Which graph shows the rule: output = 5 times the input ? explain please!!

Write a function to represent the set of ordered pairs.

77julia77 [94]

Answer:

Option C $f (x) = x^ 2 - 2$

Step-by-step explanation:

Note that the relation describing the set of ordered pairs does not change at a costing rate

$y_2 -y_1 = 7-2 = 5\\\\y_3 -y_2 = 14- 7 = 7\\\\y_4 - y_3 = 23- 14 = 9$

Therefore the relationship is not linear.

However, the exchange rate $y_n- y_{n-1}$ increases by a factor of 2 units when n increases 1 unit. This allows us to conclude that the relationship is quadratic

Note that the following ordered pairs belong to the function

$y = x ^ 2$

A = {(2, 4), (3, 9), (4, 16), (5, 25)}

The set of ordered pairs that we have is:

B = {(2, 2), (3, 7), (4, 16), (5, 23)}

Note that there is a similarity between both sets of ordered pairs.

In set B the values of y are always 2 units less than the values in y of the set A.

Then we deduce that since the function that models the set A is $y = x ^ 2$ then the function that contains the ordered pairs of the B set is:

$y = x ^ 2 -2$

The correct option is option C) $f (x) = x^ 2 - 2$

8 0

3 years ago

A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear the

LenKa [72]

Answer:

a) The probability that at least 5 ties are too tight is P=0.0432.

b) The probability that at most 12 ties are too tight is P=1.

Step-by-step explanation:

In this problem, we could represent the proabilities of this events with the Binomial distirbution, with parameter p=0.1 and sample size n=20.

a) We can express the probability that at least 5 ties are too tight as:

$P(x\geq5)=1-\sum\limits^4_{k=0} {\frac{n!}{k!(n-k)!} p^k(1-p)^{n-k}}\\\\P(x\geq5)=1-(0.1216+0.2702+0.2852+0.1901+0.0898)\\\\P(x\geq5)=1-0.9568=0.0432$

The probability that at least 5 ties are too tight is P=0.0432.

a) We can express the probability that at most 12 ties are too tight as:

$P(x\leq 12)=\sum\limits^{12}_{k=0} {\frac{n!}{k!(n-k)!} p^k(1-p)^{n-k}}\\\\P(x\leq 12)=0.1216+0.2702+0.2852+0.1901+0.0898+0.0319+0.0089+0.0020+0.0004+0.0001+0.0000+0.0000+0.0000\\\\P(x\leq 12)=1$

The probability that at most 12 ties are too tight is P=1.

5 0

3 years ago

Help pleaseeeee

Pavel [41]

Answer:

3419.46

Step-by-step explanation:

(pir^2h)/3

(3.14(121)(27)/3

3419.46

4 0

2 years ago

Y=x^2-6x-16 in vertex form

satela [25.4K]

Answer:

$y=(x-3)^{2} -25$

Step-by-step explanation:

The standard form of a quadratic equation is $y=ax^{2} +bx+c$

The vertex form of a quadratic equation is $y=a(x-h)^{2} +k$

The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.

To find the h-value of the vertex, you use the following equation:

$h=\frac{-b}{2a}$

In this case, our quadratic equation is $y=x^{2} -6x-16$ . Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.

$h=\frac{-b}{2a}$ ⇒ $h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3$

Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is $y=x^{2} -6x-16$

$y=x^{2} -6x-16$ ⇒ $y=(3)^{2} -6(3)-16$ ⇒ $y=9-18-16$ ⇒ $y=-25$

This y-value that we just found is our k-value.

Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: $y=a(x-h)^{2} +k$

a: 1

h: 3

k: -25

$y=(x-3)^{2} -25$

Hope this helps!

3 0

3 years ago

What is the area of a sector of a circle with a radius of 2.0 ft and a central angle of 2<img src="https://tex.z-dn.net/?f=%20%5

Zigmanuir [339]

$\bf \qquad \textit{area of a sector of a circle}
\\\\
A=\cfrac{\theta r^2}{2}\qquad 
\begin{cases}
\theta=\textit{angle in radians}\\
r=radius
\end{cases}$

plug in the provided radius and angle

6 0

3 years ago