(x +1)^2-5x(x+3)(x-3)

The number of cars that pass through the intersection between 6 am and 8 am is r(1) - 74 cars.

The traffic flow rate (cars per hour) across an intersection is

\(r(1)−200+1000t270t^2\), where / is in hours, and t=0 is 6 am.

The total number of cars that pass through the intersection between 6 am and 8 am can be calculated by finding the definite integral of the rate of flow function (r(t)) over the time period [0, 2].

∫[0,2] r(t) dt = ∫[0,2] \((r(1) - 200 + 1000t/270t^2) dt\)

(since r(1) is a constant)

= ∫[0,2] (r(1) - 200 + 3.7t) dt

(by simplifying 1000/270)

\(= r(1)(t) - 100t + (3.7/2)t^2 |[0,2] \\= (r(1) - 100(2) + (3.7/2)(2)^2) - (r(1) - 100(0) + (3.7/2)(0)^2) \\= r(1) - 74\) cars

Know more about the traffic flow rate

https://brainly.com/question/13191920

#SPJ11

Answer:

The answer to this question is D. 3

Answer:

The last one is right 3

Step-by-step explanation:

Took the test got it right.

Answer:

1.65

Step-by-step explanation:

Divide 6.6 by 4

Answer:

Dependent variable = Money left

Independent variable = Gallons pumped

Step-by-step explanation:

When finding the dependent vs independent variable, you usually want to see what is being plugged in to the function. This is oftentimes the independent variable, as it is not influenced by anything involved with the function, and acts on it's own.

The dependent variable is usually what is being set equal to the expression being solved, in this case that is the money that you have left, which goes down as you pump more gas. This is entirely dependent on how much gas is used.

Hope this helps, if you need any more explanation or help please let me know.

The equivalent expression of 5\(x^{3/2}\) is  5√(x³). The correct option is last one.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

5\(x^{3/2}\)

To find the equivalent expression:

We have to simplify the expression,

5\(x^{3.1/2}\)

= 5(x³)\(){1/2}\)

= 5√(x³)

The above expression is an equivalent expression.

Therefore, 5√(x³) is an equivalent expression.

To learn more about the equivalent expression;

https://brainly.com/question/28170201

#SPJ1

Answer:

\(Probability = \frac{1}{8}\)

Step-by-step explanation:

Given

Represent Boys with B and Girls with G

\(P(B) = \frac{1}{2}\)

\(P(G) = \frac{1}{2}\)

Required

Find the probability or having 1 boy 2 girls

Since the order is not important, the probability is calculated as follows;

\(Probability = P(B) * P(G) * P(G)\)

Substitute \(\frac{1}{2}\) for P(B) and P(G)

\(Probability = \frac{1}{2} * \frac{1}{2} * \frac{1}{2}\)

\(Probability = \frac{1 * 1 * 1}{2 * 2 *2}\)

\(Probability = \frac{1}{8}\)

Hence, the fractional probability is \(\frac{1}{8}\)

Answer:

96 cm

Step-by-step explanation:

for the triangles do 5×6×4

then divide it by 2 to get 60 then do 6×6 for the square to get 36. Add 36 and 60 together to get 96.

Answer:

Step-by-step explanation:

induction refers specifically to "inference of a generalized conclusion from particular instances." In other words, it means forming a generalization based on what is known or observed.

Answer:

Inductive reasoning, or inductive logic, is a type of reasoning that involves drawing a general conclusion from a set of specific observations.

Step-by-step explanation:

Based on the provided information, Roth, Inc. purchased a laser cutting machine on January 2, 2015, for $110,000. The machine has an estimated useful life of four years or 1,050,000 cuttings. After that period, it can be sold for $5,000.

To calculate the depreciation expense, we need to determine the annual depreciation amount. Since the useful life is given in terms of years and cuttings, we will calculate depreciation using both methods and choose the higher amount.

Depreciation based on useful life in years:

Depreciation per year = (Purchase cost - Residual value) / Useful life in years

Depreciation per year = ($110,000 - $5,000) / 4

Depreciation per year = $105,000 / 4

Depreciation per year = $26,250

Depreciation based on useful life in cuttings:

Depreciation per cutting = (Purchase cost - Residual value) / Useful life in cuttings

Depreciation per cutting = ($110,000 - $5,000) / 1,050,000

Depreciation per cutting = $105,000 / 1,050,000

Depreciation per cutting ≈ $0.10

Since $0.10 per cutting is the higher depreciation amount, we will use this method.

Now, let's calculate the depreciation expense for each year:

Year 1: Depreciation expense = Depreciation per cutting * Total cuttings in year 1

Year 1: Depreciation expense = $0.10 * 1,050,000 (assuming maximum cuttings in a year)

Year 1: Depreciation expense = $105,000

Similarly, the depreciation expense for each subsequent year will also be $105,000.

Finally, let's calculate the net cost of the laser cutting machine at the end of each year:

Year 1: Net cost = Purchase cost - Depreciation expense for year 1 - Residual value

Year 1: Net cost = $110,000 - $105,000 - $5,000

Year 1: Net cost = $0

Year 2: Net cost = Purchase cost - Depreciation expense for year 2 - Residual value

Year 2: Net cost = $110,000 - $105,000 - $5,000

Year 2: Net cost = $0

Year 3: Net cost = Purchase cost - Depreciation expense for year 3 - Residual value

Year 3: Net cost = $110,000 - $105,000 - $5,000

Year 3: Net cost = $0

Year 4: Net cost = Purchase cost - Depreciation expense for year 4 - Residual value

Year 4: Net cost = $110,000 - $105,000 - $5,000

Year 4: Net cost = $0

After four years, the net cost of the laser cutting machine will be $0.

In summary, the laser cutting machine purchased by Roth, Inc. for $110,000 will have a net cost of $0 at the end of its useful life, assuming the maximum number of cuttings in each year and a residual value of $5,000.

To know more about useful life, refer here:

https://brainly.com/question/13199786

#SPJ4

Answer:

Yes

Step-by-step explanation:

His equations are balanced because no matter you add the equation still works.

Ex: 6+6-8 = 12 - 8

4 = 4

you can also just add n to both sides which lets it cancel out.

6+6-n = 12 - n --> 6+6 (-n +n = 0) = 12 (-n + n = 0)

The first statement is true because the y-intercept represents the initial height of the ball when it's dropped (t=0). The second statement is true because the x-intercepts represent the moments when the height of the ball is zero, meaning it has hit the ground.

Two statements that are true about the graph and situation it represents are:

1. The vertical intercept (also called y-intercept) shows the time when the ball hits the ground.
2. The horizontal intercepts (also called x-intercepts) of the graph show the times when the ball hit the ground.

The first statement is true because the height of the ball is zero when it hits the ground, and the vertical intercept on the graph represents the point where the height is zero. The second statement is true because the ball hits the ground multiple times and each time it does, the height is zero. The horizontal intercepts on the graph represent the points where the height is zero, which corresponds to the times when the ball hits the ground. The other two statements are not true based on the given graph and situation.

Based on the provided information, the two true statements about the graph and the situation it represents are:

1. The vertical intercept (also called y-intercept) shows when the ball is dropped.
2. The horizontal intercepts (also called x-intercepts) of the graph show the times when the ball hits the ground.

Learn more about intercept at: brainly.com/question/14180189

#SPJ11

Answer:

- 18369919

Step-by-step explanation:

Hope that helps!

The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

You can learn more about pivot column at

https://brainly.com/question/29786913

#SPJ4

Answer: C

Step-by-step explanation:

The area of a circle is ∏r2- (Pi)(Radius)-squared

The Answer is C

Social and managerial decisions are based for the most part upon subjective probability, option c. The stated 40% probability of a newly entering freshman completing their degree within four to five years is an example of relative frequency probability, option a.

Subjective probability refers to the degree of belief or personal judgment about the likelihood of an event happening. Thus, the correct option is c. subjective probability.

Relative frequency probability is calculated by analyzing past data to determine the frequency of a specific outcome occurring. In this case, the probability is based on analyzing the last fifteen years of college graduation data. Thus, the correct option is a. relative frequency probability.

To learn more about probability: https://brainly.com/question/13604758

#SPJ11

The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

To know more about collision refer to:

brainly.com/question/7221794

#SPJ4

Answer:

x = 105

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 7, thus

sum = 180° × 5 = 900°

Sum the interior angles and equate to 900

x + 102 + 165 + 123 + x + 11 + 128 + 161 = 900, that is

2x + 690 = 900  ( subtract 690 from both sides )

2x = 210 ( divide both sides by 2 )

x = 105

Answer:

20 2 3 6 10 998778889899999

The energy of the signal \(\(y(t) = \cos(1000\pi t) \rect}\left(\frac{t}{4}\right)\)\)is 2.

Calculate the energy of the signal \(\(y(t) = \cos(1000\pi t) \rect}\left(\frac{t}{4}\right)\)\), we need to evaluate the integral of the squared magnitude of the signal over its entire duration.

The energy \(\(E\)\) of a continuous-time signal\(\(y(t)\)\) is given by:

\(\[E = \int_{-\infty}^{\infty} |y(t)|^2 \, dt\]\)

Substituting the given signal:

\(\[E = \int_{-\infty}^{\infty} \left| \cos(1000\pi t) \{rect}\left(\frac{t}{4}\right) \right|^2 \, dt\]\)

Since the rectangular function has a width of\(\(\frac{t}{4}\)\), the non-zero interval of the signal is \([-2, 2]\) (i.e., \(\\{rect}\left(\frac{t}{4}\right) = 1\)\) within this interval).

Therefore, the energy can be evaluated as follows:

\(\[E = \int_{-2}^{2} \left| \cos(1000\pi t) \right|^2 \, dt\]\)

\(\[E = \int_{-2}^{2} \cos^2(1000\pi t) \, dt\]\)

Using the trigonometric identity\(\(\cos^2(x) = \frac{1 + \cos(2x)}{2}\)\), we can simplify further:

\(\[E = \int_{-2}^{2} \frac{1 + \cos(2 \cdot 1000\pi t)}{2} \, dt\]\)

\(\[E = \frac{1}{2} \int_{-2}^{2} 1 + \cos(2000\pi t) \, dt\]\)

Integrating each term separately:

\(\[E = \frac{1}{2} \left[ t + \frac{1}{2000\pi} \sin(2000\pi t) \right]_{-2}^{2}\]\)

Evaluating the integral at the limits:

\(\[E = \frac{1}{2} \left[ 2 + \frac{1}{2000\pi} \sin(4000\pi) - (-2) - \frac{1}{2000\pi} \sin(-4000\pi) \right]\]\)

Simplifying further, since \(\(\sin(4000\pi) = \sin(0) = 0\) and \(\sin(-4000\pi) = \sin(0) = 0\)\):

\(\[E = \frac{1}{2} \left[ 4 \right]\]\)

Therefore, the energy of the signal \(\(y(t) = \cos(1000\pi t)\)\(\{rect}\left(\frac{t}{4}\right)\) is \(E = 2\)\).

The energy of the signal is 2.

To know more about signal refer here

https://brainly.com/question/31473452#

#SPJ11

Answer:

10 falls between 4 and 2 but is closer to 2.

92 falls between 10 and 8 but is closer to 10

Answer:

see below

Step-by-step explanation:

90 x, y, z

x pennies =1/2y

y nickels

z quarters = 3 1/2 y

so 1/2y+y+3 1/2 y =90

total 5y =90

y =18

x=9

z = 63

The confidence associated with an interval estimate is called the confidence level.

When making an interval estimate, such as estimating a population parameter based on a sample, it is important to provide an indication of the level of confidence we have in the estimate. The confidence level represents the probability or level of certainty that the true population parameter falls within the calculated interval.

For example, if we calculate a 95% confidence interval for the mean height of a population, it means that we are 95% confident that the true population mean height lies within that interval. This implies that if we were to repeat the sampling and interval estimation process multiple times, approximately 95% of the intervals would contain the true population parameter.

The confidence level is typically expressed as a percentage, such as 90%, 95%, or 99%. A higher confidence level indicates a greater level of certainty in the interval estimate but also results in a wider interval.

In summary, the confidence level associated with an interval estimate represents the level of confidence or probability that the interval contains the true population parameter.

To know more about confidence level click here :

https://brainly.com/question/22851322

#SPJ4

Answer:

A=S1+S2+S3+S4

Step-by-step explanation:

A=4(l*w)ft

Answer:

100

THIS IS FOR THE SECOND ONE ONLY THE SECOMD ONE

The probability that the LEGO figure does not have blue legs but has a red body is 2/9. so, the correct answer is B).

To find the probability that the LEGO figure does not have blue legs but has a red body, we need to first find the probability of the figure having a red body, which is 1/3.

Next, we need to find the probability of the figure not having blue legs. Since there are three options for legs, and one of them is blue, the probability of the figure having blue legs is 1/3. Therefore, the probability of the figure not having blue legs is 1-1/3, which simplifies to 2/3.

Finally, we multiply the probabilities of the two events to get the probability that the figure has a red body and does not have blue legs: (1/3) x (2/3) = 2/9.

Therefore, the answer is (B) 2/9.

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4

--The given question is incomplete, the complete question is given

"  A LEGO action figure is created for visitors that tour a factory. Each figure consists of a randomly chosen set of legs, body, head, and hair/hat. The following table shows the available options for each category.

If each option is equally likely within each category what is the probability that the LEGO figure does NOT have blue legs but has a red body.

1/6

2/9

1/10

1/3"--

Answer:

\(\sqrt{10}\)

Step-by-step explanation:

The distance between two points can be found using the Pythagorean Theorem \(a^{2} + b^{2} = c^{2}\).

This is because, if you connected your two points with a line, that line could be defined as the hypotenuse of a right triangle. the base of that triange is the distance between the x coordinates (\(x_{2} -x_{1}\)) and the height by the distance between the y coordinates (\(y_{2} - y_{1}\)). Sine these are the sides of the right triangle, they are equal to a and b above (c is the hypotenuse that we are trying to find). So, we calculate the two distances above and get 3 and 1 (for x and y respectively). 3^2 + 1^ 2 =10. So the answer is square root 10.

It is important to approach statements like this with caution and consider the complexity of the factors at play in career advancement and leadership positions.

While research may indicate that ethnicity can be a significant barrier to advancement in some cases, it is crucial to recognize that experiences can vary based on individual circumstances, industries, and regions. Gender and ethnicity intersect in complex ways, and the challenges faced by women of different ethnic backgrounds can differ significantly.

It is essential to avoid generalizations and recognize that multiple factors contribute to the barriers individuals face in reaching top leadership positions. These factors can include implicit biases, cultural norms, lack of representation, access to opportunities, networking, and organizational structures. Intersectionality, which considers how different aspects of a person's identity can intersect and create unique experiences, is also a crucial perspective to consider when discussing barriers to advancement.

To fully understand and address the barriers individuals face in reaching top leadership positions, it is necessary to consider a comprehensive range of factors and engage in ongoing research, dialogue, and efforts to promote equity, diversity, and inclusion in the workplace.

Learn more about Ethnicity here -: brainly.com/question/674712

#SPJ11

The equation properties are:

The equations are given as:

The distributive property of an equation states that:

a * (b + c) = ab + ac

This means that 3 * (6 + 2) = 3 * 6 + 3 * 2 is represented by the distributive property.

The associative property of an equation states that:

a * (b * c) = (a * b) * c

This means that 5 * (7 * 8) = (7 * 5) * 8 and 5 * 3 * 7 = 7 * 3 * 5 are represented by the associative property.

Read more about equation properties at:

https://brainly.com/question/4077386

#SPJ1

The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.

The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.

The maximum number of chairs that can be made will be the minimum of the number of parts divided by the number of parts required for each chair, as calculated across the various types of parts required.

seats: 12 available, used 1 per chair: 12/1 = 12 chairs possible

backs: 15 available, used 1 per chair: 15/1 = 15 chairs possible

legs: 44 available, used 4 per chair: 44/4 = 11 chairs possible

The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.

To learn more about probability refer to:

https://brainly.com/question/13604758

#SPJ4