A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees.


Which best describes why the function is nonlinear?

The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Answer:

(-2, 5)

Step-by-step explanation:

-4x+3y=23

x - y = - 7

x = y - 7

Substitution:

-4(y-7)+3y = 23

- 4y + 28 + 3y = 23

y = 23 - 28

-y = -5

y = 5

Substitution:

x - 5 = - 7

x = - 7 + 5

x - 2

x = price of a senior ticket

y = price of a student ticket

First day: x + 14y = $225

Second day: 7x + y = $120

Let's solve this system of equations by substitution

Subtract 14y from both sides on our first equation

First day: x = $225 - 14y

Substitute this value into our second equation for x

7($225 - 14y) + y = $120

Distribute the 7

$1575 - 98y + y = $120

Combine like terms

$1575 - 97y = $120

Subtract $1575 from both sides

-97y = -1455

Divide both sides by -97

y = $15

Plug this value into our first equation

x + 14(15) = $225

Simplify

x + $210 = $225

Subtract $210 from both sides

x = $15

The senior and student tickets cost $15

Answer:

3 7/8 cups plants food

Step-by-step explanation:

peat moss = 3 ½ cups

compost = 5 ¼ cups

fertilizer = 6 ¾ cups

Total mixture = peat moss + compost + fertilizer

= 3 ½ cups + 5 ¼ cups + 6 ¾ cups

= 7/2 + 21/4 + 27/4

= 14+21+27/4

= 62/4

Total mixture = 62/4 cups

She evenly distributed the plant food among 4 rose bushes

Each rose bush uses = Total mixture / number of rose bushes

= 62/4 ÷ 4

= 62/4 × 1/4

= 62/16

= 3 14/16

= 3 7/8 cups plants food

Each rose bush uses = 3 7/8 cups of plants food

As per the given matrix, a = 10, b = -5, c = -5, and d = -5.

Let's break down the given equation and determine the values of a, b, c, and d.

The given equation is:

-5 = [a    b] = [ 10   -5]

        [c     d]    [-20    0]

We can equate the corresponding elements of the matrices on both sides of the equation.

From the top row of the matrices, we have:

-5 = a     10

This equation tells us that the value of 'a' is 10.

Moving on to the second row:

-5 = b    -5

This equation indicates that the value of 'b' is -5.

Now, let's focus on the first column:

-5 = c

          -20

This equation shows that the value of 'c' is -5.

Finally, examining the second column:

-5 = d

           0

This equation implies that the value of 'd' is -5.

Therefore, we have determined the values of a, b, c, and d: a = 10, b = -5, c = -5, and d = -5.

These values satisfy the given equation -5 = [a    b] = [ 10   -5]

                                                                          [c     d]    [-20    0]

Thus, the solution to the system of equations is a = 10, b = -5, c = -5, and d = -5.

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After 9 years with monthly compounding and no payments, Dan will owe approximately $13,189.6

Using the formula for compound interest:

A = \(P(1 + \frac{r}{n} )^{nt}\)

Where:

A = the future amount (the amount Dan will owe after 9 years)

P = the principal amount (the initial borrowed amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Given:

P = $8000

r = 18% = 0.18 (as a decimal)

n = 12 (monthly compounding)

t = 9 years

substitute the values into the formula:

A = \(8000(1 + \frac{0.18}{12} )^{12*9}\)

A = \(8000(1 + 0.015)^{108}\)

 = \(8000(1.015)^{108}\)

 = 8000(1.6487)

A = $13,189.6

Therefore, after 9 years with monthly compounding and no payments, Dan will owe approximately $13,189.6.

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Answer:

5:6

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

y = 2/3x + 3 2/3

Step-by-step explanation:

slope intercept form: y = mx + b

isolate the y => y = 2/3(x - 2) + 5 => y = 2/3x - 4/3 + 5 => y = 2/3x + 3 2/3

Answer:

The answer is 2940ft^2

Step-by-step explanation

First convert length and width to feet using the value given (7ft=1inch).

\(10*7= 70\)

\(6*7= 42\)

Multiply these values for the actual area.

\(42*70= 2940\)

The actual area of the lawn is 2940ft^2

Answer:

72 maneiras

Step-by-step explanation:

O que acontecerá aqui é que um de cada tipo de roupa será selecionado.

Das 6 camisas, 1 será selecionada O número de maneiras pelas quais podemos fazer isso é 6C1 = 6

Das saias também, ela estará selecionando uma O número de maneiras que isso pode ser feito é 4C1 = 4

O terceiro é selecionar um par de sapatos de 3 e isso seria 3C1 = 3

assim o número de maneiras pelas quais ela pode fazer as seleções é 6 * 4 * 3 = 72 maneiras

The statement "Length of 'center' must equal the number of columns of 'x'" is generally false. The length of the 'center' variable does not necessarily need to equal the number of columns of 'x'.

The requirement for the length of 'center' depends on the specific context or purpose of its usage in relation to 'x'. In some cases, 'center' may represent a vector or an array containing the central values or positions of a dataset or matrix. In such cases, the length of 'center' would typically match the dimensionality of the dataset or matrix, which would correspond to the number of rows or columns in 'x'. However, there can be situations where 'center' represents something else entirely, such as a single value or a different set of values unrelated to the dimensions of 'x'. Therefore, it is not a general rule that the length of 'center' must always equal the number of columns of 'x'. The specific requirements and relationships between 'center' and 'x' would depend on the specific context and purpose of their usage.

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Answer:13 on each team but there wouldn’t be the Same amount

Step-by-step explanation:

Because you would divid 110 dived by 8 equals 13.75

Answer:

selling price is $26.4

Step-by-step explanation:

Here, we want to apply the markup percentage so as to get the price of the jewelry

mathematically, we have the selling price as;

$22 + (30% of $22)

= $22 + 4.4

= $26.4

The diver starts at a depth of 30 feet below sea level and then swims upward 12 feet. This means the diver has ascended by 12 feet from the initial depth. However, the question states that the diver then descends 25 feet below sea level. To determine the final depth, we need to consider both the ascent and descent.

Since the diver ascended 12 feet, we can subtract this value from the initial depth of 30 feet below sea level. This gives us 30 - 12 = 18 feet below sea level.

Next, we take into account the descent of 25 feet. Since the question specifies "below sea level," we express the descent as a negative value. Therefore, the final depth is 18 - 25 = -7 feet below sea level.

In conclusion, the diver is 7 feet below sea level after the ascent of 12 feet and descent of 25 feet.

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The probability will be 0.9940.

The provided parameters are

p = 0.05  (the true proportion or the mean )

n = 269   ( sample size )

we can calculate standard deviation as follows

σ = \(\sqrt{\frac{p(1-p)}{n} }\)

σ = 0.0132

Now the values that 'x' can take are

x = \(x_{1}\) ±  \(x_{2}\)

x = 0.05 + 0.03, 0.05 - 0.03

x = 0.08 , 0.02

Also the z-score is

z = (x - μ)/σ

z = \(\frac{0.08-0.05}{0.0132}\)  , \(\frac{0.02-0.05}{0.0132}\)

z = 2.27 , -2.27

we now find the p-values for the z-scores

p values are = 0.9970 , 0.0030

The difference in these values will give the probability

∴ P = 0.9970 - 0.0030

P =  0.9940

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The correct response is d) All the above. The arithmetic mean is equal to the median, the median is equal to the mode, and the mode is equal to the arithmetic mean.

If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.

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Answer:

k < -1 or k > 11

Step-by-step explanation:

Given quadratic equation:

\(3x^2-x+ k = kx-1\)

First, rearrange the given quadratic equation in standard form ax² + bx + c = 0:

\(\begin{aligned}3x^2-x+ k &= kx-1\\3x^2-x+ k-kx+1&=0-kx+1\\3x^2-x-kx+ k+1&=0\\3x^2-(1+k)x+ (k+1)&=0\end{aligned}\)

\(3x^2-(1+k)x+ (k+1)=0\)

Comparing this with the standard form, the coefficients a, b and c are:

\(\boxed{\begin{minipage}{7 cm}\underline{Discriminant}\\\\$\boxed{b^2-4ac}$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}\)

If the quadratic equation has two distinct roots, its discriminant is positive.

\(b^2-4ac > 0\)

Substitute the values of a, b and c into the discriminant:

\((-1 - k)^2-4(3)(k+1) > 0\)

Simplify:

\((-1 - k)(-1-k)-12(k+1) > 0\)

\(1+2k+k^2-12k-12 > 0\)

\(k^2+2k-12k+1-12 > 0\)

\(k^2-10k-11 > 0\)

Factor the left side of the inequality:

\(k^2+k-11k-11 > 0\)

\(k(k+1)-11(k+1) > 0\)

\((k-11)(k-1) > 0\)

If we graph the quadratic k² - 10k - 11, it is a parabola that opens upwards (since its leading coefficient is positive), and crosses the x-axis at k = -1 and k = 11. Therefore, the curve will be positive (above the x-axis) either side of the x-intercepts, so when k < -1 or k > 11.

Therefore, the range of values of k for which the given quadratic equation has two distinct roots is:

\(\boxed{k < -1 \; \textsf{or} \;k > 11}\)

Answer:

The answer is C

Step-by-step explanation:

Differential equations involve the study of mathematical equations that relate an unknown function to its derivatives or differentials.

Zero-input response (yzi(t)) refers to the response of the system when there is no input (x(t) = 0). To find the zero-input response of the given system, we need to solve the homogeneous equation:

d²y(t)/dt² + 4(dy(t)/dt) + 3y(t) = 0

Using the characteristic equation approach, let's assume the solution to the homogeneous equation is of the form y(t) = e^(λt). Substituting this into the equation, we get:

λ²e^(λt) + 4λe^(λt) + 3e^(λt) = 0

Dividing the equation by e^(λt) gives:

λ² + 4λ + 3 = 0

Factoring the quadratic equation, we have:

(λ + 3)(λ + 1) = 0

This gives two distinct values for λ: λ = -3 and λ = -1.

Therefore, the general solution for the homogeneous equation is:

y(t) = c₁e^(-3t) + c₂e^(-t)

Using the initial conditions y(0) = -3 and y'(0) = 2, we can find the particular solution. Differentiating y(t) with respect to t and applying the initial conditions, we obtain:

y'(t) = -3c₁e^(-3t) - c₂e^(-t)

Applying the initial conditions y(0) = -3 and y'(0) = 2, we get:

c₁ + c₂ = -3 (equation 1)

-3c₁ - c₂ = 2 (equation 2)

Solving equations 1 and 2 simultaneously, we find c₁ = -2 and c₂ = -1.

Therefore, the zero-input response of the system is given by:

yzi(t) = -2e^(-3t) - e^(-t)

To find the zero-state response (yzs(t)) of the system to the unit step input (x(t) = u(t)), we need to solve the differential equation:

d²y(t)/dt² + 4(dy(t)/dt) + 3y(t) = u(t) - 2u(t)

Taking the Laplace transform of both sides of the equation, we have:

s²Y(s) - sy(0) - y'(0) + 4sY(s) - 4y(0) + 3Y(s) = 1/s - 2/s

Applying the initial conditions y(0) = -3 and y'(0) = 2, and rearranging the equation, we get:

s²Y(s) + 4sY(s) + 3Y(s) - s(-3) - 2 + 4(-3) = 1/s - 2/s

Simplifying further, we have:

Y(s) = (s + 7)/(s² + 4s + 3) + 1/(s(s - 2))

Using partial fraction decomposition, we can express Y(s) as:

Y(s) = A/(s + 1) + B/(s + 3) + C/s + D/(s - 2)

Multiplying through by the denominator, we get:

s + 7 = A(s + 3)(s - 2) + B(s + 1)(s - 2) + C(s² - 2s) + D(s² + 4s + 3)

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Answer:

Rise over Run

Step-by-step explanation:

The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x. The y-intercept indicates the y-value when the x-value is 0.

Answer:

no

Step-by-step explanation:

A function is when x does NOT repeat

Answer:

33

Step-by-step explanation:

(

5

−

√

x

)

2

=

5

2

−

(

2

×

5

×

√

x

)

+

x

=

25

−

10

√

x

+

x

=

(

x

+

25

)

−

10

√

x

In order to eliminate the irrational

−

20

√

2

term with

x

and

y

being integers, we must have:

−

10

√

x

=

−

20

√

2

Divide both sides by

−

10

to get:

√

x

=

2

√

2

So

x

=

(

2

√

2

)

2

=

8

y

=

x

+

25

=

8

+

25

=

33

After answering the presented question, we can conclude that A function computer can execute a sequence of instructions that make up a computer programme by following this cycle.

In mathematics, a function appears to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

The fetch-decode-execute cycle, also known as the instruction cycle, illustrates how a computer's CPU (Central Processor Unit) gets instructions from memory, decodes them, and then executes them. Here's a quick rundown of each step:

Fetch: Based on the current value of the programme counter (PC) register, which corresponds to the memory address of the next instruction to be executed, the CPU retrieves the next instruction from memory.

The fetch-decode-execute cycle is an essential component of the von Neumann architecture, which serves as the foundation for most modern computers. A computer can execute a sequence of instructions that make up a computer programme by following this cycle.

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Answer:

Your answer would be A

Step-by-step explanation:

9514 1404 393

Answer:

  11,025

Step-by-step explanation:

Interestingly the sum of the first 14 cubes is the square of the sum of the first 14 integers: 105^2 = 11,025.

Answer:

11,025 is your answer

Step-by-step explanation:

High-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

A scatter plot is a graphical representation of data points, with the x-axis representing the independent variable (such as the level of production) and the y-axis representing the dependent variable (such as the cost). Linear cost behavior means that the relationship between the independent and dependent variables can be approximated by a straight line. In other words, as the independent variable increases or decreases, the dependent variable changes proportionally.

To determine if a scatter plot depicts linear cost behavior, you need to visually examine the data points. If the points appear to align closely along a straight line, it indicates a linear relationship. However, if the points are scattered and do not follow a clear pattern, it suggests non-linear cost behavior.

High-low or least squares regression analysis are statistical techniques used to estimate and quantify the linear relationship between variables. These methods help determine the equation of the line that best fits the data points and can be used to predict future values. Therefore, performing these analyses is only meaningful when the scatter plot indicates linear cost behavior.

In summary, high-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

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To prove the properties of the projection matrix, we'll assume that p is the projection matrix corresponding to a subspace S of \(R^{m}\).

(a) p² = p

To show that p² = p, we need to demonstrate that applying the projection matrix p twice is equivalent to applying it once.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, if we apply the projection matrix p again to p(x), we have:

p(p(x)) = projection of p(x) onto S

Since p(x) is already the projection of x onto S, applying the projection matrix p once more won't change the result. Hence, we can write:

p(p(x)) = p(x)

This equation holds for any vector x in \(R^{m}\), meaning that p² = p.

(b) \(p^{T}\) = p

To prove that \(p^{T}\) = p, we need to show that the transpose of the projection matrix p is equal to p.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, let's compute the transpose of p(x):

\((p(x))^{T}\) = \((projection of x onto S)^T\)

The transpose of a projection onto a subspace doesn't change the result because it only affects the column vectors of the projection matrix. The transpose of p(x) is still the projection of x onto S. Hence, we can write:

\((p(x))^T\) = p(x)

Since this equation holds for any vector x in \(R^{m}\), we can conclude that \(p^T\) = p.

Therefore, we have shown that (a) p² = p and (b) \(p^T\) = p, proving the properties of the projection matrix corresponding to a subspace S of \(R^{m}\).

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To find the sum of a convergent geometric series, we can use the formula S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio. However, since this series is divergent, we cannot use this formula to find its sum.

To determine whether the geometric series is convergent or divergent, we need to first find the common ratio (r) between each term. To do this, we can divide any term by the previous term. For example, dividing 16/3 by -4 gives us -4/3, which is the common ratio (r).

Now we need to check if the absolute value of r is less than 1 for the series to be convergent. In this case, the absolute value of r is 4/3, which is greater than 1. Therefore, the series is divergent.

To find the sum of a convergent geometric series, we can use the formula S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio. However, since this series is divergent, we cannot use this formula to find its sum.

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