Calculate the surface area of this composite shape.

Answer:

F = 585844 N

Step-by-step explanation:

Given that:

A semicircular plate with radius 7 m is submerged vertically in water so that the top is 3 m above the surface.

The objective of this question is to express the hydrostatic force against one side of the plate as an integral and evaluate it.

To start with the equation of a circle:  a² + b² = r²

The equation of  circle with radius r = 7 can be expressed as:

a² + b² = 7²

a² + b² = 49

b² = 49 - a²

b = [tex]\sqrt{49 -a}[/tex]

NOW;

The integral of the hydrostatic force with a semicircular plate with radius 7 m and the top is 3 m above the surface can be calculated as follows:

[tex]\mathtt{F = 2 \rho g \int \limits^7_3 (a -3) \sqrt{49 -y^2} \ \ da}[/tex]

[tex]\mathtt{F = 2 \rho g \begin {pmatrix}\dfrac{\sqrt{49 -a^2} \ (2a^2-9a - 98)-(441 \times sin^{-1} (\dfrac{a}{3})) }{6} \end{pmatrix}}[/tex]

where;

density of water is 1000 kg/m3

and acceleration due to gravity is 9.8 m/s

Solving the integral; we have:

F = 2 ×  1000 kg/m³ × 9.8 m/s × (29.89)

F = 585844 N

Answer:

finding the value of x first

2x + 3x + 10 = 180 (linear pair)

5x = 180 - 10

x = 170 / 5

x = 34

3x = 102

Answer:

0.0319

Step-by-step explanation:

To approximate this probability, we shall be using the Bernoulli approximation of the Binomial distribution.

Let p = probability of selecting a reference book = 65% = 0.65

Let q = probability of selecting other books= 1-p = 1-0.65 = 0.35

Now, we want to find the probability that all of these 8 books to be re-shelved are reference book.

We set up the probability as follows;

P(X = 8) = 8C8 •p^8•q^0

P(X = 8) = 1 * (0.65)^8 * (0.35)^0

P(X = 8) = 0.031864481289 which is 0.0319 to 4 decimal places

Answer:

50%

Step-by-step explanation:

22 is half of 44.

So, this means 50% of 44 is 22.

Answer:

distance from the flying object to

the ground

= 7.2 melo(unit of measurement)

Step-by-step explanation:

The distance between the robot and Jo is 5 melo( unit Of measurement)

Let the distance between the flying object and the ground= y

Let's the remaining length of the closest between robot and Jonny and the ground be x.

Y/(x+5)= tan 29.... equation 1

Y/x= tan 42.... equation 2

Equating the value of y

Tan 29(x+5) = tan42(x)

Tan29/tan 42 = x/(x+5)

0.61562(x+5)= x

3.0781= x- 0.61562x

3.0781= 0.38438x

3.0781/0.38438= x

8.008= x

8= x

Y/x= tan 42

Y/8= 0.9004

Y= 7.203

Y= 7.2 melo (unit of measurement )

Answer:

7). x = 3.2, AC = 42.8

8). a = 6, YZ = 38

Step-by-step explanation:

It is given in the question that a point B is between A and C of the line segment AC.

⇒ AB + BC = AC

By substituting the values of segments,

5x + (9x - 2) = (11x + 7.6)

14x - 2 = 11x + 7.6

14x - 11x = 7.6 + 2

3x = 9.6

x = 3.2

Therefore, AC = 11x + 7.6

                        = 11(3.2) + 7.6

                        = 35.2 + 7.6

                        = 42.8

Question (8).

If Y is a point between X and Z,

⇒ XY + YZ = XZ

By substituting the measures of these segments given in the question,

(3a - 4) + (6a + 2) = (5a + 22)

9a - 2 = 5a + 22

9a - 5a = 22 + 2

4a = 24

a = 6

Since, length of segment YZ = 6a + 2

                                                = 6(6) + 2

                                                = 38

Answer:

you could stand at 5.0 ft and still be completely in the shadow of the tree

Step-by-step explanation:

From the diagram attached below;

We consider;

[tex]\overline {BC}[/tex] to be the height of the tree and [tex]\overline {DE}[/tex] to be the height of how tall you could be and still be completely in the shadow of the tree.

∠D = ∠B = 90°

Also;

ΔEAD = ΔBAC   (similar triangles)

Therefore, their sides will also be proportional

i.e

[tex]\dfrac{\overline {DE}}{ \overline {BC}}= \dfrac{\overline{AD}}{ \overline{AC}}[/tex]

[tex]\dfrac{x}{ 45}= \dfrac{225-220}{225}[/tex]

[tex]\dfrac{x}{ 45}= \dfrac{25}{225}[/tex]

By cross multiply

225x = 45 × 25

[tex]x = \dfrac{45 \times 25}{225}[/tex]

[tex]x = \dfrac{1125}{225}[/tex]

x = 5.0 ft

Therefore, you could stand at 5.0 ft and still be completely in the shadow of the tree

Answer:

when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³

Step-by-step explanation:

Let the initial length of the sides of the cube = x unit

when the length of the cube = x ;  volume of the cube = length × breadth × height = x × x × x = x³ (unit)³

when the length increased by 1 unit,

new length = (x + 1) unit

New volume = (x + 1) × (x + 1) × (x + 1)

multiplying the first two brackets

New volume = (x² + 2x + 1 ) (x + 1)

espanding the brackets

New volume = x³ + 2x² + x + x² + 2x + 1

New volume = x³ + 3x² + 3x + 1 (unit)³

Change in volume:

(New volume) - (old volume)

(x³ + 3x² + 3x + 1) - (x³)

x³ + 3x² + 3x + 1 - x³

collecting like terms:

(x³ - x³) + 3x² + 3x + 1

0 + 3x² + 3x + 1

change in volume = 3x² + 3x + 1

Therefore, when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³

Answer:

Population Size

Step-by-step explanation:

When sampling with replacement, we can expect that the population size will remain the same. Sampling with replacement occurs when a unit or subject for research is chosen from a population at random. This chosen unit can be returned to the population and another random selection done with the possibility that a unit that was chosen before could be chosen again. So in applying this system of selection, the population size is not taken into consideration. When samples are chosen in this form, it can be referred to as a simple random sample.

So, when determining the sample size necessary for estimating the true population mean, using the sampling with replacement method, the population size is not considered.

Answer:

Step-by-step explanation:

Hello, please consider the following.

m and n are the two numbers.

m + n = 24, right?

n = 2 m

We replace n in the first equation, it comes

m + 2m =24

3m = 24 = 3*8

So, m = 8 and n = 16

Thank you

The first number is 8 and second number is 16.

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Given that the sum of two numbers is twenty-four

The second number is equal to twice the first number

Let x and y are the two numbers.

According to the question,

m + n = 24,

n = 2m

Substitute the value of n in the first equation,

m + 2m =24

3m = 24

m = 24/3

m = 8

Substitute the value of m in the n = 2m

So, n = 2(8)

n = 16

Hence, the first number is 8 and second number is 16.

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There are [tex]10[/tex] divisions between $3.2$ and $3.3$

so that means each division is $\frac{3.3-3.2}{10}=0.01$

A is the 3rd division after $3.2$, So A is $3.2+3\times0.01=3.23$

similarly, C is 3 division behind $3.2$ so it will be $3.17$

and B is $3.34$

A represents the decimal 3.23

B represents the decimal 3.34

C represents the decimal 3.17

We can see that there are 10 divisions between 3.2 and 3.3.

The difference between the two points for 10 divisions is 3.3 -3.2 = 0.1 unit.

Therefore, one division will be equal to 0.1/10 = 0.01 unit

So, point A is 3 divisions after 3.2, thus

A = 3.2 + 0.01×3

A = 3.23

Similarly,

B = 3.3 + 0.01×4

B = 3.34

And,

C = 3.2 - 0.01×3

C = 3.17

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Answer:

25 hours.

Step-by-step explanation:

We are to find the number of hours from:

Monday at  10:30

to

Tuesday at 11:30

Since the question does not state whether the times are in A.M / P.M ,

There are 24 hours upto 10:30 on Tuesday.

Adding 1 hour gives 11:30

So the answer = 24 + 1 = 25 hrs

Answer:

25 hours

Step-by-step explanation:

1 day=24 hours

11.30-10.30=1 hour

----------------------------

add the total 25 hours

Answer:

correct option is C)  2.8

Step-by-step explanation:

given data

string vibrates form =  8 loops

in water loop formed =  10 loops

solution

we consider  mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone = [tex]\rho[/tex]

case (1)  

when 8 loop form with 2 adjacent node is [tex]\frac{\lambda }{2}[/tex]

so here

[tex]l = \frac{8 \lambda _1}{2}[/tex]      ..............1

[tex]l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}[/tex]

and we know velocity is express as

velocity = frequency × wavelength   .....................2

[tex]\sqrt{\frac{Tension}{mass\ per\ unit \length }}[/tex]   =   f × [tex]\lambda_1[/tex]

here tension = mg

so

[tex]\sqrt{\frac{mg}{\mu}}[/tex]   =   f × [tex]\lambda_1[/tex]     ..........................3

and

case (2)  

when 8 loop form with 2 adjacent node is [tex]\frac{\lambda }{2}[/tex]

[tex]l = \frac{10 \lambda _1}{2}[/tex]      ..............4

[tex]l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}[/tex]

when block is immersed

equilibrium  eq will be

Tenion + force of buoyancy = mg

T + v × [tex]\rho[/tex] × g = mg

and

T = v × [tex]\rho[/tex] - v × [tex]\rho[/tex] × g    

from equation 2

f × [tex]\lambda_2[/tex] = f  × [tex]\frac{1}{5}[/tex]  

[tex]\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}[/tex]     .......................5

now we divide eq 5 by the eq 3

[tex]\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}[/tex]

solve irt we get

[tex]1 - \frac{\rho _{stone}}{\rho _{water}} = \frac{16}{25}[/tex]

so

relative density [tex]\frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}[/tex]

relative density = 2.78 ≈ 2.8

so correct option is C)  2.8

the answer is 667.

100/x = 15/100

it’s a proportion so you cross multiply. after cross multiplying you get 15x = 10,000. divided both sides by 15 and you get x = 66.6 (continuation of the 6). since it’s repeating, round it and you get 667.

by the way this is actually one of my homework questions for today ;)

The predicted number of butterflies that starts from Kansas and Missouri and migrate to Mexico is 667.

The Aim of the experiment is to measure the Monarch butterfly migration

Predicting the number of butterflies

= [tex]\frac{100}{x} = \frac{15}{100}[/tex]

= [tex]15x = ( 100 * 100)[/tex]

∴ x( predicted value ) = [tex]\frac{10000}{15 } = 667[/tex]

hence the approximate value of the number of butterflies that migrate to Mexico from Kansas and Missouri is  667

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Answer:

The price for 4 people is 52 dollars.

4 × (5.75 + 7.25) = 52

The total cost including drink and popcorn is $52 according to a given condition.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Cost of movie ticket =  $7.25/person

Cost of popcorn and drink =  $5.75/person

Total cost per person = 5.75 + 7.25 = $13

Now,

Number of people = 4

So,

4(5.75 + 7.25) = 4(13) = $52

Hence "The total cost including drink and popcorn is $52 according to a given condition".

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Answer: First a horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.

Step-by-step explanation:

Let's construct g(x) in baby steps.

Ok, we start with f(x) = x^2

The first thing we have is a horizontal translation of A units (where A is not known)

A vertical translation of N units to the right, is written as:

g(x) = f(x - N)

Then we have:

g(x) = (x - A)^2 = x^2 - 2*A*x + A^2

Now, you can see that actually g(x) has a negative leading coefficient, which means that we also have an inversion over the x-axis.

Remember that if we have a point (x, y), a reflection over the x-axis transforms our point into (x, -y)

Then if we apply also a reflection over the x-axis, we have:

g(x) = -f(x - A) = -x^2 + 2*A*x - A^2 = -x^2 + 16*x - 44

Then:

2*A = 16

A*A = 44.

The first equation says that A = 16/2 = 8

But 8^2 is not equal to 44.

Then we need another constant coefficient, which is related to a vertical translation.

If we have a relation y = f(x), a vertical translation of N units up, will be

y = f(x) + N.

Then:

g(x) = -f(x - A) + B

-x^2 + 2*A*x - A^2 + B = x^2 + 16*x - 44

Now we have:

2*A = 16

-A^2 + B = - 44

From the first equation we have A = 8, now we replace it in the second equation and get:

-8^2 + B = -44

B = -44 + 64 = 20

Then we have:

The transformation is:

First an horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.

Answer:

396 in^2

Step-by-step explanation:

The perimeter of a triangle is given by the formula:

● P = 2w+2L

L is the length and w is the width

■■■■■■■■■■■■■■■■■■■■■■■■■■

The width hereis 18 inches and the perimeter is 80 inches.

Replace w by 18 and P by 80 to find L.

● P= 2L+2w

● 80 = 2L + 2×18

● 80 = 2L + 36

Substrat 36 from both sides

● 80-36 = 2L+36-36

●44 = 2L

Divide both sides by 2

● 44/2 = 2L/2

● 22 = L

So the length is 22 inches

■■■■■■■■■■■■■■■■■■■■■■■■■■

The area of a rectangle is given by the formula:

● A= L×w

● A = 22×18

● A = 396 in^2

Answer:

From the given points above, the distance between them is 4 units.

Step-by-step explanation:

In order to find the distance between the two points, we must know the distance formula.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Now, we plug in our numbers from the coordinate points that we are given to their respectful places.

[tex]d=\sqrt{(8-8)^2+(8-4)^2}[/tex]

Now, we solve. First, simplify the terms in parentheses. So, subtract 8 from 8 and subtract 4 from 8.

[tex]d=\sqrt{(0)^2+(4)^2}[/tex]

Next, solve for the exponents.

[tex]d=\sqrt{0+16}[/tex]

Add the numbers in the radical.  

[tex]d=\sqrt{16}[/tex]

Solve the radical.

[tex]d=4[/tex]

So, the distance  between the two given points is 4 units.

Answer:

Step-by-step explanation:

As x increases from -74 to -54 (a 'run' of 20), y decreases from 18 to 12 (a 'rise' of -6.  Thus, the slope of this line is m = rise/run = -6/20 = -13/10.

From y = mx + b we get     12 = (-13/10)(12) + b, or (after dividing all terms by 12)

1 = -13/10 + b/12, or

60 = -3(6) + 5b, or

42 = - 5b, or b = -42/5

The line is y = (-13/10)x - 42/5.

At the x-intercept, y = 0.  Setting y = 0, we get:

(13/10)X = -42/5,  or  13x = -84.

Thus, x = -84/13 =  -6.46

and so the x-intercept of the line is (-6.46, 0)

Answer:

Following are the answer to this question:

Step-by-step explanation:

In the given statement, we don't agree with Ed’s conclusion, because it is not relevant simply since it is not statistically significant. The reduction of prostate cancer is the death risk, which is highly significant even if it decreases significantly. It can also be something statistically important without becoming important.

Answer:

x = 108

Step-by-step explanation:

The sum of a circle is 360

90 + x/2 + x+x = 360

Combine like terms

90 + 2x+x/2 = 360

90 + 5/2 x = 360

Subtract 90 from each side

5/2x = 270

Multiply each side by 2/5

5/2x * 2/5 = 270*2/5

x =108

Answer:

-4.5ft per sec

Step-by-step explanation:

Assume that vertical wall has a distance of y and the horizontal floor is x (6 ft).

This forms a triangle with the ladder as the hypothenus of length 10ft

We have dy/dt = 6ft per sec

According to Pythagoras law the relationship between x and y is

(x^2) + (y^2) = (hypothenus ^2) = 10^2

When we differentiate both sides of the equation

2x(dx/dt) + 2y(dy/dt) = 0

dy/dt = (x/y) * (dx/dt)

y= √(10^2) - (6^2) = 8ft

So dy/dt = (6/8)* (6/1)= -4.5 ft per sec

It is a negative rate

Answer:

13.75 dollars

Step-by-step explanation:

n=4

3n+7/n =3(4) + 7/4

=12 + 1.75

=$13.75

Answer: A) 4.75

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

find a common number that 18 and 24 are both divisible by. I chose 6. So when i divide 6 by 18, I got 3. Which I put on my numerator, when I divided 24 by 6 I got 4 which I put on my denominator. My end result was 3/4

Answer:

3/4

Step-by-step explanation:

18/24

=2*9=18

=2*12=24

=9/12

=3/4

Answer:

219.80 feet

Step-by-step explanation:

Tan 20= 80/b

Tan 20= 0.363970234266

(0.363970234266)b=80

b= 219.80 feet

The distance between the sculpture and the bottom of the building is required.

The distance between the building and sculpture is 219.80 feet.

[tex]\theta[/tex] = Angle of depression = Angle of elevation = [tex]20^{\circ}[/tex]

p = Height of building = 80 feet

b = Required length

From the trigonometric ratios we have

[tex]\tan\theta=\dfrac{p}{b}\\\Rightarrow b=\dfrac{p}{\tan\theta}\\\Rightarrow b=\dfrac{80}{\tan 20}\\\Rightarrow b=219.80\ \text{feet}[/tex]

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Answer:

216

Step-by-step explanation:

If you just paint the surface of the cube, then the inside of the cube would not have any of their faces painted red.

Just looking at the cube from a side view, you would realize that there would be a smaller cube, 6 x 6 x 6 (not 7 since you have to account for both the top side and the bottom side), and so that is the answer, 6 ^ 3, which is 216.

Answer:

216

Step-by-step explanation:

8 * 8 * 8 = 512

8 * 8 = 64

Each face is 64 cubes, overlapping at the edges, with 6 faces total.

16 + 12 = 28 for each overlapping cube on each side

64 * 6 = 384

384 - 2(28) = 328

Top & Bottom dealt with, overlap from them is 56 units total, 14 units on top and bottom of each face..

64 - 14 = 50

50 * 2 = 100

Front & Back dealt with.

328 - 100 = 228

64 - 28 = 36

36 * 2 = 72

228 - 72 = 156

...

OR

6^3 = 216

Answer:

[tex]\boxed{\sf x = 80}[/tex]

Step-by-step explanation:

A quadrilateral inscribed in a circle has opposite sides equal to 180.

So,

x + x + 20 = 180

2x + 20 = 180

Subtracting 20 from both sides

2x = 180 - 20

2x = 160

Dividing both sides by 2

x = 80

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 80

▹ Step-by-Step Explanation

x + x + 20 = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 80

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.

Step-by-step explanation:

Stepwise regression is a model which uses variables in step by step manner. The procedure involves removal or inclusion of independent variables one by one. It adds the most significant independent variable and removes the less significant independent variable. Usually stepwise selection uses R-square or Mallows Cp for picking the best fit.

Answer:

683,280 hours is what I caculated. Is that right?

Step-by-step explanation:

Answer:

There are (365 x 24) hours for each year.

and 365 x 24 are 8760.

and 8760 x 78 are 683,280.

so, the average person does not live at least 1 Million hours, but they live more than 500 thousand hours, or 5 x 10^5 hours.

Hope it helps!

Bye!

P.S. Please give me Brainliest...

I desperately need one more Brainliest...

Answer:

the answer is a and d

Step-by-step explanation:

6 + 6 + 2 +2 = 16

3 + 3 + 5 + 5 = 16

to find perimeter, double each factor and add :)