Caden is a bird enthusiast and is trying to estimate the number of hawks living in his region. He traps 23 hawks and tags them. Later, he traps 420 hawks, 14 of which are tagged. To the nearest whole number, what is the best estimate for the hawk population?

The value after the multiplication of the given expression gives 1.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given expression is (m y⁻⁴) (m⁻¹ y⁴).

We have to multiply this.

We have some of the rule of exponents that,

xᵃ . xᵇ = xᵃ⁺ᵇ and x⁰ = 1

(m y⁻⁴) (m⁻¹ y⁴) = (m m⁻¹) (y⁻⁴ y⁴)

                        = (m¹⁺⁽⁻¹⁾) (y⁽⁻⁴⁾⁺⁴)

                        = m⁰ y⁰

                        = 1

Hence the value is 1.

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Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

A

Step-by-step explanation:

To find the perimeter you must add all four sides together. Since it's a rectangle, the top and bottom are the same size and the left and right sides are the same size. You add all four together to get the perimeter.

Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for \(S_{n}\) , that is

\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )

with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then

S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188

Answer:

The lower bound = 35.443

The upper bound = 71.697

The error bound = 18.127

Step-by-step explanation:

We are given that a survey of the average amount of cents off that coupons gives was done by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News.

The following data were collected (X): 20cents; 70cents; 50cents; 65cents; 30cents; 55cents; 40cents; 40cents; 30cents; 55cents; 150 cents; 40cents; 65cents; 40cents.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                              P.Q.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean worth of coupons = \(\frac{\sum X}{n}\) = \(\frac{750}{14}\) = 53.57 cents

            s = sample standard deviation = \(\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }\) = 31.40 cents

            n = sample size = 14

            \(\mu\) = population mean worth of coupons

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, \(\mu\) is ;

P(-2.16 < \(t_1_3\) < 2.16) = 0.95  {As the critical value of t at 13 degrees of

                                             freedom are -2.16 & 2.16 with P = 2.5%}  

P(-2.16 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 2.16) = 0.95

P( \(-2.16 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}{\) < \(2.16 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

P( \(\bar X-2.16 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+2.16 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

95% confidence interval for \(\mu\) = [ \(\bar X-2.16 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+2.16 \times {\frac{s}{\sqrt{n} } }\) ]

 = [ \(53.57-2.16 \times {\frac{31.40}{\sqrt{14} } }\) , \(53.57+2.16 \times {\frac{31.40}{\sqrt{14} } }\) ]

 = [35.443, 71.697]

Therefore, a 95% confidence interval for the population mean worth of coupons is [35.443, 71.697].

Answer:

The right answer is D

Step-by-step explanation:

The slope of the first function is 2.5, the slope of the second function is 3, so function 2 has a greater rate of change by \(\frac{1}{2}\).

A cone with a diameter of 16 centimeters has a volume of 320π cubic centimeters, the height of the cone is 15 cm.

A cone should be emptied at a time after being filled with water. The cylinder is filled to a third with each cone. Since there are three of them, the cylinder will be filled. As a result, the volume of a cone is equal to one-third of the volume of a cylinder.

Cone volume is calculated using the method V=1/3πhr².

Given that,

diameter(d) = 16 cm

radius (r) = d/2 = 8 cm

volume = 320π cubic centimeters

πr²h/3 = 320π

or, [π × (8)² × h]/3 = 320π

or,  h = (3 × 320)/(8)²

or, h = 15 cm

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Answer:

x = -1

Step-by-step explanation:

6+4 = 10

14-10 = 4

2x + 6 = 4

2x (-2) = -2

-2 + 6 = 4

Answer:

Step-by-step explanation:

Let's use the formula for the area of a rectangle: Area = Length x Width.

Given that the area of the park is 25/54 square miles and the length is 5/9 miles, we can solve for the width as follows:

Area = Length x Width

25/54 = 5/9 x Width

25/54 ÷ 5/9 = Width

(25/54) x (9/5) = Width

(5/6) x (5/6) = Width

25/36 = Width

Therefore, the width of the park is 25/36 miles, which can be simplified to 5/6 miles.

So the answer is (B) 5/6.

The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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Answer: 10 points, please!

Step-by-step explanation:

1. for the medium you want to find the number thats in the middle. so you have to write out all the numbers in order. then you step by step go to the middle and theres your medium.

0, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6, 6, 7, 11

2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6, 6, 7

2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 6, 6,
2, 3, 3, 3, 3, 3, 3, 5, 5, 6,

3, 3, 3, 3, 3, 3, 5, 5,

3, 3, 3, 3, 3, 5,

3, 3, 3, 3,
3, 3,

The medium is 3.


2. for the mean you add all the numbers up and then divide based on how many numbers there are.

0 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 3 + 5 + 5 + 6 + 6 + 7 + 11 / 16

64/16

4

the average or mean is 4 which tells us that the average number of kids per houshold is 4. and none of the housholds have 4 children. we know this because of the data in the line plot.

the typical houshold size is either 3 or 4. the medium is 3 and the average or mean is 4.

10 points please

Ai = { 1 , 2 , ........ }  is n example of a countably infinite collection .

Describe finite set using an example.

In mathematics, a set is said to have a finite number of elements if it is a finite set. It can be summed up as a collection that you can complete counting. For instance, the finite set 1, 3, 5, 7 has four items.

            A natural number—a non-negative integer—is the component of the finite set. A finite/countable number of members make up a set is said to be finite. Due to their capacity for counting, finite sets are often referred to as countable sets.

Let Ai = { i }                            ; i ∈ N

 A1 = { 1}   A2 = { 2 }  A3 = { 3 } .............

 Then each Ai is a finite set

   U  Ai = { 1 , 2 , ........ }

            = N is not a finite set

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\(a*b\) must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.

Let n be an integer and a, b be relatively prime integers, each of which divides n. This means that a and b have no common factors other than 1. According to the Fundamental Theorem of Arithmetic, the prime factorization of n can be written as n = p1^k1 * p2^k2 * ... * pn^kn. Since a and b divide n, each of their prime factorizations must contain all of the prime factors of n, and the exponents must be less than or equal to the exponents of n. Therefore, a*b must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.

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Answer:

C

Step-by-step explanation:

Using the slope formula, \(\frac{9-6}{-3-(-9)}=-\frac{1}{2}\)

Answer:

j = 139.99 + 139.99 * 0.08625

Answer:

Step-by-step explanation:

The solutions to the system of equations are x = 2 and 4

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

f(x) = x - 3

g(x) = 1/(x - 3)

The solution to the system of equations implies that

f(x) = g(x)

So, we have

x - 3 = 1/(x - 3)

Cross multiply the equation

This gives

(x - 3)² = 1

So, we have

x - 3 = ±1

Add 3 to both sides

x = 3 ± 1

So, we have

x = 2 and 4

Hence, the solutions to the system of equations are x = 2 and 4

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The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.

Multiply her savings by the percent spent:

850 x 0.35 = 297.50

The tv cost $297.50

Answer:

the price of TV is = 297.5$

Step-by-step explanation:

all money= 850$

purchased money= 35% of all money ==> 850 ( 35%) = 297.5$

Answer:

B) x + 3, x > -3

Step-by-step explanation:

I just took a test with this question on it and got it right.

Hope this helps! :)

If function f is written as a piecewise function, it will include x + 3, x > -3

The absolute value function is given as:

f(x) = | x + 3 |

Given that the function is an absolute value function, this means that:

|x + 3| > 0

Remove the absolute sign

x + 3 > 0

Subtract 3 from both sides

x > -3

Hence, if function f is written as a piecewise function, it will include x + 3, x > -3

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Answer:

19e

Step-by-step explanation:

It is useful to determine the predictive accuracy of a choice model and hence option c is correct for confusion matrix

the misclassification error rate for the following xlminer confusion matrix and the accuracy value of the confusion matrix is 10.82% .

In the field of machine learning, specifically the problem of statistical classification (in unsupervised learning, it is typically referred to as a matching matrix), a confusion matrix, also known as an error matrix, is a specific table structure that enables visualizing the performance of an algorithm.

The literature describes both iterations of the matrix, where each row represents instances in an actual class and each column represents instances in a predicted class. Since it is straightforward to tell whether the system is combining two classes, the name was chosen (i.e. commonly mislabeling one as another).

accuracy is given by the formula :

Accuracy(%) = (true positive + true negative)/(positive + negative)

Here TP true positive =10

and TN true negative is 8.2

hence accuracy = (10+8.2) / (1+0)  %

Accuracy = 10.82%

Therefore the accuracy value of the confusion matrix is 10.82% .

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Answer:

yes

Step-by-step explanation:

\(16^{2} +63^{2} =65^{2} \\256+3969=4225\\4225=4225\)

The domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.

To find the domain of a rational expression, we need to identify any values of x that would result in division by zero. Division by zero is undefined in mathematics
In this case, we need to set the denominator, 4x+20, equal to zero and solve for x:
4x + 20 = 0
Subtract 20 from both sides:
4x = -20
Divide both sides by 4:
x = -5
Therefore, the value x = -5 makes the denominator zero.
Now, we need to consider the values of x for which the denominator is not zero. Since the denominator is a linear expression (a polynomial of degree 1), it is defined for all real numbers except x = -5.
So, the domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.

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The equivalent exponential equations are given as follows:

\(2^{4x} = 2^{3(x - 3)}\)

The exponential expression for this problem is defined as follows:

\(2^{4x} = 8^{x - 3}\)

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)

Meaning that the correct option is given by the fourth option.

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The correct option is (d) i.e; MD = 3 with s2 = 20 for the difference scores because it generates a repeated-measures study's population mean difference with the widest 90% confidence interval.

Given that,

Which of the following will result in the widest 90% confidence interval for the population mean difference for a repeated-measures research, provided the sample size is kept constant?

MD = 3 with s2 = 20 for the difference scores.

Therefore, the correct choice is MD = 3 with s2 = 20 for the difference scores because it produces the widest 90% confidence interval for the population mean difference for a repeated-measures study.

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Answer:

Divide both sides by 18. The new coefficients will be the reciprocals of the intercepts:

\(6x-3y=18 \rightarrow \frac6{18}x - \frac3{18}y = 1 \rightarrow \frac x3-\frac y6 =1\) The two intercepts are then 3 and -6.

(I know, dividing by 3 both sides of the equations would have made the whole process way easier).

Alternatively, plug x = 0 to find the y intercept and y=0 to find the x intercept. Either way the graph will look something like the one I'm sketching on paint.

Answer:

Sheri worked 10 hours and Niles worked 8 hours.

Step-by-step explanation:

18-2=16

16/2=8

Niles = 8 hours

Sheri = 8+2= 10 hours

Answer:

A. 511; 6

Step-by-step explanation:

The margin of error would be \(\pm\frac{517-505}{2}=\pm\frac{12}{2}=\pm 6\)

The sample mean would be \(505+6=511\) (or \(517-6=511\))

Mr. X reduces his weight in a ratio of 4:17. This means that for every 4 units of weight he loses, his initial weight was divided into 17 equal parts.

To determine the ratio by which Mr. X reduces his weight, we need to compare his initial weight of 85 kg with his target weight of 65 kg.

The reduction in weight is calculated as the difference between the initial weight and the target weight, which in this case is 85 kg - 65 kg = 20 kg.

The ratio can be expressed as a fraction, where the numerator represents the reduction in weight and the denominator represents the initial weight:

Reduction in weight / Initial weight

Substituting the values, we have:

20 kg / 85 kg

Simplifying the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 5 in this case:

(20 kg / 5) / (85 kg / 5) = 4/17

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