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Answer:

The value of d = -5

The polynomial function   x³ +5 x² - 4x -20 =0

Step-by-step explanation:

Explanation

Given that the equation is third degree polynomial

p(x) = x³ - d x² - 4x -20

Given factors x= 2 and x=-2

Substitute 'x' = 2 in given polynomial

     8 -d(2²)-4(2) - 20 =0

⇒   8 - 4 d - 8 -20=0

⇒     - 4 d-20 = 0

⇒    - 4 d = 20

⇒         d = - 5

The value of d = -5

Verification:-

After substitution d =-5 in given polynomial

x³ - (-5) x² - 4x -20 =0

put x=2

8 +5(4)-8-20 =0

             20 =20

The factors are x= 2 and x=-2 of the given polynomial

According to the image, the point F is at (4,-4). Remember that the first number is about x-coordinate, and the second number is about y-coordinate.

The solution to the inequality is x >= -2 for inequality 3x-5≥-11

The given inequality is 3x-5≥-11

Three times of x greater than or equal to minus eleven

x is the variable

3x - 5≥ -11:

Adding 5 to both sides, we get:

3x ≥ -6

Dividing both sides by 3, we get:

solution is  x≥-2

Therefore, the solution to the inequality is x >= -2.

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The expressions that are equivalent to 3^8 are:

We have to solve these out

3^8. = 6561

From the options

A. 3^2x3^4

= 9 x 81

= 729

B  3²x3^6

= 9 x 729

= 6561

C.  3^16/3^2

= 43046721/9

= 4782969

d. 3^12/3^4

= 531441 / 81

= 6561

E.  (3^4)²

= 3⁴ x 3⁴

= 3⁴⁺⁴

= 3⁸

= 6561

F. (3¹)^7

= 3⁷

= 2187

The expressions that are equivalent to 3^8 are:

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Answer:

The value is  \(H  =0.3966\)

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  50

  The  mean tail is  \(\= x  =  85.4 \cm\)

  The  number  of resplendent quetzals selected as breeders  is  \(k =  10\)

   The  mean tail breeders  is  \(\= x_1 =  91.2 \ cm\)

   The mean tail of the breeders after mating  \(\=  x_2  =  87.7 \ cm\)

Generally the selection differential is mathematically represented as

    \(D  =  \= x_1 -  \= x \)

=>  \(D  = 91.2-  85.4 \)

=>  \(D  = 5.8 \  cm \)

Generally the selection response  is mathematically represented as

       \(S =  \=  x_2  - \= x\)

=>    \(S =  87.7   - 85.4\)

=>    \(S =2.3 \  cm \)

Generally the  heritability of tail length in this resplendent quetzal population is mathematically represented as

     \(H  =  h^2 =  \frac{S}{D} \)

=>   \(H  =  h^2 =  \frac{2.3}{5.8} \)

=>  \(H  =  h^2 =  \frac{2.3}{5.8}  \)

=>  \(H  =  h^2 = 0.3966/tex]

The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

Answer:

  ∠HGB = 20°

  ∠ECD = 34°

  ∠GBH = 36°

  ∠FGH = 37°

Step-by-step explanation:

There are several useful rules regarding angles:

This last observation is a consequence of the 2nd and 3rd observations.

__

angle ECD

Using the last observation, ∠ECD = 124° -90° = 34°.

angle HGB

Again, using the last observation, ∠HGB = 110° -90° = 20°.

angle GBH

There are at least a couple of ways to find this one. We assume that lines FB and EC are parallel, so angles HBC and ECD are corresponding, hence congruent. Angle GBC is the supplement of of 110°, so is 70°. Then ...

  ∠GBH = 70° -34° = 36°

angle FGH

Again, this angle can be found multiple ways. Here, we'll use the sum of angles in triangle FGB.

  ∠FGB +∠GBF +∠BFG = 180°

  (∠FGH +∠HGB) +∠GBF +∠BFG = 180°

  ∠FGH +20° +36° +87° = 180°

  ∠FGH = 180° -143° = 37°

__

Least to greatest, the angles are ...

  ∠HGB = 20°

  ∠ECD = 34°

  ∠GBH = 36°

  ∠FGH = 37°

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

q=2

Step-by-step explanation:

I am not sure but it can't be 0 and its says higher than 1

Answer:

q=2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1+1=2

For expression  x+1= √19-x, the value of x is approximately 3.

What exactly are expressions?

In mathematics, an expression is a combination of symbols and operators that represents a quantity or a mathematical relationship. It can contain numbers, variables, operators, functions, and other mathematical symbols. Expressions are used to represent mathematical operations and relationships, and they can be evaluated or simplified using mathematical rules and properties. Examples of expressions include 3x + 2, (x + y) / (x - y), and sin(x) + cos(y).

Now,

Starting with the given equation:

x + 1 = √(19 - x)

We can begin by squaring both sides of the equation to eliminate the square root:

(x + 1)² = (√(19 - x))²

Simplifying the right-hand side:

(x + 1² = 19 - x

Expanding the left-hand side:

x² + 2x + 1 = 19 - x

Moving all the terms to one side:

x² + 3x - 18 = 0

Now we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 3, and c = -18:

x = (-3 ± √(3² - 4(1)(-18))) / 2(1)

x = (-3 ± √(81)) / 2

x = (-3 ± 9) / 2

This gives us two solutions:

x = 3 or x = -6

However, we must check both solutions to make sure they are valid in the original equation:

Checking x = 3:

x + 1 = √(19 - x)

3 + 1 = √(19 - 3)

4 = √16

4 = 4

This solution works.

Checking x = -6:

x + 1 = √(19 - x)

-6 + 1 = √(19 + 6)

-5 = √25

-5 ≠ 5

This solution does not work.

Therefore, the solution to the equation x + 1 = √(19 - x) is x = 3.

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Correct question:

What is the solution to the equation below ?

x+1= √19-x

Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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Step-by-step explanation:

jnx-avkj-uup p.l.z join

Answer:

adjacent, linear pair, supplementary

Step-by-step explanation:

adacent because they are angles side by side

linear because the angles create a straight line

supplementary because the angles equal 180 degrees

Answer:

66.15

Step-by-step explanation:

70 dollars - discount + fee

discount = 10% of total = 10% of 70 = 0.1 * 70 = 7

fee = 5% of discounted price

discounted price = original - discount = 70 -7 = 63

fee = 5% of 65 = 0.05 * 65 = 3.15

70 - 7 + 3.25 = 66.15

It's the sum of the three masses:

\(7.3\cdot10^{22} + 590\cdot10^{22} + 1.3\cdot10^{22} = (7.3 + 590 + 1.3)10^{22} = 598.6\cdot10^{22}\)

Answer: 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Based on the information provided, the residual plot makes sense based on the scatter plot.

In the given scatter plot, the points are plotted with horsepower on the x-axis and observed MPG (miles per gallon) on the y-axis. The scatter plot shows the relationship between horsepower and MPG for the motorcycles.

The residual plot, on the other hand, shows the differences between the observed MPG values and the predicted MPG values based on the regression line or model. Residuals represent the vertical distances between the observed data points and the regression line.

Looking at the residual plot, we can see that the residuals are scattered randomly around the zero line. Some residuals are positive, while others are negative, indicating that the observed MPG values deviate both above and below the predicted MPG values.

Given this information, option A is the correct answer: "The random residual plot makes sense because the scatter plot appears to have a linear relationship." The scatter plot does not necessarily suggest a positive or negative relationship between horsepower and MPG. It simply shows the general trend or pattern. The random distribution of residuals in the residual plot indicates that the regression model is capturing the relationship adequately, and the variations or deviations from the regression line are random, which is expected in a good regression model.

The residual plot created by Jorge does make sense as it reflects the negative relationship between horsepower and miles per gallon present in the original scatter plot. As the horsepower increases, the miles per gallon decreases which is depicted accurately in the residual plot made.

The best answer for this is B. The random residual plot makes sense because the scatter plot appears to have a negative relationship. A residual plot is a graph that is used to examine the goodness of fit in regression and ANOVA analysis. It is the differences between the observed and predicted values of data. The points in a residual plot are randomly dispersed around a horizontal axis if the corresponding regression model is appropriate for the data.

In this case, the scatter plot demonstrates a negative relationship between the horsepower of motorcycles and miles per gallon. As the horsepower increases, the miles per gallon decrease. This negative relationship is reflected in the pattern of residuals, which fluctuates around the zero line on the y-axis of the residual plot. Consequently, the random distribution of residuals on Jorge's plot does make sense given the scatter plot data.

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The velocity for the position function s(t) = -16t² + v₀t + s₀  as per situation is equal to

a. velocity after 3 seconds, v(3) = -120ft /s

b. velocity after falling from 112 feet, v(4.125 ) = -156 ft/s.

Ball is thrown straight down from 483 foot building.

s₀ = 483 foot

Initial velocity v₀ = -24 feet per second

Position function for free falling objects is:

s(t) = -16t² + v₀t + s₀

Differentiate both the side of the equation with respect to 't' we get,

s'(t) = -32t + v₀

s'(t) represents velocity v(t) .

a. Velocity after t = 3 seconds is equal to

⇒ v(t) = -32t + v₀

Substitute the value we get,

⇒ v(3) = -32(3) + (-24 )

⇒ v(3) = -96 -24

⇒ v(3) = -120 ft/s

b. velocity after falling from 112 feet

s(t) = 112 feet

s(t) = -16t² + v₀t + s₀

⇒ 112 = -16t² + (-24 )t + 483

⇒  -16t² + (-24 )t +371 =0

⇒ 16t² + 24t - 371 =0

⇒ t = [-24 ±√24² + 4(16)(371) ] / 2(16)

⇒ t = -5.25 or 4.125 seconds

Time cannot be negative.

t = 4.125 seconds

v(4.125) = -32(4.125) -24

            = -156 ft/s

Therefore , the required velocity for the different time is equal to

a. for t = 3 seconds , v(3) = -120ft /s

b. for t= 4.125 seconds , v(4.125 ) = -156 ft/s

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The above question is incomplete , the complete question is:

A ball is thrown straight down from the top of a 483-foot building with an initial velocity of -24 feet per second. Use the position function below for free-falling objects. s(t) = -16t² + v₀t + s₀

a. What is its velocity after 3 seconds? V(3) = _____ ft/s.

b. What is its velocity after falling 112 feet? V = _____ft/s

Answer:

12:14 or 6:7

Step-by-step explanation:

If there are 12 girls and 14 boys in class then the ratio could be simplified from 12:14 to 6:7 by dividing by 2.

The function g(x) in the form a(x-h)^2 + k is: \(g(x) = (x + 2)^2 - 4\)

Starting with\(f(x) = x^2\), the translation 2 units left and 4 units down would result in the following transformation:

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

Substituting\(f(x) = x^2:\)

\(g(x) = (x + 2)^2 - 4\)

Expanding the square:

\(g(x) = x^2 + 4x + 4 - 4\)

Simplifying:

\(g(x) = x^2 + 4x\)

Now we need to rewrite this expression in the form \(a(x-h)^2 + k.\) To do this, we will complete the square:

\(g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4\)

Therefore, the function g(x) in the form a(x-h)^2 + k is:

\(g(x) = (x + 2)^2 - 4\)

Where a = 1, h = -2, and k = -4.

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The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Using basic inference rules, we can establish the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

1. We are given the following premises:

  - p ⟹ ¬q (Premise 1)

  - q V r (Premise 2)

  - p V u (Premise 3)

  - ¬r (Premise 4)

2. To prove the conclusion, u, we need to use the premises and apply inference rules.

3. From Premise 4 (¬r) and the Disjunctive Syllogism rule, we can deduce ¬q: (¬r, q V r) ⟹ ¬q.

4. From Premise 1 (p ⟹ ¬q) and Modus Ponens, we can conclude ¬p: (p ⟹ ¬q, ¬q) ⟹ ¬p.

5. From Premise 3 (p V u) and Disjunctive Syllogism, we obtain ¬p V u.

6. Using Disjunctive Syllogism with ¬p V u and ¬p, we can derive u: (¬p V u, ¬p) ⟹ u.

7. From Premise 2 (q V r) and Disjunctive Syllogism, we have q.

8. Finally, using Modus Tollens with q and ¬q, we can deduce ¬p: (q, p ⟹ ¬q) ⟹ ¬p.

9. Therefore, combining ¬p and u, we can conclude the desired result: ¬p ∧ u.

10. Since ¬p ∧ u is logically equivalent to u, we have established the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

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Answer:

Step-by-step explanation:

If the worker drove a total of 134 miles on Monday, and received $32.13 for the work-related miles, then we can assume that the work-related miles pay rate is constant, and calculate the total pay for all the miles:

Total pay for all miles = Total miles * Pay rate per mile

Since the worker received $32.13 for the work-related miles, and we assume a constant pay rate, we can find the pay rate per mile:

Pay rate per mile = Total pay for all miles / Total miles

= $32.13 / Total work-related miles

Now we can use this pay rate per mile to calculate the percentage of work-related miles:

Percentage of work-related miles = (Pay for work-related miles / Pay rate per mile) / Total miles * 100

Plugging in the given values, we get:

Percentage of work-related miles = (32.13 / (134 - 32.13)) / (134) * 100

= 0.2874 * 100

= 28.74%

Therefore, approximately 28.74% of the worker's total miles driven on Monday were work-related.

hi

as ln(x) + ln (y) = ln (x*y)

we have :   ln(2) + ln (x-2) =  ln ( 2 * (x-2) ) = ln ( 2x -4)

so   ln (2x-4) = ln 14

        2x -4 =  14

        2x-4 +4 =  14 +4

         2x  =  18

         2x/2 = 18/2

           x = 9

let's check :     ln 2 + ln (9-2) =   ln ( 2 * (9-2) ) =   ln  (2* 7) = ln (14)

Standard deviation does not mean independent events.

No, the standard deviation is a measure of the spread or variability of a set of data. It measures how much the individual data points in a dataset deviate from the mean or average of the dataset.

Independence, on the other hand, refers to the relationship between two or more events, where the occurrence of one event does not affect the probability of the other event occurring.

Standard deviation is not directly related to the concept of independence. However, when calculating the standard deviation of a dataset, it assumes that each data point is independent and identically distributed. This means that the value of one data point does not affect the value of another data point, and that each data point is drawn from the same underlying distribution.

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