How many solutions does the following equation have?

74y-8-78y=-4y-8

The minimum value of the function f(x) = 3x on the interval [3, 6] is 9, and the maximum value of this function is 18.

We have to find the maximum and minimum values of f(x) = 3x on the interval [3, 6].

First, determine the critical points.
To find the critical points, we first find the derivative of the given function:

f'(x) = 3, which is a constant value.

Since there are no points where f'(x) = 0 or is undefined, there are no critical points within the function itself.

Now, evaluate the function at the endpoints of the interval.
Since there are no critical points, we will evaluate the function at the endpoints of the interval [3, 6] to find the maximum and minimum values.

f(3) = 3 * 3 = 9
f(6) = 3 * 6 = 18

Now, determine the maximum and minimum values.
Since 9 is the lowest value and 18 is the highest value, the minimum value of f(x) = 3x on the interval [3, 6] is 9, and the maximum value is 18.

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The solution set for the inequality is x < -4 or x > 1.

The given inequality is x²+3x-4>0.

The quadratic equation x²+3x-4=0 can be solved by factoring:

x²+3x-4 = (x+4)(x-1) = 0

This means that the solution set for the equation is x = -4 or x = 1.

Therefore, we can use these two solutions to determine the solution set for the inequality.

For x < -4, x²+3x-4 > 0.

For x > 1, x²+3x-4 > 0.

Therefore, the solution set for the inequality is x < -4 or x > 1.

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by proving the base case and establishing the inductive step, we have shown that the recursive formula S(n) : Dn = nDn−1 + (-1)^n holds true for all positive integers n, using mathematical induction.

Base Case: For n = 1, the formula becomes D1 = 1*D0 + (-1)^1, which simplifies to D1 = D0 - 1. This is true since the number of derangements of a single element is 0, as there are no ways to arrange a single element such that it is not in its original position.

Inductive Hypothesis: Assume that the formula holds for some positive integer k, i.e., Sk: Dk = kDk−1 + (-1)^k.

Inductive Step: We need to show that the formula holds for k + 1, i.e., Sk+1: Dk+1 = (k + 1)Dk + (-1)^(k+1).

Using the recursive definition of derangements, we know that Dk+1 = (k + 1)(Dk + Dk-1). Substituting the inductive hypothesis Sk, we have Dk+1 = (k + 1)((k)Dk-1 + (-1)^k) + Dk-1. Simplifying this expression, we get Dk+1 = (k + 1)Dk + (-1)^k(k + 1) + Dk-1.

Now, we need to manipulate the right-hand side of the formula to match the desired form. Rearranging terms, we have Dk+1 = kDk + (-1)^k(k + 1) + Dk-1 + Dk.

By using the property (-1)^k + (-1)^(k+1) = 0, we can simplify the equation further to Dk+1 = kDk + (-1)^(k+1) + Dk-1 + Dk. This expression matches the form of Sk+1, which completes the induction step.

Therefore, by proving the base case and establishing the inductive step, we have shown that the recursive formula S(n) : Dn = nDn−1 + (-1)^n holds true for all positive integers n, using mathematical induction.

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Answer:

y = 2/7x  

Step-by-step explanation:

Answer:

\( m\angle A = 133\degree \)

Step-by-step explanation:

Quadrilateral ABCD is inscribed In a circle.

So, ABCD is a cyclic Quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

Therefore,

(4x + 5)° + (x + 15)° = 180°

(4x + 5 + x + 15)° = 180°

(5x + 20)° = 180°

5x + 20 = 180

5x = 180 - 20

5x = 160

x = 160/5

x = 32

\( m\angle A = (4x + 5)\degree \)

\( m\angle A = (4\times 32+ 5)\degree \)

\( m\angle A = (128+ 5)\degree \)

\( m\angle A = 133\degree \)

Answer:

1) a number squared, reduced by 12

2) the quantity of twice a number divided by 3, increased by 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first expression reads "x squared less (or minus) 12."

The second expression becomes "the quotient 2x/3 plus one."    Note that 2x/3 must be computed before "one" is added, due to order of operations rules.

The third expression reads "8 less than the cube of x."

The answer is 12.

fkfkfkfk

Therefore, the correct answer is: The range is the best measure of variability, and it equals 78.

Range is a measure of variability that represents the difference between the maximum and minimum values in a dataset. It gives an indication of how spread out the data is. To find the range of a dataset, you simply subtract the minimum value from the maximum value. Range is often used as a quick and simple measure of variability, but it can be sensitive to outliers and extreme values.

Here,

1. For question 5, the appropriate measure of variability for the given data set is the range, which is the difference between the maximum value and the minimum value in the data set.

To find the maximum and minimum values from the given stem-and-leaf plot, we can look at the highest and lowest digits in each row. The highest value is 83 and the lowest value is 5, so the range is:

Range = 83 - 5 = 78

2. For question 6, the appropriate measure of center to represent the data in the given line plot is the median, because the data is skewed to the right and there are outliers present. The median is less sensitive to outliers than the mean.

Therefore, the correct answer is: The median is the best measure of center because there are outliers present.

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Samantha will receive an amount equivalent to $124.5 as commission for 15 demonstrations.

Here, we are given that Samantha tan demonstrates cookware and is paid $8.00 for each of the first 12 demonstrations in one day and $9.50 for each demonstration over 12.

She does 15 demonstrations in one day.

For the first 12, she will receive a commission of $8.00 per demonstration.

Thus, the amount received for the first 12 demonstrations will be -

12 × 8

= 96

Now, further she has to perform 3 (15 - 12) more demonstrations for which she will be paid $9.50 per demonstration.

Thus, the amount received for the 3 demonstrations will be -

9.5 × 3

= 28.5

Thus, the total commission received by her will be-

96 + 28.5

= 124.5

Thus, Samantha will receive an amount equivalent to $124.5 as commission for 15 demonstrations.

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Answer: 20/27

Step-by-step explanation:

So it is non- mutually exclusive;

Let B for the boys and H for the blond hair.

P(B) = 15/27; P(H) 11/27; P(B and H) = 6/27

Then, we have,

P(B or H) = 15/27 + 11/27 - 6/27

P(B or H) = 20/27 

Therefore,  the probability of selecting a boy or a blond-haired person is 20/27.

Step-by-step explanation:

5x +10° + 58° = 11x + 2°( Exterior angle of a triangle is equal to the sum of two opposite interior angles)

5x + 68° = 11x + 2°

11x - 5x = 68° - 2°

6x = 66°

x = 66° / 6

Therefore x = 11°

Hope it will help you :)

The amount that Damian would need to pay in studio fees if he needed to use the studio for 4.5 hours is of:

$687.50.

To obtain the amount that Damian has to pay, a linear function has to be defined, in slope-intercept format, as follows:

y = mx + b.

In which the coefficients are described as follows:

Two points on the table are given as follows:

(2,500) and (8, 950).

Given two points, the slope is calculated as the division of the change in y by the change in x, hence:

m = (950 - 500)/(8 - 2) = 75.

Hence:

y = 75x + b

When x = 2, y = 500, hence the intercept b is obtained as follows:

500 = 75(2) + b

b = 350.

Then

y = 75x + 350.

The cost for a rent of 4.5 hours is given as follows:

y = 75(4.5) + 350 = $687.50.

The table is given by the image shown at the end of the answer.

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The probability of getting a sum of 7 is 6/36, which simplifies to 1/6 or approximately 16.67%.

Here's a step-by-step explanation using the terms die, sum, spots, and drawing:

1. Die: A standard die has 6 faces with spots numbered 1 to 6.
2. Rolling the die 2 times: You roll the die once, record the number of spots, then roll it again.
3. Sum of the spots: Add the number of spots from the first roll to the number of spots from the second roll.
4. Drawing: A drawing can be a table or a chart to represent the possible outcomes and their corresponding sums.

To visualize this, you can create a 6x6 drawing (table) with rows and columns representing the spots on each roll:

```
  1  2  3  4  5  6
1  2  3  4  5  6  7
2  3  4  5  6  7  8
3  4  5  6  7  8  9
4  5  6  7  8  9 10
5  6  7  8  9 10 11
6  7  8  9 10 11 12
```

This drawing shows all possible sums (from 2 to 12) when rolling a die two times. To find the probability of a specific sum, count the number of times that sum appears in the table, and divide it by the total number of outcomes (6 x 6 = 36).

For example, the probability of getting a sum of 7 is 6/36, which simplifies to 1/6 or approximately 16.67%.

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Answer:

5 33/100

Step-by-step explanation:

5.33 can be put in expanded form to help solve this problem

5 is the whole number

0.33 out of 100 is 33/100 which is added onto the 5

So, that gets you to 5 33/100

Hope this helps!

Step-by-step explanation:

after he buys everything he has 170.83 ( total 340.17) 73.43 times x

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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The value of the rate of growth in Japan is - 0.55.

From the question above, :Birth rate = 7.7 per thousand

Death rate = 9.8 per thousand

Net migration = 0.55 per thousand

The rate of growth can be calculated using the following formula:

r = (birth rate - death rate) + net migration

Where,r = rate of growth

birth rate = number of live births per thousand in a population in a given year

death rate = number of deaths per thousand in a population in a given year

net migration = the difference between the number of people moving into a country (immigrants) and the number of people leaving a country (emigrants) per thousand in a given year

Putting the values in the formula we get,r = (7.7 - 9.8) + 0.55r = - 1.1 + 0.55r = - 0.55.

Therefore, the rate of growth in Japan is - 0.55.

Your question is incomplete but most probably your full question was:

thenet migration is confusing me. i thought of using the formula:[ (births + immigration) - (deaths + emmigration)] / total

population • 100 but im not sure how to do it with net migration.

Japan's birth rate is 7.7 per thousand and its death rate is 9.8 per thousand with a net migration of 0.55 ner thousand. Calculate r for Japan

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The Solution of the given system of equations is x = -2 , y = 5 and z = 4 .

In the question ,

it is given that ,

the system of linear equations is given as

x - y \(+\) 2z \(=\) 1           .....equation(1)

3x \(+\) y \(+\) 5z \(=\) 19      .....equation(2)

2x − y − 2z \(=\) -17      .....equation(3) ,

Multiplying equation(1) by -3 and adding with equation(2) ,

we get ,

4y - z = 16       ......equation(4)

Multiplying equation(1) by -2 and adding with equation(3) ,

we get ,

y - 6z \(=\) -19       .....equation(5)

Now , multiplying equation(5) with -4 and adding with equation(4) ,

we get ,

23z \(=\) 92

So , z = 92/23 = 4

z = 4 .

Substituting z = 4 , in 4y - z = 16   ,

we get ,

4y - 4 \(=\) 16

4y = 16 \(+\) 4

4y = 20

y = 20/4

y \(=\) 5

Substituting z = 4 and y = 5 in the equation x - y + 2z = 1   ,

we get ,

x - 5 \(+\) 2×4 \(=\) 1

x - 5 \(+\) 8 \(=\) 1

x \(+\) 3 \(=\) 1

x \(=\) -2

Therefore , the system has a unique solution that is x = -2 , y = 5 and z = 4 .

The given question is incomplete , the complete question is

Find the complete solution of the linear system, or show that it is inconsistent. (If the system has infinitely many solutions, express your answer in terms of t, where x = x(t), y = y(t), and z = t. If there is no solution, enter NO SOLUTION.)

x − y + 2z = 1

3x + y + 5z = 19

2x − y − 2z = −17

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The optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

To solve this linear programming problem using the Simplex method, we first need to convert it into standard form by introducing slack variables.

Our problem can be rewritten as follows:

Minimize w = 9x1 + 6x2

Subject to:

x1 + 2x2 + x3 = 5

2x1 + 2x2 + x4 = 8

x1 + 2x2 + 2x3 = 6

where x1, x2, x3, and x4 are all non-negative variables.

Next, we set up the initial simplex tableau:

Basic Variables x1 x2 x3 x4 RHS

x3 1 2 1 0 5

x4 2 2 0 1 8

x5 1 2 2 0 6

z -9 -6 0 0 0

The last row represents the coefficients of the objective function. The negative values in the z-row indicate that we are minimizing the objective function.

To find the pivot column, we look for the most negative coefficient in the z-row. In this case, the most negative coefficient is -9, which corresponds to x1. Therefore, x1 is our entering variable.

To find the pivot row, we calculate the ratios of the RHS values to the coefficients of the entering variable in each row. The smallest positive ratio corresponds to the pivot row. In this case, the ratios are:

Row 1: 5/1 = 5

Row 2: 8/2 = 4

Row 3: 6/1 = 6

The smallest positive ratio is 4, which corresponds to row 2. Therefore, x4 is our exiting variable.

To perform the pivot operation, we divide row 2 by 2 to make the coefficient of x1 equal to 1:

Basic Variables x1 x2 x3 x4 RHS

x3 0 1 1 -1 1

x1 1 1 0 1/2 4

x5 0 1 2 -1 2

z 0 -3 9 9/2 -18

We repeat the process until all coefficients in the z-row are non-negative. In this case, we can stop here because all coefficients in the z-row are non-negative.

Therefore, the optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

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If A is a symmetric matrix, then A³ is also a symmetric matrix.

To prove this, we can use the definition of a symmetric matrix, which is a matrix that is equal to its transpose. In other words, if A is a symmetric matrix, then A = A^T.

Now, let's look at A³:

A³ = A * A * A

We can replace each A with A^T, since they are equal:

A³ = A^T * A^T * A^T

Now, we can use the property that the transpose of a product of matrices is equal to the product of their transposes in reverse order:

A³ = (A^T * A^T * A^T)^T

A³ = (A^T)^T * (A^T)^T * (A^T)^T

Since the transpose of a transpose is the original matrix, we can simplify:

A³ = A * A * A

Therefore, A³ is also a symmetric matrix.

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Answer:

14, or f(-3)= 14

Step-by-step explanation:

Input the -3, so you will get f(-3)= -1/3(-3) + 13.
Do -1/3 x -3, which will get you 1.
Do 1 + 13, which will get you 14.
So, the answer will be 14, or f(-3)= 14.

Step-by-step explanation:

the answer from the graph is;

(3 , -2)

Answer:

Y = 3/4x + -5

___________

y = 3/4x – 5

Step-by-step explanation:

y = mx + b

m = slope = change in y/change in x = rise / run

b = y intercept = point where x = 0

The correct option is B) FDE and GDH, as their corresponding angles have the same intercepted arc and, therefore, are congruent.

To determine which angles are congruent in circle D, we need to analyze the given information about the measures of minor arcs. Since minor arcs are measured in degrees, we can use the following properties:

1. When two arcs are congruent, their corresponding central angles are also congruent.

2. The measure of a central angle is equal to the measure of its intercepted arc.

Given these properties, let's examine the answer choices:

A) EDH and FDG: We cannot determine their congruency based solely on the measures of the minor arcs.

B) FDE and GDH: These angles have the same intercepted arc, so they are congruent.

C) GDH and EDH: The intercepted arcs for these angles are different, so they are not congruent.

D) GDF and HDG: These angles have the same intercepted arc, so they are congruent.

Therefore, the correct option is B) FDE and GDH, as their corresponding angles have the same intercepted arc and, therefore, are congruent.

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Answer:

t = 9

Step-by-step explanation:

Here, we want to find the value of t

2(t-3)^2 -72 = 0

2(t-3)^2 = 72

divide both sides by 2

(t-3)^2 = 72/2

(t-3)^2 = 36

(t-3)^2 = 6^2

Since powers are equal, we equate base

t-3 = 6

t = 6 + 3

t = 9

The characteristics of the correlation coefficient are A. It must be between -1 and 1. C. If the correlation is positive, the slope of the regression line is also positive. E. The correlation coefficient tells you how strong the residuals are.

The correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. Therefore, option A is correct.

Regarding option B, the correlation coefficient does not indicate the percentage of points that lie on the regression line. Instead, it measures the overall strength and direction of the relationship between the variables.

Option C is correct because if the correlation is positive, it means that as one variable increases, the other variable tends to increase as well. This positive relationship is reflected in the positive slope of the regression line.

Option D is incorrect because the correlation coefficient can be positive, negative, or zero, depending on the nature of the relationship between the variables.

Option E is correct. The correlation coefficient provides information about the strength of the relationship between the variables, which can be used to assess the strength of the residuals or the deviations from the regression line.

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The slope of the rapids is -0.067

Kannanaski Rapids drops  62 ft vertically

The horizontal distance of 920 ft.

tan θ is a commonly used trigonometric function along with other 5 functions. tan θ is also called as law of tangent. The tangent formula for a right-angled triangle can be defined as the ratio of the opposite side of a triangle to the adjacent side. It can also be represented as a ratio of the sine of the angle to the cosine of the angle.

Slope of Rapids= tanθ= \(\frac{y}{x}=\frac{-62}{920} \\\)

=-0.067

Therefore, the slope of rapids is -0.067.

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