A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table shows the data:


Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31


Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)

Part B: Write a function that best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)

Answers

Answer 1

Answer:

Hello,

Step-by-step explanation:

Part A:

Yes

Since

y=f(x)

f(0)=4

f(1)=7 : f(1)=f(0)+1*3

f(2)=10= 7+3 : f(2)=f(1)+3 =f(0)+2*3

f(3)=13=10+3: f(3)=f(2)+3=f(0)+3*3

...

f(9)=31=28+3=f(8)+3=f(0)+9*3

f(n)=f(0)+n*3=4+n*3

Part B: y=3x+4

Part C: slope=3 , y-intercept=4

The slope indicate the grow of the plant (how many cm does it grow in function of the height it receives)

y-intercept indicate the original height of the plant.


Related Questions

When a shape is dilated, the _________ of the lengths in the image to the corresponding lengths in the pre-image are equal to the scale factor.

A. ratios
B. lengths
C. scale factors
D. proportions

Answers

when a shape is dilated the RATIOS of the lengths in the image to the corresponding lengths in the preimage are equal to the scale factor

Geometry, please answer question ASAP

Answers

Magnitude of angle D = 170
Because,
Sum of interior angles of a pentagon = 540 degree
That is,
Angle A + angle B + angle C + angle D + angle E = 540 degree
87degree + 125 degree + 63 degree + 95 degree + angle D = 540 degree

So that gives angle D = 170 degree

Hope this helps.
ArmyCee:)

Answer:

m<D = 170°

Step-by-step explanation:

In a pentagon, the angles add up to 540°. This means the sum of <A, <B, <C, <D, and <E add up to that, and we can write an equation:

m<A + m<B + m<C + m<D + m<E = 540°

We are already given the measures of all the angles except D, so we can substitute them in:

87° + 125° + 63° + m<D + 95° = 540°

Now, we can simplify and solve for <D:

m<D + 370° = 540°

m<D = 170°

An executive for a large company is considering a change to health insurance plans offered to the employees. To
assess employee satisfaction with the current plan, the executive sends an email to all company employees asking
their opinion of the current plan. A summary of the results received shows that 27% of company employees are
"highly satisfied" with the current health insurance plan. Which statement about the results is most likely to be true?

Answers

Answer:

not D

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Look at this rectangular prism:

Answers

Answer:

3 : 1

Step-by-step explanation:

volume = length * width * height

The volume of the solid as it is shown is:

volume = 10 m * 6 m * 10 m = 600 m^3

old volume = 600 m^3

Now we triple the length.

The length becomes 3 * 10 m = 30 m

The new volume is:

volume = length * width * height

volume = 30 m * 6 m * 10 m = 1800 m^3

new volume = 1800 m^3

ratio of new volume to old volume = 1800 m^3 : 600 m^3

Divide both sides of the ratio by 600 m^3.

Ratio = 3 : 1

Answer:     3 : 1

An electricity post is supported by a 12 m long strut(wire). If the strut makes an angle of 53° with the ground level, how far from the post is the strut attached to the ground?

Answers

Step-by-step explanation:

I do hope that you understand through the steps in the attachment, if not kindly reach out!

Plz help similarity theorems

Answers

Answer:

b is the answer bro and try first then ask questions

Find all complex numbers z such that z^4 = -4.

Note: All solutions should be expressed in the form a+bi, where a and b are real numbers.

Answers

26 and yeah just need points ignore this answer so sorry

Date: Pages The recent price of a car is Rs. 10.00,000: If its price reduces by to1 yearly after how many year its price will be Rs 7, 29,000?​

Answers

Answer:

729000 year it's price will Rs 729000

Ella bought a 2 bedroom unit 12 years ago for $95 000 and recently sold it for $280 000 (after deducting selling costs).
a) Find the profit.
b) Find the profit as a percentage of the buying price.
c) Find the profit as a percentage of the selling price.
d) Which percentage profit sounds better as far as Ella is concerned?

pls explain, thanks!!!!​

Answers

C.P. = $95000

S.P. = $280000

a. Profit

= S.P. - C.P.

= $280000 - $95000

= $185000

b. Let the profit% of C.P. be x.

(x/100) × $95000 = $185000

=> x/100 = $185000/$95000

=> x/100 = 37/19

=> x = (37/19) × 100

=> x = 3700/19

=> x = 194 14/19

So, profit percent of buying price is 194 14/19%.

c. Let the profit% of S.P. be x.

(x/100) × $280000 = $185000

=> x/100 = $185000/$280000

=> x/100 = 37/56

=> x = (37/56) × 100

=> x = 3700/56

=> x = 925/14

=> x = 16 1/14

So, profit percent of selling price is 16 1/14%.

d. Buying price percentage profit sounds better as far as Ella is concerned.

If a wheel has a radius of 5cm
how much is one rotation of the wheel
How many rotations can the wheel do within a distance of 50km

Answers

Answer:

circumference = 2*PI*radius

circumference = 2 * PI * 5 cm

circumference = 31.4159265358979 cm

50 km = 500,000 centimeters

rotations = 500,000  / 31.4159 cm

15,915.51  rotations

Step-by-step explanation:

Another of Bhaskara's problems results in a quadratic equation Parthava was enraged and seized a certain number of arrows to slay Karna. He expended one-half of them in defending himself. Four times the square root of the number of arrows were discharged against the horses. With six more, he transfixed Shalya, the charioteer. With three more, he rent the parasol, the standard, and the bow; and with the last one he pierced the head of Karna. How many arrows did Parthava have?

Answers

Answer:

Parthava had 100 arrows.

Step-by-step explanation:

Let's define N as the number of arrows that Parthava originally has.

He uses one-half of them in defending himself, so he used N/2 arrows

Now he uses four times the square root of the number of arrows, so now he uses:

4*√N

Then he uses 6

Then he uses 3

Then he uses the last one.

If we add all these numbers of arrows that he used, we should get the initial number of arrows that he used, then:

N/2 + 4*√N  + 6 + 3 + 1  = N

Now we have an equation that we can try to solve.

First, let's move all the terms to the same side:

N/2 + 4*√N + 6 + 3 + 1 - N  = 0

now we can simpify it:

(N/2 - N) + 4*√N + (6 + 3 + 1) = 0

-(1/2)*N + 4*√N + 10 = 0

Now we can define a new variable x = √N

Then we have: x^2 = N

now we can replace these new variables in our equation to get:

-(1/2)*x^2 + 4*x + 10 = 0

Now we just have a quadratic equation.

Remember that for a quadratic equation of the form:

0 = a*x^2 + b*x + c

The solutions were given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2a}[/tex]

Then in our case, the solutions will be:

[tex]x = \frac{-4 \pm \sqrt{4^2 - 4*(-1/2)*10} }{2*(-1/2)} = \frac{-4 \pm 6 }{-1} = 4 \pm 6[/tex]

So there are two solutions:

x = 4 + 6 = 10

x = 4 - 6 = -2

And remember that x = √N

Then x should be positive, then we take x = 10 as our solution here.

then we can use the equation:

x = 10 = √N

then

10^2 = √N^2 = N

10^2 = 100 = N

Parthava had 100 arrows.

The first term of a sequence is 1 and every term after the first one is 1 more than the square of the preceding term. What is the fifth term?

Answers

Answer:

677

Step-by-step explanation:

the sequence is 1, 2, 5, 26, 677

the first term is 1

to find the 2nd term, do: [tex]1^{2} +1=2[/tex]

3rd: [tex]2^{2} +1=4+1=5[/tex]

4th: [tex]5^{2} +1 =25 +1=26[/tex]

5th: [tex]26^{2} +1=676+1=677[/tex]

Lorraine writes the equation shown. x²+4-15=0 She wants to describe the equation using the term relation and the term function. The equation represents a relation and a function a relation but not a function a function but not a relation neither a relation nor a function

Answers

Answer:

Neither a relation nor a function

Step-by-step explanation:

A relation in mathematics is a relationship between two or more set of values in an ordered pair, such as related x and y-values

An equation is a statement that gives declare the equality between two expressions

A function is a mapping rule that maps each element in the domain set to only one element in the range set

Therefore, the given equation in one variable, x, that asserts the equality of the expressions on the left and right hand side, is neither a relation nor a function

A pendulum is swinging next to a wall. The distance D(t)D(t)D, left parenthesis, t, right parenthesis (in \text{cm}cmstart text, c, m, end text) between the bob of the pendulum and the wall as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\sin(b\cdot t)+da⋅sin(b⋅t)+da, dot, sine, left parenthesis, b, dot, t, right parenthesis, plus, d. At t=0t=0t, equals, 0, when the pendulum is exactly in the middle of its swing, the bob is 5\text{ cm}5 cm5, start text, space, c, m, end text away from the wall. The bob reaches the closest point to the wall, which is 3\text{ cm}3 cm3, start text, space, c, m, end text from the wall, 111 second later. Find D(t)D(t)D, left parenthesis, t, right parenthesis. \textit{t}tstart text, t, end text should be in radians.

Answers

Answer:

D(t)=-2sin(pi/2 t)+5

Step-by-step explanation:

i did it on Khan academy

Answer:

-2sin(pi/2 t)+5

Step-by-step explanation:

ALso did on Khan Academy (its on the sinisoidal equations excercise)

Which of these products is negative? Select all that apply.
-8 ÷ (-3)
-2 ÷ 8
0 ÷ (-2)
15 ÷ (-5)
-8 ÷ (-9)

Answers

Answer:

Positive/negative = negative

Negative/positive = negative

So -2 ÷ 8 and 15 ÷ (-5) are going to have negative quotients.

Let me know if this helps!

Find the area of the bolded outlined sector.

Answers

Outlined sector:

2 πr x 225/360 +2r

=2x3.14x10 x 225/360 +20

=59.25 cm

Hope this helped!

Taylor wirtes a exppersion with five terms all 5 terms are like terms how many terms are in equivilent exppersions with the least numbers of terms ?

Answers

Answer:

1 term

Step-by-step explanation:

Writing an expression of 5 terms such that all 5 terms are like terms ;

Using the analogy :

x, 2x, 4x, 3x, 5x

Writing as an expression :

x + 2x + 4x - 3x + 5x

7x - x + 5x

6x + 5x

11x

The least number of terms in its equivalent expression is 1 ;

As the expression x + 2x + 4x - 3x + 5x is equivalent to 11x

Determine the quotient of .     ​

Answers

of what?? the hamburgler??

Determine the measure of the interior angle at vertex E.

A. 135
B. 45
C. 225
D. 75

Answers

Answer:

135

Step-by-step explanation:

The sum of the interior angles of a pentagon is 540

3x+3x+2x+2x+2x = 540

12x = 540

Divide by 12

12x/12 = 540/12

x = 45

E = 3x = 3*45 = 135

Answer:

135

Step-by-step explanation:

NEED HELP ASAP!!!!!!!

Answers

Letter b because you need to multiply

Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
This is a triangle. side a has a length of 6 yards. side b has a length of 10 yards. side c has a length of 14 yards. The altitude to side c has a length of X yards. what is x

Answers

Answer:

3.71 yd

Step-by-step explanation:

Heron's formula:

area = 0.25 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c))

so h = 0.5 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c)) / c

a = 6

b = 10

c = 14

a+b+c = 30

-a+b+c = 18

a-b+c = 10

a+b-c = 2

x = h = 0.5×sqrt(30×18×10×2)/14 = sqrt(30×18×10×2)/28 =

= sqrt(10800)/28 = sqrt(400×9×3)/28 =

= 20×3×sqrt(3)/28 = 60×sqrt(3)/28 = 15×sqrt(3)/7 =

= 3.711537 yd

Find the values of x and y if (-x + 5, 1) = (-y, 2x - 5y).

Answers

Answer:

x = 8, y = 3

Step-by-step explanation:

Equating corresponding x and y coordinates , then

- y = - x + 5 ( multiply through by - 1 )

y = x - 5 → (1)

2x - 5y = 1 → (2)

Substitute y = x - 5 into (2)

2x - 5(x - 5) = 1 ← distribute and simplify left side

2x - 5x + 25 = 1

- 3x + 25 = 1 ( subtract 25 from both sides )

- 3x = - 24 ( divide both sides by - 3 )

x = 8

Substitute x = 8 into (1) for corresponding value of y

y = 8 - 5 = 3

Which inequality is represented by this graph? ​

Answers

Answer:

x> 0

Step-by-step explanation:

There is an open circle at 0 so this means it is not equal to

The line goes to the right so x is greater than

x> 0

A graph shows minutes on the horizontal axis from 0 to 10 and miles from start on the vertical axis from 0 to 1.5. The blue line labeled Andy begins at 0 miles in 0 minutes and ends at 1.25 miles at 10 minutes. The red line labeled Berta begins at 0.5 in 0 minutes and ends at 1.12 miles in 10 minutes. The green line labeled Caedin begins at 1.5 miles in 0 minutes, to 0 miles in 6 minutes, and ends at 1 mile in 10 minutes. [NOTE: character count is 425; possible visual bias in graph]
Three runners run along a 1.5 mile trail one Saturday morning. The graph shows the runners’ locations starting at 9:00 a.m.

Answers

Answer:

Who is at the trail start at 9:00 a.m.? : Andy

Who runs fastest? : Caedin

When do Andy and Berta cross paths? : 9:08 am

Who is closest to the 1.5 mile mark after 6 minutes? : Berta

Step-by-step explanation:

assignment

1a.-14,____,-6,____,2,____,10
b. ____, - 2,4,____,16,____,64

2.Factor of 60=
1,2,3,4,5,6,10,x,15,20,y,z
Find the sum of the values of x, y and z

Please help me to solve these question, thank you. ​

Answers

Answer:

102

Step-by-step explanation:

x= 12

y= 30

z= 60

Hope u got it

Answer:

Hello,

a) -6

b) -39

c) 102

Step-by-step explanation:

I suppose this are sequence arithemical or geometrical

[tex]a)\\u_1=-14\\u_2=x\\u_3=-6\\u_4=y\\u_5=2\\u_6=z\\u_7=10\\\\We\ see\ that\ :\\u_3-u_1=-6-(-14)=-6+14=8\\u_5-u_3=2-(-6)=2+6=8\\u_7-u_5=10-2=8\\\\We\ may \imagine\ that\ the\ difference\ bethween\ 2\ terms\ is\ =8/2=4\\\\so\ x=-10, y=-2, z=6 \ and\ x+y+z=-10+(-2)+6=-6\\[/tex]

[tex]b)\\u_1=x\\u_2=-2\\u_3=4\\u_4=y\\u_5=16\\u_6=z\\u_7=64\\\\We\ see\ that\ :\\\\\dfrac{u_5}{u_3}=\dfrac{16}{4} =4\\\dfrac{u_8}{u_6}=\dfrac{64}{16} =4\\\dfrac{u_3}{u_2}=\dfrac{4}{-2} =-2\\\\The\ common\ factor\ is\ -2\\\\u_1=x=\dfrac{u_2}{-2} =1\\\\u_4=y=\dfrac{u_5}{-2} =-8\\\\u_6=z=\dfrac{u_7}{-2} =-32\\x+y+z=1+(-8)+(-32)=-39\\[/tex]

c)

All those numbers are divisor of 3*4*5=60

x=12, y=30, z=60

x+y+z=12+30+60=102

How many solutions does the system have?








x+y=3
5x+5y=15

Answers

x=3-y

5(3-y) + 5y=15

15y-5y+5y=15

15y=15

Y= 15/15

Y= 1


X+(1)=3

X=3-1

X=2




Final answer: x=2 and y=1

Method: simultaneous equations

convert f(x) = 5x(x – 6) to standard form

Answers

Answer:

[tex]5x^{2} - 30x[/tex]

Step-by-step explanation:

Solve 3x-4>11 if the domain of x is {1,2,3,4,5,6,7,8}

Answers

Answer:

(6,7,8)

Step-by-step explanation:

solving the inequality will give x>5

what’s the scale reading

Answers

Answer:

0.026

Step-by-step explanation:

6 out of 10 steps between 0.02 and 0.03.

.026 because the longer line in between them is .025 and the one being pointed at is the one after.

Will give brainliest to the first person

Answers

Step-by-step explanation:

Area=b×h

= (x+5)×(x+6)

=x^2+6x+5x+30

=x^2+11x+30

If u simplify u will get (x+5)(x+6) as answer.

Keep smiling and hope u are satisfied with my answer.Have a good day :)

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