the bear population in a given area is increasing at a rate of 2% per year. the population is currently about 1580. if this trend continues what is the predicted population after 8 years?

Answer:

x = 3 and y = 1

Step-by-step explanation:

A) most efficient way is to multiply the first equation by 3 to eliminate the 'x' terms and get 9x - 15y = 12

if you add this to -9x + 3y = -24 you will get -12y = -12

y = 1

substitute 1 for 'y' to get 'x':  3x - 5 = 4

3x = 9

x = 3

Correct option is B, The only quadrilateral that satisfies the requirements for a kite is quadrilateral EFGH. A kite has opposed sides that are not congruent and two sets of adjacent sides that are.

One quadrilateral is a closed figure with four sides. These geometric shapes are quadrilaterals: a quadrilateral form. There is just one set of parallel sides to the shape, and there are no right angles.

Each quadrilateral has four sides, four angles, and four vertices. Its inner angles add up to 360 degrees.

4 angles

The four sides of a quadrilateral also create four angles. Here are a few quadrilateral instances. Each figure has four straight sides and four angles, as you can see. Any quadrilateral's interior angles add up to 360°.

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Complete question -

Answer:

C) y= -4 +2

Step-by-step explanation:

Example 1 (3,-10)

-10 = -4 (3) + 2

-10 = -12 + 2

-10 = -10

Example 2 (10,-38)

-38 = -4 (10) + 2

-38 = -40 + 2

-38 = -38

The word problem "the difference of twice a number and one" is equal to 2n - 1.

In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.

In order to translate this word problem into algebraic expression, we would assign a variable to the unknown number and then translate the word problem into algebraic expression as follows:

Let the variable n represent the unknown number.

Translating the word problem into an algebraic expression, we have the following;

Algebraic expression = (2 × n) - 1

Algebraic expression = 2n - 1

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The variable in the study is "miles walked per week", which represents the estimated distance that 150 people living in coastal regions of California walk each week.

The study aimed to understand the walking habits of people living in coastal regions of California by measuring the number of steps they take using pedometers. These steps were then converted into an estimate of distance traveled, and this estimate was used as the dependent variable in the study, referred to as "miles walked per week".

The goal of the study was to better understand the physical activity patterns of the participants and how it might relate to other factors, such as their health, lifestyle, and environment. The data collected could be analyzed to identify trends and make recommendations for promoting healthy physical activity.

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Answer:

Step-by-step explanation:

im pretty sure its 10 divided by 12 or smth

Answer:

Step-by-step explanation:

The graph of h(x) passes the horizontal line test.

If a bloodstain is 1.5cm wide and 30cm long, then the angle of impact is 30°.

In forensic science, the angle of impact is the angle at which a blood droplet strikes a surface. It has a range of 0 to 90 degrees and is, by definition, an acute (or right) angle.

Police can partially reconstruct a crime scene by connecting the "strings" that lead from the spatter to an origin area and knowing the angle of contact.

If a bloodstain has a tail or pattern, the angle of impact can be used to forecast how the subsequent bloodstain would look.

So, bloodstain pattern analysis examines the patterns of bloodstains found at crime scenes in an effort to piece together the sequence of events that led to the bloodshed.

Mathematically, we will have:

The angle of impact = sin⁻¹ (wide stain/length stain)

The angle of impact = sin⁻¹ (1.5/3.0)

The angle of impact = 30°

Therefore, if a bloodstain is 1.5cm wide and 30cm long, then the angle of impact is 30°.

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The probability that the system will function tomorrow is 0.2495 or 24.95%.

To find the probability that the system will function tomorrow, we need to find the probability that at least 4 out of the 6 components will function.

On a rainy day, the probability of 4 components functioning is given by:

P(rainy day and 4 components functioning) = C(6, 4) × (0.5)⁴ × (0.5)² = 15 × 0.0625 × 0.25 = 0.2344

On a non-rainy day, the probability of 4 components functioning is given by:

P(non-rainy day and 4 components functioning) = C(6, 4) × (0.8)⁴ × (0.2)² = 15 × 0.4096 × 0.04 = 0.2534

Now we can find the overall probability of the system functioning tomorrow by using the law of total probability:

P(system functioning tomorrow) = P(rainy day and 4 components functioning) × P(rain) + P(non-rainy day and 4 components functioning) × P(non-rain)

= 0.2344 × 0.20 + 0.2534 × 0.80

= 0.0468 + 0.2027

= 0.2495

Therefore, the probability that the system will function tomorrow is 0.2495 or 24.95%.

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--The given question is incomplete; the complete question is

"A k out of n system is one in which there is a group of n components, and the system will function if at least k of the components function. For a certain 4 out of 6 systems, assume that on a rainy day, each component has a probability of 0.5 of functioning and that on a non-rainy day, each component has a probability of 0.8 of functioning.

Assume that the probability of rain tomorrow is 0.20. What is the probability that the system will function tomorrow?"--

The total amount of time Rebecca's family spends at Mount Rushmore is 51 minutes.

Let's call the total amount of time Rebecca's family spends at Mount Rushmore "t".

According to the information given, 13 minutes of that time is spent watching a movie in the visitor center, which is 16% of the total time spent at Mount Rushmore.

This can be expressed as:

13 minutes / t = 16%

To find the total amount of time t, we need to isolate t in the equation. To do this, we can cross-multiply and solve for t:

13 minutes * 100% = 16% * t

13 minutes * 100% / 16% = t

So, the total amount of time t that Rebecca's family spends at Mount Rushmore is:

t = (13 minutes * 100%) / 16% = 812.5 minutes / 16 = 51 minutes

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The value of x and y of the right triangle is x = y = 15.6

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ABC

Now , the measure of the hypotenuse of the triangle AC = 22

And , the triangle is a 45 - 45 - 90 triangle

So , the sides are in the ratio n : n : n/√2

And , if the measure of the two congruent sides of such a triangle is x each, then the three sides will be x, x and √2x

From the trigonometric relations ,

sin 45° = y/22

Multiply by 22 on both sides of the equation , we get

y = ( sin 45° ) 22

y = 22/√2

On simplifying the equation , we get

y = 15.6

And , the value of x = y = 15.6

Hence , the right triangle is solved

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A histogram would be a better way to represent this data set, as it provides a clear visual representation of the frequency of different values.

A better way to represent the data set would be to use a histogram. A histogram is a graphical representation of a data set that is used to show how frequently certain values occur in the data set. A histogram can be created by first grouping the data into equal intervals, or bins, and then plotting the frequency of each bin on the y-axis of the graph. This allows for easy comparison of the frequency of different values. For example, in the case of the pharmaceutical company’s employee data, one could create a histogram with 5 bins that represent 6-10 months, 11-15 months, 16-20 months, 21-25 months, and 26-30 months. Then, one can plot the number of employees in each bin on the y-axis of the graph. This would provide a clear visual representation of the data set and make it easier to identify any patterns or trends in the data.

A histogram would be a better way to represent this data set, as it provides a clear visual representation of the frequency of different values.

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We select every fifth invoice in a file is systematic sampling.

Systematic sampling is a probability sampling technique where researchers choose individuals from the population at predetermined intervals (or k).

This method will provide you with a representative sample that can be utilized to make inferences about your community of interest if the population order is random or random-looking (for example, alphabetical).

This type of sampling is most suitable when we want to conduct a sampling method similar to simple random sampling but the list of population is unknown to us. However, this can also be used when the list of the same is available to us.

Another important condition is the order or the population, i.e. ow it is spread must be random and not in some particular order or sample. Else the result obtained will lose its credibility.

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Note that as labeled in the attached image:

1) Shapes D and F are similar

2) A and B are NOT similar because they have different ratios of side lengths

3) C and E are NOTE Similar. They are Different Shape.

1) To determine that both shapes are similar, all we need to divide the side lengths of D by two. This gives us:

Breath  - 6/2 = 3

Length - 14/ 7 = 7

Since the Breadth of F is 3ft and it's length 7ft, it means D and F are similar to the ratio of 2:1.

2) If the above logic is applied to A and B, we would see that the side lengths of both shapes have different ratios.

For both of them to be similar, since the breadths - 6/2 = 3 then the length of B ought to be 4ft since 12/4 = 3.

3) By mere observation and understanding of the definition of various shapes, we can tell that C and E are two different shapes.

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-7x² + 5x - 2 is a quadratic polynomial.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

-7x² + 5x - 2

We see that the degree of the polynomial is 2.

Now,

A polynomial with degree 2 is called a quadratic polynomial.

Thus,

It is a quadratic polynomial.

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As per unitary method there are 184 children and 190 adults are admitted.

The unitary method is a method of solving problems by breaking down a quantity into its smaller parts and then finding the relationship between these parts.

Let's represent the number of children admitted as "x" and the number of adults admitted as "y".

We know that the admission fee for children is $1.50 and for adults is $4.00. So, the total amount collected from the children can be represented as 1.5x and the total amount collected from adults can be represented as 4y.

The total number of people admitted is the sum of the number of children and the number of adults, which is

=> x + y = 374.

The total amount collected from the admission fees is $1,036.00, which is equal to the sum of the amount collected from the children and adults, which can be represented as

=> 1.5x + 4y = $1,036.00.

So, we have two equations:

x + y = 374

1.5x + 4y = $1,036.00

We can use the first equation to solve for one of the variables and then substitute that value into the second equation to find the value of the other variable.

Let's solve for y:

y = 374 - x

Now we can substitute this value of y into the second equation:

1.5x + 4(374 - x) = $1,036.00

Expanding the second equation, we get:

1.5x + 1496 - 4x = $1,036.00

Combining like terms, we get:

-2.5x + 1496 = $1,036.00

Subtracting 1496 from both sides:

-2.5x = -460

Dividing both sides by -2.5:

x = 184

So, there were 184 children admitted to the park.

We can use the first equation to find the number of adults:

y = 374 - x

y = 374 - 184

y = 190

So, there were 190 adults admitted to the park.

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A frequency distribution in which high scores are most frequent is said to be positively skewed or right-skewed.

In statistics, skewness refers to the asymmetry of a probability distribution. A frequency distribution is said to be positively skewed or right-skewed if the majority of the data is concentrated on the right side of the distribution, while a few high values are outliers on the right tail. The frequency distribution will look like a graph that is shifted to the right with a longer tail on the right side.

Positive skewness means that the mean (average) of the data will be higher than the median (middle value). The median is a more robust measure of central tendency than the mean in a positively skewed distribution, because it is not influenced by the outliers on the right tail.

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A third point charge put in the center of a square formed by four point charges of equal size will feel more force than if placed at one of the square's vacant corners.

A square is a closed two-dimensional form having four equal sides and four vertices. Its opposing sides are perpendicular to one other. A square can alternatively be thought of as a rectangle with equal length and width. Many items mimic the square form as you look around. A square is a regular quadrilateral with all four sides equal in length and all four angles equal. The square's angles are right angles or equal to 90 degrees. In addition, the square's diagonals are equal and intersect at 90 degrees.

Here,

The point charge at the center of the square will be equidistant from all four charges and will feel the vector sum of their forces, resulting in a greater net force. The point charge, on the other hand, will only be subjected to the pressures of two of the charges at one of the corners, resulting in a lesser net force.

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Answer: The answer is 34 degrees.

Step-by-step explanation: Angle 1 and angle 5 are the same.

less than 85 milligrams per liter.

To find the probability that a water specimen has an alkalinity level of fewer than 85 milligrams per liter, we can use the standard normal distribution and convert the value of 85 milligrams per liter to a standard score (z-score). The z-score can be calculated using the formula:

z = (x - mean) / standard deviation

Where x is the value of interest (85 milligrams per liter), mean is the mean of the distribution (80 milligrams per liter), and the standard deviation is the standard deviation of the distribution (4.2 milligrams per liter).

Plugging in the values, we get:

z = (85 - 80) / 4.2 = 1.19

Next, we can use a standard normal table or calculator to find the probability of getting a value less than the z-score of 1.19. This probability is approximately 0.8707, so there is about an 87.07% chance that a water specimen collected from the river has an alkalinity level of fewer than 85 milligrams per liter.

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The ratio will be Illustrated this:

1 minute or news = 20 minutes of music

2 minutes if news = 40 minutes for music

3 minutes of news = 60 minutes of music

4 minutes of news = 80 minutes of music

The ratio is 1:20.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

The ratio will be Illustrated this:

1 minute or news = 20 minutes of music

2 minutes if news = 40 minutes for music

3 minutes of news = 60 minutes of music

4 minutes of news = 80 minutes of music

In this case, one has to just multiply by 20.

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1. The value of the fractions will be:

1 5/12 - (1 1/2 - 5/12) = 1/3

2 - 2 3/4 × -1/7 = 11/28

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

= 1 5/12 - (1 1/2 - 5/12)

= 1 5/12 - (1 6/12 - 5/12)

= 1 5/12 - 1 1/12

= 4/12

= 1/3

- 2 3/4 × -1/7

= -11/4 × -1/7

= 11/28

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The smallest integer that can possibly be the sum of an infinite geometric series whose first term is 9 is not possible.

An infinite geometric series is a series that continues indefinitely, where each term is found by multiplying the previous term by a constant ratio.

To determine the convergence limit, we must first determine if the series converges. The series converges if the absolute value of the common ratio is less than 1. If the series converges, the sum can be found using the formula:

S = a / (1 - r)

Where S is the sum, a is the first term of the series (9 in this case), and r is the common ratio. For the sum to be an integer, the denominator (1 - r) must equal 1, which means r must equal 0.

This is not possible, as the absolute value of the common ratio must be less than 1 for the series to converge.

Therefore, the sum of the series cannot be an integer.

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The probability of a student completing the final examination in less than 65 minutes is 13.45%.

The time it takes to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes and a standard deviation of 12 minutes. This can be expressed mathematically as X~N(77, 12).

The probability of a student completing the final examination in less than 65 minutes can be calculated by using the Z-score formula:

Z = (x - μ) / σ

Where x = 65 minutes, μ = 77 minutes, and σ = 12 minutes.

Plugging these values into the formula, we get:

Z = (65 - 77) / 12 = -1.17

Using a Z-score table, we can find the probability of a student completing the final examination in less than 65 minutes, which is equal to 0.1345, or 13.45%. Therefore, the probability of a student completing the final examination in less than 65 minutes is 13.45%.

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The maximum area of the rectangle is 12100 square feet  when the owner of a used tire store wants to construct a fence to enclose a rectangular outdoor storage area.

To find the dimensions of the outdoor storage area with the most area, we need to maximize the product of the length and width of the rectangle.

Let's assume that the length of the rectangle is x and the width is y.

Since one side of the store, which is 240 feet long, will be used as one of the sides of the rectangle, the total length of the remaining three sides is 460 feet.

So, the sum of the lengths of the other two sides must be

[tex]460 - x = 460 - 240 = 220 feet.\\[/tex]

Since the width and length of the rectangle are related by [tex]y = 220 - x[/tex] , we can substitute this into the expression for the area, which is given by [tex]A = x * y = x * (220 - x)[/tex]

To find the maximum value of A, we can differentiate this expression with respect to x and set the derivative equal to zero, which will give us the value of x that maximizes the area.

The critical points occur at x = 0 and x = 220/2 = 110.

Since the area is a continuous function, it follows that the area will be at a maximum at the larger of the two critical points, which is x = 110.

Thus, the length and width of the rectangle with the largest area are 110 feet and 110 feet, respectively.

The maximum area of the rectangle is

[tex]x * y = 110 * 110 = 12100 ft^{2}[/tex]

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There will be total of 722 winning hands are in total.

Let's consider the two conditions for winning separately:

3 or more face cards:

There are 12 face cards in a standard deck of 52 cards, so there are [tex]${12 \choose k}$[/tex] ways to choose k face cards out of 5, where k = 3, 4, or 5.

The total number of winning hands in this case is [tex]{12 \choose 3} + {12 \choose 4} + {12 \choose 5} = 220[/tex]

All non-face cards with even numbers:

There are 16 even-numbered non-face cards in a standard deck,

So there are [tex]${16 \choose k}$[/tex] ways to choose k of these cards, where k = 0, 2, 4.

The total number of winning hands in this case will be:

[tex]{16 \choose 0} + {16 \choose 2} + {16 \choose 4} \\= 1 + 45 + 456 \\= 502[/tex]

The total number of winning hands is the sum of the number of hands that satisfy each condition,

So there are a total of 220 + 502 = 722 winning hands.

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Answer:

a) 12b

b) 10h+5

Step-by-step explanation:

a) 12b means $12 x "b" unknown amount of books

b) 10h+5 means $10 x unknown amount of hours babysitting plus $5 gas which is a set cost no matter how many hours babysitting

I don't know if you need to put the $ in your answer or not, based on the directions i would say not.

The slope of a line can be determined by taking a ratio of the change in y-axis to the change in x-axis.

The y-intercept of any graph of a linear equation is at the point where the x-value is equal to zero (x = 0).

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Generally speaking, the slope-intercept form is modeled by this equation:

y = mx + c

Where:

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Answer:

14

Step-by-step explanation:

if ​Y=1​+X+u​, where X​, Y​, and ​u=v+X are random​ variables, v is independent of X​; ​E(v​)=0, ​Var(v​)=1​, ​E(X​)=1, and ​Var(X​)=2, then Var(Y|X​) = Var ( 1 + X + u | X)  = 0 + 4*2 + 1 = 8 + 1 = 9

if ​Y=1​+X+u​, where X​, Y​, and ​u=v+X are random​ variables, v is independent of X​; ​E(v​)=0, ​Var(v​)=1​, ​E(X​)=1, and ​Var(X​)=2, the variance of the following cases are calculated as:

Var(u|X​=1) = Var( v + X | X = 1) = Var( v + 1 )    

                = Var(v) + Var(1)                            

                 = 1 + 0 = 1

Var(Y|X​=1) = Var( 1 + X + u | X = 1 )

                = Var (1 + X + v + X|X=1)

                = Var(1 + 1 + v + 1)                      

                = Var(3) + Var(v)                      

                = 0 + 1 = 1

​Var(u|X​) = Var ( v + X | X)

            = Var ( v + X)

            = Var(v) + Var(X)

            =  1 + 2  = 3

Var(Y|X​) = Var ( 1 + X + u | X)

            = Var ( 1 + X + v + X | X)

            = Var ( 1 + 2X + v)

            = Var(1) + Var(2X) + Var(v)

              = 0 + 4*2 + 1 = 8 + 1 = 9

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