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2 years ago

TASK 1

Mathematics

1 answer:

luda_lava [24]2 years ago

6 0

Remember that if f and g are inverses of one another, then

f(g(x)) = g(f(x)) = x

1/2. Take a = 0 and b = 1 (or any non-zero number) so that

f(x) = x + 0/1 ⇒ f(x) = x

If g is to be an inverse of f, we need

g(f(x)) = g(x) = x

so that c = 1 and d = 0.

3. With f(x) = x + a/b and g(x) = cx - d, we have

g(f(x)) = g(x + a/b) = c (x + a/b) - d = cx + ac/b - d

and of course, with a,b,c,d as before, we get g(f(x)) = x.

4. This would be a very uninteresting graph for the example I've cooked up here, just containing the line y = x...

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A random sample of size 100 was taken from a population. A 94% confidence interval to estimate the mean of the population was co

Firlakuza [10]

Answer:

Step-by-step explanation:

1) The z value was determined using a normal distribution table. From the normal distribution table, the corresponding z value for a 94% confidence interval is 1.88

The correct option is D

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p = 70/100 = 0.7

q = 1 - p = 1 - 0.7 = 0.3

n = number of selected users = 50

Mean, u = np = 50×0.7 = 35

Standard deviation, u = √npq = √50×0.7×0.3 = 3.24

x = number of internet users

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We want to determine the probability that no more than 25 were victims of e-mail fraud. It is expressed as

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3 years ago

Pizza Plus sold a total of 580 pizzas at $6 each and calzones at $8 each during Sunday’s football game. How many of each product

brilliants [131]

Answer:

Step-by-step explanation:

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2 years ago

Which three dimensional figure has double the number of edges as faces?

notka56 [123]

A cube because it has 6 faces/sides and 12 edges.

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2 years ago

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The perimeter of a regular pentagon is represented by the expression 35d-25. Daryl correctly wrote expression to represent the o

Triss [41]

Answer:

Each one of the sides is equal to 7d-5

Step-by-step explanation:

A regular pentagon has 5 sides of equal length.

The perimeter of a regular pentagon is given by

P = 5s where s is the side length

35d -25 = 5s

Divide each side by 5

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2 years ago

An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance around the track is 400 meter

dybincka [34]

Answer:

width of rectangle = 2R = (200/π) = 400/π meters

length of rectangle = 400 - π(200/π) = 400 - 200 = 200 meters

Step-by-step explanation:

The distance around the track (400 m) has two parts: one is the circumference of the circle and the other is twice the length of the rectangle.

Let L represent the length of the rectangle, and R the radius of one of the circular ends. Then the length of the track (the distance around it) is:

Total = circumference of the circle + twice the length of the rectangle, or

= 2πR + 2L = 400 (meters)

This equation is a 'constraint.' It simplifies to πR + L = 400. This equation can be solved for R if we wish to find L first, or for L if we wish to find R first. Solving for L, we get L = 400 - πR.

We wish to maximize the area of the rectangular region. That area is represented by A = L·W, which is equivalent here to A = L·2R = 2RL. We are to maximize this area by finding the correct R and L values.

We have already solved the constraint equation for L: L = 400 - πR. We can substitute this 400 - πR for L in

the area formula given above: A = L·2R = 2RL = 2R)(400 - πR). This product has the form of a quadratic: A = 800R - 2πR². Because the coefficient of R² is negative, the graph of this parabola opens down. We need to find the vertex of this parabola to obtain the value of R that maximizes the area of the rectangle:

-b ± √(b² - 4ac)

Using the quadratic formula, we get R = ------------------------

-800 ± √(6400 - 4(0)) -1600

or, in this particular case, R = ------------------------------------- = ---------------

2(-2π)

-800

or R = ----------- = 200/π

-4π

and so L = 400 - πR (see work done above)

These are the dimensions that result in max area of the rectangle:

width of rectangle = 2R = (200/π) = 400/π meters

length of rectangle = 400 - π(200/π) = 400 - 200 = 200 meters

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2 years ago