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3 years ago

3, 9, 10, 5, 8, 5, 9, 11, 10, 3, 10 Find the mean of the data.

Mathematics

1 answer:

slava [35]3 years ago

7 0

Answer:

7.55

Step-by-step explanation:

An arithmetic mean is the average value of all the data points.

In order to find the average value, you add all the data points then divide the resulting sum by the number of data points there are.

The sum of all data points:

3 + 9 + 10 + 5 + 8 + 5 + 9 + 11 + 10 + 3 + 10 =

The number of data points:

3, 9, 10, 5, 8, 5, 9, 11, 10, 3, 10

1,2,3,4,5,6,7,8,9,10, 11 = 11 data points

Average value/ Mean:

83 / 11 = 7.545454545454 = rounded to 7.55

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A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

<u><em>Find the area of the rectangular playground</em></u>

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

Find AD. Show how you got your answer.

stealth61 [152]

Notice the picture below
the AD line is a bisector, cutting the 36 degrees A in half,
18 and 18 degrees each half

notice the tickmarks, the triangle is an isosceles,
if those two sides are equal, so are the angles they make
down below with the base

now, the base is 8, AD is bisecting that too, to 4 and 4

now, using the Law of Sines

$\bf \textit{Law of sines}
\\ \quad \\
\cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c}\\\\
----------------------------\\\\
\cfrac{sin(18^o)}{4}=\cfrac{sin(72^o)}{\overline{AD}}\implies \overline{AD}=\cfrac{4\cdot sin(72^o)}{sin(18^o)}$

keep in mind, the angles are in degrees, so, when taking the sines, make sure your calculator is in Degree mode

4 0

3 years ago

If a translation maps ∠I onto ∠K, which of the following statements is true?

jonny [76]

The statement which is true is ΔGHI ~ ΔGJK.

<h3>What is Translation?</h3>

This is commonly used in geometry to describe a function which moves object at distances.

This therefore means that translation of ∠I onto ∠K means shifting of point I to point K.

The triangles given are HGI and JGK.

Translation in this scenario therefore means that the triangles are similar only if other angles are mapped to their corresponding angles.

It confirms that ΔGHI ~ ΔGJK thereby making it the most appropriate choice.

Read more about Translation here brainly.com/question/16253702

#SPJ1

3 0

2 years ago

Please help me quick please i don't understand

Shtirlitz [24]

Square root of 15 is an irrational number.

7 0

2 years ago

James works in a sporting goods store and earns $324 a week and 5% of his sales. One week James earned $432. What were his sales

Bogdan [553]

Answer:

His sales that week were $2,160.

Step-by-step explanation:

First, you have to subtract $324 from the amount he earned that week, to find the 5% he got from sales:

$432-$324=$108

Now, you know that he received $108 that represent 5% of his sales and you can use a rule of three to find the amount that represents 100% which would be his sales that week:

5% → 108

100% → x

x=(100*108)/5=2160

According to this, the answer is that his sales that week were $2,160.

7 0

3 years ago