you spin a spinner with 3 equal sections labeled blue, red, and purple, and it lands on purple. what is the theoretical probability?

1. 18.8 units

2. 3 units

3. 9.4 units

Breaking the circle into more sectors

1. The circumference of circle is 18.8 units

2. The height of parallelogram is 3 unit.

3. The approximate length of the parallelogram if the base were completely straight is 9.4 unit

4. The estimation is easier by breaking down into sector.

5. Area of Circle is 28. 26 unit²

The circumference of the circle is 2πr where is the radius of the circle.

1. The circumference of circle

= 2πr

= 2 x 3.14 x 3

= 18.8 units

2. From Figure the height of parallelogram is 3 unit.

3. The approximate length of the parallelogram if the base were completely straight

= 18.8 / 2

= 9.4 unit

4. The estimation is easier by breaking down into sector.

5. Area of Circle

= πr²

= 3.14 x 9

= 28. 26 unit²

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[tex]\textbf{7).}\\\\2g^2 +5g+3\\\\=2g^2 +3g+2g+3\\\\=g(2g+3)+(2g+3)\\\\=(g+1)(2g+3)\\\\\\\textbf{10).}\\\\-6k^2+5k+21\\\\=-(6k^2 -5k-21)\\\\=-(6k^2-14k+9k-21)\\\\=-\textbf{[}2k(3k-7)+3(3k-7) \textbf{]}\\\\=-(2k+3)(3k-7)\\[/tex]

Answer:

Ivy is correct

Step-by-step explanation:

the perimeter of a parallelogram can be written as P= 2(a+b), where a and b are the lengths of the sides of the parallelogram.
since the parallelogram has been dilated by a scale factor of 0.6, we multiple the original side lengths by 0.6.
12 × 0.6 = 7.2
16 × 0.6 = 9.6
Plug into the equation
P=2(7.2+9.6)
P=2(16.8)

P= 33.6

You can also solve by plugging in the original values and multiplying the answer by 0.6.
P=2(12+16)(0.6)
P=2(28)(0.6)
P=(56)(0.6)

P=33.6

By using what we know about right triangles, we will see that the distance is 1479.4 ft

We assume that the distance between the points is a hypotenuse of a right triangle whit one of the angles measuring 8°, and the adjacent cathetus measuring 1465 ft.

Then we use the relation:

Cos(a) = (adjacent cath)/(hypotenuse)

cos(8°) = (1465 ft)/(distance)

distance = (1465ft)/cos(8°) = 1479.4 ft

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Answer:

57600 words in 12 hours.

Step-by-step explanation:

80 wpm means 80 words per minute.

We need to know how many minutes are in a 1 hour which is 1 hour is 60 minutes.

We want to know how much words in 12 hours.

Given:

[tex]\frac{80 word}{1 min}, \frac{60 min}{1 hour},\frac{12 hour}{1}[/tex]

[tex]\frac{80 word}{1 min} *\frac{60 min}{1 hour} *\frac{12 hour}{1} =[/tex] 57600 words in 12 hours.

Answer: 57,600

Step-by-step explanation:

80 × 60 = 4800 in 1hr

4800 ×12 = 57, 600 in 12hrs

The probability the 51st call arriaves within 150hours is 0.0431, the probability the next call arrives within the next 2 hours 0.5488, the probability the sum of these 50 numbers is less than 356 is 0.4165.

Data;

Using poission formula,

[tex]P(x=x) = \frac{e^-^\lambda - \lambda^x}{x!}\\\lambda = 0.3 per minute[/tex]

Let's substitute the values into the formula.

For 50 calls in 150 hours

For 150 hours = x = 0.3 * 150 = 45

[tex]p(x=50) = \frac{e^-^4^5 * 45^5^0}{50!} = 0.0431[/tex]

b)

The probability the next call arrives after 2 hours.

[tex]\lambda = 0.3 * 2 = 0.6\\p(x=0) = \frac{e^-^0^.^6 * 0.6^0}{0!} = 0.5488[/tex]

c)

The number of calls recieved each day is recorded for 50 consecutive days.

for 50 days;

[tex]\lambda = 0.3 * 50 * 24 = 360[/tex]

The mean = 360

The standard deviation is given as

[tex]S.D = \sigma =\sqrt{360} = 18.974\\[/tex]

The probability the sum of these 50 number is less than 356 is

[tex]p = (x < 356) = z = \frac{356 - 360}{18.974} = -0.2108\\p(z < -0.2108) = 0.4165[/tex]

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Answer:

poly Gon have [tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex][tex] \huge\color{blue}{ \rule{1pt}{999999pt}}[/tex]

From both equations

Hence the solution set in interval notation

Answer: 17 inches

Step-by-step explanation:

The formula for finding the length of a diagonal in a rectangle is [tex]d=\sqrt{w^2+l^2}[/tex]

Where

d is the diagonal

w is the width (8 for this)

l is the length (15 for this)

Sub these values into the equation

[tex]d=\sqrt{w^2+l^2}\\d=\sqrt{(8)^2+(15)^2}[/tex]

Solve

[tex]d=\sqrt{(8)^2+(15)^2}\\d=\sqrt{64+225}\\d=\sqrt{289}\\d=17[/tex]

Answer:

0.55

Step-by-step explanation:

I think you would just divide the numbers

Answer:

1440 different trucks

Step-by-step explanation:

Multiply all of the choices for each part:

3 possible bodies * 4 possible engines * 3 possible transmission types * 8 possible colors * 5 possible options packages

And, you get:

3 * 4 * 3 * 8 * 5

= 1440 different trucks

Answer:

4320 trucks

Step-by-step explanation:

Answer:

Slope m= -12/5

Step-by-step explanation:

Slope Solution

m=riserun=ΔyΔx

m=y2−y1x2−x1

m=−9−37−2

m=−125

m=−125

In decimals:

m = -2.4

Point Slope Form

y−y1=m(x−x1)

y−3=−125(x−2)

In decimals:

y−3=−2.4(x−2)

Slope Intercept Form

Find the Equation of the Line:

y=mx+b

by solving for y using the Point Slope Equation.

y−y1=m(x−x1)

y−3=−125(x−2)

y−3=−125x−(−125×2)

y−3=−125x−−245

y−3=−125x+245

y=−125x+245+3

y=−125x+395

m=−125

b=395

In decimals:

y=−2.4x+7.8

Standard Form of a Linear Equation

Ax+By=C

Starting with y = mx + b

y=−125x+395

Multiply through by the common denominator, 5, to eliminate the fractions:

5y=−12x+39

Then rearrange to the Standard Form Equation:

12x+5y=39

A=12

B=5

C=39

y-Intercept, when x = 0

y=mx+b

y=−125x+395

When x = 0

y=−125×0+395

y=395

y-intercept=395

(x,y)=(0,395)

In decimals:

(x,y)=(0,7.8)

x-Intercept, when y = 0

y=mx+b

y=−125x+395

When y = 0

0=−125x+395

125x=395

x=395×512

x=3912

x=134

x-intercept=134

(x,y)=(134,0)

In decimals:

(x,y)=(3.25,0)

Answer:

297 ft squared

Step-by-step explanation:

find the area of the triangle, which is (bh)/2

(22*7)/2=77

find the area of the rectangle (bh)

22*10=220

add

77+220=297

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The hour hand is 20 mm and the minute hand is

The tip of the hour hand travels 1/12 of the circle and the tip of the minute hand travels full circle in one hour.

Find each length and their difference using circumference formula.

Hour hand

Minute hand

The difference between the two above

Answer:

230.38 mm

Step-by-step explanation:

The distance traveled by the tip of the hands is (part of) the circumference of the circle with radius of the lengths of the hands.

[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]

Radii

Larger circle (minute hand):  

Smaller circle (hour hand):

Minute Hand

The minute hand does a full rotation of the circle in one hour.

Therefore, the distance it travels in one hour is the complete circumference of a circle with radius 40 mm:

[tex]\begin{aligned} \implies \textsf{Distance minute hand travels} & = \sf 2 \pi (40)\\ & = \sf 80 \pi \: mm\end{aligned}[/tex]

Hour Hand

There are 12 numbers on a clock.

The hour hand travels from one number to the next in one hour.

Therefore, the distance it travels in one hour is 1/12th of the circumference of the circle:

[tex]\begin{aligned}\implies \sf \textsf{Distance hour hand travels} & =\left(\dfrac{1}{12}\right)2 \pi r\\ & = \sf \left(\dfrac{1}{12}\right)2 \pi (40)\\& = \sf \dfrac{20}{3}\pi \: mm \end{aligned}[/tex]

To find how much farther the tip of the minute hand moves than the tip of the hour hand, subtract the latter from the former:

[tex]\begin{aligned}\implies \textsf{distance} & = \textsf{minute hand distance}-\textsf{hour hand distance}\\& = \sf 80 \pi - \dfrac{20}{3} \pi \\& = \sf \dfrac{220}{3} \pi \\& = \sf 230.38\: mm \:(nearest\:hundredth) \end{aligned}[/tex]

Answer:

1.14

Step-by-step explanation:

Long division! Image attached below!

Answer

[tex] \frac{ \times -+7}{×+2} [/tex]

A quadratic equation is represented by the form ax^2+ bx + c = 0

The values of a, b and c are 1, -3 and -5, respectively

The solution is given as:

[tex]x = \frac{3 \pm \sqrt{29}}2[/tex]

The solution to a quadratic equation is represented as:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

By comparing [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex] and [tex]x = \frac{3 \pm \sqrt{29}}2[/tex], we have:

-b = 3

So, b = -3

Also, we have:

2a = 2

So, a = 1

Also, we have:

b² - 4ac = 29

Substitute values for a and b

(-3)² - 4 * 1 * c = 29

This gives

9 - 4c = 29

Subtract 9 from both sides

-4c = 20

Divide by -4

c = -5

Hence, the values of a, b and c are 1, -3 and -5, respectively

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Answer:

A (3/16)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

The spinner is evenly divided and numbered from 1 through 8.

[tex]\sf \implies Probability\:of\:landing\:on\:any\:number= \dfrac18[/tex]

There are 4 even numbers (2, 4, 6 and 8)

[tex]\sf \implies Probability\:of\:landing\:on\:an\:even\:number= \dfrac48=\dfrac12[/tex]

There are 3 numbers less than 4 (1, 2 and 3)

[tex]\sf \implies Probability\:of\:landing\:on\:a\:number\:less\:than\:4=\dfrac38[/tex]

Therefore, the probability of landing of an even number and then on a number of less than 4 is:

[tex]\sf \implies Probability=\dfrac12 \times \dfrac38=\dfrac{3}{16}[/tex]

Answer:

46

Step-by-step explanation:

Just put in least to greatest then you would scratch each number from left to right till you got to the middle number (median)

pls mark brainless

Answer:

216

Step-by-step explanation:

Split the image into geometric shapes, and then calculate the area of each shape, then add them all up to get your grand total of 216

The probability of Amy and Zach to line up at the frond and last in the line will be 11.11%

The chances of happening of any random event is called as the probability. Here in the question there are 18 class students we need find that the first and the last position should be occupied by Amy  and jach.

Total outcomes =18

favourable outcome=2

So the probability of the Amy and Zach to stand in the front and the last in the line will be

[tex]P=\dfrac{2}{18}=0.11=11\%[/tex]

Hence the  probability of Amy and Zach to line up at the frond and last in the line will be 11.11%

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Answer: [tex]\frac{12}{19}[/tex]

The quotient of 36 and a whole number increased by 3, is 20 less than four times the number. The solution to the algebraic equation here are 6 and -4.

An algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some field, often the field of the rational numbers.

The algebraic equation becomes =

[tex]\frac{36}{x+3}-20 = 4x\\[/tex]

We simplify the equation to find the value of x.

[tex]=\frac{36}{x+3}+20 = 4x\\\\= \frac{36}{x+3} = 4x -20\\\\= \frac{36}{x+3} = 4(x-5)\\\\=36 = 4(x-5)(x+3)\\\\=9 = (x-5)(x+3)\\\\=x^2-5x+3x -15 = 9\\\\= x^2-2x-24=0\\\\=x^2-6x+4x-24=0\\\\=x(x-6)+4(x-6) =0\\\\=(x+4)(x-6) =0\\\\x = -4,6[/tex]

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The answer is B

seeing there are 3 way to put it

(a+b)(a-b)=a 2-b 2

(a+b)(a-b)=a^2-b^2

(a+b)(a-b)=a2-b2

and option B matches with the second way to put it i hope this helps

Answer:

10 units²

Step-by-step explanation:

Area = bh/2

b = 4

h = 5

A = (4 x 5)/2 = 10 units²

I hope this helps!

area triangle:

b×h/2

= 11 in×10 in/2

=55 in²

area half-circle:

pi×r² /2

= 3.14×5in² /2

=78.5in² /2

=39.25 in²

Total area: area triangle+ area half-circle

= 55 in²+39.25 in²

=94.25 in²

Answer:

Below in bold.

Step-by-step explanation:

y^2 - 3y - 40

To factor this we need 2 numbers whose product is -40 and whose sum is -3.  These are -8 and +5. so the factors are:

(y - 8)(y + 5).

3x^2 + 10x + 3

To factor this we need 2 numbers whose product is (3*3) = +9 and whose sum is +10.  These are +9 and +1 so we write:

3x^2 + 9x + x + 3  

Factor by grouping:

= 3x(x + 3) + 1(x + 3)

= (3x + 1)(x + 3).

Answer:

x = 19

Step-by-step explanation:

See attched image.

[tex]-3(2x+2) < 10\\\\\implies -6x -6 < 10\\\\\implies -6x < 10 +6\\\\\implies -6x < 16 \\\\\implies x > -\dfrac{16}6\\\\\implies x > -\dfrac{8}3[/tex]