The function after synthetic division f(x) = 4x3 + 3x2 − 16x − 12

An argument can be invalid even if the premises are true and the conclusion is false.This statement is actually false.

Invalidity refers to the structure of the argument, not the truth value of the premises or conclusion. An invalid argument fails to establish the truth of its conclusion even if its premises are true. In contrast, a valid argument guarantees that the conclusion follows from the premises, regardless of the truth or falsity of the premises. Therefore, an argument can be valid with false premises, and an argument can be invalid with true premises.

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Conclude that there is no guarantee that the conclusion will be false when all the premises are false in an invalid

argument.

If an argument is invalid, then whenever the premises are all false, the conclusion must also be false.

An invalid argument is one where the conclusion does not necessarily follow from the premises, even if the premises

are all true.

In other words, it is possible for the premises to be true, but the conclusion to be false. However, in the scenario you

described, all the premises are false. In an invalid argument, there is no guarantee that the conclusion will also be false.

Identify the argument as invalid.

Recognize that all the premises are false.

Understand that in an invalid argument, the conclusion does not necessarily follow from the premises.

Conclude that there is no guarantee that the conclusion will be false when all the premises are false in an invalid

argument.

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The next proportion must be satisfied

Replacing with data,

Using quadratic formula,

The negative answer has no sense in this problem, then the length of TG is 3.

35 cents

and

40 cents

Hope this helps!! :D

Answer:

C)   \(y=-0.5x+8\)

Step-by-step explanation:

Line of best fit (trendline) : a line through a scatter plot of data points that best expresses the relationship between those points.

All the given options for the line of best fit are linear equations.

Therefore, we can add the line of best fit to the graph (see attached), remembering to have roughly the same number of points above and below the line.

Linear equation:  \(y=mx+b\)

(where \(m\) is the slope and \(b\) is the y-intercept)

From inspection of the line of best fit, we can see that the y-intercept (where x = 0) is approximately 8.  So this suggests that options C or D are the solution.

We can also see that the slope (gradient) of the line of best fit is approximately -0.5 (as the rate of change (y/x) is -1 unit of y for every +2 units of x).

Therefore, C is the solution, and the closet approximation to the line of best fit is \(y=-0.5x+8\)

Answer:

  9.  AB = (40/3)√3

  10.  BC = (20/3)√3

Step-by-step explanation:

The ratios of side lengths in the "special" 30-60-90° triangle are ...

  1 : √3 : 2

__

If D is the point where the altitude meets AB, then we have for the left triangle ...

  CD : AD : CA = 1 : √3 : 2 = 10 : 10√3 : 20

and, for the right triangle ...

  BD : CD : BC = 1 : √3 : 2 = (10/√3) : 10 : (20/√3)

and for the large triangle ...

  BC : CA : AB = 1 : √3 : 2 = (20/√3) : 20 : (40/√3)

__

The hypotenuse of ΔABC is AB, shown above to be ...

  AB = 40/√3 = (40/3)√3

__

The shorter leg of ΔABC is BC, shown above to be ...

  BC = 20/√3 = (20/3)√3

Answer:

i think ANSWER IS 8

Step-by-step explanation:

48÷8 = 6

Answer:

8 would be your answer if I'm wrong pls let me know and I will edit soon as posable.

Step-by-step explanation:

the way I did it was doing 48 divided by 6 and I got the answer 8 meaning 8 would be the correct answer

The value of the stock can be calculated by using the Gordon Growth Model. Gordon Growth Model The Gordon Growth Model is a technique that is used to value stocks using the present value of future dividend payments.

This model assumes that the dividends of the company will grow at a constant rate, and it takes into consideration the required rate of return of the investors. The formula for the Gordon Growth Model is given as follows: Stock Price = D1/(r-g)Where,D1 = Expected dividend in the next periodr = Required rate of returng = Growth rate in dividends Now, let's use the Gordon Growth Model to find the value of the stock in the given question. Dividend in the next period (D1) = Expected dividend * (1 + growth rate) = $2.48 * (1 + 3.15%) = $2.55Required rate of return (r) = 11.05%Growth rate in dividends (g) = 3.15%Stock price = D1/(r-g)= $2.55/(11.05% - 3.15%)= $30.95Therefore, the value of the stock is $30.95.Answer: The value of the stock is $30.95.

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Answer:

x(-6)

every number is multiplied by -6

3(-6)= -18

-18(-6) = 108

Answer:

the answer is 28

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

The total percentage of capital contributed by Jacklyn is 30%

The total capital contributed by Sandra, Jaclyn, and Alecia is:

$400 + $600 + $1000 = $2000

To find the percentage of capital contributed by Jacklyn contributed,

Percentage contributed by Jaclyn = (Jaclyn's contribution / Total capital) x 100

= ($600 / $2000) x 100

= 30%

Therefore, Jacklyn contributed 30% of the capital.

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Answer: 400:18

and 200:9

Step-by-step explanation:

Given: Radius of the wheel = 30 inches, Revolutions per minute = 401 rpmThe linear speed of the car in miles per hour can be calculated as follows:

Step 1: Convert the radius from inches to miles by multiplying it by 1/63360 (1 mile = 63360 inches).30 inches × 1/63360 miles/inch = 0.0004734848 milesStep 2: Calculate the distance traveled in one minute by the wheel using the circumference formula.Circumference = 2πr = 2 × π × 30 inches = 188.496 inchesDistance traveled in one minute = 188.496 inches/rev × 401 rev/min = 75507.696 inches/minStep 3: Convert the distance traveled in one minute from inches to miles by multiplying by 1/63360.75507.696 inches/min × 1/63360 miles/inch = 1.18786732 miles/minStep

4: Convert the distance traveled in one minute to miles per hour by multiplying by 60 (there are 60 minutes in one hour).1.18786732 miles/min × 60 min/hour = 71.2720392 miles/hour Therefore, the linear speed of the car is 71.3 miles per hour (rounded to the nearest tenth).Answer: 71.3

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The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, The linear speed of the car is approximately 19.2 miles per hour.

To find the linear speed of the car in miles per hour, we need to calculate the distance traveled in one minute and then convert it to miles per hour. Here's how we can do it step by step:

Calculate the circumference of the wheel:

The circumference of a circle is given by the formula

C = 2πr

where r is the radius of the wheel.

In this case, the radius is 30 inches, so the circumference is

C = 2π(30)

   = 60π inches.

Calculate the distance traveled in one revolution:

Since the circumference represents the distance traveled in one revolution, the distance traveled in inches per revolution is 60π inches.

Calculate the distance traveled in one minute:

Multiply the distance traveled in one revolution by the number of revolutions per minute.

In this case, it is 60π inches/rev * 401 rev/min = 24060π inches/min.

Convert the distance to miles per hour:

There are 12 inches in a foot, 5280 feet in a mile, and 60 minutes in an hour.

Divide the distance traveled in inches per minute by (12 * 5280) to convert it to miles per hour.

The final calculation is (24060π inches/min) / (12 * 5280) = (401π/66) miles/hour.

Approximating π to 3.14, the linear speed of the car is approximately (401 * 3.14 / 66) miles per hour, which is approximately 19.2 miles per hour.

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You have to calculate the probability of obtaining an odd number after rolling the die and obtaining tail after tossing a coin, symbolically:

Where

"O" represents the event " rolling an odd number"

"T" represents the event "tossing a coin and obtaining tail"

The events are independent, which means that the intersection between both events is equal to the product of the individual probability of each event:

So, first, we have to calculate the probabilities of "rolling an odd number" P(O) and "tossing a coin and obtaining tail" P(T)

-The die is six-sided and numbered from 1 to 6, assuming that each possible outcome has the same probability, we can calculate the probability of rolling one number (N) as follows:

The possible outcomes when you roll a die are {1, 2, 3, 4, 5, 6}

Out of these six numbers, three are odd numbers {1, 3, 5}, this is the number of favorable outcomes of the event "O", and the probability can be calculated as follows:

So, the probability of rolling an odd number is P(O)=1/2

-When you toss a coin, there are two possible outcomes: "Head" and "Tail", assuming that both outcomes are equally possible.

For the event "toss a coin and obtain tail" there is only one favorable outcome out of the two possible ones, so the probability can be calculated as:

The probability of tossing a coin and obtaining a tail is P(T)=1/2

Once calculated the individual probabilities you can determine the asked probability:

Answer:

924

Step-by-step explanation:

Find the volume of the triangular pyramid to the nearest whole number. In this case its 924

Answer:

x = 46°

Step-by-step explanation:

The measure of the exterior angle at a vertex of a triangle equal to the sum of the measures of the two opposite interior angle to this vertex

In the given parallelogram

∵ Its two diagonals intersected at a point and formed 4 triangles

∵ The angle of measure 69° is an exterior angle of the triangle that

   contains angles z, x, and 23°

∵ The opposite interior angles to the angle of measure 69° are x and

   the angle of measure 23°

→ By using the rule above

∴ x + 23° = 69°

→ Subtract 23 from both sides

∴ x + 23 - 23 = 69 - 23

∴ x = 46°

The probability that the first machine is more generous given that we lose the first bet is approximately 0.529 or 52.9%.

We can solve the given problem by applying Bayes' theorem.

Bayes' theorem states that, for any event A and B,P(A | B) = (P(B | A) * P(A)) / P(B)

Where P(A | B) is the probability of event A occurring given that event B has occurred.P(B | A) is the probability of event B occurring given that event A has occurred.

P(A) and P(B) are the probabilities of event A and B occurring respectively.

Now, let A denote the event that the first machine is more generous than the second, and B denote the event that we lose the first bet.

Then we are required to find P(A | B), the probability that the first machine is more generous given that we lose the first bet.

Let's apply Bayes' theorem.

P(A | B) = (P(B | A) * P(A)) / P(B)P(A) = P(selecting the first machine) = P(selecting the second machine) = 1/2 [initial assumption]P(B | A) = P(losing the bet on the first machine) = 90/100 = 9/10P(B) = P(B | A) * P(A) + P(B | not A) * P(not A) ... (1)

P(B | not A) = P(losing the bet on the second machine) = 80/100 = 4/5P(not A) = 1 - P(A) = 1/2P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)= (9/10) * (1/2) + (4/5) * (1/2)= (9 + 8) / (10 * 2)= 17/20

Now, we can substitute the values of P(A), P(B | A) and P(B) in the formula for P(A | B).P(A | B) = (P(B | A) * P(A)) / P(B)= (9/10 * 1/2) / (17/20)= 9/17 ≈ 0.529

Thus, the probability that the first machine is more generous given that we lose the first bet is approximately 0.529 or 52.9%.

Therefore, the probability that the machine selected is the more generous of the two machines given that we lose the first bet is 0.529 or 52.9%.

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The estimated probability that the machine selected is the more generous of the two machines, given that you lost the first bet, is approximately 0.4706 or 47.06%.

To solve this problem, we can use Bayes' theorem. Let's denote the events as follows:

A: Machine 1 is the more generous machine (pays out 20% of the time).

B: Machine 2 is the more generous machine (pays out 10% of the time).

L: You lose the first bet.

We want to find P(A|L), the probability that Machine 1 is the more generous machine given that you lost the first bet.

According to the problem, we initially assume that the two machines are equally likely to be generous, so P(A) = P(B) = 0.5.

We can now apply Bayes' theorem:

P(A|L) = (P(L|A) * P(A)) / P(L)

P(L|A) is the probability of losing the first bet given that Machine 1 is the more generous machine. Since Machine 1 pays out 20% of the time, the probability of losing on the first bet is 1 - 0.20 = 0.80.

P(L) is the probability of losing the first bet, which can be calculated using the law of total probability:

P(L) = P(L|A) * P(A) + P(L|B) * P(B)

P(L|B) is the probability of losing the first bet given that Machine 2 is the more generous machine. Since Machine 2 pays out 10% of the time, the probability of losing on the first bet is 1 - 0.10 = 0.90.

Now we can substitute the values into the formula:

P(A|L) = (0.80 * 0.5) / (0.80 * 0.5 + 0.90 * 0.5)

       = 0.40 / (0.40 + 0.45)

       = 0.40 / 0.85

       = 0.4706 (approximately)

Therefore, the estimated probability that the machine selected is the more generous of the two machines, given that you lost the first bet, is approximately 0.4706 or 47.06%.

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Answer:

10.75

11

Step-by-step explanation:

the mean is the average, so add up all of the values and divide by 8 because there are 8 values :

(11 + 17 + 14 + 11 + 4 + 7 + 11 + 11)/8 = 10.75

the median is the middle value when the numbers are written in ascending or descending order :

4, 7, 11, 11, 11, 11, 14, 17

we can cross out the values on the ends, to get to the middle. if we do this, we are left with 11, 11

find the average of these numbers :

which is 11.

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer:

D

Step-by-step explanation:

Answer: C

Step-by-step explanation:

C. Y= 3x - 4

The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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Answer:

y=10x

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula

y−y1=m(x−x1)  to find the line parallel to y=10x−45

.

The data sets with a range that is greater than 10 are:

1 5 7 8 14

5 7 9 21 23

The range of any given data set is the difference between the largest and the lowest data point in the data set.

Range for 4 5 6 7 13:

Range = 13 - 4 = 9

Range for 1 5 7 8 14:

Range = 14 - 1 = 13

Range for 10 11 14 17 18:

Range = 18 - 10 = 8

Range for 5 7 9 21 23:

Range = 23 - 5 = 18

11 11 11 11 11 has no range.

Therefore, the data sets with a range that is greater than 10 are:

1 5 7 8 14

5 7 9 21 23

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The function f(x) = - log (x-1); for plotting the graph first we have to draw the graph of f(x) = + log (x-1) and then take mirror image the entire graph, as shown in below diagram.

Graph representation is a way of representing a graph using data structures such as arrays, linked lists, or matrices.

The function f(x) = - log (x-1) has a domain of x > 1, since the argument of the logarithm must be positive.

We can choose a range of x values, such as x = 1.1, 1.2, 1.3, ..., 2.0, and then evaluate the function for each value of x in that range.

For example,

when x = 1.1, f(x) = - log(1.1 - 1) = 0.0953,

when x = 2.0, f(x) = - log(2.0 - 1) = -0.0000.

We can then plot the resulting points (1.1, 0.0953), (1.2, 0.2231), (1.3, 0.3567), ..., (2.0, -0.0000) on a graph.

The resulting graph will be a curve that starts at positive infinity reaches  minimum at x = 2 and approaches zero as x approaches positive infinity.

The graph will also have a vertical asymptote at x = 1, since the logarithm is undefined for x = 1. The graph will never touch or cross the x-axis, since the logarithm is always negative for x > 1.

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The value of c for which f '(/4) = 1 in the function f(x) = cx ln(cos x) is approximately c = -2.

To find the value of c, we first need to calculate the derivative of f(x) with respect to x. Using the product rule and the chain rule, we obtain:

f '(x) = c ln(cos x) - cx tan(x).

Next, we substitute x = π/4 into f '(x) and set it equal to 1:

f '(/4) = c ln(cos(/4)) - c(/4) tan(/4) = 1.

Simplifying the equation, we have:

c ln(√2/2) - c(1/4) = 1.

ln(√2/2) can be simplified to ln(1/√2) = -ln(√2) = -ln(2^(1/2)) = -(1/2) ln(2).

Now, rearranging the equation and solving for c:

c ln(2) = -1 + c/4.

c(ln(2) - 1/4) = -1.

c = -4/(4ln(2) - 1).

Calculating the approximate value, c ≈ -2.

Therefore, the value of c for which f '(/4) = 1 in the function f(x) = cx ln(cos x) is approximately c = -2.

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The value of f′(0) is 4.

To find f′(0), we need to differentiate the function f(x) = e^xg(x) with respect to x and evaluate it at x = 0.

Using the product rule of differentiation, the derivative of f(x) is given by:

f′(x) = e^xg(x) + e^xg′(x)

Since we are interested in f′(0), we substitute x = 0 into the derivative expression:

f′(0) = e^0g(0) + e^0g′(0)

Since e^0 = 1, the equation simplifies to:

f′(0) = g(0) + g′(0)

Given that g(0) = 1 and g′(0) = 3, we can substitute these values into the equation:

f′(0) = 1 + 3

Therefore, f′(0) = 4.

In summary, to find f′(0), we differentiate f(x) using the product rule and then substitute x = 0. The resulting expression simplifies to f′(0) = g(0) + g′(0), and by substituting the given values, we find that f′(0) = 4.

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Answer:

see details below

Step-by-step explanation:

a) week 1 :  #10" / (#10"+#12") = 509 / 736 =  69% (to nearest percent)

b) week 2 :  #10" / (#10"+#12") = 766 / 1076 = 383/538 = 71% (to nearest percent)

A).69% for week 1

B)71% for week 2