Select the correct answer from each drop-down menu.
The graph of the function f(x)
= 5/4sin (x) + 1
is shown. What are the key features of this function?

Answer:

$68,486.79

Step-by-step explanation:

the first 10 years:

23,500(1.051)^10=38,645.1522

the remaining 13 years:

38,645.1522(1.045)^13=68,486.78798

(round it)

Answer:

15.7 inches

Step-by-step explanation:

Circumference of circle = d x 3.14

d = 5 inches

Let's solve

5 x 3.14 = 15.7 inches

So, the circumference of the circle is 15.7 inches.

The critical points of h are -2 and 3

Recall that  a critical point of a function y = f(x) is a point (c, f(c)) on the graph of f(x) at which either the derivative is 0 (or) the derivative is not defined.

The given function is h(x) = [(x+2)(x-3)]

Finding the product of the brackets

(x+2)(x-3) = x²-3x+2x-6

Collecting like terms to have

h(x) = x²-x -6

h(x) = [(x+2)(x-3)] =  x²-x -6

factorizing this to get

(x²-3x)+(2x-6) = 0

x(x-3) + 2(x-3) = 0

x+2 = 0 or x-3 = 0

x=-2 or x = 3

Therefore the critical points are -2 and 3

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The expression for the nth term of the sequence is 6 + 9(n - 1)

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

6,15,24,33,

In the above sequence, we can see that the current term is added to 9 to gett the next term

So, we have

First term, a = 6

Commin difference, d = 9

The nth term is

Tn = a + (n - 1)d

So, we have

Tn = 6 + 9(n - 1)

Hence, teh nth term is 6 + 9(n - 1)

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In statement c), A and B are sets, and x is an element that belongs to both sets A and B.

What is equation?

An equation is a mathematical statement that shows the equality between two expressions, often denoted by placing an equals sign (=) between the two expressions. The expressions on either side of the equals sign are typically composed of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on.

An equation is said to be true if the expressions on both sides of the equals sign represent the same quantity or value. Equations are often used in mathematics and science to model real-world phenomena, to make predictions, and to solve problems.

a) P: It is a rock.

Q: It contains magnesium.

P → Q

b) P: The weather is nice.

Q: I am chilly.

P ∨ Q

c) P: x belongs to set A.

Q: x belongs to set B.

P ∧ Q

d) P: It is raining.

Q: The ground is wet.

P → Q

e) P: The food is hot.

Q: I will blow on it.

P → Q

f) P: The car is red.

Q: It is a convertible.

P ↔ Q

Note: In statement c), A and B are sets, and x is an element that belongs to both sets A and B.

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you will need 180 mL of the 55% alcohol mixture to create a 25% alcohol solution.

How to solve the question?

To find out how much of the 55% alcohol mixture is needed to create a 25% alcohol solution, we can use the formula:

(amount of pure alcohol in the 10% mixture + amount of pure alcohol in the 55% mixture) / total volume of solution = desired alcohol concentration

Let x be the amount of the 55% alcohol mixture needed.

First, we need to calculate the amount of pure alcohol in the 10% mixture. We know that the 10% mixture contains 10% alcohol, which means that there are 0.10 x 360 = 36 mL of pure alcohol in the mixture.

Next, we need to calculate the amount of pure alcohol in the 55% mixture. We know that the 55% mixture contains 55% alcohol, which means that there are 0.55 x x = 0.55x mL of pure alcohol in the mixture.

The total volume of the solution will be 360 mL + x mL.

Using the formula above, we can set up the equation:

(36 + 0.55x) / (360 + x) = 0.25

Simplifying the equation, we get:

36 + 0.55x = 0.25(360 + x)

36 + 0.55x = 90 + 0.25x

0.3x = 54

x = 180 mL

Therefore, you will need 180 mL of the 55% alcohol mixture to create a 25% alcohol solution.

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Step-by-step explanation:

well, do the division. a fraction is nothing else.

13 divided by 20.

13/20 = 0.65

The value of h is 0.895, the arc cosine of h is 0.462 and it terminates in the correct quadrant

Lastly, the measure of angle θ is 1.46 π

Given that

Terminal point = (-1.79, -0.89)

This means that

(x, y) = (-1.79, -0.89)

Also, we have

Radius, r = 2 units

So, the value of h is

h = |x|/r

This gives

h = |-1.79|/2

Evaluate

h = 0.895

In part (a) of this solution, we have

h = 0.895

Take the arc cos of both sides

So, we have

cos⁻¹(h) = cos⁻¹(0.895)

Evaluate the arc cos using a calculator

So, we have the following representation

h = 0.462 rad

This angle is in the first quadrant

It means that the angle terminates in the correct quadrant

For the value of θ, we have the following

This is calculated as

θ = π + tan⁻¹(-0.89/-1.79)

Evaluate

θ = π + 0.46 π

Evaluate

θ = 1.46 π

Hence, the measure of angle θ is 1.46 π

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The correct answer would be option B i.e. The inverse of the function x = -y² + 4 is a function.

What is a horizontal shift?

A horizontal shift is a type of transformation in which a function is shifted left or right along the x-axis without changing its shape or orientation. If a function f(x) is shifted to the right by a distance of c units, the resulting function is denoted by f(x - c), and if it is shifted to the left by a distance of c units, the resulting function is denoted by f(x + c). Horizontal shifts are commonly used in calculus, geometry, and other branches of mathematics to analyze the behavior of functions and to solve problems related to graphs and equations.

By plotting the inverse of the function the following graph is obtained.

We know that the function is x = -y² + 4.

The inverse of the function x = -y² + 4 would be y = , which is a vertical parabola opening upwards. When we use the horizontal line test, we find that any horizontal line would intersect the once, which means that a single input (x) would have single corresponding output (y). Therefore, the inverse of the function x = -y² + 4 is a function.

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Solving the radical expression √(x + 3) + 4 = 5 for x gives x = -2

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

√(x + 3) + 4 = 5

Subtract 4 from both sides of the equation

So, we have

√(x + 3) = 1

Take the square of both sides

x + 3 = 1

So, we have

x = -2

Hence, the solution for x is -2

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The true statement about monthly income is "The family's monthly income must be less than $5,092." (option a).

The table provided shows the median income levels for different family sizes in various states, including Georgia. To determine whether the family of three is eligible for Chapter 7 bankruptcy, we need to compare their monthly income to the median income for a three-person family in Georgia, which is $61,104.

If the family's monthly income is less than the median income for their family size in their state, they are presumed to be eligible for Chapter 7 bankruptcy. In this case, the family's monthly income must be less than $61,104.

Looking at the table, we can see that the median income for a three-person family in Georgia is $61,104, which means that the family's monthly income must be less than $5,092 in order to be eligible for Chapter 7 bankruptcy.

Therefore, the correct answer is (a) - the family's monthly income must be less than $5,092 for them to be eligible to file for Chapter 7 bankruptcy.

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 0~~)^2 + (~~5 - (-7)~~)^2} \implies d=\sqrt{(-8 +0)^2 + (5 +7)^2} \\\\\\ d=\sqrt{( -8 )^2 + ( 12 )^2} \implies d=\sqrt{ 64 + 144 } \implies d=\sqrt{ 208 }\implies d\approx 14.42[/tex]

Answer:

4√13 or 14.422205101856

Step-by-step explanation:

Distance (d) = √(-8 - 0)2 + (5 - -7)2

= √(-8)2 + (12)2

= √208

= 4√13

= 14.422205101856

Answer:

1. w = [tex]\bold{e^{7+6x}}[/tex]

2. [tex]\bold{t = 2(log_a(7) - log_a(3))}[/tex]

Step-by-step explanation:

1.

a. The exponential form of a logarithmic equation is given by:

[tex]\bold{log_a(b) }[/tex]= c is equivalent to [tex]a^c = b[/tex]

Using this rule, we can rewrite the equation:

ln w = 7 + 6x as w = [tex]\bold{e^{7+6x}}[/tex]

Therefore, the exponential form of the given equation is w = [tex]\bold{e^{7+6x}}[/tex]

2.

a. To solve for t using a logarithm with base a, we can take the logarithm of both sides of the equation:

[tex]\bold{3a^\frac{t}{2} = 7 }\\\bold{log_a3a^\frac{t}{2}= log_a(7)}[/tex]

Using the rule of logarithms that log_a(b^n) = n*log_a(b), we can simplify the left side:

[tex]\bold{log_a(3) +\frac{t}{2} log_a(a) = log_a(7)}[/tex]

Since log_a(a) = 1 for any base a, we can simplify the expression further:

[tex]\bold{log_a(3) + \frac{t}{2}*1= log_a(7)}[/tex]

Now we can solve for t by isolating it on one side of the equation:

[tex]\bold{ \frac{t}{7} = (log_a(7) - log_a(3))} \\ \bold{t = 2(log_a(7) - log_a(3))}[/tex]

Therefore, the solution for t using a logarithm with base a is[tex]\bold{t = 2(log_a(7) - log_a(3))}[/tex]

Answer:

[tex]\textsf{1.} \quad w = e^{7 + 6x}[/tex]

[tex]\textsf{2.} \quad t= \log_a\left(\dfrac{49}{9}\right)[/tex]

Step-by-step explanation:

Exponential form is a way to represent a number using an exponent, where the base is raised to a power.

The natural logarithm function is the inverse of the exponential function:

[tex]\boxed{\ln x=y \iff x=e^y}[/tex]

Therefore we can use this definition to change the given equation to exponential form:

[tex]\begin{aligned}\ln w & = 7 + 6x\\\\e^{\ln w} & = e^{7+6x}\\\\w&=e^{7+6x}\end{aligned}[/tex]

Therefore, the exponential form of the equation is:

[tex]w = e^{7 + 6x}[/tex]

[tex]\hrulefill[/tex]

To solve for t using a logarithm with base a, begin by taking the logarithm of both sides of the equation with base a:

[tex]\log_a (3a^{\frac{t}{2}})=\log_a(7)[/tex]

[tex]\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\log_a (3)+\log_a(a^{\frac{t}{2}})=\log_a(7)[/tex]

Subtract logₐ(3) from both sides of the equation:

[tex]\log_a (3)+\log_a(a^{\frac{t}{2}})-\log_a (3)=\log_a(7)-\log_a (3)[/tex]

[tex]\log_a(a^{\frac{t}{2}})=\log_a(7)-\log_a (3)[/tex]

[tex]\textsf{Apply the log quotient law:} \quad \log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)[/tex]

[tex]\log_a(a^{\frac{t}{2}})=\log_a\left(\dfrac{7}{3}\right)[/tex]

[tex]\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax[/tex]

[tex]\dfrac{t}{2}\log_a(a)=\log_a\left(\dfrac{7}{3}\right)[/tex]

Apply the log law:  logₐ(a) = 1

[tex]\dfrac{t}{2}(1)=\log_a\left(\dfrac{7}{3}\right)[/tex]

[tex]\dfrac{t}{2}=\log_a\left(\dfrac{7}{3}\right)[/tex]

Multiply both sides of the equation by 2:

[tex]2 \cdot \dfrac{t}{2}=2 \cdot \log_a\left(\dfrac{7}{3}\right)[/tex]

[tex]t=2 \log_a\left(\dfrac{7}{3}\right)[/tex]

Finally, apply the log power law:

[tex]t= \log_a\left(\dfrac{7}{3}\right)^2[/tex]

[tex]t= \log_a\left(\dfrac{7^2}{3^2}\right)[/tex]

[tex]t= \log_a\left(\dfrac{49}{9}\right)[/tex]

Therefore, the solution for t in terms of logarithm with base a is:

[tex]\boxed{t= \log_a\left(\dfrac{49}{9}\right)}[/tex]

Answer:

603.36 cubic inches.

Step-by-step explanation:

To find the approximate volume of the mailing cylinder for posters, we can use the formula for the volume of a cylinder, which is given by:

Volume of cylinder = π * r^2 * h

where π is the mathematical constant pi, r is the radius of the cylinder, and h is the height of the cylinder.

Given that the diameter of the cylinder is 8 inches, we can find the radius by dividing the diameter by 2:

Radius (r) = Diameter / 2 = 8 inches / 2 = 4 inches

Given that the length of the cylinder is 12 inches, we can use these values to calculate the approximate volume:

Volume of cylinder = 3.14 * (4 inches)^2 * 12 inches

Volume of cylinder = 3.14 * 16 square inches * 12 inches

Volume of cylinder = 603.36 cubic inches

So, the approximate volume of the mailing cylinder for posters is 603.36 cubic inches.

Answer:

6.8 with a sum of 09.28282

Step-by-step explanation:  

To find the approximate volume of the mailing cylinder for posters, we can use the formula for the volume of a cylinder, which is given by:

Volume of cylinder = π * r^2 * h

where π is the mathematical constant pi, r is the radius of the cylinder, and h is the height of the cylinder.

Given that the diameter of the cylinder is 8 inches, we can find the radius by dividing the diameter by 2:

Radius (r) = Diameter / 2 = 8 inches / 2 = 4 inches

Given that the length of the cylinder is 12 inches, we can use these values to calculate the approximate volume:

Volume of cylinder = 3.14 * (4 inches)^2 * 12 inches

Volume of cylinder = 3.14 * 16 square inches * 12 inches

The volume of cylinder = 603.36 cubic inches

So, the approximate volume of the mailing cylinder for posters is 603.36 cubic inches.

hope it helps!!!

Answer:

Let x be the width of the flag in feet. Then the length of the flag is x + 60 feet. The perimeter of the flag is the sum of the lengths of its four sides, which is:

2(x + x + 60) = 4x + 120 feet

Setting this equal to 480 feet, we have:

4x + 120 = 480

Solving for x, we get:

4x = 360

x = 90

Therefore, the width of the flag is 90 feet and the length is 150 feet.

Three situations to which this system of equations could be applied are:

A farmer wants to plant a rectangular field of flowers. He knows the perimeter of the field but needs to determine the length and width in order to calculate the area and decide how many flowers to buy.

A carpenter wants to build a rectangular frame for a painting. She knows the perimeter of the frame but needs to determine the length and width in order to calculate the amount of wood needed and the cost.

A city planner wants to design a rectangular park. She knows the perimeter of the park but needs to determine the length and width in order to calculate the area and decide how many trees and benches to place in the park.

Answer:

(d) <-21, -7>.

Step-by-step explanation:

To find 7u, we simply multiply each component of u by 7:

7u = 7<-3, -1> = <-37, -17> = <-21, -7>

Answer:

6.2

Step-by-step explanation:

For this we use a method called Pythagoras theorem.

to find '?' we will have to use this method

[tex]A^{2}[/tex] +[tex]B^{2}[/tex] =[tex]C^{2}[/tex]

since we don't know what A is we will name it x

[tex]x^{2}[/tex]+[tex]5^{2}[/tex]=[tex]8^{2}[/tex]

x+25=64

64-25=39

[tex]x^{2}[/tex]=39

x=[tex]\sqrt{39}[/tex]

x=6.2

We fail to reject the null hypothesis, and hence conclude that: Sex of the respondent is independent of the choice for the cause of global warming.

The problem boils down to the following hypotheses:

H0: The sex of the respondent is independent of the choice for the cause of global warming.

H1: The sex of the respondent is dependent on the choice for the cause of global warming.

Chosen level of significance: 0.01

Original Table ,also showing marginals and grand total

Human Activity Natural Patterns Don't Know Marginal Total

Male 323 158 39 520

Female 340 152 38 530

Marginal Total 663 310 77 1050(= Grand total)

Table of expected values :

Human Activity Natural Patterns Don't know

Male 328.343 153.524 38.133

Female 334.657 156.476 38.867

Test Statistic: X2 = (323-328.343)2 / 328.343 + (158-153.524)2 /153.524 + (39-38.133)2 / 38.133 + (340-334.657)2 /334.657 + (152-156.476)2 / 156.476 + ( 38-38.867)2 /38.867

= 0.46974 (approx) = (value of test statistic)

degree of freedom = (2-1)*(3-1)= 2

Therefore, X2 critical (critical value) = 9.210

So, we see that the value of the chi-square test statistic is less than the critical value for alpha=0.01

( 0.46974 < 9.210)

So, we fail to reject the null hypothesis,

and hence conclude that: Sex of the respondent is independent of the choice for the cause of global warming.

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Answer:

x=41

Step-by-step explanation:

If this is a polygon, I'm going to assume that it has 5 sides.

s=(5-2)(180)

s=3(180)

=540

(2x+4)+(3x+6)+(4x-23)+(3x-18)+(2x-3)=540

Now simplify.  Add the x's and the numbers together. Then divide.

14x-34=540

14x=540+34

14x=574

x=574/14

x=41

The value of x when lines MN and PQ are equal is 7

Let take note of the properties of a quadrilateral, they include;

From the information given in the diagram, we have that;

Line MN = Line PQ

Also, the expressions are;

MN = 7x + 13

PQ = 10x - 8

Now, equate the values, we get;

7x + 13 = 10x - 8

collect the like terms

7x - 10x = -8 - 13

subtract the like terms

-3x = -21

Divide both sides by the coefficient of x, we get

x = 7

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The result of multiplication of complex numbers is ¹/₈sin5π/3 -√3/8 cos5π/3 + i¹/₈(cos5π/3 - √3sin5π/3).

The result of the multiplication of the complex number is determined as follows;

-√3 + i  x ¹/₈ (cos 5π/3  + i sin 5π/3)

Multiply the bracket by grouping them as shown below;

= -√3 x ¹/₈ (cos 5π/3  + i sin 5π/3) + i x ¹/₈ (cos 5π/3  + i sin 5π/3)

Multiply out the bracket;

= -√3/8 cos5π/3 -  i√3/8 sin5π/3 + i¹/₈cos5π/3 + ¹/₈sin5π/3

note: i x i = 1

Collect similar terms together and add them if any;

= ¹/₈sin5π/3 -√3/8 cos5π/3 + i¹/₈(cos5π/3 - √3sin5π/3)

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Step-by-step explanation:

Slope  = rise / run

Using points ( -1/2  - 1/2 ) and (1/2, 0 )  

  rise = 1/2    run = 1

     rise / run = 1/2 /1 = 1/2 = slope

An equation for f', the inverse function is: f¹(x) = (x - 3)/7, for x ≥ 4.

The equation is correct as it has been shown that f(f'(x)) = x and f'(f(x)) = x.

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of function f. This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

f(x) = y = 7x + 3

x = 7y + 3

7y = x - 3

y' = f¹(x) = (x - 3)/7, for x ≥ 4.

Proof:

f(f'(x)) = f[(x - 3)/7] = 7[(x - 3)/7] + 3

f(f'(x)) = f[(x - 3)/7] = x - 3 + 3

f(f'(x)) = f[(x - 3)/7] = x.

f'(f(x)) = x

f'(f(x)) = f¹[(7x + 3)]

f'(f(x)) = (7x - 3 + 3)/7

f'(f(x)) = 7x/7

f'(f(x)) = x

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There are 168 different area codes possible with this plan by using the multiplication principle of counting.

What is multiplication principle ?

The multiplication principle of counting, also known as the rule of product, is a counting principle in combinatorics that states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

There are 7 possible choices for the first digit (0 through 6), 3 possible choices for the second digit (2, 3, or 4), and 8 possible choices for the third digit (any digit except 0 or 3). To find the total number of possible area codes, we can use the multiplication principle of counting:

Total number of area codes = Number of choices for first digit x Number of choices for second digit x Number of choices for third digit

Total number of area codes = 7 x 3 x 8

Total number of area codes = 168

Therefore, there are 168 different area codes possible with this plan.

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A:dentrite

B: cell body

C:axon terminal

D:axon

E: nucleus

Answer:

a) Area = 144, so Side length = √144 = 12

b) Area = 96, so Side length = √96 = 4√6

= sqrt96

c) Area = 36, so Side length = √36 = 6

d) Area = 35, so Side length = √35

= sqrt35

Step-by-step explanation:

the equality is: 4 × π × r × r

so the answer is

4 • π • 81

= 324π

Answer:

Step-by-step explanation:

SA= 4[tex]\pi[/tex]r²

    =4[tex]\pi[/tex]9²

    =324[tex]\pi[/tex] m² or 1017.88 m²

Answer:

the median is 100

Step-by-step explanation:

the numbers are already in order so the number in the middle is 100.

Percent decrease =

(difference in prices)/(original price) × 100

(2.85 - 2.78)/2.85 × 100

= (0.07)/2.85 ×100 ≈ 2.5%