Vanessa invests $20,000 in an account at 9.1% interest compounded continuously. Find the total value of the investment after 19 years.

The power function that models the data is 0.117t^1.585.

In 1985, the average cost of natural gas was estimated to be $7.24 per 1000 ft³.

a. To model the data with a power function, use general form of a power function:

C = ktⁿ,

where C = average cost of natural gas, t = time in years, k = a constant, and n = power.

Take the logarithm of both sides to linearize the equation:

log(C) = log(k) + n × log(t)

Use a linear regression to find the slope and y-intercept of the line, which will give us the values of k and n:

n ≈ 1.585

log(k) ≈ -0.921

k ≈ 0.117

Therefore, the power function that models the data is:

C = 0.117t^1.585

b. To estimate the average cost of natural gas in 1985, we can substitute t = 11 (since 1985 is 11 years after 1974) into the power function:

C = 0.117(11)^1.585 ≈ 7.24

Therefore, estimate the average cost of natural gas in 1985 to be $7.24 per 1000 ft³.

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The height of the square pyramid with base area 225 cm² and volume 300cm³ is equal to 4 centimeters.

Area of the base of square pyramid = 225 centimeters squared

Volume of the square pyramid = 300 centimeters cubed

Using the formula for the volume of a square pyramid,

V = (1/3) × B × h

where V is the volume,

B is the area of the base,

and h is the height of the pyramid.

Substitute this value into the formula we have,

⇒ 300 = (1/3) × 225 × h

Simplifying the equation , we get,

⇒ 900 = 225 × h

Dividing both sides by 225, we get,

⇒ h = 4

Therefore, the height of the square pyramid is 4 centimeters.

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Answer: So the vertex of the angle is located at the center of the circle, which is 8 centimeters away from the nearest centimeter.

Step-by-step explanation:

Let O be the center of the circle, and let A and B be the points of tangency of the two tangents with the circle. Since OA and OB are radii of the circle, they have the same length of 8 centimeters.

Let C be the vertex of the angle formed by the two tangents. Since the tangents are perpendicular to the radii at the points of tangency, we have that angle AOC = angle BOC = 90 degrees.

Since the measure of the angle formed by the two tangents is 80 degrees, we have that angle AOB = 180 - 80 - 80 = 20 degrees.

Let D be the foot of the perpendicular from C to line AB. Then angle OCD = 90 - 20/2 = 80 degrees, so triangle OCD is an isosceles triangle. Therefore, we have that OD = OC = 8 centimeters.

Finally, since triangle OCD is a right triangle, we can use the Pythagorean theorem to find the length of CD. We have:

CD^2 = OD^2 - OC^2 = 8^2 - 8^2 = 0

Therefore, CD = 0 centimeters.

So the vertex of the angle is located at the center of the circle, which is 8 centimeters away from the nearest centimeter.

f(4) = 537. and f(-3) = 363.  To find f(-3), we replace x with -3 in the expression similarly for x=4.

what is expression  ?

In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.

In the given question,

To find f(-3), we replace x with -3 in the expression:

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

= 3(81) - 4(-27) + 3(9) + 15 - 3

= 243 + 108 + 15 - 3

= 363

Therefore, f(-3) = 363.

To find f(4), we replace x with 4 in the expression:

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

= 3(256) - 4(64) + 3(16) - 20 - 3

= 768 - 256 + 48 - 23

= 537

Therefore, f(4) = 537.

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Hence ,the sum of ∠1 and ∠2  is 90 degrees this is a relationship between ∠1 and ∠2.

In Euclidean geometry, an  angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles  formed by two rays lie in the plane that  contains the rays. Angles are also formed by the  intersection of two planes. These are called dihedral angles.

complementary angles are two angles that add up to 90 degrees, supplementary angles are two angles that add up to 180 degrees,

vertical angles are opposite angles at an intersection of two straight lines, and adjacent angles are two angles that are next to each other.

According to figure , the sum of ∠1 and ∠2  is 90 degrees and If the sum of the two angles is equal to the measurement of a right angle .

So, the pair of angles ∠1 and ∠2  is said to be complementary angles.

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Answer: A

Step-by-step explanation: cuz of the

pie chart

The perimeter of the rhombus is approximately 7.6 units.

XZ is perpendicular to WY and XE is 4,

Since WXYZ is a rhombus because only the diagonal of the rhombus and square bisect each other at 90°

By the Pythagorean theorem, we have:

XE² = XY² + EY²

4² = XY² + (7/2)²

XY = 1.9

So the perimeter of WXYZ is 4(XY), rounded to the nearest tenth:

4(1.9) ≈ 7.6 units.

Therefore, the perimeter of the rhombus is approximately 7.6 units.

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Francine can type 38 words per minute at this rate.

To find out how many words Francine can type per minute, we need to convert the time she took to type the words into minutes. Since there are 60 minutes in 1 hour, 1 hour and 30 minutes is equivalent to 1 × 60 + 30 = 90 minutes.

Next, we can use the formula:

words per minute = total words / total minutes

where "total words" is the number of words Francine typed (3,420) and "total minutes" is the time she took in minutes (90).

Substituting these values into the formula, we get:

words per minute = 3,420 / 90 = 38

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For pythagorean theorem  the triangle is a 3, 4 ,5 triangle 15 would be the length 5, and 9 would be the lenght 3. So we would multiply each side to getthe answer your lookin for. Which the third side would be, I think im right, i just did this in my head but im only 11 so dont bully me plsssss

ANSWER 12

Answer: x = -11

Step-by-step explanation:

Sub in y= 3-1/2x into 3x+4y=1 for y, and solve for x.

[tex]3x+4(3-\frac{1}{2}x) =1\\3x + 12 - 2x =1\\\\\ x = -11[/tex]

Answer:

if f(x) = 3x, g(x) = x+4, and h(x) = x²-1, Find [h•(f•g)](3)

{h • (f • g)}(3) = 440

Step-by-step explanation:

To find {h • (f • g)}(3), we need to first evaluate the innermost function, f • g, then substitute the result into the outer function, h, and finally evaluate the resulting expression at x = 3.

Let's start by finding f • g:

f • g = f(g(x))

Substitute g(x) into f(x):

f • g = f(x + 4)

Now substitute f(x) into the above expression:

f • g = 3(x + 4)

Simplify:

f • g = 3x + 12

Now we can substitute this result into h(x):

h • (f • g) = h(3x + 12)

Substitute x = 3 into the above expression:

h • (f • g) = h(3(3) + 12)

Simplify inside the parentheses:

h • (f • g) = h(9 + 12)

Simplify further:

h • (f • g) = h(21)

Now let's evaluate h(21):

h(x) = x² - 1

h(21) = (21)² - 1

Simplify:

h(21) = 441 - 1

Final result:

{h • (f • g)}(3) = 440

The equation for the circle graphed in the coordinate axis is:

(x - 5)^2 + (y - 6)^2 = 16

Remember that the equation for a circle whose center is at (a, b) and has a radius R is.

(x - a)^2 + (y - b)^2 = R^2

On the graph, we can see that the center of the circle is at (5, 6), and the radius of the circle is R = 4 units. Then the equation for the circle in the graph is:

(x - 5)^2 + (y - 6)^2 = 4^2

(x - 5)^2 + (y - 6)^2 = 16

That is the equation we wanted to find.

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The median is the best measure of center, and it equals 8.

A measure of center is important to understand the central tendency of data.

In this case, the best measure of center for the given data is the median.

The median is preferred over the mean because it is not influenced by extreme values.

By looking at the line graph, it is clear that there are more data points around 8 than any other value.

Therefore, the median would be closest to 8, making it the best measure of center. The median can be calculated by ordering the data from smallest to largest and selecting the middle value.

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Step-by-step explanation:

yes .. when you put x=2 y will be 3 .. you get it?

Thus, Riley's maximum distance from the starting position is 55 inches.

When an input value has a defined output value in reality, functions can be applied. For instance, how long a car has been driving affects how far it has travelled (the output) (the input).

Riley is swaying on a playground swing. As stated in the table, let t denote the passing of time in seconds and let f(t) denote Riley's horizontal displacement from her starting location in inches.

t:   0 ,0.75, 1.5, 2.25, 3,  3.75, 4.5,  5.25,   6,  6.75

f(t): 0 ,38.9, 55, 38.9, 0, -28.9, -55, -38.9, 0, 38.9

Recall that f(t) is positive when Riley swings closest to the starting position and negative when Riley swings in behind starting position.

So,

started from 0 and travelled distance of 55 inches in 1.5 seconds.

She is advancing by up to 1.5 seconds.

Then she begins to move backward, returning to her starting location after 3 seconds, and continuing to do so for an additional 4.5 seconds at a distance of -55.

Then begin to advance and return to the starting position after six seconds

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we should subtract (389/600) from (7/12) + (7/8) to obtain the multiplicative inverse of (4/3) - (2/9).

To find the multiplicative inverse of a fraction, we need to find another fraction that, when multiplied by the original fraction, results in a product of 1.

Let's start by finding the multiplicative inverse of the fraction (4/3) - (2/9):

(4/3) - (2/9) = (12/9) - (2/9) = (10/9)

The multiplicative inverse of (10/9) would be a fraction (a/b) such that:

(10/9) x (a/b) = 1

Multiplying both sides by (9/10) (the reciprocal of 10/9), we get:

(a/b) = (9/10) x (1/(10/9))

Simplifying the expression on the right-hand side, we get:

(a/b) = (9/10) x (9/10) = 81/100

So the multiplicative inverse of (4/3) - (2/9) is 81/100.

Next, we need to find what we should subtract from (7/12) + (7/8) to obtain 81/100.

We can first find a common denominator between (7/12) and (7/8), which is 24:

(7/12) = (7/12) x (2/2) = 14/24

(7/8) = (7/8) x (3/3) = 21/24

So, we can rewrite (7/12) + (7/8) as:

(14/24) + (21/24) = 35/24

To obtain the difference between 35/24 and 81/100, we subtract the smaller fraction from the larger one:

81/100 - 35/24 = (81/100) x (6/6) - (35/24) x (25/25)

= 486/600 - 875/600 = -389/600

Therefore, we should subtract (389/600) from (7/12) + (7/8) to obtain the multiplicative inverse of (4/3) - (2/9).

Final answer:

(7/12) + (7/8) - (389/600) = 1.0158 (rounded to four decimal places)

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The statement you provided in the attached image is a proof from abstract algebra that any subgroup of the additive group of integers (Z) is cyclic and generated by a unique positive integer n, which is the smallest positive integer that belongs to the subgroup.

The proof uses the concept of integer division to show that any subgroup of Z must contain a smallest positive integer, and that this integer generates the entire subgroup.

This result is important in algebraic structures such as group theory, where the properties of subgroups are often studied in detail.

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Answer:

45% = 0.45

(you do this by bringing the decimal over 2 places)

multiply $55 and 0.45 to get $24.75

final answer = $24.75

The area of the rectangle is 27/70 square feet.

The area of a rectangle is given by the formula:

Area = base x height

Plugging in the given values, we get:

Area = (3/7) x (9/10)

Simplifying, we get:

Area = (27/70) square feet

Therefore, the area of the rectangle is 27/70 square feet.

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The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.

Linear function: y = 3x + 1

x y

3 10

5 16

7 22

9 28

The linear function is positive, which means that the airplane's altitude is increasing as it moves towards the right on the graph. In context, this means that the airplane is ascending as it moves away from the observer towards the rainbow.

The system of equations created by the two functions is:

y = -x^2 + 19

y = 3x + 1

By substituting y in the second equation with the first equation, we get:

-x^2 + 19 = 3x + 1

Solving for x, we get:

x = -2 or x = 5

Substituting these values of x back into either of the equations, we get the corresponding values of y:

(-2, 7) and (5, 16)

These two solutions represent the points of intersection between the rainbow and the airplane's trajectory.

The domain of the rainbow is all real numbers, while the range is y ≤ 19. In context, this means that the rainbow can appear at any point in the observer's field of view, but its highest point is at y = 19.

All of the values in the domain and range make sense in this situation since they are within the physical limits of the observer's perception.

The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.

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The ratio of the volume of both spheres is: 1/(24√3)

The formula for the volume of a sphere is expressed as:

V = ⁴/₃πr³

where:

r is radius

V is volume

We are told that the radii of the two spheres have a ratio of 1:2√3. Thus:

Volume of sphere A/Volume of sphere B = (1:2√3)³

= 1/(24√3)

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Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.

What is the Pigeonhole Principle?

The Pigeonhole Principle is a fundamental concept in combinatorics, which is a branch of mathematics that deals with counting and analyzing the properties of sets of objects. The principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.

We can solve this problem using the Pigeonhole Principle, which states that if n+1 objects are distributed among n boxes, then there is at least one box that contains two or more objects.

In this case, we want to be sure that we have at least two T-shirts that differ only by size or only by color.

So we need to find the minimum number of T-shirts that we must take out of the bag to guarantee this.

Let's consider the worst-case scenario, where we take out all the T-shirts that are of one size or one color.

If we take out all 18 small red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color (since we could still get a small black T-shirt).

Similarly, if we take out all 19 small black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

If we take out all 13 large black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

If we take out all 15 large red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.

So we need to take out at least 19 T-shirts to be sure that we have at least two T-shirts that differ only by size or only by color. (We add one to the largest number of T-shirts of one color or size.)

Therefore, Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.

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The probability that all 4 people spend more than an hour a day using the Internet is 0.053 or 5.3%.

The given problem is an example of a binomial probability distribution, where there are only two outcomes - success and failure. Here, success means spending more than an hour a day using the internet, and failure means spending an hour or less a day.

The probability of success is p = 0.48, and the probability of failure is q = 1 - p = 0.52.

To find the probability that all 4 people spend more than an hour a day using the Internet, we need to use the formula for the binomial probability distribution:

P(X = k) = (n choose k) * [tex]p^{k }* q^{(n-k)[/tex]

Here, n = 4 (the number of people selected), and k = 4 (the number of people who spend more than an hour a day using the Internet).

Plugging in the values, we get:

P(X = 4) = (4 choose 4) * 0.48⁴ * 0.52⁴⁻⁴ = 0.053

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To graph the solution set to the given system of inequalities, we first need to graph the functions f(x) = x^2 - 2 and g(x) = -x^2 + 5.

The graph of f(x) is a parabola that opens upward and has its vertex at (0, -2). The graph of g(x) is also a parabola, but it opens downward and has its vertex at (0, 5). We can plot these two graphs on the same coordinate plane as follows:

[Insert image of two parabolas on a coordinate plane]

Next, we need to shade the regions of the graph that satisfy the given inequalities. The first inequality y > x^2 - 2 represents the region above the parabola f(x) but below the line y = infinity. The second inequality y ≥ -x^2 + 5 represents the region at or above the parabola g(x). The solution set is the intersection of these two regions.  

The shaded region represents all the points (x, y) that satisfy both inequalities, and therefore, the solution set to the system of inequalities.

Answer:

To determine the number of students who voted for Candidate C, we need to first find what percent of the total votes they received. Looking at the graph, it appears that Candidate C received approximately 40% of the votes.

To find out how many students this represents, we can set up a proportion:

40% = C/150

Where C is the number of votes received by Candidate C.

To solve for C, we can cross-multiply:

0.4 x 150 = C

C = 60

Therefore, 60 students voted for Candidate C.

Charlotte's mistake was assuming that the percentage of votes for Candidate C directly corresponded to the number of students who voted for them. It's possible that more than one student voted for each candidate, and the percentage of votes represents the proportion of all votes each candidate received.

The expression Negative 3 6/7 times negative 3 1/3 has a value of -12 6/7

We have the following statement as the given parameter

Negative 3 6/7 times negative 3 1/3

Next, we rewrite the above statement using numbers and operators

-3 6/7 * 3 1/3

The above statement is a product expression that multiplies the values of -3 6/7 and 3 1/3

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

-3 6/7 * 3 1/3 = -27/7 * 10/3

Evaluate

-3 6/7 * 3 1/3 = -9/7 * 10

Rewrite as

-3 6/7 * 3 1/3 = -90/7

Simplify

-3 6/7 * 3 1/3 = -12 6/7

This means that the value of the expression is -12 6/7

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