two half-cylinders of diameter 2 meet at a right angle in the accompanying figure. find the volume of the solid region common to both half-cylinders. (hint: consider slices parallel to the base of the solid.)

The probability that the sum will be an even number on the toss of two dice is  5/9 .

In the question ,

it is given that ,

the numbers on the faces of the dice are 1, 2, 3, 5, 7, and 8 .

the probability of getting an odd number first is = 4/6 = 2/3,

the probability of getting an even number first is = 2/6 = 1/3,

To get an even, we must get either 2 odds or 2 evens.

The probability of getting 2 odds is 4/6 × 4/6 = 16/36 .

The probability of getting 2 evens is 2/6 × 2/6 = 4/36.

If we add them together,

we get ,

= 16/36 + 4/36

= 20/36

= 10/18 = 5/9

Therefore , the required probability is 5/9  .

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The speed will be calculated by the formula by the product of frequency and wavelength.

The speed of sound is the distance travelled by a sound wave per unit of time as it propagates through an elastic medium. At 20 degrees Celsius, the speed of sound in air is approximately 343 metres per second or one kilometre in 2.91 seconds or one mile in 4.69 seconds.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

The speed of the sound will be calculated by the multiplication of frequency and wavelength.

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Answer:

I'm pretty sure it's 0.625kg

Step-by-step explanation:

There are 1000g in 1kg so 7kg would be 7000g plus 500g which is 7500g.

7500g divided by 12 is 625g. Divide by 1000 to get kg and you get 0.625kg.

Hope this helps!

Answer:

  (2)  11

Step-by-step explanation:

You want the area of the triangle with vertices (1, 3), (3, -1), and (-2, -2).

Pick's theorem says the area of a figure drawn on a grid can be found by counting the grid points on the boundary (b) and the interior grid points (i). Then the area is ...

  A = (b/2) +i -1

This figure has a boundary grid point at (2, 1) in addition to the three vertices. So, b = 4.

There are 10 interior grid points, a number that can be arrived at by counting them. The numbers in each row, starting from the bottom, are 4, 3, 2, 1.

Then the area is ...

  A = (4/2) +10 -1 = 11

The area of the triangle is 11 square units.

The area can be computed from the coordinates by the formula ...

  A = 1/2|x1(y2 -y3) +x2(y3 -y1) +x3(y1 -y2)|

  A = 1/2|1(-1 -(-2)) +3(-2 -3) +(-2)(3 -(-1))| = 1/2|1 -15 -8| = 11

The area is 11 square units.

The triangle can be bounded by a square 5 units on a side. The triangle area is smaller than the square area by the sum of the three triangles cut from the corners of the square. Clockwise from left, those triangle areas are ...

  1/2(5·3) +1/2(4·2) +1/2(1·5) = 1/2(15 +8 +5) = 14

Then the area of the triangle of interest is ...

  5² -14 = 11

The area of the triangle is 11 square units.

The angle the bottom edge makes with the horizontal is ...

  arctan(1/5) ≈ 11.3099°

and the length of that edge is ...

  5/cos(11.3099°) ≈ 5.099

The angle the left side makes with the horizontal is ...

  arctan(5/3) ≈ 59.0362°

and the length of that edge is ...

  3/cos(59.0362°) ≈ 5.831

The area of the triangle with sides 'a' and 'b' and angle C between them is ...

  Area = 1/2(ab·sin(C)) = 1/2(5.099·5.831·sin(59.0362° -11.3099°)) = 11

The area of the triangle is 11 square units.

__

Additional comment

Side lengths could also be determined using the Pythagorean theorem, and the angle between any two of them could be found using the Law of Cosines.

Heron's formula could be used to find the area from the three side lengths.

Answer:

x = 3

Step-by-step explanation:

Solve for x:

35 + 6x - 2 = 13x + 12

Simplifying on the left side:

33 + 6x = 13x + 12

Subtracting 33 on both sides:

6x = 13x - 21

Subtracting 13x on both sides:

-7x = -21

Dividing by -7 on both sides:

x = 3

The element of this group is {0, 1, 2, 3, ...., 25}, this group is a cyclic group, and 16 is not a generator for this group but 5 is a generator for this group.

[tex]Z_{26}[/tex] ≡ Group of integers under addition modulo 26

addition modulo is all addition of integer in ordinary way than remove integral multiple. For example, addition modulo a+mb is a+b than remove all integral multiple m and the result is lower than m (residue).

a) The elements of this group is all the integers remainder after mod 26. So,

x = k (mod 26) where 0 ≤ k < 26

or we can write each of them as {0, 1, 2, ..., 23, 24, 25}

b) Cyclic group is a group that is generated by 1 element. Since, the group is integers under addition modulo with all integers can be generated by adding 1 repeatedly, so the group [tex]Z_{26}[/tex] is cyclic group.

c) As 1 ∈ [tex]Z_{26}[/tex] but there is no m ∈ N such that [tex]16^m[/tex] = 1, but for [tex]5^m[/tex] is

{0, 5, 10, 15, 20, 25, 4, 9, 14, 19, 24, 3, 8, 13, 18, 23, 2, 7, 12, 17, 22, 1, 6, 11, 16, 21}

or in simply way, we can say there is m ∈ N for [tex]5^m[/tex] = 1. So, 16 is not generator of this group, but 5 is generator of this group.

Thus, the number of {0, 1, 2, 3, ...., 25} is the element for this group, cyclic group is a type of this group, and 5 is a generator for this group but 16 is not a generator for this group.

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The graph of linear function d = 4.5t and the time to cover 30km is 6.67s

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here;

The linear function given in the question is;

d = 4.5t

a) The graph of the function d = 4.5t is attached below.

b) The time it takes to cover 30km will be

d = 4.5t

30 = 4.5t

t = 30 / 4.5

t = 6.67 s

The time it takes to cover a distance of 30km is 6.67s

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The no of student ticket, x = 30

The no of adult ticket, y = 37

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.

The drama club is selling tickets to their play to raise money for the show's expenses.

Let the student ticket be represented as x and adult ticket as y

Cost of student ticket,x = $7

Cost of adult ticket,y = $9

The total number of tickets, x + y = 67 ... (1)

There was a total of $543 in revenue from the sale of 67 total tickets.

7x + 9y = 543 ...(2)

Multiplying eq(1) by 7, we get

7x + 7y = 469 ...(3)

Subtract eq (3) from (2), we get

2y = 74

y = 37, sub in eq (1)

x = 30

The no of student ticket, x = 30

The no of adult ticket, y = 37

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Answer: Let s= the number of student tickets sold Let

               Let a=the number of adult tickets sold

  7s+9a=543

  s+a=67

Step-by-step explanation:

Answer:

Step-by-step explanation:

it would be devided into 3 sections so the thing would look like this

The frictional loss will be greater for aspect ratio of 2 as friction will be more when the height of the duct is higher compared to the increase in width.

In a straight duct with constant cross sectional area , the velocity of the water is changed. The change in static pressure is the frictional loss .

In the duct the energy is constant. Therefore when water moves upwards with the increase in height the frictional loss or the pressure loss will be more more.

When width increases there will be less pressure, So frictional loss will be increased with height.

Let the width and height be a and b respectively.

now area = ab

and a\b =2

or, a = 2b

again a\b = 4 or, a = 4b

if ab is constant then the height for the aspect ratio of 4 is greater.

Therefore there will be more frictional loss for the increased height.

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Answer:

[tex]M=\left(-1, \dfrac{7}{2} \right)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

Given endpoints:

Substitute the given points in the midpoint formula:

[tex]\implies M=\left(\dfrac{x_C+x_A}{2}, \dfrac{y_C+y_A}{2} \right)[/tex]

[tex]\implies M=\left(\dfrac{-5+3}{2}, \dfrac{16+(-9)}{2} \right)[/tex]

[tex]\implies M=\left(\dfrac{-2}{2}, \dfrac{7}{2} \right)[/tex]

[tex]\implies M=\left(-1, \dfrac{7}{2} \right)[/tex]

Answer:

[tex]5c+\frac{9-8c}{24}[/tex]

Step-by-step explanation:

Simplify

[tex]5c+\frac{1*(\frac{3}{4}-\frac{2c}{3} )}{2}[/tex]

[tex]5c+\frac{9-8c}{24}[/tex]

Probability that randomly selected audient attend all the concerts is 0.05.

What is probability?

P(A) = 28/100 = 0.28

P(B) = 42/100 = 0.42

P(C) = 30/100 = 0.30

P(A∩B) = 10/100 = 0.10

P(A∩C) = 8/100 = 0.08

P(B∩C) = 7/100 = 0.07

P(A∪B∪C) = 80/100 = 0.80

P(A∩B∩C) = ?

P(A∪B∪C) = P(A) + P(B) + P(C) - P(A∩B) - P(A∩C)  - P(B∩C) + P(A∩B∩C)

P(A∩B∩C) = - 0.28 - 0.42 - 0.30 + 0.10 + 0.08 + 0.07 + 0.80

= 0.05

Probability that randomly selected audient attend all the concerts is 0.05.

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If a satellite flies 136640 miles in 17.8 hours then in 9.87 hours the satellite flows down to 75766.6 miles

Given that:

A satellite flies 136640 miles in 17.8 hours

We will find the unit rate first,

Unit rate = 136640/17.8

Unit rate = 7676.40 miles per hour.

Miles flown in 9.87 hours,

Miles flown = 7676.40 × 9.87

Miles flown = 75766.6 miles

Hence Miles flown in 9.87 hours is 75766.6 miles

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They need to put 14.4 grams of onion powder in each bottle.

Given,

The quantity of onion powder in a seasoning blend = 4%

We have to find the quantity of pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder;

How much is a percentage?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."

Here,

Let x be the seasoning blend.

Now, 4% of 72=20% of x

⇒ 0.04×72=0.2×x

⇒ 0.2x=2.88

⇒ x=2.88/0.2

⇒ x=14.4 g

Therefore, a container should contain 14.4 grams of onion powder.

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In the gym, there are 100 feet between the opposing corners.

Given,

The length of the rectangular gymnasium = 80 feet

The width of the rectangular gymnasium = 60 feet

We have to find the distance between opposite corners of the gymnasium;

Here,

The distance between opposite corners of the gymnasium is the diagonal of the rectangle;

Diagonal of rectangle = [tex]\sqrt{width^{2} + length^{2} }[/tex]

Then,

Diagonal = [tex]\sqrt{80^{2} +60^{2} }[/tex]

Diagonal = [tex]\sqrt{6400+3600}[/tex]

Diagonal = √10000

Diagonal = 100 feet

That is,

The distance between the opposite corners if the gymnasium is 100 feet.

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Answer:

640 1/4 lbs

Step-by-step explanation:

The triple integral f(x, y, z)dV for the following function f is 256π(256 - x - y)² as an iterated integral in cylindrical coordinates.

The iterated integral in cylindrical coordinates is given by:

∫∫∫f(ρ, θ, z)dV = ∫∫∫xρcos(θ)ρsin(θ)zdρdθdz

Evaluating the integral yields:

∫∫∫f(ρ, θ, z)dV = 256π∫zdz

= 256πz²

= 256π(256 - x - y)²

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The average speed of John for the whole journey is 54km/h.

Calculating average speed involves dividing the total distance traveled by the total time it took to cover that distance.

Speed is the rate of movement of something at a specific time.

Average speed refers to the average speed over the course of a journey.

So, the average speed will be:

Distance = speed x time

d₁ = v₁ x t₁

d₁ = 50 x 3

d₁ = 150 km

d₂ = v₂ x t₂

d₂ = 60 x 2

d₂ = 120 km

So,

D = d₁ + d₂

D = 150 + 120

D = 270 km

Utilizing the S formula:

S = D/ T

S = 270 / 5

S = 54 km/hr

S = 54km/hr

Therefore, the average speed of John for the whole journey is 54km/h.

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For ΔDEF , Length of shorter side = 6, Length of medium side = 8 , Length of longer side = 12.

For ΔGHI , Length of shorter side = 9, Length of medium side = 12 , Length of longer side = 18.

For ΔJKL , Length of shorter side = 3/2, Length of medium side = 2 , Length of longer side = 3.

What are Similar Triangles ?

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

In the given figure below, two triangles ΔABC and ΔXYZ are similar only if,

i)       ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z

ii)       AB/XY = BC/YZ = AC/XZ (Similar triangles proportions)

Hence, if the above-mentioned conditions are satisfied, then we can say that ΔABC ~ ΔXYZ

It is interesting to know that if the corresponding angles of two triangles are equal, then such triangles are known as equiangular triangles. For two equiangular triangles we can state the Basic Proportionality Theorem (better known as Thales Theorem) as follows:

For two equiangular triangles, the ratio of any two corresponding sides is always the same

Given that ,

For ΔABC , Length of shorter side = 3, Length of medium side = 4 , Length of longer side = 6.

Now,

For ΔDEF ,

Scale Factor = 2

Length of shorter side = 2*3 = 6, Length of medium side =2*4 = 8 , Length of longer side =2*6 = 12.

For ΔGHI ,

Scale Factor = 3

Length of shorter side = 3*3 = 9, Length of medium side =3*4 = 12 , Length of longer side =3*6= 18.

For ΔJKL ,

Scale Factor = 1/2

Length of shorter side =3*1/2 = 3/2, Length of medium side =4*1/2= 2 , Length of longer side =6*1/2= 3.

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the proportion of all ucf and usf students who prefer to use hand sanitizer is in between 2.646% and 7.65%

What is z test?

If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.

When there are multiple alternatives accessible, hypothesis testing is utilised. To decide whether to accept or reject the null hypothesis, the z test is performed in the mean, which determines the t value. This value is then compared with the p value. The alternate explanation in this case is mu, which is represented. For P1 and P2, the 90% confidence interval is (- 0.0765, 0.02646).

Hence, the proportion of all ucf and usf students who prefer to use hand sanitizer is in between 2.646% and 7.65%

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The numerical will be equal to 159 ÷ 16 and the polynomial will be (9x +15)/x.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

In comparison to the divisor, the dividend will be 15 times greater. It seems that you are free to select any divisor. It must be more than 15 if the divisor is totally numerical.

Numerical:

Divisor = 16,

so we have,

(9×16 +15) ÷ 16

= 159 ÷ 16

Polynomial:

The simplest divisor we can have is a single variable: x.

(9x +15)/x

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Step-by-step explanation:

H is the plan

F is the side

A is the plan

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The control limits for the x chart for a sample of size 10,

a-Develop the control limits for the $\oveline x$ chart for samples of size 10, 20, and 30

UCL = 359.48

LCL = 340.51

b. What happens to the control limits as the sample size is increased

The control limits for the x chart for a sample of size 20,

UCL = 356.71

LCL = 343.29

c-What happens when a Type I error is made

The control limits for the x chart for a sample of size 30,

UCL = 355.47

d- What happens when a Type II error is made? e. What is the probability of a Type I error for samples of size 10, 20, and 30

LCL = 344.52

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event.

The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Probability generally refers to the degree to which something is likely to occur.

This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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Answer:

1.097174699×10^²⁶

Step-by-step explanation:

100×100×325×1773×3.44554×34444×6878755×23324=

1.097174699×10^²⁶

If the bond angle between two adjacent hybrid orbitals is 180 degree then the hybridization  is sp hybridization , it forms linear molecules with an angle of 180°.

Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.

In sp hybridization, the s orbital of the excited state carbon is mixed with only one out of the three 2p orbitals. It is called sp hybridization because two orbitals (one s and one p) are mixed.

The resulting two sp hybrid orbitals are then positioned at 90 degree and 180 degree, respectively, with the two 2p unhybridized orbitals:

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The positive solution is 5.

given,

When 10 is subtracted from a number's square, the result is three times the number.

let x be the number

according to given statement the quadratic equation will be

[tex]x^2-10=3x\\\\x^2-3x-10\\\\x^2+2x-5x-10=0\\\\x(x+2)-5(x+2)=0\\\\(x-5)(x+2)=0\\\\x=5\ or\ -2[/tex]

Thus, the positive solution is 5.

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The probability of no more than 8 heads given that at least one toss resulted in heads will be 511/512.

What is probability ?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

A coin has two possibility, either head or tail.

So, there will be 2 possible outcomes when a coin is tossed.

hence, Total no. of outcomes (T) =  2^9. = 512

  Now,  Probability of getting one tail = 1/2^9 = 1/512

and, Probability of getting at most 8 heads

       = 1 - Probability of getting one tail

       = 1 - 1/512

       = 511/512.

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Answer:

[tex]\frac{2}{13}[/tex]

Step-by-step explanation:

All the sides have equal lengths.  Set the two sides equal to each other and solve for y

[tex]\frac{5}{4}[/tex]y + 1 = [tex]\frac{7}{3}[/tex]y  -2  I am going to clear the fractions by multiplying through by 12

[tex](\frac{12}{1})[/tex][tex]\frac{5}{4}[/tex] y + (12)(-1) = [tex](\frac{12}{1})[/tex][tex]\frac{7}{3}[/tex] y - (12)2

15y - 12 = 28y - 24  Subtract 15y from both sides

-12 = 13y - 24  Add 24 to both sides

12 = 13y  Divide both sides by 13

[tex]\frac{12}{13}[/tex] =  y

Plug 12/13 into the expression for either side to find the length of BC.  All the sides have the same length

[tex]\frac{7}{3}[/tex][tex](\frac{12}{13})[/tex]  -  2

[tex]\frac{28}{13}[/tex] - [tex]\frac{26}{13}[/tex] = [tex]\frac{2}{13}[/tex]

Answer:

(2x+2)=(3x-52)

2x+2=3x-52

2x-3x=-52-2

-x=-54

x=54