The initial population of a town is 15 000, and it grows with a
doubling time of 10 years. What will the population be in 12 years?
24 years?

Using cross product, the vector can be proven as [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.

The vector OB can be expressed as OB = b since b is a unit vector and O is the origin.

The vector OA can be expressed as OA = 2b since the magnitude of a is twice that of b.

The angle between a and b is 60°, so we have:

|a| |b| cos 60° = a · b

2|b| · 1/2 = a · b

|b| = a · b

We can now express the vector [OB + (1 - O)A] as:

[OB + (1 - O)A] = b + (1 - O)2b

= (2 - O) b

The cross product of a and [OB + (1 - O)A] is:

a × [OB + (1 - O)A] = a × [(2 - O) b]

= (2 - O) (a × b)

The magnitude of the cross product is:

|a × [OB + (1 - O)A]| = |(2 - O) (a × b)|

= |2 - O| |a| |b| sin 60°

= √3 |2 - O| |b| |a| / 2

= √3 |2 - O| |b|^2 |b| / 2

= √3 |2 - O| |b|^3 / 2

Substituting |b| = a · b, we get:

|a × [OB + (1 - O)A]| = √3 |2 - O| (a · b)^3 / 2

Since |a × [OB + (1 - O)A]| is equal to √k for some constant k, we can set:

√k = √3 |2 - O| (a · b)^3 / 2

Squaring both sides, we get:

k = 3 (2 - O)^2 (a · b)^6 / 4

Therefore, [a×[ob + (1-o)a] = √k is shown to be true, where k = 3 (2 - O)^2 (a · b)^6 / 4.

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Answer:

Step-by-step explanation:

To solve the equation 9x^2 - 36x = 0 by using the square root method, we first need to rearrange the terms to get x^2 and x on one side:

9x^2 - 36x = 0

Factor out 9x from the left-hand side:

9x(x - 4) = 0

Now we have two factors: 9x = 0 and x - 4 = 0. Solving for x in each factor gives us:

9x = 0: x = 0

x - 4 = 0: x = 4

Therefore, the solutions to the equation are x = 0 and x = 4.

Answer:

x = 0, x = 4

Step-by-step explanation:

Unfortunately, the equation 9x^2 - 36x = 0 cannot be solved using the square root method directly. The square root method is used to solve quadratic equations of the form ax^2 + bx + c = 0 by isolating the x^2 term, taking the square root of both sides, and solving for x. However, in the given equation, there is no constant term (c = 0), and therefore, we need to use a different method to solve it.

As I mentioned earlier, we can factor the equation and use the zero product property to solve for x. This method involves finding two factors of the quadratic equation that multiply to give 0, setting each factor equal to 0, and solving for x. In this case, we can factor out x and obtain the factors x and (9x - 36), which multiply to give 0. By setting each factor equal to 0 and solving for x, we obtain the solutions x = 0 and x = 4.

To solve the equation 9x^2 - 36x = 0 using the factorization method:

Factor out x from the left-hand side of the equation to get:

x(9x - 36) = 0

Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, set each factor equal to zero and solve for x:

x = 0 or 9x - 36 = 0

For the second equation, solve for x:

9x - 36 = 0

9x = 36

x = 4

Therefore, the solutions to the equation are x = 0 and x = 4.

Note that this method involves factoring the quadratic equation and then using the zero product property to obtain the solutions. It works for any quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a is not equal to zero.

The cost price of the article when a profit of 22% is made after selling it for a certain price 's' can be calculated using the formula c = 0.78 * s.

Let's assume the cost price of the article is 'c'. Then, the profit made on selling the article is:

Profit = Selling price - Cost price

Since a profit of 22% was made on the selling price 's', we can express the selling price as:

Selling price = Cost price + Profit

= Cost price + 0.22 * Selling price

Rearranging this equation, we get:

0.78 * Selling price = Cost price

Substituting the given selling price 's' into this equation, we get:

0.78 * s = c

Therefore, the cost price of the article is 0.78 times the selling price. If we know the selling price 's', we can calculate the cost price 'c' using this formula. For example, if the selling price of the article is $100, then the cost price would be:

c = 0.78 * s

= 0.78 * $100

= $78

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If you spend a $5 per turn on a fair game to win $15 for each win and you lose the first round but win the next two rounds, then the net payoff is $15

Since you spend $5 per turn and play three rounds, your total cost is $5 x 3 = $15.

If you win a game, you receive $15, so winning two games will give you $15 x 2 = $30.

However, since you lost the first round, you only won two out of three rounds. Therefore, your net payoff is:

= $30 - $15

Subtract the numbers

= $15

Therefore, your net payoff is $15

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The eccentricity for r=5/2+1sin theta and  the equation of the directrix of r=26. 4/4+4. 4 cos theta is 0.5 and x=6

To find the eccentricity of the polar equation r = 5/2 + 1sin(θ), we first need to convert it to rectangular form:

r = 5/2 + 1sin(θ)

r = 5/2 + 1y/r

r^2 = (5/2)r + y

x^2 + y^2 = (5/2)r + y

x^2 + y^2 = (5/2)√(x^2 + y^2) + y

x^2 - (5/2)√(x^2 + y^2) + y^2 = 0

We can see that this is the equation of a conic section, specifically an ellipse, since the signs of the x^2 and y^2 terms are the same. The standard form of an ellipse centered at the origin is:

x^2/a^2 + y^2/b^2 = 1

Comparing this to our equation, we can see that a^2 = (5/2) and b^2 = 1. The eccentricity of an ellipse is given by:

e = √(1 - b^2/a^2)

Plugging in our values, we get:

e = √(1 - 1/(5/2))

e = √(3/5)

e ≈ 0.5

Therefore, the answer is (A) 0.5.

To find the equation of the directrix for the polar equation r = 26.4/4 + 4.4cos(θ), we first need to convert it to rectangular form:

r = 26.4/4 + 4.4cos(θ)

r = 6.6 + 4.4x/r

r^2 = 6.6r + 4.4x

x = (r^2 - 6.6r)/4.4

We can see that this is the equation of a parabola, since the highest degree of the variable r is 2. The standard form of a parabola with its focus at (0, p) is:

y = (1/4p)x^2

Comparing this to our equation, we can see that p = -6.6/4 = -1.65. The directrix of a parabola is a line perpendicular to the axis of symmetry and located at a distance of |p| from the focus. Since the axis of symmetry is the x-axis, the equation of the directrix is:

y = 1.65

However, since the question asks for the equation of the directrix in terms of x, we can rewrite this as:

x = 0

Therefore, the answer is (C) x = 6.

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Answer:

The answer is G

Answer:  B

Step-by-step explanation:

A two-way relative frequency table, in general, is an effective instrument for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and conduct methodical hypothesis testing.

A tool used to display the connection between two sets of paired data is a two-way relative frequency table, which arranges the data in rows and columns. The frequency of each combination is indicated in the chart, which can also be used to determine its relative frequency, which is calculated as the frequency of the combination divided by the total number of observations.

The benefit of using a two-way relative frequency table to illustrate relationships between pairs of paired data is that it gives a more comprehensive image of the data and the interrelationships between the variables. More specifically, it enables us to:

Finding patterns and trends is simple thanks to the table's presentation of the data. We can see which combinations are more or less prevalent than others by examining the relative frequencies of each set of values, and we can spot patterns in the data that might not be obvious otherwise.

Calculate conditional probabilities: Conditional probabilities are the likelihoods of one event given the occurrence of another event, and they can be determined using the chart. We can determine the likelihood that a smoker is male or female and the likelihood that a non-smoker is male or female, for instance, if we have a two-way table illustrating the connection between gender and smoking status.

Testing hypothesis: The table can be used to evaluate theories about how the variables are related to one another. A chi-square test, for instance, can be used to determine whether gender and smoking status are significantly associated.

In general, a two-way relative frequency table is an effective tool for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and test theories in a methodical manner.

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Answer:

2 ounces per person

Step-by-step explanation:

So, if we have the original coordinates of point G, we can swap the x and y values and negate the new y-value to find the coordinates of point G after a 90° counterclockwise rotation about the origin.

To perform a 90° counterclockwise rotation about the origin, we can use the following transformation:

x' = -y

y' = x

This means that the new x-coordinate (x') will be the negative of the original y-coordinate (y), and the new y-coordinate (y') will be the original x-coordinate (x).

If we have the coordinates of point G, we can apply this transformation to find the new coordinates after the rotation.

Let's say that the coordinates of point G are (x, y). Then, the new coordinates (x', y') after the rotation will be:

x' = -y

y' = x

So, the new coordinates will be (-y, x). Therefore, if we want to find the new coordinates after a 90° counterclockwise rotation, we just need to swap the x and y values and negate the new y-value. This gives us the following coordinates for point G after the rotation:

G' = (-y, x)

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The areas of each part of the composite figure are;

Triangle A = 20 Square units

Triangle B = 2 Square units

Rectangle C = 4 Square units

Triangle D = 6 Square units

Area is a measurement of the two-dimensional surface of a shape or object. Area is often used when measuring the size of a plot of land or other physical space, such as a room or an outdoor area.

The area of each part of the figure can be found by adding the areas of the individual shapes that make up the figure. The area of a triangle can be found by using the formula A = 1/2bh, where b is the base and h is the height of the triangle. For a rectangle, the area is equal to the length multiplied by the width.

The composite figure's component parts' respective areas are;

20 Square Units = Triangle A

Triangle B = 2 units of the square

Square units = 4 for the rectangle C.

Triangle D = 6 units of the square

The formula for a triangle's area is straightforward;

A = 0.5 × base × height

Triangle A's area is;

Triangle A: (6 + 2 + 2) × 4 × 1/2

= ¹/₂ × 10 × 4

equals 20 square units

Triangle B's perimeter is;

Triangle A equals 1/2 × 2 × 2

equals 2 square units

Length × Width = Area of Rectangle C

= 2 × 2

equals 4 square units

Triangle D's area is;

Triangle D is equal to.5 × 6.

equals 6 square units

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Complete question -

Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.

Base area of the bag = 4 × 2 = 8 in²

Base area of the candle = 2 × 1 = 2 in²

therefore, we know that base area to be filled with sand:

= 8 - 2 = 6 in²

now, height of sand is known to be between 1/2 and 3/4 inches,

therefore, we can make out that the volume of land is between 6 × 1/2 in³ and 6 × 3/4 in³

3 in³ and 4.5 in ³

therefore, amount of sand is between 3 cubic inches and 4.5 cubic inches, with this we know that Sal should put the sand which is in between the amount of 3 cubic inches and 4.5 cubic inches inside the bag surrounding the base of the candle.

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Answer:

429

Step-by-step explanation:

The area of the triangle is 715.7 square units, rounded off to one decimal place.

The given triangle's side lengths and the angles are a = 52, B = 115°, and C = 29°. The area of the triangle can be determined by applying the formula:A = (1/2) a² sin B sin C, where a is the length of the side opposite to angle A.The area of the triangle is  (rounding off to one decimal place)Therefore, the area of the triangle is 715.7 square units, rounded off to one decimal place.

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Answer:

429

Step-by-step explanation:

The remainder when f(x)=-6x^23+x^11-x^6+2x is divided by x+1 is -7.

Explanation: In this question, we can solve the problem by using the Remainder Theorem. The remainder theorem states that when we divide a polynomial f(x) by x−a then we get a remainder equal to f(a). So, here we can take a=−1 and find the remainder of f(x).

Here is the given polynomial,

()=−6^23+^11−^6+2

We are asked to find the remainder when f(x) is divided by x+1. Using the remainder theorem, we can find the remainder of f(x) by evaluating f(−1).

(−1)=−6(−1)^23+(−1)^11−(−1)^6+2(−1)=6+1+1−2=6

Now, we have the remainder as 6. However, we need the remainder when f(x) is divided by x+1. The relationship between the remainder and the divisor of a polynomial is that when we divide a polynomial f(x) by x−a, we get a remainder of r(x) such that:

()=(−)()+()

where q(x) is the quotient of the division.

So, the question asks us to divide the polynomial f(x) by x+1 and get the remainder. Here is the long division of f(x) by x+1:

The remainder is −7. Therefore, the remainder when f(x) is divided by x+1 is -7.

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Answer:

x = 1 , y = 10

Step-by-step explanation:

Given : y = 8 + 2x

by substitution,

4x + 8 + 2x = 14
6x + 8 = 14
6x = 14 - 8
6x = 6
x = 6/6 = 1


y = 8 + 2x
y = 8 + 2(1)
y= 10

Proof :
if x = 1,

4 (1) + 8 +2 (1) = 14
4 + 8 + 2 = 14
14 = 14

if y = 10 and x = 1

4 ( 1) + 10 = 14
4 + 10 = 14
14 = 14



For both equations, LHS = RHS
Therefore Proved.


hope it helps!

Answer:

14, 7, 0, -7.

Step-by-step explanation:

To find the first four terms of the sequence, we can substitute different values of n into the given expression and simplify.

The expression for the nth term of the sequence is 7(3 - n).

Let's find the value of the first term (n = 1):

T₁ = 7(3 - 1) = 7(2) = 14

The first term of the sequence is 14.

Now, let's find the value of the second term (n = 2):

T₂ = 7(3 - 2) = 7(1) = 7

The second term of the sequence is 7.

Next, let's find the value of the third term (n = 3):

T₃ = 7(3 - 3) = 7(0) = 0

The third term of the sequence is 0.

Finally, let's find the value of the fourth term (n = 4):

T₄ = 7(3 - 4) = 7(-1) = -7

The fourth term of the sequence is -7.

Therefore, the first four terms of the sequence are:

To find the first four terms of the sequence, we can substitute different values of n into the given expression and simplify.

The expression for the nth term of the sequence is 7(3 - n).

Let's find the value of the first term (n = 1):

T₁ = 7(3 - 1) = 7(2) = 14

The first term of the sequence is 14.

Now, let's find the value of the second term (n = 2):

T₂ = 7(3 - 2) = 7(1) = 7

The second term of the sequence is 7.

Next, let's find the value of the third term (n = 3):

T₃ = 7(3 - 3) = 7(0) = 0

The third term of the sequence is 0.

Finally, let's find the value of the fourth term (n = 4):

T₄ = 7(3 - 4) = 7(-1) = -7

The fourth term of the sequence is -7.

Therefore, the first four terms of the sequence are:

14, 7, 0, -7.

Therefore , the solution of the given problem of probability comes out to be the medium addition because it has the greatest expected utility (0.72).

The primary goal of the structures within a methodology expression known as criteria is to provide an indication of the probability that the assertion is true or that a specific event will occur. Any number between zero and one, at which 0 is frequently indicated as a possibility and 1 has frequently used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.

Here,

The following formula can be used to determine each option's anticipated financial value:

=> EMV of big addition =  (0.4 * $100,000) plus (0.6 * -$40,000) for a total of $16,000.

=>  EMV of the middle addition is

= (0.4 * $40,000) plus (0.6 * -$10,000) for a total of $14,000.

=>  EMV of a minor addition =  (0.4 * 10,000) plus (0.6 * 5,000), which equals $6,000

The large addition should be chosen by the physicians as it has the greatest expected financial value of $16,000.

dividing each outcome's usefulness value by its likelihood, then adding the results:

=> (0.4 * 1.0) + (0.6 * 0.0) = 0.4 is the EU of the big addition.

=> (0.4 * 0.9) + (0.6 * 0.6) = 0.72 is the EU of medium addition.

Smaller EU =  (0.4 * 0.5) +  (0.6 * 0.6) = 0.58

The doctors should choose the medium addition because it has the greatest expected utility (0.72), according to expected utility theory.

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From the given information provided, the percent of yellow tint in the new mixture is 36.4%.

The total amount of yellow tint in the original mixture is:

0.30 × 50 liters = 15 liters

When 5 liters of yellow tint are added to the mixture, the total amount of yellow tint becomes:

15 + 5 = 20 liters

The total amount of new mixture is:

50 + 5 = 55 liters

To find the percentage of yellow tint in the new mixture, we divide the amount of yellow tint by the total amount of the mixture and multiply by 100:

(20/55) × 100 = 36.4%

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Answer:

yes you are right

Step-by-step explanation:

move 4 to other side so its -3x=12

divide 12 by -3

x=-4

Answer:

What's your question

Step-by-step explanation:

How many customers in each tower

Using the binomial expansion theorem, the values of integers p and q are -8 and 24, respectively

From the question, we are to use the binomial expansion to expand the given expression and determine the values of p and q.

We can expand (1 - 2x)^4 using the binomial theorem as follows:

(1 - 2x)^4 = 1^4 - 4(1^3)(2x) + 6(1^2)(2x)^2 - 4(1)(2x)^3 + (2x)^4

= 1 - 8x + 24x^2 - 32x^3 + 16x^4

Now, we will compare this expression to the given expression

Comparing the expression to the given expression, 1 + px + qx^2 - 32x^3 + 16x^4

We see that:

p = -8

q = 24

Hence, the values p and q are -8 and 24, respectively.

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Answer:  1 hour 50 minutes  

Step-by-step explanation: it took her 2 hours to get home

she left home at 11:30 am it took her 45 minutes to jog to the park by the time she got to the park it was 12:15 pm she exercised for  1 hour and 55 minutes by the time she was done her work out it is 1:10 if she finished at 3 pm it took her 1 hour 50 minutes to get home

Answer:

the answer to ur question is: 1218816

Answer: we can't see the images

Step-by-step explanation:

Answer:

Step-by-step explanation:

be can not see the pictures sir do better ni***

Answer:

cubic unit eg m³

Step-by-step explanation:

Raised to power 3

Answer:

Units cubed or unit^3

Explanation:

Volume= (base)(width)(height), therefore, this would be cubed. x^3

Area=(base)(height), therefore, this would be squared. x^2

Answer: To find the relative frequency for each discount, we need to divide the number of customers who received each discount by the total number of customers.

Discount           Number of customers                          Relative Frequency

10%                    70                                                            0.35

25%                   99                                                            0.495

30%                   31                                                             0.155

To determine if it is appropriate for the manager to want approximately half of the customers to receive the 25% discount, we can calculate the relative frequency for the 25% discount and compare it to 0.5 (or 50%).

Relative frequency for 25% discount = 99/200 = 0.495

Since the relative frequency for the 25% discount is already very close to 0.5, it seems like an appropriate method to achieve the manager's goal. However, it's worth noting that this method may not be the most effective in terms of maximizing profits or customer satisfaction. It's always important for businesses to carefully consider their pricing strategies and discount policies.

Step-by-step explanation: