3.37 examples of correlated variables. give an example of two variables in your field of study that are a. positively correlated b. negatively correlated

Approximately it takes 6 years to the population be fewer than 11,000.

If the constant decrease in population be R% per annum, then the population after n years = P(1-R/100)ⁿ.

Given that, A=11,000, rate of interest=8% and P=18,000.

Here, 11,000=18,000(1-8/100)ⁿ

11/18=(1-0.08)ⁿ

0.611=(0.92)ⁿ

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Exact Form:

n=ln(0.611)/ln(0.92)

Decimal Form: n=5.90847701…

n=6

Therefore, approximately it takes 6 years to the population be fewer than 11,000.

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"Your question is incomplete, probably the complete question/missing part is:"

The population of a town is 18,000. it decreases at a rate of 8% per year. In about how many years will the population be fewer than 11,000?

Given the equation AB = BC, we want to find B, assuming that A, B, and C are square matrices and B is invertible. We can conclude that B is invertible.

To do this, we will use the fact that if A is invertible, then we can multiply both sides of the equation by its inverse to isolate B:

AB = BC

[tex]A^-1 AB = A^-1 BC[/tex]

B = A^-1 BC

Here, A^-1 is the inverse of A, and it satisfies the equation[tex]A A^-1 = A^-1 A[/tex]= I, where I is the identity matrix. By multiplying both sides of the equation [tex]AB = BC by A^-1[/tex], we obtain the expression for B.

Now, let's consider the invertibility of B. If A and B are invertible, then the product AB is also invertible. This is because the product of two invertible matrices is invertible, and its inverse is given by the formula [tex](AB)^-1 = B^-1A^-1[/tex]. In this case, since[tex]B = A^-1 BC,[/tex] we can conclude that B is invertible.

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The answers are:

To calculate the interest and maturity value, we need to use the formula:

Interest = Principal x Rate x Time

Maturity Value = Principal + Interest

Where:

For the given information, we have:

Drum Set:

Principal = $900.00

Rate = 4% = 0.04

Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)

Interest = $900.00 x 0.04 x 0.0274 = $0.98

Maturity Value = $900.00 + $0.98 = $900.98

Used Car:

Principal = $1,960.00

Rate = 6% = 0.06

Time = 9/365 = 0.0247 years (assuming an exact interest calculation based on days)

Interest = $1,960.00 x 0.06 x 0.0247 = $2.88

Maturity Value = $1,960.00 + $2.88 = $1,962.88

Used Dirt Bike:

Principal = $4,800.00

Rate = 4% = 0.04

Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)

Interest = $4,800.00 x 0.04 x 0.0274 = $5.23

Maturity Value = $4,800.00 + $5.23 = $4,805.23

School Tuition for Twins:

Principal = $9,675.00

Rate = 6% = 0.06

Time = not specified

We don't have the time period for this investment, so we can't calculate the interest or maturity value without that information.

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The statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.

To determine which statement about 4 √2x + 4 √x + 3 = 0 is true, we need to solve the equation.

However, it is not possible to solve the equation exactly because it contains square roots. We can simplify the equation by multiplying both sides by the conjugates of the square roots, which eliminates the square roots.

Multiplying both sides by (2x + x + 3) / (2x + x + 3), we get:

(4 √2x + 4 √x + 3) * (2x + x + 3) / (2x + x + 3) = 0 * (2x + x + 3) / (2x + x + 3)

Expanding the left-hand side, we get:

12x + 6 = 0

Solving for x, we get:

x = -1/2

So, the statement that is true is: The equation 4 √2x + 4 √x + 3 = 0 has one solution, which is x = -1/2.

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We can interpret from the results that the distribution of data might be negatively skewed.

In the given question it is mentioned that while Morgan was analyzing her data, she notices that the value of her mean is quite a bit smaller than the value of her median.

As we know that, in statistics, when the mean is smaller than the median and mode, it indicates a negatively skewed distribution.

A negatively skewed distribution or left skewed distribution is a type of distribution in which more values are concentrated on the right side of the distribution graph while the left side of the graph is longer.

Hence, we can interpret from these information that the distribution of data of Morgan are negatively skewed.

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The incidence rate of active cases of tb for the 6-month period was  0.00014

An incidence rate describes how quickly disease occurs in a population.

Incidence rate is the rate of new occurrence of a particular disease divided by the population of people at risk of the disease.

So for this question

The number of new  active cases of tb occurring between January 1 and June 30, 2012 was 26

Population at risk  in Baltimore is 183,000

Incidence rate = 26/183,000

The incidence rate of active cases of tb for the 6-month period was           0.00014 or 14 per 100,000 population.

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In circle M, m/NMO = 144º, and the area of the shaded sector = 107. then the length of MN is 23.19 units.

What is the sector of the circle?

That the portion (or part) of the circular region enclosed by two radii and the corresponding arc is called a sector of the circle.

The area of the shaded sector of circle M can be represented as follows:

Area of sector = (m/NMO / 360) * π * r²

We know that m/NMO = 144° and the area of the sector is 107, so we can substitute these values into the equation and solve for the radius:

107 = (144 / 360) * π * r²

Multiplying both sides of the equation by 360 / 144 gives:

360 * 107 / 144 = π * r²

Dividing both sides of the equation by pi gives:

r² = 360 * 107 / (144 * π)

Taking the square root of both sides of the equation gives:

r = √(360 * 107 / (144 * π))

Now that we know the radius, we can use it to find the length of MN.

The length of the minor arc MN is equal to the length of the central angle NMO in radians times the radius:

MN = m/NMO * π * r / 180

Substituting in the values for m/NMO and r gives:

MN = 144 * π * √(360 * 107 / (144 * π)) / 180

Hence, In circle M, m/NMO = 144º, and the area of the shaded sector = 107. then the length of MN is 23.19 units.

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Answer:

ST = 12 units

Step-by-step explanation:

Δ STE and Δ SRA are similar ( AA postulate ) , then the ratios of corresponding sides are in proportion, that is

[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{RA}[/tex] ( substitute values )

[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )

6 ST = 8(21 - ST)

6 ST = 168 - 8 ST ( add 8 ST to both sides )

14 ST = 168 ( divide both sides by 14 )

ST = 12 units

In all together, Clara ate 20 nuts.

A system of equations is a set of one or more equations involving a number of variables.

The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.

Given that Clara snacked on a mix of almonds and pecans. She ate 3 almonds for every 1 pecan. Clara ate 10 more almonds than pecans.

Let the number of pecans be x and the number of almonds is y.

We can write the system of equations as:

y = 3x

y = x + 10

Equating the value of {y}, we get -

3x = x + 10

2x = 10

x = 5          ...(1)

y = x + 10 = 15

y = 15         ...(2)

x + y = 15 + 5 = 20

Therefore, in together, Clara ate 20 nuts.

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Answer:

Step-by-step explanation:

200 rimwjh hdwqheywgygwuivug

Plugging in our known values, we get h = 12,560/3.14(10)^2 = 40.16 feet. Therefore, height of the water tower is 40.16 feet tall.

To calculate the height of the water tower, we can use the formula for the volume of a cylinder. This formula is V = πr^2h, where V is the volume, π is the constant pi (3.14), r is the radius of the cylinder, and h is the height of the cylinder. In this case, the radius of the cylinder is 10 feet and the volume of the cylinder is 12,560 gallons. We can rearrange the formula to solve for h, giving us h = V/πr^2. Plugging in our known values, we get h = 12,560/3.14(10)^2 = 40.16 feet. Therefore, the water tower is 40.16 feet tall.

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Area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To find the area of a parallelogram, we use this equation:

Now that we have this equation, we can apply it to each parallelogram.

Now, we can figure out which has the greatest area.

Therefore, the parallelogram that has the greatest area is 3, or III.

Answer:

III

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

I

A = 3 × 5 = 15 units²

II

A = 5 × 3 = 15 units²

III

A = 4 × 4 = 16 units²

IV

A = 4 × 3 = 12 units²

parallelogram III has the greatest area

Based on the Venn diagram, the number of people in each set are follows:

The number of people in each set in the Venn diagram is calculated as follows:

The universal set has a total of 50 people

Let the intersection of A and B be x

A∩B = x

The number of people in A alone = 24 - x

The number of people in B alone = 30 - x

x + (24 - x) + (30 - x) + 7 = 50

61 - x = 50

x = 61 - 50

x = 11

A∩B = 11

Hence;

The number of people in A alone = 24 - 11

The number of people in A alone = 13

The number of people in B alone = 30 - 11

The number of people in B alone = 19

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The required proportionality relationship between Jordan and his friend for the sit-up is y = 2x.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
Jordan recorded the number of sit-ups he completed during the first 4 track practices, we can establish the proportionality relationship between Jordan and his friend by comparing the number of sit-ups each completed during each practice.

Let's call the number of sit-ups that Jordan and his friend completed during each practice "x" and "y". Then, the number of sit-ups that his friend completed during each practice would be "2x".

The proportionality relationship between Jordan and his friend can be expressed as,

y = 2x

This means that for every 1 sit-up that Jordan completed, his friend completed 2 sit-ups, or that Jordan's friend completed twice the number of sit-ups that Jordan completed during each practice.

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Answer:

hope this helps!! <3

Step-by-step explanation:

A fraction is represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Answer:

$1.89/gal

Step-by-step explanation:

The equation of the line that cuts the x-axis at x = 1 and has a slope of -1 is y = -x + 1.

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

Since the line has a slope of -1 and cuts the x-axis at x = 1, we can find the y-intercept by using the point-slope form of the line equation:

y - y₁ = m(x - x₁)

y - 0 = -1(x - 1)

y = -x + 1

So the equation of the line that cuts the x-axis at x = 1 and has a slope of -1 is y = -x + 1.

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The functions are solved for the inverses and matched as follows

1. not inverse function

2. not inverse function

3. inverse functions

4. not inverse function

5. not inverse function

6. not inverse function

1. g(n) = -1/n + 1 and f(n) = -1/(n - 1)

say y = g(n) = -1/n + 1

y - 1 = -1/n

-y + 1 = 1/n

n = -1/(y - 1)

interchanging the variables

y = -1/(n - 1)

2. The cube root of 4 not in the inverse hence this is not inverse function.

3. g(x) = (x + 2)³ - 3 and f(x) = ∛(x + 3) - 2

say y = g(x) = (x + 2)³ - 3

y + 3 = (x + 2)³

x + 2 = ∛(y + 3)

x = ∛(y + 3) - 2

interchanging the variables

y = f(x) = ∛(x + 3) - 2 this is inverse functions

4.f(n) = 4/(n - 1) - 3 and g(n) = -2/n + 1

say y = f(n) = 4/(n - 1) - 3

y + 3 = 4/(n - 1)

1 / (y + 3) = (n - 1) / 4

4 / (y + 3) = n - 1

4 / (y + 3) + 1 = n

interchanging the variables

y = 4/(n + 3) + 1 this is not inverse functions

5. g(x) = 4/(x - 3) - 2 and f(x) = -2/(x + 1)

say y = g(x) = 4/(x - 3) - 2

y + 2 = 4/(x - 3)

1 / (y + 2) = (x - 3) / 4

4 / (y + 2) = x - 3

4 / (y + 2) + 3 = x

interchanging the variables

y = 4/(x + 2) + 3 this is not inverse functions

6. f(x) = 2/(x - 3) - 1 and g(x) = -3(-x + 2) - 2

say y =  f(x) = 2(x - 3) - 1

y + 1 = 2/(x - 3)

1 / (y + 1) = (x - 3) / 2

2 / (y + 1) = x - 3

2 / (y + 1) + 3 = x

interchanging the variables

y = 1/(x + 1) + 3 this is not inverse functions

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1)

it took

25 min : 35 mile

?? min : 70 mile

cross multiply we get 50 minutes

25 x 70 then divide by 35

2) we used:

4 cups : 90 batches

? cups. : 112.5 batches

cross multiply we get: 5 cups

112.5 x 4 then divide by 90

Pair of ratios can form a true proportion I would usually give 45 points but i have 35 soo ye 25/20, 16/21.

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On solving the provided question we can say that  7/8 show 87 and 1/2% as a fraction

Any number of equal parts or fractions can be used to represent a whole. Standard English fractions indicate how many units of a particular size there are. 8, 3/4. Whole contains fractions. The numerator to denominator ratio is a way of representing numbers in mathematics. Each of these is a simple fractional integer. A complex number has a fraction in its numerator or denominator. A proper fraction has a numerator that is smaller than the denominator. A fraction is a sum that is part of a grand total. It can be evaluated by breaking it down into smaller parts. For example, a whole number or half article is represented as 12.  

7/8 show 87 and 1/2% as a fraction

87 and 1/2% should be written as 87.5%

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The solution is, Right answer: C) -7 is a solution.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

We have the equation 2x² +5x -63 = 0

First, let's find the coefficients a, b and c as ax² +bx +c = 0:

• a = 2

• b = 5,

• c = -63

Now, we will use the formula below to solve this equation:

x = -b ±√b²-4ac/2a

Let's replace the coefficients with the values that we already found:

putting the values we get,

x = -5±23/4

Now, let's divide it into two solutions, look:

x1 = 9/2

x2 = -7

Right answer: C) -7 is a solution.

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The additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem is option C, MN/LK||MN.

The SAS (Side-Angle-Side) similarity theorem states that if two triangles have two pairs of corresponding sides that are in proportion, and the included angles are congruent, then the triangles are similar.

In this case, we know that ΔLKN and ΔKNM share the angle at vertex K, and we also know that LN/MN and LK/KN are in proportion.

However, we need to establish that MN/LK||MN, which means that MN is parallel to LK and forms a transversal with LN.

This information is necessary to establish that the included angles between the corresponding sides are congruent, which is required for the triangles to be similar.

Therefore, option C is the correct additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem.

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The amount that was paid by Ashley is $ 28.05.  

To find the discount on a given price, multiply the discount that is given by the original price and divide the result by 100.
To find the amount that can be paid by the consumer, subtract the resultant discount from the original price.

Final price of item = Original price - Discount  

Here we have

An item is regularly priced at $33.  

The discount that Ashley bought it = 15% off the regular price.  

The amount that Ashely paid for it = $ 33 - 15% of $ 33  

=> $ 33 - $ (15/100 × 33)

=> $ 33 - $ (0.15 × 33)

=> $ 33 - $ 4.95  

=> $ 28.05  

Therefore,

The amount that was paid by Ashley is $ 28.05.

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The approximate side length of the largest square envelope that can be placed into the mailbox without bending it is 0.71x.

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles of 90 degrees each. It is a two-dimensional shape that can be represented by a closed polygon with four straight sides and four right angles.

First, we need to measure the size of the mailbox. Let's say that the length of each side of the mailbox opening is "x" inches. We can then set up an inequality to find the maximum size of the side of the square envelope that can fit into the mailbox. The inequality is:

side length of square envelope ≤ x

This inequality tells us that the side length of the square envelope must be less than or equal to the size of the mailbox opening. We want to find the largest possible side length of the square envelope, so we'll use the "less than or equal to" symbol.

To find the largest possible side length of the square envelope, we'll use the value of "x" to set up an equation. We know that the diagonal of the square envelope will be equal to the length of the side of the square envelope multiplied by the square root of 2. Therefore, we can set up the following equation:

diagonal of square envelope = side length of square envelope × √2

We want to find the maximum side length of the square envelope, so we'll use the maximum value of the diagonal of the envelope. We know that the diagonal of the envelope must be less than or equal to the length of the mailbox opening (which is "x"), so we can set up the inequality:

side length of square envelope × √2 ≤ x

We can solve for the side length of the square envelope by dividing both sides of the inequality by the square root of 2:

side length of square envelope ≤ x/√2

To get the largest possible side length of the square envelope, we'll use the maximum value of "x". Therefore, the largest possible side length of the square envelope that can fit into the mailbox without bending is:

side length of square envelope ≤ x/√2 ≈ 0.71x

We can round this value to two decimal places, which gives us:

side length of square envelope ≈ 0.71x

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Answer:

In trapezium PQRS, AB is parallel to PS and PS is parallel to QR. Since we know the lengths of PA, AQ, and BR, we can calculate the length of SB as follows:

SB = PA + BR - AQ = 3 + 2.1 - 1.4 = 3.7 cm

Answer:

The length of one lap around the path is 2π x 350 m, which is equal to 2200 m.

Jimmy jogs 2200 m x 3 laps x 5 days, which is equal to 33000 m or 33 km.

Step-by-step explanation:

30 minutes twice a day for 184 days, total 368 gallons of water will be used in each hole.

Assuming that each hole uses one gallon of water per 30 minutes.

1 hole = 1 gallon of water

The total amount of water used in each hole over 184 days would be 184 gallons.

So, in 184 days = 184 gallons of water

This is because each hole would be watered twice a day for 184 days, which comes out to 368 separate waterings.

= 184 × 2

= 368 gallons

The total amount of water used would be 368 gallons.

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The complete question is:

How many gallons of water will be used in each hole if 30 minutes is spent twice a day for 184 days?