A power company serves 17,000
customer's homes in a town. The
population of the town is decreasing by
about 3% every year. Which function
would represent the number of
homes,"H", the company will serve after
"n" years.

Given Information:Each of n sticks is broken into one long and one short part. The 2n parts are arranged into n pairs from which new sticks are formed.Pairing each long part with a short part gives n possible pairs.Explanation:a. Probability that the parts will be joined in the original orderWe have n sticks that are broken into 2 parts

each.So, total parts = 2nOut of 2n parts, we can select n parts in n! ways. (Order is important as we have to join them in the original order)For each such n! arrangement, there is only 1 main answer that is the original order of n sticks.Now, total number of ways to arrange the parts is 2n!.So, probability that the parts will be joined in the original order = Number of favourable outcomes / Total number of possible outcomes= n! / 2n! = 1 / 2n-1b. Probability that long parts are paired with short partsWe have n pairs out of which one part is long and other is short.Each long part can be paired with a short part in n ways.Out of n pairs, one pair can be selected in nC1 ways. Similarly, the other pairs can be selected in n-1 C 1 ways, n-2 C 1 ways and so on

Total number of ways to select n pairs is n * (n-1) * (n-2) *... * 1 = n!So, probability that long parts are paired with short parts= Number of favourable outcomes / Total number of possible outcomes= n! / 2n! = 1 / 2n-1Therefore, the main answer to the problem is:(a) Probability that the parts will be joined in the original order= n! / 2n!(b) Probability that long parts are paired with short parts= n! / 2n!

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The future value of the annuity is approximately $17,636.45.

An annuity is a series of equal payments made at regular intervals. In this case, you started an annuity of $200 per month. The interest on the account is 3% compounded monthly.

To calculate the amount of money you will have in 3 years, we can use the formula for the future value of an annuity. The formula is:

FV = P * [(1 + r)^n - 1] / r

Where:
FV is the future value of the annuity
P is the monthly payment ($200)
r is the interest rate per period (3% per month, or 0.03)
n is the number of periods (3 years, or 36 months)

Plugging in the values into the formula, we have:

FV = 200 * [(1 + 0.03)^36 - 1] / 0.03

Calculating this expression, we find that the future value of the annuity is approximately $17,636.45.

Therefore, the correct answer is $17,636.45.

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Answer:

-8

Step-by-step explanation:

-24=6-(4x24)+18= 6-96+18=-90+18=-72

-8=6-(4x8)+18= 6-32+18=-26+18=-8

Answer:

coordinates for vertex are (5, -9)

Step-by-step explanation:

Given

\(a=1\\\\b=-10\\\\c=16\)

using the formula for the x coordinate of the vertex which is \(\frac{-b}{2a}\) it yields:

\(x_{vertex}=\frac{-(-10)}{2}=5\)

We now have the x-coordinates of the vertex, by applying the x coordinate in the equation we get:

\(5^2-(10\times 5)+16\\\\=25-50+16\\\\=-9\)

thus the \(y_{vertex}=-9\)

Thus the coordinates of the vertex should be (5, -9)

The given expression has sin A = BC/AC=36/85, cos A = AB/AC=77/85, tan A = BC/AB=36/77

In trigonometry, the values of sin, cos, and tan are the main functions we consider when solving trigonometric problems. Using these trigonometric values, the angles and sides of a right-angle triangle are calculated. In addition to sine, cosine, and tangent values, the other three significant values are cotangent, secant, and cosecant.

Normally, when calculating the sin, cos, and tan values for a triangle, the angles of 0°, 30°, 45°, 60°, and 90° are taken into consideration. These specific angles' values are easy to remember. What the trigonometric values are all about is knowing the standard angles for a specific triangle according to the trigonometric ratios (sine, cosine, tangent, cotangent, secant and cosecant).

We have, AB = 77 , BC = 36.and CA=85

When we consider the t-ratios of ∠A, we have

Base = AB = 77, Perpendicular = BC = 36, Hypotenuse = AC =85.

∴sin A = BC/AC=36/85 , cos A = AB/AC=77/85 , tan A = BC/AB=36/77

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The predicted weight of a lizardfish that is 12 cm long, based on the given model, is approximately 13.80 grams.

The predicted weight of a lizardfish that is 12 cm long, based on the given regression model lnW = -5.36 + 3.216lnL, is approximately 13.80 grams.

To calculate the predicted weight, we substitute the value of L = 12 cm into the regression equation. Taking the natural logarithm of both sides, we get:

lnW = -5.36 + 3.216ln(12)

Evaluating the right-hand side of the equation, we have:

lnW ≈ -5.36 + 3.216ln(12)

≈ -5.36 + 3.216(2.48491) [ln(12) ≈ 2.48491]

≈ -5.36 + 7.99604

≈ 2.63604

Taking the inverse of the natural logarithm (exponential function), we find:

W ≈ e^(2.63604)

≈ 13.80 grams

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The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

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Answer:

Exact form: √ 113

Decimal form: 10.63014581...

Step-by-step explanation:

Answer:

91

Step-by-step explanation:

3^4=81

2x5=10

81+10

91

Answer:

91

Step-by-step explanation:

\(3^4 + 2 x5\)

\(3^4 + 2 x5 = 3 x 3 x 3 x 3 + 10= 9 x 9+10=81+10=91\)

Hope this helps :)

To partition the number 459 in the ratio 2:4:3, follow these steps:

Step 1: Determine the total number of parts.
Add the ratio values together: 2 + 4 + 3 = 9 parts.

Step 2: Calculate the value of each part.
Divide the number 459 by the total number of parts: 459 ÷ 9 = 51.

Step 3: Distribute the parts according to the given ratio.
For the first part (2), multiply the value of each part by the ratio: 51 × 2 = 102.
For the second part (4), multiply the value of each part by the ratio: 51 × 4 = 204.
For the third part (3), multiply the value of each part by the ratio: 51 × 3 = 153.

So, the partitioned numbers are 102, 204, and 153, which correspond to the ratio 2:4:3.

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Answer:

12:1

Step-by-step explanation:

each pack contains 12 eggs

108/9 = 12

Hope this helps

Answer:

Line (H,J) is perpendicular to a slope of \(\frac{1}{2}\).

Step-by-step explanation:

Line (A,B) has a slope of \(\frac{1}{2}\) and line (H,J) is perpendicular to (A,B)

The rate of change between 75 and 125 miles is calculated by dividing the difference between the fuel cost at 125 and 75 miles by the distance traveled. The fuel cost at 75 miles is $3.85, while the fuel cost at 125 is $6.35. The rate of change is $0.05 per mile.

To calculate the rate of change between 75 and 125 miles, subtract the fuel cost at 125 miles from the fuel cost at 75 miles and divide the difference by the distance travelled:

Rate of change = (fuel cost at 125 miles - fuel cost at 75 miles) / (125 - 75)

First, we need to find the fuel cost at 75 miles:

() = 0.1 + 0.05x

() = 0.1 + 0.05(75)

() = 3.85

The fuel cost at 75 miles is $3.85.

Next, we need to find the fuel cost at 125 miles:

() = 0.1 + 0.05x

() = 0.1 + 0.05(125)

() = 6.35

The fuel cost at 125 miles is $6.35.

Now we can substitute these values into the rate of change formula:

Rate of change = (6.35 - 3.85) / (125 - 75)

Rate of change = 2.5 / 50

Rate of change = 0.05

The rate of change of the cost of fuel when the car travels from 75 miles to 125 miles is $0.05 per mile.

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The complete question is: If a car travels x miles, the cost of fuel used is given by the function () = 0.1 + 0.05x dollars. What is the rate of change of the cost of fuel when the car travels from 75 miles to 125 miles?

Answer:

The distance is 816 km

Step-by-step explanation:

We can define average velocity as the quotient between the total distance traveled and the time it takes to travel that distance.

Here we will get the average velocity of 1,000 km/h.

----------------------------

To get the average velocity of the rocket, we need to know the distance that it travels and the time it needs to travel that distance.

We know that:

Then the average velocity is given by:

AV = (2,200 km)/(2.2 h) = 1,000 km/h.

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Answer:

Step-by-step explanation:

Answer:

x = 8

y = 21

Step-by-step explanation:

y = 4x − 11

x + y = 29

Solve for x:

x + y = 29

x + 4x − 11 = 29

5x − 11 = 29

5x = 40

x = 8

Solve for y:

y = 4x − 11

y = 4 × 8 − 11

y = 21

Given the two functions

We are tasked to plot (F-G)(x).

The first step here is to get the resulting function (F-G)(x). We have

Now, we need to assign values of x and evaluate them at the function (F-G)(x) to get a value. We will get coordinate points and we will plot them at the cartesian coordinate plane. I will use values of x = [-3,3]. We get the following results

The plot is provided by the image below.

Answer:

well the sequence is the perfect squares

Step-by-step explanation:

Answer:

\(a_{n}\) = (n + 1)²

Step-by-step explanation:

The sequence of square numbers is

n    |    1      2      3     4     5     6

n² |    1      4       9   16    25    36

Given

4  , 9,  16,  25,  36 ← moved 1 place to the right

Thus

4 = (1 + 1)²  , 9 = (2 + 1)² ,  16 = (3 + 1)² , etc

In general the n th term is

\(a_{n}\) = (n + 1)²

Answer:

1. YES

1. YES2. YES

1. YES2. YES3.YES

4.NO

Hope it helps

The position vector of the particle is:r(t) = 1/6 t^3 + e t j + e-t k + 2k t + 1

To find the position vector of the particle, we need to integrate the given acceleration function twice. First, we integrate a(t) with respect to time t to get the velocity function v(t):

v(t) = ∫ a(t) dt = ∫ ti+et j+e-t k dt = 1/2 t^2 + e t j - e-t k + C1

Using the given initial velocity v(0) = k, we can solve for the constant C1:

v(0) = 1/2 (0)^2 + e (0) j - e-(0) k + C1 = k

C1 = k + k = 2k

Now we integrate v(t) with respect to time t again to get the position function r(t):

r(t) = ∫ v(t) dt = ∫ (1/2 t^2 + e t j - e-t k + C1) dt

= 1/6 t^3 + e t j + e-t k + C1 t + C2

Using the given initial position r(0) = 1 + k, we can solve for the constant C2:

r(0) = 1/6 (0)^3 + e (0) j + e-(0) k + C1 (0) + C2 = 1 + k

C2 = 1

Therefore, the position vector of the particle is:

r(t) = 1/6 t^3 + e t j + e-t k + 2k t + 1

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If speed is important and the array is large, the a. Binary search algorithm should be used. This algorithm is designed to efficiently search through sorted arrays by repeatedly dividing the search interval in half.

It has a time complexity of O(log n), which means that as the size of the array increases, the time it takes to search for an item will not increase at the same rate.
On the other hand, ascending bubble sort and other sorting algorithms such as selection sort and insertion sort have a time complexity of O(n^2), which means that as the size of the array increases, the time it takes to sort the array will increase exponentially. Therefore, these algorithms are not efficient for large arrays and should not be used if speed is important.
In summary, when dealing with large arrays and speed is important, binary search is the best algorithm to use for searching, while ascending bubble sort and other sorting algorithms with a time complexity of O(n^2) should be avoided.

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The equation of a line into slope-intercept form is represented as:

y = mx + c

where m = slope of the line

c = y-intercept of the line

On simplifying 8x - 20y = 40, the equation will be:

⇒ 2 (4x - 10y) = 2 (20)

⇒ 4x - 10y = 20

⇒ 2x - 5y = 10

⇒ 2x - 10 = 5y

⇒ 5y = 2x + (-10)

⇒ y = 2x/5 + (-10/5)

⇒ y = 2x/5 + (-2)

The slope of this line = 2/5

y-intercept of the line = -2

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Answer:

3.25

Step-by-step explanation:

total 18.25 - 2.00 tip = 16.25

16.25/5=3.25

Answer:

Igloo Ice has the lowest delivery charge.

Step-by-step explanation:

Igloo Ice when you plug in 120 for the y you get 25.714 as the x.

Freds freeze at 120 is 20.

And lastly Tasty treats at 120 is 24, so Igloo Ice has the lowest delivery charge per person (you pay $120 for 25.714 people.)

Answer:

Igloo Ice

Step-by-step explanation:

Igloo Ice C(n) = 1.75n + 75

Fred's Freeze C(n) = 2n + 80

Tasty Treats C(n) = 1.25n + 90

75 is the lowest delivery charge

C(n) is total charge including what they are delivering

Answer:

(2.5, 6.25)

Step-by-step explanation:

Given

A = (-2,4)

C = (4,7)

If B is located on AC such that AB to AC is 1:3

X coordinate of B;

X = ax1+bx2/a+b

X = 1(-2)+3(4)/1+3

X = -2+12/4

X = 10/4

X = 2.5

Y coordinate of B;

Y = ay1+by2/a+b

Y = 1(4)+3(7)/1+3

Y = 4+21/4

Y = 25/4

Y = 6.25

hence the coordinate of B is at (2.5, 6.25)

The 6th term of the sequence is 4

The given parameters are:

a1 = -4096

a4 = 64

The nth term of the sequence is:

a(n) = a1 * r^(n-1)

So, we have:

a4 = a1 * r^3

This gives

r^3 = a4/a1

Substitute the known values

r^3 = 64/-4096

Evaluate

r^3 = -1/64

Take the cube roots

r = -1/4

The 6th term is

a(6) =a1 * r^5

This gives

a(6) = -4096 * (-1/4)^5

Evaluate

a(6) = 4

Hence, the 6th term of the sequence is 4

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Answer: The largest area of a rectangle is 32 square units. A rectangle has its base on x-axis and its upper two vertices on the parabola y= 12 - x^2.

Step-by-step explanation:

This is the answer