What is the sum of 5.21 and 3.97?

Step-by-step explanation:

Hey, there!!

Let's simply work with it,

The given coordinates are, P(-2,3) and Q(5,4).

Now, finding the P' and Q'.

Reflection on x- axis .

P(x,y)---------> P' (x,-y)

P (-2,3)----------> P'(-2,-3)

Now, let's find Q'

Reflection on y-axis.

Q(x,y)----------> Q'(-x,y)

Q(5,4)---------> Q'(-5,4)

Now, The points are P'(-2,-3) and Q'(-5,4)

By distance formulae,

\(P'Q' = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } \)

Putting their values,

\(P'Q' = \sqrt{( { - 5 + 2)}^{2}( {4 + 3)}^{2} } \)

\(P'Q' = \sqrt{( { - 3)}^{2} + ( {7)}^{2} } \)

Simplifying them we get,

\(pq = \sqrt{58} \)

Therefore, the distance between P'and Q' is root under 58 units.

Hope it helps...

f(t) = t3 − 8t2 + 25t + 10. When all the parts are put together, the equation represents a combination of the 3 components, representing a law of motion for a particle.

This equation represents a law of motion, where t is measured in seconds and s in feet. This equation can be broken down into 3 parts; t3, -8t2 and 25t + 10. The t3 part of the equation represents a cubic function, which is usually associated with acceleration. The -8t2 part is a quadratic function, which is typically associated with velocity. Finally, the 25t + 10 is a linear function, which is usually associated with displacement. When all the parts are put together, the equation represents a combination of the 3 components, representing a law of motion for a particle.

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Answer:

s = p - q - 1

Step-by-step explanation:

q + 1 + s = p  Subtract q and 1 from both sides

q -q +1 - 1 + s = p - q -1

s = p - q - 1

Helping in the name of Jesus.

Answer:

f(x)= -2x+490

Step-by-step explanation:

f(x)=mx+b

where m=slope and b=y-intercept

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Toni had 17 points, Effie had 25 points and Linda had 18 points.

The question is asking to find the number of points each girl had in a girl's basketball game. To find out how many points Effie had, you must multiply Toni's points by 3, subtract 8, and then multiply the difference by 2. To find out how many points Linda had, you must add 9 to Toni's points and divide the sum by 3. The given information is that Effie scored 9 more than Toni and Linda combined.

Formula and Calculation:

Toni's Points = x

Effie's Points = 3x-8

Linda's Points = (x+9)/3

Effie scored 9 more than Toni and Linda combined, so:

3x-8 = x+9/3 + 9

2x-8 = x+9

x = 17

Therefore, Toni had 17 points, Effie had 25 points and Linda had 18 points.

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The solution of the inequality is, x ∈ (- ∞, 5) ∪ (10, ∞)

Where, x represent the number of totts.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

My friend Raw has either no more than 5 toots and more than 10 toots.

Now, Let number of toots = x

Hence, We get;

⇒ x < 5

And, x > 10

Thus, The solution of the inequality is,

⇒ x ∈ (- ∞, 5) ∪ (10, ∞)

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The coordinate vector [x]b is: [x]b = [c1, c2]^T = [3, 2/5]^T relative to the given basis B. 31 - - 11 - 3 and B = {b1, b2} 0 [3] O P 이 5

To find the coordinate vector [x]b of the vector x relative to the basis B = {b1, b2}, we need to express x as a linear combination of b1 and b2, and then write down the coefficients as the coordinate vector.
Let's first find the coefficients by solving the system of equations:
x = c1*b1 + c2*b2
where x = [3, -1]^T, b1 = [1, -1]^T, and b2 = [0, 5]^T.
Substituting the values, we get:
[3, -1]^T = c1*[1, -1]^T + c2*[0, 5]^T
which gives us the following two equations:
3 = c1

-1 = -c1 + 5c2
Solving for c1 and c2, we get:
c1 = 3
c2 = 2/5
Therefore, the coordinate vector [x]b is:
[x]b = [c1, c2]^T = [3, 2/5]^T
To find the coordinate vector [x]_B of the vector x relative to the given basis B, you need to express x as a linear combination of the basis vectors b1 and b2. Based on the information provided, we have:
x = (31, -11, -3)
B = {b1, b2}
However, it seems that the values of b1 and b2 are missing or not clearly provided. If you could provide the correct values for b1 and b2.

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Step-by-step explanation:

m(x) = x+3

y = x+3

=> x = y-3

m`¹(x) = x-3

If the function approaches a specific value (y = c) as x approaches infinity or negative infinity, then it has a horizontal asymptote at y = c.

To determine if a function has a horizontal asymptote, consider the behavior of the function as x approaches positive or negative infinity. The main idea is to analyze the end behavior of the function.

Degree of Polynomials:

If the degree of the numerator is less than the degree of the denominator, the function has a horizontal asymptote at y = 0 (the x-axis). If the degree of the numerator is equal to the degree of the denominator, divide the coefficients of the highest degree terms. The resulting ratio determines the horizontal asymptote. If the degrees are unequal, there is no horizontal asymptote.

Limits:

Take the limit of the function as x approaches positive or negative infinity. If the limit evaluates to a finite value, that value represents the horizontal asymptote. If the limit is infinite (∞) or does not exist, there is no horizontal asymptote.

Infinity:

If the function involves terms like exponential functions or logarithmic functions, analyze their behavior as x approaches infinity. Exponential functions with positive exponents tend to infinity, while those with negative exponents approach zero. Logarithmic functions tend to negative infinity as x approaches zero.

By considering these methods, you can determine if a function has a horizontal asymptote and find its equation or behavior as x approaches infinity or negative infinity. Remember to apply these techniques with caution and consider the specific characteristics of the function being analyzed.

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Mrs. Vilakazi will make a profit of r233,88 if she bakes 204 scones and sells 171.

The profit is the difference between the total revenue and the total cost.

The total cost is the cost per scone multiplied by the number of scones baked:

total cost = r0,53/scone × 204 scones = r108,12

The total revenue is the selling price per scone multiplied by the number of scones sold:

total revenue = r2,00/scone × 171 scones = r342,00

Therefore, the profit is:

profit = total revenue - total cost

profit = r342,00 - r108,12

profit = r233,88

Mrs. Vilakazi will make a profit of r233,88 if she bakes 204 scones and sells 171.

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The Weighted Average Cost of Capital (WACC) for Snuggly Baby Corp. is calculated based on the company's capital structure, including common equity, preferred equity, and bonds. The WACC is influenced by the expected returns and prices of these securities.

To calculate the WACC, we need to determine the proportion of each component in the capital structure and multiply it by its respective cost of capital.

For Snuggly Baby Corp., the capital structure consists of 6,130,000 shares of common equity, 1,006,000 shares of preferred equity, and 81,400 bonds.

The cost of common equity is calculated using the expected return and the price of the shares. Similarly, the cost of preferred equity is calculated using the expected return and the price of the preferred shares. The cost of debt, represented by the bonds, is calculated using the yield-to-maturity.

Once we have the costs of each component, we multiply them by their respective proportions in the capital structure and sum them up to determine the overall WACC. Please note that to provide an accurate calculation of the WACC, additional information is required, such as the market value of each component and the weights assigned to them in the capital structure. Without this information, it is not possible to provide an exact WACC calculation.

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To complete squares on the quadratic equation we need to add 16 in both sides.

Here we want to complete squares on the quadratic equation:

x^2 - 8x = 9

Remember the perfect square trinomial:

(a + b)^2 = a^2 + 2ab + b^2

We can rewrite the give expression as:

x^2 - 2*4*x = 9

Then we need toa add (-4)^2 = 16 in both sides, then we will get:

x^2 - 2*4*x + 16 = 9 + 16

(x - 4)^2 = 25

So we need to add 16 in both sides.

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The sample space for rolling a fair seven-sided die is S = {1, 2, 3, 4, 5, 6, 7}

The sample space for rolling a fair seven-sided die consists of the possible outcomes, which are the numbers that can appear on the die.

Since the die has seven sides, the numbers on the die must range from 1 to 7, inclusive.

Therefore, the sample space is:

S = {1, 2, 3, 4, 5, 6, 7}

Hence, the sample space for rolling a fair seven-sided die is S = {1, 2, 3, 4, 5, 6, 7}

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Cosine Similarity is a measure used to evaluate the similarity between two documents and is commonly used in text analysis for document similarity measurement.

Given two vectors A and B, the Cosine Similarity of A and B is given by the formula: CS (A, B) = A . B / ||A|| ||B||Where, . represents the dot product of two vectors, and ||A|| and ||B|| represent the magnitudes of A and B respectively.In this problem, we are given two vectors:

Document 1 (A) and Document 2 (B). They are as follows:

Document 1: [1, 1, 1, 1, 1, 0] let’s refer to this as A

Document 2: [1, 1, 1, 1, 0, 1] let’s refer to this as BTo find the cosine similarity between A and B, we can substitute the values of A and B in the formula and evaluate it.

CS (A, B) = A . B / ||A|| ||B||We need to calculate three things: the dot product of A and B, magnitude of A, and magnitude of B.

Dot product of A and B: A . B = 1 * 1 + 1 * 1 + 1 * 1 + 1 * 1 + 1 * 0 + 0 * 1= 4 Magnitude of A:

\(||A|| = √(1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 0^2)= √5 Magnitude of B: ||B|| = √(1^2 + 1^2 + 1^2 + 1^2 + 0^2 + 1^2)= √5\)

Substituting these values in the formula, we get:CS (A, B) = 4 / ( √5 * √5 )= 4 / 5 The cosine similarity between Document 1 and Document 2 is 4/5 or 0.8.

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Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

The first molecule will have a ZERO dipole moment since all the F atoms are at 120 degree making the net dipole zero.

A molecule is a group of two or more atoms held together by chemical bonds; depending on the context, the term may or may not include ions that meet this criterion.

A molecule is a particle composed of two or more atoms that are chemically bonded together; the number of atomic nuclei constituting a molecule is fixed. HCl(g), for example, is a molecule composed of one hydrogen atom bonded to one chlorine atom. It is a diatomic molecule because it is composed of two atoms.

The second molecule will have a NON ZERO dipole moment. The net dipole moment will be downwards. The third molecule will have a NON ZERO dipole moment.

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Answer:

B.)8ft

Step-by-step explanation:

Set up a proportional to the roof slope:

2/5 = x/20

Cross multiply:

40/5 = 5x/5

x=8ft

Answer: B) 8 ft

Step-by-step explanation:

\(\frac{2}{5}*\frac{4}{4} =\frac{8}{20}\)

Answer:

Variance (σ²) = 230

Step-by-step explanation:

Variance is a way to measure how spread out or varied a set of numbers is from the mean. It is calculated by subtracting the mean from each data point, squaring the result, and then taking the average of those squared differences.

Given data set:

To find the variance of a set of data, we first need to calculate the mean of the data by dividing the sum of the data points by the number of data points:

\(\textsf{Mean $(\overline{x})$}=\dfrac{251+224+237+255+268}{5}=\dfrac{1235}{5}=247\)

Subtract the found mean from each data point, and square the result:

\((251 - 247)^2 = 4^2=16\)

\((224 - 247)^2 = (-23)^2=529\)

\((237 - 247)^2 = (-10)^2=100\)

\((255 - 247)^2 = 8^2=64\)

\((268 - 247)^2 = 21^2=441\)

The variance of the data is the mean of the squared differences:

\(\textsf{Variance $(\sigma^2)$} = \dfrac{16 + 529 + 100 + 64 + 441}{5}=\dfrac{1150}{5}=230\)

Therefore, the variance of the given data set is 230.

The regular price of a ticket to the game is equal to $25.5.

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

From the data given in the question,

The total price paid for 14 tickets is $283.50.

Price of 1 ticket :  $283.50/14 = $20.25

Price saved per ticket = $5.25

The regular price of 1 ticket is :  $20.25 +  $5.25 = $25.5

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Answer:

okay so I spent alot of time tying to figure this out and then I had to go over to my cousin and ask her if it's correct and it is.

so! here is your answer and ofc have an amazing day good luck

Step-by-step explanation:

theres your answer in that photo i just put

The phrases that imply correlation without causation are:

These correlations do not imply a causal relationship, meaning that an increase or decrease in one variable does not directly cause a corresponding change in the other variable.

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Answer:

We can use the formula for continuous compounding:

A = Pe^(rt)

where A is the amount of money in the account after t years, P is the principal amount (initial deposit), e is the constant 2.71828 (from natural logarithms), r is the interest rate as a decimal, and t is the time in years.

We want to solve for t when the amount in the account is $30,000:

30,000 = 8,000e^(0.056t)

Divide both sides by 8,000:

3.75 = e^(0.056t)

Take the natural logarithm of both sides:

ln(3.75) = 0.056t

Solve for t by dividing both sides by 0.056:

t = ln(3.75) / 0.056 ≈ 20.1 years

Therefore, it will take Mark approximately 20.1 years for his account to reach $30,000.

Answer:

8/5

Step-by-step explanation:

[8-(-8)]/[2-(-6)] = 16/10 = 8/5

Answer:

1. y=3x-2 -> x= (y+2)/3

Step-by-step explanation:

You simply sub-in the m and b, then "reverse" the problem by doing the steps to get from the 2nd, to the first.

Answer:

Step-by-step explanation:

1.y=3x-2

2.y=2/5x+2

3.y=-1/2x+4

4.y=-4x+3

5.y=5x+18

8.y=-3/2+1

you didn't include 6 & 7 that's why i skipped them

hope this helped :)

1. The upper bound for the perimeter of the regular hexagon is 21.9 cm.

2. All figures on the calculator display for the calculation of Kelly's average speed is: 99.5 / 10.51 = 9.46717412

3. the lower bound for the area of the rectangle is 2.55 × 10⁵ mm²

4. Upper bound for area = 937.6525 cm²

1. The upper bound for the perimeter of the regular hexagon can be calculated by multiplying the length of one side by 6 (the number of sides in a hexagon):

Upper bound for perimeter = 6 × (3.6 + 0.05) = 21.9 cm (rounded to one decimal place)

2. Kelly's average speed can be calculated by dividing the distance she ran by the time she took:

Average speed = distance / time

The lower bound for the distance is 99.5 m (since 100 m was measured to the nearest meter, the actual distance could be as low as 99.5 m).

The lower bound for the time is 10.51 s (since 10.52 s was measured to the nearest hundredth of a second, the actual time could be as low as 10.51 s).

Therefore, the lower bound for Kelly's average speed is:

Average speed = 99.5 / 10.51 = 9.4617 m/s (rounded to 4 decimal places)

3. The length of the rectangle is 645 mm correct to the nearest 5 mm, which means it could be as small as 642.5 mm or as large as 647.5 mm. We can express this as:

645 mm ± 2.5 mm, similarly

400 mm ± 2.5 mm

Lower bound for length = 645 - 2.5 = 642.5 mm

Lower bound for width = 400 - 2.5 = 397.5 mm

Lower bound for area = 642.5 × 397.5 = 255393.75 mm²

Rounded to 3 significant figures, the lower bound for the area of the rectangle is 2.55 × 10⁵ mm².

4. To calculate the upper bound for the area of the rectangle, we need to multiply the upper bounds for the length and width of the rectangle:

Upper bound for length = 35 + 0.45 = 35.45 cm

Upper bound for width = 26 + 0.45 = 26.45 cm

Upper bound for area = 35.45 × 26.45 = 937.6525 cm²

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The ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

For given question,

We have been given the unit conversion.

A traditional unit of length in Japan is the ken

and 1 ken = 1.97 m

We need to find the the ratios of (a) square kens to square meters.

First we find the square of 1 ken.

⇒ 1 square kens = (1.97 m)²

⇒ 1 square kens = 1.97 × 1.97 m²

⇒ 1 square kens = 3.88 m²                  ..................(1)

And 1 square meters = 1 m²                 ................. (2)

Now we take the ratio of square kens to square meters.

From (1) and (2),

⇒ 1 ken² / 1 m² = 3.88 / 1

⇒ 1 ken² / 1 m² = 3.88

Therefore, the ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

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The results in APA format for the given values are as follows: Ot(75) = 1.60, p < .05; t(77) = 2.50, p < .05; t(75) = 1.60, p > .05; and t(76) = 1.60, p > .05.

To report the results in APA format, we need to provide the relevant statistics, degrees of freedom, t-values, and p-values. Let's break down the provided information step by step.

First, we have Ot(75) = 1.60, p < .05. This indicates a one-sample t-test with 75 degrees of freedom. The t-value is 1.60, and the p-value is less than .05, suggesting that there is a significant difference between the sample mean and the population mean.

Next, we have t(77) = 2.50, p < .05. This represents an independent samples t-test with 77 degrees of freedom. The t-value is 2.50, and the p-value is less than .05, indicating a significant difference between the means of two independent groups.

Moving on, we have t(75) = 1.60, p > .05. This denotes a paired samples t-test with 75 degrees of freedom. The t-value is 1.60, but the p-value is greater than .05. Therefore, there is insufficient evidence to reject the null hypothesis, suggesting that there is no significant difference between the paired observations.

Finally, we have t(76) = 1.60, p > .05. This is another paired samples t-test with 76 degrees of freedom. The t-value is 1.60, and the p-value is greater than .05, again indicating no significant difference between the paired observations.

In summary, the provided results in APA format are as follows: Ot(75) = 1.60, p < .05; t(77) = 2.50, p < .05; t(75) = 1.60, p > .05; and t(76) = 1.60, p > .05.

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Answer:

D.3

hope i was fast enough

Answer:

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