A population of a certain species of bird is 18,000 animals and is increasing at the rate of 9% per year.Write an equation for y , the population at time t (in years), representing the situation.y= How many birds are in the population after 14 years?

\(10^3 = 10 \times 10 \times 10 = 1000\)

Answer:

Alberta's total overtime pay of the week was $ 145.80.

Step-by-step explanation:

Given that Alberta worked 6 hours at time-and-a-half pay, and 3 hours at double-time pay, and that the value of her regular work hour is $ 9.72, to determine the value of the pay of his overtime, the following equation must be performed:

6x1.5x9.72 + 3x2x9.72 = X

9x9.72 + 6x9.72 = X

87.48 + 58.32 = X

145.8 = X

Therefore, Alberta's total overtime pay of the week was $ 145.80.

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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Answer:

hgkgbnnhm,

Step-by-step explanation:

the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

Answer:

10 and 5

Step-by-step explanation:

10-5=5

10+5=15

Answer:

10 and 5

Step-by-step explanation:

Difference means subtraction and sum means addition, so two numbers added together is 15 but subtracted is 5 so we know that the sum is 15 and when one of the numbers subtracts the other, the difference is 5, so 5 is one of the numbers. Therefore:

15 - 5 = 10, 10 is the other number

The place value in the thousands for the 0 in 10,000 is three (3).

A place value refers to a numerical value which denotes a digit based on its position in a given number and it includes:

In this scenario, the place value in the thousands for the 0 in 10,000 is three (3).

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9514 1404 393

Answer:

  5/6

Step-by-step explanation:

We assume you want the ratio ...

  (20 hr)/(24 hr) = (4·5)/(4·6) = 5/6 . . . . . factors of 4 and hours cancel

The ratio is 5/6.

given that m is parallel to n,

the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.

using the corresponding angle rule we know that:

2x + 16 = 96

2x = 80

so x = 40

If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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Answer:

let's hope for the best ....XD

Answer:

ummmm....iam sorry I tried but failed ,umm...I think he got your answer see from there!! sorry!!

Answer:

The frequency table is shown below.

Step-by-step explanation:

The data set arranged ascending order is:

S = {33 , 34 , 39 , 48 , 49 , 50 , 53 , 54 , 55 , 56 , 58 , 58,  60 , 63 , 64 , 65 , 70 , 71 , 74 , 84}

It is asked to use the minimum value from the data set as the lower class limit for the first row.

So, the lower class limit for the first class interval is 33.

To determine the class width compute the range as follows:

\(\text{Range}=\text{Maximum}-\text{Minimum}\)

          \(=84-33\\=51\)

The number of classes requires is 5.

The class width is:

\(\text{Class width}=\frac{Range}{5}=\frac{51}{2}=10.2\approx 10\)

So, the class width is 10.

The classes are:

33 - 42

43 - 52

53 - 62

63 - 72

73 - 82

83 - 92

Compute the frequencies of each class as follows:

Class Interval                  Values                        Frequency

   33 - 42                      33 , 34 , 39                             3

   43 - 52                      48 , 49 , 50                            3

   53 - 62          53 , 54 , 55 , 56 , 58 , 58,  60              7

   63 - 72                 63 , 64 , 65 , 70 , 71                      5

   73 - 82                              74                                  1

   83 - 92                             84                                   1

   TOTAL                                                                   20

Compute the relative frequencies as follows:

Class Interval          Frequency        Relative Frequency

   33 - 42                        3                   \(\frac{3}{20}\times 100\%=15\%\)

   43 - 52                        3                   \(\frac{3}{20}\times 100\%=15\%\)

   53 - 62                        7                   \(\frac{7}{20}\times 100\%=35\%\)

   63 - 72                        5                   \(\frac{5}{20}\times 100\%=25\%\)

   73 - 82                         1                   \(\frac{1}{20}\times 100\%=5\%\)

   83 - 92                         1                   \(\frac{1}{20}\times 100\%=5\%\)

   TOTAL                        20                          100%

Step-by-step explanation:

\( \frac{5}{135} \times 100\% = 3.703\% \\ \\ = 3.7\%\)

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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You bought:

1 notebook

4 eraser

Total Cost = 25.

Now, given Notebook = $5, so

25 - 5 = 20 dollars are left for [4 erasers]

So, each eraser would cost:

20/4 = 6 dollars

Thus,

Each Eraser Cost = $6

Answer:52Step-by-step explanation:4^2*6^2 ( find 4 to the power of 2 & 6 to the power of 2 )= 16+36 ( add )= 52 ( final answer )

Answer:

52

Step-by-step explanation:

4² + 6² = ?

4 · 4 = 16

6 · 6 = 36

16 + 36 = 52

Hope this helps!

Answer:

The set D has 5 elements - 3, 6, 9, 12, and 15, all of which are multiples of 3.

The particle travels approximately 45.63 units along the path. The displacement is the straight-line distance between the initial and final positions of the particle is 2781.

To find the distance the particle travels along the path, we can integrate the speed over the interval of time. The speed of the particle is given by the magnitude of its velocity vector.

The velocity vector is the derivative of the position function r(t):

\(v(t) = (d/dt)(t^3/3, t^2, 2t)\)

\(= (t^2, 2t, 2)\)

The speed of the particle at any given time t is:

|v(t)| = √((t^2)^2 + (2t)^2 + 2^2)

= √(t^4 + 4t^2 + 4)

= √((t^2 + 2)^2)

To find the distance traveled along the path, we integrate the speed function over the given interval of time. The particle travels from t = -1/3 to t = 9.

distance = ∫[from -1/3 to 9] |v(t)| dt

= ∫[from -1/3 to 9] |t^2 + 2| dt

= ∫[from -1/3 to 0] -(t^2 + 2) dt + ∫[from 0 to 9] (t^2 + 2) dt

= [-1/3 * t^3 - 2t] (from -1/3 to 0) + [1/3 * t^3 + 2t] (from 0 to 9)

Evaluating the definite integrals:

distance = [-1/3 * 0^3 - 2 * 0 - (-1/3 * (-1/3)^3 - 2 * (-1/3))] + [1/3 * 9^3 + 2 * 9 - (1/3 * 0^3 + 2 * 0)]

= [0 - (1/3 * (-1/27) + 2/3)] + [1/3 * 729 + 18]

= [1/27 + 2/3] + [729/3 + 18]

= 1/27 + 2/3 + 729/3 + 18

= 1/27 + 18/27 + 729/3 + 18

= (1 + 18 + 729)/27 + 18

= 748/27 + 18

= 27.63 + 18

= 45.63 units (approximately)

Therefore, the particle travels approximately 45.63 units along the path.

To find the average speed, we divide the distance traveled by the time taken. The time taken is 9 - (-1/3) = 9 1/3 = 28/3.

average speed = distance / time

= 45.63 / (28/3)

= 45.63 * (3/28)

= 4.9179 units per unit time (approximately)

The displacement is the straight-line distance between the initial and final positions of the particle.

displacement = |r(9) - r(-1/3)|

= |(9^3/3, 9^2, 2 * 9) - ((-1/3)^3/3, (-1/3)^2, 2 * (-1/3))|

= |(27, 81, 18) - (-1/27, 1/9, -2/3)|

= |(27 + 1/27, 81

= 2781.

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Answer:

The answer should be 236g.

Step-by-step explanation:

If we take the amount of flour used for the cake as 'x,' the flour used to make the scones would be (500-x)×2/3 as 2/3 of the remaining is used for the scones.

We know that 60g more flour is used for the cake.

So,

x-60=(500-x)×2/3

Cross multiply, and brng the 3 to the other side.

3(x-60)=(500-x)2

3x-180=1000-2x

Bring the x-terms to one side and the numbers to one side.

3x+2x=1000+180

5x=1180

Divide both sides by 5 to find x(the amount of flour used to make the cake)

Therefore,

x=236g

The factored form is (5x+2)(x-4).

What is factorization?

A number, matrix, or polynomial may be broken up or decomposed into factors that, when multiplied together, produce the original number, matrix, etc. This process is known as factorization or factoring.

Here, we have

Given:  5 x squared minus 18 x minus 8

we have to find the factored form.

= 5x² - 18x - 8

= 5x² - 20x + 2x - 8

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

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

Hence, the factored form is (5x+2)(x-4).

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Answer:

$ 2,890

Step-by-step explanation:

Volume of a cube = width x length height

Cubic root of 4913 = 17 feet

Area of the floor = 17 x 17 = 289

289 x 10 = $2,890

Answer:

2/5 (2 by 5) hope this helps :)

Answer:

Vertex N corresponds to Vertex S

Side QR corresponds to Side LM

Answer: the answer is A

Step-by-step explanation:

Answer:

b. 15

Step-by-step explanation:

Given that:

There are 4 independent variables, then the subset regression total is 2⁴ = 16 attainable regression model.

However, out of these 16 regression models, 1 Model contains no predictors which only intercept 3 Model with \((X_1), (X_2), (X_3)\), 3 Model with\((X_1,X_2), (X_1,X_3), (X_2,X_3)\). and 1 Model which comprises all the independent variables.

Therefore, when applying best subsets regression with a model that possesses four (4) independent variables, the number of different combinations of regression models that can be considered is 15.

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer: B i think

Step-by-step explanation:

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms.