How would one prove that:
arccos (-x) = π - arccos x for -1 ≤ x ≤ 1

Answer:

Clustering Data

Step-by-step explanation:

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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Answer:

the value of x is 18

Step-by-step explanation:

4x+17+91=180(Liner pair)

4x=180-108

4x=72

x=72/4

so,x=18

Answer:

12x+20

Step-by-step explanation:

2(5x+2)+2(x+8)

or (simplified)

10x+4+2x+16=12x+20

Answer:

12x+20

Step-by-step explanation:

5x+2+x+8+5x+2+x+8

12x+20

According to the FIFO method, the ending inventory balance for Commodity Z is $1,405

FIFO means that earlier inventory is sold first and later inventory would be the last goods left.

Since there were 23 units left, all 16 units from the last purchase and 7 units from the second purchase would be available:

= (16 x 62) + (7 x 59)

= 992 + 413

= $1,405

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Answer:

18.

Step-by-step explanation:

If the tens digit is x^3 the unit digit is x^3 + 7

So 10 * x^3 + x^3 + 7 < 100    (as its a 2 digit number).

11x^3 < 93

x^3 < 8 5/11

x <  2.04

As x must be an integer it is either 1 or 2.

It cannot be 2 as 2^3 = 8 and 8+7 = 15 which cannot be the tens digit so it must be 1.

The answer is 1  and (1+7)  = 18.

Answer:  

18.  

Step-by-step explanation:  

If the tens digit is x^3 the unit digit is x^3 + 7  

So 10 * x^3 + x^3 + 7 < 100    (as its a 2 digit number).  

11x^3 < 93  

x^3 < 8 5/11  

x <  2.04  

As x must be an integer it is either 1 or 2.  

It cannot be 2 as 2^3 = 8 and 8+7 = 15 which cannot be the tens digit so it must be 1.  

The answer is 1  and (1+7)  = 18.

Answer: The value of the limit of the function may not be equal to the value of the function evaluated at a particular x-value. In other words, just because a function takes on a certain value at a particular x-value doesn't mean that the limit of the function at that x-value is equal to that value. To determine the limit of the function, you may need to use different methods such as L'Hopital's Rule or other limit laws. Additionally, it's important to keep in mind that the limit of the function may not exist, in which case it wouldn't be equal to any specific value.

Step-by-step explanation:

The range and IQR values of the Boxplot given are 12 and 5 respectively.

Range = 56 - 44 = 12

IQR = 53 - 48 = 5

Therefore, the range and IQR values are 12 and 5 respectively.

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Question:

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

30

∑  (−3i+5)

i=1

Answer:

The first three terms are : 2, -1 and -4

The last term is: -85

The sum of the sequence is: -1245

Step-by-step explanation:

Given;

==================================

30

∑  (−3i+5)                    -------------------(i)

i=1

==================================

Where the ith term aₙ is given by;

\(a_{i}\) = \(-3i + 5\)         -------------------(ii)

(a) Therefore, to get the first three terms (\(a_1, a_2, a_3\)), we substitute i=1,2 and 3 into equation (ii) as follows;

\(a_{1}\) = \(-3(1) + 5\) = 2

\(a_2 = -3(2) + 5 = -1\)

\(a_3 = -3(3) + 5\)\(= -4\)

Since the sum expression in equation (i) goes from i=1 to 30, then the last term of the sequence is when i = 30. This is given by;

\(a_{30} = -3(30) + 5 = -85\)

(b) The sum \(s_n\) of an arithmetic sequence is given by;

\(s_n = \frac{n}{2}[a_1 + a_n]\)   -----------------(iii)

Where;

n = number of terms in the sequence = 30

\(a_1\) = first term = 2

\(a_n\) = last term = -85

Substitute the corresponding values of n, \(a_1\) and \(a_n\) into equation (iii) as follows;

\(s_n = \frac{30}{2}[2 + (-85)]\)

\(s_n\) = 15[-83]

\(s_n\) = -1245

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

a) 1 km

b) Amaya

c) Jorge

HOPE THIS HELPS ;P

The value of the coin in 2019 would be approximately $132.

To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.

Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:

Value in 2019 = Initial value * (1 + Rate)^n

where Rate is the annual increase rate and n is the number of years between 2010 and 2019.

Plugging in the values:

Value in 2019 = $40 * (1 + 0.169)^9

Value in 2019 ≈ $40 * 2.996

Value in 2019 ≈ $119.84

Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.

However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.

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Answer:

x = -4

Step-by-step explanation:

Step 1: Write equation

71 + x + 74 + 39 = 180

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

Answer:

Step-by-step explanation:

f(x) = x²

f(4) = 4² = 16

f(1) = 1² = 1

f(-3) = -3² = 9

f(t) = t²

Always wise to us the ^ symbol to represent powers to avoid confusion

4^2 = 4² = 16

-3^2 = 9

t^2

if you are on a PC, the square symbol (²) can be typed by holding down the "alt" key while pressing and releasing "2","5","3" on the keypad, then release "alt". Unfortunately this does not work if you only have the row of numbers on the keyBoard to work with.

Answer:

The answer is simply 26,25/3 which gives that each book costed 8,75 dollars assuming of course that all books have the same price.

The height of the balloon above the ground is about 7.07 feet.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let h represent the height of the balloon from the ground, hence:

sin(45) = h/10

h = 7.07 feet

The height of the balloon above the ground is about 7.07 feet.

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The component form of the following vectors is Option A. V = (38.3, 32.1).

To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.

The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.

In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.

The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).

Let's calculate the components:

x = 50 * cos(50°) ≈ 38.3

y = 50 * sin(50°) ≈ 32.1

Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).

Therefore, the correct answer is A. V = (38.3, 32.1).

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The question is incomplete. Find the full content below:

Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 50, direction angle θ = 50°

A. V = (38.3, 32.1)

B. V = (33.8, 31.2)

C. V = (32.1, 38.3)

D. V = (31.2, 33.8)

Answer:

Step-by-step explanation:

Explanation:

As you know, each electron that's part of an atom has its own unique set of four quantum numbers that describes its position and spin.

This means that looking for the number of unique sets of quantum numbers is equivalent to looking for the number of electrons that can occupy the third energy level.

As you know, the number of orbitals you get per energy level is given by the equation

no. of orbitals

=

n

2

, where

n

- the principal quantum number, the ones that gives the energy level.

So, if you're dealing with the third energy level, you can say that it will contain a total of

no. of orbitals

=

3

2

=

9

distinct orbitals.

Now, each orbital can contain a maximum of

2

electrons of opposite spins. This means that the third energy level will contain a maximum number of

no. of electron

=

9

⋅

2

=

18 e

−

So, if each electron is described by an unique set of quantum numbers, you can conclude that

18

sets of quantum numbers are possible for the third energy level.

ok maybe that will help!

Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

Answer: 6. 35 hours

7. 741 Miles

8. 1.5 or 1.54

Step-by-step explanation:

6. 142.20/6=23.7

829.50/23.7=35

7. 117/3=39

39x19=741

8.19/12.35=1.538

Humanity would achieve a life expectancy of 110 years in approximately 60 years.

To calculate the number of years it would take for humanity to achieve a life expectancy of 110 years, we need to determine the number of decades required to reach this goal based on the given rate of increase.

In 2009, the life expectancy was about 80 years. From that point, we need to calculate the difference between the current life expectancy and the target life expectancy of 110 years.

110 years - 80 years = 30 years

Since the rate of increase is 5.3 years every decade, we can divide the difference by the rate to determine the number of decades required:

30 years / 5.3 years per decade ≈ 5.66 decades

Since we can't have a fraction of a decade, we need to round up to the nearest whole number. Therefore, it would take approximately 6 decades for humanity to achieve a life expectancy of 110 years.

To calculate the number of years, we multiply the number of decades by 10:

6 decades * 10 years per decade = 60 years

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The fraction of magazines that were delivered to families who were home written as a decimal is 0.4

Difference between fraction and decimal?

Total number of families = 25

Number of families in home = 10

Then, number of families away = 25 - 10 = 15

Fraction of magazines that were delivered to families who were home

= Number of families in home/ Total number of families

= 10 / 25

= 0.4

Hence, the fraction of magazines that were delivered to families who

were home written as a decimal is 0.4

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Answer:

ssssss

Step-by-step explanation:

Answer:addidion

Step-by-step explanation:

x - 6y = -9 that is option c is the equation of the line in standard form.

A way of expressing linear equations is in their standard form, commonly referred to as the general form. Different formats for writing a linear equation exist, including the standard form, the slope-intercept form, and the point-slope form. One variable and two variables are the two ways that a linear equation can be stated in its standard form. Ax + b = 0, where a and b are constants and the letter x denotes the variable, is the way a linear equation with one variable is typically represented. The equation ax + by = c, where a, b, and c are real values, and x and y are the variables, is written as a linear equation with two variables.

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Answer:

The graph of y = 4x - 11 is translated up 8 units. Which equation represents the translated graph? f y = 4x - 19 g y = 4x - 3 h y = 12x - 11 j y = 12x - 3

Answer: x=-8.   (graph with open circle going left from -8 for khan academy)

Step-by-step explanation:   -21-11<-32

4x>-32

x<-8

Answer:

If what you're asking is what is the cosine of 3 is 0.999986292247

Step-by-step explanation:

calculator

Answer:

L = 1/3 W

Step-by-step explanation:

If you look at the table, you can see that all of the water is divided by three to find the amount of lemon juice. Using the process of elimination, this answer choice is the only one containing the number "3."

Answer:

huh?

Step-by-step explanation: