what is 5x^2 + 6x - 10 subtracted from 7x2 -9x - 3

To show that the location parameter of the minimum extreme value distribution is the mode of the distribution, we set the first derivative of the density function, f(t), equal to zero and solve for t. The resulting value of t is the mode of the distribution.

The minimum extreme value distribution is characterized by its density function, which is given by:

f(t) = (1/β) * exp((t-α)/β) * exp(-exp((t-α)/β))

where α is the location parameter and β is the scale parameter. The mode of a distribution represents the value at which the density function has the highest point.

To find the mode of the minimum extreme value distribution, we differentiate the density function with respect to t and set it equal to zero:

d/dt [f(t)] = (1/β) * exp((t-α)/β) * exp(-exp((t-α)/β)) * (1/β) * (1/β) * exp((t-α)/β)

Setting the above expression equal to zero, we can simplify it to:

exp((t-α)/β) * exp(-exp((t-α)/β)) = (1/β)^2

By taking the logarithm of both sides, we have:

(t-α)/β - exp((t-α)/β) = -2 * log(β)

This equation does not have a closed-form solution. Therefore, to find the mode, we typically use numerical methods such as iterative algorithms or optimization techniques.

In conclusion, the mode of the minimum extreme value distribution can be obtained by setting the first derivative of the density function equal to zero and solving the resulting equation. However, due to the lack of a closed-form solution, numerical methods are generally used to find the mode.

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The factors of a polynomial function are the zeros of the function

It is true that x - 3 is a factor of m(x) = x^3 - x^2 - 5x - 3

The function is given as:

m(x) = x^3 - x^2 - 5x - 3

The factor is given as:

x - 3

Set the factor to 0

x - 3 = 0

Solve for x

x = 3

Substitute 3 for x in the function

m(3) = 3^3 - 3^2 - 5(3) - 3

Evaluate

m(3) =0

Since the value of m(3) is 0, then x - 3 is a factor of m(x) = x^3 - x^2 - 5x - 3

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Answer:

x=10.50

Step-by-step explanation:

14 =  5

________
29.40 = x

cross multiply - 29.40 x 5 = 147

Then u would divide like this

14/14=1      147/14=10.5

Answer:

18 servings

Step-by-step explanation:

If one serving is 1/3 cup, one cup is 3 servings. Therefore, we can multiply 3 x 6 for an answer of 18 servings

There are 1820 different groups of applicants for 4 management trainee positions, 126 different groups of trainees consisting entirely of women, and a 0.0692 probability that the trainee class will consist entirely of women.

The number of different groups of applicants that can be selected for the four management trainee positions can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of applicants (16 in this case) and r is the number of positions to be filled (4 in this case).

So the number of different groups of applicants that can be selected is:

16C4 = 1820

Therefore, there are 1820 different groups of applicants that can be selected for the four management trainee positions.

The number of different groups of trainees that would consist entirely of women can be calculated using the combination formula again, but this time we are selecting all 4 positions from the 9 female applicants:

9C4 = 126

Therefore, there are 126 different groups of trainees that would consist entirely of women.

Assuming that all groups of four are equally likely to be selected, the probability that the trainee class will consist entirely of women can be calculated by dividing the number of different groups of trainees that consist entirely of women (126) by the total number of different groups of applicants (1820):

Probability = 126 / 1820 = 0.0692

So the probability that the trainee class will consist entirely of women is 0.0692 (rounded to four decimal places).

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The percentage of the population in decimal is p=0.42

The mean of the sample of the binomial distribution=75.6

The standard deviation of the sample of the binomial distribution=6.622

How to convert a decimal to a percentage?

To convert a decimal number into a percentage value, multiply the decimal by 100.

What is binomial distribution?

The binomial distribution gives out either success or failure as two possible results in an experiment, is the discrete probability distribution used in probability theory and statistics.

Given that,

p = 42% = 0.42

q = 1 - p = 1 - 0.42 = 0.58

n = 180

Using the binomial distribution,

mean = \(n \times p\) = \(180 \times 0.42\) = 75.6

standard deviation = \(\sqrt{n \times p \times q}\) = \(\sqrt{180 \times 0.42 \times 0.58}\) = 6.622

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The percentage of the population in decimal is p=0.42

The mean of the sample of the binomial distribution=75.6

The standard deviation of the sample of the binomial distribution=6.622

How to convert a decimal to a percentage?

To convert a decimal number into a percentage value, multiply the decimal by 100.

What is binomial distribution?

The binomial distribution gives out either success or failure as two possible results in an experiment, is the discrete probability distribution used in probability theory and statistics.

Given that,

p = 42% = 0.42

q = 1 - p = 1 - 0.42 = 0.58

n = 180

Using the binomial distribution,

mean =   75.6

standard deviation =  6.622

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In a wheel game with eight equally spaced sectors, Keisha's chances of winning a reward on both spins are 1/16.

Probability—the possibility that an occurrence will happen—is calculated by dividing here the same number of favorable outcomes by the total number of possible outcomes. A coin toss serves as the most simple instance. If you flip a coin, there are only two possible outcomes: heads or tails.

The spinners will get a reward each everytime she lands on white. She will spin the wheel twice.

Here, there are two instances of such color white in the wheel, and there are a total of eight sectors. the likelihood that white will appear in the spin for the first time is,

P = 2/8

P = 1/4

The second case's circumstances are the same. In this instance, the outcomes including both wheel revolutions are independent of one another.

According to the product rule, the likelihood that a white sector will both spin and emerge is,

P = 1/4 * 1/4

P = 1/16

In a wheel game with eight equally spaced sectors, Keisha has a 1/16 chance of winning a reward on both spins.

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The complete question is-

Keisha is playing a game using a wheel divided into eight equal sectors, as shown in the diagram. Each time the spinner lands on white, she will win a prize. If she spins this wheel twice, what is the probability she will win a prize on both spins? Please show all steps!

A vertical stretch of scale factor 2, followed by a translation of 4 units left and 1 unit down is written as:

g(x) = 2*f(x + 4) - 1

For a general function f(x), a vertical stretch of scale factor K is written as:

g(x) = K*f(x).

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:

g(x) = 2*f(x)

Then we translate it 4 units left:

g(x) = 2*f(x + 4)

Then we translate 1 unit down:

g(x) = 2*f(x + 4) - 1

This is the equation for the transformation.

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Answer:

3x² - 21x + 30

Step-by-step explanation:

y = 3(x - 5)(x - 2) ← expand factors using FOIL

  = 3(x² - 7x + 10) ← distribute parenthesis by 3

y = 3x² - 21x + 30 ← in standard form

Answer:

x=3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

To construct a 98% confidence interval for B₁, we can use the t-distribution since the sample size is small (n = 12).

Given the sample mean (B₁ = 46), sample standard deviation (s = 5.7), and sum of squares (SSzz = 57), we can calculate the confidence interval.

The formula for a confidence interval is:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

For a 98% confidence level and n = 12, the critical value is approximately 2.681 (obtained from a t-distribution table).

The standard error is calculated as the sample standard deviation divided by the square root of the sample size (s / √n).

Plugging in the values:

Standard Error = 5.7 / √12 ≈ 1.647

Confidence Interval = 46 ± (2.681 * 1.647)

Therefore, the 98% confidence interval for B₁ is approximately (42.21, 49.79).

In conclusion, we can be 98% confident that the true value of B₁ falls within the range of 42.21 to 49.79 based on the given sample data.

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The value of F'(0) = 42

Consider:

y = f(g(x))

Then by the chain rule the derivative is:

f'(g(x)) . g'(x) .Thus the derivative of y = f(g(h(x)))  will be derived as being:

f'(g(h(x))) is derivative of g(h(x))

f'(g(h(x))) . g'(h(x)). h'(x)

If we return our attention to the problem at hand, we get:

F'(x) =  f'(7f(6f(x))) .7f'(6f(x)). 6f'(x)

F'(0) =   f'(7f(6f(0))) .7f'(6f(0)). 6f'(0)

Substituting our knowns:

F'(0) = f' (7f(0)). 7f'(0) . 6(1)

F'(0) = f'(0). 7(1) .6

F'(0) = 1 . 7 . 6

F'(0) = 42.

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Answer:

hope this helps you.......

Step-by-step explanation:

sorry for the bad picture

hope it helps you

have a good day

To find the hypotenuse of a right triangle using trigonometry, we can utilize the Pythagorean theorem and the trigonometric ratios of sine, cosine, or tangent. Here's a step-by-step explanation:

1. Identify the right triangle: Ensure that the triangle has a right angle, which is a 90-degree angle.

2. Label the sides: Identify the two sides of the right triangle that are not the hypotenuse. These sides are typically referred to as the adjacent side and the opposite side.

3. Choose the appropriate trigonometric ratio: Depending on the information you have, select the appropriate trigonometric ratio that relates the sides you know.

- If you have the adjacent side and the hypotenuse, use cosine: cosθ = adjacent/hypotenuse.

- If you have the opposite side and the hypotenuse, use sine: sinθ = opposite/hypotenuse.

- If you have the opposite side and the adjacent side, use tangent: tanθ = opposite/adjacent.

4. Substitute the known values: Plug in the values you have into the trigonometric equation and solve for the unknown side (hypotenuse).

5. Apply the Pythagorean theorem: If you don't have the hypotenuse directly but know the lengths of both the adjacent and opposite sides, you can use the Pythagorean theorem, which states that the sum of the squares of the two legs (adjacent and opposite sides) is equal to the square of the hypotenuse. The formula is a² + b² = c², where c represents the hypotenuse.

6. Simplify and calculate: After substituting the known values into the equation, simplify and solve for the hypotenuse.

By following these steps and applying the appropriate trigonometric ratio or the Pythagorean theorem, you can find the length of the hypotenuse in a right triangle using trigonometry.

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Answer: ≥ without the line on the bottom.

Step-by-step explanation:

I am assuming the expression you are talking about are

\(3w^{2} +1\) and \(10w+8\).

If we were to replace w with 4 and calculate, we will find the answer:

\(3*4^{2} +1=3*16+1=48+1=49\)

\(10*4+8=40+8=48\)

Since the first expression, \(3w^{2} +1\), is bigger than the second expression, the correct symbol to use is ≥ without the line on the bottom.

Answer:

What reasons might venita give for saying that the 1916 coin is most likely in her bag? Sherelle claims that she has 26 which is closer to 16 hence her chances are more.

Step-by-step explanation:

a) To obtain the potential pressure drop in the wellbore, we can use the hydrostatic pressure equation.

The potential pressure drop is equal to the pressure gradient multiplied by the length of the wellbore. The pressure gradient can be calculated using the equation: Pressure gradient = (density of oil × acceleration due to gravity) × sin(θ), where θ is the deviation angle of the wellbore from horizontal flow. In this case, the pressure gradient would be (48 lbm/ft^3 × 32.2 ft/s^2) × sin(15°). Multiplying the pressure gradient by the wellbore length of 6,000 ft gives the potential pressure drop.

b) To determine the frictional pressure drop in the wellbore, we can use the Darcy-Weisbach equation. The Darcy-Weisbach equation states that the pressure drop is equal to the friction factor multiplied by the pipe length, density, squared velocity, and divided by the pipe diameter. However, to calculate the friction factor, we need the Reynolds number. The Reynolds number can be calculated as (density × velocity × diameter) divided by the oil viscosity. Once the Reynolds number is known, the friction factor can be determined. Finally, using the friction factor, we can calculate the frictional pressure drop.

c) To calculate the in-situ oil velocity, we need to consider the total volume of the pipe, including both oil and gas. The total pipe volume is calculated as the pipe cross-sectional area multiplied by the wellbore length. Subtracting the gas volume from the total volume gives the oil volume. Dividing the oil volume by the total time taken by the oil to flow through the pipe (converted to seconds) gives the average oil velocity.

d) The flow regime of the two-phase flow can be determined based on the oil and gas mixture properties and flow conditions. Common flow regimes include bubble flow, slug flow, annular flow, and mist flow. These regimes are characterized by different distribution and interaction of the oil and gas phases. To determine the specific flow regime, various parameters such as gas and liquid velocities, mixture density, viscosity, and surface tension need to be considered. Additional information would be required to accurately determine the flow regime in this scenario.

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Let's assume the height of the rectangle is h cm. According to the problem, the base is 1 cm more than the height, so the base would be (h + 1) cm. The formula for the area of a rectangle is given by A = length × width.

Given that the area is 100 cm², we can write the equation as follows:

100 = h × (h + 1)

To solve this equation using a trial and improvement method, we can start by assuming a value for h and check if it satisfies the equation. Let's try h = 9:

100 = 9 × (9 + 1)

100 = 9 × 10

100 = 90

Since 90 is not equal to 100, we can try a different value. Let's try h = 10:

100 = 10 × (10 + 1)

100 = 10 × 11

100 = 110

Again, 110 is not equal to 100. We can continue this process until we find a value of h that satisfies the equation. Let's try h = 9.5:

100 = 9.5 × (9.5 + 1)

100 = 9.5 × 10.5

100 = 99.75

Now, 99.75 is close to 100 but not exactly. Let's try h = 9.6:

100 = 9.6 × (9.6 + 1)

100 = 9.6 × 10.6

100 = 101.76

101.76 is greater than 100, so we can conclude that the value of h is closer to 9.5 than 9.6. Therefore, the value of h, correct to 1 decimal place, is approximately 9.5 cm.

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To determine the amount in Tina's account after 25 years, we can calculate the future value of her contributions and the employer's matching contributions, taking into account the interest rate of her 401(k) plan.

Given information:

Tina contributes 9.5% of her monthly salary towards her 401(k).

Her employer matches her contribution up to 5.4% of her annual salary.

The interest rate of her 401(k) is 8.1% compounded monthly.

Her monthly salary is $2,461.

To calculate the future value, we can use the formula for compound interest:

FV = P * (1 + r/n)^(n*t)

Where:

FV = Future Value

P = Principal (initial investment or contribution)

r = Annual interest rate (as a decimal)

n = Number of compounding periods per year

t = Number of years

Let's calculate the future value step by step:

Calculate Tina's monthly contribution:

Monthly contribution = 9.5% * $2,461 = $233.995

Calculate Tina's annual salary:

Annual salary = $2,461 * 12 = $29,532

Calculate Tina's employer's matching contribution:

Matching contribution = 5.4% * $29,532 = $1,595.728

Calculate the total contribution per month:

Total contribution per month = Monthly contribution + Employer's matching contribution

Total contribution per month = $233.995 + $1,595.728 = $1,829.723

Therefore, the amount in Tina's account after 25 years is approximately $347,269.59.

From the provided answer choices, the closest option is d. $347,269.59.

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The probability that all remaining balls are white is equal to the number of white balls divided by the total number of balls in the urn.

To find the probability that all remaining balls in the urn are white, we can consider the following scenario: Let's assume there are initially n white balls and m black balls in the urn, where n and m are positive integers. The total number of balls in the urn is n + m. The first ball withdrawn can be either white or black, with probabilities of n/(n+m) and m/(n+m), respectively. If the first ball withdrawn is white, there are now n-1 white balls and m black balls remaining in the urn. The probability that the remaining balls are all white is the same as the probability that all remaining balls are white in an urn with n-1 white balls and m black balls. If the first ball withdrawn is black, there are now n white balls and m-1 black balls remaining in the urn. The probability that the remaining balls are all white is the same as the probability that all remaining balls are white in an urn with n white balls and m-1 black balls. We can express this probability recursively as follows: P(n, m) = (n/(n+m)) * P(n-1, m) + (m/(n+m)) * P(n, m-1) . The base cases for this recursion are: P(n, 0) = 1 (if there are no black balls remaining, then all the remaining balls are white). P(0, m) = 0 (if there are no white balls remaining, then it is not possible for all the remaining balls to be white). Using this recursive formula and considering the base cases, we can calculate the probability that all remaining balls are white in the urn.

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A rock that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge is a(n)  ventifact:

A rock refers to the solid portion of the earth crust which contains minerals. There are three types of rocks; The sedimentary rock: They are formed from dead plants, dead animals, sand etc.

The metamorphic rock: They are formed from previously existing rocks. The igneous rock: They are formed from the solidification of the molten magma.

Hence, ventifact are rock  that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge.

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By using the concept of maxima, it can be calculated that

Length of the  rectangle of perimeter 72 m with maximum area is 18 m

Breadth of the  rectangle of perimeter 72 m with maximum area is 18 m

What is maxima of a function?

Maxima of a function gives the maximum value of the function in a given interval or in the whole domain.

Let the length of the rectangle be l m and width of the rectangle be w m

Perimeter (P) = 2(l + w)

By the problem,

2(l + w) = 72

l + w = \(\frac{72}{2}\)

l + w = 36

w = 36 - l

Area (A) = l \(\times\) w

A = l \(\times\) (36 - l) = \(36l - l^2\)

Differentiation with A with respect to l

\(\frac{dA}{dl} = 36 - 2l\)

For maximum area,

\(\frac{dA}{dl} = 0\)

36 - 2l = 0

2l = 36

l = \(\frac{36}{2}\)

l = 18 m

\(\frac{d^2A}{dl^2} = -2 < 0\)

Hence area is maximum

w = 36 - 18 = 18 m

Length of the  rectangle of perimeter 72 m with maximum area is 18 m

Breadth of the  rectangle of perimeter 72 m with maximum area is 18 m

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Answer:

Part A: Missing Numbers are 64 and 7 going downwards

Part B: Make a TABLE representing how much money they made for 5, 6, 8 hours which they made $64

Part C: ??

Step-by-step explanation:

Answer:

-20y+15

Step-by-step explanation:

The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

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The computed values are:

u + v = (-3, -2)

v + u = (-3, -2)

5u = (10, -15)

2u + 3v = (-11, -3)

2u + 4w = (0, 2, 0)

u - v + 2w = (5, 0, 0)

|v + w| = 7.95

Vector addition is the operation of adding two vectors together to obtain a new vector. It is performed by adding the corresponding components of the vectors. For example, if we have two vectors u = \((u_1, u_2, u_3)\) and v = \((v_1, v_2, v_3)\), their sum u + v is given by \((u_1 + v_1, u_2 + v_2, u_3 + v_3)\).

Scalar multiplication is the operation of multiplying a vector by a scalar (a real number). It is performed by multiplying each component of the vector by the scalar. For example, if we have a vector u = \((u_1, u_2, u_3)\) and a scalar k, their product k * u is given by \((k * u_1, k * u_2, k * u_3\)).

Both vector addition and scalar multiplication are fundamental operations in linear algebra and are used to manipulate and combine vectors in various applications.

To compute the given expressions, we perform vector addition and scalar multiplication as follows:

u + v =

\(= (2, -3) + (-5, 1) \\= (2 - 5, -3 + 1) \\= (-3, -2)\)

v + u =

\(=(-5, 1) + (2, -3) \\= (-5 + 2, 1 - 3) \\= (-3, -2)\)

5u =

\(= 5 * (2, -3) \\= (5 * 2, 5 * -3)\\ = (10, -15)\)

2u + 3v =

\(=2 * (2, -3) + 3 * (-5, 1) \\= (4, -6) + (-15, 3)\\ = (4 - 15, -6 + 3) \\= (-11, -3)\)

2u + 4w =

\(= 2 * (2, -3) + 4 * (-1, 2, 3/2) \\= (4, -6) + (-4, 8, 6)\\ = (4 - 4, -6 + 8, -6 + 6)\\ = (0, 2, 0)\)

u - v + 2w =

\(= (2, -3) - (-5, 1) + 2 * (-1, 2, 3/2) \\= (2, -3) + (5, -1) + (-2, 4, 3) \\= (2 + 5 - 2, -3 - 1 + 4, 0 - 3 + 3) \\= (5, 0, 0)\)

|v + w| =

\(= |(-5, 1) + (-1, 2, 3/2)| \\= |(-5 - 1, 1 + 2, 0 + 3/2)| \\= |(-6, 3, 3/2)| \\= \sqrt{((-6)^2 + 3^2 + (3/2)^2)} \\= \sqrt{(36 + 9 + 9/4)} \\= \sqrt{(63.25)} \\= 7.95\)

Therefore, the computed values are:

u + v = (-3, -2)

v + u = (-3, -2)

5u = (10, -15)

2u + 3v = (-11, -3)

2u + 4w = (0, 2, 0)

u - v + 2w = (5, 0, 0)

|v + w| = 7.95

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