Order the measurements from greatest to least. 45 inches, 6 yards, and 2 1/4" feet

Percentage increase= $768÷32000=0.024

=0.024×100=2.4%

Answer:

A. Thermal energy is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.
Explanation:

Just took the Quick Check :)

The best description of thermal energy is that it is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.

Thermal energy is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.

It is a type of internal energy, which is the energy possessed by a system due to the movement and interactions of its constituent particles.

We have,

Thermal energy is a measure of an object or substance’s heat:

While thermal energy and heat are related, they are not exactly the same thing.

Heat is the transfer of thermal energy between objects or substances due to a temperature difference.

Thermal energy, on the other hand, is the energy contained in an object or substance due to the movement of its particles.

Thermal energy is kinetic energy:

While thermal energy is related to kinetic energy, they are not exactly the same thing.

Kinetic energy is the energy of motion, while thermal energy specifically refers to the kinetic energy of an object's particles.

Thermal energy is the energy stored in an object’s chemical bonds:

While chemical bonds do store energy, this is not the best description of thermal energy.

Thermal energy specifically refers to the energy stored in the movement of an object's particles.

Therefore,

The best description of thermal energy is that it is the kinetic energy contained in an object or substance due to the movement of its atoms and/or molecules.

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9514 1404 393

Answer:

  yes

Step-by-step explanation:

The parent function e^x has a horizontal asymptote at y=0.

Answer:

145.12

Step-by-step explanation:

3.14 * 16 / 2 + 120

I basically got the same answer

The series ∑[infinity]n = 1(−1)^n−1x^n/n5^n has a radius of convergence of 5 and an interval of convergence of (-5, 5].

To find the radius of convergence and interval of convergence of the given series, we can use the ratio test. The ratio test states that for a power series ∑[infinity]n = 1 c_nx^n, if the limit of |c_(n+1)/c_n| as n approaches infinity exists, then the series converges if the limit is less than 1 and diverges if the limit is greater than 1.

Applying the ratio test to the given series, we have:

|((-1)^(n-1)x^(n+1)/((n+1)5^(n+1))) / ((-1)^(n-1)x^n/(n5^n))|

= |(-x/(n+1)(5/5))^n|

Taking the limit as n approaches infinity, we have:

lim (n→∞) |(-x/(n+1)(5/5))^n| = |x/5|

For convergence, we need |x/5| < 1, which implies |x| < 5. Therefore, the radius of convergence is 5.

To find the interval of convergence, we need to check the endpoints. When x = -5, the series becomes ∑[infinity]n = 1 (-1)^(n-1) / n, which is the alternating harmonic series. This series converges by the alternating series test. When x = 5, the series becomes ∑[infinity]n = 1 1/n, which is the harmonic series that diverges.

Hence, the interval of convergence is (-5, 5], including -5 and excluding 5.

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Answer:

The answer would be 3/4 > 5/8

At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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The weighted average cost of capital (WACC) for company C is 6.63%.

The weighted average cost of capital (WACC) is a financial metric that represents the average rate of return a company must earn on its investments to satisfy its shareholders and creditors. It takes into account the proportion of debt and equity in a company's capital structure and the respective costs associated with each.

To calculate WACC, we need to consider the cost of debt and the cost of equity. The cost of debt is the interest rate a company pays on its debt, adjusted for taxes. In this case, the pre-tax cost of debt is 2% and the tax rate is 24%. Therefore, the after-tax cost of debt is calculated as (1 - Tax Rate) multiplied by the pre-tax cost of debt, resulting in 1.52%.

The cost of equity represents the return required by equity investors to compensate for the risk associated with owning the company's stock. Here, the cost of equity for company C is 6%.

The debt represents 10% of the total capital, while the equity represents the remaining 90%. To calculate the weighted average cost of capital (WACC), we multiply the cost of debt by the proportion of debt in the capital structure and add it to the cost of equity multiplied by the proportion of equity.

WACC = (Proportion of Debt * Cost of Debt) + (Proportion of Equity * Cost of Equity)

In this case, the calculation is as follows:

WACC = (0.10 * 1.52%) + (0.90 * 6%) = 0.152% + 5.4% = 6.552%

Therefore, the weighted average cost of capital (WACC) for company C is approximately 6.63%.

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The average length of the five largest tunnels in the United State is 38,156.

The table shows the five largest vehicle tunnels in the UNITED STATES.

Here we need to find the average length of the tunnel.

To find the average length, determine the arithmetic mean of the five tunnels.

The arithmetic mean is mainly used to find the center of the values. To find the arithmetic mean add up all the values and divide the number of values.

\(Arithmetic mean = \frac{sum of all number}{total number} \\\)

\(Arithmetic mean = \frac{13000 + 8959 + 8941 + 6072 + 5920}{5\\}\)

\(Arithmetic mean = \frac{42892}{5}\)

Therefore the arithmetic mean = 38,156

The average length of the tunnels is 38,156.

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The efficiency of the system is approximately 54.5%. To calculate the efficiency of the system, we need to compare the actual number of students trained to the maximum capacity of the class.

In the given scenario, the maximum capacity per month is 1100 students, and the actual number of students trained in the past month is 600. Efficiency can be calculated by dividing the actual number of students trained by the maximum capacity and multiplying by 100 to express it as a percentage. Using the given values:

Efficiency = (Actual number of students trained / Maximum capacity) * 100

= (600 / 1100) * 100

≈ 54.5%. Therefore, the efficiency of the system is approximately 54.5%. This indicates that the class was utilized to around 54.5% of its maximum capacity in the past month.

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Answer: width = 4m, perimeter = 26m

Step-by-step explanation:

area of rectangle = width x length

9x = 36

x = 4

width = 4m

perimeter:

9 + 9 +4+4 = 26 m

Answer:40

Step-by-step explanation:

40 beacause you have to round to the nearset 10

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

B. x = 12.5

Step-by-step explanation:

We have similar quadrilaterals, so the ratios of corresponding sides are equal.

\( \frac{15}{12} = \frac{x}{10} \)

\(12x = 150\)

\(x = 12.5\)

The area of the deck, in terms of the side length of the pool (s), is given by the expression 2s² + 11s + 15.

The length of the deck is 5 units longer than twice the side length of the pool.

So, the length of the deck can be expressed as (2s + 5).

The width of the deck is 3 units longer than the side length of the pool. Therefore, the width of the deck can be expressed as (s + 3).

The area of a rectangle is calculated by multiplying its length by its width. Thus, the area of the deck can be found by multiplying the length and width obtained from steps 1 and 2, respectively.

Area of the deck = Length × Width

= (2s + 5) × (s + 3)

= 2s² + 6s + 5s + 15

= 2s² + 11s + 15

Therefore, the area of the deck, in terms of the side length of the pool (s), is given by the expression 2s² + 11s + 15.

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Answer:

55/100 Because 55/100=9/11

Step-by-step explanation:

\(2A +B = -2 \cdot (2z +8 -2z-4) = -2 \cdot 4 = -8\)

No, 6 is not considered as a prime number, it is a composite number.

As given in the question,

Given number is equal to :

6

Prime numbers are those numbers which has only two factors one and the number itself.

Example of prime numbers are :

2, 3, 5, 7, 11, 13,... so on.

Here six has more than two factors .

Factors of 6 are equal to :

1, 2, 3, 6

There are four factors of six.

When a number has more than two factors then it is considered as composite number.

Example of composite factors are :

4, 6, 8, 9, 10, ... so on.

6 is a composite number.

Therefore, 6 is not a prime number it is a composite number.

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Answer:

2

Step-by-step explanation:

(0.5)(6x-2)-3(x-1) = (3x-1)-(3x-3)

                           = 3x-1-3x+3

                           = 2

Answer:

\(y = \dfrac{5}{2}x - 7\)

Step-by-step explanation:

Step-by-step explanation:

Take any two points (x1, y1) and (x2, y2) from the table

Slope intercept equation is y = mx + b where m is slope and b = y-intercept

Slope = (y2-y1)/(x2-x1)

In this case

Let's choose the last two points

These are (6,  8) and (8, 13)

Slope = (13 - 8)/(8-6) = 5/2

So the equation is y = (5/2)x + b

To compute b, plug in x, y values for any point and solve for b

Choose the first point (0, -7)

Plug in:

-7 = (5/2)(0) + b

-7 = 0 + b or b = -7

So the equation of the line is
\(y = \dfrac{5}{2}x - 7\)

We can verify by computing the y value for another point and seeing it agrees with table values

Choose point (4, 3)

y = 5/2 x 4 - 7

= 10 - 7 = 3

which agrees with the table value for y which is 3 when x = 4

Answer:

$720

Step-by-step explanation:

10% x 2 (since it's 2 years)

20% of 600 = 120

600 + 120 = 720

Answer:

B = -6

Step-by-step explanation:

so yes, you're correct.

Answer:

54.67%

Step-by-step explanation:

18.75 -8.75     x 100% = 54.67

    18.75

Based on the given information, the estimate for the number of cells in a T75 flask can be calculated by comparing the number of cells in the picture to the field of view area and then scaling it up to the size of the T75 flask.

Given that there are 55 cells in the picture, we can use this information to estimate the density of cells in the field of view. The field of view has dimensions of 1.85 mm x 1.23 mm, which gives an area of 2.7095 square millimeters (\(mm^2\)). To calculate the cell density, we divide the number of cells (55) by the area (2.7095 \(mm^2\)), resulting in an approximate cell density of 20.3 cells per \(mm^2\).

Now, to estimate the number of cells in a T75 flask, we need to know the size of the flask's growth area. A T75 flask typically has a growth area of about 75 \(cm^2\). To convert this to \(mm^2\), we multiply by 100 to get 7500 \(mm^2\).

To estimate the number of cells in the T75 flask, we multiply the cell density (20.3 cells/\(mm^2\)) by the growth area of the flask (7500 \(mm^2\)). This calculation gives us an approximate estimate of 152,250 cells in the T75 flask. It's important to note that this is just an estimate, and actual cell counts may vary depending on various factors such as cell size, confluency, and experimental conditions.

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Answer:

The solution to the system of equations is:

\(x=10,\:y=4\)

Step-by-step explanation:

Given the system of equations

\(\begin{bmatrix}5x-4y=34\\ -x+8y=22\end{bmatrix}\)

Multiply -x+8y=22 by 5:  -5x+40y=110

\(\begin{bmatrix}5x-4y=34\\ -5x+40y=110\end{bmatrix}\)

so adding the equations

\(-5x+40y=110\)

\(+\)

\(\underline{5x-4y=34}\)

\(36y=144\)

solve 36y = 144 for y:

\(36y=144\)

divide both sides by 36

\(\frac{36y}{36}=\frac{144}{36}\)

Simplify

\(y=4\)

For 5x-4y=34 plug in y=4

\(5x-4\cdot \:4=34\)

\(5x-16=34\)

Add 16 to both sides

\(5x-16+16=34+16\)

Simplify

\(5x=50\)

Divide both sides by 5

\(\frac{5x}{5}=\frac{50}{5}\)

Simplify

\(x=10\)

Therefore, the solution to the system of equations is:

\(x=10,\:y=4\)

In this scenario, the null hypothesis states that a surgical procedure is successful at least 80% of the time, while the alternative hypothesis claims that it is less than 80% successful.

In hypothesis testing, Type II error occurs when the null hypothesis is not rejected even though it is false. The Type II error, denoted by β, would occur if we fail to reject the null hypothesis even though it is false, i.e., when the actual success rate of the surgical procedure is less than 80%.

Therefore, β represents the probability of accepting the null hypothesis when the alternative hypothesis is true. It is also known as the false negative rate, as it occurs when we fail to detect a significant difference between the sample and population due to random chance or other factors.

The value of β depends on various factors, such as the sample size, significance level, and effect size. To calculate β, we need to specify these values and use statistical software or tables to find the probability of Type II error.

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The value of x for the given triangle is 4.5

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of all three angles of a triangle is always 180°

In the given triangle ABC,

∠A=(9x+16)°, ∠B=(6x+15)°

And the extrior angle ∠C=(19x+3)°

Use the external angle property,

The sum of two interior angles is equal to an exterior angle.

Therefor,

∠C=∠A+∠B

(19x+3)°=(9x+16)°+(6x+5)°

19x+3=15x+21

4x=18

x=4.5

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Answer:

 0.0714

Step-by-step explanation:

The probability that the first is "working in nature" is 3/8.

The probability that the 2nd is "working in nature" is 2/7.

The probability that the 3rd is "not working in nature" is 5/6.

The probability that the 4th is "not working in nature" is 4/5.

Thus the probability that the first two of 4 opportunities are "working in nature" is ...

  (3·2·5·4)/(8·7·6·5) = 1/14 ≈ 0.0714

Answer:

a

Step-by-step explanation:

2x^2-4x 6x^2-5x

2x^2 times 6x^2= 12x^4

2x^2 times -5x= -10x^3

-4x times 6x^2= -24x^3

-4x times -5x= 20x^2

12x^4-10x^3-24x^3+20x^2

12x^4-34x^3+20x^2

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-2.7 x 10^-2 in scientific notation is -0.027.

Answer:-0.027

Step-by-step explanation:

We keep all of the numbers that's why there's still the 2 and 7 and it's negative, then we move the decimal point left 2 times because that is the power of 10.

When the number next to the 10 is positive, we would move the decimal point to the right, when it is negative like it is here (-2), it is moved to the left. I hope that helps!