What is the sum of the measures of the interior angles of the decagon?

Answer:

400 ml of lemon juice

Step-by-step explanation:

We know that there are 700 ml of salad dressing, and the ratio of lemon juice to vinegar is 4:3. We know that therefore, there are 7 equal parts. To find how many ml are in one part, we divide 700 by 7, which gives us 100. Then we can multiply that answer by 4 to find how many ml of lemon juice and 3 to find how many ml of vinegar.

100 x 4 = 400

Therefore, Vicky uses 400 ml of lemon juice.

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

60

Step-by-step explanation:

119-59 = 60

The  values of  A = 2 and B = -4.

And, the value of ∫(10\(x^2\)+ 8/[(x+1)(5x-1)]) dx is given by 2x + 2ln|x+1| - 4ln|5x-1| + C, where C is the constant of integration.

(a) The expression is 10\(x^2\) + 8/[(x+1)(5x-1)]. To write it in the desired form, we need to find A and B such that:

10\(x^2\) + 8/[(x+1)(5x-1)] = 2 + A/(x+1) + B/(5x-1)

To find the values of A and B, we can multiply both sides of the equation by the common denominator, which is (x+1)(5x-1):

(10\(x^2\) + 8) = 2(x+1)(5x-1) + A(5x-1) + B(x+1)

Expanding the right side of the equation:

10\(x^2\) + 8 = 10\(x^2\) - 2x + 4 + 5Ax - A + Bx + B

Comparing the coefficients of like terms on both sides, we can determine the values of A and B:

-2x + 5Ax + Bx = 0x

-2 + 5A + B = 0

Solving the system of equations, we find A = 2 and B = -4.

(b) Using the values of A = 2 and B = -4, we can rewrite the expression as:

10\(x^2\) + 8/[(x+1)(5x-1)] = 2 + 2/(x+1) - 4/(5x-1)

Now, to find the integral of the expression 10\(x^2\) + 8/[(x+1)(5x-1)] with respect to x, we can split it into three separate integrals:

∫(10\(x^2\) + 8/[(x+1)(5x-1)]) dx = ∫2 dx + ∫2/(x+1) dx - ∫4/(5x-1) dx

The integral of a constant is the constant multiplied by x:

∫2 dx = 2x

The integral of 1/(x+1) can be found by substituting u = x+1:

∫2/(x+1) dx = 2∫1/u du = 2ln|u| + C = 2ln|x+1| + C

Similarly, the integral of 1/(5x-1) can be found by substituting v = 5x-1:

∫4/(5x-1) dx = 4∫1/v dv = 4ln|v| + C = 4ln|5x-1| + C

Combining the results, we have:

∫(10\(x^2\)+ 8/[(x+1)(5x-1)]) dx = 2x + 2ln|x+1| - 4ln|5x-1| + C

Therefore, the value of ∫(10x^2 + 8/[(x+1)(5x-1)]) dx is given by 2x + 2ln|x+1| - 4ln|5x-1| + C, where C is the constant of integration.

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If f and g are differentiable, then d dx[f(x) g(x)] = f 0 (x) g 0 (x).- TRUE

This statement is true. The product rule of differentiation states that

d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x).

Therefore, if f(x) and g(x) are differentiable, then,

d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)

= f0(x)g(x) + f(x)g0(x),

which is equivalent to:

d/dx[f(x)g(x)] = f0(x)g(x) + f(x)g0(x).

Therefore, the statement is true.
The statement is TRUE (T). If f and g are differentiable, then the product rule applies when differentiating the product f(x)g(x). The product rule states that the derivative of a product of two functions is:
d/dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
This is not the same as f'(x)g'(x), which is stated in the question.

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Answer:  (- 2h + 1) + 2(3h - 4) = 4h -7

Step-by-step explanation:

First, remove unnecessary parentheses

- 2h + 1 + 2(3h - 4)

then distribute 2 through the parentheses

- 2h + 1 + 2(3h - 4) = -2h + 1 + 6h -8

Combine like terms

-2h + 1 + 6h -8 = 4h + 1 - 8

1-8= 7

So the answer is

4h - 7

Answer: 180

Step-by-step explanation:

1) Add the two angles together

160 + 20 = 180

180

You can tell this because a 180-degree line is flat, just like in this picture.

Answer:

2806.72

Step-by-step explanation:

use the phythagrome theorm

Answer:

\(\sqrt{x^{2}-7\)

Step-by-step explanation:

Negative exponents flip the fraction, fraction exponents imply a radical to the denominator's degree, so flip the fraction and take the square root of what is in parentheses

We know that :

\(\bigstar \ \ \boxed{\mathsf{a^{-1} = \dfrac{1}{a}}}\)

\(\mathsf{Given \ question \ is : \dfrac{1}{(x^2 - 7)^{\frac{-1}{2}}}}\)

Using the above formula, we can write it as :

\(\implies \mathsf{\dfrac{1}{\dfrac{1}{(x^2 - 7)^{\frac{1}{2}}}}}\)

\(\implies \mathsf{(x^2 - 7)^{\frac{1}{2}}}\)

\(\implies \mathsf{\sqrt{x^2 - 7}}\)

False.

Dialtions change the size of the figure but does not change the angles

Answer:

i think it is false

Step-by-step explanation:

UV = 11 and TV = 41

A line segment has two fixed end points in a line. The length of the line segment is the distance between two fixed points. The length can be measured by units such as centimeters, millimeters, feet or inches

The points on a line are matched one to one with the real numbers in ruler postulate.  Coordinate of the point is the real number that corresponds to a point. The distance between points A and B (AB) is equal to the difference of the coordinates of A and B.

As given,

TU = 16, UV = x+4  and TV = 8x -15

TU + UV = TV

16 + x+4 = 8x -15

16 + 4 +1 5 = 8x - x

35 = 7x

x = 35/5

x= 7

We can find UV = x + 4 by substituting the value of x

= 7 +4

= 11

and TV = 8x - 15

= (8*7) - 15

=56 - 15

=41

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Answer: 7.6 is the base

Step-by-step explanation: To find this, we work backwards. So, multiply the area by 2, then divide that by the height. That gets us the number 7.6 in this case. To test this, we can then follow the normal steps to getting area of a triangle

Answer:

7.6

Step-by-step explanation:

The screen shot below is your explanation.

Answer:

\( \sqrt{3} \)

Step-by-step explanation:

- since it's an isosceles triangle, the other two angle is the same, so 180-90÷2=45

- i use SOH, CAH, TOA rule and in this case, i use SOH.

Answer:

x = √3

Step-by-step explanation:

Let us use the Pythagoras theorem to find the value of x.

Accordingly,

x² + x² = (√6)²

2x² = 6

Divide both sides by 2.

x² = 3

Put square roots on both sides.

x = √3

The answer is: 0.0362

The total number of Master's degree holders = 2848 (from the question)

In order to choose people 40 and above from this Master's degree holder subset,

You choose:

People 40-49 AND People 50 and over.

Number of people 40-49 = 475

Number of people 50 and over = 699

But we also need to take into consideration, the probability of picking a person 40-49 years old OR 50 and over

total Number of people 40 - 49 are 3518

The total Number of people 50 and above are 6518

Thus, we can write the probability as:

The final answer is: 0.0362

We show that p(n) = Θ(\(n^k\)) for constants c1 = a_k, c2 = (|a_k| + |a_k-1| + ... + |a_0|), and n0 ≥ 1.

To show that p(n) = Θ(\(n^k\)), we need to prove that p(n) is both bounded above and bounded below by multiples of \(n^k\) for sufficiently large values of n. In other words, we need to find constants c1, c2, and n0 such that c1 * \(n^k ≤ p(n) ≤ c2 * n^k\)for all n ≥ n0.

Since p(n) is a polynomial of degree k, we know that for sufficiently large n, the dominant term in p(n) will be a_k * \(n^k\). Thus, we can choose c1 = a_k to bound p(n) from below.

To bound p(n) from above, we can observe that for sufficiently large n, each term in the polynomial p(n) will be dominated by the highest degree term a_k * \(n^k\). Therefore, we can choose c2 = (|a_k| + |a_k-1| + ... + |a_0|) to bound p(n) from above.

Now, for n ≥ n0, we have:

\(c1 * n^k ≤ a_k * n^k + a_k−1 * n^k−1 + … + a_1 * n + a_0 = p(n) ≤ (|a_k| + |a_k-1| + ... + |a_0|) * n^k = c2 * n^k.\)

Therefore, we have shown that p(n) = Θ(\(n^k\)) for constants c1 = a_k, c2 = (|a_k| + |a_k-1| + ... + |a_0|), and n0 ≥ 1.

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The net Commission or proceeds due to Mark Ofori from the sale of the equipment truck and tractor is £127,068.96.

Given data

Commission rates on gross proceeds from the truck = 8%

Commission rates on gross proceeds from the tractor =  8. 45%

Selling truck at =  $62,500

Selling a tractor at = $88500

Pay to deliver the truck =  $510

Pay to deliver the tractor = $732

Total gross proceeds from the truck = selling charges + delivery charges  = $62,500 + $510 = £63,010

The tractor's gross sales earnings =  £88,500 + £732 = £89,232.

Ussif and Co. charged a commission on the truck = 0.080 x £63,010

= £5,040.80

Ussif and Co. charged a commission on the tractor = 0.0845 x £89,232

= £7,542.24.

We deduct the total gross proceeds from the total commission paid by Ussif and Co.

Net proceeds = total gross proceeds - total commission

= (£63,010 + £89,232) - (£12,583.04)

= £139,652 - £12,583.04

= £127,068.96

Therefore, the net proceeds of the truck and tractor due to Mark Ofori is £127,068.96.

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The equation of the line in fully simplified intersect is y = mx + b

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Answer:

-3 + -6= -9

because there is answer given

Answer: r=0

Step-by-step explanation: Hope this help :D

If the sample size is large and the probability of success is not too close to 0 or 1, using the normal distribution to approximate the binomial probability will generally give a more accurate answer than using the binomial tables. However, if the sample size is small or the probability of success is very close to 0 or 1, using the binomial tables may be more accurate.

If the sample size is large (typically, n ≥ 30) and suppose that the probability of success (p) is not too close to 0 or 1, then we can use the normal distribution. As it gives more approximate value to the binomial probability which will generally give a more accurate answer than using the binomial tables.

This is because the normal distribution provides a more precise approximation of the binomial distribution as the sample size increases.

However, if the the probability of success is very close to 0 or 1 or sample size is small then using the binomial tables to calculate the probability directly may be more accurate. In general, it's important to check the conditions for using the normal approximation before using it and to use good judgment in deciding which method is more appropriate for a given problem.

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Answer: 0.000032672

Step-by-step explanation: use long division or a calculator to solve.

Answer:

Step-by-step explanation:

To find the eigenvalues of a matrix M, we need to solve the characteristic equation det(M - λI) = 0, where I is the identity matrix of the same size as M, and λ is the eigenvalue we are trying to find.

For the matrix M = [ -4.5 2.5

-7.5 5.5 ]

the characteristic equation is:

det(M - λI) = det([ -4.5 - λ 2.5

-7.5 5.5 - λ ])

Expanding this determinant using the first row, we get:

(-4.5 - λ) (5.5 - λ) - 2.5 (-7.5) = 0

Simplifying and rearranging, we get:

λ^2 - λ - 6 = 0

This is a quadratic equation with solutions:

λ = (1 ± √(1 + 24))/2

λ = (1 ± 5)/2

So the possible eigenvalues of M are λ = -2 or λ = 3.

Note that we have not yet found the eigenvectors associated with each eigenvalue. To do so, we need to solve the equation (M - λI)x = 0 for each eigenvalue. This will give us a set of linearly independent eigenvectors that span the eigenspace associated with that eigenvalue.

The possible eigenvalues are:

λ1 = 1/2 + (√(11)/2)i

λ2 = 1/2 - (√(11)/2)i

To find the eigenvalues of the given matrix, we need to solve the characteristic equation:

|−4.5 − λ 2.5| = (−4.5 − λ)(5.5 − λ) − (−7.5)(2.5)

|−7.5 5.5 − λ| = λ² − 1λ + 3

Expanding the determinant and simplifying, we get:

λ² − 1λ + 3 = 0

Using the quadratic formula, we can solve for λ:

λ = (1 ± √(1 - 4(1)(3))) / 2

= (1 ± √(1 - 12)) / 2

= (1 ± √(-11)) / 2

Since the discriminant is negative, there are no real eigenvalues. The two eigenvalues are complex conjugates:

λ1 = (1 + √(-11)) / 2

λ2 = (1 - √(-11)) / 2

Therefore, the possible eigenvalues are:

λ1 = 1/2 + (√(11)/2)i

λ2 = 1/2 - (√(11)/2)i

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Answer:

Step-by-step explanation:

answer should be 0.39

The probability that the placekicker will make 4 of his next 5 attempts from the 20-yard line is 0.39.

Probability in mathematics is the possibility of an event in time. In simple words how many times does that incident is happening in any given time interval?

Given:

A placekicker for a football team makes field goals 85% of the time when kicking from the 20-yard line.

Assuming that field goal attempts can be considered random events.

P = 0.85

n = 5

Standard deviation = √{5 x 0.85 x (1 - 0.85) = 0.79

The probability that the placekicker will make 4 of his next 5 attempts from the 20-yard line is,

= P (X ≥ 4)

= P (X ≥ 3.5)

= 1 - P(X < 3.5)

= 0.39

Therefore, the probability is 0.39.

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Answer:

---------------------

The angle formed by a tangent and secant is half the difference of the intercepted arcs:

Find the measure of ∠MLJ by substituting 4 for x in the angle measure:

y = 29 - 0.75x (option C)

The initial amount of gallons of diesel fuel = 29 gallons

Rate of consumption of fuel = 0.75 gallons per hour

we write the above information in the form of a liear equation:

y = mx + c

m = rate of consumption of fuel = 0.75 gallons per hour

c = intial amout of diesel fuel = 29

SInce, we are using up the fuel, it means the initial amount will be reducing every hour.

Our rate of consumption will be negative.

The equation becomes:

y = - 0.75x + 29

y = 29 - 0.75x (option C)

Answer: show a picture please

Step-by-step explanation:

(a) The predicted amount of money spent on entertainment for a student who doesn't work any hours is $1.32.

(b) The predicted amount of money spent on entertainment for a student who works 2 hours is $5.

(c) The expected increase in money spent on amusement is $1.84.

(a) To find the predicted amount of money spent on entertainment for a student who doesn't work any hours (x = 0), we can substitute x = 0 into the equation of the line:

y = 1.84x + 1.32

y = 1.84(0) + 1.32

y = 0 + 1.32

Therefore, the predicted amount of money spent on entertainment for a student who doesn't work any hours is $1.32.

(b) To find the predicted amount of money spent on entertainment for a student who works 2 hours (x = 2), we substitute x = 2 into the equation:

y = 1.84x + 1.32

y = 1.84(2) + 1.32

y = 3.68 + 1.32

y = 5

Therefore, the predicted amount of money spent on entertainment for a student who works 2 hours is $5.

(c) To find the predicted increase in the amount of money spent on entertainment for an increase of one hour in time worked, we can compare the predicted amounts for x and x+1. Let's calculate the difference:

For x: y1 = 1.84x + 1.32

For x+1: y2 = 1.84(x+1) + 1.32

The predicted increase in the amount of money spent on entertainment is given by y2 - y1:

(y2 - y1) = [1.84(x+1) + 1.32] - [1.84x + 1.32]

Simplifying:

(y2 - y1) = 1.84x + 1.84 + 1.32 - 1.84x - 1.32

The x terms cancel out, and we're left with:

(y2 - y1) = 1.84

As a result, for every additional hour worked, the expected increase in money spent on amusement is $1.84.

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Complete question:

The scatter plot shows the number of hours worked, X and the amount of money spent on entertalnment; Y, by each of 23 students. Amount 0f Money spent On entertainment (in dollars) Number of hours worked Use the equation of the line of best fit, y=1.84x+1.32, to answer the questions below Give exact answers not rounded approximations.

(a) What is the predicted amount of money spent on entertainment for a student who doesn't work any hours?

(b) What Is the predicted amount of money spent on entertainment for a student who works [2 hours?

(c) For an increase of one hour In time worked, what is the predicted increase In the amount of money spent on entertainment?

Answer:

D

Step-by-step explanation:

For a circle, the equation of the circumference is c = π * 2r (radius). Since in this case, the circumference is 15.3, that means π * 2r = 15.3. I'm going to assume that pi is 3.14 because the four answers aren't particularly close to each other. This means that 2r = approx. 4.872. If you then divide both sides by 2 you get r = approx. 2.436, which is closest to answer D.