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3 years ago

Determine the domain on which the following function is increasing.

Mathematics

1 answer:

mars1129 [50]3 years ago

7 0

Answer:

(-∞, -2]

Step-by-step explanation:

Domain of a function is defined by the x-values (Input values) and y-values define It's range.

From the graph of a parabola,

Graph shows the increase in the value from x = -∞ to x = -2 then the values are decreased from x = -2 to ∞.

Therefore, domain in which the function is increasing : (-∞ , -2]

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To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin tablets that are similar in

lukranit [14]

Answer: $\dfrac{26}{27}$

Step-by-step explanation:

Given : To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin tablets that are similar in appearance.

Proportion of success : $p=\dfrac{6}{9}=\dfrac{2}{3}$

Sample size taken by customs oﬃcial : n= 3

Let x be a binomial variable that represents the tablets in the bottle.

Using Binomial probability formula :-

$P(X=x)=^nC_xp^x(1-p)^{n-x}$

The probability that the traveler will be arrested for illegal possession of narcotics = $P(x\geq1)=1-P(x=0)$

$1-^3C_0(\dfrac{2}{3})^0(1-\dfrac{2}{3})^3\\\\=1-(1)(1)(\dfrac{1}{3})^3\ [\becuase ^nC_0=1]\\\\=1-\dfrac{1}{27}=\dfrac{26}{27}$

Hence, the probability that the traveler will be arrested for illegal possession of narcotics = $\dfrac{26}{27}$

8 0

3 years ago

A parabola has a vertex at (4, 0) and passes through the point (6, 1). Which of the following is the equation of this parabola i

Doss [256]

Easy

y=a(x-h)^2+k
vertex is (h,k)
we know that vertex is (4,0)
input that point for (h,k)
y=a(x-4)^2+0
y=a(x-4)^2
passes thorugh the point (6,1)
input that point to find a
1=a(6-4)^2
1=a(2)^2
1=a(4)
divide both sides by 4
1/4=a

thefor the equation is
y=(1/4)(x-4)^2
or
y=(1/4)x^2-2x+4

7 0

3 years ago

What are all the answers to this screenshot

sp2606 [1]

Answer:

b. 0.1 difference

c. 1.04 times

d. 6th, 8th, 7th

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3 years ago

Identify the maximum and minimum values of the function y = 10 cos x in the interval [-2π, 2π]

grigory [225]

Hello,

-1<=cos x <=1
==>-10<=10*cos x <=10
max y=10 if x=0 +2kπ ==>x=0,-2π,2π
min y=-10 if x=π+2kπ ==>x=-π,π

6 0

3 years ago

Pentagon VWXYZ is shown on the coordinate grid. A student reflected pentagon VWXYZ across the x-axis to create pentagon V’W’X’Y’

pav-90 [236]

Reflecting across the x axis maintains the same x coordinate, but changes the sign of the y coordinate.

So, the transformation is

$(x,y)\mapsto (x,-y)$

7 0

3 years ago