Factorise the following x^2-8x-9

The 95% confidence interval for the true population proportion of adults who favor the proposed environmental laws is 38.1% to 47.9%.

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

where the Margin of Error is determined by the critical value multiplied by the standard error.

The sample proportion is 43% (0.43) as given in the survey.

The critical value for a 95% confidence level is approximately 1.96, which corresponds to the standard normal distribution.

The standard error can be calculated using the formula:

Standard Error = \(\sqrt{(Sample Proportion * (1 - Sample Proportion)) / Sample Size}\)

In this case, the sample size is 418.

Plugging in the values, we can calculate the standard error as follows:

Standard Error = \(\sqrt{(0.43 * (1 - 0.43)) / 418}\) ≈ 0.0257

Now, we can calculate the margin of error by multiplying the critical value (1.96) by the standard error:

Margin of Error = 1.96 * 0.0257 ≈ 0.0504

Finally, we can construct the confidence interval by subtracting and adding the margin of error to the sample proportion:

Confidence Interval = 43% ± 0.0504 = 38.1% to 47.9%

Therefore, the 95% confidence interval for the true population proportion of adults who favor the proposed environmental laws is 38.1% to 47.9%.

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To produce 1 ATP molecule, approximately 3 H ions must be moved into the matrix.

ATP synthesis in cells occurs through a process called oxidative phosphorylation, which takes place in the mitochondria.

During oxidative phosphorylation, a series of protein complexes, known as the electron transport chain, transfer electrons from electron donors to electron acceptors.

As electrons are transferred, protons (H ions) are pumped from the matrix to the intermembrane space, creating an electrochemical gradient.

The electrochemical gradient created by the movement of protons (H ions) across the inner mitochondrial membrane is harnessed by an enzyme called ATP synthase.

ATP synthase acts as a molecular turbine, utilizing the energy from the movement of H ions to produce ATP.

The exact number of H ions required to synthesize one ATP molecule can vary slightly depending on the specific cellular conditions.

However, on average, it is estimated that around 3 H ions need to move back into the matrix through ATP synthase for the synthesis of 1 ATP molecule.

This process, known as chemiosmosis, is essential for the generation of ATP, which serves as the primary energy currency in cells.

By utilizing the energy derived from the movement of H ions down the electrochemical gradient, cells are able to produce ATP efficiently and meet their energy demands for various cellular processes.

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Answer:

Producer's surplus = (1/2) x (2) x (10) = 10

Step-by-step explanation:

To find the producer's surplus, we need to first determine the equilibrium quantity and price at which the supply and demand functions intersect.

Setting the supply function S(x) equal to the demand function D(x) and solving for x, we get:

4x + 2 = 14 - x^2

Rearranging and simplifying, we get a quadratic equation in standard form:

x^2 + 4x - 12 = 0

Using the quadratic formula, we get:

x = (-4 ± √(4^2 - 4(1)(-12))) / (2(1))

x = (-4 ± √64) / 2

x = -2 ± 4

x = -6 or x = 2

Since we're interested in a positive quantity, we'll take x = 2 as the equilibrium quantity.

To find the equilibrium price, we substitute x = 2 into either the supply or demand function:

D(2) = 14 - 2^2 = 10

So the equilibrium price is P = 10.

The producer's surplus is the area above the supply curve and below the equilibrium price. Since the supply function is linear, we can find the producer's surplus by calculating the area of a triangle with base x = 2 and height S(2) = 10:

Producer's surplus = (1/2) x (2) x (10) = 10

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The value of angle V which is ∠V is calculated as:  64.01°

The trigonometric ratios are used to find the angles and lengths of a right angle triangle.

Some of the trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

The parameters given are:

∠W = 90°

UW = 39

WV = 80

VU = 89

Thus, using trigonometric ratios, we have:

∠V = tan⁻¹(80/39)

∠V = 64.01°

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The form of the exponential function is

Where a is the value of y at x = 0

b is the base of the exponential function

Let us use 2 points from the table to find a and b

∵ At x = 0, y = 4

∵ a is the value of y at x = 0

∴ a = 4

Substitute it in the form of the function

Now let us use the point (-1, 4/3)

Divide both sides by 4

To change the power of b to +1, reciprocal 1/3

The function of the table is

The answer is D

Answer:

A.

I hope it helps

There were the most observations of female tokoeka kiwis in the given frequency table so option (A) will be correct.

A frequency table is a list of objects with the frequency of each item shown in the table.

The frequency of an occurrence or a value is the number of times it happens.

Given the frequency table of kiwi birds with their gender.

Number of female tokoeka kiwis = 44

Now if we look at the table there is none of any bird that is greater than 44 which means it is the most observations in the research.

Hence  "There were the most observations of female tokoeka kiwis".

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Answer: 640 students.

Step-by-step explanation:

given data:

number of student chosen to attend by the mayor = 160

amount this student represents of the total population = \(\frac{1}{4}\)

solution:

since \(\frac{1}{4}\) was chosen which is 160 this means that \(\frac{1}{4} is \geq 160\)

therefore;

\(\frac{1}{4} = 160\\\)

multiply both sides by 4

\(\frac{1}{4} . 4 = 160 .4\\= 640\)

the least number of students that attend melvins school is 640.

The function that could be described is f(x) = 10cos(2πx/3), where the amplitude is 10, the period is 3, and the maximum value is 20.

In a cosine function, the amplitude represents the vertical distance from the midline to the maximum or minimum value. Here, the maximum value is 20, which means the amplitude is half of that, i.e., 10. The period of the function is the distance it takes for one complete cycle, and in this case, it is 3 units.

By using the formula f(x) = A*cos(2πx/P), where A is the amplitude and P is the period, we can determine that the given function matches the described characteristics.

The function f(x) = 10cos(2πx/3) has a maximum value of 20 and a minimum value of 0, and it completes one cycle over the interval of the period, which is 3 units.

In conclusion, the function f(x) = 10cos(2πx/3) satisfies all the given conditions and represents the described function.

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Therefore, the original number is 10x + y = 10(10) + 7 = 107.

Given that the sum of the digits is seventeen, we have the equation:

x + y = 17 (equation 1)

The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. The number with the digits reversed would be 10y + x.

According to the given information, we have the equation:

10y + x = 5x + 30 (equation 2)

To solve the system of equations, we can substitute equation 1 into equation 2:

10(17 - x) + x = 5x + 30

Expanding and simplifying:

170 - 10x + x = 5x + 30

170 - 30 = 5x + 10x - x

140 = 14x

x = 10

Substituting the value of x back into equation 1:

10 + y = 17

y = 7

Therefore, the original number is 10x + y = 10(10) + 7 = 107.

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Given:

Consider a rhombus.

To find:

Which of the given statements about a rhombus is not true?

Solution:

Properties of a Rhombus:

1. It is a quadrilateral which is a special case of a parallelogram.

2. It has four equal sides.

3. It has two sets of parallel sides.

4. Opposite angles are equal.

5. Diagonals are perpendicular bisectors.

Since a rhombus doesn't has four right angles, therefore the last statement in the given options is not true about the rhombus.

Hence, the correct option is D.

Single Sampling Plan: AQL = 0, LTPD = 3.41, AOQ = 1.79 Double Sampling Plan: AQL = 0, LTPD = 2.72, AOQ = 1.48

The values for the ASN (Average Sample Number) curves for the given single sampling plan and double sampling plan are:

Single Sampling Plan (n=80, c=3):

ASN curve values: AQL = 0, LTPD = 3.41, AOQ = 1.79

Double Sampling Plan (n1=50, c1=1, r1=4, n2=50, c2=4, r2):

ASN curve values: AQL = 0, LTPD = 2.72, AOQ = 1.48

The ASN curves provide information about the performance of a sampling plan by plotting the average sample number (ASN) against various acceptance quality levels (AQL). The AQL represents the maximum acceptable defect rate, while the LTPD (Lot Tolerance Percent Defective) represents the maximum defect rate that the consumer is willing to tolerate.

For the single sampling plan, the values n=80 (sample size) and c=3 (acceptance number) are used to calculate the ASN curve. The AQL is 0, meaning no defects are allowed, while the LTPD is 3.41. The Average Outgoing Quality (AOQ) is 1.79, representing the average quality level of outgoing lots.

For the equally effective double sampling plan, the values n1=50, c1=1, r1=4, n2=50, c2=4, and r2 are used. The AQL and LTPD values are the same as in the single sampling plan. The AOQ is 1.48, indicating the average quality level of outgoing lots in this double sampling plan.

These ASN curve values provide insights into the expected performance of the sampling plans in terms of lot acceptance and outgoing quality.

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Richard gets an average of 17 calls during his 8 hour work day. in order to find the probability that richard will get at most 5 calls in a 2 hour portion of his work day using the poisson distribution,The probability that Richard will receive at most 5 calls in a 2-hour portion of his work day is approximately 0.092.

In this scenario, the random variable X represents the number of calls that Richard receives during a 2-hour portion of his 8-hour work day.

The Poisson distribution is commonly used to model the probability of a certain number of rare events occurring in a fixed interval of time or space. In this case, we can use the Poisson distribution to model the number of calls that Richard receives in a 2-hour period, given that we know the average number of calls he receives in an 8-hour work day.

The Poisson distribution has a single parameter, λ, which represents the average rate at which the rare events occur. In this case, λ = 17/8 = 2.125, since Richard receives an average of 17 calls in an 8-hour work day.

To find the probability that Richard will receive at most 5 calls in a 2-hour portion of his work day, we can use the Poisson probability mass function (PMF), which gives the probability of observing k events in a given time interval, given the average rate λ. The PMF is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

where k is the number of events, λ is the average rate, and e is the mathematical constant approximately equal to 2.71828.

So in this case, we want to find the probability that X ≤ 5, i.e., the probability that Richard will receive 0, 1, 2, 3, 4, or 5 calls in a 2-hour portion of his work day. We can use the cumulative distribution function (CDF) of the Poisson distribution to find this probability:

P(X ≤ 5) = Σ(k=0 to 5) P(X = k)

where Σ is the summation symbol.

Plugging in the values, we get:

P(X ≤ 5) = Σ(k=0 to 5) (e^(-λ) * λ^k) / k! = (e^(-2.125) * 2.125^0 / 0!) + (e^(-2.125) * 2.125^1 / 1!) + (e^(-2.125) * 2.125^2 / 2!) + (e^(-2.125) * 2.125^3 / 3!) + (e^(-2.125) * 2.125^4 / 4!) + (e^(-2.125) * 2.125^5 / 5!) ≈ 0.092

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The dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.

Let the dimension of the rectangle be x and y m.

According to the given question.

The area of the rectangle is 1728 square meter.

⇒ x × y = 1728

⇒ x = 1728/y

Since, the perimeter of the rectangle is the sum of the length of its boundary.

Therefore,

Perimeter of the recatngle with dimensions x and y is given by

Perimeter of the rectangle, P = 2(x + y)

⇒ P = 2(1728/y + y)

⇒ P = 3456/y + 2y

Differentiate the above equation with respect to y

⇒ \(P^{'} = -\frac{3456}{y^{2} } + 2\)

For the minimum(small) perimeter equate the above equation to 0.

⇒ \(-\frac{3456}{y^{2} } + 2 = 0\)

⇒ \(2y^{2} =3456\)

⇒ \(y^{2} = \frac{3456}{2}\)

⇒ y^2 = 1728

⇒ y = √1728

⇒ y = 41.56 m

Therefore,

x = 1728/41.56

⇒ x = 41.57 m

Hence, the dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.

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SRRC is a pulse shaping filter used in digital communications to minimize intersymbol interference and improve the signal-to-noise ratio.

The square root raised cosine (SRRC) is a famous heartbeat molding channel utilized in computerized correspondences, especially in applications like advanced tweak and demodulation. It is intended to limit intersymbol obstruction (ISI) by restricting the data transmission of the sent sign while keeping a consistent envelope.

The SRRC channel is described by a reaction that is like the raised cosine channel, yet with a square root capability applied to the recurrence reaction. This outcomes in a smoother change between the passband and stopband, which assists with decreasing ISI and work on the sign to-clamor proportion.

The SRRC channel is usually utilized in correspondence frameworks that utilization quadrature sufficiency regulation (QAM) or stage shift keying (PSK) tweak plans, as it gives great ghastly control and heartbeat molding properties that are appropriate to these kinds of signs.

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Answer:

144 carrots

Step-by-step explanation:

Let C stand for the number of carrots that a student can plant.

We are told that carrots may be planted at a density of 9 carrots/ft^2.

Let A be the area, in ft^2, that can be planted with carrots.  The area of a rectangle is Base x Length (in feet).

We can therefore write:

C = (9 carrots/ft^2)*A

In the garden shown, the area is A = (4 ft) x (4 ft) = 16 ft^2

C = 9 carrots/ft^2)*(16 ft^2)

C = 144 carrots

So here area of square

\(\\ \rm\rightarrowtail x^2\)

So students can plant 9carrots

\(\\ \rm\rightarrowtail x^2=9\)

\(\\ \rm\rightarrowtail x=3\)

So let carrots be x

\(\\ \rm\rightarrowtail \dfrac{3}{9}=\dfrac{4}{x}\)

\(\\ \rm\rightarrowtail \dfrac{1}{3}=\dfrac{4}{x}\)

\(\\ \rm\rightarrowtail x=12\)

Answer:

3

Step-by-step explanation:

2

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

See image

Step-by-step explanation:

You need to use a common denominator in order to add fractions. The first fraction can be changed by multiplying by 3/3. The second fraction remains the same. The sum in the third line uses the two fractions with common denominators (both now have a 12 on the bottom). 8/12 can be reduced by dividing 8 and 12 by 4 to get 2/3 see image

Answer:

a) y = \(\frac{1}{2} x\)

b) y = \(\frac{5}{2}\)

Step-by-step explanation:

I. If y = 9 and x = 18

  so x is double value of y or y * 2

  y will be half of x value

 that makes y = \(\frac{1}{2}\) x

II. If x = 5, replace x with 5

    y = \(\frac{1}{2}\) (5)

    y = \(\frac{5}{2}\)

Answer:

(a).

\({ \boxed{ \sf{y = \frac{1}{2}x }}}\)

b).

\({ \boxed { \sf{y = \frac{5}{2} }}}\)

Step-by-step explanation:

explanation for (a):

\({ \sf{y \: \alpha \: x}} \\ { \sf{y = kx}} \)

when y is 9, x is 18

\({ \sf{9 = (k \times 18)}} \\ { \sf{k = \frac{1}{2} }}\)

therefore equation is:

\({ \sf{y = \frac{1}{2}x }}\)

explanation for (b):

when x is 5:

\({ \sf{y = \frac{1}{2}x }} \\ \\ { \sf{y = \frac{1}{2} \times 5}} \\ \\ { \sf{y = \frac{5}{2} }}\)

Answer:

u = 2\(\sqrt{3}\)

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin60° = \(\frac{\sqrt{3} }{2}\) , then

sin60° = \(\frac{opposite}{hypotenuse}\) = \(\frac{u}{4}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

2u = 4\(\sqrt{3}\) ( divide both sides by 2 )

u = 2\(\sqrt{3}\)

we know the median stems out of vertex N and on the half-way between L and M, so let's find the midpoint of LM firstly.

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 13 + 15}{2}~~~ ,~~~ \cfrac{ 5 + 15}{2} \right)\implies \left(\cfrac{28}{2}~~,~~\cfrac{20}{2} \right)\implies (14~~,~~10)\)

so we're really looking for the equation of a line that goes through (14,10) and (-3,-3), Check the picture below.

\((\stackrel{x_1}{14}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{14}}}\implies \cfrac{-13}{-17}\implies \cfrac{13}{17}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{\cfrac{13}{17}}(x-\stackrel{x_1}{14}) \\\\\\ y-10=\cfrac{13}{17}x-\cfrac{182}{17}\implies y=\cfrac{13}{17}x-\cfrac{182}{17}+10\implies y=\cfrac{13}{17}x-\cfrac{12}{17}\)

9514 1404 393

Answer:

  a = -2, h = -3, k = -1

  vertex = (-3, -1)

Step-by-step explanation:

Compare the given equation ...

  g(x) = -2(x +3)² -1

to the vertex form ...

  g(x) = a(x -h)² +k

You see that ...

  a = -2

  -h = +3  ⇒  h = -3

  +k = -1  ⇒  k = -1

The vertex is (h, k), so is ...

  vertex = (-3, -1)

Let's break down the given information and solve the problem step by step:

Let's assume:

The cost of the burger is 'b' dollars.

The cost of the souvenir is 's' dollars.

The cost of the pass is 'p' dollars.

According to the given information:

The burger was 1/6 as much as the souvenir. This can be expressed as: b = (1/6) * s.

The souvenir cost 3/4 the cost of the pass. This can be expressed as: s = (3/4) * p.

Erica had $4.00 left over after buying these items. This can be expressed as: b + s + p + 4 = 30.25.

Now, let's solve these equations to find the cost of each item.

Substituting the value of 's' from equation 2 into equation 1:

b = (1/6) * ((3/4) * p)

b = (3/24) * p

b = (1/8) * p

Substituting the values of 'b' and 's' into equation 3:

(1/8) * p + ((3/4) * p) + p + 4 = 30.25

Multiply through by 8 to eliminate the fraction:

p + 6p + 8p + 32 = 242

15p + 32 = 242

15p = 210

p = 210 / 15

p = 14

Substituting the value of 'p' into equation 2 to find 's':

s = (3/4) * 14

s = 10.50

Substituting the value of 'p' into equation 1 to find 'b':

b = (1/8) * 14

b = 1.75

Therefore, the cost of the burger is $1.75, the cost of the souvenir is $10.50, and the cost of the pass is $14.0

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Answer:

-1 1/3, 0.3, 1.2, 3/5,  3,  

Step-by-step explanation:

Hope I helped, can I plz have brainliest, ive never gotten one before!

Part A: The monthly payment for the truck is $595.07

Part B: Kevin will spend $63.75 when he fills the truck's 25-gallon tank.

Part C: Kevin's cost per mile is $0.304.

An annuity is a financial product that provides a stream of payments to an individual over a specified period of time. An annuity is typically purchased from an insurance company or financial institution in exchange for a lump sum of money.

An average is a mathematical value that represents a typical or central value within a set of data. There are different types of averages, including the mean, median, and mode.The mean, or arithmetic mean, is the most common type of average, and it is calculated by adding up all of the values in a data set and dividing by the number of values.

Part A:

To calculate the monthly payment for the truck, we can use the formula for the present value of an annuity:

Monthly payment = (PV * r) / (1 - (1 + r)⁽⁻ⁿ⁾)

Where:

PV = Present value of the loan (truck cost - down payment)

r = Interest rate per period (annual rate / 12)

n = Total number of periods (5 years * 12 months per year)

Using this formula, we have:

PV = $35,500 - $4,200 = $31,300

r = 6% / 12 = 0.005

n = 5 years * 12 months per year = 60

Monthly payment = ($31,300 * 0.005) / (1 - (1 + 0.005)⁽⁻⁶⁰⁾) = $595.07

Therefore, the monthly payment for the truck is $595.07.

Part B:

To calculate how much Kevin will spend when he fills the truck's 25-gallon tank, we can multiply the number of gallons by the average gas price:

Cost of filling tank = 25 gallons * $2.55/gallon = $63.75

Therefore, Kevin will spend $63.75 when he fills the truck's 25-gallon tank.

Part C:

To calculate Kevin's cost per mile, we need to first calculate how much he spends on gas per mile.

In one year, Kevin fills up his tank 2 times per month, for a total of 24 times per year. If he drives 7,500 miles in the first year, then he drives an average of 7,500 / 24 = 312.5 miles between fill-ups.

So, Kevin spends $63.75 every 312.5 miles on gas, or $0.204 per mile.

In addition to gas, Kevin spends $750 per year on insurance.

Therefore, Kevin's total cost per mile is:

Cost per mile = (gas cost per mile) + (insurance cost per year / miles driven per year)

Cost per mile = ($0.204) + ($750 / 7,500) = $0.304 per mile

Therefore, Kevin's cost per mile is $0.304.

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Yes, this sample of the trees in the county likely to be representative if each forest is the same size.

Representative sample, the sample must accurately reflect the population studied in demographics and characteristics of the chosen subjects.

For example, a representative sample will reflect only those within the study population and should not extend to those outside the study. If Jose is interested in studying the exercise habits of college athletes, only the population of college athletes should be considered for the selection of a representative sample. Jose will not choose athletes from high school or career athletes as part of his representative sample.

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Time can't be negative so we need to get absolute value of x .