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andrezito [222]
3 years ago
12

Four friends are trying to decide what kind of cake to order for a party: cheesecake, chocolate, or yellow. Everyone was asked t

o vote for their favorite, and the winner under the unknown voting method was chocolate. Upon calling the store, they found out that the store was out of yellow cake. They decide to recalculate the winner given this new information, and the winning cake is cheesecake. Which fairness criterion has been violated in this election
Mathematics
1 answer:
Zepler [3.9K]3 years ago
5 0

Step-by-step explanation:

I think chocolate fairness criterion has been violated because under the unknown voting method the winner was chocolate but upon calling the store they ordered for yellow cake not chocolate

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alexdok [17]
A because the square is in the (10) place and the circle is in the (1) place and 10 is 10 times bigger than 1
4 0
2 years ago
A traffic consultant wants to estimate the true proportion of cars on a certain street that have more than two occupants. She st
neonofarm [45]

Answer:

The data is a simple random sample from the population of interest.

Step-by-step explanation:

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7 0
2 years ago
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x3 − 6x2 − 15x + 4 (a) Find the interval on which
kozerog [31]

Answer:

a) The function, f(x) is increasing at the intervals (x < -1.45) and (x > 3.45)

Written in interval form

(-∞, -1.45) and (3.45, ∞)

- The function, f(x) is decreasing at the interval (-1.45 < x < 3.45)

(-1.45, 3.45)

b) Local minimum value of f(x) = -78.1, occurring at x = 3.45

Local maximum value of f(x) = 10.1, occurring at x = -1.45

c) Inflection point = (x, y) = (1, -16)

Interval where the function is concave up

= (x > 1), written in interval form, (1, ∞)

Interval where the function is concave down

= (x < 1), written in interval form, (-∞, 1)

Step-by-step explanation:

f(x) = x³ - 6x² - 15x + 4

a) Find the interval on which f is increasing.

A function is said to be increasing in any interval where f'(x) > 0

f(x) = x³ - 6x² - 15x + 4

f'(x) = 3x² - 6x - 15

the function is increasing at the points where

f'(x) = 3x² - 6x - 15 > 0

x² - 2x - 5 > 0

(x - 3.45)(x + 1.45) > 0

we then do the inequality check to see which intervals where f'(x) is greater than 0

Function | x < -1.45 | -1.45 < x < 3.45 | x > 3.45

(x - 3.45) | negative | negative | positive

(x + 1.45) | negative | positive | positive

(x - 3.45)(x + 1.45) | +ve | -ve | +ve

So, the function (x - 3.45)(x + 1.45) is positive (+ve) at the intervals (x < -1.45) and (x > 3.45).

Hence, the function, f(x) is increasing at the intervals (x < -1.45) and (x > 3.45)

Find the interval on which f is decreasing.

At the interval where f(x) is decreasing, f'(x) < 0

from above,

f'(x) = 3x² - 6x - 15

the function is decreasing at the points where

f'(x) = 3x² - 6x - 15 < 0

x² - 2x - 5 < 0

(x - 3.45)(x + 1.45) < 0

With the similar inequality check for where f'(x) is less than 0

Function | x < -1.45 | -1.45 < x < 3.45 | x > 3.45

(x - 3.45) | negative | negative | positive

(x + 1.45) | negative | positive | positive

(x - 3.45)(x + 1.45) | +ve | -ve | +ve

Hence, the function, f(x) is decreasing at the intervals (-1.45 < x < 3.45)

b) Find the local minimum and maximum values of f.

For the local maximum and minimum points,

f'(x) = 0

but f"(x) < 0 for a local maximum

And f"(x) > 0 for a local minimum

From (a) above

f'(x) = 3x² - 6x - 15

f'(x) = 3x² - 6x - 15 = 0

(x - 3.45)(x + 1.45) = 0

x = 3.45 or x = -1.45

To now investigate the points that corresponds to a minimum and a maximum point, we need f"(x)

f"(x) = 6x - 6

At x = -1.45,

f"(x) = (6×-1.45) - 6 = -14.7 < 0

Hence, x = -1.45 corresponds to a maximum point

At x = 3.45

f"(x) = (6×3.45) - 6 = 14.7 > 0

Hence, x = 3.45 corresponds to a minimum point.

So, at minimum point, x = 3.45

f(x) = x³ - 6x² - 15x + 4

f(3.45) = 3.45³ - 6(3.45²) - 15(3.45) + 4

= -78.101375 = -78.1

At maximum point, x = -1.45

f(x) = x³ - 6x² - 15x + 4

f(-1.45) = (-1.45)³ - 6(-1.45)² - 15(-1.45) + 4

= 10.086375 = 10.1

c) Find the inflection point.

The inflection point is the point where the curve changes from concave up to concave down and vice versa.

This occurs at the point f"(x) = 0

f(x) = x³ - 6x² - 15x + 4

f'(x) = 3x² - 6x - 15

f"(x) = 6x - 6

At inflection point, f"(x) = 0

f"(x) = 6x - 6 = 0

6x = 6

x = 1

At this point where x = 1, f(x) will be

f(x) = x³ - 6x² - 15x + 4

f(1) = 1³ - 6(1²) - 15(1) + 4 = -16

Hence, the inflection point is at (x, y) = (1, -16)

- Find the interval on which f is concave up.

The curve is said to be concave up when on a given interval, the graph of the function always lies above its tangent lines on that interval. In other words, if you draw a tangent line at any given point, then the graph seems to curve upwards, away from the line.

At the interval where the curve is concave up, f"(x) > 0

f"(x) = 6x - 6 > 0

6x > 6

x > 1

- Find the interval on which f is concave down.

A curve/function is said to be concave down on an interval if, on that interval, the graph of the function always lies below its tangent lines on that interval. That is the graph seems to curve downwards, away from its tangent line at any given point.

At the interval where the curve is concave down, f"(x) < 0

f"(x) = 6x - 6 < 0

6x < 6

x < 1

Hope this Helps!!!

5 0
3 years ago
Ms.Ellis has a crate that is 5 feet tall, 6 feet wide, and 8 feet long. How many square feet of paint does she need to cover the
Vladimir [108]

Answer:

The answer to your question is 236 ft²

Step-by-step explanation:

Data

height = 5 ft

width = 6 ft

length = 8 ft

Area = ?

Process

I will consider that the crate is a rectangular prism which has 6 sides

1.- Find the area of the sides that measure 8 x 6

Area = 2 (8 x 6)

        = 2(48)

        = 96 ft²

2.- Find the area of the sides that measure 8 x 5

Area = 2(8 x 5)

Area = 2(40)

Area = 80 ft²

3.- Find the area of the sides that measure 6 x 5

Area = 2( 6 x 5)

Area = 2(30)

Area = 60

4.- Find the total area

Area = 96 + 80 + 60

Area = 236 ft²

5.- Conclusion

She needs 236 ft² of paint

3 0
3 years ago
raj has $10. if he buys 8 pears and 5 mangoes, he will be short of $1.10. if he buys 5 pears and 4 mangoes , he will receive $1.
Paladinen [302]

Answer:

1 pear = $0.45

1 mango = 1.5

Step-by-step explanation:

8 pears + 5 mangoes = $11.10 ➡ 8p + 5m = 11.10

5 pears + 4 mangoes = $8.25 ➡ 5p + 4m = 8.25

multiply first equation by -4 and second one by 5

-4 ×(8p+5m) = 11.10 ➡ -32p - 20m = 44.4

5 ×(5p+4m) = 8.25 ➡ 25p + 20m = 41.25

add both equations up

-32p - 20m + 25p + 20m = 44.4 + 41.25

-7p = 3.15 ➡ p = $0.45

use this value to find the price of mango

5×0.45 + 4×m = 8.25 ➡ 2.25 + 4m = 8.25 ➡ 4m = 6 ➡ m = $1.5

8 0
3 years ago
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