Priya creates a scatter plot showing the relationship between the number of steps she takes and her heart rate. The correlation coefficient of the line of best fit is 0.88.


1. Are they correlated? Explain your reasoning.

2. Does either of the variables cause the other to change? Explain your reasoning.

Answer:

AE - 3, EB - 2, EC - 5

Step-by-step explanation:

Use the Pythagorean theorem and you'll find that these are the answers.

I'll answer problem 19

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

Part (a)

The tickmarks on segments DE and DC indicate they are the same length. We're also told that |DC| = |DE| = 5.

So DE is also 5 cm long. Triangle DAE is a right triangle with the 90 degree angle at angle A. Let x be the length of segment AE.

We'll use the pythagorean theorem to find x

a^2 + b^2 = c^2

(AE)^2 + (AD)^2 = (DE)^2

x^2 + 4^2 = 5^2

x^2 + 16 = 25

x^2 = 25-16

x^2 = 9

x = sqrt(9)

x = 3

Segment AE is 3 cm long

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

Part (b)

For any rectangle, the opposite sides are parallel and the same length. This means AB = DC = 5 cm.

We found earlier that AE = 3 cm, so,

AE+EB = AB

3+EB = 5

EB = 5-3

EB = 2

Segment EB is 2 cm long

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

Part (c)

We know that AD = BC = 4 cm, because the opposite sides are the same length.

Earlier in part (b), we found that segment EB was 2 cm long.

Triangle EBC is a right triangle with legs EB = 2 and BC = 4. Let's apply the pythagorean theorem to find EC. Let y = EC.

a^2 + b^2 = c^2

(EB)^2 + (BC)^2 = (EC)^2

2^2 + 4^2 = y^2

4 + 16 = y^2

20 = y^2

y^2 = 20

y = sqrt(20)

y = sqrt(4*5)

y = sqrt(4)*sqrt(5)

y = 2*sqrt(5)

y = 4.4721359

As an exact value, EC is sqrt(20) or 2*sqrt(5) cm long.

As an approximate value, EC is roughly 4.4721359 cm long.

I would ask your teacher if you should use the exact or approximate value.

Answer:

8/12, 6/19 and 9/10!

Step-by-step explanation:

All of them cannot be simplified.

but the rest can like  

4/26 can be simplified by 2

and 10.22 can be simplified by 2

Answer:

[tex]m^{4}n^{5}[/tex]

Step-by-step explanation: ( I'm a student, I'm not really good at explaining maths )

When dividing variables with exponents, you subtract the exponents that has the same variables, like this:

[tex]m^{16-12}n^{10-5}[/tex]

Simplifying this becomes:

[tex]m^{4}n^{5}[/tex]

Answer:

A

Step-by-step explanation:

Answer:

The employees will work for 1 hour, will earn $5 per hour and will be paid $5

Step-by-step explanation:

System of Equations

The number of hours the employees work is x.

And the hourly wage that they are paid is y. The store manager is willing to pay the employees a wage given by the equation

10y-30x=20

The business owner states that the employees should be paid a wage given by the equation

6y+30x=60

Adding both equations we have:

16y = 80

Dividing by 16:

y = 80/16 = 5

Substituting into the first equation:

10*5-30x=20

Operating and simplifying:

50-30x=20

50 - 20 = 30x

30x = 30

x = 30/30 = 1

Thus, the employees will work for 1 hour, will earn $5 per hour and will be paid $5

Answer:

0     7

1     7.20

2    7.40

3    7.60

Step-by-step explanation:

Answer:

$65.02

Step-by-step explanation:

15% of 85 = 12.75

sale price = 85-12.75 = 72.25

10% of 72.25 = 7.225 = 7.23

final cost = 72.25 - 7.23 = 65.02

Answer: 4 gallons.

Step-by-step explanation:

With this equation, we can use the ratio 1/2 : 1/8. For every 1/2 gallon of paint, 1/8 of a wall is painted.

If 1/2 gallons covers 1/8 of a wall, then we need 8 of the 1/2 gallons to cover the whole wall. We canrepresent this by multiplying 8 and 1/2.

8 x 1/2 = 4.

Because of this, 4 gallons of paint are needed to cover he entire wall.

(Quick note: I don't know why, but the answer choices seem kind of weird. But the answer is 4 :])

A) 3/4 ÷ 5 1/5.

Answer:

[tex] \frac{15}{104} [/tex]

B) 3/7 ÷ 2 1/2.

Answer:

[tex] \frac{6}{35} [/tex]

C) 5/8 ÷ 6 5/6.

Answer:

[tex] \frac{15}{164} [/tex]

D) 8 3/10 ÷ 5/8.

Answer:

[tex]13 \frac{7}{25} [/tex]

Answer:

I have no idea. Is this a real question? If it, I'll answer it to the best of my ability. :)

Step-by-step explanation:

Answer:

y = -2x - 4

Step-by-step explanation:

We transform the line equation of L:

2x + y = 3 --(-2x)--> f(x) = y = -2x + 3

We now know that L intersects the y-axis at 3 and it has a slope of -2.

In order to construct a parallel line M, it needs to have an identical slope to L.

All we need to do now is to move one step from the given point (1,-6) towards 0 with the predetermined slope of -2, resulting in the point (0,-4).

Since we know slope and intersection with the y-axis (0,-4), we can construct the line equation:

f(x) = y = -2x - 4 for line M.

Answer: 108°

Step-by-step explanation:

Answer:

Remember that the total amount of degrees in a pentagon is: 540, and there are 5 sides, so divide 5 by 540:

540/5 = 108

108 is your answer.

Answer:

Step-by-step explanation:

x=2

Answer:

B. s = 32t

Step-by-step explanation:

The equation would be in the form of s = mt.

Where, m = rate of change

Find rate of change using any two values given in the table, say (1, 32) and (2, 64)

Rate of change (m) = ∆s/∆m = (64 - 32)/(2 - 1) = 32/1 = 32

✔️To write the equation, substite m = 32 into s = mt

s = 32t

Answer:

4x+4y

Step-by-step explanation:

You can write an equivalent expression by simply simplifying the expression. In order to simplify this expression, distribute the numbers.

You'll get:

(2*2x)+(2*2y) = 4x + 4y

4x + 4y is an equivalent expression.

Answer:

Step-by-step explanation:

Use the formula,

distance = √[(x1-x2)^2 + (y1-y2)^2]

Answer:

v = 1

Step-by-step explanation:

volume of a cube = side cubed

1 cubed = 1

Answer:

answer is 1 cubic unit

hope this helps

Answer:

Step-by-step explanation:

Ok

Answer:

what

Step-by-step explanation:

:(

Answer:

I think your problem didn't copy correctly because you didn't provide a function. if you could provide it to me I would be glad to help and give you the answer.

I also do exams and quizzes if your interested

Answer:

12

Step-by-step explanation:

Answer:

(x-114.5), (x-14.05)

Step-by-step explanation:

Answer attached

Answer:

x² + 9x + 14 can be factored as (x+2)(x+7)

Step-by-step explanation:

The general form is ax² + bx + c. If a=1, then you can start looking for two numbers that multiplied give c and added give b.

14 = 2*7

and

9 = 2+7

hence the easy factorization

(x+2)(x+7)

Keep in mind that it only works if a=1.

Answer:

( + 2 ) (x+7 )

Step-by-step explanation:

Use the sum-product pattern   2 + 9 + 1 4 2 + 7 + 2 + 1 4 2

Common factor from the two pairs   2 + 7 + 2 + 1 4 ( + 7 ) + 2 ( + 7 ) 3

Rewrite in factored form   ( + 7 ) + 2 ( + 7 ) ( + 2 ) ( + 7 )

Answer:

Linear polynomial.

Step-by-step explanation:

A linear polynomial is written with a degree 1. An example of a linear polynomials includes 3x + 5. This is what 5b - 1 is.

Hope it helps!

Answer: y = 2 and x = 2

Step-by-step explanation:

[tex]9x^2+4(y-2)^2=36\\x^2=2y[/tex]

First, get the entire thing in terms of y, because you cant solve for two variables at the same time. They gave us the fact that x^2 = 2y

[tex]9(2y)+4(y-2)^2=36\\18y+4(y^2-4y+4)=36\\18y+4y^2-16y+16=36\\4y^2+2y-20=0[/tex]

What two numbers multiply to equal -80 but add to equal 2? That is +10 and -8.

[tex]4y^2+2y-20=0\\(4y^2-8y)+(10y-20)=0\\4y(y-2)+10(y-2=0)\\(4y+10)(y-2)=0\\y=-5/2\\y=2[/tex]

Now solve for x by plugging in y to the easier equation

[tex]x^2=2(-5/2)\\x\neq \sqrt{-5}[/tex]

If I didn't make a mistake, this should be the only answer. In the case of y = -5/2, you would get an imaginary x-value. Therefore y cannot equal -5/2

[tex]x^2=2(2)\\x=2[/tex]

The solution of the expression are,

x = 2.28 , y = 2.62

Or, x = 3.9i , y = - 7.62

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equations are,

9x² + 4 (y - 2)² = 36  .. (i)

x² = 2y  .. (ii)

Substitute the value of x² from (ii) in (i);

9x² + 4 (y - 2)² = 36

9 × 2y + 4 (y - 2)² = 36

18y + 4 (y - 2)² = 36

9y + 2 (y - 2)² = 18

9y + 2 (y² + 4 - 2y) = 18

9y + 2y² + 8 - 4y = 18

2y² + 5y + 8 - 18 = 0

2y² + 5y - 10 = 0

y = - 5 ± √5² - 4×2×- 10 / 2×2

y = - 5 ± √ 25 + 80 / 2

y = - 5 ± √ 105 / 2

y = - 5 ± 10.24 / 2

y = - 5 + 10.24 / 2

y = 5.24/2

y = 2.62

y = - 5 - 10.24 / 2

y = - 15.24 / 2

y = - 7.62

From (ii);

x² = 2y

x² = 2 × 2.62

x² = 5.24

x = 2.28

x² = 2y

x² = 2 × - 7.62

x² = - 15.24

x = 3.9i

Thus, The solution of the expression are,

x = 2.28 , y = 2.62

Or, x = 3.9i , y = - 7.62

Learn more about the mathematical expression visit:

brainly.com/question/1859113

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M < 7 / 12

(1) < 7 / 12

(1) < 0.583333333 (false statement)

(-1) < 7 / 12

(-1) < 0.583333333 (true statement)

(-9) < 7 / 12

(-9) < 0.583333333 (true statement)

(-5) < 7 / 12

(-5) < 0.583333333 (true statement)

B C D maybe?

First Answer:

x = 12

First Step-by-step explanation:

12 + x = -3(4 - x)

12 + x = -12 + 3x

- x - x

—————————

12 = -12 + 2x

+ 12 + 12

—————————

24 = 2x

24/2 = 2x/2

12 = x

Second Answer:

No solution

Second Step-by-step explanation:

2(x - 1/2) = 8 + 2x

2x - 1 = 8 + 2x

+1 +1

—————————

2x = 9 + 2x

- 2x - 2x

—————————

0 = 9

^^ No solution

Answer:

Base = 3√5

Step-by-step explanation:

Given:

Hypotenuse = 9

Perpendicular = 6

Find:

Base(x)

Computation:

Using Pythagorean theorem

Base = √Hypotenuse² - Perpendicular²

Base = √9² - 6²

Base = √81 - 36

Base = √45

Base = 3√5