The population of a town increased from 3800 in 2007 to 6100 in 2010 find the absolute and relative (percent) increase.

Binomial expansion is used to factor expressions that can be expressed as the power of the sum of two numbers.

The proof that (1.01)^12 exceeds (1.02)^6 by 0.0007 is\(\mathbf{(1.01)^{12} - (1.02)^6 \approx 0.0007 }\)

The expressions are given as:

\(\mathbf{(1.01)^{12}\ and\ (1.02)^6}\)

A binomial expression is represented as:

\(\mathbf{(a + b)^n = \sum\limits^n_{k=0}^nC_k a^{n - k}b^k}\)

Express 1.01 as 1 + 0.01

So, we have:

\(\mathbf{(1.01)^{12} = (1 + 0.01)^{12}}\)

Apply the above formula

\(\mathbf{(1.01)^{12} = ^{12}C_0 \times 1^{12 - 0} \times 0.01^0 + ......... .......... + ^{12}C_{12} \times 1^{12 - 12} \times 0.01^{12} }}\)

\(\mathbf{(1.01)^{12} = 1 \times 1 \times 1 + ......... .......... + 1 \times 1 \times 10^{-24} }}\)

\(\mathbf{(1.01)^{12} = 1 + ......... .......... + 10^{-24} }}\)

This gives

\(\mathbf{(1.01)^{12} = 1.1268\ (approximated)}\)

Similarly,

Express 1.02 as 1 + 0.02

So, we have:

\(\mathbf{(1.02)^6 = (1 + 0.02)^6}\)

Apply \(\mathbf{(a + b)^n = \sum\limits^n_{k=0}^nC_k a^{n - k}b^k}\)

\(\mathbf{(1.02)^6 = ^6C_0 \times 1^{6 - 0} \times 0.02^0 + ^6C_1 \times 1^{6 - 1} \times 0.02^1 +.............. + ^6C_6 \times 1^{6 - 6} \times 0.02^6 }\)\(\mathbf{(1.02)^6 = 1 \times 1 \times 1 + 6 \times 1 \times 0.02 +.............. + 1 \times 1 \times 6.4 \times 10^{-11} }\)

\(\mathbf{(1.02)^6 = 1 + 0.12 +.............. + 6.4 \times 10^{-11} }\)

This gives

\(\mathbf{(1.02)^6 = 1.1261\ (approximated) }\)

Calculate the difference as follows:

\(\mathbf{(1.01)^{12} - (1.02)^6 \approx 1.1268 - 1.1261 }\)

\(\mathbf{(1.01)^{12} - (1.02)^6 \approx 0.0007 }\)

The above equation means that:

(1.01)^12 exceed the value of (1.02)^6 by 0.0007

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Answer:

\(\frac{50}{50\\}\) \(= \frac{65}{50}\)

Now cross-multiply

Let p represent the percentage

50(50) = 50(65) ; 2500p = 3250

now divide 2500 on both sides to find p

2500p/2500 and 3250/2500

p = 1.3 ; percentage change is equal to %1.3 increase

Answer: Yes, they are independent, and 0.4444444...

Step-by-step explanation:

A: Yes, they are independent. in this situation, no matter what either gender takes, it will not effect the other gender.

B: 30/67.5=0.44444444444444444444444444444444444444 etc

            We can just do 30/65=6/13= approx 0.46

Answer:

See explanation

Step-by-step explanation:

For the first question, gender should be an independent variable, not affected by the number of people that take Spanish or french. Though it should be noted that women appear to take fewer courses of Spanish nd french, and both take less for french than Spanish, the women to a harsher degree.

For the second question, it would be 30/67.5 or 0.444, etc.

Answer: 3

3,000,000,000

Step-by-step explanation:

Billions have 9 zeros

Answer:

the digit is 6

263,136,816,799

           |

Step-by-step explanation:

i put  a line below which 6 it is hope this helps!

Answer: Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A

Step-by-step explanation:

Taking LHS  :

⇒Cosec 2 A + Cot 4 A

⇒Cosec 2 A + ( Cot 2 A )2

⇒Cosec 2 A + ( Cosec 2 A - 1 )2  (  we know : 1 + Cot 2 θ =  Cosec 2 θ )

⇒Cosec 2 A +  Cosec 4 A  + 1  - 2 Cosec 2 A

⇒ Cosec 4 A  + 1  - Cosec 2 A

⇒ Cosec 4 A  + 1  - ( 1 + Cot 2 A)

⇒ Cosec 4 A  + 1  -  1 - Cot 2 A

⇒ Cosec 4 A  - Cot 2 A

or cosec2A+cosec4A=cotA-cot4A

Answer:

-8

Step-by-step explanation:

●Answer attached●

☆Hope it helps☆

Answer:

its option one

Step-by-step explanation:

Answer:

D. Both of the dot A and B have the same mean

Answer:

S - 8

Step-by-step explanation:

S - 8.

hope this helps! Have a great day!

Answer:

Hi it is like

Find the greatest common factor​ (GCF) of 42a3b, 24a2b2, and 24ab38

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Take the amount it takes carlos add the difference between carlos and raj to get the amount it takes raj

4+3=7

The equation shows that the number of toys that must be bought for them to have equal profit will be 212 toys.

From the information, it should be noted that the equation that can be used to represent the information about Jaclyn company will be:

= 2125 + (49.99 × x)

= 2125 + 49.99x

The equation that can be used to represent the information about Richie company will be:

= (39.95 × x)

= 39.95x

Therefore, we will equate both equations:

2125 + 49.99x = 39.95x

49.99x - 39.95x =2125

10.04x = 2125

x = 212

Therefore, the number of toys that must be bought for them to have equal profit will be 212 toys.

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9514 1404 393

Answer:

Step-by-step explanation:

5(t +2h) --- the group total is 5 times the individual total. Each bought one ticket and 2 hot dogs.

__

5t +10h --- the group total is the total spent for tickets plus the total spent for hot dogs. 5 tickets and 10 hot dogs were purchased by the group.

Answer:

a = 150

Step-by-step explanation:

Sum to infinity of a geometric series

\(S_{\infty}=\dfrac{a}{1-r}\:\textsf{ for }|r| < 1\)

where:

Given:

Substitute the given values into the formula and solve for a:

\(\begin{aligned}S_{\infty} & =\dfrac{a}{1-r}\\\\\implies 100 & =\dfrac{a}{1-\left(-\frac{1}{2}\right)}\\\\ 100 & =\dfrac{a}{1+\frac{1}{2}}\\\\100 & = \dfrac{a}{\frac{3}{2}}\\\\a & = \dfrac{3}{2} \cdot 100\\\\a & = 150\end{aligned}\)

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Answer: The total cost of the gas before it was split among the friends.

Explanation: If they split it equally, they divide. 3g is divided by 4 so you know that there are 4 friends/people.

Since they are splitting the [total] amount of gas for 4 people, 3g must be the total cost of the gas.

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Answer:

c

Step-by-step explanation:

i took the quiz

Answer:

Step-by-step explanation:

Givens

L = 5       inches

w = 4/3   inches.

Formula

Area = L * w

Solution

Area = 5 * 4/3

Area = 20/3

Area = 6 2/3

Or area = 6.67 square inches

Answer:

X = 5

Step-by-step explanation:

28 = 7x + 3 - 2x

28 = 5x + 3

28 - 3 = 5x + 3 - 3

25 = 5x

25/5 = 5x/5

X = 5

Answer:

X = 5

Step-by-step explanation:

1. Combine like terms.

2. Subtract 3 from both sides.

3. Simplify.

4. Divide both sides of the equation by the same term.

5. Simplify.

Hope this helps!

Answer: See explanation

Step-by-step explanation:

Your question isn't complete but let me help out.

You said that you thought of number J, and then subtracted half of it from 34. This can be mathematically written as:

= 34 - (J/2)

Let's reframe the question and assume that you thought of a number J, and then subtracted half of it from 34 and the answer you get is 12. To find J goes thus:

You subtract half of J from 34 and equate it to 12. This will be:

34 - (J/2) = 12

Collect like terms

34 - 12 = J/2

22 = J/2

J = 22 × 2

J = 44

In this scenario, J = 44. We can check to confirm.

Check: 34 - (J/2)

= 34 - (44/2)

= 34 - 22

= 12

Answer:

34 - (J/2)

Step-by-step explanation:

Answer: 99

Step-by-step explanation:

Supplementary angles add to 180 degrees, 180-81=99

Explanation:

The y coordinate can be thought of the height of each point. As long as the height is above ground, then y is greater than 0.

For point A, its height is y = 3.5 and point D has height y = 2.5

It might help to draw horizontal lines from the point until you reach the y axis to determine the height.

Points B and C have negative heights. They can be thought of as locations somewhere underground.

The functions for this problem are defined as follows:

The functions for this problem are given as follows:

The addition and subtraction functions for this problem are given as follows:

At x = -2, the numeric value of the subtraction function is given as follows:

(t - s)(-2) = -2³ - 5(-2)²

(t - s)(-2) = -28.

The product function for this problem is given as follows:

(ts)(x) = \(5x^5\)

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Answer:

Line B is y=-1/8x-4

Step-by-step explanation:

We are given that:

Line A is y=8x+12

Line C is y=-x-4

Line B is perpendicular to Line A, and has the same y intercept as line C.

The equations are written in slope-intercept form, or y=mx+b, where m is the slope and b is the y intercept

The y intercept of line B is -4, which is also the y intercept of line C

here's our equation for line B so far:

y=mx-4

perpendicular lines have slopes that are negative and reciprocal; when you multiply them, they equal to -1.

To find the slope of Line B, use this formula:

8m=-1

divide by 8

m=-1/8

the slope of Line B is -1/8

So Line B is y=-1/8x-4

Hope this helps!

We conclude that the image of (-8, -8), after a dilation by a scale factor of 1/4, is (-2, -2).

For a point (x, y), a dilation by a scale factor of k gives the point (k*x, k*y).

Now, in this case, we have the point (-8, -8) and the scale factor is k = 1/4.

Then, using the above relation, we can write the coordinates of the image after the dilation as:

(-8*(1/4), -8*(1/4)) = (-2, -2).

We conclude that the image of (-8, -8), after a dilation by a scale factor of 1/4, is (-2, -2).

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Answer:

x = -3

y = 0

Step-by-step explanation:

The values of the coordinates x and y is P ( 6 , 3 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( x , y )

Let the second point be Q ( 0 , 0 )

Now , the slope of the line is m₁ = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = y / x

m₁ = 1/2

So , y/x = 1/2

And , x = 2y

Now , the third point is R ( 7 , 5 )

m₂ = ( 5 - y ) / ( 7 - x )

m₂ = 2

On simplifying , we get

( 5 - y ) / ( 7 - x ) = 2

Multiply by ( 7 - x ) , we get

5 - y = 14 - 2x

Adding 2x and subtracting 5 on both sides , we get

2x - y = 9

Substitute the value of x from m₁ , we get

2 ( 2y ) - y = 0

3y = 9

Divide by 3 on both sides , we get

y = 3

And , the value of x = 6

Hence , the coordinate of the point P is P ( 6 , 3 )

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Answer:

x - y + z = 8

2x +3y -z= -2

3x - 2y -9z = 9

Step-by-step explanation:

[1 - 1  1  8]

[2  3  -1 -2]

[3 -2 -9  9]

Answer:

the answer is b

Step-by-step explanation:

i got the question correct with the answer b

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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Answer: X = 21/6

Step-by-step explanation:

The angle is a 90 degree angle.

that means we know 21x+6=90

21x = 90-6

21x=84

x = 84/24

x = 21/6

x = 21/6

this is the answer I believe