= 400 times

B. How many hits the website must have for thread to appear 1000 times with 0.05 probability that an ad appears when the website is loaded.

= 20,000 hits

Step-by-step explanation:

A. The probability that an ad appears when a particular website is loaded = 0.2

When the website gets 2,000 hits a day, the ad appears

= 2,000 x 0.2

= 400 times

B. When the probability that an ad appears when the website is loaded is 0.05.

Therefore, the website must have 20,000 hits for thread to appear 1,000 times

= 1,000/0.05

= 20,000 times

The probability of an ad appearing when a website is loaded is the chance that the event happens (i.e. the ad appears) from the many events that can happen.

I need help with this please answer

Answers

Answer:

B. [tex]1\frac{1}{7}[/tex]

Step-by-step explanation:

[tex]-9\frac{2}{7}[/tex]=[tex]-\frac{65}{7}[/tex]

[tex]-10\frac{3}{7}[/tex]=[tex]-\frac{73}{7}[/tex]

[tex]-\frac{65}{7}[/tex]-([tex]-\frac{73}{7}[/tex])=8/7

8/7=[tex]1\frac{1}{7}[/tex]

Hope this helped!!!

The vertex of this parabola at (-5,-2). When the c - value is -4 the y-value is 2 what is the coefficient of the squared expression in the parabolas equation. ( to answer gets brainliest )

Answers

Answer:

4

Step-by-step explanation:

The vertex formula of a quadratic equation is:

●y= a(x-h)^2 +k

(h,k) are the coordinates of the vertex

Here: h = -5 and k= -2

y is 2 and x is -4

● 2 = a (-4-(-5))^2 + (-2)

● 2 = a (-4+5)^2 -2

● 2 = a *1^2 -2

● 2 = a -2

● 4 = a

The time between failures for an electrical appliance is exponentially distributed with a mean of 25 months. What is the probability that the next failure will not occur before 30 months have elapsed

Answers

Answer:

The probability that the next failure will not occur before 30 months have elapsed is 0.0454

Step-by-step explanation:

Using Poisson distribution  where

t= number of units of time

x= number of occurrences in t units of time

λ= average number of occurrences per unit of time

P(x;λt) = e raise to power (-λt)  multiplied by λtˣ divided by x!

here λt = 25

x= 30

P(x= 30) = 25³⁰e⁻²⁵/ 30!

P (x= 30) = 8.67 E41 * 1.3887 E-11/30!    (where E= exponent)

P (x=30) = 1.204 E31/30!

Solving it with a statistical calculator would give

P (x=30) = 0.0454

The probability that the next failure will not occur before 30 months have elapsed is 0.0454

The length of the room is 2½ times the breadth. The perimeter of the room is 70 m. What are the length and breadth of the room.

Answers

According to the questionLet breadth be xSo length = 5/2. XNow perimeter of rectangle = 2(l+b).so70 = 2 × ( X + 5/2 X)35 = 7x/2x = 35 × 2/7x = 10So breadth = 10mlength = 5/2 × 10 = 25m

Answer:

Length = 25 cmBreadth = 10 cm

Step-by-step explanation:

Let breadth of the room be 'x'

Let length of the room be '[tex]2 \frac{1}{2} x = \frac{5}{2} = 2.5 \: x[/tex]'

Perimeter ( P ) = 70 cm

Now, let's find the breadth of the room 'x '

Perimeter of rectangle = [tex]2(l + b)[/tex]

plug the values

[tex]70 = 2(2.5x + x)[/tex]

Collect the like terms

[tex]70 = 2 \times 3.5x[/tex]

Calculate the product

[tex]70 = 7x[/tex]

Swap the sides of the equation

[tex]7x = 70[/tex]

Divide both sides of the equation by 7

[tex] \frac{7x}{7} = \frac{70}{7} [/tex]

Calculate

[tex]x = 10 \: cm[/tex]

Breadth = 10 cm

Now, Let's find the length of the room ' 2.5x '

Length of the room = [tex]2.5x[/tex]

Plug the value of X

[tex] = 2.5 \times 10[/tex]

Calculate the product

[tex] = 25 \: cm[/tex]

Thus , The length and breadth of the room is 25 cm and 10 cm respectively.

Hope this helps..

Best regards!!

I WILL GIVE BRAINLIEST!!!! Calculate cos M if a= 4, b= 12.5, c= 13.1244 **Round your answer up to four decimal places.

Answers

Answer:

cosM ≈ 0.3048

Step-by-step explanation:

remember SOH CAH TOA = sine: opposite/hypotenuse; cosine: adjacent/hypotenuse; tangent: opposite/adjacent

cos = CAH

cosM= a / c

cosM = 4.0 / 13.1244

cosM = 0.30477

cosM ≈ 0.3048

Solve the inequality for y.
y - 9x > 6
please help!!!!!!!

Answers

Answer:

y>9x+6

Step-by-step explanation:

y-9x+(9x)>6+(9x)

y>9x+6

let [tex]p=x^{2}+6[/tex]

Which equation is equivalent to [tex](x^{2}+6)^{2}-21=4x^{2}+24[/tex] in terms of [tex]p[/tex]?

Answers

Answer:

Hello There. ☆~---~--___●♡●__~--☆ Since p = x² - 7, you can substitute/plug in p for x² - 7

So:

(x² - 7)² - 4x² + 28 = 5

(p)² - 4x² + 28 = 5   You can factor out -4 from (-4x² + 28)

p² - 4(x² - 7) = 5        Plug in p

p² - 4p = 5        Subtract 5

p² - 4p - 5 = 0  And, your correct answer is C.

Hope It Helps!~

ItsNobody~ ☆

Find the midline for f(x)=2cos(3x−5π6)−2

Answers

Answer:  y = -2

Step-by-step explanation:

f(x) = A cos (Bx - C) + D

                                  ↓

                                center line (aka midline)

f(x) = 2 cos (3x - 5π/6) - 2

                                      ↓

                                  midline = -2

The midline of the cos function f(x) = 2cos(3x − 5π/6) − 2 is y = -2 after comparing with standard cos function f(x) = Acos(Bx - C) + D

What is cos function?

It is defined as a function that is sin-cos wave in nature, and it has a domain of all real numbers and lies between the [a, a] where is the amplitude of the function.

It is given that the cos function is:

f(x) = 2cos(3x - 5π/6) - 2

As we know, the standard form of the cos function is:

f(x) = Acos(Bx - C) + D

Here, A is the amplitude

B is the period of the cos function

C is the phase shift of the cos function

D is the vertical shift of the cos function/midline

On comparing:

D = -2

The midline:

y = -2

Thus, the midline of the cos function f(x) = 2cos(3x − 5π/6) − 2 is y = -2 after comparing with standard cos function f(x) = Acos(Bx - C) + D

Learn more about the cos function here:

https://brainly.com/question/14397255

#SPJ5

Find the values of k so that the area of the triangle with vertices (1, -1), (-4,2k) and (-k, – 5) is 24 sq. units

Answers

Step-by-step explanation:

We need to find the value of k so that the triangle with vertices (1, -1), (-4,2k) and (-k, – 5) is 24 sq. units.

The area of triangle is given by :

[tex]A=\dfrac{1}{2}\times [x_1(y_2-y_3)-x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]

Here,

x₁ = 1, y₁ = -1, x₂ = -4, y₂ = 2k, x₃ = -k and y₃ = -5

So,

[tex]24=\dfrac{1}{2}\times [1(2k-(-5))-(-4)((-5)-(-1))+(-k)((-1)-(2k))][/tex]

We need to solve the above equation,

[tex]48=[1(2k-(-5))-(-4)((-5)-(-1))+(-k)((-1)-(2k))][/tex]

On solving the above equation we get the value of k as :

k = 4.7

Explain how you would decide whether to use a dot plot or a box plot to display a data set. Give some strengths and weaknesses of each type of display to support your explanation.

Answers

Answer:

A box plot should be used in a situation when you need the median and quartiles.  A dot plot should be used when you need exact numbers.  The strengths of a box plot is that it shows a big data sets into a rounded form.  The strengths of a data set is that you can show the exact numbers but it would work best with small numbers.

Hope this helped?

AB is tangent to circle D. Find the value of x.

Answers

Answer:

c     15

Step-by-step explanation:

Tangent AB is tangent to circle D at point A. The angle made by a tangent to a circle and a radius of the circle at the point of tangency is a right angle. That means that angle is a right angle, and triangle ABD is a right triangle.

We can use the Pythagoren theorem.

a^2 + b^2 = c^2

x^2 + 20^2 = (x + 10)^2

x^2 + 400 = (x + 10)(x + 10)

x^2 + 400 = x^2 + 10x + 10x + 100

400 = 20x + 100

20x = 300

x = 15

which of the following is equivalent to (x+4)(3x^2+2x)??

Answers

Answer:

c

Step-by-step explanation:

Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula.

Answers

Answer:

The explicit formula for the sequence is

44 - 6n

Step-by-step explanation:

The above sequence is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 38

d = 32 - 38 = - 6 or 20 - 26 = - 6 or

14 - 20 = - 6

So the formula for the sequence is

A(n) = 38 + ( n - 1)-6

= 38 - 6n + 6

We have the final answer as

A(n) = 44 - 6n

Hope this helps you

Answer:

[tex]\huge\boxed{a_n=-6n+44}[/tex]

Step-by-step explanation:

This is an arithmetic sequence:

32 - 38 = -6

26 - 32 = -6

20 - 26 = -6

14 - 20 = -6

The common difference d = -6.

The explicit formula of an arithmetic formula:

[tex]a_n=a_1+(n-1)(d)[/tex]

Substitute:

[tex]a_1=38;\ d=-6[/tex]

[tex]a_n=38+(n-1)(-6)[/tex]         use the distributive property

[tex]a_n=38+(n)(-6)+(-1)(-6)\\\\a_n=38-6n+6\\\\a_n=-6n+(38+6)\\\\a_n=-6n+44[/tex]

the dot plot shows the number of text messages mr.garcia sent each day so far this month. which statement best describes the shape of the graph?

Answers

Answer:

where is the dot plot also describe if it increases or decreases

A group of students made trees out of paper for a scene in a school play. The trees are shaped like square pyramids. 70 cm70\text{ cm} 70 cm 140 cm140\text{ cm} 140 cm How much paper will it take to make each tree, including the bottom?

Answers

Answer:

24500 cm^2

Step-by-step explanation:

A box is filled with 9 red crayons, 2 blue crayons, and 5 yellow crayons. A crayon is chosen at random from the box. Find the probability that it is a red or a blue crayon. Write your answer as a fraction in simplest form.

Answers

Answer:

[tex]P(Red\ or\ Blue) = \frac{11}{16}[/tex]

Step-by-step explanation:

Given

[tex]Red = 9[/tex]

[tex]Blue = 2[/tex]

[tex]Yellow = 5[/tex]

Required

Probability of Red or Blue

First, it should be noted that the event described in the question are mutually exclusive or disjoint events;

Meaning that the probability of one have no effect the other;

Having said that; the Probability of Red ot Blue is as follows

[tex]P(Red\ or\ Blue) = P(Red) + P(Blue)[/tex]

Calculating [tex]P(Blue)[/tex]

[tex]P(Blue) = Number\ of\ blue\ crayon / total\ crayon[/tex]

[tex]P(Blue) = \frac{2}{9+ 2 + 5}[/tex]

[tex]P(Blue) = \frac{2}{16}[/tex]

Calculating [tex]P(Red)[/tex]

[tex]P(Red) = Number\ of\ red\ crayon / total\ crayon[/tex]

[tex]P(Red) = \frac{9}{9+ 2 + 5}[/tex]

[tex]P(Red) = \frac{9}{16}[/tex]

Substitute these values in the formula given above

[tex]P(Red\ or\ Blue) = P(Red) + P(Blue)[/tex]

[tex]P(Red\ or\ Blue) = \frac{9}{16} + \frac{2}{16}[/tex]

Take LCM

[tex]P(Red\ or\ Blue) = \frac{9 + 2}{16}[/tex]

[tex]P(Red\ or\ Blue) = \frac{11}{16}[/tex]

Hence, the probability of a red or blue crayon is

[tex]P(Red\ or\ Blue) = \frac{11}{16}[/tex]

A hair color manufacturer performed a survey which was normally distributed. They found that the average age at which a person's hair starts turning gray is 32 years, with a standard deviation of 4 years. Which of the following graphs displays the normal distribution of the average age at which a person's hair starts turning gray?


W.
X.

Y.
Z.

Answers

Answer: X

Step-by-step explanation:

4xy-3x+8y2-6y 8y-6 please help someone thank you

Answers

Answer:

x=6, y=2.5

Step-by-step explanation:

WILL GIVE BRAILIEST! Find the mean of the data in the bar chart below. _________puppets

Answers

Answer: 2.5

Step-by-step explanation:

To find a mean, the average, we have to add everything together.

So we add 1 + 4 + 3 + 2, which is equal to 10. The next step to find the average is to divide by the total number of “things” which is the 4 puppeteers.

10/4 is 2.5

I need help with this problem! Must explain why.

Answers

Answer:

95°

Step-by-step explanation:

Angle 1 and 4 are opposite angles, thus equal, so:

3x+10 = 4x-15 =>

x = 25

Angle 1 and 4 are 85°

Angle 4 and angle 6 are called allied (or co-interior) angles, which are supplementary, i.e., angle 6 = 180 - angle 4, so angle 6 = 95°.

Angle 6 and 7 are again opposite, so angle 7 is 95° as well!

In ∠QRS, m∠R=65°, and m∠S=35°. Which side of ΔQRS is the longest?

Answers

Answer:

The longest side of the ΔQRS is Side RS.

Step-by-step explanation:

Given:  m∠R=65°, m∠S=35° we don't know what m∠Q is in ΔQRS.

To find m∠Q , we first need to know that all triangles have a sum of 180°. Since we are already given two angle measurements ( m∠R and  m∠S) we can add them both measurements up which gives us 100°. Then we subtract 100 from the triangle sum which is 180° (180°-100°) and we are left with 80°. Which mean that m∠Q got to be 80°.

Now we know the all the angles measurements we can immediately find out which side is the longest. To find the longest side its always lie opposite the largest angle which in this m∠Q (80°). Which mean that side RS is the longest side in the triangle.

Suppose xy > 0. Describe the points whose coordinates are solutions to the inequality. please answer in detail

Answers

Answer

so,if x*y> than zero, we know that neither x nor y can be zero, because anything multiplied by zero is equal to zero. now , we also know, that a negative  times a negative is positive, and a positive  times a positive times a positive is a positive

Step-by-step explanation:

En un rectangulo el ancho es menor en 5cm al largo . si el P= 38cm calcule su area

Answers

Answer:

84cm²

Step-by-step explanation:

Perímetro de un rectángulo = 2L + 2W

Representemos la longitud del rectángulo = L

En la pregunta anterior se nos dijo que el ancho del rectángulo = es menor que 5 en la longitud

Por lo tanto, ancho del rectángulo = L - 5

Perímetro del rectángulo = 38 cm

Por lo tanto

38 = 2 (L) + 2 (L - 5)

38 = 2L + 2L - 10

38 + 10 = 4L

48 = 4L

L = 48/4

L = 12 cm

La longitud del rectángulo = 12 cm

Como L = 12, encontramos el ancho

Ancho = L - 5

= 12 cm - 5 cm

= 7 cm

El ancho del rectángulo = 7 cm

En la pregunta nos pidieron encontrar el área del rectángulo.

Área del rectángulo = Largo × Ancho

Área del rectángulo = 12 cm × 7 cm

Área del rectángulo = 84cm²

what is the exact area of a circle having diameter 4in

Answers

The diameter of a circle is calculated by using the formula D=r2pi so plug in the known values to find r=2/pi. Next plug r into the area of a circle formula(A=r^2pi) do so and get 4/pi

HELP!! please. What is the area of the polygon shown?

Answers

Answer:

38 cm squared

Step-by-step explanation:

Given figure : Trapezoid

Base sides,

a = 11 cm

b = 11 - 3 = 8 cm

height ( h ) = 4 cm

Now, finding the area:

[tex] \frac{1}{2} (a + b) \: h[/tex]

plug the values

[tex] \frac{1}{2} \times (11 + 8) \times 4[/tex]

Calculate the sum

[tex] \frac{1}{2} \times 19 \times 4[/tex]

Reduce the numbers with G.C.F 2

[tex]19 \times 2[/tex]

Calculate the product

[tex]38 \: {cm}^{2} [/tex]

Hope this helps...

Best regards!

Starting from an airport, an airplane flies 290 miles east and then 290 miles northwest. How far, in miles, from the airport is the plane? (Round your answer to the nearest mile.)

Answers

Answer:

The airplane is 222 miles far from the airport.

Step-by-step explanation:

After a careful reading of the statement, distances can be described in a vectorial way. A vector is represented by a magnitude and direction. That is:

Airplane flies 290 miles (east) (290 km with an angle of 0º)

[tex]\vec r_{A} = (290\,mi)\cdot i[/tex]

Airplane flies 290 miles (northwest) (290 km with and angle of 135º)

[tex]\vec r_{B} = [(290\,mi)\cdot \cos 135^{\circ}]\cdot i + [(290\,mi)\cdot \sin 135^{\circ}]\cdot j[/tex]

The resultant vector is equal to the sum of the two vectors:

[tex]\vec r_{C} = \vec r_{A} + \vec r_{B}[/tex]

[tex]\vec r_{C} = \{(290\,mi) + \left[(290\,mi)\cdot \cos 135^{\circ}\right]\}\cdot i + \left[(290\,mi)\cdot \sin 135^{\circ}\right]\cdot j[/tex]

[tex]\vec r_{C} = (84.939\,mi)\cdot i + (205.061\,mi)\cdot j[/tex]

The magnitude of the final distance of the airplane from the airport is obtained by the Pythagorean Theorem:

[tex]\|\vec r_{C}\|=\sqrt{(84.939\,mi)^{2}+(205.061\,mi)^{2}}[/tex]

[tex]\|\vec r_{C}\| = 221.956\,mi[/tex]

The airplane is 222 miles far from the airport.

22. “n is less than 15 and greater than or equal to 3”

Complete the following steps to receive full credit for this question:

• The inequality translated in numerical form
• The solution graphed on a number line
• The solution in interval form

Answers

Answer:

3 ≤ n < 15

not nnot nyes nyes nyes nyes nyes nyes nyes nyes nyes nyes nyes nyes nnot n

 1-2. not n

3-4. yes n

5-6. yes n

 7-8. yes n

9-10. yes n

11-12. yes n

13-14. yes n

15-16. not n

Step-by-step explanation:

Everything on this side is less than, < but everything on this side is greater.

Everything on this side could be equal or less, ≤ but everything on this side is

not.

I'm had a hard time with the number line, but imagine a line going through the periods and there being a dot where the yes ns end, and start.

Intervals has each point represent more than one number making the line shorter.

A. 60
B. 15
C. 120
D. 6

Answers

Answer:

C. 120

Step-by-step explanation:

The figure shows that angles BEC and KEC are congruent. Their measures are equal.

m<KEC = m<BEC

10x = 6x + 24

4x = 24

x = 6

m<BEK = 2m<KEC

m<BEK = 2 * 10x

m<BEK = 2 * (10)(6)

m<BEK = 2 * 60

m<BEK = 120

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Martha will be remembered for her hard work and personality. Sketch the graphs:y=-x+5 Read the excerpt from President Ronald Reagans Address at Moscow State University.The explorers of the modern era are the entrepreneurs, men with vision, with the courage to take risks and faith enough to brave the unknown. These entrepreneurs and their small enterprises are responsible for almost all the economic growth in the United States. They are the prime movers of the technological revolution. In fact, one of the largest personal computer firms in the United States was started by two college students, no older than you, in the garage behind their home. Some people, even in my own country, look at the riot of experiment that is the free market and see only waste. What of all the entrepreneurs that fail? Well, many do, particularly the successful ones; often several times. And if you ask them the secret of their success, they'll tell you it's all that they learned in their struggles along the way; yes, it's what they learned from failing. Like an athlete in competition or a scholar in pursuit of the truth, experience is the greatest teacher.Which is a substantiated opinion?One of the largest computer companies began in a garage.Small businesses are the reason America has a strong economy.Experience is the best way for entrepreneurs to learn.People are often wasteful in free market societies. You are given 10.00 mL of a solution of an unknown acid. The pH of this solution is exactly 2.18. You determine that the concentration of the unknown acid was 0.2230 M. You also determined that the acid was monoprotic (HA). What is the pKa of your unknown acid Answer question 18 or 19 in the image thank you and please help #The Fibonacci sequence is a number sequence where each #number is the sum of the previous two numbers. The first #two numbers are defined as 0 and 1, so the third number is #1 (0 + 1 = 1), the fourth number is 2 (1 + 1 = 2), the #fifth number is 3 (1 + 2 = 3), the sixth number is 5 #(2 + 3 = 5), and so on. # #Below we've started a class called FibSeq. At any time, #FibSeq holds two values from the Fibonacci sequence: #back1 and back2. # #Create a new method inside FibSeq called next_number. The #next_number method should: # # - Calculate and return the next number in the sequence, # based on the previous 2. # - Update back2 with the former value of back1, and update # back1 with the new next item in the sequence. # #This means that consecutive calls to next_number should #yield each consecutive number from the Fibonacci sequence. #Calling next_number 5 times would print 1, 2, 3, 5, and 8.class FibSeq: def __init__(self): self.back1 = 1 self.back2 = 0 def next_number(self): self.back1=self.back1+self.back2 # updated the back1 value to the next number in the series first self.back2=self.back1-self.back2 #updated the back2 value with previous back1 value yield (self.back1) # yielded the next number in the series since it is updated as back1 so yielded back1 f = FibSeq() for i in range(5): # here i have iterated the series only 5 times u can change it as you like s=f.next_number() print(next(s))# here next is an iterator function for the yield generator. #The code below will test your method. It's not used for #grading, so feel free to change it. As written, it should #print 1, 2, 3, 5, and 8. newFib = FibSeq() print(newFib.next_number()) print(newFib.next_number()) print(newFib.next_number()) print(newFib.next_number()) print(newFib.next_number()) A company makes a product that sells for $80 per unit. Variable expenses are $40.00 per unit, and fixed expenses total $200,000 per year. Its operating results for last year were as follows: Sales $ 2,080,000 Variable expenses 1,040,000 Contribution margin 1,040,000 Fixed expenses 200,000 Net operating income $ 840,000 The company president wants to add new features to the product, which will increase the variable expenses by $1.90 per unit. She thinks that the new features, combined with some increase in marketing spending, would increase this year's sales by 25%. How much could the president increase this year's fixed marketing expense and still earn the same $840,000 net operating income as last year Which two parts of this excerpt reflect Winston Churchill's belief that the Nazis could be overcome only through the collaboration of Great Britain and its alles