A circular hall has a hemispherical roof.
The greatest height is equal to the
inner diameter. If the capacity of
the hals is
the
floor is.
43510 m^3

then
area
of the​

Answers

Answer 1

Answer:

Area=1,288.88m²

Step-by-step explanation:

A circular hall(big room) has a hemispherical roof.The greatest height is equal to the inner diameter.Find the area of the floor,given that the capacity of the hall is 43510 cubic meter

Solution

let

diameter = D

radius,r = D/2

Greatest height = D

height of cylindrical part (h)= D-r = r

radius of cylindrical part = r

area of floor = πr²

volume = volume of cylindrical part + volume of hemispherical part

= πr²h + 2/3 πr³

Recall h=r

volume = πr³ + 2/3 πr³

43510=5/3πr³

Make r the subject

r=3√(43510*3)/5π

=3√(130,530/15.7

=3√8,314.01

=20.26

Area of floor = πr²

=3.14*(20.26)²

=3.14*410.47

=1,288.88m²


Related Questions

Where r is the radius of the cylinder and h is the height of the cylinder. Find the surface area when r is 3 inches and h is 5 inches. A. 50π in² B. 112π in² C. 48π in² D. 80π in²

Answers

Answer:

C

Step-by-step explanation:

The surface area of a cylinder is given by this formula:

● Sa = 2×r^2× PI + 2r×Pi×h

r is 3 inches and h is 5 inches.

● Sa = 2×3^2 × Pi + 2×3×Pi×5

● Sa = 48 × Pi in^2

We can calculate E, the amount of euros that has the same value as D U.S. dollars, using the equation e=17/20d. How many U.S. dollars have the same value as 1 euro?

Answers

Answer:

1.18 dollar.

Step-by-step explanation:

E = 17/20D

E => The amount in euros.

D => The amount in dollars.

From the question given,

E = 1

D =?

E = 17/20D

1 = 17/20D

Cross multiply

20 x 1 = 17D

20 = 17D

Divide both side by 17

D = 20/17

D = 1.18

Therefore, 1.18 dollar is equivalent to 1 euro.

Answer:

How many Euros have the same value as 1 U.S. dollar?

17/20 euros

How many U.S. dollars have the same value as 1 euro?

59/50 dollars

(or 0.85 either one is correct)

Step-by-step explanation:

Khan Academy

Hope this helps! ;)

What two times could this be on the 24-hour clock?

Answers

I think it’s 1:40 am or 1:40 pm

A laptop has a listed price of $703.98 before tax. If the sales tax rate is 9.25% , find the total cost of the laptop with sales tax included. Round your answer to the nearest cent, as necessary.

Answers

Answer:

The cost of the laptop is $769.10

Step-by-step explanation:

In this problem we are required to find the cost of the laptop when 9.25% of the cost is added as tax

we are given that the tax rate is 9.25% of the initial cost

and the initial cost is $703.98

 let us calculate 9.25% of  $703.98

(9.25/100)* 703.98= 0.0925*703.98= $65.12

Hence the charges for tax is $65.12

The total cost of the laptop when tax is included is

the initial cost Plus the tax charges= $703.98+$65.12= $769.098

$769.10

Expand the following using the Binomial Theorem and Pascal’s triangle. Show your work. (x + 2)6 (x − 4)4 (2x + 3)5 (2x − 3y)4 In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5

Answers

Answer:

The answer is below

Step-by-step explanation:

Expansion using pascal triangle:

a)  (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)

                 = x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64

b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴

              =x⁴-16x³+96x²-256x+256

c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ =

                  = 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴

                  = 16x⁴- 96x³ + 216x² - 216x + 81

Expansion using binomial where [tex]C(n,r)=\frac{n!}{(n-r)!r!}[/tex]

a)  (x + 2)⁶ = C(6,0)[x⁶2⁰] + C(6,1)[(x⁵)(2)¹] + C(6,2)[(x⁴)(2²)] + C(6,3)[(x³)(2³)] + C(6,4)[(x²)(2⁴)] + C(6,5)[(x)(2⁵)] + C(6,6)[(2⁶)]

                = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)

                 = x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64

b) (x-4)⁴ = C(4,0)[x⁴] + C(4,1)[(x³)(-4)] + C(4,2)[(x²)(-4)²] + C(4,3)[(x)(-4)³] + C(4,4)[(x⁰)(-4)⁴]

              = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴

              =x⁴-16x³+96x²-256x+256

c) (2x + 3)⁵   = C(5,0)[(2x)⁵] + C(5,1)[(2x)⁴(3)] + C(5,2)[(2x)³(3)²] + C(5,3)[(2x)²(3)³] + C(5,4)[(2x)(3)⁴] + C(5,5)[(2x)⁰(3)⁵]

                   = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵

                  = 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

d) (2x-3y)⁴ = C(4,0){(2x)⁴(-3y)⁰} + C(4,1)[(2x)³(-3y)] + C(4,2)[(2x)²(-3y)²] + C(4,3)[(2x)(-3y)³] + C(4,4)[(2x)⁰(-3y)⁴]

                  = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴

                  = 16x⁴- 96x³ + 216x² - 216x + 81

In the expansion of (3a + 4b)⁸, the only possible variable terms are a⁵b³, b⁸, a⁴b⁴, a⁸, ab⁷ because for each of them, the sum of there powers is eight. If the sum of the powers is not 8 then it is not correct.

For a²b³, the sum of the power is 5, for ab⁸ the sum of power is 9 and for a⁶b⁵ the sum of the power is 11 therefore thy are not correct.

As per the question expand the bimonoidal theorem and the pascal triangle. Showing the (x+2)6 (x-4)4 (2x+3)5 (2x-3y)4.

Expansion using pascal triangle:a)  (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)      = x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)  =x⁴-16x³+96x²-256x+256c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ = 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴ = 16x⁴- 96x³ + 216x² - 216x + 81.

Learn more about the use the binomial theorem.

brainly.com/question/11995132.

Please answer ASAP. The question is down below

Answers

Answer:  A

Step-by-step explanation:

Notes: Dividing by a fraction means to multiply by its reciprocal.

           The denominator cannot equal zero.

[tex]\dfrac{5a^3bc}{8ab^3}\div\dfrac{-ab^2}{6a^5b}\cdot \dfrac{2a^2b^3}{3b}\qquad \rightarrow a\neq 0,b\neq 0\\\\\\=\dfrac{5a^3bc}{8ab^3}\cdot\dfrac{6a^5b}{-ab^2}\cdot \dfrac{2a^2b^3}{3b}\\\\\\=\dfrac{5\cdot 6\cdot 2\quad a^3\cdot a^5\cdot a^2\quad b\cdot b\cdot b^3\quad c}{8\cdot -1 \cdot 3\quad a\cdot a\qquad b^3\cdot b^2\cdot b \quad}\\\\\\=\dfrac{-60a^{10}b^5c}{-24a^2b^6}\\\\\\=\dfrac{-5a^8c}{2b}[/tex]

I have no chair, no church, no philosophy, I lead no man to a dinner-table, library, exchange, But each man and each woman of you I lead upon a knoll, My left hand hooking you round the waist, My right hand pointing to landscapes of continents and the public road. Which statement best describes how these lines reflect the theme of the poem?

Answers

This question is missing the options, here is the complete question:

Read the quotation from "Song of Myself."

I have no chair, no church, no philosophy,

I lead no man to a dinner-table, library, exchange,

But each man and each woman of you I lead upon a knoll,

My left hand hooking you round the waist,

My right hand pointing to landscapes of continents and the public road.

Which statement best describes how these lines reflect the theme of the poem?

A. They indicate that Whitman is more interested in communicating with individuals than society.

B. They show Whitman’s sociability and his interest in human nature.

C. They reflect Whitman’s desire to share his love of the wilderness.

D. They suggest that Whitman views all individuals as equals who should communicate with each other as such.

The answer to this question is A. They indicate that Whitman is more interested in communicating with individuals than society.

Explanation:

In the poem "Song of Myself", Walt Whitman focuses on recognizing his value as an individual and the value of other individuals in society. In the section presented, the author shows the importance of communicating and interacting with individuals as he explains "My left hand hooking you round the waist", which shows through figurative language the interaction between individuals. This is emphasized by the use of "each man and each woman" as Whitman does not refer to others as a group but recognizes individuality. Thus, the theme or message about the importance of individuals is reflected in these lines because "they indicate that Whitman is more interested in communicating with individuals than society."

Answer:

A: They indicate that Whitman is more interested in communicating with individuals than society.

Step-by-step explanation:

Edge 2021

y-3x=13 solve for y ‍♀️

Answers

Answer:

y = 3x+13

Step-by-step explanation:

y-3x=13

Add 3x to each side

y-3x+3x=3x+13

y = 3x+13

The value of y for the given equation y - 3x = 13 is calculated to be y = 3x + 13.

Given that:

y - 3x = 13

It is required to find the value of y.

In order to find the value of y, the equation has to be solved in such a way that y has to be kept on one side.

Consider:

y - 3x = 13

Add 3x on both sides.

y - 3x + 3x = 13 + 3x

y = 13 + 3x

Hence, the value of y is 13 + 3x.

Learn more about Equations here :

https://brainly.com/question/29657992

#SPJ6

Please help me! This is Algerbra 1

Answers

Answer:

A. x > -1 or x < -1

Step-by-step explanation:

5x - 29 > -34                     or                   2x + 31 < 29

Add 29 to both sides.                             Subtract 31 from both sides.

5x > -5                              or                    2x < -2

Divide both sides by 5.                          Divide both sides by 2.

x > -1                                 or                    x < -1

Answer: x > -1 or x < -1

Given that f(x)=2x+1 and g(x)=-5x+2 slice for f(g(x)) when x=3?

Answers

Answer:

x = -25.

Step-by-step explanation:

If f(x) = 2x + 1, and g(x) = -5x + 2, then f(g(x)) = 2(-5x + 2) + 1 = -10x + 4 + 1 = -10x + 5.

f(g(x)) = -10x + 5, and x = 3.

-10 * 3 + 5

= -30 + 5

= -25.

Hope this helps!

there are 63 students marching in a band, and they're marching in 7 rows how many students are in each row

Answers

Answer:

9 people per row

Step-by-step explanation:

63/7=9

let me now if right

63/7 =9
So because all students are 63 you have to divide the 63 into rows and then you’ll find out how many students are in a row

What were Malcolm's and Ravi's maximum speeds?

Answers

Answer:

Malcom's maximum speed = 200 km/h

Ravi's maximum speed = 320 km/h

Step-by-step explanation:

Represent the maximum speed of Malcolm and Ravi with equation as follows:

Let Malcom's speed be x, and Ravi's speed by y.

The average of speed is said to be 260 km/h. An equation to represent this is: [tex] \frac{x + y}{2} = 260 [/tex]

[tex] x + y = 260*2 [/tex]

[tex] x + y = 520 [/tex] => equation 1.

We are also told that when Malcom's speed (x) is doubled it equal 80 km/hr more than Ravi's speed (y). An equation can be created for this, which is [tex] 2x = y + 80 [/tex]

[tex] 2x - y = 80 [/tex] => equation 2

Now that we have 2 equations as a system, solve for the values of x and y simultaneously.

Add both equations together to eliminate y

[tex] x + y = 520 [/tex]

[tex] 2x - y = 80 [/tex]

[tex] 3x = 600 [/tex]

[tex] x = \frac{600}{3} [/tex]

[tex] x = 200 [/tex]

Plug in the value of x into equation 1 to find y.

[tex] 200 + y = 520 [/tex]

[tex] y = 520 - 200 [/tex]

[tex] y = 320 [/tex]

Malcom's maximum speed = x = 200 km/h

Ravi's maximum speed = y = 320 km/h

in a polynomial function of degree 5, what is the maximum number of extreme that could be possible? (please explain with the answer if possible!)

Answers

Answer:

4 maximum extrema

Step-by-step explanation:

5th degree means that it can change direction 5 times, therefore creating a maximum of 4 extrema

There are (43)2⋅ 40 strawberries on a farm. What is the total number of strawberries on the farm?

Answers

Answer:

3,440 strawberries

Step-by-step explanation:

Because of PEMDAS you want to start with the parentheses, and want to treat them like the distributive property.

So,

43 x 2 = 86

Then,

86 x 40 = 3440.

I hope that helps!!

Answer: 3440 strawberries on the farm.

Step-by-step explanation: (43)(2)⋅40                                                                     (86)(40)                                                                                                                     3440

Please answer quickly i will give you brainliest if its correct- it has to be a simplified fraction please

Answers

Answer:

[tex]\large \boxed{{r=\frac{1}{9}}}[/tex]

Step-by-step explanation:

x and y are proportional.

[tex]y=rx[/tex]

Let x = 45 and y = 5.

[tex]5=r(45)[/tex]

Solve for r (constant of proportionality).

Divide both sides by 45.

[tex]\displaystyle \frac{5}{45} =r[/tex]

Simplify and switch sides.

[tex]\displaystyle r=\frac{1}{9}[/tex]

Determine the standard form of the equation of the line that passes through (-8, -6) and (-4, 9)

Answers

Answer:

15/4 x-y=-24

Step-by-step explanation:

the standard form is ax+by=c

two points (x1,x2) , (y2,y1)

x1=-8       x2=-6

y1=-4        y2=9

find slope m: y2-y1/x2-x1

m=9-(-6)/-4-(-8)

m=15/4

find b: take any point(-8,-6)

y=mx+b

-6=15/4 (-8)+b

-6=-30+b

b=-6+30

b=24

y=15/4 x+24

standard form: y-15/4x=24

OR : 15/4 x-y=-24

find the interest rate r when p = 800, a = 2700, and t = 3.​

Answers

Answer:

r = 0.5 or 1/2

Step-by-step explanation:

Simple Interest Rate Formula: A = P(1 + r)^t

Simply plug in our known variables:

2700 = 800(1 + r)³

Now we solve for r:

Divide both sides by 800

27/8 = (1 + r)³

Take the cube root on both sides

∛27/8 = ∛(1 + r)³

Simplify

3/2 = 1 + r

Subtract 1 on both sides

r = 1/2

r = 0.5

Answer:

For compound interest, 50%.

Step-by-step explanation:

(I'm assuming this question is asking for the compound interest):

The formula for compound interest is given by:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Plug in the values we know. We can use 1 for n:

[tex]2700=800(1+r)^3\\27/8=(1+r)^3\\1+r=\sqrt[3]{27/8}\\r=3/2-1\\r=1/2=.5[/tex]

So, the interest rate is 50%.

Hii, can you help me ?

Answers

Answer:

100, 101, 102, 103, 104

Step-by-step explanation:

Basically, if the units (or ones, it's the same thing) digit of the first number is 0, the units digit of the second number should be 1, then 2, and so on. Therefore, one possible list of numbers is as follows: 100, 101, 102, 103, 104.

100
101
102
103
104
105

Hope it helps❄️

What is the length of the shortest altitude in a triangle, if the lengths of the sides are 24 cm, 25 cm, 7 cm?

Answers

Answer:

The shortest altitude is 6.72 cm

Step-by-step explanation:

Given that the side lengths are

24 cm, 25 cm, 7 cm

The area of a triangle =

[tex]A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}[/tex]

Where;

s = Half the perimeter = (24 + 25 +  7)/2 = 28

A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²

We note that 84/7 = 12

Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7

To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude

Altitude  = A/(1/2 ×base)

Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;

We set the base to 25 cm to get;

Area of the triangle A =  1/2 × base × Altitude

84 = 1/2 × 25 × Altitude

Altitude = 84/(1/2 × 25) = 6.72 cm

The shortest altitude = 6.72 cm.

420 miles in 6.5 hours unit rate​

Answers

Step-by-step explanation:

Given,

distance =420 miles

time 6.5 hrs

now,

420miles took 6.5 hrs.

1mile took 6.5/420hrs

=0.015476hrs

Therefore, 0.015476hrs to cover 1 mile distance.

Hope it helps...

Answer:

64.6153846 miles/hour

0.0154761905 hours/mile

Step-by-step explanation:

If we want to find the miles driven in one hour, we must divide the total miles by the total hours.

miles / hours

We know that 420 miles were driven in 6.5 hours

420 miles/ 6.5 hours

Divide 420 by 6.5

420/6.5=64.6153846

64.6153846 miles/hour

In one hour, 64.6153846 miles are driven.

If we want to find the time to drive one mile, divide the time (hours) by the miles.

hours / miles

We know that 420 miles were driven in 6.5 hours.

6.5 hours/420 miles

Divide 6.5 by 420

6.5/420=0.0154761905

0.0154761905 hours/ mile

It will take 0.0154761905 of an hour to drive one mile.

Brian is building a wood frame around a window in his house. If the window is 4 feet by 5 feet, how much wood does he need for the frame?

Answers

Answer:

18 feet

Step-by-step explanation:

to find the frame around the widow means need to find the perimeter around the window:

P=2l+2w

P= 2(5+4)

P=18 feet

how many are 1 raised to 2 ???​

Answers

Answer:

1

Step-by-step explanation:

1^2

Means 1 multiplied by itself 2 times

1*1

1

Find the coordinates of point X that lies along the directed line segment from Y(-8, 8) to T(-15, -13) and partitions the segment in the ratio of 5:2. A. (-5, -15) B. (-23, -5) C. (-13, -7) D. (-11.5, -2.5)

Answers

Answer:

C. (-13, -7)

Step-by-step explanation:

The location of a point O(x, y) that divides a line AB with location A[tex](x_1,y_1)[/tex] and B[tex](x_2,y_2)[/tex] in the ratio m:n is given by:

[tex]x=\frac{m}{m+n} (x_2-x_1)+x_1\\\\y=\frac{m}{m+n} (y_2-y_1)+y_1[/tex]

Therefore the coordinates of point X That divides line segment from Y(-8, 8) to T(-15, -13) in the ratio 5:2 is:

[tex]x=\frac{5}{5+2} (-15-(-8))+(-8)\\\\x=\frac{5}{7} (-15+8)-8=\frac{5}{7}(-7)-8=-5-8=-13 \\\\\\y=\frac{5}{5+2} (-13-8)+8\\\\y=\frac{5}{7} (-21)+8=5(-3)+8=-15+8=-7[/tex]

Therefore the coordinates of point X is at (-13, -7)

The perimeter of a rectangle is 10 feet. If twice the width is equal to half of the length , find the dimensions of this rectangle.

WRITE AS AN EQUATION​

Answers

Answer:

w = 1ft

l = 4ft

Step-by-step explanation:

P  =2w + 2l

2w = l/2 => l = 4w

10ft = 2w + 2×4w

10ft = 2w + 8w

10ft = 10w

w = 10ft/10

w = 1 ft

l = 4w

l = 4×1ft

l = 4 ft

Answer:

length = 4 ft

Width = 1 ft

Step-by-step explanation:

Let length = l ft

Width = w feet

[tex]\frac{1}{2}l = 2w\\\\l = 2w*2\\\\l = 4w[/tex]

Perimeter = 10 ft

2*(l +w)= 10

2*( 4w + w ) = 10

2*5w = 10

10w = 10

Equation:  10w = 10

Divide both sides by 10

10w/10 = 10/10

w = 1 ft

Plug in the value of w in l = 4w

l = 4 *1

l = 4 ft

3(x-4)=-5 solve for x

Answers

Answer:

x = 7/3

Step-by-step explanation:

3(x-4)=-5

Distribute

3x - 12 = -5

Add 12 to each side

3x -12+12 = -5+12

3x = 7

Divide by 3

3x/3 = 7/3

x = 7/3

Answer:

x = 7/3

Step-by-step explanation:

3(x-4)=-5

3x -12= -5

3x = 7

x =7/3

Observe how the land division was planned for the preparation of a vegetable garden.
In it, lettuce, tomatoes, carrots, beets and corn will be planted.
Determine the monomial that represents the measure:

1-lettuce
2-beets
3-tomato
4-corn
5-carrot​

Answers

Answer:

1-lettuce 4ab x 12ab = 48a²b²

2-beets 3ab x 3ab = 9a²b²

3-tomato 4ab x 5ab = 20a²b²

4-corn 2ab x 3ab = 6a²b²

5-carrot 12ab x 3ab = 36a²b²

Step-by-step explanation:

The body paint, an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to 11/2hours.


What is the probability that the painting time will be less than or equal to an hour?

What is the probability that the painting time will be more than 50 minutes?

Determine the expected painting time and its standard deviation.

Answers

Answer:

a. [tex]\mathbf{P(Y \leq 60) = 0.3333}[/tex]

b. P(Y>50) = 0.8889

c. E(y) = 67.5 and  Standard deviation [tex]\sigma[/tex] = 12.99

Step-by-step explanation:

From the information given :

an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to [tex]1\frac{1}{2}[/tex]hours.

The objective is to determine  the probability that the painting time will be less than or equal to an hour?

since 60 minutes make an hour;

[tex]1\frac{1}{2}[/tex]hours = 60 +30 minutes = 90 minutes

Let Y be the painting time of the automobile; then,

the probability that  the painting time will be less than or equal to an hour ca be  computed as :

[tex]P(Y \leq 60) = \int ^{60}_{45} f(y) dy \\ \\ \\ P(Y \leq 60) = \int ^{60}_{45} \dfrac{1}{45} dy \\ \\ \\ P(Y \leq 60) = \dfrac{1}{45} \begin {pmatrix} x\end {pmatrix}^{60}_{45} \\ \\ \\ P(Y \leq 60) = \dfrac{60-45}{45 } \\ \\ \\ P(Y \leq 60) = \dfrac{15}{45} \\ \\ \\ P(Y \leq 60) = \dfrac{1}{3} \\ \\ \\ P(Y \leq 60) = 0.3333[/tex]

What is the probability that the painting time will be more than 50 minutes?

The probability that the painting will be more than 50 minutes is P(Y>50)

So;

[tex]P(Y>50) = \int \limits ^{90}_{50} f(y) dy[/tex]

[tex]P(Y>50) = \int \limits ^{90}_{50} \dfrac {1}{45} dy[/tex]

[tex]P(Y>50) = \dfrac{1}{45}[x]^{90}_{50}[/tex]

[tex]P(Y>50) = (\dfrac{90-50}{45})[/tex]

[tex]P(Y>50) = \dfrac{40}{45}[/tex]

P(Y>50) = 0.8889

Determine the expected painting time and its standard deviation.

Let consider E to be the expected painting time

Then :

[tex]E(y) = \int \limits ^{90}_{45} y f(y) dy \\ \\ \\ E(y) = \int \limits ^{90}_{45} y \dfrac{1}{45} dy \\ \\ \\ E(y) = \dfrac{1}{45} [\dfrac{y^2}{2}]^{90}_{45} \\ \\ \\ E(y) = \dfrac{1}{45}[\dfrac{(90^2-45^2)}{2}] \\ \\ \\ E(y) = \dfrac{1}{45} (\dfrac{6075}{2}) \\ \\ \\ E(y) = \dfrac{1}{45} \times 3037.8 \\ \\ \\ \mathbf{E(y) = 67.5}[/tex]

[tex]E(y^2) = \int \limits ^{90}_{45} y^2 f(y) dy \\ \\ \\ E(y^2) = \int \limits ^{90}_{45} y^2 \dfrac{1}{45} dy \\ \\ \\ E(y^2) = \dfrac{1}{45} [\dfrac{y^3}{3}]^{90}_{45} \\ \\ \\ E(y^2) = \dfrac{1}{45}[\dfrac{(90^3-45^3)}{3}] \\ \\ \\ E(y^2) = \dfrac{1}{45} (\dfrac{637875}{3}) \\ \\ \\ E(y^2) = \dfrac{1}{45} \times 2126.25 \\ \\ \\ \mathbf{E(y^2) = 4725}[/tex]

To determine the standard deviation, we need to first know what is the value of our variance,

So:

Variance [tex]\sigma^2[/tex] = E(x²) - [E(x)]²

Variance [tex]\sigma^2[/tex] = 4725 - (67.5)²

Variance [tex]\sigma^2[/tex] = 4725 - 4556.25

Variance [tex]\sigma^2[/tex] = 168.75

Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{variance}[/tex]

Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{168.75}[/tex]

Standard deviation [tex]\sigma[/tex] = 12.99

A car can cover a distance of 522 km on 36 liters of petrol. How far can it travel on 14 liters of petrol?

Answers

522km / 36= 14.5km PER litre

14.5 x 14= 203

what expression is equivalent to this Expression?
(-5cd-4)(2cd2)2​

Answers

Answer:

[tex]-40c^{2} d^{2} -32cd[/tex]

Step-by-step explanation:

-20c³ is the expression which is equivalent to (-5cd⁻⁴)(2cd²)².

To simplify the given expression, (-5cd⁻⁴)(2cd²)², we can apply the power of a product rule, which states that (ab)² is equal to a²b².

Let's break down the expression step by step:

(-5cd⁻⁴)(2cd²)²

First, let's square the expression (2cd²)²:

(2cd²)² = (2)²(c)²(d²)² = 4c²d⁴

Now, we substitute this result back into the original expression:

(-5cd⁻⁴)(4c²d⁴)

To simplify further, we can multiply the coefficients and combine the variables:

(-5)(4) = -20

(c)(c²) = c³

(d⁻⁴)(d⁴) = 1

Putting it all together, the expression (-5cd⁻⁴)(2cd²)² simplifies to -20c³.

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Can someone explain probability with permutations and combinations and explain where they are applied?

Answers

Answer:

If the order doesn't matter then we have a combination, if the order do matter then we have a permutation. One could say that a permutation is an ordered combination. The number of permutations of n objects taken r at a time is determined by the following formula: P(n,r)=n!

Step-by-step explanation:

To calculate the probability of a combination, you will need to consider the number of favorable outcomes over the number of total outcomes. Combinations are used to calculate events where order does not matter. In this lesson, we will explore the connection between these two essential topics.

Answer:

combination : If the order of numbers  or  operations does not matter

Permutation : when the order of numbers matter ( common example most teachers use : a code of 4 numbers has to be in a certain order and the numbers are from 0 to 9 , how many permutation can you make if you use the number one time)

P=n!/(n-r)!

n! ( are number from 0-9 we have 10 numbers)

r is the number of digits in the code = 4

n!=10*9*8*7*6*5*4*2*1

(n-r)!=(10-4)!=6!=6*5*4*3*2*1

P=5040 ways ( if the order matter)

If the order does not matter

Combination C(n,r)=n!/(n-r)!r!

C(10,4)=(10*9*8*7*6*5*4*2*1)/[(6*5*4*3*2*1)(4*3*2*1)]

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