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2 years ago

EOC 2.27

Mathematics

1 answer:

Dovator [93]2 years ago

4 0

The variable that cannot be illustrated by a stem-and-leaf plot is C. Number of doctor visits during the past year.

It can be inferred that a stem and leaf plot simply means the technique that is used to classify continuous or discrete variables.

In this case, the variable that cannot be illustrated by a stem-and-leaf plot is the number of doctor visits during the past year. This is because it's an ordinal variable.

Learn more about stem and leaf plot on:

brainly.com/question/12276901

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What is the coefficient of x2y3 in the expansion of (2x + y)5?

Zigmanuir [339]

Option C:

The coefficient of $x^{2} y^{3}$ is 40.

Solution:

Given expression:

$(2 x+y)^{5}$

Using binomial theorem:

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here $a=2 x, b=y$

Substitute in the binomial formula, we get

$(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}$

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}$

$$+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}$

Let us solve the term one by one.

$$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}$

$$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y$

$$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}$

$$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}$

$$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}$

$$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}$

Substitute these into the above expansion.

$(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}$

The coefficient of $x^{2} y^{3}$ is 40.

Option C is the correct answer.

5 0

2 years ago

4 gallons, 3 quarts are equal to how many pints

Lelu [443]

Answer:

14 pints

Step-by-step explanation:

1 gallon = 8 pints

3 quarts= 6 pints

8+6=14

3 0

2 years ago

Tim needs 3 pounds of vegetables for a vegetable soup recipe.

klio [65]

Answer:

25/12 - pounds more vegetables

Step-by-step explanation:

first we need to put these variables into like terms

36/12 - 3

8/12 - 2/3

3/12 - 1/4

add the last two up and subtract from the first and you get how much you need left over

8 0

2 years ago

Find the area of the triangle below.

Rom4ik [11]

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

in our case we have a baseline with its associated height right there. and so the area is

17 × 6 / 2 = 17 × 3 = 51 ft²

6 0

1 year ago

A complex number z=a+bi had an absolute value of 3.28. What could the values of a and b be ? A.a=1.5,b=1.7 C.a=1.7,b=2.8

Levart [38]

The given complex number is ⇒ z = a + b i
The absolute value of z = √( a² + b² ) = 3.28
So, we will check which of the options will give 3.28

( A) IF ⇒⇒ a=1.5 and b=1.7

∴ √( a² + b² ) = √( 1.5² + 1.7²) = √5.14 ≈ 2.27

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

(B) IF ⇒⇒ a=1.5 and b=3.3

∴ √( a² + b² ) = √(1.5² + 3.3²) = √13.14 ≈ 3.62

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

(C) IF ⇒⇒ a=1.7 and b=2.8

∴ √( a² + b² ) = √(1.7² + 2.8²) = √10.73 ≈ 3.28

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

(D) IF ⇒⇒ a=2.8 and b=3.3

∴ √( a² + b² ) = √(2.8² + 3.3²) = √18.73 ≈ 4.33
=====================================
So, the correct answer is option (C) a=1.7,b=2.8

4 0

2 years ago