If a polynomial function f(x) has roots 0, 4, and 3 + StartRoot 11 EndRoot, what must also be a root of f(x)? 3 + i StartRoot 11

Assuming we start with a full standard deck of 52 and then draw 4 spades along with 1 card from a different suit, that leaves us with 47 cards still in the deck. We are hoping to draw another spade from these remaining cards. Initially, there were 13 spades, but after drawing five cards, 9 spades remain in the deck. The likelihood of pulling one of these 9 spades from the 47 cards is



In other words, we want to get any 1 of the available 9 spades while avoiding any of the other 38 non-spades, and we're drawing just a single card from the 47 cards total.

There are 28 combinations. Step-by-step explanation: Initially, each of the seven bins holds one ball, leaving two remaining. If both are placed in the same bin, that offers 7 options. Conversely, if each remaining ball is positioned in different bins, the combination comes down to: 21 + 7 = 28 ways.

Answer:

a) Null hypothesis:    

Alternative hypothesis:  

b)   (1)  

Where  

c)    

d) In this scenario, we notice that thus the conclusion for this case would indicate

Step-by-step explanation:

Information provided

denote the number of men possessing smartphones  

signify the number of women possessing smartphones

group of men sampled

group of women sampled

symbolize the proportion of men with smartphones

symbolize the proportion of women with smartphones

denote the pooled estimate of p

z would denote the test statistic

signify the value

Part a

The objective is to evaluate if there is a disparity in smartphone ownership between men and women; the hypothesis statements would be:  

Null hypothesis:    

Alternative hypothesis:    

Part b

The statistic relevant to this case is expressed as:

  (1)  

Where  

Part c

By substituting the provided information, we find:

   

Part d

In this instance, it is evident that thus the conclusion for this case would seem

Answer:

Step-by-step explanation:

The graph can take on three forms as displayed in the figure.

(a) having no intersections

(b) having a single point of intersection (tangency)

(c) having two points of intersection.

Consequently, the maximum number of intersections that these graphs can yield is 2, as illustrated in figure (c).

The solution to the equation is 75.