how do i solve this?

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\( \frac{-9 y-81}{y+9} \) simplifies to -9.

To simplify the given expression, \( \frac{-9 y-81}{y+9} \), we need to factor out the common factor of -9 from the numerator.

Factor out the common factor of -9 from the numerator.
\( \frac{-9(y+9)}{y+9} \)

Simplify the expression by canceling out the common factor of (y+9) from the numerator and denominator.
\( \frac{-9 \cancel{(y+9)}}{\cancel{y+9}} \)

The final simplified expression is -9.
\( -9 \)

\( \frac{-9 y-81}{y+9} \) simplifies to -9.

It is important to check for any restrictions on the variable y. In this case, y cannot be equal to -9, as it would make the denominator of the original expression equal to 0 and the expression would be undefined. Therefore, the simplified expression is valid for all values of y except -9.

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The y-intercept of f(x)=−3(x−2)(x+1)(x+4)  is 0,the y-intercept of f(x)=x2(x−1)3(x−4)  is 0.

f(x)=−3(x−2)(x+1)(x+4)End Behavior:  The end behavior of this function is that as x approaches negative infinity, the function approaches negative infinity, and as x approaches positive infinity, the function approaches positive infinity.

Model Degree: This is a cubic function, as the highest degree of the function is 3. Leading Coefficient: The leading coefficient of this function is -3. End Behavior (using limit notation):

lim x→-∞ f(x) = -∞
lim x→+∞ f(x) = +∞
y-intercept: The y-intercept of this function is 0.

f(x)=x2(x−1)3(x−4)End Behavior: The end behavior of this function is that as x approaches negative infinity, the function approaches negative infinity, and as x approaches positive infinity, the function approaches positive infinity.

Model Degree: This is a quartic function, as the highest degree of the function is 4. Leading Coefficient: The leading coefficient of this function is 1. End Behavior (using limit notation):
lim x→-∞ f(x) = -∞
lim x→+∞ f(x) = +∞

y-intercept: The y-intercept of this function is 0.

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The coefficient is 3 and, in the situation, it represents the distance covered per unit

From the question, we have the following parameters that can be used in our computation:

M = 20 + 3d

Given an expression ax, where the variable is x

The coefficient in this variable is a

Using the above as a guide, we have the following:

The coefficient in M = 20 + 3d is 3

And it represents the slope of the relation

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The average of the first ten terms of the series is 306.9. Alternative C. is correct.

The average of the first ten terms in a geometric series can be found by using the formula for the sum of a geometric series and then dividing by the number of terms. The formula for the sum of a geometric series is:

S = a(1 - rⁿ) / (1 - r)

Where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 3, r = 2, and n = 10. Plugging these values into the formula, we get:

S = 3(1 - 2¹⁰) / (1 - 2)
S = 3(-1023) / (-1)
S = 3069

Now, to find the average of the first ten terms, we simply divide the sum by the number of terms:

Average = S / n

Average = 3069 / 10

Average = 306.9

Therefore, the answer is (C) 306.9.

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The area of triangle PTSQ with sides ST=4, TQ=20, PQ=25, PS=13 is calculated to be 260 square units.

To find the area of triangle PTSQ, we can use the formula for the area of a triangle:

Area = (1/2) × base × height

First, we need to find the height of the triangle. We can do this by drawing an altitude from point T to side PS. Let the foot of the altitude be point R. Then, triangle TRS is similar to triangle TQP by the AA similarity criterion, since angle TRS = angle TQP (both are right angles), and angle STR = angle PTQ (both are vertical angles).

Therefore, we can set up the following proportion:

TR / TS = TQ / TP

TR / 13 = 20 / (25 - TP)

Cross-multiplying, we get:

25TR - 13TQ = 260

Substituting the given values, we get:

25TR - 13(20) = 260

25TR = 520

TR = 20.8

Now, we can use the formula for the area of triangle PTSQ:

Area = (1/2) × PQ × TR

Substituting the given values, we get:

Area = (1/2) * 25 * 20.8 = 260 square units

Therefore, the area of triangle PTSQ is 260² units.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The t-statistic associated with this sample if information from the government reveals that the actual average salary is 2

The t-statistic can be calculated using the formula: t = (sample mean - population mean) / (sample standard deviation / √(sample size))

In this case, the sample mean is $50,000, the population mean is $49,000, the sample standard deviation is $5,000, and the sample size is 100.

Plugging these values into the formula, we get:

t = ($50,000 - $49,000) / ($5,000 / √(100))

t = $1,000 / ($5,000 / 10)

t = $1,000 / $500

t = 2

Therefore, the t-statistic for this sample indicates that the actual average pay is $2, according to data from the government.

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The coordinates after the dilation with a scale factor of 1.5 are given as follows:

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The scale factor for this problem are given as follows:

k = 1.5.

Hence the coordinates of the image are obtained multiplying the coordinates of the original image by 1.5.

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Statement 1, BD ≅ SD and ED ≅ TD would not be sufficient to prove quadrilateral BEST is a parallelogram.

A quadrilateral is a parallelogram if it satisfies any of the following conditions: Opposite sides are parallel and congruent, Opposite angles are congruent, Diagonals bisect each other. If a quadrilateral satisfies any of these conditions, it is a parallelogram.

Although BD ≅ SD and ED ≅ TD indicate that the diagonals bisect each other, it does not necessarily mean that the opposite sides are parallel. For example, a kite has diagonals that bisect each other but its opposite sides are not parallel.

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Mr Tan earns a total of $96.

Let the selling price of a cup of apple juice be x.

Then the selling price of a cup of lemon juice is 3/2 times x, which is (3/2)x.

Let the number of cups of lemon juice sold be L, and the number of cups of apple juice sold be A.

We know that for every 2 cups of lemon juice sold, Mr Tan sells 5 cups of apple juice. So we can write:

A = (5/2)L

His earnings from apple juice minus his earnings from lemon juice is $12. So we can write:

Ax - L(3/2)x = $12

Simplifying this equation, we get:

(5/2)Lx - (3/2)Lx = $12

Lx = $24

Now we can use this information to find the values of L and A:

L = $24/x

A = (5/2)L = (5/2)($24/x) = $60/x

Finally, we can calculate Mr Tan's total earnings by adding his earnings from apple juice and lemon juice:

Total earnings = Ax + L(3/2)x

= $60 + (3/2)($24)

= $96

Therefore, Mr Tan earns a total of $96.

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We can start by first finding the value of 8°F, where F represents the function f(x) = x² - 8.

So, we have:

8°F = 8(f(x)) = 8(x² - 8) = 8x² - 64

Now, substituting x = -3, we get:

8°F(-3) = 8(-3)² - 64 = 8(9) - 64 = 8

Finally, substituting this value into the given expression, we have:

8°F(-3) - 4 = 8 - 4 = 4

Therefore, the statement "True" is correct.

1. The x-intercepts are x=3 and x=1. Since 3 is greater than 1, the greatest x-intercept is x=3.

2. The y-intercept is -8.

3. g(x) has the greatest y-intercept.

1. The x-intercept of a function is found by setting f(x) = 0 and solving for x. So for f(x) = 2x²-8x+6, we have:

0 = 2x²-8x+6

0 = x²-4x+3

0 = (x-3)(x-1)

Therefore, the x-intercepts are x=3 and x=1. Since 3 is greater than 1, the greatest x-intercept is x=3.

2. The y-intercept of a function is found by setting x = 0 and evaluating f(x). So for f(x) = -x²-6x-8, we have:

f(0) = -(0)²-6(0)-8 = -8

Therefore, the y-intercept is -8.

For g(x), we have:

g(0) = 2(0)²+16(0)+31 = 31

Therefore, g(x) has the greatest y-intercept.

3. Similar to question 2, we find the y-intercept by setting x=0 and evaluating f(x):

f(0) = -(0)²-8(0)-12 = -12

Therefore, the y-intercept is -12.

4. To find the x-intercepts of f(x) = (x+8)²-4, we set f(x) = 0:

0 = (x+8)²-4

4 = (x+8)²

±2 = x+8

x = -8 ± 2

Therefore, the x-intercepts are x=-6 and x=-10. Since -6 is greater than -10, the greatest x-intercept is x=-6.

5. The axis of symmetry of a quadratic function in the form f(x) = ax²+bx+c is given by x = -b/(2a).

For f(x) = -2x²-12x-16, we have a = -2 and b = -12, so the axis of symmetry is x = -(-12)/(2*-2) = 3.

For g(x) = 2x²+16x+31, we have a = 2 and b = 16, so the axis of symmetry is x = -16/(2*2) = -4.

Therefore, f(x) has the greatest axis of symmetry.

6. To find the y-intercept, we set x=0 and evaluate the functions:

f(0) = 2(0-3)²+1 = 19

g(0) = 2(0+3)²+2 = 20

Therefore, g(x) has the greatest y-intercept.

7. To find the x-intercept, we set f(x) = 0:

0 = -(x+1)²+1

1 = (x+1)²

±1 = x+1

x = -1 ± 1

Therefore, the x-intercepts are x=-2 and x=0. Since -2 is greater than 0, g(x) has the greatest x-intercept.

8. Similar to question 6, we find the y-intercept by setting x=0 and evaluating the functions:

f(0) = -2(0+2)²+2 = -6

g(0) = 2(0+3)²-4 = 14

Therefore, g(x) has the greatest y-intercept.

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The probability that no more than 32 patients out of 120 will have had side effects from the medicine is 0.8289.

The probability that a patient has side effects from the medicine is 23%, or 0.23. We can use the normal approximation to the binomial to find the probability that among 120 patients, no more than 32 will have had side effects.

First, we need to find the mean and standard deviation of the binomial distribution. The mean is np, where n is the number of trials (120 patients) and p is the probability of success (0.23). The mean is 120*0.23 = 27.6.

The standard deviation is sqrt(np(1-p)), or sqrt(120*0.23*(1-0.23)) = 4.65.

Now we can use the normal approximation to find the probability that no more than 32 patients will have had side effects. We need to find the z-score for 32, which is (32-27.6)/4.65 = 0.95. Using a z-table, we find that the probability of getting a z-score less than or equal to 0.95 is 0.8289.

Therefore, the probability that no more than 32 patients out of 120 will have had side effects from the medicine is 0.8289.

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Answer: $460

Step-by-step explanation:

To calculate the total amount of money you will pay back after borrowing $400 for 5 years at an annual interest rate of 3%, you can use the following formula:

Total amount = principal + interest

Principal = the amount you borrowed = $400

Interest = the amount of interest paid over the 5 years period.

To calculate the interest, we can use the formula:

Interest = Principal x Rate x Time

Rate = the annual interest rate expressed as a decimal = 0.03

Time = the time period in years = 5

So, the interest for the 5-year period is:

Interest = $400 x 0.03 x 5 = $60

Therefore, the total amount of money you will pay back is:

Total amount = $400 + $60 = $460

You will pay back $460 over five years if you borrow $400 at an annual interest rate of 3%.

Answer: To calculate the total amount of money to be paid back for borrowing $400 for 5 years at an annual interest rate of 3%, we need to use the formula for simple interest:

Simple interest = Principal x Rate x Time

where:

Principal = $400 (the amount borrowed)

Rate = 3% per year

Time = 5 years

Plugging these values into the formula, we get:

Simple interest = $400 x 0.03 x 5

= $60

Therefore, the total amount of money to be paid back is the sum of the principal and the simple interest:

Total amount = Principal + Simple interest

= $400 + $60

= $460

So, you will need to pay back a total of $460 after 5 years of borrowing $400 at an annual interest rate of 3%.

Step-by-step explanation:

The determinant of the given matrix is 12.

Answer: \(\left|\begin{array}{cccc}-3 & 0 & 1 & 2 \\ -1 & 4 & 2 & 1 \\ 0 & 3 & -1 & -2 \\ 5 & -1 & 1 & 0\end{array}\right| = 12\)

The determinant of a 4x4 matrix can be calculated using the formula: \( \left|\begin{array}{cccc}a & b & c & d \\ e & f & g & h \\ i & j & k & l \\ m & n & o & p\end{array}\right| = a\left|\begin{array}{ccc}f & g & h \\ j & k & l \\ n & o & p\end{array}\right| - b\left|\begin{array}{ccc}e & g & h \\ i & k & l \\ m & o & p\end{array}\right| + c\left|\begin{array}{ccc}e & f & h \\ i & j & l \\ m & n & p\end{array}\right| - d\left|\begin{array}{ccc}e & f & g \\ i & j & k \\ m & n & o\end{array}\right|\)

Plugging in the values from the given matrix, we get: \(-3\left|\begin{array}{ccc}4 & 2 & 1 \\ 3 & -1 & -2 \\ -1 & 1 & 0\end{array}\right| - 0\left|\begin{array}{ccc}-1 & 2 & 1 \\ 0 & -1 & -2 \\ 5 & 1 & 0\end{array}\right| + 1\left|\begin{array}{ccc}-1 & 4 & 1 \\ 0 & 3 & -2 \\ 5 & -1 & 0\end{array}\right| - 2\left|\begin{array}{ccc}-1 & 4 & 2 \\ 0 & 3 & -1 \\ 5 & -1 & 1\end{array}\right|\)

Calculating the determinants of the 3x3 matrices, we get: \(-3(-4) - 0(0) + 1(-8) - 2(-4) = 12 - 8 + 8 = 12\)

Therefore, the determinant of the given matrix is 12.

Answer: \(\left|\begin{array}{cccc}-3 & 0 & 1 & 2 \\ -1 & 4 & 2 & 1 \\ 0 & 3 & -1 & -2 \\ 5 & -1 & 1 & 0\end{array}\right| = 12\)

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To find all the vectors that are in the subspace V of R³, we need to solve the system of equations given in the question. We can use the Gaussian elimination method to do this.

First, let's write the system of equations in matrix form:
\[ \begin{bmatrix} 1 & 2 & -3 \\ 0 & 1 & -2 \end{bmatrix} \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \]

Now, we can use the Gaussian elimination method to find the solution:
Step 1: Subtract 2 times the second equation from the first equation to eliminate x₂:
\[ \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & -2 \end{bmatrix} \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \]
Step 2: Solve for x₁ and x₂ in terms of x₃:
x₁ = -x₃
x₂ = 2x₃
Step 3: Write the solution in vector form:
\[ \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} = \begin{bmatrix} -x_{3} \\ 2x_{3} \\ x_{3} \end{bmatrix} = x_{3} \begin{bmatrix} -1 \\ 2 \\ 1 \end{bmatrix} \]

So, the subspace V is the set of all scalar multiples of the vector (-1, 2, 1). In other words, V = {x₃(-1, 2, 1) | x₃ ∈ R}.

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Answer:

Step one: The parent absolute value function will be reflected across the x-axis and translated down four units.

Step two: The vertex of the parent is (0,0). A reflection does not change the vertex, but the translation will move the vertex (plot 0,-4)

Step three: Evaluate the function at two more points on either side of the vertex. f(-1)=-5 f(1)=-5

Step-by-step explanation:

sorry if im wrong =/

The solution to the system is (x, y, z) = (6, 0, -2).

To solve the system, we can use the elimination method. First, we will eliminate x from the second and third equations by adding the first equation to them:

{5y - 10z = 20
{-3y + 4z = -8

Next, we will eliminate y from the second and third equations by subtracting the second equation from the third equation:

{15y - 30z = 60
{15y + 20z = -40
{-10z = 20

Now we can solve for z:
z = -2

Next, we can substitute z back into the second equation to solve for y:

5y - 10(-2) = 20
2y + 20 = 20
2y = 0
y = 0

Finally, we can substitute z and y back into the first equation to solve for x:

2x + 3(0) - 4(-2) = 20
2x + 8 = 20
2x = 12
x = 6

So the solution to the system is (x, y, z) = (6, 0, -2).

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The x-coordinate of point P is approximately -5.33.

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.

To find the x-coordinate of point P, we can use the formula:

x-coordinate of P = (4x-coordinate of A + 2x-coordinate of B) / (4+2)

We are given the coordinates of points A and B:

A(-8, -9) and B(0, -2)

Using the formula, we can substitute the x- and y-coordinates of A and B into the formula and simplify:

x-coordinate of P = (4(-8) + 2(0)) / (4+2)

= (-32) / 6

= -5.33 (rounded to 2 decimal places)

Therefore, the x-coordinate of point P is approximately -5.33.

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(a) The profit function is found by subtracting the cost function from the revenue function. In this case, the profit function P(x) can be found by subtracting C(x) from R(x):

P(x) = R(x) - C(x) = (−1x^2+370x) - (5x+2400)

Simplifying the expression gives:

P(x) = -1x^2 + 370x - 5x - 2400

P(x) = -1x^2 + 365x - 2400

Therefore, the profit function is P(x) = -1x^2 + 365x - 2400.

(b) The average profit function is found by dividing the profit function by the number of items sold, x. In this case, the average profit function Pˉ(x) can be found by dividing P(x) by x:

Pˉ(x) = P(x) / x = (-1x^2 + 365x - 2400) / x

Simplifying the expression gives:

Pˉ(x) = -1x + 365 - 2400/x

Therefore, the average profit function is Pˉ(x) = -1x + 365 - 2400/x.

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The difference quotient for the function f(x) = 4x^2 + 1 is 8x

The difference quotient is a formula used to find the average rate of change of a function over an interval. It is represented by the formula: (f(x+h) - f(x))/h. In this case, we are asked to evaluate the difference quotient for the function f(x) = 4x^2 + 1.

Step 1: Substitute the function into the difference quotient formula:
(f(x+h) - f(x))/h = ((4(x+h)^2 + 1) - (4x^2 + 1))/h

Step 2: Simplify the expression:
= ((4x^2 + 8xh + 4h^2 + 1) - (4x^2 + 1))/h
= (8xh + 4h^2)/h

Step 3: Factor out h from the numerator:
= h(8x + 4h)/h

Step 4: Cancel out the h terms:
= 8x + 4h

Step 5: Substitute h = 0 to find the final answer:
= 8x + 4(0)
= 8x

Therefore, the difference quotient for the function f(x) = 4x^2 + 1 is 8x. This is the final answer for this Assignment. Remember to always show all work when evaluating the difference quotient.

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The remainder when doing the division problem (15x^(2)+4x-37) ÷ (3x-4) is (-5).

To find the remainder, we can use polynomial long division. Here are the steps:

1. Divide the first term of the dividend (15x^(2)) by the first term of the divisor (3x) to get the first term of the quotient (5x).
2. Multiply the first term of the quotient (5x) by the divisor (3x-4) to get (15x^(2)-20x).
3. Subtract (15x^(2)-20x) from the dividend (15x^(2)+4x-37) to get the new dividend (24x-37).
4. Repeat steps 1-3 with the new dividend (24x-37) and the divisor (3x-4) to get the second term of the quotient (8) and the new dividend (-5).
5. Since the degree of the new dividend (-5) is less than the degree of the divisor (3x-4), we stop here and the new dividend (-5) is the remainder.

So, the remainder when doing the division problem (15x^(2)+4x-37) ÷ (3x-4) is (-5).

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The best method to use to solve the system of equation will be Elimination method.

According to the description of the elimination approach, it involves removing a phrase that contains any of the variables from the equation in order to simplify the computations. To achieve this, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same. The term is then eliminated or removed from the result by adding or subtracting from both equations. Because of this, the addition technique is another name for the elimination approach. For illustration, let's use the elimination approach to resolve two linear equations with two variables.

The two equations are:

3x+7y=-19

-3x+4y=12

From the above equations we can observe that the value of the coefficient of x is same, as well as, they have opposite sign.

Hence, the best method to use to solve the system of equation will be Elimination method.

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The value of hypotenuse for given right angles triangle is :

Part 1:  c = 1.5

Part 2: c = 3.5

Part 1:

a = 3, c = ?

using sin function.

sin 30 = 3/c

c = 3 * sin 30

c = 1.5

Part 2:

a = 7√3

cos 30 = 7√3 / c

c = cos 30 * 7√3

c = 7/2

c = 3.5

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Answer:

total salary=$20000

spend%=70%

now,

spend no=70% of $20000

=70/100 ×20000

=$14000

now,

total of spend amount of each month=

spend amount×12

=140000×12

=$168000

The probability that a person has the disease given that his test result is positive is approximately 0.166 or 16.6%.

The Bayes theorem's assumption that the prior probabilities are known with certainty is one of its limitations. These probabilities, however, could not be known or be impossible to predict precisely in many real-world settings. Moreover, Bayes' theorem makes the assumption that each occurrence is independent, which may not necessarily be true in real-world circumstances.

Given that,

P(D) = 0.001

P(D') = 1- 0.001 = 0.999

P(T|D) = 0.99 (the test is 99% effective in detecting the disease)

P(T'|D') = 0.995

The Baye's theorem is given as follows:

P(A|B) = P(B|A) * P(A) / P(B)

Substituting the values:

P(T) = (0.99 * 0.001) + (0.005 * 0.999) = 0.00594

P(D|T) = (0.99 * 0.001) / 0.00594 ≈ 0.166

Hence, the probability that a person has the disease given that his test result is positive is approximately 0.166 or 16.6%.

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The complete question is:

Answer:

21 times

Step-by-step explanation:

3x21=62

Answer: I’m pretty sure it’s the first box, second box and third box

Step-by-step explanation:

Answer:

720m

Step-by-step explanation:

60×4 = 240

240×3 = 720