Consider a cube of mass m with edges of length a. The moment of inertia I_0 of the cube about an axis through its center of mass and perpendicular to one of its faces is given by I_0 = 1/6ma^2. Find I_edge, the moment of inertia about an axis p through one of the edges of the cube. Express I_edge in terms of m and a. Use fractions rather than decimal numbers in your answer.

Step-by-step explanation:

3^(2x) - 1 = 27^x - 1

3^(2x) = 27^x

3^(2x) = (3^3)^x

3^(2x) = 3^(3x)

Therefore 2x = 3x and x = 0.

The average rate of change of the function is the slope of the secant line passing through the given two points (4,f(4)) and (-3,f(-3)).

Given the equation for the average rate of change:

Average rate of change = (f(4) - f(-3)) / (4 - (-3))

The average rate of change is the slope of the secant line joining two points on the function f(x) where the points are (4,f(4)) and (-3,f(-3)).

We can find the slope of the secant line joining two points by using the following formula:

Slope = Change in y / Change in x

Therefore, the slope of the secant line joining the two points (4,f(4)) and (-3,f(-3)) is given by:(f(4) - f(-3)) / (4 - (-3))

Now, we have to put the values of f(4) and f(-3) into the above formula to get the value of the slope.

The average rate of change of the function is the slope of the secant line passing through the given two points (4,f(4)) and (-3,f(-3)).

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The angle ACB would be 80 degrees.

What is tangent to a circle?

The tangent always makes a single-point contact with the circle. It never intersects the circle twice. Tangents from an external point to a circle have the same length.

In the given figure,

angle AOB = 40.

So angle OBA = 40.

Then the angle AOB = 180 - 40 -40

                          AOB = 100.

By the theorem of circles,

          AOB + ACB = 180

          100 + ACB = 180

              ACB = 80.

Hence, the angle ACB would be 80 degrees.

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Answer:

∅ ≈ 48.2º

Step-by-step explanation:

cos∅ = adj/hyp = 10/15 = 2/3

Therefor

∅ = arccos 2/3

use calculator

∅ = 48.189685104221402

∅ ≈ 48.2º

Answer:

A. Minimum = 54, Q1= 69.5, Median = 75, Q3= 106, Maximum = 183

Step-by-step explanation:

Arranging the data set in order from least to greastest we get:

54, 68, 71, 72, 75, 84, 104, 108, 183

From this, we can see that the minimum value is 54 and the maximum value is 183.

Taking a number off one by one on each side of the data set gives the median. In the middle lies 75, so that is our median

To find quartile ranges, split the data set into two where the median lies, then, find the median of those two data sets. The medians will be the values of the upper (Q3) and lower quartiles (Q1).

Q1: 54, 68, 71, 72

68 + 71 = 139
139 ÷ 2 = 69.5

-----

Q3: 84, 104, 108, 183

104 + 108 = 212

212 ÷ 2 = 106

Option A is the only answer with all of these values, therefore, it is the answer.

hope this helps!

ok

The length of s = 1/3

The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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Answer:

b6 2hich method

Step-by-step explanation:

I solv3 this

Answer:

46

Step-by-step explanation:

(PEMDAS)

12 x 7 - 33 + 15 - 20

84 - 33 + 15 - 20

46

It should be noted that to measure the diameter of a tin, you will need a ruler or a measuring tape. Follow these steps:

In geometry, it should be noted that a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

In this case, make sure to measure across the widest part of the tin to get an accurate diameter. If the tin is not perfectly round, you can take multiple measurements at different points and calculate the average to get a more accurate diameter.

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The correct order of the polynomial 8y^(4)−2y^(2)+10−y+4y^(6) is shown below:

4y^(6) + 8y^(4) − 2y^(2) − y + 10.

A polynomial is a mathematical expression with more than one term.

For example, 5x^{2} + 3x − 4 is a polynomial. It has three terms:

5x^{2}, 3x, and −4.

The terms of a polynomial are combined using the operations of addition, subtraction, multiplication, and division, and variables can be raised to exponents that are positive or negative integers or fractions.

A polynomial with a single variable is called a univariate polynomial.

Polynomials with more than one variable are called multivariate polynomials.

The degree of a polynomial is the greatest degree of any one term in the polynomial.

For example, the degree of 5x^{2} + 3x − 4 is 2.

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Answer:

x = 69

Step-by-step explanation:

Knowns:

y = 69

Problem Workout

180 - z = 2y

180 - z = 2 (69)

180 - z = 138

-z = -42

z = 42

Since there is no picture, I am guessing x is the third angle.

x = 180 - (y + z)

x = 180 - (69 + 42)

x = 180 - 111

x = 69

Answer:

Coordinates are numbers which determine the position of a point or a shape in a particular space (a map or a graph).

In primary school children are taught Cartesian coordinates, which they are introduced to in Year 4. Points are marked by how far along they are on the x axis (the horizontal axis) and how far up they are on the y axis (the vertical axis).

Step-by-step explanation:

Check the picture below.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{s}\\ o=\stackrel{opposite}{s} \end{cases} \\\\\\ (13)^2= (s)^2 + (s)^2\implies 13^2=2s^2\implies \cfrac{13^2}{2}=s^2 \\\\\\ \sqrt{\cfrac{13^2}{2}}=s\implies \cfrac{\sqrt{13^2}}{\sqrt{2}}=s\implies \cfrac{13}{\sqrt{2}}=s\)

Answer:

\(\frac{13 \sqrt{2} }{2}\)  OR 9.19

Step-by-step explanation:

hypotenuse =\(\sqrt{2}\) * leg

13 = \(\sqrt{2}\) * s

\(\frac{13 \sqrt{2} }{2}\)

OR (using pythagorean theorem)

\(13^{2}\) = 169

169 / 2 = 84.5

\(\sqrt{84.5}\) = 9.19

Answer:

x = 75

Step-by-step explanation:

Answer:

23°

Step-by-step explanation:

Complement angles are two angles that add up to 90°.

Since we’re given that one of them is 67°, the other one must add up to 90°

90 - 67 = 23

The other angle is 23°

Answer:

the complement of 67° is the angle that when added to 67° forms when a right angle (90°)

Based on the statistical analysis at the 0.01 level of significance, there is not enough evidence to show that a statistically significant linear relationship exists between the independent and dependent variables.

To determine if a statistically significant linear relationship exists between the independent and dependent variables, a statistical test such as a regression analysis can be conducted. The 0.01 level of significance indicates a high threshold for accepting the presence of a relationship.

In this case, after conducting the analysis, the results indicate that the p-value associated with the test statistic is greater than 0.01. This means that the observed relationship between the independent and dependent variables is not statistically significant. The p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming there is no true relationship between the variables.

Therefore, based on the data and the statistical analysis conducted, there is not enough evidence to conclude that a statistically significant linear relationship exists between the independent and dependent variables. It is important to note that this conclusion is specific to the given data set and the chosen level of significance.

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Answer:

11

Step-by-step explanation:

Answer:

option (c) 2

Step-by-step explanation:

We have the linear equation :-

→ 3x - 8 = -2

add 8 both sides

→ 3x - 8 + 8 = -2 + 8

→ 3x = 6

→ x = 6 ÷ 3

→ x = 2

Answer:

In total she works 21 hours and for the equation its gn=g+n

Step-by-step explanation:

got the equation i just put gn but that can be replaced with 21 since g and n both represent the number of hours fawzia works

The sector of the circle is bounded by 2 radii, and the measure of the central angle that forms the sector is 120 degrees

The given parameters are:

The area is calculated using

Area = α/360 * πr^2

So, we have:

α/360 * π * 15^2 = 75π

Evaluate the exponent

α/360 * π * 225 = 75π

Divide both sides by 75π

α/360 * 3 = 1

Multiply

α/120  = 1

Multiply both sides by 120

α = 120

Hence, the measure of the central angle that forms the sector is 120 degrees

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The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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Answer:

26x - y

Step-by-step explanation:

4x(5) + 6x - y

20x + 6x = 26x

26x - y

Hopefully this helps you :)

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Answer:

8+2g=11

1. subtract 8 from both sides

2g=3

2. Divide both sides by 2

ANSWER: g=1.5

19x + 7x + 10x = 180°

36x = 180

x = 5°

largest angle = 19 * 5 = 95°

Answer:

C. 95°

Step-by-step explanation:

19x+ 7x +10x = 180 (sum of the interior angles of a triangle is 180)

36x = 180

x= 180÷36

x= 5

Magnitude of the largest angle

= 19× x

= 19× 5

= 95

Answer:

I don't know what the answer choices are because this question is used twice But if im guessing correctly you mean the one where the answer choices are 6, 8, 12, and 24. The Correct answer is 6

a2 + 8a + 12 = (a + 2)(a + )

The answer is 6

Step-by-step explanation:

The volume of the gas approximately directly proportional to its number of moles of gas when both temperature and pressure are constant.

V∝ n at constant P and T

V = constant × (n)

Vn = constant

This can be mathematically stated as follows: As before, we can anticipate what will change to the volume of the a sample of gas as we adjust the number of moles using Avogadro's law.

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We will repeat the exact same procedure. Something may have gone wrong.                                                                                                    

The special theory of relativity by German-born scientist Albert Einstein contains the equation \(E=mc^{2}\), which conveys the idea that mass and energy are one and the same physical substance and may be transformed into one another. The kinetic energy (E) of a body is equal to its increased relativistic mass (m) multiplied by the square root of the speed of light.

Because the mass and the speed of light are both constants, we are unable to test a new variable. Since our findings don't match the accepted formula, we cannot share them.

The result obtained is wrong we cannot apply it to another experiment. The only way we can find the correct result is by repeating the experiment. Because something may have gone wrong on the first attempt.

Therefore, the correct answer is

d) Repeat the exact same procedure.  

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The correct question is: Suppose you conduct one experiment and find that the \(E=mc^{3}\), rather than the historically accepted formula, \(E=mc^{2}\). What should you do next?

a.Test a new variable

b.Share your findings

c.Apply your results to a new experiment

d.Repeat the exact same procedure                                                                                                                                                                                                                                                                                                                                                                                      

Thus, the annual arithmetic mean number of degrees awarded in computer science over the most recent seven years is approximately 7,525.14.

To find the annual arithmetic mean number of degrees awarded in computer science over the most recent seven years, we need to add up the total number of degrees awarded over those years and then divide that total by seven (the number of years being considered).

So, adding up the numbers given in the question, we get:

4,820 + 13,188 + 4,614 + 5,920 + 12,372 + 5,885 + 5,877 = 52,676

Now, to find the mean, we divide this total by seven:

52,676 ÷ 7 = 7,525.14

So, the annual arithmetic mean number of degrees awarded in computer science over the most recent seven years is approximately 7,525.14.

If we wanted to understand more about how the number of degrees awarded in computer science has changed over time, we would need to look at additional data and analyze it in more detail.

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Answer:

9.25

Step-by-step explanation:

No problem..