11. The height of a plant over 4 weeks is shown in the graph below.
Height of Plant (cm)
16
23
Week
What is the rate of growth of the plant, in centimeters per week?
A 2
B. 3
C. 8
D. 12

Student A rewrote the expression correctly. When the factor is multiplied by the quotient, it yields the dividend.

Student B did not rewrite the expression correctly. When the factor is multiplied by the quotient, it does not yield the dividend.

Student C rewrote the expression correctly. When the factor is multiplied by the quotient, it yields the dividend.

The expression when it is rewritten is 4x²(9x + 4x³)

The factor of a number is a number that perfectly divides a number. A common factor is a factor that two or more numbers share. An example of a common factor of 10 and 20 is 10.

In order to determine if the students rewrote the expressions correctly, use the distributive property to determine if it would yield the initial expression. If it does, the students are correct.

Student A = 4x³(9 + 4x²) = 36x³ + 16\(x^{5}\)

Student B = 3x²(12x + 2x³) = 36x³ + 6\(x^{5}\)

Student C = 2x(18x² + 8\(x^{4}\)) = 36x³ + 16\(x^{5}\)

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The final solution is -sin(1).

To evaluate the iterated integral, we need to integrate with respect to the outer variable first, then integrate with respect to the inner variable.

The given iterated integral is:

\(∫(1 to 0) ∫(s^4 to 0) cos(s^5) dt ds\)

To evaluate this, we need to integrate with respect to t first, and then integrate with respect to s.

\(∫(1 to 0) ∫(s^4 to 0) cos(s^5) dt ds = ∫(1 to 0) [∫(s^4 to 0) cos(s^5) dt] ds= ∫(1 to 0) (-1/s^5 * sin(s^5)) \\ds= [-1/s^5 * sin(s^5)] \\evaluated at s = 1,0= (-1/1^5 * sin(1^5)) - (-1/0^5 * sin(0^5))= (-1/1 * sin(1)) - (0)= -sin(1)\)

So the final solution is -sin(1)

Note that the integral is not defined for s=0, \(s^5=0\) , as the function is not defined there.

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The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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From Mark studies of a parallelogram and discovering that the slope of the diagonals are 5/3 and -3/5 the conjecture that can be made is

The diagonals are perpendicular to each other

The two different lines that cross each other at a 90° angle are called perpendicular lines.

If two lines intersect at a 90 degree angle, we say that the two lines are perpendicular.

Perpendicular lines have a feature which relates with the slope of the line as being a negative reciprocal

In the context of the given problem,

diagonal 1 has slope 5/3, the negative reciprocal is -3/5.

Since the two diagonals posses this relationship they are said to be parallel

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Answer:

The length of cell A is 50 times of the length of cell B

Step-by-step explanation:

Given that,

The length of cell A, \(l_A=5\times 10^{-3}\ cm\)

The length of cell B, \(l_B=1\times 10^{-4}\ cm\)

Taking the ratio of length of cell A to the length of cell B.

\(\dfrac{l_A}{l_B}=\dfrac{5\times 10^{-3}}{10^{-4}}\\\\\dfrac{l_A}{l_B}=50\\\\l_A=50\times l_B\)

It means, the length of cell A is 50 times of the length of cell B. Hence, the correct option is (d).

The required mass of the solid is 8.52g. Hence option B is correct.

We have,
mb = mass/89.0, ΔTb = 2.42° C and Kb = 2.53°C•kg/mol.

Mass of the object is defined as the space occupied by an object.

Given equation, ΔTb=Kb x mb
2.42 = 2.53 x mb
mb =0.95
mass / 89.0 x 0.1 = 0.95
mass = 8.52 g

Thus, the required mass of the solid is 8.52g.

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The number of kilograms of the weight of the boy will be 21.32 kg.

Conversion means to convert the same thing into different units.

A boy weighs 47 pounds.

Then the number of kilograms of the weight of boy will be

We know the conversion

1 pound = 0.45359237 kg

Then we have

47 pound = 47 x 0.45359237 kg

47 pound = 21.31884139 kg

47 pound = 21.32 kg

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An expression for x in terms of a and b is y = b - 2x and an expression for y in terms of a and b is y = 2a - b.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A system of equations x + y = a and 2x + y = b.

Now,

x + y = a.

x = a - y and y = a - x.

2x + y = b.

2x = b - y.

x = (b - y)/2.

y = b - 2x.

An expression for x in terms of a and b is,

x + y = a

x + b - 2x = a.

- x = a - b.

x = b - a.

An expression for y in terms of a and b is,

2(a - y) + y = b.

2a - 2y + y = b.

2a - y = b.

- y = b - 2a.

y = 2a - b.

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\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.4\% of 16.83}}{\left( \cfrac{8.4}{100} \right)16.83} ~~ \approx ~~ 1.41~\hfill \underset{ Total~for~lunch }{\stackrel{ 16.83~~ + ~~1.41 }{\approx\text{\LARGE 18.24}}}\)

Answer:

Step-by-step explanation: 1,872

Answer: 1,872

Step-by-step explanation:

Answer:

187

Step-by-step explanation:

1870/210=187

Also / means divide

Answer:

(x-2)²+(y-3)²=5².

Step-by-step explanation:

1. the equation of line through points (5;7) and (2;-2) is:

\(\frac{x-5}{3} =\frac{y-7}{9}; \ => \ 3x-y-8=0.\)

2. to find the equation of the line, which is perpendicular to the line 3x-y-8=0:

the vector (3;-1) is perpendicular to the line 3x-y-8=0 and it is the vector-pointer for the requred line, and if |n₁|*|n₂|=0 (where n₁ is normal vector to the line 3x-y-8=0 and n₂ is normal vector to the required line), then 3*x-1*y=0 (where 'x' and 'y' any numbers). x=1; y=3, then n₂(1;3), then the required line is x+3y+C=0, where C - is unknown number.

3. to find the equation of the line, which is perpendicular to the line 3x-y-8=0 and passes through the middle point of (5;7) and (2;-2):

middle point is (7/2;5/2), then after substitution of coordinates of the middle point into the equation x+3y+C=0 it will be 3.5+3*2.5+C=0, ⇒ C= -11.

the required equation is x+3y-11=0

4. to calculate the intersection point of x+3y-11=0 and 2x-y=1:

\(\left \{ {{2x-y=1} \atop {x+3y=11}} \right. \ => \ (2;3)\)

the point (2;3) is the centre of the required circle.

5. to calculate the radius² of the required circle:

r²=(5-2)²+(7-3)² or r²=(2-2)²+(2+3)², then r²=5².

6. if the centre of the required circle is (2;3) and its r²=25, then it is possible to make up the equiation of the circle:

(x-2)²+(y-3)²=5².

Answer:

one or three I'm not sure

A scatter plot visually represents the relationship between two variables. It shows a positive correlation between the number of books read per month and SAT Verbal Test scores, with the equation y = 6.4828x + 520.6962.

A scatter plot is a graphical representation of a set of data that allows the observer to observe the relationship between two variables. It is used to graphically display how one variable is affected by the other. It is a chart of data points plotted on a two-dimensional graph with one variable represented on the X-axis and the other variable on the Y-axis.

Scatter Plot of the Data: From the data provided by the Language Arts department, we can create the scatter plot as shown below:
Equation of the line of best fit: The line of best fit is a straight line that is used to model the relationship between the two variables. It is determined by minimizing the sum of the squares of the differences between the observed values and the predicted values.

From the scatter plot, we can see that there is a positive correlation between the number of books read per month and the score on the SAT Verbal Test. This suggests that the more books a student reads per month, the higher their score on the SAT Verbal Test.

The equation of the line of best fit for the given data set is y = 6.4828x + 520.6962. Here, y represents the score on the SAT Verbal Test and x represents the number of books read per month.

To find the equation of the line of best fit, we can use a regression analysis tool such as Excel. The regression analysis will give us the values of the slope and intercept of the line of best fit, which we can use to write the equation of the line.

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Answer:

a) \(10[1-e^{-y/3} ] ^{2} e^{-y}\)

b)    ≈ 0.76

Step-by-step explanation:

Given that : Y1 < Y2 < Y3 < Y4 < Y5   are the order statistics of five independent observations

mean of θ  = 3

a) Determine the P.d.f of the sample median

P.d.f of sample median ( y3 ) = \(10[1-e^{-y/3} ] ^{2} e^{-y}\)    

attached below is the detailed solution

b) determine the probability that Y4 is < 5

p( Y4 < 5 ) = G4( 5 )

                 = 0.7599 ≈ 0.76

attached below is the detailed solutions

Answer:

i) Given

ii) Definition of angle bisector

iii) angle addition

iv) Substitution

v) Combine like terms

Mark me brainliest pls

Answer:

1) Given

2) Definition of Angle Bisector

3) Angle Addition

4) Substitution

5) Combine Like Terms

Step-by-step explanation: Hope this helps!

⊥T

Hope this is what you're looking for! (✿◠‿◠)

Answer:

You'll see this character in the list over on Wikipedia, and you'll notice that there's a code next to it, in this case 0287 is the Unicode character code for the upside-down T

Step-by-step explanation:

please mark me brainliest

Answer:

y = 1/3x + 13/3

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Step 1: Find slope m

\(m=\frac{4-6}{-1-5}\)

\(m=\frac{-2}{-6}\)

\(m=\frac{1}{3}\)

y = 1/3x + b

Step 2: Find y-intercept b

4 = 1/3(-1) + b

4 = -1/3 + b

b = 13/3

Step 3: Write linear equation

y = 1/3x + 13/3

Answer:

y = (1/3)x + 13/3

Step-by-step explanation:

1. Find the slope (m)

slope = change in y divided by change in x

m= \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{6-4}{5-(-1)} = \frac{2}{5+1} = \frac{2}{6} = \frac{1}{3}\)

2. Subsitute 1/3 for m and pick one point to plug into y =mx+b

Ex: (5, 6) -> y= 6 x = 5

6 = 1/3(5) + b

3. Simplify: 6 = 1/3(5) + b

6 = 5/3 + b

4. Solve for b (isolating the variable) by adding 1/3 to both sides

6 - 5/3 = 5/3 - 5/3  + b

5. Simplify: 6 - 5/3 = 5/3 - 5/3  + b

18/3 - 5/3 = b -> 13/3 = b

5. plug in 13/3 for b and 1/3 for m in y = mx + b

y = mx + b -> y = (1/3)x + 13/3

Answer:

2x+6y=2

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:

Find the slope of the provided line.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.

Substituting the values, the equation of the perpendicular line becomes:

y - 5 = (-1/m)(x - 2)

Simplifying the equation further, we can rewrite it in point-slope form:

y - 5 = (-1/m)x + (2/m)

Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

We can see that Natalie is reducing the amount she owes by $18 every two weeks.

Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.

This means that after n weeks, the amount she still owes is:

$180 - $18n

Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:

$180 - P

After two weeks, she will owe:

($180 - P) - P = $180 - 2P

After four weeks, she will owe:

($180 - 2P) - P - P = $180 - 4P

After six weeks, she will owe:

($180 - 4P) - P - P = $180 - 6P

And after eight weeks, she will owe:

($180 - 6P) - P - P = $180 - 8P

We can set up an equation using the information we have:

$180 - 8P = $108

Solving for P, we get:

P = $9

Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

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The complete question:

Natalie borrowed money from her parents to pay for a trip. ​Natalie will ​pay her parents in equal amounts every week until she pays back the ​entire amount she borrowed. ​ ​The table below shows the amount of ​money Natalie still owes her parents at the end of every two weeks for ​the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?

Week 0 = $180

Week 2 = $162

Weeks 4 = $144

Week 6 = $126

Week 8 = $108

Answer:

An unconditioned stimulus is a stimulus that leads to an automatic response.

Answer:

Step-by-step explanation:

First off, you need to add up AB and BC. You would get the equation:

2(3x-4)=62, since there are two segments. Solve it/simplfy.

6x-8=62 => 6x=70 => x= 11.66666(forever)

Since you alreday solved one, you easily know the answer is c.

Answer:

A. is the answer did you need an explanation

Answer:

s-8

Step-by-step explanation:

ezyyyy

Answer:

convert the lengths to meters

10dm=1m

1dm=0.1m

hence, firs ribbon

2m+0.1m=2.1m

Second Ribbon

3m and 9dm

convert 9dm into Metres we get 0.9m

hence, 3m+0.9m=3.9m

Third Ribbon

6m+0.4m=6.4m