A coin is tossed. What is the theoretical probability of the coin NOT showing tails?
P(Not tails) =

A = (-7,-6)

B = (8,-9)

Find the slope of line AB

m = (y2-y1)/(x2-x1)

m = (-9-(-6))/(8-(-7))

m = (-9+6)/(8+7)

m = -3/15

m = -1/5

The slope of line AB is -1/5.

Flip the fraction and the sign to go from -1/5 to +5/1 = 5. The perpendicular slope is 5.

Let m = 5.

Use the coordinates of point C (2,12) along with the perpendicular slope to get

y - y1 = m(x - x1)

y - 12 = 5(x - 2)

y - 12 = 5x - 10

y = 5x - 10+12

y = 5x + 2

Lastly, convert this to standard form

y = 5x + 2

5x+2 = y

5x+2-y = 0

5x-y = -2

Choice A is the closest match, but the -56 should be -2 instead. It seems like your teacher made a typo somewhere.

Answer:

5x - y = -2.

Step-by-step explanation:

The equation of this altitude line has a slope = -1/m where m is the slope of line AB . It will also pass through the point C.

The slope of line AB = (-9 - (-6)) / (8 - (-7))

= -3/15

= -1/5

So the slope  of the required line = -1 / -1/5 = 5.

Using the point C and the point-slope form of a line:

y - y1 = m(x - x1)

y - 12 =  5(x - 2)

y - 5x = -10 + 12

y - 5x = 2

5x - y = -2.

The missing probability P(A∪B) will be 37/50.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Given information;

P(A)= 7/20,

P(B)=3/5,

P(A∩B) =21/100 ,

We need to find the missing probability P(A∪B).

We know that

P(A∪B)= P(A) + P(B) + P(A∩B)

P(A∪B) = 7/20 + 3/5 + 21/100

P (A U B) = 37/50

Therefore, the missing probability P(A∪B) will be 37/50.

Learn more about probability here;

https://brainly.com/question/11234923

#SPJ5

Answer:

Option B.

Step-by-step explanation:

Consider the correct question is "Which statement correctly compares

1. -201  and  151

-201 = 151

-201 < 51

-201 > 151"

The given numbers are -201 and 151. We need to compare these numbers.

We know that all negative numbers are less than positive numbers.

So,

-201 < 151

If both numbers are negative, then the larger negative number is the smaller number.

Therefore, the correct option is B.

Answer:

1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle

2) The joint equations of diagonals are;

5·y = 56 - 6·x and 5·y = 6·x + 14.

Step-by-step explanation:

The equations are;

x² - 7·x + 6 = 0......................(1)

y² - 14·y + 40 = 0.................(2)

Factorizing equation (1) and equation (2) , we get

x² - 7·x + 6 = (x - 6)·(x - 1) = 0

Which are vertical lines at points x = 6 and x = 1

For equation (2) , we get

y² - 14·y + 40 = (y - 10)·(y - 4) = 0

Which are horizontal lines at point y = 4 and y = 10

The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle

2) The points of intersection of the equations are;

(1, 4), (1, 10), (6, 4), and (6, 10)

The end point of the diagonals are;

(1, 10), (6, 4) and  (1, 4), (6, 10)

The slope of the diagonals are;

(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5

The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)

y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5

5·y = 56 - 6·x

The other diagonal is therefore;

y - 4 = 6/5×(x - 1)

y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5

5·y = 6·x + 14.

The joint equations of diagonals are therefore;

5·y = 56 - 6·x and 5·y = 6·x + 14.

Answer:

I hope this helps!

Answer D

Step-by-step explanation:

Step-by-step explanation:

salary per day =$140

bonus on sales =14%

sales on Saturday =$600

bonus on Saturday sales=14/100*$600

=$84

sales on Sunday =$1200

bonus on Sunday sales=14/100*$1200

=$168

total amount she earned over the two days=$140+$84+$168

=$532

===================================================

Work Shown:

[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]

Notice how 33*77 = 2541 and 11*231 = 2541

[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.

So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]

Answer: You are correct. There is only one answer and that is choice B) vertical line of symmetry.

We can draw a vertical line through the center to have one half mirror over this line to get the other half. We can't do the same with a horizontal line or any other kind of line.

We do not have rotational symmetry. Rotating the figure will produce an image different from the original. The angle of rotation is some angle x such that 0 < x < 360.

Answer:

Theres more than one answer so b and a

Step-by-step explanation:

Answer:

Step-by-step explanation:

The diagonals of the rhombus divide it into 4 congruent right triangles.

So we can use Pythagorean theorem to calculate side of a rhombus.

[tex](\frac e2)^2+(\frac f2)^2=s^2\\\\e=30\,cm\quad\implies\quad\frac e2=15\,cm\\\\f=16\,cm\quad\implies\quad\frac f2=8\,cm\\\\15^2+8^2=s^2\\\\s^2=225+64\\\\s^2=289\\\\s=17[/tex]

Perimeter:

P = 4s = 4•17 = 68 cm

Answer:

d) More than 3.

Step-by-step explanation:

The polynomial (x - 5)(x + 2)  ( = x^2  - 3x + 10) has zeros of -2 and 5 but so have the polynomials formed by multiplying this by any integer:

- for example 2(x - 5)(x + 2) , 4(x - 5)(x + 2) and so on.

Answer:

h = 10

Step-by-step explanation:

Given

[tex]\frac{3}{7}[/tex] = [tex]\frac{h}{14}[/tex] - [tex]\frac{2}{7}[/tex]

Multiply through by 14 to clear the fractions

6 = h - 4 ( add 4 to both sides )

10 = h

Answer:

10

Step-by-step explanation:

We start out with 3/7 = h/14 - 2/7

add 2/7 to both sides:

(5/7) = h/14

Multiply both sides by 14 to get rid of the fraction:

h = 10

As per the question,

We have to find what's the coefficient.

Let's start to seperate the expression.

Here,

x is the variable,

4 is a number.

-3 is also a number.

4, -3x

The number with x here is -3 in (-3x) as the coefficient is (-3) in the given equation.

Answer:

Hey there!

Rearrange the expression to: -3x+4

The coefficient would be -3.

Let me know if this helps :)

Answer: [tex]y-1=\dfrac32(x+3)[/tex]

Step-by-step explanation:

Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

In graph(below) given line is passing through (-2,-4) and (2,2) .

Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]

Since parallel lines have equal slope . That means slope of the required line would be .

Equation of a line passing through (a,b) and has slope m is given by :_

(y-b)=m(x-a)

Then, Equation of a line passing through(-3, 1) and has slope =  is given by

[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]

Required equation: [tex]y-1=\dfrac32(x+3)[/tex]

Answer:

5 times

Step-by-step explanation:

Jenna wil most likely pull a yellow marble 1/3 of the time, because the total number of marbles is 6, and there are 2 yellow marbles, 2/6 which is 1/3. 1/3 times 15 is 5. So Jenna will most likely pull a yellow marble 5 times.

Answer:

C. 2[tex]\sqrt{29}[/tex]

Step-by-step explanation:

Square root of 116 is 10.7703296

Square root of 29 is 5.38516481, but as it is multiplied by 2, it becomes 10.7703296

Answer:

(D) There are [tex]5 \frac{1}{2}[/tex]  three-fourths in [tex]4 \frac{1}{8}[/tex]

Step-by-step explanation:

We can see that in this model, the student tried to put [tex]\frac{3}{4}[/tex] into  [tex]4 \frac{1}{8}[/tex]. We know this because the top of Step 2 is  [tex]4 \frac{1}{8}[/tex] and he is counting how many fourths in the bottom.

So this becomes the division statement:

[tex]4 \frac{1}{8} \div \frac{3}{4}[/tex].

We can convert  [tex]4 \frac{1}{8}[/tex] into a mixed number by multiplying 8 and 4, then adding 1.

[tex]\frac{33}{8} \div \frac{3}{4}[/tex].

Multiply by the reciprocal:

[tex]\frac{33}{8} \cdot \frac{4}{3} = \frac{132}{24}[/tex]

Which simplifies down to

[tex]\frac{11}{2}[/tex], which is just [tex]5 \frac{1}{2}[/tex] in improper form.

Hope this helped!

Answer:

D

Step-by-step explanation:

Answer:

288.4m

Step-by-step explanation:

This track is split into a rectangle and two semi-circles.

We can find the length of the semi-circles by finding its circumference with the formula [tex]2\pi r[/tex].

[tex]2\cdot3.14\cdot30\\188.4[/tex]

However this is half a circle, so:

[tex]188.4\div2=94.2[/tex].

There are two semi-circles.

[tex]94.2\cdot2=188.4[/tex]

Since there are two legs of 50m each, we add 100 to 188.4

[tex]188.4+100=288.4[/tex]m

Hope this helped!

Answer:

Step-by-step explanation:

To solve for the perimeter, we first look at the rectangle in the middle. the length is 50m, and there are two sides to it, so: 50 * 2 = 100m for the top and bottom of the track.

For the circle, we can see the diameter is 30m. To solve for the circumference, we need to use the formula 2πr.

15 * 2π ≈ 94.2477796077

We add that to 100m and get:

194.2477796077

Answer:

The age of Noi is 13.333 Years and the age of Noy is 12.67 years

Step-by-step explanation:

The given  information are;

The sum of the ages of Noi and Noy = 26 years

Four times Noi's age - Two times Noy's age = 28

Let the age of Noi = X and let the age of Noy = Y

We have;

X + Y = 26 years.................(1)

4X - 2Y = 28 years.............(2)

Divide equation (2) by 2 to get;

(4X - 2Y)/2 = (28 years)/2 which gives;

2X - Y = 14 years.................(3)

Add equation (3) to equation (1), to get;

X + Y +  2X - Y = 26 years + 14  years

3X = 40 years

X = 40/3 = 13.333 Years

From equation (1), X + Y = 26 years, therefore;

Y = 26 - X = 26 - 13.33 = 12.67 years

Therefore, the age of Noi = 13.333 Years and the age of Noy = 12.67 years.

Answer:

25[tex]\sqrt{3}[/tex] +60

Step-by-step explanation: The first thing you need to do is realize that, this figure is a isosceles trapezoid due to the markings on each side.

So now we know both sides are 10.

We also know the the top two angles are congruent to each other and so are the bottom two angles due to the trapezoid being isosceles.

So the top two angles are 120 degrees and bottom two angles are 60 degrees.

It seems like we can't find the sides, let's try drawing two lines from each top angle all the way down to form two right triangles.

Wow, these two triangles are special right triangles in the form of

30 - 60 - 90 degrees.

shorter side = n

longer side = n[tex]\sqrt{3}[/tex]

hypotenuse = 2n

So, 2n = 10

n = 5 for the short side

The bottom base is 4[tex]\sqrt{3}[/tex] + 5 + 5 = 10 + 4[tex]\sqrt{3}[/tex]

The longer side is  5[tex]\sqrt{3}[/tex].

The area of trapezoid = (base1 + base2)/2 * height

= (4[tex]\sqrt{3}[/tex] + 10 + 4[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (10 + 8[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (5+4[tex]\sqrt{3}[/tex])*5[tex]\sqrt{3}[/tex] = 25[tex]\sqrt{3}[/tex] +60

So, 25[tex]\sqrt{3}[/tex] + 60 is our answer.

Answer:

  60 +25√3

Step-by-step explanation:

In the figure of the isosceles trapezoid below, the angles at C and D are supplementary to the given angle, so are 60°. That makes triangle BDE a 30°-60°-90° right triangle, which has side length ratios ...

  DE : BE : BD = 1 : √3 : 2 = 5 : 5√3 : 10

Triangle BDE can be relocated to the other end of the figure to become triangle CAD'. Then the area of concern is that of the rectangle with height 5√3 and length 5+4√3. The area is then ...

  Area = lh = (5√3)(5 +4√3) = 5·5√3 +5·4·3

  Area = 60 +25√3 . . . square units

_____

In the figure, 6.93 = 4√3, and 8.66 = 5√3, 16.93 = 10+4√3.

Answer:

See below.

Step-by-step explanation:

[tex]\frac{u-x}{v-x}=\frac{u}{v^2} \\[/tex]

Cross multiply and distribute.

[tex]u(v-x)=v^2(u-x)\\uv-ux=uv^2-xv^2[/tex]

Move all the u to the left side:

[tex]uv-ux-uv^2=-xv^2[/tex]

Factor out a u:

[tex]u(v-x-v^2)=-xv^2[/tex]

Divide:

[tex]u=\frac{-xv^2}{v-x-v^2}=\frac{xv^2}{x+v^2-v}[/tex]

(I factored out a negative in the second term.)

Answer:

[tex]\Huge \boxed{3}[/tex]

Step-by-step explanation:

The function is given :

f(x) = 4x + 15

For f(-3), the input for the function f(x) is -3.

Replace the x variable with -3.

f(-3) = 4(-3) + 15

Evaluate.

f(-3) = -12 + 15

f(-3) = 3

The output for f(-3) is 3.

Answer: f(-3) = 3

Step-by-step explanation: Notice that f is a function of x.

So we want to find f(-3).

We find f(-3) by plugging -3 in for x,

everywhere that x appears in the function.

So we have 4(-3) + 15.

4(-3) is -12 so we have -12 + 15 which is 3.

So f(-3) is 3.

Answer:

9:45 A.M.

Step-by-step explanation:

First, add the time that took him to hike:

6:30 + 2 hours and 15 minutes = 8:45 A.M.

Next, add the 1 hour that he played volleyball for:

8:45 + 1 hour = 9:45 A.M.

So, he finished playing volleyball at 9:45 A.M.

Answer:

9:45 am

Step-by-step explanation:

He went at 6:30 am to a hike.

It took him 2 hours 15 minutes

=> 6 : 30

+  2    15

=> 8 : 45

He came back from the Hike at 8:45 am

He played volleyball for 1 hour.

=> 8 : 45

+  1

=> 9 : 45

He finished playing volleyball at 9:45 am

Greetings from Brasil...

a - whole number

FALSE

3/5, for example isnt a whole number

b. natural number

FALSE

0,457888..., for example isnt a natural number

c. integer

FALSE - like a

d. real number

TRUE

The set of real numbers contains the set of rational numbers

ℝ ⊃ ℚ

Answer:

1

Step-by-step explanation:

split the shape to triangle and a rectangle

the rectangle at the original trapezoid has 2 squares in width and 3 squares for height multiply those numbers by 1/2 you will get 1 square for width and 1.5 squares for the height which is showen in option 1

Answer:

Here's what I get  

Step-by-step explanation:

Part A

The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.

Part B

The standard form of a cubic equation is

y = ax³ + bx² + cx + d

The factored form of a cubic equation is

y = a(x - b₁)(x² + b₂x + b₃)

If you can factor the quadratic, the factored form becomes

y = a(x - c₁)(x - c₂)(x - c₃)

Part C

The zeros of the function are at x = -25, x = - 15, and x = 15.

Part D

The linear factors of the function are x + 25, x + 15, and x - 15.

Part E

y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)  

y = a(x³ + 25x² - 225x - 5625)

Part F

When x = 0, y = 1.

1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a

a = -1/5625

Part G

[tex]y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}[/tex]

Answer

Actually, the answer should be -0.0007(x+20)(x+5)(x-15)

Step-by-step explanation:

This is continuing off of the previous answer

PART C

The zeros should be (15,0), (-5,0), and (-20,0)

PART D

x - 15, x + 5, and x + 20

PART E

a(x - 15)(x + 5)(x + 20)

Standard: [tex]a(x^{3} + 10x^{2} -275x-1500)[/tex]

PART F

The y-intercept is at (0,1), so we replace the x's with 0:

1 =[tex][(0)x^{3} +10(0)x^{2} -275(0)-1500][/tex] and this gives us (0+0-0-1500) which also equals -1500

Then we do [tex]\frac{1}{-1500}[/tex] which gives us -0.0006 repeating which rounds to -0.0007

a= -0.0007

PART G

Just place the numbers where they should go and your answer is

y =-0.0007(x + 20)(x + 5)(x - 15)  

the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007

Answer:

[tex] IJ = 2(KL) [/tex]

Step-by-step explanation:

From the information given, the smaller figure was dilated on a scale factor of 2, to produce the bigger figure. In essence, the bigger figure is times 2 of the smaller figure.

Therefore, line IJ would be twice the length of KL.

The relationship that both lines have can be represented as: [tex] IJ = 2(KL) [/tex]

Answer:

elimination method

x+2y=4     1

5x-2y=8     2

1+2

6x=12

x=2

plug into x+2y=4

2+2y=4

2y=4-2

2y=2

y=1

(2,1)

so graph 1

Answer:

-16, 0 real solutions. (Complex Roots)

Step-by-step explanation:

[tex]5x^2-2x=-1\\5x^2-2x+1\\A=5\\B=-2\\C=1\\(-b±√(b^2-4ac))/2a\\=\\=-2^2-4(5)(1)\\=4-20\\=-16[/tex]

Answer:

298.3 square centimeters

Step-by-step explanation:

We are given

Slant height (l)= 14cm

Radius (r)= 5cm

Since we are given the slant height ,

the formula for surface area of a cone =

πrl + πr²

πr(l + r)

π = 3.14

Hence,

3.14 × 5(14 + 5)

3.14 × 5(19)

= 298.3 square centimeters

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x).  The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.

Cheers.

Answer: (-1, -2)

Step-by-step explanation:

so at first you have (1, 2)

then you were asked to reflect about y=x which is (x, y) = (y, -x)

(1, 2) = (2, -1)

then followed by y=-x which is (x, y) = (-y, -x)

(2, -1) = (-1, -2)

I hope this helps!