if alpha and beta are the zeroes of the polynomial f(x) = 6x² + x - 2, find the value of 1/alpha + 1/beta - alphabeta​

Largest value can decreased by 49 without affecting the value of median.

The median is the middle score in the set. To find the median, you take these steps:

Step 1: Arrange the scores in numerical order

Step 2: Count how many scores you have

Step 3: Divide the total scores by 2

Step 4: If you have an odd number of total scores, round up to get the position of the median number. If you have an even number of total scores, go to the number in that position and average it with the number in the next higher position to get the median.

For example:

given sets: 5, 4, 3, 6, 8

now rearrange the sets in increasing order: 3, 4, 5, 6, 8

median = ( n + 1 ) / 2 = ( 5 + 1) / 2 = 3

here median = 5

We have given that:

384, 350,  354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.

when we arrange it in increasing order.

here n = 26

median = ( n + 1 ) / 2

median =  average of 13th and 14th element

median = 371

larger value can be decreased by 420 - 371 = 49

Hence,

Largest value can decreased by 49 without affecting the value of median.

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Disclaimer: The question given was incomplete on the portal. Here is the complete question.

Question: A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape:

384, 350,  354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.

By how much could the largest sample observation be decreased without affecting the value of the median?

The largest sample observation could be decreased by 54.5 without affecting the value of the median.

We have given the data:

384, 350,  354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.

Now, we arrange it in increasing order.

321, 329, 330, 339, 350, 354, 354, 359, 361, 363, 365, 366, 369, 370, 374, 376, 376,378, 384, 393, 394, 396, 398,404, 424

Here n = 26

median = ( n + 1 ) / 2

median =  369 + 370 / 2

median = 369.5

Larger value can be decreased by 424 - 369.5= 54.5

Therefore, the largest sample observation could be decreased by 54.5 without affecting the value of the median.

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The question given was incomplete on the portal. Here is the complete question.

A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape:

384, 350,  354, 361, 378, 424, 321, 396, 404, 374, 376, 370, 363, 366, 365 329, 339, 394, 393, 369, 376, 359, 354, 408, 330, 398.

By how much could the largest sample observation be decreased without affecting the value of the median?

1) In the method, two independent variable are assumed to have: (b) High collinearity

2) If variance of coefficient cannot be applied, we cannot conduct test for: (b) Determination

1. The method of least squares regression assumes that the independent variables are not perfectly correlated with each other. If two independent variables are perfectly correlated, then the least squares estimator will be biased. This is because the least squares estimator will try to fit the data as closely as possible, and if two independent variables are perfectly correlated, then any change in one variable will cause a change in the other variable. This will make it difficult for the least squares estimator to distinguish between the effects of the two variables.

2. The variance of coefficient is a measure of the uncertainty in the estimated coefficient. If the variance of coefficient is high, then we cannot be confident in the estimated coefficient. This means that we cannot be confident in the results of the test of determination.

The test of determination is a statistical test that is used to determine the proportion of the variance in the dependent variable that is explained by the independent variables. If the variance of coefficient is high, then we cannot be confident in the results of the test of determination, and we cannot conclude that the independent variables do a good job of explaining the variance in the dependent variable.

Here are some additional information about the two methods:

Least squares regression: Least squares regression is a statistical method that is used to fit a line to a set of data points. The line that is fit is the line that minimizes the sum of the squared residuals. The residuals are the difference between the observed values of the dependent variable and the predicted values of the dependent variable.

Test of determination: The test of determination is a statistical test that is used to determine the proportion of the variance in the dependent variable that is explained by the independent variables. The test is based on the coefficient of determination, which is a measure of the correlation between the independent variables and the dependent variable.

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The situation that shows causation are:

Causation in mathematics can be desrcibed as the term used in indicating a relationship between two events where there is a relationship between the two events and one of the event is affected by the other.

It shoud be note that In statistics, when the value of one event, increases or decreases due to the relationship beteen them, the other events is affected, it is said there is causation.

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comlete question;

Which situation shows causation?

When the number of people in a bus increases, the number of animals in a zoo also increases.

When the number of hours worked each week by an hourly employee decreases, the amount of money earned

by the employee also decreases.

When the amount of a discount for a sale increases, the number of items sold during the sale decreases.

6 When the number of bike trails in a city decreases, the amount of rainfall in the city increases.

Answer:

There will be 12 servings in total!

Step-by-step explanation:

4 ÷ 1/3 = 12

Easy!

Answer:

12

Step-by-step explanation:

Divide 4 by 1/3 and get a 12 over 1 witch makes a whole 12.

(a) The probability that exactly seven people arrive at the bike repair shop in a one hour period of time is 0.104.

(b) The probability that at most seven people arrive at the bike repair shop in a one hour period of time is 0.646.

(c) The probability that at most seven people arrive at the bike repair shop in a one hour period of time is 0.646.

(d) The probability that between 4 and 9 people, inclusively, arrive at the bike repair shop in a one hour period of time is 0.759.

(a)

The probability that seven people arrive at the bike repair shop in a one hour period of time can be calculated using the Poisson distribution formula:

P(X = 7) = (e^(-λ) * λ^x) / x!

where λ = 5 (average number of arrivals per hour) and x = 7.

P(X = 7) = (e^(-5) * 5^7) / 7! = 0.104

So, the probability that exactly seven people arrive at the bike repair shop in a one hour period of time is 0.104.

(b) The probability that at most seven people arrive at the bike repair shop in a one hour period of time can be calculated as the sum of probabilities for x = 0, 1, 2, ..., 7:

P(X ≤ 7) = Σ P(X = x) for x = 0 to 7

Using the Poisson distribution formula with λ = 5, we get:

P(X ≤ 7) = Σ (e^(-5) * 5^x) / x! for x = 0 to 7

P(X ≤ 7) = 0.033 + 0.140 + 0.175 + 0.146 + 0.092 + 0.046 + 0.018 + 0.006

P(X ≤ 7) = 0.646

So, the probability that at most seven people arrive at the bike repair shop in a one hour period of time is 0.646.

(c) The probability that more than seven people arrive at the bike repair shop in a one hour period of time can be calculated as:

P(X > 7) = 1 - P(X ≤ 7)

Using the result from part (b), we get:

P(X > 7) = 1 - 0.646 = 0.354

So, the probability that more than seven people arrive at the bike repair shop in a one hour period of time is 0.354.

(d) The probability that between 4 and 9 people, inclusively, arrive at the bike repair shop in a one hour period of time can be calculated as the sum of probabilities for x = 4, 5, 6, 7, 8, 9:

P(4 ≤ X ≤ 9) = Σ P(X = x) for x = 4 to 9

Using the Poisson distribution formula with λ = 5, we get:

P(4 ≤ X ≤ 9) = Σ (e^(-5) * 5^x) / x! for x = 4 to 9

P(4 ≤ X ≤ 9) = 0.104 + 0.175 + 0.175 + 0.146 + 0.098 + 0.061

P(4 ≤ X ≤ 9) = 0.759

So, the probability that between 4 and 9 people, inclusively, arrive at the bike repair shop in a one hour period of time is 0.759.

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Answer:

If your going to graph it , it would be x=3/2y+ -9/2

Step-by-step explanation:

Answer:

40ft

Step-by-step explanation:

To calculate a square area you need to multiply two sides by each other. The area is 100 cubed feet. If you do the process backwards, You should get a square with 10ft sides. 10*4 = 40

:) hope this helps

Answer:

Step-by-step explanation:

25 × 4.5= 112.5 and that is you answer

The amount invested into 7% simple interest and 5% simple interest is $17,000 and $3,000 respectively.

Let

x + y = 20,000

0.07x + 0.05y = 1340

From (1)

x = 20,000 - y

Substitute into (2)

0.07x + 0.05y = 1340

0.07(20,000 - y) + 0.05y = 1340

1,400 - 0.07y + 0.05y = 1340

- 0.07y + 0.05y = 1340 - 1400

-0.02y = -60

y = -60 / -0.02

y = 3,000

Substitute y = 3,000 into (1)

x + y = 20,000

x + 3,000 = 20,000

x = 20,000 - 3,000

x = 17,000

Therefore, $17,000 and $3,000 was invested into into 7% simple interest and 5% simple interest respectively.

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Answer:

674

Step-by-step explanation:

Answer:

woah woah woah woah calm down there buddy its 674 :)

Answer:

-5.126

Step-by-step explanation:

PEMDAS

-4.326 + (-0.32) ÷ 0.4

-0.32 ÷ 0.4

= -0.8

-4.326 + (-0.8)

= -4.326 - 0.8

= -5.126

The quotient and remainder are x³ -5x² + 10x - 17 and 55.

What is Synthetic division?

When the divisor is a linear factor, synthetic division is a technique used to carry out the division operation on polynomials.

Here, (x+2) is a linear factor which indicates that synthetic division can be applied.

So, we will divide the x^4 - 3x^3 - 7x + 1 by x+2.

(refer the attached solution)

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Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Step-by-step explanation:

(8*4):2 + 4=

32:2+4=

16+4=20

Answer:

x=9 and y=115

Step-by-step explanation:

Solve y=9x+34;y=16x−29

Steps:

I will solve your system by substitution.

y=9x+34;y=16x−29

Step: Solvey=9x+34for y:

Step: Substitute9x+34foryiny=16x−29:

y=16x−29

9x+34=16x−29

9x+34+−16x=16x−29+−16x(Add -16x to both sides)

−7x+34=−29

−7x+34+−34=−29+−34(Add -34 to both sides)

−7x=−63

−7x

−7

=

−63

−7

(Divide both sides by -7)

x=9

Step: Substitute9forxiny=9x+34:

y=9x+34

y=(9)(9)+34

y=115(Simplify both sides of the equation)

Hope this helps :)

Answer:

C)  There is a positive linear association between the math and science scores, with one of the data points being an outlier.

Step-by-step explanation:

Correlation measures how closely two variables are linked.  

If two variables are correlated, you can draw a line of best fit on the scatter plot.

From inspection of the given scatter plot:

All data points (with the exception of one) are very close to being in a straight line with a positive slope.  This is called a positive linear correlation.

As the one data point is far from the general pattern of the other points, it is an outlier.

There is a positive linear association between the math and science scores, with one of the data points being an outlier.

To find the value of C, we can use the formula for the gradient (slope) of a line, which is the change in y divided by the change in x between two points on the line. In this case, the points are A(5, -C²) and B(C, -3).

The gradient (m) is given by:

m = (change in y) / (change in x)

Let's calculate the change in y and the change in x:

Change in y = y₂ - y₁

= (-3) - (-C²)

= -3 + C²

Change in x = x₂ - x₁

= C - 5

Now, using the gradient formula:

C = (change in y) / (change in x)

= (-3 + C²) / (C - 5)

We can solve this equation for C. Multiplying both sides by (C - 5) gives:

C(C - 5) = -3 + C²

C² - 5C = -3 + C²

-5C = -3

C = -3 / -5

C = 3/5

Therefore, the value of C is 3/5.

By trigonometric functions we find that the measure of angle A is approximately 0.12π radians.

In this question we have a right triangle, of which the length of two sides are known (AB, BC). We can know the measure of angle A by trigonometric functions:

\(\tan A = \frac{BC}{AC}\)

\(\tan A = \frac{2}{5}\)

A ≈ 0.12π radians

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Answer:

12.56 in ^2

Step-by-step explanation:

First find the area of a circle with radius 4

A = pi r^2

A = (3.14) 4^2

A =50.24

Since it is 1/4 of a circle, multiply by 1/4

1/4 ( 50.24)

12.56

Answer:

Quarter circle's area is 12.56 inches².

Step-by-step explanation:

Concept:- Firstly, we need to find the area of circle and Since, it is quarter of circle we need to multiply the area of circle by 1/4. and we get answer

Finding area of circle

Using Formula

Area of circle = π × r ²

Where,

And we have given

Substitute the value into the formula

Area of circle = 3.14 × ( 4 in. )/²

now,

Area of circle = 3.14 × 16 in ².

multiply , we get

Area of circle is 50.24 nches ²

As have to find the quarter circle's area ,

and we know that quarter is the one fourth of the circle .

Quarter circle's area = Area of circle × 1/4

Multiply , we get

Quarter circle's area = 50.24 × 1/4

Therefore, quarter circle's area is 12.56 inches².

Answer:

\(x = 10.6\)

Step-by-step explanation:

\( \sin( {62}^{o} ) = \frac{x}{12 } \\ x = 12 \sin( {62}^{o} ) \\ x = 10.6\)

The number of ways to select a committee of four Republicans, three Democrats, and two Independents from a group of 10 distinct Republicans, 12 distinct Democrats, and four distinct Independents is: 277,200.

This can be calculated using the formula for combinations, which states that the number of ways to choose k objects from a set of n distinct objects is given by

nCk = n! / (k! * (n-k)!),

where ! denotes the factorial function.

In this case, we use this formula to calculate the number of ways to choose four Republicans from a group of 10, three Democrats from a group of 12, and two Independents from a group of 4.

We then multiply these values together to get the total number of possible committees:

(10C4) x (12C3) x (4C2) = 210 x 220 x 6 = 277,200

The final answer is 277,200.

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305 R 5

-----------------------------------------------

Answer:divideing by the whole number

Step-by-step explanation:

a) The logistic equation for this problem is L dP/dt = P(1 - P/L), where L = 2000 and Po = 100.

b)  The maximum reproduction rate is 0.03465 times the current population.

a. The logistic equation for this problem is:

L dP/dt = P(1 - P/L)

where L is the carrying capacity of the lake, P is the current population, and dP/dt is the rate of change of the population over time.

We know that at t = 0, P = 100, and one year later at t = 1, P = 200. So we can use this information to find k, which is the growth rate coefficient:

P(t) = L / (1 + (L / Po - 1) * exp(-kt))

200 = L / (1 + (L / 100 - 1) * exp(-k))

200 = L / (1 + (L - 100) * exp(-k))

200 + 200L - 20000 = L * (1 + (L - 100) * exp(-k))

200L -\(L^2\) * exp(-k) + 200L * exp(-k) - 10000 * exp(-k) = 0

\(L^2\) - 400L + 5000 = (L - 200)^2 - 30000

\((L - 200)^2\) = 35000

L = 200 + sqrt(35000) ≈ 223.6

So L ≈ 223.6, and we can use this to find k:

2000 = 223.6 / (1 + (223.6 / 100 - 1) * exp(-k))

20000 + 2000L - 2236 = L * (1 + (L - 100) * exp(-k))

2236 - \(L^2\)  * exp(-k) + 2236 * exp(-k) - 100 * exp(-k) = 0

\(L^2\) - 4472L + 220000 = 0

(L - 2000)(L - 100) = 0

So either L = 2000 or L = 100. We know that L ≠ 100, since we know that the population stabilizes at 2000 after a long time. Therefore, L = 2000, and we can solve for k:

k = -ln((L / Po - 1) / (1 + (L / Po - 1))) / t

k = -ln((2000 / 100 - 1) / (1 + (2000 / 100 - 1))) / 1

k ≈ 0.0693

Therefore, the logistic equation for this problem is:

L dP/dt = P(1 - P/L)

dP/dt = 0.0693P(1 - P/2000)

b. The maximum reproduction rate occurs when the population is halfway to the carrying capacity, or P = L/2. At this point, the equation becomes:

dP/dt = 0.0693P(1 - 0.5)

dP/dt = 0.03465P

Therefore, the maximum reproduction rate is 0.03465 times the current population. For example, if the current population is 1000, the maximum reproduction rate is 34.65 fish per year.

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Full Question : Logistic Equation: L dP dt P(1-2). P() = L - Po Po 1+ 4e ki Where A 1. Fish population in a lake grows according to the logistic law. The initial population of 100 fish and year later it was 200. After a long time fish population stabilized at 2000.

a. Write down the logistic equation for this problem.

b. What is the maximum reproduction rate (fish/year)?

Answer: At point (0,12)  line q cross the y-axis.

Step-by-step explanation:

Equation of a line passing through (a,b) and (c,d) :

\((y-b)=\dfrac{d-b}{c-a}(x-a)\)

Given: Line q goes through points (-3, 3) and (-5, -3).

Equation of line q:

\((y-3)=\dfrac{-3-3}{-5(-(-3)}(x-(-3))\\\\\Rightarrow\ (y-3)=\dfrac{-6}{-5+3}(x+3)\\\\\Rightarrow\ (y-3)=\dfrac{-6}{-2}(x+3)\\\\\Rightarrow\ y-3=3(x+3)\)

When line crosses y-axis , x=0 .

So,

\(y-3=3(3)\\\\\Rightarrow\ y-3=9\\\\\Rightarrow\ y=9+3\\\\\Rightarrow\ y=12\)

Hence, At point (0,12)  line q cross the y-axis.

Option d is not correct as it uses "II" which is not a commonly used symbol to indicate less than and greater than.

The correct expression to indicate that x is greater than 10 and less than 20 is:

a. 10 < x < 20

This is read as "10 is less than x, and x is less than 20." The symbols "<" and ">" indicate "less than" and "greater than," respectively.

Option b is not correct as it uses parentheses instead of the less than/greater than symbols.

Option c is not correct as it uses "&" and "&&" which are not commonly used symbols to indicate less than and greater than.

Option d is not correct as it uses "II" which is not a commonly used symbol to indicate less than and greater than.

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Answer:

7-B (congruent)

8-D (supplement)

9-B (congruent)

10-B (congruent)

11-D (supplement)

Step-by-step explanation:

7- 1 and 3 are congruent using the corresponding angles theorem

8- they are supplements using the same side interior angle theorem

9- they are congruent using alternate interior angle theorem

10- they are congruent using the alternate exterior angle theorem

11- they are supplements using the same side exterior angle theorem

ur wlcm :)

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