Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

a. no correlation
b. positive correlation; as time passes, the birth rate increases.
c. positive correlation; as time passes, the birth rate decreases.
d. negative correlation; as time passes, the birth rate decreases.

If Alex sells 30 bracelets in the first month and increases her sales by 6 bracelets each month, she will sell a total of 360 bracelets in the first 12 months.

To determine the total number of bracelets Alex will sell in the first 12 months, we can use a simple arithmetic progression. Alex sells 30 bracelets in the first month, and her goal is to sell 6 more bracelets each subsequent month. This means that in the second month, she will sell 30 + 6 = 36 bracelets. In the third month, she will sell 36 + 6 = 42 bracelets, and so on.

We can observe that the number of bracelets sold forms an arithmetic sequence with a common difference of 6. To find the total number of bracelets sold in the first 12 months, we can sum the terms of this arithmetic sequence. Using the formula for the sum of an arithmetic series, which is Sn = (n/2)(2a + (n-1)d), where a is the first term, d is the common difference, and n is the number of terms, we can calculate the total number of bracelets sold.

In this case, a = 30 (the first term), d = 6 (the common difference), and n = 12 (the number of terms). Substituting these values into the formula, we get Sn = (12/2)(2(30) + (12-1)(6)) = 6(60 + 11*6) = 360.

Therefore, Alex will sell a total of 360 bracelets in the first 12 months if she meets her goal of selling 6 more bracelets each month than the previous month.

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Answer:

a

Step-by-step explanation:

20 min x 6 = 2 hour

18 feet x 6 = 108 feet

Answer:

ok, the correct answer should be R(1.5)=R(2)!

Step-by-step explanation:

I did this my class before!

Answer:

1. Limited representation: Polar coordinates can only represent points on a two-dimensional plane. Therefore, it is not well-suited to represent three-dimensional shapes or objects.

2. Complex conversion: Polar coordinates can be hard to convert into Cartesian coordinates (x,y) or vice versa, especially for complicated functions. This makes it difficult to work with in many mathematical applications.

3. Ambiguity: Sometimes there can be more than one polar coordinate representation for a single point, which can lead to confusion and errors.

4. Limited domain: The polar coordinate system is limited to functions with a radial symmetry, which is a significant disadvantage in many mathematical applications.

5. Difficulty in visualizing complex functions: It can be difficult to visualize complex functions in polar coordinates, especially without advanced computer software or graphing tools.

6. Not universally used: The Cartesian coordinate system is widely used in most fields, including math, physics, and engineering. Polar coordinates are not as widely used, which can make it difficult to communicate concepts effectively.

Step-by-step explanation:

142 degrees

Since alternate exterior angles are equal, therefore;

Find the angle measures

Since both angles are equal, the sum of the angles is expressed as;

Therefore the sum of the angle measures is 142 degrees

Answer:

1) g < -6

2) x < -5

3) f < 2

4) y ≤ -2

5) p ≥ 2

Answer:

4-5i

Step-by-step explanation:

Answer:

4-5i

Step-by-step explanation:

(5-2i)-(1+3i)

5-2i-1-3i

5-1-2i-3i

4-5i

Answer:

-2

Step-by-step explanation:

the answer is -2

The solution to the equation 1/5x - 2 = 4 is given by x = 30.

Given data:

To solve the equation (1/5)x - 2 = 4, we will isolate the variable x as:

Step 1: Add 2 to both sides of the equation to eliminate the -2 term on the left side:

(1/5)x - 2 + 2 = 4 + 2

On simplifying:

(1/5)x = 6

Step 2: Multiply both sides of the equation by 5 to get rid of the fraction (1/5):

5 * (1/5)x = 5 * 6

On simplifying:

x = 30

Hence, the solution x = 30.

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Answer:

x=6

Step-by-step explanation:

11, 3, x, x+2, 5, 10

in ascending order the data points:

Answer: X is less than or equal to 5.

Step-by-step explanation: The amount of money she spends is either less than 5, or at 5.

Answer: 12m

Step-by-step explanation:

Each member sells 12 tickets, so you would have to multiply the amount of tickets(12) by the amount of members(m).

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

Explanation:

1 person sells 12*1 = 12 tickets

2 people sell 12*2 = 24 tickets

3 people sell 12*3 = 36 tickets

....

m people sell 12*m = 12m tickets

m is a placeholder for a positive whole number (1,2,3,...)

Answer:

The fourth answer, WBD is correct.

Step-by-step explanation:

As you can see the three points W, B and D all fall on the same line, which means that they are indeed colinear.

Answer:

W, B and D all fall on the same line, which means that they are indeed colinear.

Step-by-step explanation:

Answer:

34.16

Step-by-step explanation:

42.7

x 0.8

-------

34.16

Answer:

34.16

Step-by-step explanation:  

2 5

42.7

 x

0.8

 =  

43.16

Answer:

The mean is,

C) 68

Step-by-step explanation:

The mean is calculated using the formula,

\(m = (sum \ of \ the \ terms)/(number \ of \ terms)\\\)

Now, there are 6 terms (in this case numbers) so,

we have to divide by 6,

and sum them.

\(m = (57+90+70+68+61+62)/6\\m=408/6\\\\m=68\)

Hence the mean is 68

Answer:

an = a1 + (n-1)d

Untuk barisan ini, kita dapat menentukan a1 = 4 dan d = 3, karena selisih antar suku bertambah 3. Jadi, rumusnya menjadi:

an = 4 + (n-1)3

a5 = 4 + (5-1)3

a5 = 4 + 12

a5 = 16

Jadi, suku ke-5 dari barisan ini adalah 16.

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Answer:

You have to apply Trigonometry Formula :

\( {sin}^{2} θ + {cos}^{2} θ = 1\)

\(1 + {tan}^{2} θ = {sec}^{2} θ\)

Next, you have to prove it :

\((1 + {tan}^{2} θ)(1 - {cos}^{2} θ) = {tan}^{2} θ\)

\(LHS = (1 + {tan}^{2} θ)(1 - {cos}^{2} θ)\)

\(LHS = ( {sec}^{2} θ)( {sin}^{2} θ)\)

\(LHS = ( \frac{1}{ {cos}^{2} θ} )( {sin}^{2} θ)\)

\(LHS = \frac{ {sin}^{2} θ}{ {cos}^{2} θ} \)

\(LHS = {tan}^{2} θ\)

\(∴LHS = RHS \: (proven)\)

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

4(7y-8)

Step-by-step explanation:

The set that best represents the domain of this function would be:

{0, 1, 2, 3, 4, 5, 6, 7, 8}

What is domain?

In mathematics, a domain typically refers to a set of values for which a mathematical function or expression is defined and produces a valid output.

The domain of a function represents the set of all possible input values that the function can take. In this case, the function represents the number of bouquets used by the florist for the wedding, and the constraint is that no more than 8 bouquets can be used.

Therefore, the set that best represents the domain of this function would be:

{0, 1, 2, 3, 4, 5, 6, 7, 8}

This set includes all possible values of bouquets that the florist can use, and it satisfies the given constraint of not using more than 8 bouquets.

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Answer:

Pencils: 7 boxes

Erasers: 5 boxes

Step-by-step explanation:

She should buy 70 pencils and 70 erasers.

There are 7 pencil boxes for 70 pencils.

There are 5 eraser boxes for 70 erasers.

These are the smallest number of boxes she can buy without getting a fraction of a box.

Therefore, the dimensions of the largest area he can enclose are 749 yards by 1498 yards with an area of 1,121,502 square yards.

Let the length of the rectangular grazing land be x and the width be y. Then we know that the total amount of fencing used is given by:

2x + y = 2996

We want to maximize the area A of the grazing land, which is given by:

A = xy

We can solve the first equation for y:

y = 2996 - 2x

and substitute into the equation for A:

A = x(2996 - 2x)

Expanding the equation, we get:

A = 2996x - 2x^2

To find the maximum value of A, we take the derivative and set it equal to zero:

dA/dx = 2996 - 4x = 0

Solving for x, we get:

x = 749

Substituting this value back into the equation for y, we get:

y = 1498

Therefore, the dimensions of the largest area he can enclose are 749 yards by 1498 yards. The area is:

A = xy = 749 * 1498 = 1,121,502 square yards.

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In 1940, John Atanasoff, a physicist from Iowa State University, wanted to solve a 29 x 29 linear system of equations. To solve this system using Gaussian elimination, it would have required approximately 29^3/3 = 24389 arithmetic operations.

In 1940, John Atanasoff developed the Atanasoff-Berry Computer (ABC), which was the first electronic computer. Atanasoff wanted to use the ABC to solve a 29 x 29 linear system of equations.

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The global maximum and minimum values of f(x, y) subject to the constraint x^2 + y^2 = 80 are both approximately 15.314, and they occur at the points (2√5, -4√5) and (-2√5, 4√5), respectively.

To use Lagrange multipliers, we need to define the Lagrangian function as follows:

L(x, y, λ) = f(x, y) - λg(x, y)

where g(x, y) is the constraint function, which in this case is g(x, y) = x^2 + y^2 - 80.

So, we have:

L(x, y, λ) = (x - 1)^2 + (y + 2)^2 - λ(x^2 + y^2 - 80)

Next, we need to find the partial derivatives of L with respect to x, y, and λ, and set them equal to 0:

∂L/∂x = 2(x - 1) - 2λx = 0

∂L/∂y = 2(y + 2) - 2λy = 0

∂L/∂λ = x^2 + y^2 - 80 = 0

Simplifying the first two equations, we get:

x(1 - λ) = 1

y(1 - λ) = -2

Dividing these two equations, we get:

x/y = 1/-2 => x = -y/2

Substituting this into the constraint equation, we get:

(y/2)^2 + y^2 = 80 => 5y^2 = 320 => y = ±4√5

Substituting this back into x = -y/2, we get:

x = ∓2√5

So, the critical points are (2√5, -4√5) and (-2√5, 4√5).

To determine whether these are maximum or minimum values, we need to compute the second partial derivatives of L:

∂^2L/∂x^2 = 2 - 2λ

∂^2L/∂y^2 = 2 - 2λ

∂^2L/∂x∂y = 0

At the critical points, we have λ = 1/5, so:

∂^2L/∂x^2 = -2/5 < 0, so (2√5, -4√5) is a local maximum.

∂^2L/∂y^2 = -2/5 < 0, so (-2√5, 4√5) is a local maximum.

To determine whether these are global maximum or minimum values, we need to compare the values of L at these critical points and at the endpoints of the constraint region:

L(2√5, -4√5) ≈ 15.314

L(-2√5, 4√5) ≈ 15.314

L(4√2, 0) = 18

L(-4√2, 0) = 18

So, the global maximum and minimum values of f(x, y) subject to the constraint x^2 + y^2 = 80 are both approximately 15.314, and they occur at the points (2√5, -4√5) and (-2√5, 4√5), respectively.

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A: In a frequency table, each category listed in one column has a characteristic about it in the second column. The table described in the given statement has this property.

B: The set of states is clearly defined and each state has a clearly defined capitol.

A frequency table is a tabular representation of data that shows the number of times each category or value occurs. In a frequency table, one column represents the categories or values, and the other column represents their corresponding frequencies.

A: The statement makes sense. In a frequency table, each category listed in one column has a characteristic about it in the second column. The table described in the given statement has this property.

B: The statement makes sense. The set of states is clearly defined and each state has a clearly defined capitol.

C: The statement does not make sense. In a frequency table, each category must have a frequency greater than 1. Because each state has exactly one capitol, each category in the table described in the given statement would have frequency 1.

D: The statement does not make sense. In a frequency table, one of the columns lists the frequency of each category, which is the number of data values in the category. The table described in the given statement does not have this column.

The correct answer is:

A: In a frequency table, each category listed in one column has a characteristic about it in the second column. The table described in the given statement has this property.

B: The set of states is clearly defined and each state has a clearly defined capitol.

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Answer:

3 1/8

Step-by-step explanation:

1. You can add the 2 halves together making 1

2. Then add a 3/4 and one 1/4 together making another 1

3. With the remaining two 1/4s, that makes another half. So at the moment, you have 2 1/2

4. Convert 2 1/2 to eighths. 2 4/8

5. Finally add one 5/8.

So the answer is 3 1/8

Jill drinks \(\rm 3\dfrac{1}{8} gallons\) of water in a week.

A Line plot can be defined as a graph that displays data as points or check marks above a number line, showing the frequency of each value.

It is given in the question that Jill drinks

1/4 gallons for 3 days

1/2 gallons for 2 days

5/8 gallons for 1 day

and 3/4 gallons for 1 day

The total amount of water Jill drinks is

(1/4)*3+(1/2)*2+(5/8)*1+(3/4)*1

=(3/4)+1+(5/8)+(3/4)

=25/8

\(\rm = 3\dfrac{1}{8} gallons\)

Therefore Jill drinks \(\rm 3\dfrac{1}{8} gallons\) of water in a week.

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Answer: Since y = tan θ = y / x , and y and x are coordinates of a point, y can be any real number and x can be any real number except 0. Thus, the ratio y / x can be any real number, and we conclude that the range of y = tan θ is all real numbers. ... y = csc θ = r/ y , since sin θ and csc θ are reciprocals of one another.

Step-by-step explanation:

Since y = tan θ = y / x , and y and x are coordinates of a point, y can be any real number and x can be any real number except 0. Thus, the ratio y / x can be any real number, and we conclude that the range of y = tan θ is all real numbers. ... y = csc θ = r/ y , since sin θ and csc θ are reciprocals of one another.

The period of the function is the interval between repetitions of any function. A trigonometric function's period is the length of one whole cycle. As a starting point, we can use x = 0 for any trigonometry graph function. Trigonometric functions have a periodic nature. As opposed to tangent and cotangent, which have period, sine, cosine, secant, and cosecant all have period 2.

Studying the correlations between triangle side lengths and angles is the subject of trigonometry, a branch of mathematics. By using geometry to study astronomy, the field first appeared in the Hellenistic civilization during the third century BC. The earliest documented tables of values for trigonometric ratios (sometimes called trigonometric functions) such as sine were developed by mathematicians in India, while the Greeks concentrated on chord calculation.

Geodesy, surveying, celestial mechanics, and navigation are just a few of the fields where trigonometry has been used historically. The various identities of trigonometry are well recognized.

These trigonometric identities are frequently used to simplify, discover a more practical form for, or solve equations involving trigonometric expressions.

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complete question:

Explain what is meant by the period of a trigonometric function. what are the periods of the six trigonometric functions?

1.Substitute

2.Calculate

Hope it helps

Answer: idrek

Step-by-step explanation:..