Use the order of operations to simplify the expression
9²-72+6²•8-3

50626 ways with a probability of 0.77

If a coin is tossed once, there are two possible results - a head or a tail. i.e 2¹ = 2

If the coin is tossed twice, there are four possible results - 4 heads no tail, 4 tails no head, 1 head 3tails or 2 heads 2 tails. That is 2² = 4

If the coin is tossed thrice, there are eight possible results. That is 2³ = 8.

Now, if the coin is tossed 16 times, there are 2¹⁶ = 65536 likely results.

From these 16 tosses, let's calculate the number of ways of achieving or selecting 7, 8, 9, 10, 11, 12, 13 or 14 heads. We use the combination formula given as follows;

Cₙ, ₓ = n! ÷ [ (n-x)! (x)! ]

Where;

n = number of tosses

x = number of selection

number of ways of getting 7 heads;

n = 16

x = 7

=> C₁₆, ₇ = 16! ÷ [ (16-7)! (7)! ]

=> C₁₆, ₇ = 16! ÷ [ (9)! (7)! ]

=> C₁₆, ₇ = 11440

number of ways of getting 8 heads;

n = 16

x = 8

=> C₁₆, ₈ = 16! ÷ [ (16-8)! (8)! ]

=> C₁₆, ₈ = 16! ÷ [ (8)! (8)! ]

=> C₁₆, ₈ = 12870

number of ways of getting 9 heads;

n = 16

x = 9

=> C₁₆, ₉ = 16! ÷ [ (16-9)! (9)! ]

=> C₁₆, ₉ = 16! ÷ [ (7)! (9)! ]

=> C₁₆, ₉ = 11440

number of ways of getting 10 heads;

n = 16

x = 10

=> C₁₆, ₁₀ = 16! ÷ [ (16-10)! (10)! ]

=> C₁₆, ₁₀ = 16! ÷ [ (6)! (10)! ]

=> C₁₆, ₁₀ = 8008

number of ways of getting 11 heads;

n = 16

x = 11

=> C₁₆, ₁₁ = 16! ÷ [ (16-11)! (11)! ]

=> C₁₆, ₁₁ = 16! ÷ [ (5)! (11)! ]

=> C₁₆, ₁₁ = 4368

number of ways of getting 12 heads;

n = 16

x = 12

=> C₁₆, ₁₂ = 16! ÷ [ (16-12)! (12)! ]

=> C₁₆, ₁₂ = 16! ÷ [ (4)! (12)! ]

=> C₁₆, ₁₂ = 1820

number of ways of getting 13 heads;

n = 16

x = 13

=> C₁₆, ₁₃ = 16! ÷ [ (16-13)! (13)! ]

=> C₁₆, ₁₃ = 16! ÷ [ (3)! (13)! ]

=> C₁₆, ₁₃ = 560

number of ways of getting 14 heads;

n = 16

x = 14

=> C₁₆, ₁₄ = 16! ÷ [ (16-14)! (14)! ]

=> C₁₆, ₁₄ = 16! ÷ [ (2)! (14)! ]

=> C₁₆, ₁₄ = 120

Therefore, the total number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 heads is the sum of the results above. i.e

11440 + 12870 + 11440 + 8008 + 4368 + 1820 + 560 + 120 = 50626 ways

P(getting number of heads between 7 and 14 inclusive) = [number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 ] ÷ [total number of possible outcomes]

= [tex]\frac{50626}{65536}[/tex]

= 0.77

Answer:

Check explanation

Step-by-step explanation:

I'll give you my way of solving it and you can figure it out from there.

<CEA = <DEB due to vertical angles

AE = ED due to midpoint theorem

<CAD = <ADB due to alternating angles theorem

thus two triangles congruent due to ASA

Answer:

We reject H₀, we have enough argument to explain that the production line is out of control. Is producing sprinkler out of specification

Step-by-step explanation:

Data information:

27 41 22 27 23 35 30 33 24 27 28 22 24

sample size  n  =  13

sample mean    x  =   27.92

sample standard deviation   s  =  5.39

The manufacturing process under control will always produce an output with normal distribution, in this case as n < 30  we will use t-student distribution in our test.

Hypothesis Test:

Null Hypothesis                                H₀            x  =  25

Alternative Hypothesis                    Hₐ            x  >  25

The Alternative hypothesis indicates that the test is a one-tail test.

Significance level is  α = 0.05

From z-table and for  α = 0.05  and  df =  n  - 1  df = 13 - 1  df = 12

p-value  = 1.782

t(s)  =  (  x   -    25 ) / s/√n

t(s) = ( 27.92 -  25 )/ 5.39/√13

t(s)  =  2.92*3.605/ 5.39

t(s) = 1.95

From t-table  df = 12  we find that 1.95 corresponds to a p-value < 0.05

then as p-value < 0.05  we are in the rejection region for H₀  then we reject H₀. We can deduce that the production line for sprinkler is given products out of specification

Answer:

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

Let's consider each of the statements.

1. Six below zero.

⟹ Any number below zero will be negative. So, the value will be [tex]\boxed{-6}[/tex]

____________________

2. The opposite of six.

⟹ The opposite of 6 wil be negative 6. The value again will be [tex]\boxed{-6}[/tex]

____________________

3. Negative six.

⟹ Negative six in numerical form is [tex]\boxed{-6}[/tex]

____________________

4. The absolute value of six.

⟹ Here they've asked the absolute value of 6 which will be [tex]\boxed{6}[/tex]

____________________

⏩ So, the statement which doesn't have the same value will be ⇻ [tex]\boxed{statement \ 4}[/tex]

____________________

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

[tex]RainbowSalt2^{2}2^{2}[/tex]

Answer:

DE = 24

Step-by-step explanation:

The midsegment DE is half the length of the third side AC , that is

DE = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × 48 = 24

[tex]\longrightarrow{\blue{ -2753}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]2 + 2 - 35 \times 62 + 88 - 1 \times 675[/tex]

[tex] = 2 + 2 - 2170 + 88 - 675[/tex]

[tex] = 92 - 2170 - 675[/tex]

[tex] = 92 - 2845[/tex]

[tex] = - 2753[/tex]

[tex]\sf\pink{PEMDAS\: rule.}[/tex]

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

[tex]2[/tex]

Step-by-step explanation:

Every time the x-value increases by 1, the y-value increases by 2. Therefore, the slope of the line must be equal to [tex]2/1=\boxed{2}[/tex] (rise/y-values over run/x-values). In slope-intercept form [tex]y=mx+b[/tex], [tex]m[/tex] represents the slope of the line, [tex]b[/tex] represents the y-intercept, and [tex](x,y)[/tex] represents any point the line passes through.

Since [tex]m[/tex] represents the slope of the line, the value of

While the question only asks for this value, it's good to note that the equation of the function is [tex]y=2x+7[/tex] (find 7 by substituting any ordered pair in the table with [tex]m=2[/tex]).

Answer:

y = 2x + 7

Step-by-step explanation:

y = mx + b

For every increase of 1 in x,

there is an increase of 2 in y

m = 2

When x is 0,

y is 7

b = 7

y = 2x + 7

Step-by-step explanation:

Tập nghiệm của [tex]2^x=-1[/tex] là tập rỗng nha bạn. Vì 2 là số dương nên mũ mấy cũng dương hết.

Answer:

Y=x+3

Step-by-step explanation:

we have :

     x1= -7

     y1= -4

    m=1

as we know Y-y1=m(X-x1)

Y+4=(X+7)

Y+4=X+7

Y=X+7-4

Y=X+3

Answer: 3 and 4

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

this answer is correct , i think if you think of it in logically

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {Your\:answer\:is\:59.}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]

1. My number has two digits.

2. Double my number is less than 150.

3. I am not divisible by 12.

4. My digits are different from each other.

5. The second digit in my number is divisible by an odd number.

6. My first digit is less than my second digit.

7. My digits add up to 14.

Therefore, the required number is [tex]\sf\pink{59}[/tex].

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

59

Step-by-step explanation:

two digits, 59=118, unable to divide by twelve since its an odd number, 9÷3=3, 5<9, 5+9=14

Answer:

5

Step-by-step explanation:

275x5= 1375

1375+55=1430

Answer:

h=A-πr²÷2πr

Step-by-step explanation:

Making h subject

A=2πrh+πr²

A-πr²=2πrh

A-πr²÷2πr=h

h=A-πr²÷2πr

Answer:

The answer is [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].

Step-by-step explanation:

To solve for (h), start by subtracting ([tex]\pi r^{2}[/tex]) from both sides, and the equation will look like [tex]A-\pi r^{2}= 2\pi rh+\pi r^2-\pi r^2[/tex]. The next step is to simplify the equation, which will look like [tex]A-\pi r^{2} =2\pi rh[/tex].

Next, divide both sides of the equation by [tex]2\pi r[/tex], and it will look like [tex]\frac{A-\pi r^{2} }{2\pi r} =\frac{2\pi rh}{2\pi r}[/tex]. Finally, simplify the equation, and the answer will be [tex]h=\frac{A+-\pi r^{2} }{2\pi r}[/tex].

Answer:

x<8

Step-by-step explanation:

Answer:

2 pounds

Step-by-step explanation:

1 pound  =  16 ounces

x pound =  32  ounces

[tex]x = \frac{32}{16} = 2 \ pounds[/tex]                

Answer:

the answer to 32ounces is 2 pounds

Answer:

The functions in Python is as follows:

from math import *

def CalculateTravelSpeed(startX,startY,endX,endY,travelTime):

   travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime

   return travelSpeed

def EuclideanDist(startX, startY, endX, endY):

   dist = sqrt((startX - endX)**2 + (startY - endY)**2)

   return dist

Step-by-step explanation:

from math import *

This defines the CalculateTravelSpeed function

def CalculateTravelSpeed(startX,startY,endX,endY,travelTime):

This calls the EuclideanDist function to calculate the distance; Next, the speed is calculated

   travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime

This returns the calculated speed

   return travelSpeed

This defines the EuclideanDist function

def EuclideanDist(startX, startY, endX, endY):

This calculates the distance from the given coordinates

   dist = sqrt((startX - endX)**2 + (startY - endY)**2)

This returns the calculated distance

   return dist

Answer: the answer is x= -11.

Answer:

Step-by-step explanation:

chia hình tứ giác thành 1 hình chữ nhật và một tam giác vuông từ đó y=4/sin(45)= 4,7 ; x=3+4/tan(45)=5,469

Answer:

65

Step-by-step explanation:

To find the amount of something given a percentage, we first must translate the percentage into a fraction or decimal. One way to do this is to divide the percentage by 100. In this case, we can divide 10% by 100 to get 0.1

We can then multiply the percent by the total, or 100%. In this case, we have 0.1 of 650, so we multiply the two to get 0.1 * 650 = 65 as 10% of 650, or how many cards Scarlett sold

Answer:

65

Step-by-step explanation:

650 x .10 (or 10%)=65

Answer:

226=2×113

321=3×107

305=5×61

133=7×19

Answer:

1- statistical

2- statistical

4 - statistical

remaining others are non statistical in my opinion

9514 1404 393

Answer:

  A(x) = 20000(0.88)^x

Step-by-step explanation:

The general form of these exponential equations is ...

  A(x) = a·b^x

where 'a' is the initial value, and b is the annual growth factor. x is the elapsed time in years.

The growth factor is ...

  growth factor = 1 + growth rate

Here, the growth rate per year is -12%, so the growth factor is ...

  b = 1 -12% = 88% = 0.88

Of course, the initial value is a=20,000, so the equation is ...

  A(x) = 20000(0.88)^x

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hagg

Answer:

C

Step-by-step explanation:

Answer:

y = 0 or 12

Step-by-step explanation:

[tex]Let \ (x _ 1 , y _ 1) \ and \ (x _ 2 , y _ 2 ) \ be \ the \ coordinates \ \\\\Distance \ between \ the \ points = \sqrt{(x_2 - x_1)^2 + (y_ 2 -y_1)^2}\\\\[/tex]

[tex]Given : distance = 10 \ units , (x_1 , y _ 1 ) = ( - 1 , 6 ) \ and \ (x_2 , y _ 2 ) = (7 , y )\\\\[/tex]

[tex]Substituting \ the \ values \ \\\\10 = \sqrt{(7 -(-1))^2 + (y - 6)^2}\\\\10 = \sqrt{(7 + 1)^2 + ( y - 6 )^2}\\\\10 = \sqrt{8^2 + ( y - 6)^2 }\\\\10 = \sqrt{64 + (y -6)^2 } \\\\Squaring \ both \ sides \\\\10^2 = (\sqrt{64 + (y -6)^2 })^2\\\\100 = 64 + ( y -6)^2\\\\100 - 6 4 = ( y -6)^2 \\\\36 = ( y - 6 )^2\\\\\sqrt{36} = y - 6\\\\\pm 6 = y - 6 \\\\So, \\\\\ y - 6 = 6 => y = 12\\\\\ \ \ \ y - 6 = - 6 => y = 0[/tex]

The y coordinate of the point is P ( 7 , 12 ) or P ( 7 , 0 ) where the distance of the point is 10 units from Q ( -1 , 6 )

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the first point be P ( 7 , y )

Let the second point be Q ( -1 , 6 )

Now , the distance between P and Q is D = 10 units

So , on simplifying the equation , we get

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

10 = √ [ ( 7 - ( - 1 ) )² + ( y - 6 )² ]

Squaring both sides of the equation , we get

100 = ( 8 )² + ( y - 6 )²

Subtracting 64 on both sides of the equation , we get

( y - 6 )² = 36

Taking square roots on both sides , we get

y - 6 = ±6

Adding 6 on both sides , we get

y = +6 + 6 = 12

or y = -6 + 6 = 0

So , the coordinates of the point P is  P ( 7 , 12 ) or P ( 7 , 0 )

Hence , the distance formula is solved and coordinates of the point P is  P ( 7 , 12 ) or P ( 7 , 0 )

To learn more about distance between 2 points click :

https://brainly.com/question/18234495

#SPJ2

Step-by-step explanation:

everything can be found in the picture

Answer:

O=74

Step-by-step explanation:

L=N

180-106=74

M=O

Answer:

Step-by-step explanation:

Lets assume that Kyle fill "a" 10-oz cups of coffee, "b" 14-oz cups of coffee and "c" 20 oz cups of coffee.

a + b + c = 16     (1)

10*a + 14*b + 20*c = 224       (2)

0.95*a + 1.15*b + 1.50*c = 18.60    (3)

Now, multiplying equation (1) by 10 and subtracting it from equation (2), we get

4b + 10c = 64  (4)

Again, multiplying equation (1) by 0.95 and substracting it from equation (3), we get,

0.2b + 0.55c = 3.4    (5)

Now,

Multiplying equation (5) by 20 and subtracting it from equation (4), we get

-c = -4,

Hence, c= 4

Putting this value in equation (4),

4b + 40 = 64

Hence, 4b = 24

So, b = 6

Again, putting the values of b and c in equation (1),

a + 6 + 4 = 16

Thus,

a = 6

Hence, the solution is

a = 6, 10oz cups of coffee

b = 6, 14 oz cups of coffee

c = 4, 20 oz cups of coffee