a garden pond is in the shape of a rectangle that measures 5 m by 3 m. a stone path is built all around the pond. this path is the same width all the way around. the area of the pond and the path together is 39 m². how wide is the path?​

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: the answer is x= -11.

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:

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:

option 2

Step-by-step explanation:

4)

Equation of a Circle with centre ( a , b) and radius r

[tex](x - a)^2 + (y-b)^2 = r^2\\[/tex]

Given centre = ( -3 , 4), r = 5

Therefore Equation

                       [tex](x - ( - 3))^2 + (y-4)^2 = 5^2\\\\(x + 3)^2 + (y-4)^2 = 25[/tex]

5)

Centre =  ( 2 , 0) , radius, r = 3

[tex](x - 2)^2 + (y-0)^2 = 3^2\\\\(x -2)^2 + y^2 = 9[/tex]

Answer:

Area of the hurricane = 7853 or 3.14  x  50 squared

Answer:

x<8

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

Answer:

Where's the graph?

Step-by-step explanation:

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

[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]

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:

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: 3 and 4

Step-by-step explanation:

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

Answer:

tan= 4

Step-by-step explanation:

This is actually very easy, basically u have 5 - 9.

So you have positive nine and a negative sign, which is used for subtraction, so in the integers rule, positive- negative= negative

so its 4.

I HOPE ITS RIGHT, IM 11

If tan(A)=5 and tan(B)=9 the value of tan(A−B) will be -0.086.

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle. The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

It discusses how triangle side lengths and angles relate to one another. Using trigonometric formulas and functions, it is mostly used to determine the unknown side lengths and angles of a right-angled triangle. Six different functions are frequently employed in trigonometry.

It is given that tan(A)=5 and tan(B)=9

As we know,

[tex]\rm tan(A -B) = \frac{tan A - tan B}{1- tan A tan B}[/tex]

Substitute the given values we get,

tan(A -B) = (tan A - tan B)/(1 + tan A tan B)

tan(A -B)  = (5-9) / (1 + 5 × 9)

tan(A -B) = (-4) / (1 + 45)

tan(A -B) = -4 / 46

tan(A -B) = -2/23

tan(A -B) = - 0.086

Thus ,if tan(A)=5 and tan(B)=9 the value of tan(A−B) will be -0.086.

Learn more about trigonometry here:

brainly.com/question/26719838

#SPJ2

Answer:

experimental study.

Step-by-step explanation:

This study is an example of an experimental study.

The type of training program is the independent variable. The number of incidents of bullying is the dependent variable.

Since the participants of our study are affected directly in the research (the fourth-grade children) by not training against anti-bullying, the study is experimental research.

An independent variable is one that is somehow controlled or adjusted to evaluate the effects of a different variable, the dependent. Since we control whether we do bullying training here or not, our kind of training program is our independent variable, which is our dependent variable since we measure its impact on instances of bullying no.

Answer:

y = 72.5

x = 35.

Step-by-step explanation:

First Off, Let's Divide the question.

Let's Find the variable y :

there are 2 y(s), so it is 2y.

equation:   2y +35   =180.

I put 180 because A straight Line is always 180.

2y+35=180

1. Subtract both sides.

2y =  145

y = 72.5

Next,Find x

So y + y + x = 180.

We already know y, which is 72.5

72.5 +72.5 + x = 180

72.5 +72.5

x + 145 = 180

x =  35.

Hope This Helps!

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

9514 1404 393

Answer:

Step-by-step explanation:

I find the easiest way to answer these questions is to use a graphing calculator. It can show you the extreme values and the intercepts. The graph below shows the maximum height is 26.5 ft. The time in air is about 2.5 seconds.

__

If you prefer to solve this algebraically, you can use the equation of the axis of symmetry to find the time of the maximum height:

  t = -b/(2a) = -(40)/(2×-16) = 5/4

Then the maximum height is ...

  h(5/4) = -16(5/4)² +40(5/4) +1.5 = -25 +50 +1.5 = 26.5 . . . feet

__

Now that we know the vertex of the function, we can write it in vertex form:

  h(t) = -16(t -5/4)² +26.5

Solving for the value of t that makes this zero, we get ...

  0 = -16(t -5/4)² +26.5

  16(t -5/4)² = 26.5

  (t -5/4)² = 26.5/16 = 1.65625

Then ...

  t = 1.25 +√1.65625 ≈ 2.536954

The cannon ball is in the air about 2.5 seconds.

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

Answer:

5

Step-by-step explanation:

275x5= 1375

1375+55=1430

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:

x^2-2x=10

a few more steps...

the answer is 1+the square root of 11

Answer:

[tex]Probability = \frac{4}{15}[/tex]

Step-by-step explanation:

B1 = first bag

B2= second bag

B3 = third bag

Let A = ball drawn is red

Since, there are three bags.

Probability of choosing one bag=  P(B1) = P(B2) = P(B3) = 1/3.

From B1: Total balls = 10

3 red + 7 black balls.

Probability of drawing 1 red ball from it , P(A) = 3/10.

From B2: Total balls = 10

8 red + 2 black

Probability of drawing 1 red ball is, P(A) = 8/10

From B3 : Total Balls = 10

4 red + 6 black

Probability of drawing 1 red ball, P(A) = 4/10 .

To find Probability given that the ball drawn is red, that the ball is drawn from the third bag by Bayes' rule.

That is , P(B3|A)

                     [tex]=\frac{\frac{1}{3} \times \frac{4}{10}} { \frac{1}{3} \times \frac{3}{10} + \frac{1}{3} \times\frac{8}{10} + \frac{1}{3} \times \frac{4}{10}}[/tex]

                    [tex]=\frac{4}{30} \times \frac{30}{15}\\\\=\frac{4}{15}[/tex]

Therefore, the probability that it is drawn from the third bag is 4/15.

Answer:

4/15

Step-by-step explanation:

Solution of conditional probability problem:

Given:

Bags (3R,7B), (8R,2B), (4R,6B)

Let

P(R,i) = probability of drawing a red AND from bag i

P(R, 1) = 3/10 * (1/3) = 3/30

P(R, 2) = 8/10 * (1/3) = 8/30

P(R, 3) = 4/10 * (1/3) = 4/30

Let

Let P(R) = probability of drawing a red from any bag

P(R) = sum P(R,i)  for i = 1 to 3   using the addition rule

= 3/30 + 8/30 + 4/30

= 15/30

= 1 / 2

Conditional Probability of drawing from the third bag GIVEN that it is a red

= P(3 | R)

= P(R, 3) / P(R)

= 4/30 / (1/2)

= 8/30

= 4 / 15

(Since all bags contain 10 balls, by intuition, 4 red from third / 15 total red = 4/15)

Answer:

What ever.....

tan46 = x/8

x = 8×tan46

x = 8,28424251

Answer:

-1/4x² + 3

Step-by-step explanation:

Given that:

Path of sprinkler is modeled by the quadratic function :

w(x) = -1/4(x^2 -12 )

w(x) = height of the water, in meters, at position x

The height of ceiling as a constant or Coefficient = w(x)

Expanding w(x)

-1/4(x^2 -12 )

-1/4 * x² + 1/4 * 12

-1/4x² + 3

The height of ceiling is -1/4x² + 3

Answer:

Step-by-step explanation: