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2 years ago

The growth rate of the sunflower from day 14 to day

1 answer:

7 0

Option B) h = 4.5t – 27 is the equation of the straight line that best models the height h, in centimeters, of the sunflower t days after it begins to grow.

From the above graph we can see that from day 14 to day 35 , it is a straight line.

And equation of a straight line is y = mx + c or y – y1 = m(x – x1)

Where, m =slope of the line

c = intercept

the equation can be rewritten as h – h1 = m(t – t1) (1)

So, to find the equation of line , first we will calculate the slope of the line.

To find the slope : m = (h2 – h1 ) / (t2 – t1) (2)

From the graph and the table given, the coordinates (t1 , h1 ) and ( t2 , h2 ) are (14 , 36.6) and (35, 131) respectively.

Putting these values in equation (2), we get

m = (131 – 36.6)/(35 – 14)

m = 94.4/21

m = 4.5

now to find the equation of line we put the values in equation (1), we get

h – 36.6 = 4.5(t – 14)

h – 36.6 = 4.5t – 63

h = 4.5t -63 + 36.6

h = 4.5t -27

Hence the equation of the line is , option B) h = 4.5t -27

Learn more about the straight line here : brainly.com/question/6977417

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Help, I don't remember

GenaCL600 [577]

Answer:

x = 144

Step-by-step explanation:

What you need to remember about this geometry is that all of the triangles are similar. As with any similar triangles, that means ratios of corresponding sides are proportional. Here, we can write the ratios of the long leg to the short leg and set them equal to find x.

x/60 = 60/25

Multiply by 60 to find x:

x = (60·60)/25

x = 144

_____

<em>Comment on this geometry</em>

You may have noticed that the above equation can be written in the form ...

60 = √(25x)

That is, the altitude from the hypotenuse (60) is equal to the geometric mean of the lengths into which it divides the hypotenuse (25 and x).

This same sort of "geometric mean" relation holds for other parts of this geometry, as well. The short leg of the largest triangle (the hypotenuse of the one with legs 25 and 60) is the geometric mean of the short hypotenuse segment (25) and the total hypotenuse (25+x).

And, the long leg of the large triangle (the hypotenuse of the one with legs 60 and x) is the geometric mean of the long hypotenuse segment (x) and the total hypotenuse (25+x).

While it can be a shortcut in some problems to remember these geometric mean relationships, you can always come up with what you need by simply remembering that the triangles are all similar.

3 0

3 years ago

Find the area of the parallelogram with vertices:________.

marin [14]

Answer:

97.98

Step-by-step explanation:

The area of the parallelogram PQR is the magnitude of the cross product of any two adjacent sides. Using PQ and PS as the adjacent sides;

Area of the parallelogram = |PQ×PS|

PQ = Q-P and PS = S-P

Given P(0,0,0), Q(4,-5,3), R(4,-7,1), S(8,-12,4)

PQ = (4,-5,3) - (0,0,0)

PQ = (4,-5,3)

Also, PS = S-P

PS = (8,-12,4)-(0,0,0)

PS = (8,-12,4)

Taking the cross product of both vectors i.e PQ×PS

(4,5,-3)×(8,-12,4)

PQ×PS = (20-36)i - (16-(-24))j + (-48-40)k

PQ×PS = -16i - 40j -88k

|PQ×PS| = √(-16)²+(-40)²+(-88)²

|PQ×PS| = √256+1600+7744

|PQ×PS| = √9600

|PQ×PS| ≈ 97.98

Hence the area of the parallelogram is 97.98

3 0

3 years ago

I need help with this one to / surface area :)

zzz [600]

Answer:

389.9 to 1 decimal place

If you need another explanation comment on this one

5 0

2 years ago

Read 2 more answers

The functions f(x)=√x^2+12x+36 and g(x)=x^3-12 are defined below. Which expression is equal to f(x) · g(x)? A.x^4-6x^3-12x+72 B.

Lostsunrise [7]

Answer:

C: x^4+6x^3-12x-72

Step-by-step explanation:

For the function : f(x)=√x^2+12x+36

It can be factorized to

f(x)=√(x+6)²

=x+6

f(x)*g(x)

=(x+6)(x^3-12)

Expand the brackets

=x^4-12x+6x^3-72

rearrange the numbers

x^4+6x^3-12x-72

3 0

2 years ago

These data can be approximated quite well by a N(3.4, 3.1) model. Economists become alarmed when productivity decreases. Accordi

CaHeK987 [17]

Answer:

First part

$P(X< 3.4-0.6*3.1) = P(X$

And for this case we can use the z score formula given by:

$z = \frac{x- \mu}{\sigma}$

And using this formula we got:

$P(X$

And we can use the normal standard table or excel and we got:

$P(Z$

Second part

For the other part of the question we want to find the following probability:

$P(-1.715$

And using the score we got:

$P(-1.715$

And we can find this probability with this difference:

$P(-1.65< Z< 1.210)=P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the data of a population, and for this case we know the distribution for X is given by:

$X \sim N(3.4,3.1)$

Where $\mu=3.4$ and $\sigma=3.1$

First part

And for this case we want this probability:

$P(X< 3.4-0.6*3.1) = P(X$

And for this case we can use the z score formula given by:

$z = \frac{x- \mu}{\sigma}$

And using this formula we got:

$P(X$

And we can use the normal standard table or excel and we got:

$P(Z$

Second part

For the other part of the question we want to find the following probability:

$P(-1.715$

And using the score we got:

$P(-1.715$

And we can find this probability with this difference:

$P(-1.65< Z< 1.210)=P(Z$

8 0

3 years ago