Let x^8+3x^4-4=p_1(x)p_2(x)...p_k(x) where each non-constant polynomial p_i(x) is monic with integer coefficients, and cannot be factored further over the integers. Compute p_1(1)+p_2(1)+...+p_k(1).

Answer:

We can use the formula for the area of a circle to solve this problem. We know that the area of one piece of pizza is 14.13 in². If the pizza is cut into eight equal pieces, then the total area of the pizza is 8 times the area of one piece of pizza, which is 8 * 14.13 = 113.04 in².

The formula for the area of a circle is A = πr², where A is the area of the circle and r is the radius. Solving for r, we get r = √(A/π). Substituting the total area of the pizza, we get:

r = √(113.04/π) ≈ 6

Therefore, the radius of the pizza is approximately 6 inches.

Step-by-step explanation:

To construct a proof demonstrating the validity of the argument ∃xF x → ∀xF x, F g ∴ Mg, we need to use the rules of propositional logic and quantifier rules.

1. Assume ∃xF x (Assumption)
2. Choose an arbitrary element g and assume F g (Assumption)
3. From ∃xF x, we can conclude that there exists an element x such that F x (Existential Elimination)
4. Since we assumed F g in step 2, we can use Universal Instantiation to conclude that ∀xF x (g is an arbitrary element)
5. From the premise ∃xF x → ∀xF x, we can use Implication Elimination to conclude ∀xF x
6. Using Universal Elimination, we can conclude F g from ∀xF x
7. From F g and the premise F g ∴ Mg, we can use Modus Ponens to conclude Mg
8. Since we assumed ∃xF x in step 1 and derived Mg in step 7, we can use Existential Introduction to conclude ∃xMx

Therefore, we have constructed a proof demonstrating the validity of the argument ∃xF x → ∀xF x, F g ∴ Mg, which can be summarized as follows:

1. ∃xF x (Assumption)
2. F g (Assumption)
3. ∃xF x → ∀xF x (Premise)
4. ∃x F x (Existential Elimination)
5. ∀xF x (Implication Elimination)
6. F g (Universal Elimination)
7. F g ∴ Mg (Premise)
8. Mg (Modus Ponens)
9. ∃xMx (Existential Introduction)

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Answer:

1344

Step-by-step explanation:

multiply the length(12in) ×width(14in)×height(8in)

Answer:

no

Step-by-step explanation:

to be a right triangle it must satisfy the Pythagoras theorem. 5-12-13 works

Answer:

Yes.

Step-by-step explanation:

29,61,90 are right triangles

15+11+13 is 29 therefor its a right triangle

A characteristic that cannot be observed cannot be measured in an epidemiologic study. This statement is False

Epidemiologic studies can measure various characteristics that cannot be directly observed, such as underlying health conditions, genetic factors, psychological traits, and attitudes.

These characteristics can be assessed through self-reported information, medical records, laboratory tests, and other types of data collection methods. However, some characteristics may be more difficult to measure accurately than others, and measurement error can affect the validity and reliability of study findings.

While it is challenging to measure unobservable characteristics in an epidemiologic study, researchers can use various methods, such as proxy measures, questionnaires, or interviews, to indirectly assess these characteristics. Thus, it is not impossible to measure them in an epidemiologic study.

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Answer:

33 qt

Step-by-step explanation:

theirs 4 quarts in a gallon so multiply the volume value by 4 :)

The distance of the student from the foot of the tower is 25.63m the nearest 1/2 is 25.5m.

Given that From the top of a tower 14m high

The angle of depression of a student is 32°

we can use trigonometry to find the distance from the foot of the tower to the student:

tan(32°) = opposite/adjacent = 14/distance

Rearranging this equation gives:

distance = 14/tan(32°)

= 25.63m

Therefore, the distance of the student from the foot of the tower is approximately 25.63m nearest 1/2, this is 25.5m.

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The probability that a student studied for exactly 5 hours is 0.17. (third option)

Probability calculates the chances that an event would happen. The probability the event occurs with certainty is 1 and the probability that the event would not occur with certainty is 0. The more likely the event is to happen, the closer the probability value would be to 1.

Probability that a student studied for exactly 5 hours = number of students that studied for 5 hours / total students surveyed

= 6 / 35 = 0.17

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The total number of ways to select the jerseys is [tex]$38220+499200=537420$[/tex].

(i) If he would like to hang up more or equal number of football jerseys than basketball jerseys, there are two cases:

Case 1: He hangs up 6 football jerseys and 0 basketball jerseys.

He can select 6 football jerseys from 15 in [tex]$\binom{15}{6}=5005$[/tex]ways.

Case 2: He hangs up 5 football jerseys and 1 basketball jersey.

He can select 5 football jerseys from 15 in [tex]$\binom{15}{5}=3003$[/tex] ways.

He can select 1 basketball jersey from 10 in [tex]$\binom{10}{1}=10$[/tex] ways.

Therefore, the total number of ways to select the jerseys is [tex]$5005+3003\times10=32035$[/tex].

(ii) If he would like to hang up an equal number of football and basketball jerseys, but he can't hang up Surya's basketball jersey without also hanging up Ashu's football jersey, there are two cases:

Case 1: He hangs up 3 football jerseys and 3 basketball jerseys, without Surya's jersey.

He can select 3 football jerseys from 15 in [tex]$\binom{15}{3}=455$[/tex] ways.

He can select 3 basketball jerseys (excluding Surya's) from 9 in [tex]$\binom{9}{3}=84$[/tex] ways.

Therefore, the total number of ways to select the jerseys is [tex]$455\times84=38220$[/tex].

Case 2: He hangs up 4 football jerseys and 2 basketball jerseys, with Surya's jersey.

He can select Surya's basketball jersey and Ashu's football jersey, then select 3 football jerseys from the remaining 13 and 1 basketball jersey from the remaining 8.

He can select 2 basketball jerseys (excluding Surya's) from 8 in [tex]$\binom{8}{2}=28$[/tex] ways.

Therefore, the total number of ways to select the jerseys is [tex]$2\times\binom{13}{3}\times\binom{8}{2}=499200$[/tex].

Thus, the total number of ways to select the jerseys is [tex]$38220+499200=537420$[/tex].

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Answer:

0.0

Step-by-step explanation:

0.019 or 0.0

Answer:

In a right-angled triangle XOY, with right angle at O, let M and N be the midpoints of legs OX and OY, respectively. If XN = 19 cm and YM = 22 cm , we need to find the length of XY.

We can use the Pythagorean theorem to solve this problem. Let the length of OX be a and the length of OY be b. Then, from the midpoint theorem, we know that XN = (1/2)b and YM = (1/2)a.

Using the Pythagorean theorem, we have:

a^2 + b^2 = OX^2 + OY^2 = XY^2

Substituting XN and YM in terms of a and b, we get:

(1/4)b^2 + (1/4)a^2 = (1/2)XY^2

Substituting the given values of XN and YM, we get:

19^2 + 22^2 = (1/2)XY^2

Simplifying, we get:

XY^2 = 865

Taking the square root of both sides, we get:

XY = sqrt(865) = 29.4 cm (approx.)

Therefore, the length of XY is approximately 29.4 cm.

Step-by-step explanation:

If the radius of the bullseye in the dart board is 0.5 cm, then the area of dartboard not including the bullseye is 182.5 cm².

The outer circumference of the dartboard is 48 centimeters, so we can use this to find the radius of the dartboard:

⇒ 48 = 2πr,

Dividing both sides by 2π, we get:

⇒ r = 48/2π ≈ 7.64,

So, radius of the dartboard is 7.64 centimeters.

The area(A) of a circle is = πr²,

where "r" is = radius,

The area of the bull's eye is:

⇒ Area of Bullseye = π × (0.5)²,

⇒ 0.785,

To find the area of the dartboard not including the bull's eye,

We subtract the area of the bull's eye from the area of the whole dartboard:

⇒ Area of dartboard not including bullseye = πr² - (area of bullseye),

⇒ Area of dartboard not including bullseye = 3.14×7.64×7.64 - 0.785,

⇒ Area of dartboard not including bullseye = 183.28 - 0.785,

⇒ Area of dartboard not including bullseye ≈ 182.5,

Therefore, the area of the dartboard not including the bull's eye is approximately 182.5 cm².

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(a) standard error (SE) = 2.0512

(b) probability that the sample mean is smaller than 128 = 0.1635

(c) probability that the sample mean is at least 131 = 0.3121

(a) To calculate the standard error (SE), we use the formula:

SE = (population standard deviation) / sqrt(sample size).

In this case, the population standard deviation is 20, and the sample size is 95.

Therefore,

SE = 20 / sqrt(95) ≈ 2.0512.

(b) To calculate the probability that the sample mean is smaller than 128, first find the z-value using the formula:

z = (sample mean - population mean) / SE.

In this case,

z = (128 - 130) / 2.0512 ≈ -0.98.

Then, use a z-table or calculator to find the probability associated with the z-value:

P(z < -0.98) ≈ 0.1635.

Thus, P(x < 128) = P(z < -0.98) = 0.1635.

(c) To calculate the probability that the sample mean is at least 131, first find the z-value:

z = (131 - 130) / 2.0512 ≈ 0.49.

Then, we need to find the probability P(z ≥ 0.49). Since z-tables provide the probability for z ≤ a given value, we can use the complement rule:

P(z ≥ 0.49) = 1 - P(z ≤ 0.49) ≈ 1 - 0.6879 = 0.3121.

Thus, P(x ≥ 131) = P(z ≥ 0.49) = 0.3121.

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The percentage of his budget allotted to the variable expenses is 46%.

Winston has $2,003 to budget each month. He budgets $1,081 for fixed expenses and the remainder of his budget is set aside for variable expenses.

Therefore, the percentage allotted for variable expenses can be calculated as follows:

Hence,

percent for allotted for variable expenses = 2003 - 1081 / 2003 × 100

percent for allotted for variable expenses = 922 / 2003 × 100

percent for allotted for variable expenses = 92200 / 2003

percent for allotted for variable expenses = 46.0309535696

percent for allotted for variable expenses = 46%

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Answer:

24 and 7/100 written as a decimal is 24.07.

Step-by-step explanation:

The matrix A that allows x(t) = 5e^(2t) - 3e^(t) to be a solution to the system x'(t) = Ax(t) is:

A = [2 0; 0 2]

We can find A by plugging in x(t) = 5e^(2t) - 3e^(t) into x'(t) = Ax(t) and solving for A.

x'(t) = d/dt (5e^(2t) - 3e^(t)) = 10e^(2t) - 3e^(t)

Ax(t) = A(5e^(2t) - 3e^(t)) = 5Ae^(2t) - 3Ae^(t)

For x(t) to be a solution to x'(t) = Ax(t), we must have:

10e^(2t) - 3e^(t) = 5Ae^(2t) - 3Ae^(t)

Simplifying this equation, we get:

(5A - 10)e^(2t) + 3Ae^(t) - 3e^(t) = 0

This equation must hold for all t, so the coefficients of e^(2t), e^(t), and the constant term must all be zero.

Thus, we get the following system of equations:

5A - 10 = 0

3A - 3 = 0

Solving this system, we find A = 2.

Therefore, the matrix A that allows x(t) = 5e^(2t) - 3e^(t) to be a solution to the system x'(t) = Ax(t) is:

A = [2 0; 0 2]

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In the given Markov chain X, all states other than the absorbing state s are transient.

To answer this question, we need to show that all states other than the absorbing state s are transient.

First, let's define what it means for a state to be transient. A state i is said to be transient if, starting from state i, the Markov chain has a non-zero probability of never returning to state i. In other words, there is some positive probability that the Markov chain will eventually leave state i and never come back.

Now, we know that all states communicate with the absorbing state s, which means that there is some positive probability Pis(n) for each state i to eventually reach s after n steps. Since s is an absorbing state, once the Markov chain reaches state s, it will stay there forever.

Therefore, if a state i is not equal to s, then there must be some positive probability that the Markov chain will eventually leave state i and reach state s, where it will stay forever. In other words, state i is transient since there is some positive probability that the Markov chain will never return to state i after leaving it.

So, to summarize, all states other than the absorbing state s are transient in this Markov chain. I hope this helps! Let me know if you have any other questions.

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You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0.11. This means that (c) in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to 11%.

The correct answer is (c) in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to 11%. This is because the given probability is an estimate based on a large number of bridge deals, and the law of large numbers states that as the number of trials (bridge deals) increases, the observed percentage will approach the true probability. Option (a) is incorrect because the given probability is not a guarantee for every 100 bridge deals. Option (b) is incorrect because the number of deals with each player having one ace will vary and may not be exactly 110,000. Option (d) is incorrect because the given probability only refers to the likelihood of each player having one ace, not the average number of aces in a hand.

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Answer:

Area= Length × Width

Area= 45 × 15 (you get 45 as your Length because it says in the equation that the Length of the end table is 45 inches and you get 15 as the width because in the equation it says the width is 15 inches)

Answer = 45 × 15=675

The balance payment offered in Option B is approximately $432,215.64.

To find the balance payment offered in Option B, we'll need to determine the present value of the payment in Option A and compare it to the upfront payment in Option B.

Option A: $540,000 payment in 5 years
Interest rate: 6% compounded quarterly, so 1.5% (0.015) per quarter
Number of quarters: 5 years * 4 quarters/year = 20 quarters

Present Value of Option A = 540,000 / (1 + 0.015)^20
PV_A = $402,265.62 (rounded to the nearest cent)

Option B: $80,000 paid upfront
PV_B = $80,000

To find the balance payment, we'll first determine the remaining present value for Option B:

Remaining PV_B = PV_A - PV_B
Remaining PV_B = $402,265.62 - $80,000
Remaining PV_B = $322,265.62

Now, we'll convert the remaining present value back to its future value (in 5 years) using the same interest rate and compounding period:

Balance payment = Remaining PV_B * (1 + 0.015)^20
Balance payment = $322,265.62 * (1 + 0.015)^20
Balance payment = $432,215.64 (rounded to the nearest cent)

So, we can state that the balance payment offered in Option B is approximately $432,215.64.

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Rectangle A’B’C’D’ is the image of rectangle ABCD then 90 degrees rotation about the origin is true

To determine which rotation was done to transform point BBCD to A'B'C'D'

90 degrees rotation about the origin

This transformation would map point ABCD to A'B'C'D" which is the same as A'.

However, this transformation is clockwise, whereas the actual transformation was counterclockwise.

Hence, 90 degrees rotation about the origin, followed by a reflection about the y-axis is correct

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We can see that the constant of proportionality between x and y is k = 8, using that we can see that when x = 12 the value of y is 96

We know that x and y vary directly, then we can write the equation that relates these variables as.

y = kx

Where k is a constant

We know that y = 48 when x = 6, then we can write.

48 = k*6

48/6 = k

8 = k

The relation is:

y = 8*x

Then if x = 12, we have.

y = 8*12

y = 96

That is the value of y.

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Answer:25.2

Step-by-step explanation:

To find the value of x, we first need to find the missing angle value, which is 180-90-59, making it 31.

Now that we have that value, we can use SOH to find the hypotenuse.

The equation would look something like this:

[tex]\sin\left(31\right)=\frac{13}{x}[/tex]

Which we can change to get the x value like this:

[tex]\frac{13}{\sin\left(31\right)}=x[/tex]

This makes the X value equal to 25.241.

Since you need it as the nearest tenth, you can round it down to 25.2.

The team that had the best overall record for the season is C. Eagles; they have a larger mean value of about 22 points Falcons; they have a larger mean value of about 20.9 points

The best measure of center to compare the overall records of the two teams is the mean (average) value of the points earned in each game. This is because the mean is a commonly used measure of center in statistics and provides a good overall summary of the data set.

In this case, the Eagles have a larger mean value of about 22 points (calculated by summing the points and dividing by the number of games) compared to the Falcons' mean value of about 20.9 points. So, the correct answer would be Eagles; they have a larger mean value of about 22 points

It's worth noting that using the median value in this case is not the most accurate, because this will give you a more robust representation of the center of the dataset in cases where data have outliers.

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The probability that he/she has Internet service given that he/she had already television service is 62.5%.

We need to find the probability that a resident has at least one of the two services and the probability that a resident has Internet service given they already have television service.

(1) To find the probability of a resident having at least one of these two services, we can use the formula                     P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where A represents Internet service and B represents television service.

P(A) = 0.60 (60% have Internet service)
P(B) = 0.80 (80% have television service)
P(A ∩ B) = 0.50 (50% have both services)

P(A ∪ B) = 0.60 + 0.80 - 0.50 = 0.90 (90%)

Therefore, the probability that a resident has at least one of the two services is 90%.

(2) To find the probability of a resident having Internet service given they have television service, we can use the formula P(A | B) = P(A ∩ B) / P(B).

P(A | B) = P(A ∩ B) / P(B) = 0.50 / 0.80 = 0.625 (62.5%)

So, the probability that a resident has Internet service given they already have television service is 62.5%.

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The volume of cone is 2 cubic units.

In this image, we have :

The cylinder has a volume of 18 cubic units and a height of 3.

The cone has a congruent base and the same height.

We have to find the volume of the cone.

We know that:

Volume of the cylinder is :

Volume of cylinder = [tex]\pi r^{2} h[/tex]__(A)

18 = [tex]\pi r^2(3)[/tex]

[tex]\pi r^2= 6[/tex]

Now, Volume of cone = [tex](1/3)\pi r^{2} h[/tex]___(B)

and, The cone has a congruent base and the same height.

substitute equation A in equation B

Volume of cone = (1/3)volume of cylinder

Volume of cone = (1/3) × 6

Volume of cone = 2 units.

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The measure of a central angle of a regular polygon with 24 sides is 15°. There is no need to round the answer as it is already in whole degrees.

The measure of a central angle of a regular polygon with 24 sides. A central angle is formed by two radii drawn from the center of the polygon to two consecutive vertices. In a regular polygon, all the sides and angles are equal.

To find the measure of a central angle, you can use the formula: Central Angle = (360°) / (Number of Sides) In this case, the regular polygon has 24 sides.

So the formula would be: Central Angle = (360°) / (24) Now, we can solve for the central angle: Central Angle = 15° So, the measure of a central angle in a regular polygon with 24 sides is 15 degrees. Since the result is already in whole degrees, there's no need to round it to the nearest tenth of a degree

To find the measure of a central angle of a regular polygon with 24 sides, you can use the formula:

Central angle = (360°) / (number of sides)

In this case, the number of sides is 24, so the formula becomes:

Central angle = (360°) / 24

Central angle = 15°

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The measure of <Z is B. 66^o.

A triangle is a figure bounded by three straight lines called its sides. As such, the sum of the internal angles of a triangle is 180^o.

From the given diagram, it can be seen that;

<Y = 90^o, and <X = 24^o

Thus,

<X + <Y + <Z = 180^o

24 + 90 + <Z = 180

114 + <Z = 180

<Z = 180 - 114

    = 66

<Z = 66^o

The measure of <Z is 66^o. Thus option B.

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The closest option is (d) 12.054 to 15.946.

To find the confidence interval for the mean of a normal population, we use the formula:

CI = x ± z* (σ/√n)

where x is the sample mean, z* is the critical value from the standard normal distribution corresponding to the desired confidence level (80% in this case), σ is the population standard deviation (unknown), and n is the sample size.

Since the population standard deviation is unknown, we can estimate it using the sample standard deviation:

s = √[ Σ(xi - x)² / (n - 1) ]

where xi is the ith observation, x is the sample mean, and n is the sample size.

Plugging in the values from the sample, we get:

x = (10 + 12 + 18 + 16) / 4 = 14

s = √[ (10-14)² + (12-14)² + (18-14)² + (16-14)² / 3 ] = 2.94

To find the critical value, we look it up from a standard normal distribution table or use a calculator. For an 80% confidence interval, the critical value is approximately 1.282.

Plugging in all the values, we get:

CI = 14 ± 1.282 * (2.94 / √4) = 14 ± 1.4952

Therefore, the 80% confidence interval for the mean is:

CI = (14 - 1.4952, 14 + 1.4952) = (12.5048, 15.4952)

The closest option is (d) 12.054 to 15.946.

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