Mathematics College

Find the probability that a randomly selected point within the circle falls in the red shaded area (square). Round to the nearest tenth of a percent.​

Find The Probability That A Randomly Selected Point Within The Circle Falls In The Red Shaded Area (square).

Answers

Answer 1

Answer:

probability of selecting the square is 63.7% approximately

Step-by-step explanation:

First of all, the probability of the point of choice is within the red square can be obtained with this formula

probability = expected outcome / total number of possible outcomes

In this case, we are not dealing with discrete values which can be counted. instead, we are dealing with areas.

We are to go about this problem by finding the area of the internal square and dividing it by the area of the circle.

Area of the square

Area of the square = [tex]l^2[/tex]

where length = [tex]4\sqrt{2}[/tex]

Area = [tex](4\sqrt{2}) ^2 = 32cm^2[/tex]

Area of the circle

Area of the circle = [tex]\pi r^2[/tex]

area of circle =[tex]\pi \times 4^2 =50.26cm^2[/tex]

Probablity of selecting the square =

32/50.26 = 0.6366

To express this as a percentage, we multiply our answer by 100.

This will give us 0.6366 X 100 = 63.7% approximately

Related Questions

Which graph represents the following piecewise defined function?

Answers

Answer: is B

Step-by-step explanation:

on edge 2020

The graph that represents the following piecewise defined function is graph D (Image attached).

What is piecewise defined function?

A piecewise function is known to be a type of function that is known to be formed or created from scratch (pieces) of different functions over different intervals.

An example, a person can make a piecewise function f(x) where f(x) = -9 when -8 < x ≤ -4, f(x) = 5 when -4 < x ≤ -1, and f(x) = -6 when -1 <x ≤ 9. Looking at the graph attached, you can see that it tells us more about  piecewise defined function.

Learn more about  piecewise defined function from

https://brainly.com/question/24313105

What is the width of a rectangle with a length of 3/8 ft and and area of
4 square feet?

Answers

L: 3/8ft
A: 4
W: 10.6666666668881

Explanation: 3/8ft x 10.6666666668881 = 4ft

Select the correct answer.
In a sequence described by a function, what does the notation f(3) = 1 mean?
OA.
The third term in the sequence has a value of 1.
OB.
The common difference I of the sequence is 3.
O C.
The first term in the sequence has a value of 3.
OD
The common ratio of the sequence is 3.

Answers

Answer:

c is correct

Step-by-step explanation:

Answer:

c is right answer

Step-by-step explanation:

HOPE IT HELPS U

FOLLOW MY ACCOUNT PLS PLS

Paul earns twice as much as john​

Answers

Answer:

Wat?

Mark me as brainlist

Answer:

whats the question

Step-by-step explanation:

Help!! Will give brainliest and bonus air-hugs!!
Can someone please explain a few steps and try to help me understand this!?!

Part A
Which measurements do you need to know to find the volume of a cylinder?

Part B
Since the base of the refraction cup is a half circle, how can you find the radius? What is the radius?

Part C
If you put two refraction cups together, what three-dimensional shape do you have?

Part D
The formula for the volume of a cylinder is v= 3.14r^2h.
What is the approximate volume of two refraction cups use 3.14 for pi.

Part E
Since one refraction cup is half of a cylinder, how could you change the formula for the volume of a cylinder to calculate the volume of a refraction cup?

Part F
Using the equation from Part E, what is the approximate volume of one refraction? What is the relationship between this value and the value from part D? Use 3.14 for pi.

Answers

Answer:

Part A: To find the volume of a cylinder, we need the dimensions of the cylinder such as the radius of the base of the cylinder and the height of the cylinder.

Part B: We have given the base of the refraction cup as a half-circle, we can calculate the radius of the base.

The diameter is given as 8 cm so, the radius would be half of the diameter.

r = 4cm

Part C:  If you put two refraction cups together, we get the full three-dimensional shape that is a circle.

Part D: The formula for the volume of a cylinder is V=pi r^2 h.

Part E: The volume of a refraction cup =

= 4/3 (3.14)(8)

= 33.49

Part F: The relationship between the value D and the value from Part D is as follows

The volume of a cylinder = 3 times the volume of a refraction cup

Step-by-step explanation:

Are these slopes equal? Explain if they are or if there not.

Answers

Answer:

Yes

Step-by-step explanation:

When dividing (or multiplying) two negative numbers, you end up with a positive number. The other slope is already positive. So 4/5=4/5

Please Help Me ASAP.

Answers

Answer:

C

Step-by-step explanation:

cuz itz IRRATIONAL

Please help ASAP 60 pts!
Write the equation of a circle with endpoints of the diameter at (4, -3) and (-2, 5).
Show your work for credit.

Answers

Answer:

(x - 1)² + (y - 1)² = 25

Step-by-step explanation:

Find the center, the midpoint of the diameter:

x = (4 - 2)/2 = 1, this is h of the circle equationy = (-3 + 5)/2 = 1, his is k of the circle equation

Find the square of the radius by distance formula:

r² = (1 - 4)² + (1 + 3)² = 25

Equation of the circle:

(x - h)² + (y - k)² = r²,

Substitute the values to get:

(x - 1)² + (y - 1)² = 25

Answer:

solution given:

points at (4, -3) and (-2, 5

diameter [d]=

[tex]d = \sqrt{(4 + 2) {}^{2} +( - 3 - 5) {}^{2} } \\ d = 10units \\ radius(r) = 5units [/tex]

centre[h,k]={(4-2)/2,(-3+5)/2}=(1,1)

now equation of a circle

(x-h)²+(y-k)²=r²

(x-1)²+(y-1)²=25 is a required equation

(2.4 x 10^4)(4.5 x 10^3)

Answers

2.4x104(4.5x103)

Simplifies to:

10.8x11000

=10.8x11000

Your answer will be =1.08 x 10^8

write the following rational numbers in their lowest terms:
1. 24/192
2. 12/168
3. 21/49​

Answers

Answer:

The Answer is gonna be 1. 24/192

Answer:

24/192 = 1/8

12/168 = 1/14

21/49 = 3/7

Step-by-step explanation:

A right triangle has a hypotenuse of 15 cm. What is the length for the missing leg if one of the two legs of the triangle is 5?

Answers

Answer:

The other leg is  12 cm  long.

Step-by-step explanation:

c

2

=

a

2

+

b

2

,

where:

c

is the hypotenuse, and  

a

and  

b

are the other two sides (legs).

Let  

a

=

9 cm

Rearrange the equation to isolate  

b

2

. Plug in the values for  

a

and  

c

, and solve.

b

2

=

c

2

−

a

2

b

2

=

(

15 cm

)

2

−

(

9 cm

)

2

Simplify.

b

2

=

225 cm

2

−

81

cm

2

b

2

=

144 cm

2

Take the square root of both sides.

b

=

√

144 cm

2

Simplify.

b

=

12 cm

Answer:

14.14 cm

Step-by-step explanation:

using the Pythagorean theorem:

?² = 15² - 5² = 225 - 25 = 200

? = √200 = 14.14 cm

can somebody help me please and thank you

Answers

1. 12/40 or 30% chance

2. 60

Explanation: 1. Not gonna lie i searched it up

2. x/200 times 12/40 = 2400/40

A psychologist has designed a questionnaire to measure individuals' aggressiveness. Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80. Suppose also that exactly 15% of the scores exceed 700. Find the mean of the distribution of scores. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

Answers

Answer:

The mean score is of 617.4.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80.

This means that [tex]\sigma = 80[/tex]

Suppose also that exactly 15% of the scores exceed 700.

This means that when X = 700, Z has a pvalue of 0.85. So X when X = 700, Z = 1.033. We use this to find [tex]\mu[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.033 = \frac{700 - \mu}{80}[/tex]

[tex]700 - \mu = 80*1.033[/tex]

[tex]\mu = 700 - 80*1.033[/tex]

[tex]\mu = 617.4[/tex]

The mean score is of 617.4.

Using first principle find derivatives of x2
​

Answers

Answer:

[tex]\displaystyle f'(x) = 2x[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                     [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Differentiation

DerivativesDerivative NotationDefinition of a Derivative:                                                                             [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = x^2[/tex]

Step 2: Differentiate

Substitute in function [Definition of a Derivative]:                                       [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{(x + h)^2 - x^2}{h}[/tex]Expand:                                                                                                         [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{x^2 + 2hx + h^2 - x^2}{h}[/tex]Simplify:                                                                                                         [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{2hx + h^2}{h}[/tex]Factor:                                                                                                           [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{h(2x + h)}{h}[/tex]Simplify:                                                                                                         [tex]\displaystyle f'(x) = \lim_{h \to 0} 2x + h[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]:                           [tex]\displaystyle f'(x) = 2x[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Which expression is equivalent to 1/5(150x - 80y + 50 - 50x - 25y + 20)?

Answers

Answer:

20x - 21y + 14

1/5(150x - 80y + 50 -50x - 25y + 20)

30x -16y + 10 - 10x - 5y + 4

30x -10x -16y - 5y + 10 + 4

20x -21y + 14

Answer:

20x-21y+14

Step-by-step explanation:

add up like terms and divide them by 5

Quadrilateral K is the image of Quadrilateral K under a dilation

Answers

What is the question
I’m confused

What is the diameter of a circle that has a radius of 7
inches?

Answers

Answer:

d=14in

Step-by-step explanation:

Solution

d=2r=2·7=14in

Hope this helped!!!

Find the f^-1(x) and it’s domain

Answers

Answer:

[tex]f^{-1}(x) = (x + 8)^2[/tex]

[tex]x \ge -8[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \sqrt x - 8[/tex]

Solving (a): [tex]f^{-1}(x)[/tex]

We have:

[tex]f(x) = \sqrt x - 8[/tex]

Express f(x) as y

[tex]y = \sqrt x - 8[/tex]

Swap x and y

[tex]x = \sqrt y - 8[/tex]

Add 8 to [tex]both\ sides[/tex]

[tex]x + 8 = \sqrt y - 8 + 8[/tex]

[tex]x + 8 = \sqrt y[/tex]

Square both sides

[tex](x + 8)^2 = y[/tex]

Rewrite as:

[tex]y = (x + 8)^2[/tex]

Express y as: [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x) = (x + 8)^2[/tex]

To determine the domain, we have:

The original function is [tex]f(x) = \sqrt x - 8[/tex]

The range of this is: [tex]f(x) \ge -8[/tex]

The [tex]domain[/tex] of the [tex]inverse[/tex] function is the [tex]range[/tex] of the [tex]original[/tex] function.

Hence, the domain is:

[tex]x \ge -8[/tex]

hewo the whole world that i hate^^

Royston plays a video game 7 times. His scores are 60, 65, 66, 74, 69, 72, and 63. Which is the best measure of center of Royston's performance?


median


middle number


mean


mode

Answers

Answer:

Mean: 67

Median: 66

Mode: no mode

Range: 14

Step-by-step explanation:

Answer:

mean

Step-by-step explanation:

Find $m\angle1$ and $m\angle2$ .

Answers

Answer:

m<1 = 125°

m<2 = 55°

Step-by-step explanation:

Okay, so we're dealing with alternate interior angles and all that sorta stuff, so I'll try to explain it best I can, if I'm too confusing let me know, let's go:

So the angle labeled 125° and angle 1 are alternate interior angles, so they're equal (yes, we're ignoring the fact that that might not me right because the other line isn't straight, I don't have another solution okay) anyways, so that means that:

1 = 125°

Now we know what 1 and 2 are on the same plane or axis or something like that, so basically, 1 and 2 HAVE TO add up to 180°, so that means that:

125 + x = 180

And now we just have to do the inverse operations thing:

180 - 125 = 55

So, m<1 = 125° and m<2 = 55°

tell me if this is wrong so I can fix it

hope this helps:)

URGENT!!! Help pls. U could literally just give me the equations

Answers

Answer:

Step-by-step explanation:

Terminal points of vector u has been given as (4, 0), (9, 4).

Therefore, vector u can be represented by,

[tex]\vec{u}=\vec{u_2}-\vec{u_1}[/tex]

[tex]\vec{u}=(9i+4j)-(4i)[/tex]

[tex]\vec{u}=5i+4j[/tex]

And the magnitude of the vector u will be,

|| u || = [tex]\sqrt{5^2+4^2}[/tex]

       = [tex]\sqrt{41}[/tex]

Slope of vector passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the expression,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of vector u will be,

Slope = [tex]\frac{4-0}{9-4}[/tex]

          = [tex]\frac{4}{5}[/tex]

Similarly, terminal points of vector v are (-7, 1) and (3, 9).

So the vector v will be,

[tex]\vec{v}=(3i+9j)-(-7i+1j)[/tex]

[tex]\vec{v}=(3i+7i)+(9j-1j)[/tex]

[tex]\vec{v}=10i+8j[/tex]

Therefore, magnitude of vector v will be,

|| v || = [tex]\sqrt{10^2+8^2}[/tex]

        = [tex]\sqrt{164}[/tex]

        = [tex]2\sqrt{41}[/tex]

Slope of vector v = [tex]\frac{9-1}{3+7}[/tex]

                             = [tex]\frac{8}{10}[/tex]

                             = [tex]\frac{4}{5}[/tex]

A sprinkler sprays in a circular pattern at a radius of 12 meters. If the degree of the circle that
is covered is 100°, what is the area of the lawn that is covered by the water from the
sprinker? (Round to the nearest hundredth of a meter)

Answers

Answer:

The area of the lawn that is covered by the water from the  sprinkler is

[tex]125.6[/tex] square meter

Step-by-step explanation:

Given

The radius of the circle is 12 m

Area of the circle is [tex]\pi r^2 = \pi * 12^2 = 144\pi[/tex]

For one complete circle,  the degree of rotation is 360 degrees.

Area of lawn covered by rotation of 100 degrees only is 100/360 = 5/18

The area of the lawn that is covered by the water from the  sprinkler is

[tex]\frac{5}{18} * 3.14*144 = 125.6[/tex] square meter

A student has been tracking his progress in French class. He notes each
grade he receives along with the date he received it. At the end of the
semester, he decides to create a data display to illustrate how his grades
have improved over time. What kind of display is his best choice?
O A. Stem-and-leaf plot
O B. Line graph
O C. Bar graph
D. Circle graph

Answers

Line because it will show the gradual increase or decrease

Answer:

B) Line graph

3x (7+8)x2+6 = ? HM?

Answers

Answer96

Step-by-step explanation:

3x (7+8)x2+6=96

Answer:

SHORTYYYYYYYYYYYYYYYYYYYYYYYYYYY ANSWER MEH YOU PRECIOUS CHILD

Step-by-step explanation:

It's meh Min you better not have forgotten who I am-

Find the value of x.
B
2
X
А A
30°
5
30°
5

Answers

Answer:

the x value is 2

because the triangles are similar

i think

The value of x, that is chord CD is 2 cm.

We need to find the value of x.

What is the statement of equal chords of a circle?

Equal chords of a circle subtend equal angles at the centre. The converse of the theorem is if two chords subtend equal angles at the centre, they are equal.

In the given diagram chord AB and chord CD subtend the equal angles which are 30°. Therefore, AB=CD=2 cm.

Hence, the value of x, that is chord CD is 2 cm.

To learn more about circle theorems visit:

https://brainly.com/question/19906255.

#SPJ2

Please help! Due today

Answers

Answer:

-4 5/12

Step-by-step explanation:

Please Help!
Using Heron’s formula, calculate the area of the parallelogram to the nearest tenth of a square unit.
Area ≈ ____ square units
Thank you!

Answers

Step-by-step explanation:

Hello! In order to get the best explication for your question, here's the link to a useful website:

https://geometryhelp.net/area-parallelogram-diagonals/

I believe, it's better for you to understand how to use the Heron's formula in other contexts so as to understand deeper into details how to apply it

Hope it helped!

Answer:36.7

Step-by-step explanation:

Hey morning help please thanks

Answers

Answer:

metaphor

Step-by-step explanation:

Answer:

Metaphor!

Step-by-step explanation:

Kites are described as "colorful fishes swimming in the sky".

Metaphors don't use like or as but still compare.

help me 5⋅f(1)+5⋅g(9)

Answers

Answer:

-50

Step-by-step explanation:

 5f(1) +5g(9) = 5(-5) + 5(-5) = -25 +(-25) = -50

Answer:

5f+45g

Step-by-step explanation:

A basketball team won 80% of the games played.if the team played 25 games,how many games did they lose?

Answers

Answer:

5

Step-by-step explanation:

80% of 25 is 20.
25-20 is 5.
They lost 5 games.
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