A local nursery sells a large number of ornamental trees every year. The owners have determined the cost per tree C for buying and caring for each tree before it is sold is C = 0.001n2 - 0.3n + 50. In this function, C is the cost per tree in dollars and n is the number of trees in stock.
a. How many trees will minimize the cost per tree?
b. What will the minimum cost per tree be?

Given problem represent Fundamental Counting Theorem.

Fundamental Counting Theorem states that if an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m×n.

Here Taylor has 5 baskets and there are 6 balls in each basket.

That is m = 5 and n = 6

Therefore Taylor have m×n= 5×6 =30 balls

Hence here we use Fundamental counting theorem.

To know more about Fundamental counting theorem here

https://brainly.com/question/16025130

#SPJ1

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

To know more about proportional savings, refer here:

https://brainly.com/question/29251832#

#SPJ11

Answer:

5

Step-by-step explanation: 5x5 =25$

The value of the expression (8.4 × 10^-3) × (7 × 10^-2) is 5.88 × 10^-4.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

The expression is given as:

(8.4 × 10^-3) × (7 × 10^-2)

= 0.0084 × 0.07

= 0.000588

= 5.88 × 10^-4

The value of the expression is 5.88 × 10^-4.

Learn more about exponents on

brainly.com/question/13669161

#SPJ1

Answer:

y = (-1/2)x + 1

Step-by-step explanation:

y = mx + b  

Where m = slope and b is the y intercept

Let's find the slope = change in y/change in x

m = (4-2)/(-6+2) = 2/-4 = -1/2

Now we have:

y = (-1/2)x + b

Now substitute point (-6,4)

4 = (-1/2)(-6) + b

4 = 3 + b

b = 1

So y = (-1/2)x + 1 is the equation.

Answer:

25

Step-by-step explanation:

The probability of the coins penny and nickel both should show heads when four coins flip simultaneously is equal to 1/4.

As given in the question,

Number of coins flip simultaneously = 4

Possible outcomes on flipping a outcome = { head , tail}

Total outcomes = 2

Probability of getting a head for each coin = 1 /2

Probability of getting heads on both the coins penny and nickel

= ( 1 / 2 ) × ( 1 / 2 )

= ( 1 / 4 )

Therefore, the probability of getting heads on both the coins penny and nickel is equal to 1 / 4.

Learn more about probability here

brainly.com/question/11234923

#SPJ4

Answer:

I am not too sure but i think 6+5=11

Step-by-step explanation:

where 6 comes first then 11 comes second and that equals 11

Answer:

\( \sqrt{48} \times \sqrt{3} \\ \sqrt{144} \\ 12\)

We need to use the concept of proprotionality for the given question.The value of y is 25.7, value of R is 1 and value of t is 144.

It is given that y varies directly as the square root of x which means that y is directly proportional to x, we can write it as

y∝\(\sqrt{x}\) which can again be written as y=\(\sqrt{x} k\) where k is a proportionality constant,we need to find the value of k inorder to find the value of y.We know that y=12 when x=49

12=\(\sqrt{49} k\)=7k⇒12=7k⇒k=\(\frac{12}{7}\)

when x=225 then y=\(\sqrt{225}\)×\(\frac{12}{7}\)=15×\(\frac{12}{7}\)=25.7

R is inversely proportional to the cube of S,we can write it as

R∝\(\frac{1}{S^{3} }\) ⇒R=\(\frac{k}{S^{3} }\)

We need to find the value of k inorder to find the value of R, it is given that R=8 when S=3

8=\(\frac{k}{27}\)

k=27x8=216

Value of R when S=6 will be

R=\(\frac{216}{6^{3} } =\frac{216}{216} =1\)

It is given that n varies directly as the square root of t and inversely as l,we can write it as

n∝\(\frac{\sqrt{t} }{l}\) which can be again written as n=\(\frac{\sqrt{t} }{l} k\) where k is a proportionality constant,we need to find the value of k first to find the value of t

We know that n=5 when t=16 and l=2

5=\(\frac{\sqrt{16} }{2}k=\frac{4}{2} k=2k\)

k=\(\frac{5}{2}\)

We know that n=10,l=3 and k=\(\frac{5}{2}\) substituting these values we can get the value of t

t=\((\frac{nl}{k} )^{2}\)=\((\frac{10.3.2}{5} )^{2} =12^{2} =144\)

Thus we can see that using the concept of proportionality we found out the values of y,R and t. Value of y is 25.7, R is 1 and t is 144.

Learn more about proportionality from here:

https://brainly.com/question/14083977

#SPJ9

Answer:

$180.00

Step-by-step explanation:

The painting is rectangular and it measures 1 meter by 2 meters. The frame shop charges $30.00 per meter for a wooden frame.

To find the cost, we need to find the perimeter of the painting and then multiply it by the cost of a wooden frame per meter.

The perimeter of a rectangle is:

P = 2(L + B)

P = 2(1 + 2) = 2 * 3 = 6 m

The cost of the frame is therefore:

6 * 30 = $180.00

Answer:

3/13 which is 0.23 as a decimal

Step-by-step explanation:

The correct answer is a. Z-score for $60 = 0b. Z-score for $75 ≈ 1.25

c. Z-score for $58 ≈ -0.17

To find the z-scores associated with the given bills, we can use the formula: z = (x - μ) / σ

where x is the bill amount, μ is the mean, and σ is the standard deviation.

a. For a bill of $60:

z = (60 - 60) / 12 = 0 / 12 = 0

b. For a bill of $75:

z = (75 - 60) / 12 ≈ 1.25

c. For a bill of $58:

z = (58 - 60) / 12 ≈ -0.17

So, the z-scores associated with the bills are approximately:

a. 0

b. 1.25

c. -0.17

Learn more about statistics here:

https://brainly.com/question/30915447

#SPJ11

Answer:

Part A: the parabola opens upwards

Part B: \(x=\frac{3}{2}\)

Part C: The vertex point is \((\frac{3}{2},-\frac{1}{2})\)

Part D: \(y=4\)

Part E: \(x_{1}=1\) and \(x_{2}=2\)

Step-by-step explanation:

We have the function:

\(f(x)=2x^{2}-6x+4\)

Where the coefficients are:

a = 2

b = -6

c = 4

Part A:

Here we can see that the leading coefficient of our parabola (a = 2) is positive, so by the definition, the parabola opens upwards.    

Part B:

The axis of the symmetry equation is given by:

\(x=\frac{-b}{2a}\)

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

\(x=\frac{6}{4}\)

\(x=\frac{3}{2}\)

Part C:

The vertex is the minimum point of our parabola.

Using the x value founded in Part B we can find f(x)=y.

\(y=2(3/2)^{2}-6(3/2)+4\)

\(y=2(9/4)-6(3/2)+4\)

\(y=(9/2)-3(3)+4\)

\(y=(9/2)-9+4\)

\(y=-\frac{1}{2}\)

Therefore, the vertex point is \((\frac{3}{2},-\frac{1}{2})\)

Part D:

To get the y-intercept we just need to do x = 0.

\(y=2(0)^{2}-6(0)+4\)

\(y=4\)

The y-intercept is (0,4)

Part E:

To get the x-intercept we just need to do y = 0.

\(0=2x^{2}-6x+4\)

\(2(x-2)(x-1)=0\)

\(x_{1}=1\)

\(x_{2}=2\)

The x-intercept is (1,0) and (2,0)

I hope it helps you!

Answer:

2x/y ??

Step-by-step explanation:

Answer: If the sign missing is supposed to be a plus sign, then the answer is 12x+24y

Step-by-step explanation:

Answer:

931 Days

Step-by-step explanation:

Answer:

931 days pls brainliest

Step-by-step explanation:

Answer:

Line D is the answer because the y-intercept is negative because it starts at -2 and the slope is one half because well its kinda obvious! May I have brainliest? Hope this helps:)

Step-by-step explanation:

Answer:

Line D

Step-by-step explanation:

has negative y intercept and has slope of 1/2

If x is the point reached by F after t seconds, and y is the point reached by S after t seconds, then x = 3t, y = 2t. 30 seconds after leaving point 0, 30 units far apart are F and S. At 100 seconds, F and S will be 100 units apart.

The speed of F reached 12 units in 4 seconds or 3 units per second.

 x = 3t

The speed of S reached 8 units in 4 seconds or 2 units per second.

 y = 2t

x - y = 3t -2t = t

After 30 seconds, the bugs will be apart by (x -y) = 30 units

x - y = 100 = t

After 100 seconds, The bugs will be 100 units apart.

To know more about speed, here

https://brainly.com/question/312131

#SPJ4

Answer:

LN ≈ 14.2

Step-by-step explanation:

Given that the triangles are similar then corresponding sides are in proportion, that is

\(\frac{LN}{IK}\) = \(\frac{MN}{JK}\) , substitute values

\(\frac{LN}{41}\) = \(\frac{9}{26}\) ( cross- multiply )

26 LN = 9 × 41 = 369 ( divide both sides by 26 )

LN = \(\frac{369}{26}\) ≈ 14.2 ( to the nearest tenth )

The solution to the given differential equation d²y/dt² + 40(dy/dt) = 0 exhibits subcritical damping.

The given differential equation is d²y/dt² + 40(dy/dt) = 0, which represents a second-order linear homogeneous differential equation with a damping term.

To analyze the type of damping, we consider the characteristic equation associated with the differential equation, which is obtained by assuming a solution of the form y(t) = e^(rt) and substituting it into the equation. In this case, the characteristic equation is r² + 40r = 0.

Simplifying the equation and factoring out an r, we have r(r + 40) = 0. The solutions to this equation are r = 0 and r = -40.

The discriminant of the characteristic equation is Δ = (40)^2 - 4(1)(0) = 1600.

Since the discriminant is positive (Δ > 0), the damping is classified as subcritical damping. Subcritical damping occurs when the damping coefficient is less than the critical damping coefficient, resulting in oscillatory behavior that gradually diminishes over time.

Therefore, the solution to the given differential equation exhibits subcritical damping.

Learn more about discriminant here:

https://brainly.com/question/27922708

#SPJ11

Answer:

y = 10x - 6

Step-by-step explanation:

If we know the function is linear then we can use any two coordinate pairs to find the slope of the line.

Note that the first pair is (0, -6) and the last pair is (4, 34).  The 'run' is from x = 0 to x = 4, a 'run' of 4.  The 'rise' is from -6 to34, a 'rise' of 40.  Thus, the slope of this line is m = rise / run = 40/4 = 10.

Again using the coordinate pair (0, -6), along with the slope-intercept form of the equation of a straight line, we get:

-6 = 10(0) + b, so we know that b = - 6 and that the equation of this line must therefore be:

y = 10x - 6

The required slope-intercept form of the function is y = 10x - 6.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
m = (y₂ - y₁) /  (x₂ - x₁)
Substitute 2 pairs from the table in the above equation,
m = (4 + 6)/(1-0)
m = 10
Now put the slope and one pair in the slope-intercept form of the equation

y - y₁ = m (x - x₁)
y + 6 = 10(x - 0)
y = 10x - 6

Thus, the required slope-intercept form of the function is y = 10x - 6

Learn more about slopes here:

https://brainly.com/question/3605446

#SPJ2

The line that passes through (12, 5) and (12, 9) is a vertical line, and its equation is:

x = 12

We know that we have a line that passes through points (12, 5) and (12, 9).

Notice that the x-value of the two points is the same one, then we will have a vertical line of the form:

x = a

The x-value in both points is 12, then the constant value of the line is 12, thus the equation for the line that passes through these two points is:

x = 12.

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

x = 15  or x = -3

Step-by-step explanation:

I assume this is an absolute value equation.

|x - 6| + 8 = 17

|x - 6| = 9

x - 6 = 9  or  -(x - 6) = 9

x = 15  or  x - 6 = -9

x = 15  or x = -3

The correct solution to the equation x - 6 + 8 = 17 is:

x - 6 + 8 = 17

Combining like terms, we have:

x + 2 = 17

Next, we isolate x by subtracting 2 from both sides:

x + 2 - 2 = 17 - 2

x = 15

Therefore, the correct solution is x = 15.

However, none of the given answer choices (OA, B, C, or OD) accurately represent the solution to the equation. The correct answer is x = 15, and there is no value of 'a' mentioned in the original equation, so there is no solution for 'a'.

Answer:

b

Step-by-step explanation:

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

Learn more about Budget:

https://brainly.com/question/26894404

#SPJ11

STEP - BY - STEP EXPLANATION

What to find?

The z- score of 72

Given:

mean (μ) = 65

standard deviation (σ) = 13

x = 72

Step 1

Recall the z- score formula.

Step 2

Substitute the values into the formula and simplify.

ANSWER

0.54

Answer:

C

Step-by-step explanation:

Yes. A leg of a right triangle can indicate the distance that separates two vertical or horizontal points, and the hypotenuse can represent the distance between two non-vertical or non-horizontal points.

We can use this theorem to calculate the distances between two locations on a coordinate grid. Consider the following example using the points:

( 3, 4 ) and ( − 2, 1 )

We can see how to make a right triangle with the hypotenuse as that of the line connecting these two spots. A right angle is formed at the coordinates ( 3, 1), where the vertical line from ( 3, 4 ) and the horizontal line from ( 2, 1 ) intersect.

To learn more about the distance between any two points, use the link below.

https://brainly.com/question/20436215?referrer=searchResults

#SPJ4