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Trava [24]
3 years ago
10

The following graph describes function 1 and the equation below it describes function 2:

Mathematics
1 answer:
Tanya [424]3 years ago
8 0
Function 1: 
f(x) = -x² + 8(x-15)f(x) = -x² <span>+ 8x - 120
Function 2:
</span>f(x) = -x² + 4x+1
Taking derivative will find the highest point of the parabola, since the slope of the parabola at its maximum is 0, and the derivative will allow us to find that.
Function 1 derivative: -2x + 8 ⇒ -2x + 8 = 0 ⇒ - 2x = -8 ⇒ x = -8/-2 = 4

Function 2 derivative:  -2x+4 ⇒ -2x + 4 = 0 ⇒ -2x = -4 ⇒ x = -4/-2 ⇒  x= 2
Function 1: f(x) = -x² <span>+ 8x - 120 ; x = 4
f(4) = -4</span>² + 8(4) - 120 = 16 + 32 - 120 = -72
<span>
Function 2: </span>f(x) = -x²<span> + 4x+1 ; x = 2
</span>f(2) = -2² + 4(2) + 1 = 4 + 8 + 1 = 13

Function 2 has the larger maximum.
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Computer software generated 500 random numbers that should look like they are from the uniform distribution on the interval 0 to
Tanya [424]

Answer:

0.2 ; 100 ; 4.84

Step-by-step explanation:

Given that the probability of each of the 5 groups is the same :

Sum of probability = 1

Hence, Probability of each group = 1 / number of groups = 1 / 5 = 0.2

Expected number for each interval for a sample of 500 : ; X = 500

E(X) = X * P(x) = 500 * 0.2 = 100

Goodness of fit (X²) :

X² = Σ(X - E)² ÷ E

Groups :

113, 95, 108, 99, and 85

X : 113 ____ 95 ____ 108 ____ 99 _____ 85

(113 - 100)^2 / 100 = 1.69

(95 - 100)^2 / 100 = 0.25

(108 - 100)^2 / 100 = 0.64

(99 - 100)^2 / 100 = 0.01

(85 - 100)^2 / 100 = 2.25

(1.69 + 0.25 + 0.64 + 0.01 + 2.25) = 4.84

7 0
2 years ago
Find the product of the complex numbers. Express your answer in trigonometric form.
Marianna [84]
In order to find the product of two complex numbers their magnitudes are multiplied and their arguments(measure of angles) are added up.

For z₁
Magnitude = 4
Argument = π/3

For z₂
Magnitude = 3
Argument = 2π/5

So, the product of z₁ and  z₂ will be:

z_{1} z_{2} =4*3(cos( \frac{ \pi }{3}+\frac{2 \pi }{5})+isin( \frac{ \pi }{3}+\frac{2 \pi }{5})) \\  \\ &#10;z_{1} z_{2} =12(cos( \frac{11 \pi }{5}+isin( \frac{11 \pi }{5}))
6 0
3 years ago
there are 7 white, 4 blue and 3 red marbles in the box. we are randomly taking marbles one by one (without returning in the box)
EastWind [94]
It is probable its 25%
5 0
3 years ago
The perimeter of the square is 2.25x and the equilateral triangle is 1.5x + 6. What is the value of x?
Bond [772]

Answer:

x = 4

Step-by-step explanation:

2.25x=1.5x+6

divide on both sides by 1.5x which equals

1.5x=6

divide both sides by 1.5

x=4

6 0
3 years ago
What is the area of 4 1/5 and 1 4/9 as a mixed number.
marusya05 [52]

Answer:

10 1/9

Step-by-step explanation:

To make it easier to answer, make both of them into an improper fraction

4 1/5 = 21/3

1 4/9 = 13/9

Now we can multiply them easier

21/3 x 13/9 = 273/27

27 goes into 273 10 times and the left over is 3 so the mixed fraction would be

10 3/27, to simplify

10 1/9

5 0
3 years ago
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