ƒ (x) = x² − 2x – 4.
What is the average rate of change for the quadratic function from x = − 1 to x =4

Using the hypergeometric distribution, it is found that there is a 0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, we have that the values of the parameters are:

N = 10, k = 4, n = 2.

The probability that both are green is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,10,2,4) = \frac{C_{4,2}C_{6,0}}{C_{10,2}} = 0.1333[/tex]

0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.

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8v + 3 -4v = 4v + 5 -3 has infinitely many solutions

7v - 11 = 7v + 11 has no solution

3(v-4) = 2(v-6) has one solution

5(2v+3) - 2 = 12v + 12 -2v has no solution

A linear equation is said to have infinitely many solution when the variable term and the constant term are the same on both sides of the equation.

A linear equation is said to have no solution, if the coefficient of the variable term is zero and the constant term a non-zero term

A linear equation is said to have one solution if the coefficient of both the constant term and the variable terms are no zero.

Analysis:

8v + 3 -4v = 4v + 5-2

4v +3 = 4v+3

The equation has an infinitely many solutions

7v-11 = 7v+11

7v-7v = 11+11

0v = 22

The equation has no solution since the coefficient of the variable term is 0

3(v-4) = 2(v-6)

3v -12 = 2v - 12

v = 12-12 = 0

The equation has one solution

5(2v+3) -2 = 12v + 12-2v

10v+15-2 = 10v +12

0v = -1

The equation has no solution.

In conclusion,

8v + 3 -4v = 4v + 5 -3 has infinitely many solutions

7v - 11 = 7v + 11 has no solution

3(v-4) = 2(v-6) has one solution

5(2v+3) - 2 = 12v + 12 -2v has no solution

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Answer:

A

Step-by-step explanation:

h(x) = 2x² + 15 = 2×f(x) + 15

so, every y value of f(x) is multiplied by 2, and that means the whole curve is stretched up and down (vertically).

and then we add constantly 15 to every y value. that moves then the previous stretched result up by 15 units.

The most appropriate statement is the interquartile range for the Wolverines, 30 is less than the IQR for the panthers, 40.

The box plot is used to show the distribution of data. The box plot can be used to determine the range, interquartile range and median of the data set.

The range is the difference between the two ends of the whiskers.

Range for the Wolverines = 96 - 35 = 61

Range for the Panthers = 107 - 33 = 74

The interquartile range is the difference between the first and third lines on the box

IQR for the Wolverines = 85 - 55 = 30

Range for the Panthers = 90 - 50 = 40

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The answer choices which could be a constraint to the scenario are;

It follows from the task content that the scenario is modelled by means of a system of inequalities. However, only the variables in the model can be constrained and hence, only time and depth factors could be part of the constraints.

On this note, the constraints area as indicated above.

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Answer:

A

Step-by-step explanation:

A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario?

The pool is 1 meter deep.

The pool is 2 meters deep.

The toy falls at a rate of at least a Negative one-half meter per second.

The toy sinks at a rate of no more than a Negative one-half meter per second.

Answer: Absolute value function

The type of parent function is f(x)= |x| is Absolute valued function

An absolute value function is a function that contains an algebraic expression within absolute value symbols.

Given function:

f(x)= |x|

As, we know the modulus generally give the absolute value of any function and also the modulus always give the positive value.

The above property perfectly resemble the absolute valued function.

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The probability of randomly selecting a tree or a flower is 8/15.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of randomly selecting a tree or a flower = (number of trees / total number of flash cards) + (number of flowers / total number of flash cards)

8/30 + 8/30 = 16/30  = 8/15

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Step-by-step explanation:

From what I know

3x-1=0

3*(-2)-1=0

-6-1=0

=-7.

I'm not sure but u can try it.

The value of f(-2) in this function is f(-2) = -7

To solve this expression, just replace 'x' with -2. When the expression is ready, let's calculate it.

First we multiply or divide, then add or subtract.

f( x ) = 3x - 1

f(-2) = 3 · (-2) - 1

f(-2) = -6 - 1

f(-2) = -7

So, the alternative value is f(-2) = -7

Answer:

x = 0

Step-by-step explanation:

The slope relation is given as :

y = mx + b

Now, if we take x = 0, there is no way of finding out the value of m as the product of mx will be equal to 0.

Hence, x = 0 represents a line with undefined slope.

Answer:



Step-by-step explanation:

Answer:

221.16

Step-by-step explanation:

Find the difference between each day. Add all the differences together, then divide that number by 6 (the number of differences) to find the mean.

Answer:

189.57 miles per day.

Step-by-step explanation:

I took the test

Step-by-step explanation:

mx=n

⟹x=mn

Since m and n are both negative, x=mn will be positive.

Hence, the solution of mx=n will be a positive number.

other sulotion :-

Answer:

y=15 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

if the guppies are doubling, that means whatever they were yesterday, today is 100% more, so the rate of growth is 100%.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=4(1 + 1.)^{t}\implies A=4(2)^t~\hfill \stackrel{\textit{after 4 days, t = 4}}{A=4(2)^4}\implies A=64[/tex]

Answer:

1 pound is equivalent to 453.59237 Grams.

✎let's answer it :3

☟ answer

-> ( 453.59237 grams )

hope it helps

Answer:

x = 90°

y = 40°

z = 40°

Explanation (Concepts) :

A straight line has total 180° angle. A square has 4 sides of each 90° angle. A triangle is build up of 180° interior angle.

Workouts:

z + 90° + 50° = 180°

z = 180° - 90° - 50°

z = 40°

=================

x + 90° = 180°

x = 180° - 90°

x = 90°

==================

50° + 90° + y = 180°

y = 180° - 90° - 50°

y = 40°

Answer:

Step-by-step explanation:

x = 90°

…………………

y = 90 - 50

  = 40°

……………………………

z = 180 - (50 + 90)

  = 180 - 140

  = 40°

Answer:

Mean = 23

Median = 24

Mode = 24

Step-by-step explanation:

Mean:  The sum of all data values divided by the total number of data values.

⇒ Mean = (24 + 20 + 26 + 24 + 21) ÷ 5 = 23

Median:  The middle value when all data values are placed in order of size.

Ordered data values:  20, 21, 24, 24, 26

⇒ Median = 24

Mode:  The most frequently occurring data value.

20, 21, 24, 24, 26

⇒ Mode = 24

Answer:

theta = pi/6 and

theta = 5pi/6

Step-by-step explanation:

see image. Factor the expression. Solve for sin theta. Then use a calculator or unit circle to solve for theta. See image.

Let's simplify the problem down a little:

 ⇒ set 'sin(θ)' as x

    ⇒ the new equation looks like: [tex]2x^2+5x-3=0[/tex]

Now let's solve this equation as a quadratic:

 [tex]2x^2+5x-3=0\\(2x-1)(x+3)=0\\\\2x-1=0\\x = \frac{1}{2} \\\\x+3 = 0\\x=-3[/tex]

Now set the x value of '1/2', to sin(θ)

         sin(θ) = 1/2

            θ = π/6, which is between the range given

Answer: π/6

Hope that helps!

[tex]-3x^3 +12x^2 -15x +6\\\\=-3(x^3 -4x^2 +5x-2)\\\\=-3(x^3 -2x^2-2x^2 +4x+x-2)\\\\=-3\textbf{[} x^2(x-2) -2x(x-2)+ (x-2)\textbf{]}\\\\=-3(x-2)(x^2 -2x +1)\\\\=-3(x-2)(x-1)^2[/tex]

Answer:

9

Step-by-step explanation:

5*x=15

X=3

3*3=9

[tex]\\ \rm\dashrightarrow \dfrac{5}{3}=\dfrac{15}{x}[/tex]

[tex]\\ \rm\dashrightarrow 5x=45[/tex]

[tex]\\ \rm\dashrightarrow x=\dfrac{45}{5}[/tex]

[tex]\\ \rm\dashrightarrow x=9[/tex}

Answer:

deductive reasoning

Step-by-step explanation:

it is based on what is true based on what happened before

Answer:

2 option, deductive reasoning

Step-by-step explanation:

based on true events

Answer:

A and E

Step-by-step explanation:

A is already given by the basic fact that DE = FG. this makes the 2 lines automatically also congruent.

but this does not tell us anything about EF.

E and F could be very close together or far apart, and still DE = FG can be true in either case.

and that is why B, C and D could be true, but they are not in all cases true, and therefore these statements are in general false.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(-10,7)\qquad R(8,-5)\qquad \qquad \stackrel{\textit{ratio from P to R}}{4:5} \\\\\\ \cfrac{P\underline{Q}}{\underline{Q} R} = \cfrac{4}{5}\implies \cfrac{P}{R} = \cfrac{4}{5}\implies 5P=4R\implies 5(-10,7)=4(8,-5)[/tex]

[tex](\stackrel{x}{-50}~~,~~ \stackrel{y}{35})=(\stackrel{x}{32}~~,~~ \stackrel{y}{-20})\implies Q=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-50 +32}}{4+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{35 -20}}{4+5} \right)} \\\\\\ Q=\left( \cfrac{-18}{9}~~,~~\cfrac{15}{9} \right)\implies Q=\left( -2~~,~~\cfrac{5}{3} \right)[/tex]

Answer:

c

Step-by-step explanation:

the -2 causes a shift 2 units right