P ( x ) = | x | and the image I ( x ) = 1 2 ⋅ P ( x ) graph

Answer:

y = x² + 6x + 16

= (x² + 6x + 9) - 9 + 16

= (x + 3)² + 7 ← vertex form

Therefore, vertex is (-3, 7) and since the coefficient of (x + 3)² is positive the vertex is a minimum.

Answer:

minimum (3,7)

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(X)=3x-12

To find f(2) substitute the value in the bracket which is 2 into f(x)

That's

f(2) = 3(2) - 12

= 6 - 12

= - 6

Hope this helps you

Answer:

-6

Step-by-step explanation:

Answer:

  (0, -5)

Step-by-step explanation:

You have (x, f(x)) = (0, 0) and you want (x, f(x) -5).

That would be ...

  (x, f(x) -5) = (0, 0 -5) = (0, -5)

Hey there! :)

Answer:

P = 48xy + 4 units.

Step-by-step explanation:

To find the perimeter of a square, the formula P = 4s (where 's' is the side-length):

Substitute in 12xy + 1 for s:

P = 4(12xy + 1)

Distribute the 4:

P = 4(12xy) + 4(1)

P = 48xy + 4 units.

Answer:

4.9 × 10^1

hopefully this helped :3

Answer:

4.9 * 10 ^1

Step-by-step explanation:

We want one digit to the left of the decimal

49

4.9

We moved the decimal one place to the left

One is the exponent.  Since we moved to the left the exponent is positive

4.9 * 10 ^1

Answer:

82 units.

Step-by-step explanation:

The Pythagorean Theorem is a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the legs.

In this case, 18 and 80 are the legs.

18^2 + 80^2 = c^2

324 + 6,400 = c^2

6,724 = c^2

c^2 = 6,724

c^2 = 82^2

c = plus or minus 82

Since measurements cannot be negative, the length of the hypotenuse is 82 units.

Hope this helps!

Answer:

82 units   indeed!

Step-by-step explanation:

c = [tex]\sqrt{ 18^{2} + 80^{2} }[/tex]

c = 82

Answer:

b

Step-by-step explanation:

Answer:

There is no real number that can satisfy this equation

Step-by-step explanation:

Answer: Evaluate the Function, right?

Hello!

~~~~~~~~~~~~~~~~~~

A) 4x = -4 [x=-1] =

4x = -4 =

x = -1 = x = -1

( The steps : Substitute the given value into the function and evaluate.)

B) 2(x-3) =-12 [x=3] =

2 ( x - 3) = -12 = x = -3

x = 3 = x = 3

( The steps : Substitute the given value into the function and evaluate.)

C) 8x - 4x = 24 [x = 1/2] =

8x - 4x = 24 = x = 6

x = 1/2 = x = 1/2

( The steps : Substitute the given value into the function and evaluate.)

D) 9x - 4x = 24 [x=18] =

9x - 4x = 24 = x = 24/5

x = 18 = x = 18

( The steps : Substitute the given value into the function and evaluate.)

~~~~~~~~~~~~~~~~~~

Step-by-step explanation: All the steps are the same. Substitute the given value into the function and evaluate.

Hope this helped you!

Answer:

  f(0) = 1/2

Step-by-step explanation:

At x=0, the inequality tells you ...

  1/2 ≤ 1 -f(0) ≤ 1/2

That is, ...

  1 - f(0) = 1/2

  f(0) = 1/2

  [tex]\boxed{\lim\limits_{x\to 0}{f(x)}=\dfrac{1}{2}}[/tex]

Answer:

Step-by-step explanation:

While the pareto distributions are continuous in nature, they are sometimes used to model discrete data in fields such as Social Sciences, Humanities, Geophysics, and Actuarial Sciences.

The Pareto Distribution is a power-law probability distribution used in studies of observable phenomena.

The probability density function (PDF) for a Pareto Distribution is:

Xn = 1

for various Alpha levels

Where Xn is the probability value of X

As Alpha tends to infinity, the pareto distribution tends to ¶ [X-Xn]

Where ¶ is the Dirac Delta function.

Answer:

a) x-4+9

b) x-2

For part b, I am not 100% sure about my answer, but I am sure about part a.

Answer:

a) If interest rates go up, share prices go down : this will be assigned p→q

b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r)

c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q)

d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park.  P → (q∨r)

e) My sister wants a black and white cat. p∧q

Step-by-step explanation:

A statement  is said to be propositionally logical if the statement that can be assigned either true or false.

∧and

∨or

¬not

→implies

a) If interest rates go up, share prices go down : this will be assigned p→q implies because the occurrence of event (share prices go down) depends on the possibility of the other event happening.

b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r) : either of the two of the other events (i.e. he has sold his car or he has not paid his mortgage ) can only occur if the first event occur

c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q) : either of the events can occur but not both i.e. they are mutually exclusive

d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park.  P → (q∨r) either of the two of the other events (i.e. they had a cup of coffee together or they took a walk in the park ) can only occur if the first event (Sam met Jane yesterday) occur

e) My sister wants a black and white cat. p∧q : both events can only occur together

Answer:

Option C.

Step-by-step explanation:

The given function is

[tex]y=\dfrac{2x+1}{x^2}[/tex]

We need to find the slope of the function when x=4.

Differentiate the given function w.r.t. x.

[tex]\dfrac{dy}{dx}=\dfrac{x^2\dfrac{d}{dx}(2x+1)-(2x+1)\dfrac{d}{dx}x^2}{(x^2)^2}[/tex]    (Using quotient rule)

[tex]\dfrac{dy}{dx}=\dfrac{x^2(2+0)-(2x+1)(2x)}{x^4}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{2x^2-4x^2-2x}{x^4}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{-2x^2-2x}{x^4}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{-2x(x+1)}{x^4}[/tex]

[tex]\dfrac{dy}{dx}=\dfrac{-2(x+1)}{x^3}[/tex]

Now substitute x=4 in the above equation.

[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-2(4+1)}{4^3}[/tex]

[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-2(5)}{64}[/tex]

[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-10}{64}[/tex]

[tex]\dfrac{dy}{dx}_{x=4}=-0.15625[/tex]

[tex]\dfrac{dy}{dx}_{x=4}\approx -0.16[/tex]

Therefore, the correct option is C.

Answer:

41.18% probability of drawing a white counter or a green counter

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

There are 3+10+4 = 17 counters.

Of those, 3+4 = 7 are white or green

7/17 = 0.4118

41.18% probability of drawing a white counter or a green counter

Answer:

54 cm²

Step-by-step explanation:

Area of a Rectangle Formula: A = lw

We are given 18 as l and 3 as w, so simply plug it into the formula:

A = 18(3)

A = 54

Hey there! :)

Answer:

(-1, -3)

Step-by-step explanation:

Use the midpoint formula to derive the coordinates of the midpoint:

[tex](x_{m} ,y_{m} ) = (\frac{x_{1} +x_{2} }{2}, \frac{y_{1}+ y_{2} }{2} )[/tex]

Plug in the coordinates given:

[tex](\frac{-5+3 }{2}, \frac{2-8 }{2} )[/tex]

Simplify:

[tex](\frac{-2 }{2}, \frac{-6 }{2} )[/tex]

(-1, -3) are the coordinates of the midpoint.

Answer:

[tex]\boxed{Midpoint = (-1,-3)}[/tex]

Step-by-step explanation:

The coordinates are (-5,2) and (3,-8)

M(x,y) = [tex](\frac{x1+x2}{2} , \frac{y1+y2}{2} )[/tex]

M(x,y) = [tex](\frac{-5+3}{2} , \frac{2-8}{2} )[/tex]

M(x,y) = [tex](\frac{-2}{2} , \frac{-6}{2} )[/tex]

M(x,y) = (-1,-3)

Answer:

[tex]slope:1/8y-intercept:-7\\COORDINATES(x,-7)\\\\(56,0)[/tex]

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

480/(1+3)

480/4

= 120

1 × 120 : 3 × 120

120 : 360

Boys to girls are in the ratio 120:360.

There are 120 boys.

Answer:

paper = $4 and stapler = $7

Step-by-step explanation:

let p represent paper and s represent stapler, then

3p + 4s = 40 → (1)

5p + 6s = 62 → (2)

Multiplying (1) by 5 and (2) by - 3 and adding will eliminate p

15p + 20s = 200 → (3)

- 15p - 18s = - 186 → (4)

Add (3) and (4) term by term to eliminate p

2s = 14 ( divide both sides by 2 )

s = 7

Substitute s = 7 into either of the 2 equations and evaluate for p

Substituting into (1)

3p + 4(7) = 40

3p + 28 = 40 ( subtract 28 from both sides )

3p = 12 ( divide both sides by 3 )

p = 4

Thus package of paper costs $4 and stapler costs $7

Answer: c. 0.1743

Step-by-step explanation: Poisson Probability or Poisson Distribution is a discrete distribution that models the number of events ocurring in a given period of time.

The mean, or expected value, of the observed frequencies is:

E(X) = ∑xP(x)

E(X) = 0*3/150 + 1*(10/150) + 2*(15/150) + 3*(23/150) + 4*(30/150) + 5*(24/150) + 6*(20/150) + 7*(13/150) + 8*(8/150) + 9*(4/150)

E(X) = 4.399

The Poisson distribution is calculated by:

P(X = k) = [tex]\frac{mean^{k}.e^{-mean}}{k!}[/tex]

The question asks for the expected frequency of exactly 3 cars:

P(X = 3) = [tex]\frac{4.399^{3}.e^{-4.399}}{3!}[/tex]

P(X = 3) = [tex]\frac{4.399^{3}.e^{-4.399}}{3.2.1}[/tex]

P(X = 3) = 0.1743

The expected frequency of exactly 3 cars is 0.1743

Answer:

y=5 or y=-4

Step-by-step explanation:

6y - 3| + 8 = 35

|6y-3|=35-8

|6y-3|=27

either 6y-3=-27 then 6y=27+3

y=30/6=5

or 6y-3=-27

6y=-27+3

y=-24/6

y=-4

Answer:

3bat + 3b² - 6a²t²

Step-by-step explanation:

First you have to expand it to get;

3b(b - at) + 6at(b - at)

Then you can now multiply.

3b² - 3bat + 6bat - 6at²

Group like terms

6bat - 3bat + 3b² -6at²

3bat + 3b² - 6a²t²

okay the answer is attached. i was the first to answer, but brainly decided to delete it >:(

The number 27 when rounded to the nearest ten using the number line will give the number 30.

On the number line, the numbers are marked from 10 to 50.

So, the tens are 10, 20, 30, 40, and 50.

The number 27 has to be rounded to the nearest ten.

The one position will be 0.

Now, 27 lies in between the tens 20 and 30 on the number line.

Now, it is required to find which number is 27 closer to.

There are 7 units from 20 to 27.

But there are only 3 units far from 27 to 30.

So, 27 can be rounded to 30 to the nearest ten.

Learn more about Rounding Off here :

https://brainly.com/question/24234983

#SPJ6

Answer:

99.48% probability that the sample mean would be greater than 64.8 kilograms.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 67, \sigma = \sqrt{121} = 11, n = 164, s = \frac{11}{\sqrt{164}} = 0.86[/tex]

What is the probability that the sample mean would be greater than 64.8 kilograms?

This is 1 subtracted by the pvalue of Z when X = 64.8.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{64.8 - 67}{0.86}[/tex]

[tex]Z = -2.56[/tex]

[tex]Z = -2.56[/tex] has a pvalue of 0.0052

1 - 0.0052 = 0.9948

99.48% probability that the sample mean would be greater than 64.8 kilograms.

Answer:

Step-by-step explanation:

We will apply the vertical line test in the given graphs to test them for a function.

Option (1) [First in top row]

If we draw a vertical line from any point, none other point of the graph passes through it.

Therefore, Graph (1) is a function.

Option (2) [2nd in the top row]

When we draw a vertical line through (2, 1), another point (2, -1) will pass through this line.

Therefore, Graph (2) is not a function.

Option (3) [1st in the second row]

In this option when a vertical line is drawn from (2, 1) two more points (2, 2) and (2, 3) pass through this line.

Therefore, graph (4) is not a function.

Option (4). [2nd in the 2nd row]

In this graph only one point lie on the vertical lines drawn.

Therefore, Graph (4) is a function.

Answer:

Regular Pentagon

Step-by-step explanation:

A regular icosahedron is a twenty-faced polyhedron, each face being an equiangular triangle.  Each vertex is joined together by 5 faces, therefore the polygon formed at each vertex is a regular pentagon.

We can also figure out the number of faces at each vertex using Euler's formula

F+V=E+2

F=number of faces = 20

E=number of edges = number of triangular faces * edges/triangle /2

(since each edge is shared between two faces)

= 20*3/2

=30

Number of vertices

= E+2-F = 30+2-20 = 12

So number of edges meeting at each vertex

= 30 / (12/2) = 30/6 = 5

(12/2 because each edge joins two vertices).

See attached figure, courtesy of Wikipedia.