11. The ages (in years) of 11 children and the number of words in their vocabulary. Find the correlation coefficient r.


Age, x

1

2

3

4

5

6

3

5

2

4

6

Vocabulary size, y

3

220

540

1100

2100

2600

730

2200

260

1200

2500

Answer:

Step-by-step explanation:

You need to use vertex form of a quadratic to solve this.

Consider the vertex to be [tex](h,k)[/tex]

Another way of representing a quadratic is in "vertex form":

[tex]f(x) = a(x-h)^2+k[/tex]

Now all you have to do is solve for a.  You know that the vertex is [tex](0,2)[/tex] and you have know the point of [tex](1,8)[/tex].  Now, all you have to do is plug in these values and solve for a.

[tex]8 = a(1-0)^2+2\\8=a(1)^2+2\\8=a+2\\a=6[/tex]

Now you know the equation is [tex]f(x) = 6(x-0)^2+2[/tex] , but you need it in quadratic form.  All you have to do is solve is distribute the 6:

[tex]6x^2+2[/tex]

You get:

a = 6

b = 0

c = 2

Please mark this as brainliest if it satisfies your question

Answer: Where is the rest of the question?

Step-by-step explanation:

Answer:

The solution is the point (3, -1)

Step-by-step explanation:

We have the system of equations:

x = 3

y + 1 = 0

To solve this graphically, we need to graph these two lines and see in which point the lines intersect.

To graph the line x = 3, we need to draw a vertical line that passes through x = 3.

To graph y + 1 = 0

First we should isolate y.

y = -1

This is graphed as a horizontal line that passes through y = -1

The graph of these two lines can be seen in the image below.

Where the green line is x = 3, and the blue line is y = -1

Now, looking at the graph we can see that the lines do intersect in the point (3, -1)

Then the solution of the system is the point (3, -1)

Answer:

Step-by-step explanation:

As each step has the same depth and rise, they are respectively 1.2/4=0.3m and 1.8/4=0.45m.

Dividing the steps along the dotted lines, the total rise of the 4 concrete steps  = (1+2+3+4)*0.45

= 4.5m

Total concrete volume = total rise * depth * width

= 4.5*0.3*1.8

= 2.43m^3

Answer:30

Step-by-step explanation:

Answer:

x = -0.2

Step-by-step explanation:

(5x + 2) = 1

      - 2     -2      

--------------------

5x = -1

Divide each side by 5

-1/5

= -0.2

Check:

(5x + 2) = 1

replace x with -0.2

(-1 + 2) = 1

1 = 1

The equation is true.

Hope this helped :)

Answer: 1,145,375cm^3

Step-by-step explanation:

Answer:

It is option one

Step-by-step explanation:

I don’t know why but I’m doing a quizzizz with the same question and i picked option 2 but option one was the correct answer

Answer:

The fraction would be 5/10 or 1/2 and the decimal would be 0.5

Step-by-step explanation:

5 are shaded in out of 10 so that shaded part would be 5 out of 10 or 5/10. Same goes for the decimal, 5 are shaded which means that is 5 tenths or 0.5.

I hope this helps!

Answer:

5 is c 6 is b

Step-by-step explanation:

Answer:

5) C 6) B

Step-by-step explanation:

Yw

Answer:

Step-by-step explanation:

Question 13.

By applying cosine rule,

cos(45°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{\sqrt{2} }=\frac{10}{y}[/tex]

y = 10√2

By applying sine rule,

sin(45°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{\sqrt{2} }=\frac{x}{y}[/tex]

[tex]\frac{1}{\sqrt{2} }=\frac{x}{10\sqrt{2} }[/tex]

x = 10

Question 15.

By applying sine rule,

sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{\sqrt{3} }{2}=\frac{y}{32}[/tex]

y = 16√3

By applying cosine rule,

cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{2}=\frac{x}{32}[/tex]

x = 16

Question 17.

By applying sine rule,

sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{\sqrt{3} }{2}=\frac{11\sqrt{3} }{y}[/tex]

y = 22

By applying cosine rule,

cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{2}=\frac{x}{y}[/tex]

[tex]\frac{1}{2}=\frac{x}{22}[/tex]

x = 11

Answer: Since her art and music sections each only had half the number of sheets of paper as a core subject, together the two sections had the same amount of paper as a core subject. Therefore, it is almost like her notebook had five core subjects, rather than four core subjects and two electives. If she divided the 200 sheets equally among the five core subjects, there would be 200 ÷ 5 = 40 sheets in each section. Now we can see that art would actually have half of this amount, or 20 sheets of paper.

Answer:

Hey Aryabd interested to talk with me. Come in comments.

The  US Dollars for Rs 21000 would be 200 USD

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that  the rate of Rs 105 per US Dollar,

We have to calculate the US Dollars for Rs 21000.​

105 Rs = 1 USD

21000 Rs = x USD

Now the proportion can be;

105x =21000

x =21000 /105

x= 200 USD

Learn more about multiplications;

https://brainly.com/question/14059007

#SPJ2

Answer:

6 and 2/5

Step-by-step explanation:

Answer:

Decimal form: 6.4

Fraction form: 32/5

Step-by-step explanation:

of = times

2/5 x 16 = 6.4

Answer:

√49

Step-by-step explanation:

It's a perfect square root.

Please brainliest ;)

Answer: i think $35

Step-by-step explanation: have a great day

Answer:

rectangle

Step-by-step explanation:

A rectangle represents a figure with four sides having equal opposite sides and the inside angle between the two adjacent sides is ninety degree.

When any plane is made to pass through the cylinder creating a cross section which is perpendicular to its base, it results a two-dimensional cross sectional shape of a rectangle.

It's 12 because if you divide 6 by 0.5 you should get 12, so basically use the opposite operation.

Hope that helps!

Answer:

Explanation: Realize that 4x2−25 is a difference of squares. Differences of squares, such as a2−b2 , can be factored into (a+b)(a−b) . Since 4x2=(2x)2 and 25=(5)2 , we can say that 4x2−25=(2x+5)(2x−5)

Step-by-step explanation:

Answer:

(2x + 5)(2x - 5)

Step-by-step explanation:

a² - b² = (a + b)(a - b)

4x² = 2²x²= (2x)²

25= 5* 5 = 5²

4x² - 25 = (2x)² -  5²         {a= 2x  ; b = 5}

             = (2x + 5)(2x - 5)

Answer:

2x^2+8x - 16

Step-by-step explanation:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

Given

R(x) = 6x ^ 2 + 5x - 8

C(x) = 4x ^ 2 - 3x + 7

P(x) = 6x ^ 2 + 5x - 8-(4x ^ 2 - 3x + 7)

P(x) = 6x ^ 2 + 5x - 8 - 4x ^ 2 + 3x - 8

Collect the like terms;

P(x) = 6x^2-4x^2+5x+3x-8-8

P(x) = 2x^2+8x - 16

Hence the company's profit for the fiscal year is 2x^2+8x - 16

Answer:

48

Step-by-step explanation:

The nth term of an AP is expressed as;

Tn = a+(n-1)d

Id 12th term is 32, hence;

T12 = a+11d

32 = a+11d ...1

If the 5th term is 18, then;

T5 = a+4d

18 = a + 4d ....2

Subtract 1 from 2;

32 - 18 = 11d - 4d

14 = 7d

d = 14/7

d = 2

From 1; 32 = a+11d

32 = a+ 11(2)

32 = a + 22

a = 32-22

a = 10

Get the 20th term

T20 = a+19d

T20 = 10 + 19(2)

T20 = 10 + 38

T20 = 48

Hence the 20th term is 48

Answer:

xr 30 degrees

Step-by-step explanation:

the angles always add up to 180 sooo

53+97=150

180-150=30

there's how u solve these kinds of problems

hope this helps

Answer:

I'm not that good at math sorry for waiting your time:)

Answer:

hi dear friend the answer is 6.245. hope that helps it has been a pleasure to help you can always look out for me if you have a math problem.

Answer:

the first one.

Step-by-step explanation:

Answer: -7

Because if y is -7 then the equation would be 4 - 7 = -3 which is true :)

Answer:

The difference after 5 years is 772.57

Answer:

[tex]15c - 1[/tex]

Step-by-step explanation:

[tex]3(5c + 3) - 10[/tex]

Apply the distributive property.

[tex]3(5c) + 3 \times 3 - 10[/tex]

Multiply 5 by 3.

[tex]15c + 3 \times 3 - 10[/tex]

Multiply 3 by 3.

[tex]15c + 9 - 10[/tex]

Subtract 10 from 9.

[tex]15c - 1[/tex]