a. How did you identify and name the semicircles?

As the time increases, the angular velocity i.e. omega also increases quadratically with time.

Given,

From the figure,

Radius of wheel = 0.2 m

Acceleration, a = 4t m/s^2

then the angular acceleration of wheel can be determined by formula,

[tex]a=\alpha * r[/tex]

Where, r=radius of wheel =0.2 m

[tex]4t=\alpha * 0.2\\20t=\alpha[/tex]

We know that the angular acceleration is the change in angular velocity over time.

[tex]\alpha=\frac{d\omega}{dt}\\\\20t=\frac{d\omega}{dt}\\\\d\omega=20tdt\\\\\omega=\int\limits^t_0 {20t} \, dt \\\\\omega=\frac{20t^2}{2}-0\\\\\omega=10t^2[/tex]

From the above equation it is clear that omega i.e. angular velocity is dependent of time

omega is directly proportional to square of time

For

t=1 then ω=10

t=2 then ω=10(4)=40

t=3 then ω=10(9)=90.....and so on.

It means as time increases, then angular velocity also increases quadratically with time.

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Your question is incomplete, here is the complete question.

When a body rotates about fixed axis , any point located in the body travels along the circular path. the angular acceleration α measures the rate of change of angular velocity. A cord is wrapped around a wheel, which is initially at rest when θ=0. The force F gives the cord an acceleration [tex]a= 4t\ m/s^2.[/tex]

How does omega change over time?

The length of the Yangtze River is 5530 kilometers.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

The length of the Nile river = 6,690 kilometers.

Also, The Nile river is 1,160 kilometers longer than the Yangtze River.

Let the length of Yangtze River is x kilometers,

Use equation format,

x + 1160 = 6690

x = 6690 - 1160

x = 5530

The length of the Yangtze River is 5530 kilometers.

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The rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0 is zero.

Given that,

Seawater has a density of 1025 kg/m³ and moves at a constant velocity field defined by the equations v = yi + xj, where x, y, and z are measured in meters and the components of V are expressed in meters per second.

We have to find the rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0.

We know that,

v= yi + xj, and density = 1025 kg/m³

F=1025(yi + xj)

After solving the R(u,v) we get zero.

Therefore, the rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0 is zero.

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The unit rate for the ratio 6 deliveries in 2 hours is 3 deliveries per hours

From the question, we have the following parameters that can be used in our computation:

Ratio = 6 deliveries in 2 hours

The unit rate is simply the value of the above ratio

However, with a denominator of 1

This means that we evaluate the quotient in the above expression

So, we have the following representation

Ratio = 6 deliveries/2 hours

Express as unit rate

Unit rate = 3 deliveries per hours

Hence, the unit rate is 3 deliveries per hours

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The equation of the line passing through (3,4) and having slope m = 3/2 is y = 3/2x + 4.

Given points : (3,4)

The equation of a line with slope 3/2 and passing through point (3,4) is y = 3/2x + 4. This equation can be used to calculate the y-coordinate of any point on the line, given its x-coordinate. For example, if the x-coordinate of a point is 6, then its corresponding y-coordinate is 11. In general, for any x-coordinate, the corresponding y-coordinate is given by 3/2 times the x-coordinate plus 4.

Given slope : m = 3/2

We know that the equation of a line with slope m and passing through point (x1, y1)is given by :

y - y1 = m(x - x1)

Substituting the given values, we get

y - 4 = 3/2(x - 3)

Simplifying equation, we get

y = 3/2x + 4

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When the scale factor is greater than one, then the size of the object will enlarge

The scale factor is defined as the ratio of the new measurements of the object to the original measurements of the object

We can enlarge or shrink the size of the object by keeping the shape of the object same
The enlarge or shrink of he object can be determined by the value of scale factor

If the value of scale factor is between 0 and 1, then the object shirks and if the value of scale factor is greater than 1, then the object enlarge

Therefore, the size of the object will enlarge when the scale factor is greater than one

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Answer:

To find the product of 1/4 and 1/6, we need to first find a common denominator. In this case, we can use the least common multiple of 4 and 6, which is 12. We can then rewrite 1/4 and 1/6 as 6/12 and 2/12, respectively. The product of these two fractions is then 6/12 * 2/12 = (6 * 2)/(12 * 12) = 1/12. Therefore, 1/4 x 1/6 = 1/12.

Alternatively, we can simply cancel out common factors in the numerator and denominator of the two fractions before multiplying them. In this case, we can cancel out the common factor of 1 in the numerator and the common factor of 4 in the denominator to get 1/4 * 1/6 = 1/(4 * 6) = 1/24.

Both methods give us the same answer, so we can use either one to solve this problem.

Step-by-step explanation:

Answer:

1/24

Step-by-step explanation:

We want to multiply fractions

1           1

---   *   ----

4            6

Multiply the numerators

1 * 1 = 1

Multiply the denominators

4 * 6 = 24

The result is

1           1             1

---   *   ----   =    -----

4            6          24

Answer:

-18

Step-by-step explanation:

[tex]\frac{2}{3}n=-12 \\ \\ \frac{3}{2} \cdot \frac{2}{3}n=\frac{3}{2}(-12) \\ \\ n=-18[/tex]

Answer:

C

Step-by-step explanation:

Everything else doesn't really make sense

Answer:

C. headquarters

Step-by-step explanation:

is the correct answer. A headquarters is the main office or center of operations for a business, particularly a large multinational corporation. A subsidiary, on the other hand, is a company that is owned or controlled by another company, often referred to as the parent company or holding company. A home locale is not a commonly used term in business, but it could refer to the location where a company is based or originated.

Therefore, the solution to the given problem is a) ME= 1.93 and b) confidence interval= (19.59,23.45)

Using test statistics to judge statistical hypotheses is a widespread technique. A test statistic, which is a count of a data set that can be used to run the test and simplifies the data to a single number, is a common approach to express a hypothesis test.

Here,

a) Sample of customers is 64, population standard deviation is 6 and confidence level is 99%

Sample mean= 21.52

Sample size= 64

Confidence level= 99%

Population standard deviation= 6

Standard error of the mean= 0.75

Z-value= -2.5758 (From Z table)

Interval half width= 1.9319

Margin of error at 99% confidence interval is 1.93 from the output.

b) Confidence interval

Interval upper limit= 19.59

Interval lower limit= 23.45

99% confidence interval is (19.59, 23.45) from the output.

ME= (23.45- 19.59)/2 = 1.93

Therefore a) ME= 1.93 b) confidence interval= (19.59,23.45)

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The equation of a line passing through (x1, y1) is y - y1 = m(x - x1).

The equation of a line:

The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The most popular form in algebra is the "slope-intercept" form. y = mx + b. This in effect uses x as a parameter and writes y as a function of x: y = f(x) = mx+b.

Here we have to find the equation of a line passing through (x1, y1) and the slope.

Data given:

Point on the line = (x1, y1)

Slope = m

By this we get the equation of a line as:

y - y1 = m(x - x1)

Therefore the equation of a line is y - y1 = m(x-x1).

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Answer:

21

Step-by-step explanation:

For this problem, we basically want to find 2016/96.

2016=1920+96. So, 2016/96 = (1920+96)/96=20+1=21.

So, the hot air balloon travels 21 miles each hour.

''21'' because 2016 divided by 96 is 21

(12x+5y)/3z

substitute in values

(12(12) + 5(6)) / 3(3)

simplify

(144 + 30) / 9

add

174 / 9

factor out a 3

58 / 3

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Answer:

453.75

Step-by-step explanation:

To find the volume of a pyramid, we can use the formula V = (1/3)Bh, where V is the volume of the pyramid, B is the area of the base, and h is the height of the pyramid.

Since the base of the pyramid is a square, we can use the formula for the area of a square to find the area of the base. The formula for the area of a square is A = s^2, where A is the area of the square and s is the length of one side of the square. In this case, each side of the square base is 11 inches, so the area of the base is 11^2 = 121 square inches.

Now that we know the area of the base, we can use the volume formula to find the volume of the pyramid. The height of the pyramid is 15 inches, so the volume of the pyramid is V = (1/3) * 121 * 15 = 605 cubic inches.

Since Lucinda plans to fill the pyramid three fourths full with sand, the volume of the pyramid that will be filled with sand is 3/4 * 605 = <<3/4*605=453.75>>453.75 cubic inches.

Answer:the answer is 16 feet

Step-by-step explanation:

the answer is 4

Step-by-step explanation:

Answer:Binary Variable

Step-by-step explanation:Binary variable: a variable that can only take on two values, usually 0/1.

Answer:

24 girls

Step-by-step explanation:

245÷5= 49

49÷2=24.5 so you can estimate that it is 24

An icosahedron have 36 interior diagonals.

Given that:

Icosahedron :

Faces = 20 =F

Vertices = 12 = V

Edges = ? = E

For convex 3-dimensional polyhedral Euler's formula:  or

    E = V + F -2

⇒ E = 12 + 20 - 2

⇒ 30

Interior diagonals :

[tex]\left[\begin{array}{ccc} Vertices\\2\end{array}\right] - Edge[/tex]

= [tex]\left[\begin{array}{ccc} 12\\2\end{array}\right][/tex] - 30

= 12/2 × 11/1 - 30

= 66 - 30

= 36

An icosahedron has 36 interior diagonals.

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We can conclude that the given situation of Andy is perfectly represented by a graph (A).

The set of ordered pairs is the graph of a function f in mathematics, where These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

To develop a graph is to make a diagram that depicts the relationship between two or more objects.

Make a sequence of bars on graph paper as an example of a graph.

So, we know that:

Andy pedals rapidly.

Then maintain the speed for some time.

Then again, he rapidly pedals the bike he has.

Then suddenly, he put breaks.

All these details are shown in graph (A).

(Refer to the attached (A) graph below)

Therefore, we can conclude that the given situation of Andy is perfectly represented by a graph (A).

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The features of the function are given as follows:

The horizontal asymptote is the limit of f(x) as x goes to infinity. To obtain this limit, we consider only the terms with the highest exponent of the numerator and of the denominator, hence:

g(x) = -5x/x -> y = 5 is the horizontal asymptote.

The vertical asymptote is the value of x for which the function is not defined, hence it is the zero of the denominator, thus:

x - 2 = 0 -> x = 2.

The x-intercept is the point (x,0), in which x is found when y = 0, hence:

-5x + 10 = 0

-5x = -10

5x = 10

x = 2.

However, the function is not defined at x = 2, meaning that it has no x-intercept.

The y-intercept is the value of y when x = 0, hence:

y = 10/-2 = -5.

The coordinates are (0,-5).

The entire function can be simplified as follows:

(-5x + 10)/(x - 2) = [-5(x - 2)]/(x - 2) = -5.

Meaning that the function has no holes.

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Answer: the answer is 1

Step-by-step explanation: if you divide 12 by 12

The length of the longer and shorter pieces of hose is equal to 19ft and 8ft respectively.

As given in the question,

length of the hose = 27ft

Let 'x' be the length of the longer piece

and 'y' be the length of shorter piece

As per given condition:

System of equations are:

x = 2y + 3  __(1)

x + y = 27 __(2)

Substitute the value x from (1) in (2) we get,

2y + 3 + y = 27

⇒3y + 3 = 27

⇒ 3y = 27 - 3

⇒3y = 24

⇒y = 24/3

⇒y = 8ft.

Now,

x = 2(8) + 3

⇒ x = 19ft

Therefore, the length of the longer and shorter piece cut from a 27ft long hose is equal to 19ft and 8ft respectively.

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Answer:

  y ≈ 60.6 units

Step-by-step explanation:

Given a triangle with angles 18° and 117°, and sides 21 opposite 18° and y opposite 117°, you want to know the value of y.

The law of sines tells you the ratios of side length to the sine of the opposite angle are the same for all side/angle pairs in the triangle.

  y/sin(117°) = 21/sin(18°)

  y = 21·sin(117°)/sin(18°) ≈ 60.55

The value of y is about 60.6 units.

Answer:

S=7

t=1

Step-by-step explanation:

Since we need to make these triangles congruent, s+36=43, and t+39=40. Solve for s by subtracting 36 from both sides of the equation (s+36-36=43-36 s=7), then solve for t by subtracting 39 from both sides (t+39-39=40-39  t=1)

-Hope this helped & Happy Holidays!

Answer:

Step-by-step explanation: first we need to add 4 to 48 with will give us 52, then if we divide 52 by 4 we will get the answer for the price per pizza, 52 divided by 4 is 13 with means that Mr. Lee paid 13 dollars per pizza.

Therefore , the test statistic comes out to be t = 8.645.

A test statistic is a statistic used in statistical hypothesis testing .A hypothesis test is typically expressed as a test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to perform the hypothesis test.

Here,

Parameter = u1 - u2

where

[tex]{X^{'}_{1}[/tex] = 3.27

[tex]{X^{'}_{2}[/tex] = 2.95

S1=0.23 and S2=0.29

So using formula

=> t = [tex]\frac{X^{'}_{1} - X^{'}_{2} }{Sp\sqrt{\frac{1}{n1} +\frac{1}{n2} } }[/tex]

=> t = [tex]\frac{3.27 - 2.95 }{0.23\sqrt{\frac{1}{100} +\frac{1}{100} } }[/tex]

=> t = 9.838

and

=> t = [tex]\frac{3.27 - 2.95 }{0.29\sqrt{\frac{1}{100} +\frac{1}{100} } }[/tex]

=> t = 7.802

thus,

=> t = (9.838 + 7.802) / 5 =8.645

thus t = 8.645

Therefore , the test statistic comes out to be t = 8.645.

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The initial speed of the ball traveling when it leaves the bat is  95.9 mph and the angle at it initially forms with the horizon is  39.49°.

A parallelogram is a four-sided shape having two sets of parallel sides, with the opposite sides being equal in length and the angles opposite each other being equal. A triangle is a three-sided shape with three angles, the sum of which adds up to 180 degrees.

∠x + ∠y + ∠z = 180°

The baseball was hit by the batter with a starting speed of 74 miles per hour horizontally and a lift of 61 miles per hour. The initial speed

v = √(v(h)² + v(c)²)

v = √((74)² + (61)²)

v = 95.9 mph

The angle made will be -

Ф = tan⁻¹(61/74) = 39.49°

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