[tex]\frac{1-5}{6-3} =\frac{-4}{3} =[/tex]

The trigonometric equation is tan 2A cot A-1 = sec 2A

We have to prove the trigonometric equation

tan 2A cot A-1 = sec 2A

Now let us take LHS

tan 2A cot A-1  

2tanA/1-tan²A - 1 . cotA - 1

2-1+tan²A/1-tan²A

1+tan²A/1-tan²A

sec2A

Hence, the trigonometric equation is tan 2A cot A-1 = sec 2A

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The simplified expression of the expression (x)³(−x³y)² is x⁹y²

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

(x)3(−x3y)2

Express properly

So, we have

(x)³(−x³y)²

Open the brackets

(x)³(−x³y)² = x³ * x⁶y²

Multiply (x)³ and x⁶ in the expression

So, we have the following representation

(x)³(−x³y)² = x⁹y²

Hence, the simplified expression is x⁹y²

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Answer:

-7

Step-by-step explanation:

divide by 7 on both sides and you get i = -7

The area of the composite shape is 125units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A composite shape can be defines as a shape created with two or more basic shapes.

The composite shape can be divided into 2 equal squares and a rectangles.

Area of the square = l²

= 5× 5 = 25

For two squares it will be;

25 × 2

= 50 units²

area of the rectangle = l× w

where w is the width

A = 15 × 5

= 75 units²

Therefore the area of the composite shape = 50 + 75 = 125 units²

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The price of the jeans will decrease because supply is greater than demand hence the stores will sell them at discounted prices.

The store owners would be forced to cut pricing if the jeans weren't purchased at all or as frequently as the other brands. Either they choose that choice, return the goods if possible  or just toss the jeans away. It generally takes some trial and error to determine the proper price.

For instance, the owner may lower the price to $75 and test whether the 25% discount works or not if the jeans initially sell for $100 and nobody buys them for a week.

The price might remain there if people continue to buy and if not, the cost might decrease even further.

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The probability values are P(30 ≤ Amount ≤ 59) = 0.43, P(Amount ≥ 60 or Amount < 30) = 0.57 and P(Amount ≥ 40) = 0.45

At least $30 but not more than $59

This means that we use the money spent from 30 to 59

So, we have

30 to 59 = 76 + 58 + 67

30 to 59 = 201

Total = 85 + 98 + 201 + 84

Total = 468

Next, we have

P(30 ≤ Amount ≤ 59) = 201/468

P(30 ≤ Amount ≤ 59) = 0.43

At least $60 or less than $30

This means that we use the money spent less than 30 and greater than or equal to 60

So, we have

At least $60 or less than $30 = 84 + 85 + 98

At least $60 or less than $30 = 267

Next, we have

P(Amount ≥ 60 or Amount < 30) = 267/468

P(Amount ≥ 60 or Amount < 30) = 0.57

At least $40

This means that we use the money spent greater than or equal to 40

So, we have

At least $40 = 58 + 67 + 84

At least $40 = 209

Next, we have

P(Amount ≥ 40) = 209/468

P(Amount ≥ 40) = 0.45

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The graph of the given function is attached.

Given is a function for the rainfall in 5 months in inches.

We need to display the data,

So, as we can see that the data is not showing any proportion or pattern,

So, it can be displayed as a line chart.

Hence the chart is attached for the function.

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The values of the function are 5 and 1.5 and the domain is,

⇒ - ∞ < x < ∞

Here, The equation of the function is given as

f(x) = 5 (1.3)ˣ

The above function is an exponential function.

An exponential function is represented as

f(x) = abˣ

Where

a represents the initial value, b represents the rate of growth or decay

While x and f(x) are the input and output values

Hence, By comparison, we have

a = 5 and b = 1.3

This means that the function values are 5 and 1.3.

Since, the function is an exponential function.

The domain of an exponential function is the set of all real values

Hence, the domain of f(x) is the set of all real values.

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Answer:

-3x + 3

Step-by-step explanation:

To find the equation of a line perpendicular to the line passing through (-2, 1) and (4, 3), we need to determine the slope of the original line first. Then, we can use the negative reciprocal of that slope to find the slope of the perpendicular line. Finally, we can use the point-slope form to write the equation of the perpendicular line.

Step 1: Find the slope of the original line.

Slope (m) = (change in y) / (change in x)

m = (3 - 1) / (4 - (-2))

m = 2 / 6

m = 1/3

Step 2: Determine the slope of the perpendicular line.

The slope of the perpendicular line is the negative reciprocal of the original line's slope.

Perpendicular slope = -1 / (1/3)

Perpendicular slope = -3

Step 3: Use the point-slope form to write the equation.

The point-slope form is given by:

y - y1 = m(x - x1)

Using the point (-2, 9) and the perpendicular slope (-3), we can write the equation as:

y - 9 = -3(x - (-2))

y - 9 = -3(x + 2)

y - 9 = -3x - 6

y = -3x + 3

Therefore, the equation of the line perpendicular to the line passing through (-2, 1) and (4, 3) and passing through (-2, 9) is y = -3x + 3.

The sequence based on the information would be: B. an = [tex]10 1/2^{-1}[/tex]average rate of change is negative fifteen halves.

This question is about exponent function/series. You are given 3 points from the function, point A (1,10), point B( 2, 5), and point  C(4,1.25).  

If you insert point A to the function, an will give a result of 10 for n=1.

For n=0, the result would be:

an= 10([tex]1/2^{-1}[/tex])

= 10 * 2

= 20

Then the average rate of change from n=0 to n=2 would be:

Rate of change= (y₂ -y₁)/ (x₂ -x₁)

Rate of change= (5-20)/ (2-0)

= -15/2

= negative fifteen halves

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Here are the steps to calculate the expression √20 + 5 - 43 :

Step 1: Simplify the square root of 20:

[tex]\sqrt{20}[/tex]

Step 2: Calculate the value of the square root:

[tex]\sqrt{20} = 2\sqrt{5}[/tex]

Step 3: Substitute the value of the square root into the expression:

[tex]2\sqrt{5} + 5 - 43[/tex]

Step 4: Perform addition:

[tex]2\sqrt{5} + 5 = 2\sqrt{5} + \frac{5}{1} = \frac{2\sqrt{5} + 5}{1}[/tex]

Step 5: Perform subtraction:

[tex]\frac{2\sqrt{5} + 5}{1} - 43 = \frac{2\sqrt{5} + 5 - 43}{1}[/tex]

Step 6: Simplify the numerator:

[tex]\frac{2\sqrt{5} - 38}{1}[/tex]

Step 7: Simplify the expression:

[tex]2\sqrt{5} - 38[/tex]

Therefore, the calculation √20 + 5 - 43 simplifies to 2√5 - 38.

From the relationship of AC bar ≅ BD bar, we can tell that ABCD is a rectangle.

A quadrilateral with two sets of parallel sides is known as a parallelogram.

If ABCD is a parallelogram where AC and BD have equal lengths, then the opposite sides of ABCD are also equal. ABCD has two sets of sides that are parallel and have the same length.

The fact that ABCD possesses two sets of sides that are parallel and of equal length logically leads to the conclusion that it also has four angles that are right. One reason for this is that the angles opposite each other in a parallelogram are of equal measure, while the sum of the angles at each corner of a parallelogram is always 180 degrees.Therefore, ABCD is a rectangle.

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Answer:

130.4

Step-by-step explanation:

6 x 14 = 84

8 x 4 = 32

(4 x 7.2)/2 = 14.4

54° is the value of the given angle BAC.

As we know that the arc and angles formed by intersecting chords,

θ = (α + β)/2    .....(i)

According to the given figure, we have

θ = 10x+4

α =9x-12

β = 12x +15

Substitute the value in equation (1)

10x+4 = (9x-12+12x +15)/2

20x+8 = 21x +3

x = 8-3

x = 5

Thus,

∠BAC = θ

= 10*5+4

= 50 + 4

=54

Therefore, the value of the given angle will be 54°.

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Answer:

4,12,36,108,324.....

Step-by-step explanation:

The sequence represented by the equation [tex]a=4(3)^{n-1}[/tex]is a geometric sequence with first term 5 and common ratio 3. The first 4 terms of the sequence are:

[tex]a_1 = 4(3)^{1-1} =4(3)^0 = 4[/tex]

[tex]a_2 =4(3)^{2-1} = 4(3)^1 = 12[/tex]

[tex]a_3 =4(3)^{3-1} = 4(3)^2 = 36[/tex]

[tex]a_4 = 4(3)^{4-1} =4(3)^3 = 108[/tex]

[tex]a_5=4(3)^{5-1} =4(3)^4=324[/tex]

The sequence can be written as:

[tex]a_n = 4(3)^{n-1}[/tex]

where n is the term number.

Therefore, the sequence is 4,12,36,108,324.....

Answer:

The answer is 4,12,36,108,324

Step-by-step Explanation:

a1=4(3)¹‐¹=4(3)⁰=4

a2=4(3)²‐¹=4×3=12

a3=4(3)³‐¹=4(3)²=4×9=36

a4=4(3)⁴‐¹=4(3)³=4×27=108

a5=4(3)⁵‐¹=4(3)⁴=4×81=324

Answer:

Step-by-step explanation:

To determine the significance level for the difference in means between the first two groups, we need to refer to the provided normal distribution. However, you haven't provided the details or parameters of the normal distribution, such as the mean and standard deviation. Without this information, it is not possible to determine the exact significance level required.

In hypothesis testing, the significance level, typically denoted as α (alpha), is chosen by the researcher before conducting the experiment. It represents the threshold at which the researcher considers the results to be statistically significant. Commonly used significance levels are 0.05 (5%) or 0.01 (1%).

Please provide the necessary parameters or more information about the normal distribution to determine the specific significance level for the difference in means between the first two groups.

No matter the values of P, V, T, p, and t, as long as the equation PV/T = pv/t holds true, the solution for v is always equal to V.

To solve for v in the equation PV/T = pv/t, we can manipulate the equation to isolate v on one side.

Starting with the given equation:

PV/T = pv/t

To isolate v, we can cross-multiply:

PVt = pVt

Next, we divide both sides of the equation by pt:

V = v

Therefore, the solution is v = V.

In other words, v is equal to V, which means they represent the same values.

This implies that v and V are interchangeable and can be used interchangeably in the equation.

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The calculated number of plants the flower bed can contain is 120

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

Dimensions = 16 m by 9 m

So, the area of the flower bed is

Area = 16 * 9

Evaluate

Area =  144

Also, we have

Each plant requires a space of 1.2m x 1m?

This means that

Plant area = 1.2 * 1

Plant area = 1.2

So, we have

Plants = 144/1.2

Evaluate

Plants = 120

Hence, the number of plants is 120

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Answer:

Step-by-step explanation:

To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.

The area of the flower bed is calculated by multiplying its length and breadth.

So, the area of the flower bed is 16m x 9m = 144 sq.m.

Each plant requires a space of 1.2m x 1m = 1.2 sq.m.

Therefore, the number of plants that can be planted in the flower bed is:

144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.

So, you can plant 120 plants in the rectangular flower bed.

The Area function [tex]A(x) = 2x * \sqrt(16 - x^2).[/tex]

(a) For a rectangle inscribed in a semicircle of radius 4 cm, let half-length be x and height be y.

Therefore, the Area function [tex]A(x) = 2x * \sqrt(16 - x^2).[/tex]

(b) Maximum area occurs when x = [tex]4 * sin(\pi/4), so A(4 * sin(\pi/4)) = 16 cm^2.[/tex]

(c) Dimensions for the largest inscribed rectangle are smaller dimension (height) ≈ of 2.83 cm, a larger dimension (base) ≈ of 5.66 cm.

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The calculated value of x in the right triangle is 12.5

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

The right triangle

The value of x can be calculated using the following cosine rule

So, we have

cos(28) = 11/x

make x the subject of the formula

So, we have

x = 11/cos(28)

Evaluate the quotient

This gives

x = 12.5

Hence, the value of x is 12.5

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A) The inequality that the weight of a child who has outgrown the small T-shirt is w > 55. B) The inequality that the weight of a child who is not ready for the small T-shirt yet. Is y < 43

a. To describe the weight (w) of a child who has outgrown the small T-shirt, we can use the inequality:

w > 55

This inequality states that the weight of a child (w) must be greater than 55 pounds for them to have outgrown the small T-shirt.

b. To describe the weight (y) of a child who is not ready for the small T-shirt yet, we can use the inequality:

y < 43

This inequality states that the weight of a child (y) must be less than 43 pounds for them to not be ready for the small T-shirt yet.

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Answer:

B, C

Step-by-step explanation:

x^2 = 5x - 6

x = 2 or x = 3

Okay, let's break this down step-by-step:

* The telephone pole is 54 feet tall

* The guy wire runs 83 feet from point A (top of pole) to point B (ground)

* So the hypotenuse (AB) of the right triangle is 83 feet

* The opposite side (AC) is 54 feet (height of pole)

To find the adjacent side (BC), we use the Pythagorean theorem:

a^2 + b^2 = c^2

54^2 + BC^2 = 83^2

Solving for BC gives:

BC = sqrt(83^2 - 54^2) = sqrt(1296 - 2916) = sqrt(1620) = 40 feet

So the guy wire is secured 40 feet from the base of the telephone pole.

Rounded to the nearest tenth is 40.0 feet.

Therefore, the final answer is:

40.0

Let me know if you have any other questions!

Answer:

5/4 = h/44, so h = 55

The height of the tree is 55 feet.

D is correct.

Answer: True

Step-by-step explanation:

Solving linear equations using matrices involves steps ranging from creating an augmented matrix, performing row operations, back substitution, and then interpreting results

To solve a system of linear equations using matrices:

Step 1: Write the system of linear equations in matrix form.

Represent the coefficients of the variables as a matrix (called the coefficient matrix), and the constants on the right side of the equations as another matrix (called the constant matrix).

Step 2: Create the augmented matrix.

Combine the coefficient matrix and the constant matrix into a single matrix by appending the constant matrix as an additional column. This combined matrix is called the augmented matrix.

Step 3: Perform row operations to achieve row-echelon form.

Use row operations (swapping rows, multiplying a row by a constant, or adding/subtracting rows) to manipulate the augmented matrix into row-echelon form. Row-echelon form has zeroes below the diagonal and non-zero elements on the diagonal.

Step 4: Perform back-substitution.

Starting from the last row of the row-echelon form matrix, solve for the variables using back-substitution. Substitute the values of the variables you find into the previous rows to determine the remaining variable values.

Step 5: Interpret the results.

Once you have solved all the variables, you have found the solution to the system of linear equations. If there are infinitely many solutions or no solutions, this will be indicated by the row-echelon form.

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Answer:

The phrase "The product of a number and five added to 17" can be represented mathematically as:

5x + 17

In this expression, 'x' represents the unknown number. The product of the number and five is calculated by multiplying the number by 5, and then 17 is added to the result.

The middle half of the data values vary by:

Interquartile = [tex]Q_3-Q_1[/tex] =>  19.25 - 13.5 = 5.25

The given data is :

15, 16, 18, 9, 18, 4, 19, 20, 17, and 36 apps.

We have to find:

Use the range and interquartile range to describe how the data vary.

We have to arrange the data from smallest to largest.

4, 9, 15, 16, 17, 18, 18, 19, 20, 36

Range of the data is : Highest no. - lowest no.

Range of the data is: 36 - 4 = 32

The location of the [tex]Q_1[/tex] = (n + 1) × 0.25 (where n is the total no. in the data)

The location of the [tex]Q_1[/tex] = (10 + 1)  × 0.25 = 11  × 0.25 = 2.75

∴[tex]Q_1[/tex] = 15 × 0.75 + 9 × 0.25  = 13.5

The location of the [tex]Q_3[/tex] = (n + 1) × 0.75

The location of the [tex]Q_3[/tex] = 11 × 0.75 = 8.75

∴[tex]Q_3[/tex] = 19 × 0.75 + 20 × 0.25 = 19.25

Hence, The middle half of the data values vary by:

Interquartile = [tex]Q_3-Q_1[/tex] =>  19.25 - 13.5 = 5.25

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