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Nutka1998 [239]
3 years ago
15

Drag and drop the correct numbers into the boxes to show the initial value and the range for each of the linear functions f(x) a

nd g(x).
The domain of each function is the set of all real numbers x such that 2 ≤ x ≤ 5. The table shows some ordered pairs for f(x). The function g(x) is defined by the rule g(x) = x + 5.


x f(x)

2 4

3 6

4 8

5 10



The initial value of f(x) is .

The initial value of g(x) is .

The range for the function f(x) is ≤ f(x) ≤ .

The range for the function g(x) is ≤ g(x) ≤ .

7 10 6 4 8 9 4 4 7 7 10 10 9 9 6 6 8 8 4 10 6
Mathematics
1 answer:
tatuchka [14]3 years ago
6 0
I think  the answer is the 4th one
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For the function f(x)=5x2−5x, evaluate and simplify.
Marianna [84]

9514 1404 393

Answer:

  10x -5 +5h

Step-by-step explanation:

Use the function definition with the given arguments.

  \dfrac{f(x+h)-f(x)}{h}=\dfrac{(5(x+h)^2-5(x+h))-(5x^2-5x)}{h}\\\\=\dfrac{(5(x^2+2hx+h^2)-5(x+h))-(5x^2-5x)}{h}\\\\=\dfrac{5x^2+10hx+5h^2-5x-5h-5x^2+5x}{h}=\dfrac{10hx-5h+5h^2}{h}\\\\=\boxed{10x-5+5h}

7 0
3 years ago
Kiran said that this diagram can show the solution to 16÷8=? or 16÷2=?, depending on how we think about the equations and the “?
nignag [31]

Answer:

16÷2

Step-by-step explanation:

It would be 16 divided by 2. This is because in the diagram they are splitting 16 by 2. Splitting 16 by 2 gets you two 8's.

8 0
3 years ago
16x 2 + 8x - 15 Mathematics?
Gala2k [10]
If you're factoring, your answer is

(4x - 3)(4x + 5)

You'll work it out this way:

16x^2 + 8x - 15

Since there's no GCF here, you multiply the first and third terms, giving you -240. Your next step is to find two numbers that have a sum of 8 and a product of -240. These numbers are 20 and -12. Plug those in and you've got:

16x^2 + 20x - 12x - 15

From here you divide it into two binomials. These are (16x^2 + 20x) and (-12x - 15).
When you take out the greatest common factors (4x and -3), they become:

4x(4x + 5) - 3(4x + 5)

Then you group what's outside of the parentheses together (4x - 3)
And bring what's inside of the parentheses down (4x + 5).
This brings your answer to

(4x - 3)(4x + 5)
5 0
3 years ago
The equation of the line of best fit of a scatter plot y equals negative five x minus two what is the slope of the equation
sattari [20]
Y=-5x-2 
-2= y-intercept
-5x= slope
find y-intercept on a graph, make a dot.
then use slope from y-intercept dot, make another dot.
Draw line.
Is it a positive or Negative slope?
Hope that helps.
5 0
3 years ago
According to a study done by a university​ student, the probability a randomly selected individual will not cover his or her mou
VikaD [51]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

 P(X = 8) =  0.0037

b

 P(X <  5) =  0.805

c

 P(X > 6) =  0.0206

I would be surprised because the value is very small , less the 0.05

Step-by-step explanation:

From the question we are told that

The probability a randomly selected individual will not cover his or her mouth when sneezing is p = 0.267

Generally data collected from this study follows  binomial  distribution because the number of trials is  finite , there are only two outcomes, (covering  , and  not covering mouth when sneezing ) , the trial are independent

Hence for a randomly selected variable  X we have that  

   X \ \ \~ \ \ { B ( p , n )}

The probability distribution function for binomial  distribution is  

    P(X = x ) =  ^nC_x *  p^x *  (1 -p) ^{n-x}

Considering question a

Generally the  the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when​ sneezing is mathematically represented as

     P(X = 8) =  ^{12} C_8 *  (0.267)^8 *  (1- 0.267)^{12-8}

Here C denotes  combination

So

     P(X = 8) =  495  *  0.000025828 * 0.28867947

    P(X = 8) =  0.0037

Considering question b

Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when​ sneezing is mathematically represented as

     P(X <  5 ) =[P(X = 0 ) + \cdots + P(X = 4)]

=>   P(X <  5 ) =[ ^{12} C_0 *  (0.267)^0 *  (1- 0.267)^{12-0} + \cdots +  ^{12} C_4 *  (0.267)^4 *  (1- 0.267)^{12-4} ]

=> P(X <  5 )  =  0.02406 +  0.10516 + 0.21067 + 0.25580 + 0.20964

=>  P(X <  5) =  0.805

Considering question c

Generally the probability that fewer than half(6) covered their mouth when​ sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as

      P(X > 6) =  1 - p(X \le  6)

=>    P(X > 6) = 1 - [P(X = 0) + \cdots + P(X =6)]

=>    P(X > 6)=1 - [^{12} C_0 *  (0.267)^0 *  (1- 0.267)^{12-0}+ \cdots + ^{12} C_4 *  (0.267)^6 *  (1- 0.267)^{12-6} ]

=>    P(X > 6)= 1 - [0.02406 + \cdots + 0.0519 ]  

=>    P(X > 6) =  0.0206

I would be surprised because the value is very small , less the 0.05

8 0
3 years ago
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