What is the perfect square of 4 with an exponent of 2

Each of the expressions has been simplified and solved by using properties of exponents as shown below.

In Mathematics and Geometry, an exponent is a mathematical operation that is written as an algebraic expression, so as to raise a quantity to the power of another.

Therefore, an exponent can be modeled by the following mathematical expression;

bⁿ

Where:

By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:

(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷

12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴

5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵

6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶

9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸

1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶

(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴

3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷

9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵

3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶

1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.

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The sum of the measures of the exterior angles of any polygon, including a triangle, is always 360 degrees.

We have,

An exterior angle of a polygon is formed by extending one of its sides outward.

In the case of a triangle, when we extend each side, we create three exterior angles.

These exterior angles are located outside the triangle.

The key concept to understand is that the sum of the exterior angles of any polygon is always 360 degrees.

This property holds true for all polygons, regardless of their shape or size.

To visualize this, imagine starting at any vertex of a triangle and moving along its sides while measuring the exterior angles.

As you move around the triangle, the sum of the exterior angles will always add up to 360 degrees.

This is because, at each vertex, the exterior angle supplements the interior angle to form a straight angle of 180 degrees.

In a triangle, each interior angle measures less than 180 degrees.

So, when we extend each side to create the exterior angles, they collectively compensate for the deficiency of the interior angles, resulting in a sum of 360 degrees.

Therefore,

The sum of the measures of the exterior angles of a triangle is always 360 degrees.

This principle holds true for all polygons, making it a fundamental property of geometry.

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Answer:

Step-by-step explanation:

y=3x^2+12x = 3x (x+4)

zeroes: x={0, -4}

y = x^2+20x+100 = (x+10)^2

zeroes: x = -10 (twice)  

or x={-10, -10}

Answer:29

Step-by-step explanation:

1885/65

The ratio of the horizontal change to the vertical change of a line would not be used to describe a slope. Thus the correct option is option C.

The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) of a line.

Slope=Vertical Change/Horizontal Change

This is also represented as the "ratio of rise to run of a line".

Slope=Rise/Run

In the given question, however, option C states that the "ratio of the horizontal change to the vertical change of a line".

Horizontal Change/ Vertical Change= 1/slope

This is an incorrect statement since the ratio of the horizontal change to the vertical change of a line is the reciprocal of the correct ratio.

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30 maybe, not to sure, sorry if its wrong

Answer:

3n - 7 = 2n + 5

Step-by-step explanation:

n=12

that is the answer

When we reflect every point over the x axis...

The rule you use is \((x,y) \to (x,-y)\)

The x coordinate stays the same while the y coordinate flips in sign (in this case from negative to positive)

The answer should be

780x + 1500y=31000

please correct me if i'm wrong

Answer:

its 780x+1600>29,000

Step-by-step explanation:

The answer is (-3, -6)

Step-by-step explanation:

turn the x into a y, and the y into a opposite x.

a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

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Answer:

−8r+13

Step-by-step explanation:

2+12−8r−1

=2+12+−8r+−1

Combine Like Terms:

=2+12+−8r+−1

=(−8r)+(2+12+−1)

=−8r+13

Answer:

81.7 in (nearest tenth)

Step-by-step explanation:

\(\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}\)

Given:

Substituting given value into the formula:

\(\begin{aligned}\implies \textsf{Circumference} & =2 \pi \cdot 13\\ & = 26 \pi\\ & = 81.7\: \sf in\:(nearest\:tenth)\end{aligned}\)

Based on the calculations, the value of number x is equal to 22.

In order to determine the value of x, we would translate the word problem into an algebraic expression.

For the expression, six less than twice a number x is given by:

2x - 6.

Next, we would equate it to 38:

2x - 6 = 38

2x = 38 + 6

2x = 44

x = 44/2

x = 22.

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If the provided SHA hash value is different from the one I calculated, it indicates that there has been a modification or alteration in the data or the process used to calculate the hash.

This inconsistency raises concerns about data integrity and the authenticity of the information.

SHA (Secure Hash Algorithm) is a cryptographic hash function that generates a unique hash value for a given input. It is designed to be highly sensitive to any changes in the input data, meaning even a small alteration in the data will result in a completely different hash value. Therefore, if the provided SHA hash value differs from the one I calculated, it suggests that either the input data has been tampered with, or there is an error in the hash calculation process.

In such a situation, it is important to investigate the cause of the discrepancy and determine the source of the error. It could be due to accidental data corruption, intentional tampering, or an error in the hash calculation algorithm or implementation. Validating the integrity of the data becomes crucial to ensure the accuracy and trustworthiness of the information.

To resolve the issue, a comparison of the original and modified data should be conducted, and the hash calculation process should be carefully reviewed. It is also advisable to verify the integrity of the data through other means, such as using digital signatures or checksums, to detect any unauthorized modifications.

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Answer:

D) - 2.2y - 1.8

Step-by-step explanation:

Given expression;

1.2y + 4.5 - 3.4y - 6.3

simplify the expression by collecting like terms

= (1.2y - 3.4y) + (4.5 - 6.3)

= -2.2y - 1.8

Therefore, the correct option is D.

D) - 2.2y - 1.8

Your lack of cogscitis has a previous probability of 0.5 according to Dr. B.

Prior probability quantifies how likely a theory is to be correct before any supporting data are taken into account. Your lack of cognitis has a previous probability of 0.5 according to Dr. B. This means that according to Doctor B, there is a 50/50 likelihood that you do not have cognitis before any supporting evidence is considered. This impartial viewpoint is frequently employed in scientific research and medical diagnostics. Prior probability is a crucial component of Bayesian inference, which is used to update a hypothesis' probability after all available data has been considered. Prior probability can help scientists and medical practitioners make better decisions.

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Answer:

86.4

Step-by-step explanation:

12% of 240 * 3 = 86.4

The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

log(6, 216) - log(6, 17)

To write log base 6 of 216 as a difference of logarithms, we can apply the Quotient Property of Logarithms. According to this property, the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator.

In this case, we have log base 6 of 216 divided by 17. By applying the Quotient Property, we can express this as the difference of two logarithms: log base 6 of 216 minus log base 6 of 17.

Now, let's simplify if possible. We can further evaluate the logarithms using the fact that log base a of b is equal to the exponent to which we must raise a to obtain b. In other words, log base a of b is the power to which we raise a to get b.

Therefore, log base 6 of 216 can be simplified as the exponent to which we raise 6 to obtain 216, which is 3. Similarly, log base 6 of 17 can be simplified as the exponent to which we raise 6 to obtain 17, which is less than 3.

Hence, the simplified expression becomes 3 - log base 6 of a number less than 6.

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The x-coordinate of the x-intercept of line k is -5/2.

Since this point lies on the x-axis, its y-coordinate is 0.

Given that the line has a y-intercept at the point (0, p), where p is a positive constant. This means that when x = 0, y = p.

As we know that the equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept.

Here, the slope is the negative of the fraction 2p/5, so the equation of line k is y = -2p/5 x + p.

Substitute y = 0 into the equation and solve for x:

0 = -2p/5 x + p

Subtract p from both sides and then multiply by 5/(-2p):

-2p/5 x = -p

x = (-p)(5/2p)

x = -5/2

Therefore, the x-coordinate of the x-intercept of line k is -5/2.

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Answer:

B)

the (8+7) x (10 + 7) x (6 + 4)

Step-by-step explanation:

Answer:

D- (8×10×6) + (7×7×4)

Step-by-step explanation:

The formula for volume is Length×Width×Height.

So you have to find the volume for each one individually then add them up together.

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:)

Answer:

70 miles

Step-by-step explanation:

30 (mi) +40 (mi) =70

Answer:

42

Step-by-step explanation:

Answer:

The answer would be 12.75.

Christina saved $12.75 on her 3 shirts

Step-by-step explanation:

Since it's a right triangle, you can use Pythagoras

a^2 + b^2 = c^2

We have b and c, we just need a, so let's plug it in

\( {x}^{2} + {24}^{2} = {25}^{2} \)

\( {x}^{2} + 576 = 625\)

\( {x}^{2} = 49\)

\(x = 7\)

Answer: 7ft

Step-by-step explanation:

hypotenuse (h) = 25

perpendicular (p) = 24

base (b) = ?

We know by using Pythagoras theorem

b = √h² - p²

= √ 25² - 24²

= √ 49

= 7 ft

It seems you're asking about the results of an experiment where a student modified a six-sided die by drilling a hole and filling it with lead weight, then rolling it 200 times.

You provided the observed frequencies for outcomes 1, 2, 3, 4, and 5, but the frequencies are not included in your question. However, I can still provide a general analysis of such an experiment. When a die is tampered with by adding weight, it can affect the probabilities of certain outcomes. The added weight may cause the die to be biased, making some outcomes more likely than others. In a fair, unmodified six-sided die, the probability of each outcome is equal, 1/6 or approximately 16.67%. After rolling the modified die 200 times, the student should record the frequencies of each outcome (1, 2, 3, 4, 5, and 6) and calculate the relative frequency (observed frequency / total number of rolls) for each side. By comparing the relative frequencies to the expected probability of 16.67%, the student can determine if the die is biased towards specific outcomes. If the relative frequencies are significantly different from the expected probabilities, it suggests the added weight has impacted the fairness of the die. In conclusion, drilling a hole and adding weight to a six-sided die may affect the probability distribution of the outcomes, resulting in a biased die. Analyzing the observed frequencies in comparison to the expected probabilities can help determine the degree of bias.

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Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

To match the capital budgeting method to its specific characteristic, we need to consider the characteristics of different capital budgeting methods.

Here are the commonly used capital budgeting methods and their characteristics:

Payback Period:

Characteristic: Measures the time required to recover the initial investment.

Description: The payback period method calculates the time it takes for a project to generate cash flows that equal or exceed the initial investment. It focuses on the time aspect and provides a quick assessment of liquidity and risk.

Net Present Value (NPV):

Characteristic: Incorporates the time value of money and provides an absolute dollar value.

Description: NPV calculates the present value of cash inflows and outflows over the project's life, taking into account the time value of money. It helps determine the project's profitability and indicates the amount of value created or lost.

Internal Rate of Return (IRR):

Characteristic: Considers the discount rate at which NPV equals zero.

Description: IRR is the discount rate that makes the NPV of a project equal to zero. It represents the project's expected rate of return and compares it to the required rate of return or the cost of capital. It helps determine the feasibility and attractiveness of the project.

Profitability Index (PI):

Characteristic: Measures the value created per unit of investment.

Description: The profitability index calculates the present value of future cash flows per unit of initial investment. It is obtained by dividing the present value of cash inflows by the initial investment. A profitability index greater than 1 indicates a positive net present value.

Accounting Rate of Return (ARR):

Characteristic: Focuses on the accounting profitability of the project.

Description: ARR measures the average annual profit generated by a project as a percentage of the initial investment or average investment. It assesses the project's profitability based on accounting figures such as net income or operating profit.

By matching the methods to their specific characteristics, we can summarize them as follows:

Payback Period: Measures the time required to recover the initial investment.

Net Present Value (NPV): Incorporates the time value of money and provides an absolute dollar value.

Internal Rate of Return (IRR): Considers the discount rate at which NPV equals zero.

Profitability Index (PI): Measures the value created per unit of investment.

Accounting Rate of Return (ARR): Focuses on the accounting profitability of the project.

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