Jacqueline buys 2 fourths yard of green ribbon and 1 fourths yard of pink ribbon. How many yards of ribbon does she buy?

Answer:

Step-by-step explanation:

There are lots of ways we can think about the typical number of cavities.

• What was the most common number of cavities?

• If we split the cavities evenly among all the patients, how many cavities would each patient have?

• What would be the balance point of the data?

• What is the middlemost number of cavities?  

The most patients had 0cavities.  

If we split the cavities evenly, each patient would have 2 or 3 cavities.  

If we put our dot plot on a balance scale, it would balance when the pivot was between 2 and 3 cavities.

The scale would tip if, for example, we put the pivot at 5 cavities.

There are 8 patients with 2 cavities each. About half of the rest of the patients have fewer than 2 cavities and about half have more than 2 cavities.

Of the choices, it is reasonable to say that a patient typically had about 2 cavities.

,                                  -Written in

Final answer:

The 'typical' number of cavities one patient had can be determined by finding the mode (most common number) in the data set, which should be represented in the dot plot. To do this, one would count the number of dots at each value on the dot plot. The value with the most dots would be the 'typical' number of cavities.

Explanation:

The question is asking for a 'typical' number of cavities one patient had out of Dr. Vance's 63 patients. In statistics, a typical, or 'common', value can be shown by calculating the mode, which is the number that appears most frequently in a data set.

Unfortunately, the dot plot is missing from the information provided. However, to find the mode (or typical value) using a dot plot, you would typically count how many dots are at each value on the plot. The value with the most dots (indicating the most patients with that number of cavities) is the mode. This would be the 'typical' number of cavities a patient of Dr. Vance had last month.

Let's create a hypothetical scenario. If your dot plot looked like this:

• 0 cavities: 10 patients
• 1 cavity: 15 patients
• 2 cavities: 24 patients
• 3 cavities: 8 patients
• 4 cavities: 6 patients

The mode would be 2 cavities because 24 patients had this amount, more than any other amount. Therefore, the 'typical' number of cavities one patient had would be 2.

Learn more about Dot Plot & Mode here:

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Answer:

x=2

Step-by-step explanation:

All of the angles equal 360. So if side z is equal to 100 then 360-200 = 160. The side on the left also is equal to the right side. 160-140 =20. 20/10 is 2. X is equal to 2.

Answer:

x=3

Step-by-step explanation:

4x+6=18

4x=18-6

4x=12

x=12÷4

x=3

Answer:

1. a = -31/9

2. -3/4

3. Different degree polynomials

4. Yes, of a degree 2n

5. a. Even-degree variables

b. Odd- degree variables

Step-by-step explanation:

1. Suppose f(x) = x^4-2x^3+ax^2+x+3. If f(3) = 2, then what is a?

Plugging in 3 for x:

f(3)= 3^4 - 2*3^3 + a*3^2 + 3 + 3= 81 - 54 + 6 + 9a = 33 + 9a and f(3)= 2

• 9a+33= 2
• 9a= -31
• a = -31/9

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2. Let f, g, and h be polynomials such that h(x) = f(x) * g(x). If the constant term of f(x) is -4 and the constant term of h(x) is 3, what is g(0)?

• f(0)= -4, h(0)= 3, g(0) = ?
• h(x)= f(x)*g(x)
• g(x)= h(x)/f(x)
• g(0) = h(0)/f(0) = 3/-4= -3/4
• g(0)= -3/4

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3. Suppose the polynomials f and g are both monic polynomials. If the sum f(x) + g(x) is also monic, what can we deduce about the degrees of f and g?

• A monic polynomial is a single-variable polynomial in which the leading coefficient is equal to 1.

If the sum of monic polynomials f(x) + g(x) is also monic, then f(x) and g(x) are of different degree and their sum only change the one with the lower degree, leaving the higher degree variable unchanged.

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4. If f(x) is a polynomial, is f(x^2) also a polynomial?

• If f(x) is a polynomial of degree n, then f(x^2) is a polynomial of degree 2n

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5. Consider the polynomial function g(x) = x^4-3x^2+9

a. What must be true of a polynomial function f(x) if f(x) and f(-x) are the same polynomial?

• If f(x) and f(-x) are same polynomials, then they have even-degree variables.

b.What must be true of a polynomial function f(x) if f(x) and -f(-x) are the same polynomial?

• If f(x) and -f(-x) are the same polynomials, then they have odd-degree variables.

Answer:

x = 3

y = 1

Step-by-step explanation:

The equations are:

and

Putting second equation in the first one:

=>

Subtracting 27 to both sides

=>

=>

Taking power 7 to both sides

=> y = 1

Now,

Taking cube root on the both sides

x = 3

Answer: (3,1)

Step-by-step explanation:

First, to find x, simply take the cube root of 27, or 3.  Thus, x = 3.

Then, simply plug it in:

Thus, y = 1

Hope it helps <3

p.s. for some reason, in a graphing calculator, it shows no solutions

Hope it helps <3

2 in a row!