nth term of quadratic sequence 3,11,25.45

Using statistics helps us make decisions based on empirical evidence, which is obtained through data analysis and inference.

Statistics provides us with a set of tools and methods to collect, analyze, and interpret data. By applying statistical techniques, we can make decisions based on evidence derived from empirical observations and measurements.

Statistics allows us to summarize and describe data, identify patterns and relationships, and draw conclusions from samples or populations. It helps us quantify uncertainty and assess the strength of evidence supporting different claims or hypotheses.

Decision-making based on statistics involves making inferences about a larger population based on the information available from a sample. By using probability theory and statistical models, we can estimate population parameters, test hypotheses, and make predictions about future events or outcomes.

Statistics provides a systematic and rigorous framework for evaluating evidence and reducing bias in decision-making. It allows us to objectively assess the reliability and validity of information, making decisions that are informed by data-driven analysis rather than intuition or anecdotal evidence.

In summary, statistics helps us make decisions based on evidence obtained through data analysis, enabling us to draw reliable conclusions, quantify uncertainty, and make informed choices in various fields such as business, medicine, social sciences, and more.

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Answer:

f(x):f(x)=2/7x-9

Step-by-step explanation:

If it is wrong than i am sorry

Answer:

42+25n

Step-by-step explanation:

\(7+5(7+5n)\\=7+35+25n\\=42+25n\)

Answer:

624 times

Step-by-step explanation:

345000/1800=191 2/3, but you can't level up 2/3 of a time, so you round up to 192. Then, you do 192*3.25, because you need to sleep 3 times and then use 1/4 of the XP from the 4th time. This gets you 624

Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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The value of x which makes the given expression 1/2(3x+4) = 1/2x true is -2

We have to simplify the given expression to find the value of x

1/2(3x + 4) = 1/2x

Cancel 1/2 from both sides

⇒ 3x + 4 = x

⇒ 2x = -4

⇒ x = -2

Hence, the value of x is -2 which makes the given expression true.

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Answer:

A) 9 x - 6 y

Step-by-step explanation:

: 5x - 6y + 4x

5x + 4x - 6y =9 x - 6 y

Answer:

\(11\)

Step-by-step explanation:

\(5 \times x - 4\)

\(5 \times 3 - 4\)

\(15 - 4\)

\(11\)

A) The rate of change in the direction of motion is approximately 2.94.

B) The direction in which the bug should move from P for the temperature to increase the fastest is in the direction of <-0.649, -0.761>.

C) The magnitude of the rate of change of temperature in that direction is given by ||∇T(2,3) · v|| = ||∇T(2,3)|| ||v|| cosθ

We can use the gradient of the temperature function to find the direction of maximum increase and the rate of change in that direction.

The gradient of T(x,y) is given by:

∇T(x,y) = <-2x/5, -y>

At point P=(2,3), the gradient is:

∇T(2,3) = <-4/5, -3>

The direction of maximum increase is given by the unit vector in the direction of the gradient. We can find this by normalizing the gradient:

u = ∇T(2,3) / ||∇T(2,3)||

Where ||∇T(2,3)|| is the magnitude of the gradient at point P:

||∇T(2,3)|| = √((-4/5)² + (-3)²) = √(16/25 + 9) = √(41/5)

Therefore,

u = <-4/5, -3> / √(41/5) = <-0.649, -0.761>

So the direction in which the bug should move from P for the temperature to increase the fastest is in the direction of <-0.649, -0.761>.

To find the rate of change in the direction of motion, we need to project the gradient onto the unit vector connecting P and Q. Let R be the position vector of the point on the line connecting P and Q that is closest to P. Then the direction of motion is given by the unit vector:

v = (Q - P) / ||Q - P||

Where ||Q - P|| is the distance between P and Q:

||Q - P|| = √((3 - 2)² + (-2 - 3)²) = √26

Therefore,

v = <1/√26, -5/√26>

The rate of change in the direction of motion is given by the dot product of the gradient and the unit vector v:

∇T(2,3) · v = (-4/5)(1/√26) + (-3)(-5/√26) = 15/√26 ≈ 2.94

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Let A = playing football, B = playing basketball,  P(A) = 32%,  P(A ∩ B) = 18% .

We are supposed to calculate the probability of playing basketball given the student plays football that is P(B|A).The probability of playing both football and basketball can be given as, P(A ∩ B) = P(B|A) * P(A).

Now, substituting the values given in the problem, we get, 18% = P(B|A) * 32%Thus, P(B|A) = 18%/32% = 9/16 = 0.5625 = 56%.Therefore, the required probability is 56% (option a).

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Answer:

$1673.25

Step-by-step explanation:

si year 1 = $1500 * 0.0385 =57.75       si yr 3 =57.75*3 = $173.25    return total = 1500+ 173.25 = $1673.25

The one decreases, the other must increase to maintain the balance.

As the level of significance, α, decreases, the probability of making a Type II​ error, β​, increases. This is because Type I and Type II errors are inversely related. Type I error occurs when we reject a true null hypothesis, while Type II error occurs when we fail to reject a false null hypothesis.

If we decrease the level of significance, α, we are essentially making it more difficult to reject the null hypothesis. This means that we are less likely to make a Type I error, but more likely to make a Type II error.

In other words, as the level of significance, α, decreases, the probability of making a Type II​ error, β​, increases because the sum of α and β always equals 1. So if one decreases, the other must increase to maintain the balance.

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Answer:

0.43715

Step-by-step explanation:

We solve using z score calculator

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = $276,000

σ is the population standard deviation = 32,000

For x = $276,000

z = 276,000 - 276,000/32000

z = 0

Probability value from Z-Table:

P(x = 276000) = 0.5

For x = $325,000

z = 325,000 - 276,000/32000

z = 1.53125

Probability value from Z-Table:

P(x = 325000) = 0.93715

The probability that the next house in the community will sell for between $276,000 and $325,000 is

P(x = 325000) - P(x = 276000)

= 0.93715 - 0.5

= 0.43715

Answer:

The expression would be (x + 3)(x - 8) and if we multiplied those together we would get x^2 - 5x - 24

Step-by-step explanation:

Answer: $3.50

Step-by-step explanation:

He came home with $3.00.

He gave Rene $1.50 which means that $1.50 was deducted from his money.

Pedro gave him $1.00 which added to his money.

Money he had therefore was:

= 3 + 1.50 - 1

= $3.50

Answer:

-3

Step-by-step explanation:

x, y  x^2,y^2

(-1,8) (3,-4)

y^2-y/x^2-x

-4-8/3-(-1)

-12/4

= -3

Answer: -3

Step-by-step explanation:

Slope can be represented as \(\frac{y_1-y_2}{x_1-x_2}\).  plug in the values to get: \(\frac{8-(-4)}{-1-3}\)  Simplify this to get: \(\frac{12}{-4}\) then -3.

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Answer:

The random variable \(\bar x\) has approximately a normal distribution because of the central limit theorem.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n ≥ 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

\(\mu_{\bar x}=\mu\)

And the standard deviation of the sample means is given by,

\(\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}\)

Let the random variable X be defined as the age of cars owned by residents of a small city.

It is provided that:

μ = 6 years

σ = 2.2 years

n = 400

As the sample selected is too large, i.e. n = 400 > 30, according to the central limit theorem the sampling distribution of the sample mean (\(\bar x\)) will be approximately normally distributed.  

Answer:

36+2w=96

2w=96-36=60

w=60/2=30

Step-by-step explanation:

perimeter is 96, that means length + length + width + width = 96.

say l is length and w is width.

since we know length is 18, 18+18+width+width = 96

36+2w=96

2w=96-36=60

w=60/2=30

Answer:

Step-by-step explanation:

perimeter of the rectangle = length x width

P = 2 (l + w)

96 = 2 (18 + w)

96 = 36 + 2w

60 = 2w

w = 60/2

w = 30 cm

We are required to calculate how many minutes does it take Autumn to walk to work now

The number of minutes does it take Autumn to walk to work now is 25.35 minutes

Time taken to walk to work = 39 minutes

Percentage decrease = 35%

Decrease in time = 35% of 39 minutes

= 35/100 × 39 minutes

= 0.35 × 39 minutes

= 13.65 minutes

Number of minutes does it take Autumn to walk to work now

= 39 minutes - 13.65 minutes

= 25.35 minutes

Therefore, the number of minutes does it take Autumn to walk to work now is 25.35 minutes

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The width of the border is 1/2 feet

From the information given, we have that;

Cherry wood of area to border and surrounded glass of area 9 square feet.

The combined area will be area of glass + area of the border made from cherry wood

The total area of coffee table would be ;

= 9 + 7 = 16 square feet.

Since the center glass piece is a square thus the surrounding border of cherry wood also would be of square shape.

So each side of the square is √16 = 4 feet

Outside of cherry border has 4 feet length and width while the inside of cherry border, which is same as the length and width of glass is 3 feet.

The difference is 4 -3 = 1 feet

Since border is on both sides therefore the width of the border= 1/2 feet

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The graph has three turns, which is an odd number, and it extends to a negative infinity.

What is the name of a polynomial graph?

A polynomial function's graph is essentially a continuous, smooth curve. You can use a few key features of this kind of graph to assist construct the curve. I'll explain how to use the polynomial function's leading term to analyze the graph's final performance.

If the number of turns is an odd integer, the functions have an even degree.

If the graph's behavior shifts to the negative infinity, the functional does have a negative leading coefficient.

Just this graph met the requirements among the options.

The graph has 3 turns (an odd number) and it goes to the negative infinity.

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Answer: 243

Step-by-step explanation:

To find f(g(9)), we need to first substitute g(9) into the function f(x), and then evaluate the resulting expression.

Given that g(x) = 3√x, we can replace x with 9 (since we're looking for g(9)) in the expression for g(x):

g(9) = 3√9

Simplifying the square root of 9, we get:

g(9) = 3 * 3

g(9) = 9

Now, we can substitute g(9) into the function f(x) = x^3/3, replacing x with 9:

f(g(9)) = (9)^3/3

Using the exponent rule for cube, we get:

f(g(9)) = 729/3

Simplifying the division, we get:

f(g(9)) = 243

So, the value of f(g(9)) is 243.

Jhon was between 6:12 p.m and 6:52 p.m. So, Jhon left home for exact 40 minutes. Using the angle made by the hands in the clock, the required value is calculated.

The general formula for finding the angle between the minute hand and the hour hand is

M = \(\frac{2}{11}\) (H × 30 ± θ)

It is given that,

Jhon left home after 6 p.m with an angle of 110° formed by the minute hand and hour hand.

So,

M = \(\frac{2}{11}\) (H × 30 - θ)

   = \(\frac{2}{11}\) (6 × 30 - 110)

   = \(\frac{2}{11}\) (180 - 110)

   = \(\frac{2}{11}\) × 70

   = 140/11

So, he left after 6:12 p.m

Jhon returned home before 7 p.m with angle of 110° formed by the minute hand and hour hand.

M = \(\frac{2}{11}\) (H × 30 + θ)

   = \(\frac{2}{11}\) (6 × 30 + 110)

   = \(\frac{2}{11}\) (180 + 110)

   = \(\frac{2}{11}\) × 290

   = 580/11

So, he returned before 6:52 p.m

Then,

The time taken for returning home = 580/11 - 140/11 = 440/11 = 40 minutes.

Therefore, he took 40 minutes to return home.

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If all the numbers coming from P= - n² + 41 are prime numbers. Yes, 41 is a prime number.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In this case, when n = 1, P = -1^2 + 41 = 40 + 1 = 41, which is a prime number.

When n = 37, P = -37^2 + 41 = -1368, which is not a prime number since it is divisible by 2, -2, 3, -3, 4, and -4. Therefore, when n = 37, P is not a prime number.

If we choose n = 39, P = -39^2 + 41 = -1520, which is not a prime number since it is divisible by 2, -2, 4, -5, 8, -10, 19, -20, 38, and -76. Therefore, when n = 39, P is not a prime number.

If we choose n = 40, P = -40^2 + 41 = -1599, which is not a prime number since it is divisible by 3, -3, 7, -9, 21, and -63. Therefore, when n = 40, P is not a prime number.

If we choose n = 41, P = -41^2 + 41 = -1680, which is not a prime number since it is divisible by 2, -2, 3, -4, 5, -6, 8, -10, 12, -15, 20, -24, 30, -40, 60, and -120. Therefore, when n = 41, P is not a prime number.

Therefore, not all numbers obtained from P = -n^2 + 41 are prime numbers.

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Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

The value of the length f is 6. 7

To determine the value, we have to know the different trigonometric identities.

These trigonometric identities are enumerated as;

To determine the length of f

Let us use the tangent identity, we have that;

tan θ = opposite/adjacent

substitute the values, we have;

tan 24 = f/15

Multiply the values, we get;

f = 0. 4452(15)

multiply the values

f = 6. 7

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Answer:

The pairs of lines that do not intersect or meet at any point are called parallel lines. These lines lie on the same plane but do not intersect. The line segments or rays that lie on the same plane but do not intersect are also parallel.

Step-by-step explanation:

Answer

A parallel line is a position of two lines on a plane that does not have a point of intersection even though the two lines are extended.Geometrically, parallel lines will never meet each other because they have the same slope (gradient). Parallel lines do not have to be the same length

Answer:

B

Step-by-step explanation:

Here, we are to find the odds against drawing a purple or yellow marble.

Mathematically, the odds against drawing a particular marble color = 1 - the probability of drawing that particular marble color

probability of drawing a purple colored marble = number of purple colored marbles/total number of marbles

= 84/(84 + 42 + 21 + 14 + 7) = 84/168 = 1/2

So the odds against drawing a purple colored marble = 1 - 1/2 = 1/2

The odds against drawing a yellow marble color = 1 - probability of drawing a yellow colored marble

Probability of drawing a yellow colored marble = number of yellow marbles/total number of marbles = 14/168 = 1/12

So the probability of drawing a yellow colored marble or purple colored marble = 1/12 + 1/2 = 7/12

Now, the odds against drawing either of the two = 1 - the probability of drawing either of the 2 = 1 -7/12 = 5/12

or simply put 5 to 12

Answer:

yea

Step-by-step explanation:

Answer:

y=41^2

Step-by-step explanation:

Answer: y=1

Step-by-step explanation: You’ll need to isolate the variable by dividing each side by factors that don't contain the variable.