Can someone please explain how to solve this type of equation? ​

The rotational inertia of the block about an axis of rotation through one of the corners of the block which is perpendicular to the large faces will be M(a²+b²)/3.

Any item that can be rotated has the property of rotational inertia. It is a scalar value that indicates how challenging it is to alter an object's rotational velocity around a certain rotational axis. The role of mass in linear mechanics is analogous to that of rotational inertia in rotational mechanics. Because it measures moment of inertia as it is rotating, this property is also known as rotational inertia. A measurement of an object's resistance to changes in its angular velocity is called rotational inertia. Imagine turning an item with a specific torque. As the torque is being applied, measure the angular acceleration. The rotational inertia of the item increases as the resultant angular acceleration decreases.

Here,

The major calculations are attached in image.

Moment of Inertia of plate passing through O is I = Ma²/12

and, ly = Mb²/12

by perpendicular axis theorem I2 = Ma²/12+Mb²/12

The distance of edge and the center is d = √(a²+b²)/4

So by parallel axis theorem, IA = Ma²/12+ Mb²/12 + Md² = M(a²+b²)/3

M(a²+b²)/3 is the rotational inertia of the block about a rotating axis passing through one of its corners and perpendicular to its large faces.

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The small town would take up 5 years to double the population from 500 people.

As its sign is "%," the word "percent" implies "for every hundred". Since it is read as a percentage, "x%" should be read as "x percent." So, a percent is a fraction with a denominator of 100. 30%, for instance, equals 30/100 (i.e. 30 parts from 100). You can also write this as 0.30.

Population of small town = 500

Population Growth rate = 15 %

To find :

              Time when the population is doubled.

We will use successive change

500 People after 1 year = 575

575 People after 1 year = 661.25

661.25 People after 1 year = 760.4375

760.4375 People after 1 year = 874.503125

874.503125 People after 1 year = 1005.67859

Hence it will total take the time of 5 years to double the population.

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Answer:

C = 50.27

Step-by-step explanation:

Hope this helps!

Answer:

C = 16 pi

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi * r

C = 2 * pi * 8

C = 16 pi

The squares cut from the corners should be large in width and length 6 to hold the box as much as possible. The dimensions of the box with the largest volume are 6 x 6.

If the squares cut from the corners are h × h inches

The open-top box will have

A height of h

A width of 12 - 2h

and a length of 12 - 2h

So its volume will be

V(h) = h × (12 - 2h) × (12 - 2h)

= 4h³ - 48h² + 144h    (square inches)

dV/dh= 12h² - 96h + 144

Critical points occur when the derivative (dV/dh) is zero.

12h² - 96h + 144 = 0

h² - 8h + 12 = 0

(h − 2)(h − 6) = 0

It is clear that h = 6 is not the crucial point for the maximum as it would produce widths and lengths of zero (and so a volume of zero).

In order to cut out squares measuring 6 × 6 inches from the corners of the bigger sheet, the most volume may be obtained.

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The confidence interval for the true percent of car owners in the city  who received a speeding ticket be, (139.27 , 160.73).

Subtract 1 from your sample size. 1000 – 1 = 999. This provides the degrees of freedom.

Subtract the confidence level from 1, and then divide by two.

(1 – .95) / 2 = .025

Now, df = 999 and α = 0.025

from the table at df = 999 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

150 / √(10) = 4.74

Now, 2.262 × 4.74 = 10.73

So, the confidence interval be,

(150 - 10.73 , 150 + 10.73) = (139.27 , 160.73)

Hence, the confidence interval for the true percent of car owners in the city  who received a speeding ticket be, (139.27 , 160.73).

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Answer:

29

Step-by-step explanation:

(14+8²︎) ÷ 2 - 10

(14+64) ÷ 2 - 10

(78) ÷ 2 - 10

39 - 10

29

Could you please mark me brainliest for this? Thank you!

When building a regression model provided the given information from the four remaining independent variables the variable to be entered next (second) would be variable with the highest coefficient of partial determination. (Option A)

A regression model refers to a function that illustrates the relationship between one or more independent variables and a response, target, dependent variable. The primary uses of regression analysis are forecasting, time series modeling and identifying the cause-and-effect relationship between variables. When building a regression model with five potential independent variables to explain the variation in the dependent variable, at step 1, variable x3 enters the regression model. Of the four remaining independent variables, the variable entered next into the model would be the variable with the highest coefficient of partial determination. A coefficient of partial determination refers to the measurement of marginal (extra) contribution of X variable or percentage of variation in the response variable that can be explained by the explanatory variables and can be used to measure how strongly two variables are related to one another.

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The ordered pair that lie on the graph of the exponential function ​f(x)=3(14)ˣ is (-1, 12)

A curve that depicts an exponential function is known as an exponential graph.

The curve have a horizontal asymptote and either an increasing slope or a decreasing slope. this is to say that the curve begins as a horizontal line, increases or drops gradually, and then the growth or decay accelerates. It may or may not cut the x-axis, but it always cuts the y-axis at some point.

An exponential graph will almost always have a y-intercept but not necessarily an x-intercept.

The given function was plotted on a graph and the point that lie on the graph is (-1, 12).

the point (-3,-192)  is way out of the graph

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Answer: y=2x-1

Step-by-step explanation:

(1,1) (2,3) (3,5) (4,7)
1=2(1)-1
3=2(2)-1
5=2(3)-1
7=2(4)-1

The population of the small town in 2025 is 22234

The given parameters in the question are

These parameters can be represented as

a = 24597

r = 2%

The equation of the function can be represented as

P(t) = a(1 - r)^t

So, we have

P(t) = 24597 * (1 - 2%)^t

In 2025, we have

Year = 2025

This means that

t = 2025 - 2020

So, we have

t = 5

Substitute t = 5 in P(t) = 24597 * (1 - 2%)^t

P(5) = 24597 * (1 - 2%)^5

Evaluate the expression

P(5) = 22234

Hence, the population is 22234

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The inequality that represents at least how many minutes it will take to download the whole game

is x ≥ (2.2 - 0.5)/0.01

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this scenario, 2.2 GB game is being downloaded onto your laptop and when you have downloaded half a gigabyte, you notice that your computer has been downloading at a rate of .01GB/min.

The inequality will be illustrated. Let the number of minutes be x.

x ≥ (2.2 - 0.5)/0.01

This illustrates the inequality.

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Based on the information provided, it can be determined that there are 120 steps visible on the escalator at any given time.

Assume that there are x total steps, e for the escalator speed, and b for Bob's pace.

Bob noticed 75 stairs and climbed the entire escalator in the time it took him to ascend it. As a result, the escalator must have added an extra x + 75 steps.

Let e and b be the speeds of the escalator and Bob, respectively.

Alice took 150 steps at a speed of (3b-e) step rate as she descended the stairs.

Bob took 75 steps at a speed of (b+e) each step as he ascended.

Since, Al and Bob were walking the same distance at a time , we have,

150(3b-e) = 75(b+e)  

Solving  these two equation we get ,  e/b = 3/5

Thus while Bob took 75 steps to go up, the escalator contributed an extra

3/5 * 75 = 45 steps

Finally, there is a total of 75+45=120 steps in the length of the escalator.

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Answer: $225

Step-by-step explanation: .25 x 900 = 225

Answer: $225

Step-by-step explanation:

You earn $.25 for every quart picked. You pick 900 quarts. take 900 and times it by .25. You get 225 so you earn $225

answer:

1.92 pounds or 23/12 lb

step-by-step explanation:

first convert 3/4 and 1/3 to fractions that have the same denominator such as 9/12 and 4/12. then add the two numbers together and subtract it by 3 to get the answer. hope that helps!

Answer:

-2.8y-7.52

Step-by-step explanation:

multiply 0.4 by each of the numbers in the parentheses then simplify

Answer: -2.8y-7.52

Step-by-step explanation:

The variance over an interval for a uniform distribution is

V(X) = ( b - a )²/ 12

Here,

a and b are intervals .

By the definition of the variance, V(X) = E[X2] − (EX)2.

On solving ,

V(X)

=(a²+ab+b²)/3−(a²+2ab+b²)/4

=(a²−2ab+b²)/12

=( b - a )²/ 12

A continuous probability distribution is a Uniform distribution and is related to the events which are equally likely to occur. It is defined by two parameters, x and y, where x = minimum value and y = maximum value. It is generally denoted by u(x, y).

A two-parameter family of curves known as the uniform distribution (sometimes known as the rectangle distribution) is famous for having a constant probability distribution function (pdf) between its two bounding parameters.

For values tabulated to a specific number of decimal places, this distribution is suitable for illustrating the distribution of round-off mistakes. Techniques for generating random numbers , like the inversion method, use the uniform distribution.

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Answer:

Step-by-step explanation:

The easiest way to do this is to clear the decimal by multiplying the numerator and the denominator by

10

.

You can reduce the fraction later.

40

m

48

m

2) Reduce the fraction to its simplest form

Cancel out

8

from the top and the bottom

5

m

6

m

←

answer

This answer means that the numerator and denominator of the given fraction

4

m

4.8

m

are in a

5

:

6

ratio relationship with each other.

Check

Is

4

4.8

equal to

5

6

?

Cross multiply

(

4

)

(

6

)

should be equal to

(

5

)

(

4.8

)

24

is equal to

24.0

C

h

e

c

k

Sketching the nyquist plot based on the bode plots for the mentioned systems require a certain understanding of bode plots explained in detail.

In reality, Bode plots are a collection of graphs that display a system's frequency response. This system might be any system (not simply a circuit!) that changes its behavior when its frequency (cycles per second) changes.

Frequency Response simply describes how our system will alter in response to a specific input frequency. This collection of notes will be referred to as our input frequency.

Bode charts often have two graphs. We'll refer to one as the magnitude plot and the other as the phase angle plot.

We'll need something initially called a transfer function. Typically represented as H(s) or H(j). A transfer function often equates to the ratio of the output to the input.

A). >KG ( s) a= K( s+2 ) / s + 10 B.>KG ( s) = K / ( s + 10 )(s+2)2 C).>KG ( s) = K (s+10)(s+10) / (s+100)(s+2)3 D)

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Answer:

(x + 1 ) (2x-9)

Step-by-step explanation:

Break The expression into groups

= ([tex]2x^{2} +2x)+(-9x-9)[/tex]

Factor out 2x from [tex]2x^{2}[/tex] + 2x: 2x (x + 1)

and then you want to factor out the -9x - 9 -9( x + 1 )

and that equals 2x( x + 1 ) [tex]-9(x+1)[/tex]

And now do it again Factor out common term x + 1

and now it " Equals" [tex](x + 1)(2x-9)[/tex]

Check the picture below.

[tex]\textit{Circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=1.57 \end{cases}\implies 1.57=2\pi r\implies \cfrac{1.57}{2\pi }=r\implies {\Large \begin{array}{llll} \stackrel{meters}{0.25}\approx r \end{array}}[/tex]

The probability that her third child would be a girl is 50%.

Probability:

In math probability means the possible of happening a particular event amount the total number of event.

Given,

Here we need to find if a woman's first child is a girl and her second child is also a girl, what is the probability that her third child would be a girl.

We already know that, there are two sex chromosomes X and Y.

And in the humans are diploid having two sex chromosomes, in females a pair of the X chromosome is found while in males an X and Y chromosome is present.

So, there is  50% chance that the subsequent child is going to be a girl because it entirely depends upon the chromosome of the sperm which fertilizes the ovum.

For each pregnancy features a  50% chance of leading to a boy or girl and this doesn't include the likelihood of multiples.

Here already having 2 girls previously doesn't affect the probabilities of any resulting pregnancy.

Therefore, the prospect of getting a girl remains at  50%.

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The number of revolution per minute for Gear C is 200 rpm

It is given that

The gear ratio r:s is ratio of number of teeth of two connected gear

Also , the gear A is rotated at rate of = 100rpm

Since, Gear A has 20 teeth and Gear B has 60

Ratio = r : s

=> 20 : 60

=> 1 : 3

Thus , the ratio of number of revolution per minute for two gear is s:r

=> 3 : 1

Means Gear A turns at 3 rpm , Gear B turns at 1 rpm

Similarly , for Gear B and Gear C

The ratio of rpms for these two will be =>

10 : 60

=> 1 : 6

That is , when Gear B turns at 1rpm , Gear C turns at 6rpms

Therefore, If Gear A turns at 100 rpms

the Gear B turns at = 100/3 rpms

Hence , Gear C turns at = 100/3 × 6

=> 200 rpms

I've answered the question in general as the question is incomplete

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The total number of sessions they did in that year will be equal to 20.

Equations are mathematical expressions with two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be similar to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a simple fundamental equation.

As per the data given in the question,

The charge per session = $25

Annual membership charge = $45

Total money paid = $545

Money left after paying for the annual membership = $545 - $45= $500

The total number of sessions in $500 will be,

T = 500/25

T = 20 sessions.  

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Look at the point in which the x-value is equal to -1

k(-1) = 7

Answer: 29 inches.

Step-by-step explanation:

The formula to find the hypotenuse is a^2 + b^2 = c^2.

20^2= 400, and 21^2=441. Together, it was 841. Square root that, and your answer is 29.

-

a^2 + b^2 = c^2

20^2 + 21^2 = c^2

400 + 441= c^2

881 = c^2

29=29

Answer:

x = -2y - 4

Step-by-step explanation:

x + 2y = -4

Subtract 2y from both sides.

x = -4 - 2y

Answer:

x = 2

this is the answer hope u pass

Using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².

A shape's area can be calculated by contrasting it with squares of a known size.

The square meter (abbreviated as m2), which is the area of a square whose sides are one meter long, is the common unit of area in the International System of Units (SI).

Three such squares would be the same size as a form with a three-square-meter area.

The area of any other shape or surface is a dimensionless real number, and the unit square is defined in mathematics to have area one.

So, the area of the square:

A = b²

Where B is the square's long side.

A = 450in²

A = b²

b² = 450

b = √450

b = 15√2 in

Therefore, using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².

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Correct question:
Which represents a side length of a square that has an area of 450 square inches?

a. 15 start root 2 end root inches in.

b. 16 start root 3 end root inches in.

c. 112. 5 in.

d. 115. 5 in.