Match each polynomial function with its leading coefficient.

Column A
1.
P(x) = (x + 2) (2x - 3) (4x +7):
P(x) = (x + 2) (2x - 3) (4x +7)
2.
P(x) = 1/2(x - 2) (2x - 3) (4x + 7):
P(x) = 1/2(x - 2) (2x - 3) (4x + 7)
3.
P(x)= 5(x - 2) (2x - 3) (4x + 7):
P(x)= 5(x - 2) (2x - 3) (4x + 7)
4.
P(x) = -(x - 2) (2x - 3) (4x + 7):
P(x) = -(x - 2) (2x - 3) (4x + 7)
5.
P(x) = 1/4(X + 2) (2x - 3) (4x + 7):
P(x) = 1/4(X + 2) (2x - 3) (4x + 7)
Column B
a.2
b.8
c.-8
d.4
e.40

Answer:

-4409/100

bcoz there is decimal next to 2 numbers

Answer:

53

Step-by-step explanation:

5/1x2+6x7

5x2+6x7

10+6x7

10+42

53

Answer:

y= mx+c

-3=-4(6)+c

-3=-24+c

-3+24=c

21=c

c=21

y=-4x+21

The probability that one of the scores in the sample is less than 1484 is 0.2437 .

a)Given that mean u = 1403

standard deviation σ = 200

sample size n = 32

P(x>1484) = P(X-u/σ > 1484-1403/200)

                = P (z > 0.405)

P(x>1484) = 0.2437 .

hence the probability that one score is greater than 1484 is 0.405 .

b) Now we have to find the average of the scores of 48 samples.

P(x>1484)

= P(x-μ/ σ/√n> 1484-1403 /200/√48)

= P(z>2.805.)

Now we will use the normal distribution table to calculate the p value to be 0.002516.

p-value = 0.0025

Normal distributions are very crucial to statistics because not only they are commonly used in the natural and social sciences but also to describe real-valued random variables with uncertain distributions.

They are important in part because of the central limit theorem. This claim states that, in some cases, the average of many samples (observations) of a random process with infinite mean and variance is itself a random variable, whose distribution tends to become normal as the number of samples increases.

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The surface area of the prism shown in the figure is equal to 480 square inches. (Right choice: B)

In this problem we need to determine the surface area of a prism, that is, the sum of the areas of the five faces of the prism. There are three rectangles and two right triangles as faces of the prism, whose area formulas are described below:

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Where:

Now we proceed to determine the areas of all faces of the prism:

A = (8 in) · (9 in) + 2 · 0.5 · (15 in) · (8 in) + (9 in) · (15 in) + (17 in) · (9 in)

A = 480 in²

The prism shown in the figure has a surface area of 480 square inches.

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The parametrization of the circle with the given conditions is:
x(t) = -1 + 4 * cos(t - π/2)
y(t) = 1 + 4 * sin(t - π/2)

To find a parametrization of the circle of radius 4 in the xy-plane, centered at (-1, 1), oriented counterclockwise, and with the point (3, 1) corresponding to t = 0, we can use the following parametric equations,
x(t) = -1 + 4 * cos(t)
y(t) = 1 + 4 * sin(t)
However, we need to adjust the starting point of the parameter t to correspond to the point (3, 1). To do this, we need to find the angle that corresponds to this point on the circle. Since it lies on the positive x-axis, the angle is 0 degrees or 0 radians. We will introduce a phase shift in the trigonometric functions to account for this:
x(t) = -1 + 4 * cos(t - π/2)
y(t) = 1 + 4 * sin(t - π/2)

So, the parametrization of the circle with the given conditions is,
x(t) = -1 + 4 * cos(t - π/2)
y(t) = 1 + 4 * sin(t - π/2)

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The parametrization of the circle with the given conditions is:
x(t) = -1 + 4 * cos(t - π/2)
y(t) = 1 + 4 * sin(t - π/2)

To find a parametrization of the circle of radius 4 in the xy-plane, centered at (-1, 1), oriented counterclockwise, and with the point (3, 1) corresponding to t = 0, we can use the following parametric equations,
x(t) = -1 + 4 * cos(t)
y(t) = 1 + 4 * sin(t)
However, we need to adjust the starting point of the parameter t to correspond to the point (3, 1). To do this, we need to find the angle that corresponds to this point on the circle. Since it lies on the positive x-axis, the angle is 0 degrees or 0 radians. We will introduce a phase shift in the trigonometric functions to account for this:
x(t) = -1 + 4 * cos(t - π/2)
y(t) = 1 + 4 * sin(t - π/2)

So, the parametrization of the circle with the given conditions is,
x(t) = -1 + 4 * cos(t - π/2)
y(t) = 1 + 4 * sin(t - π/2)

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Answer:

Rm5.40

Step-by-step explanation:

First, 20/100 × Rm4.50 = Rm0.90. Second, Rm4.50 + Rm 0.90 = Rm5.40

Please give me brainliest hehe.

Answer: 0.90 BUT IF YOU ROUND UP TO HOLE DOLLARS THEN YOUR TIP WOULD BE 1 DOLLAR

Step-by-step explanation: THAT IS YOUR ANSWER HOPE I HELPED :D

In order for the system of equations to be a consistent system, the value of k must be equal to -4.

To determine the value of k that makes the system of equations consistent, we can use the method of elimination or substitution. Let's use the method of elimination.

First, we can multiply the first equation by 5, the second equation by -1, and the third equation by 2 to make the coefficients of x in the three equations cancel each other out when added together.

The modified system of equations becomes:

5x - 10y + 20z = 20

5x - 9y + 22z = 16

-4x + 6y - 20z = 2k

Now, let's subtract the first equation from the second equation:

(5x - 9y + 22z) - (5x - 10y + 20z) = 16 - 20

y + 2z = -4

Next, let's add this equation to the third equation:

(-4x + 6y - 20z) + (y + 2z) = 2k - 4

-4x + 7y - 18z = 2k - 4

For the system of equations to be consistent, there must be no contradictions or inconsistencies. This means that the equations must be linearly dependent, and the last equation must be a multiple of the second equation.

Comparing the last equation (-4x + 7y - 18z = 2k - 4) with the second equation (y + 2z = -4), we can see that the two equations will be dependent and consistent if 2k - 4 is equal to 0.

2k - 4 = 0

2k = 4

k = 2

Therefore, in order for the system of equations to be a consistent system, the value of k must be equal to -4.

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You can use the following formula:

A = (b*h)/2

Where:

b = Base = 12cm

h = Height = 6cm

So:

A = (12*6)/2 = 72/2 = 36cm²7

Answer: $732

Step-by-step explanation:

If the band performs 3 wedding a week where they make $350 per performance, the total revenue they make is:

= 350 * 3

= $1,050

Cost in total will be:

= 106 * 3

= $318

Profit = Revenue - Cost

= 1,050 - 318

= $732

a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.

The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

     = 200 / √400

     = 200 / 20

     = 10

To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:

For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.

For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.

We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.

(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).

The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).

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Answer:

Because (-x²+2x+3)+(-x²-2x-1) = -x²+2x+3-x²-2x-1 = -2x²+2

Step-by-step explanation:

Hope It Helps!

A line graph is used when an independent variable is a continuous quantitative variable. A line graph is a type of chart used to represent data over time with the help of lines connecting various data points.

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The value of f(x) = 3x² - 2x at x = 4 is 40.

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math.

Here, the given function;

    f(x) = 3x² - 2x

put the value of x = 4, we get

     f(4) = 3 X 4² - 2 X 4

     f(4) = 3 X 16 - 8

      f(4) = 48 - 8

     f(4) = 40

Thus, the value of f(x) = 3x² - 2x at x = 4 is 40.

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The solution to the system of equations graphed below is,

⇒ (0, 1)

Since, We have to given that;

Two system of equations are,

⇒ g (x) = 3x + 2

⇒ f (x) = |x - 1| + 1

Here, The graph of both system of equation are shown in graph.

We know that;

In a graph, the solution of system of equation are represented by a intersection point of both graph.

Here, In the graph of system of equation,

Intersection point is,

⇒ (0, 1)

Hence, The solution to the system of equations graphed below is,

⇒ (0, 1)

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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:

im sorry i dont remember that one

Step-by-step explanation:

1. Analytics is important to business in today's society because of the following reasons 2. I use analytics on a regular basis in my personal and professional life. 3.  To become an advocate for analytics in business, an individual must do the following Become an Expert, Share Your Insights. 4. To improve one's analytical mindset, the following areas must be worked upon, Data Gathering, Analysis, Visualization, Communication.

Increased Efficiency:

Analytics are used to identify areas of waste and inefficiency, allowing companies to improve processes, save money, and become more productive.

Customer Intelligence:

Analytics can assist businesses in gaining a deeper understanding of their clients and what they need. This information can be used to develop new goods, improve current ones, and create targeted marketing campaigns.

Operations Management:

Businesses may utilise analytics to keep track of production and inventory levels, as well as forecast demand and identify areas for improvement. This can help businesses reduce waste, lower costs, and improve efficiency.

Risk Management:

Analytics can assist companies in identifying potential risks and developing strategies to mitigate them.

2. I use analytics on a regular basis in my personal and professional life. To better understand customers and forecast trends, I utilise data analytics in my job as a digital marketing professional. I track engagement, conversions, and other metrics to determine how our marketing campaigns are doing and how we can improve them.In my personal life, I use analytics to monitor my physical fitness. I monitor my calorie intake, exercise routine, and sleep patterns to better understand my health and make informed decisions about how to stay healthy.

3.  To become an advocate for analytics in business, an individual must do the following:

Become an Expert:

To persuade others about the importance of analytics, you must first understand it thoroughly. Take courses, read books and articles, and work on analytics tasks.Build a Network: Build a network of like-minded people who share your interests in analytics. Attend conferences, join discussion groups, and follow industry experts.

Share Your Insights:

Share your findings with others in your organisation. You can use analytics to discover opportunities for growth or to mitigate risks.

4. To improve one's analytical mindset, the following areas must be worked upon:

Data Gathering: Make sure that you have access to high-quality data that is relevant to your work.

Analysis:

Develop analytical skills that will allow you to turn raw data into actionable insights

Visualization:

Create visualisations that communicate complex data in an easy-to-understand format.

Communication:

Be able to present your findings in a way that is easy for others to understand.

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Answer:

60 inches²

Step-by-step explanation:

Unit test

Answer:

200miles

Step-by-step explanation:

Given data

Rent-For-Less

charges $50 for a deposit and $1.25 per mile

let the number of miles be x

and the total distance be y

y=50+1.25x-------------1

Cheap Rides

charges $1.30 per mile and a $40 deposit

y=40+1.30x-------------2

Equate 1 and 2 above we have

50+1.25x=40+1.30x

collect liker terms

50-40= 1.3x-1.25x

10=0.05x

divide both side by 0.05

x= 10/0.05

x=200 miles

Hence the distance in miles is 200miles

If the measure of arc HJ is 66 degrees, find the m<HIJ 33. 33 degrees.

An angle at the circumference of a circle exists half the angle at the center standing on the identical arc. The angle of circumference m∠HIJ is 33°.

An angle at the circumference of a circle exists half the angle at the center standing on the identical arc. - Two angles at the circumference standing on the exact arc stand equivalent.

Given: arc HJ = 66°

and \($m\angle HIJ=\frac{1}{2}{arcHJ}\right.$\)

\($m \angle H I J=\frac{1}{2} \times 66^{\circ}$\)

angle of circumference exists \($\frac{1}{2}$\) of \($m\angle L H I J=33^{\circ} \quad$\) central angle.

Therefore, m∠HIJ is 33°

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Answer:

3 is in the ones place

0 is in the tens place

9 is in the thousandths place

Step-by-step explanation:

thousands, hundreds, tens, ones (DECIMAL) tenths, hundredths, thousandths

I'm assuming the surfaces are the cylinder \(x^2+y^2=16\) and the plane \(z=2x+3y\).

Let \(x=4\cos(t)\) and \(y=4\sin(t)\). Then

\(z=2x+3y=8\cos(t)+12\sin(t)\)

We can simplify this using the identity

\(R \cos(\alpha + \beta) = R \cos(\alpha)\cos(\beta) - R \sin(\alpha) \sin(\beta)\)

Let \(\alpha=t\), then

\(R \cos(t + \beta) = R \cos(t)\cos(\beta) - R \sin(t) \sin(\beta) = 8\cos(t)+12\sin(t)\)

\(\implies \begin{cases}R\cos(\beta) = 8 \\ R\sin(\beta) = -12\end{cases}\)

We have

\(\left(R\cos(\beta)\right)^2 + \left(R\sin(\beta)\right)^2 = 8^2 + (-12)^2 \implies R^2 = 208 \implies R = 4\sqrt{13}\)

and

\(\dfrac{R\sin(\beta)}{R\cos(\beta)} = -\dfrac{12}8 \implies \tan(\beta) = -\dfrac32 \implies \beta = -\arctan\left(\dfrac32\right)\)

Then the vector function for the curve is

\(\vec r(t) = 4\cos(t)\,\vec\imath + 4\sin(t)\,\vec\jmath + 4\sqrt{13}\,\cos\left(t - \arctan\left(\dfrac32\right)\right)\,\vec k\)

with \(0\le t\le2\pi\).

The total number of ways to distribute all the fruits to the 30 children, ensuring each child who prefers apples gets at least 2 apples and each child who prefers oranges gets at least 2 oranges, is given by the product of C(29, 9) and C(59, 19).

To find the total number of ways, we can consider the distribution of apples and oranges separately. For the children who prefer apples, we need to distribute 20 apples among 10 children, with each child receiving at least 2 apples. This can be calculated using the stars and bars combinatorial technique. Similarly, for the children who prefer oranges, we need to distribute 40 oranges among 20 children, with each child receiving at least 2 oranges.

The number of ways to distribute the apples can be calculated as C(20+10-1, 10-1) = C(29, 9). Likewise, the number of ways to distribute the oranges can be calculated as C(40+20-1, 20-1) = C(59, 19). To find the total number of ways to distribute both fruits, we multiply these two values together.

Therefore, the total number of ways to distribute all the fruits to the 30 children while satisfying the given conditions is C(29, 9) x C(59, 19).

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Answer:

142 l/hr

Step-by-step explanation:

Answer:142

Step-by-step explanation:

A number that represents the property of the sample is the statistics.

Statistics refer to that number that describes a particular property of a sample set of numbers. It is the common property shared by all the numbers of the sample set. It involves the collection of data and information and then categorizing them according to their properties and inferences.

'Mean and proportion' is mathematical calculations that can be carried out on statistic number sets.

Mean refers to the average of the number set that is provided to us. It is calculated by adding the numbers and dividing them by the number of terms.

Proportion refers to the fraction of the number set according to some characteristics shared by the numbers.

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