If f(x)f(x) is an exponential function where f(4.5)=16f(4.5)=16 and f(9.5)=60f(9.5)=60, then find the value of f(15)f(15), .

Answer: 10/36 or 5/8

Step-by-step explanation:

Let’s start by solving how many pens Rohan has left. 36-11-15=36-26=10. Rohan has 10 pens left. Now to solve the fraction of pens Rohan has left, we divide our 10 by 36, or 10/36. Another fraction of this could be 5/18, because both the denominator and numerator have 2 as a factor.

The area of the triangle is approximately 6.4936 square centimeters.

We can use Heron's formula to find the area of a triangle given the lengths of its sides. Heron's formula states that the area (A) of a triangle with sides a, b, and c is:

A = √[s(s-a)(s-b)(s-c)]

where s is the semi-perimeter of the triangle, defined as:

s = (a + b + c) / 2

Using the values given in the problem, we have:

a = 7 cm, b = 3 cm, c = 5 cm

The semi-perimeter is:

s = (a + b + c) / 2 = (7 + 3 + 5) / 2 = 7.5 cm

Substituting these values into Heron's formula, we get:

A = √[s(s-a)(s-b)(s-c)]

= √[7.5(7.5-7)(7.5-3)(7.5-5)]

= √[7.5(0.5)(4.5)(2.5)]

= √[42.1875]

= 6.4936 cm² (rounded to 4 decimal places)

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bAnswer:

Step-by-step explanation:

The combined volume of the cylinder and cone with diameters of 2 feet and heights of 9 feet is 42.39 ft3.

The volume of the cylinder and cone can be calculated using the formula V=πr2h. The radius of both is 1 foot and the height of both is 9 feet. Therefore, the volume of the cylinder is Vcylinder = π(1)2(9) = 28.26 ft3. The volume of the cone can be calculated using Vcone = π(1)2(4.5) = 14.13 ft3, where 4.5 is the height of the cone. To calculate the combined volume, add the volumes of the cylinder and the cone: Vtotal = 28.26 + 14.13 = 42.39 ft3.

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Answer:

5 and 13

Step-by-step explanation:

given the first number is x and the second number is y

then x + y = 18 => y = 18 - x

also

x^2 + y^2 = 194

substitute

x^2 + (18 - x)^2 = 194

x^2 + x^2 - 36x + 324 = 194

2x^2 - 36x + 130 = 0

2(x^2 - 18x + 65) = 0

x^2 - 18x + 65 = 0/2

x^2 - 13x - 5x + 65 = 0

x(x - 13) - 5(x - 13) = 0

(x - 13)(x - 5) = 0

=> x - 13 = 0 => x = 13

=> x - 5 = 0 => x = 5

if x = 13, y = 18 - 13 = 5

if x = 5, y = 18 - 5 = 13

so x and y can be either 5 and 13

Using this formula, we can calculate that the chance that the plane will be overbooked is 35.1%. This means that there is a 35.1% chance that more than 300 passengers will show up for the flight despite the airline only having 300 seats.

The chance that a plane will be overbooked is calculated using a binomial probability formula. The formula is P(x) = nCx * p^x * (1 - p)^(n - x), where n is the number of trials (in this case, 300), x is the number of successes (in this case, 324 reservations), and p is the probability of success (in this case, 90%).

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Answer: Let's start by representing the number of Blu-Ray discs sold as x.

According to the problem, the store sold 2/3 as many DVDs as Blu-Ray discs. So the number of DVDs sold is 2/3 of x, or (2/3)x.

We also know that the total number of DVDs and Blu-Ray discs sold was 280. So we can set up an equation:

(2/3)x + x = 280

To solve for x, we can simplify the equation by combining like terms:

(5/3)x = 280

Multiplying both sides by 3/5, we get:

x = 168

So the number of Blu-Ray discs sold was 168.

To find the number of DVDs sold, we can use the expression we derived earlier:

(2/3)x = (2/3) * 168 = 112

Therefore, the store sold 112 DVDs on that day.

Step-by-step explanation:

The cube root of 126.2 is approximately 0.016 larger than the cube root of 125.

Linear approximation is a strategy for approximating the values of complicated functions. When a graph is relatively straight, this approximation is quite effective. A linear approximation for a function is a straight line that represents a close approximation of the original function.

The formula to be used is given by

df/dx = (f(x+dx)-f(x))/dx

The first derivative of the cube root of x can be computed as follows:

f(x) = x^(1/3)

df/dx = (1/3)*x^(-2/3)

Using this formula, we can calculate the linear approximation of the cube root of 126.2. This can be done as follows:

f(x + dx) ≈ f(x) + df/dx * dx

In the given case, the f(x) = ∛125 ⇒ 5

Let dx = 126.2 - 125 ⇒ 1.2

Then the linear approximation of the cube root of 126.2 is given by

f(126.2) ≈ f(125) + df/dx * dx

⇒ f(126.2) ≈ 5 + (1/3)*125^(-2/3) * 1.2

⇒ f(126.2) ≈ 5 + 0.016

⇒ f(126.2) ≈ 5.016

Therefore, the cube root of 126.2 is roughly 0.016 greater than the cube root of 125.

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Answer:

<COA MESURES = 61

<AOH MESURES = 46

<HOG MESURES = 73

<FOE MESURES = 73

Step-by-step explanation:

Therefore , the solution of the given problem of unitary comes out to be each asset class as part of the diversification plan.

By combining the information obtained using this nanosection technique with all variable additional data from two individuals who used a specific strategy, the task can be completed. Simply put, this mean that, if the desired outcome materialises, either the specified entity will be known or, actually, the colour from both enormous processes will be skipped. For forty pens, a refundable charge of Rupees ($1.01) might be required.

Here,

The next two are methods for reducing the danger associated with investing out of the four you offered:

Dollar-cost averaging is the term used to describe this method of spreading investments out over time. Regardless of the investment's price, it entails making a set amount of investments at regular intervals over a length of time.

Spread your investments across various asset classes (such as stocks, bonds, real estate, etc.) and/or various companies within each asset class as part of the diversification plan.

Since currency values can be influenced by a number of variables and are sometimes unpredictable, investing in a particular currency (such as the British pound) is not always a risk management plan.

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Two rays with the same endpoint would form an angle, where the common endpoint is the vertex of the angle.

A ray is a part of a line that has a fixed starting point, called the endpoint, and extends infinitely in one direction. Thus, a ray can be thought of as a half-line. If two rays have the same endpoint, they will form an angle. The common endpoint is the vertex of the angle, and the two rays extend outward from the vertex in opposite directions, forming a straight line on one side of the vertex. In mathematical notation, the angle formed by two rays with the same endpoint A can be denoted as ∠BAC, where B and C are the points where the rays extend outwards. Note that the order in which the rays are written matters; ∠BAC and ∠CAB represent different angles.

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Answer:

8 Mangoes

Step-by-step explanation:

Since he decides to buy 4 apples, that would cost him: 4 × $1 = $4

That leaves him: $20 - $4 = $16.

So, how many mangoes can Noah possibly buy with $16?

That is: $16/$2 = 8(We divide by $2 because it is the cost of one mango)

so let's put the prism upright, Check the picture below.

keeping in mind that for a triangular prism the bases are the triangular parts, so le'ts find the area of those guys

[tex]\stackrel{ \textit{\LARGE Lateral} }{\stackrel{ \textit{Area of the three rectangles} }{(7)(5)~~ + ~~(3)(7)~~ + ~~(4)(7)}}\implies \text{\LARGE 84} \\\\\\ \stackrel{ \textit{\LARGE Total} }{\stackrel{ \textit{Area of the bases} }{2\left[\cfrac{1}{2}(\underset{b}{4})(\underset{h}{3}) \right]}~~ + ~~84}\implies \text{\LARGE 96}[/tex]

Answer:

x = 4

Step-by-step explanation:

x + 8 = 3x

8 = 2x

x = 4

So, the answer is x = 4

Using functions we can find that there would be nine roadways for six cities. This is due to the fact that each city must be connected to every other city, and since there are 5 pairs of connected cities, there must be 5 highways.

A function is a statement, concept, or rule that establishes an association between two variables.

Functions in mathematics are required for the development of meaningful relationships. If there are more than one dependent values for a particular independent value, then we are aware of this.

In that situation, the relation is not a function. Nevertheless, if there are multiple dependent values for a given independent value.

The relationship is then a function.

Now as per the question,

The remaining 4 cities must then be connected, which requires building an additional 4 roads, for a total of 9.

There would be 12 roadways for 7 cities.

This is due to the fact that each city must be connected to every other city, and since there are 6 pairs of connected cities, there must be 6 highways.

Then, the final five cities must be connected, which requires five more roads, for a total of twelve.

The number of highways for N cities would be N(N-1)/2.

This is because there are N(N-1)/2 pairs of cities that need to be connected, and each city must be connected to every other city.

For instance, if N = 10, 90 highways or 10× 9 = 90 pairs of cities must be connected.

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The complete question is:

There are five cities in a country, and two are connected with one road that goes straight between them. How many roads would be in this country if there were 6 cities? 7 cities? And N cities?

Answer:

Quadratic Function, Second Difference

The sample that has a greater mass is given as follows:

The sample of rock.

The sample of rock has a mass that is 5000 times the mass of the sample of dry sponge.

A number in scientific notation is given by the notation presented as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.

To obtain which amount is greater, we must verify the bases when the exponent is the same, hence:

Hence the rock has the greater mass, and the ratio is given as follows:

10/0.002 = 5000.

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a)  E

b)  C

c) p-value 0.03 significant difference in two procedures

A. No, neither procedure A appears to be normal nor procedure B appears to be normal

B. There appears to be more variation in the 1st procedure than in the 2nd.

C. The p-value of the test is 0.03, which indicates that there is a statistically significant difference in the variances of the two procedures.

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Answer:

116

Step-by-step explanation:

We can see that the two lines in between the triangle are the same size. This must mean that if we were to move the inner triangle and line it up to the triangle on the edge it must be the same size. We are also told that one of the angles on the side is 116. This means that the value of x must also be 116!

Hope this helps, have a lovely day! :)

Answer:

31/7

Step-by-step explanation:

7 i - 15 = 16

1. add 15 to both sides you will get

7i = 31

2. dividing both sides gives us 31/7

3. i = 31/7

Answer:

4*sqrt(2)

Step-by-step explanation:

To find the distance between two points, we use the distance formula, which is the following:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the values for the given points, we get the following:

d = sqrt((1 - (-3))^2 + (-2 - (-6))^2)

= sqrt((1 + 3)^2 + (-2 + 6)^2)

= sqrt(4^2 + 4^2)

= sqrt(32)

= 4*sqrt(2)

Therefore, the distance between the points (-3, -6) and (1, -2) is 4*sqrt(2).

Answer:

Sale Price-$48  What Percent Represents the reg. Price?-%100

Step-by-step explanation:

20% of 60 is 12, so if supplies are 20% off, they are $12 off, so 60 - 12 =48.

And if the regular price is $60, then $60 is the whole price, a.k.a. 100% of the price. So, the percent that represents the regular price of supplies is 100%.

In general, you would need to know the number of polygons in the original shape and the rule for how the shape is expanded or repeated in each iteration to calculate the number of polygons in a fractal expansion.

A fractal is a geometric shape that has intricate detail at arbitrarily small scales and typically has fractal dimensions that rigorously surpass topological dimensions. Several fractals resemble one another at different scales, as shown in the Mandelbrot set's sequential magnifications. Self-similarity, also known as expanding symmetry or unfolding symmetry, is the display of similar patterns at progressively smaller scales; if this replication is precisely the same at every scale, as in the Menger sponge, the shape is referred to as affine self-similar. The academic field of measure theory includes fractal geometry.

Depending on the particular kind of fractal under consideration, a polygon's fractal expansion can be calculated using a specific algorithm. However, the formula will typically entail iteratively transforming the original polygon with geometric operations.

For instance, by continually removing the central triangle from a larger equilateral triangle, the Sierpinski triangle—a well-known fractal—can be created. The remaining triangle is divided into three smaller replicas, which are then put together to make an equilateral triangle at the end of each iteration. The formula below can be used to determine the amount of triangles in each iteration:

the number of triangles in the nth repetition is represented by

Another illustration is the Koch snowflake, which is created by repeatedly dividing each of an equilateral triangle's three sides into two segments and swapping out the middle segment for two segments that also make an equilateral triangle. The following algorithm can be used to determine how many line segments are used in each iteration:

the number of line segments in the nth cycle is represented by L(n).

Generally speaking, the expansion formula for a fractal will rely on the particular rule or algorithm that was used to create the fractal.

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Answer:

Step-by-step explanation:

In order to find a hole, you have to factor the denominator to see if it matches an expression in the numerator and can therefore be crossed out.

The factored form of the denominator is shown below:

[tex]f(x)=\frac{x-1}{(x-3)(x-1)}[/tex]

Because the term x-1 is in both the numerator and the denominator, it is a hole, or removeable discontinuity. To find the hole, we plug in a 1 to the fraction that remains after we cancel the hole:

[tex]f(1)=\frac{1}{1-3}=-\frac{1}{2}[/tex]

The hole is found at (1, -1/2)

Answer:

To find the best line model for the data, we will use linear regression analysis.

First, we need to calculate the mean of x and y:

mean of x = (0 + 2 + 4 + 6 + 8 + 10 + 12 + 24 + 14) / 9 = 8

mean of y = (9 + 9 + 10 + 11 + 11 + 12 + 13 + 13 + 14) / 9 = 11

Next, we need to calculate the deviations of x and y from their respective means:

deviation of x = x - mean of x

deviation of y = y - mean of y

x y deviation of x deviation of y (deviation of x)^2 deviation of x * deviation of y

0 9 -8 -2 64 16

2 9 -6 -2 36 12

4 10 -4 -1 16 4

6 11 -2 0 4 0

8 11 0 0 0 0

10 12 2 1 4 2

12 13 4 2 16 8

24 13 16 2 256 32

14 14 6 3 36 18

Then, we can calculate the slope (b) of the best-fit line using the formula:

b = sum of (deviation of x * deviation of y) / sum of (deviation of x)^2

b = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) = 0.190

Next, we can calculate the y-intercept (a) of the best-fit line using the formula:

a = mean of y - b * mean of x

a = 11 - 0.190 * 8 = 7.48

Therefore, the equation of the best-fit line is:

y = 0.190x + 7.48

Finally, we can calculate the correlation coefficient (r) using the formula:

r = sum of (deviation of x * deviation of y) / (sqrt(sum of (deviation of x)^2) * sqrt(sum of (deviation of y)^2))

r = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (sqrt(64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) * sqrt(16 + 16 + 1 + 0 + 0 + 1 + 4 + 4 + 1)) = 0.905

Therefore, the best-fit line for the given data is y = 0.190x + 7.48, and the correlation coefficient is r = 0.905.

Step-by-step explanation:

The simplified expression with only positive exponents is 729 / 19^7.

We can simplify the expression as follows, using the exponent rules:

19 to the -3rd power = 1 / (19^3)

19×19 to the -4th power = (19^2)^-2 = 1 / (19^2)^2 = 1 / (19^4)

nine to the third power = 9^3

Therefore, the expression can be written as:

(1 / (19^3)) × (1 / (19^4)) × (9^3)

To simplify further, we can combine the two terms with powers of 19 into a single term:

(1 / (19^3 × 19^4)) × (9^3) = (1 / 19^7) × (9^3)

Finally, we can evaluate 9^3 to get the final answer:

(1 / 19^7) × (9^3) = (1 / 19^7) × 729 = 729 / 19^7

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The given question is incomplete, the complete question is:

19 to the -3rd power times 19×19 to the -4th power times nine to the third power. Simplify the expression using only positive exponents

Step-by-step explanation:

To rewrite (24 + 40) as an integer times the sum of two integers, Gracie first factored out 2, obtaining:

(24 + 40) = 2 × (12 + 20)

We can check that this is true by distributing the 2:

2 × (12 + 20) = 2 × 12 + 2 × 20 = 24 + 40

Now, Gracie is looking for other numbers greater than 2 that she can factor out of (24 + 40) to rewrite the expression as an integer times the sum of two integers.

One way to approach this is to look for other common factors between 24 and 40. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The common factors of 24 and 40 are 1, 2, 4, 8, and the largest factor is 8.

Therefore, Gracie can factor out 4 or 8 to rewrite the expression as an integer times the sum of two integers. For example:

(24 + 40) = 4 × (6 + 10)

(24 + 40) = 8 × (3 + 5)

Note that we can also factor out 1 or 2, but that would not change the expression in any meaningful way.

The maximum value οf the prοbability οf any event cannοt exceed 1.

The maximum value οf the prοbability οf an event is 1. The prοbability οf an event represents the likelihοοd οr chance that the event will οccur, and it is always expressed as a number between 0 and 1. A prοbability οf 0 means the event is impοssible, while a prοbability οf 1 means the event is certain tο οccur.

Prοbabilities between 0 and 1 represent the degree οf uncertainty οr likelihοοd οf the event. Since the sum οf prοbabilities οf all pοssible οutcοmes is always 1, the maximum value οf the prοbability οf any event cannοt exceed 1.

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If VAR[-4X+5]=13 and E[X]=2.5, so E[(X-3)²] will be 1.06. The correct answer is A

We have VAR[-4X+5] = 13, which means VAR[-4X] = 13 since VAR[c] = 0 for any constant c, and VAR[aX] = a² VAR[X] for any constant a.

So we have:

VAR[-4X] = (-4)² VAR[X] = 16 VAR[X] = 13

Solving for VAR[X], we get:

VAR[X] = 13/16

Now, we want to find E[(X-3)^2]:

E[(X-3)²] = E[X² - 6X + 9]

= E[X²] - 6E[X] + 9 (by linearity of expectation)

We can use the formula VAR[X] = E[X²] - (E[X])² to solve for E[X²]:

VAR[X] = E[X²] - (E[X])²

13/16 = E[X²] - (2.5)²

E[X²] = 13/16 + 6.25

E[X²] = 7.31

Therefore, we have:

E[(X-3)²] = E[X²] - 6E[X] + 9

= 7.31 - 6(2.5) + 9

= 1.06

So the answer is (a) 1.06.

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