find the polynomial equation with the given roots (precalc)

Answer:

its c)

Step-by-step explanation:

just looked it up

Answer: m <2 = 104 degrees.

Step-by-step explanation:

Those trees make parallel lines.

The Alternate Interior Angle Theorem says that angles inside of the parallel lines and on the opposite side of each other are congruent.

The angle next to angle two is the alternate to the 76-degree angle.

Since a straight line sums to 180 degrees, you can find the measure of angle 2 by subtracting 76 from 180. 180-76 = 104.

The ΔH (enthalpy change) for aluminum when it is heated from 0.0°C to 100.0°C is 2074.19 J.

The expression given for the temperature-dependent heat capacity of a substance is:

c_p = a + bT + cT^2

where c_p is the heat capacity in J/K, T is the temperature in °C, and a, b, and c are coefficients.

To calculate the ΔH (enthalpy change) for aluminum when it is heated from 0.0°C to 100.0°C, we need to integrate the heat capacity expression with respect to temperature over the given temperature range.

ΔH = ∫(c_p dT)

First, let's substitute the given coefficients into the expression:

c_p = 20.68 + (12.38×10^-3)T + 0

Next, we integrate the expression over the temperature range of 0.0°C to 100.0°C:

ΔH = ∫[20.68 + (12.38×10^-3)T] dT

Integrating with respect to T gives:

ΔH = 20.68T + (12.38×10^-3)(T^2/2)

To evaluate the integral, we substitute the upper and lower temperature limits:

ΔH = 20.68(100.0) + (12.38×10^-3)((100.0)^2/2) - [20.68(0.0) + (12.38×10^-3)((0.0)^2/2)]

Simplifying the equation gives:

ΔH = 2068 + 6.19

ΔH = 2074.19 J

Therefore, the enthalpy change (ΔH) for aluminum when it is heated from 0.0°C to 100.0°C is 2074.19 J.

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If \(h(x)=\frac{-5}{6} x+\frac{7}{8}\)  then the value of h(3) = -13/8  , h(4) = -59/24 ,  h(-1/2) = 31/24 .

In the question , the equation is given as

\(h(x)=\frac{-5}{6} x+\frac{7}{8}\)      ....(i)

Part(a)

To find the value of h(3)

we substitute the value of x=3 .

On substituting the value of x=3 in equation (i),

we get ,

h(3) = (-5/6)3+7/8

= -15/6+7/8

taking LCM of 6 and 8 as 24, we get

= -60/24 + 21/24

= (-60+21)/24

= -39/24

Writing in the simplest form we get

= -13/8

so, the value of h(3)= -13/8 .

Part(b)

for h(4) ,we substitute the value of x=4 .

On substituting the value of x=4 in equation (i) ,

we get ,

h(4) = (-5/6)4+7/8

= -20/6+7/8

taking LCM of 6 and 8 as 24, we get

= -80/24 + 21/24

= (-80+21)/24

= -59/24

so , the value of h(4)= -59/24 .

Part(c)

for h(-1/2) ,we substitute the value of x as -1/2 .

On substituting the value of x = -1/2 in equation (i) ,

we get ,

\(h(\frac{-1}{2} )=\frac{-5}{6} *\frac{-1}{2} +\frac{7}{8}\)

= 5/12 +7/8

taking LCM of 12 and 8 as 24, we get

= 10/24 + 21/24

= (10+21)/24

= 31/24

so , the value of h(-1/2)= 31/24 .

Therefore , if h(x) = (-5/6)x+7/8 the the value of h(3)= -13/8  , h(4)= -59/24 and h(-1/2)= 31/24 .

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The value of the N must be in order of the 31 so that the value of the Sn will get exceeded by 4.

Only when the kind of sequence is known can the sum of n words in a sequence be calculated. Normally, while computing the sum of an n-number of terms, we take into account arithmetic progression.

The common distinction between each following phrase and each preceding term remains unchanged throughout this process. Natural numbers are an illustration of AP, where the common difference is 1. Hence, in order to determine the sum of all natural numbers, we must be aware of the formula.

\(S_N = \sum^N_{k=1} \frac{1}{k}\)

= 1 + 1/2 + 1/3 + 1/4 + ..... 1/N

It is a harmonic series,

Therefore, by trial and error method we get N = 31 to exceed Sn = 4

There are some elimination methods,

ln N + 1/N < Sn < ln N+1

we want Sn > 4

ln N+1/N < 4

maximum value of N is ln N+1/N =4

4<ln N+1 → ln N > 3, N > e³

5<ln N+1 → ln 4, N > e⁴

For Sn to exceed it value maybe in between

e³ < N < e⁴.

20.08 < N < 54.5

As I said it is an approximation it won't give exact value.

By taking a value in that range and check for desired value.

for N = 31 Sn willl exceed '4'.

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Complete question:

How large must N be in order for

\(S_N = \sum^N_{k=1} \frac{1}{k}\)

to exceed 100 to exceed 4? Note: Computer calculations show that for SN to exceed 20, N = 272, 400, 600 and for Sn to exceed 100, N = 1.5x10⁴³.

N = ?

Answer:

Step-by-step explanation:

To find the volume of the solid of revolution, we can use the formula for the volume of a solid of revolution:

V = π∫[a,b] (f(x))^2 dx

where f(x) is the distance between the x-axis and the upper half of the ellipse at x, a and b are the limits of integration.

The upper half of the ellipse can be written as y = b√(1 - x^2/a^2). Thus, the distance between the x-axis and the ellipse at x is given by f(x) = b√(1 - x^2/a^2). Substituting this into the formula for the volume of a solid of revolution, we get:

V = π∫[-a,a] (b√(1 - x^2/a^2))^2 dx

= 2πb^2∫[0,a] (1 - x^2/a^2) dx (because the integrand is even)

= 2πb^2 [x - x^3/(3a^2)]|[0,a]

= 2πb^2 [a - a^3/(3a^2)]

= (4π*b^2*a^2)/3

Therefore, the volume of the solid of revolution is (4π*b^2*a^2)/3, which is the volume of a prolate spheroid.

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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If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that the population mean CO2 level has increased. If the p-value is greater than 0.05.

Null hypothesis (H0): The population means \(CO_2\) level is equal to 418 ppm.

Alternative hypothesis (Ha): The population means \(CO_2\) level is greater than 418 ppm.

A p-value, or probability value, is a statistical measure that helps to determine the significance of results obtained from a hypothesis test. It is the probability of observing a test statistic as extreme as the one computed, assuming that the null hypothesis is true. The null hypothesis is a statement that there is no significant difference between two populations or that there is no effect of an intervention or treatment.

The p-value is used to decide whether or not to reject the null hypothesis based on a pre-determined significance level, typically 0.05 or 0.01. If the p-value is less than the significance level, the null hypothesis is rejected, indicating that the observed results are unlikely to have occurred by chance alone, and that the alternative hypothesis is likely true. Conversely, if the p-value is greater than the significance level, the null hypothesis is not rejected, indicating that the observed results are consistent with the null hypothesis.

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Answers:

3 chocolate cones

1 strawberry cones

===========================================================

Explanation:

Let's isolate the variable c in the first equation

c+s = 4

c = 4-s

we subtract s from both sides to get c all by itself. This will then be plugged into the second equation. I'm using the substitution property.

1.75c + 1.3s = 6.55

1.75(4-s) + 1.3s = 6.55 ..... replace c with 4-s

1.75*4 + 1.75*(-s) + 1.3s = 6.55

7 - 1.75s + 1.3s = 6.55

-0.45s + 7 = 6.55

-0.45s = 6.55 - 7

-0.45s = -0.45

s = -0.45/(-0.45)

s = 1

So he bought 1 strawberry cone. Use this value of s to find c

c = 4-s

c = 4-1

c = 3

This says he also bought 3 chocolate cones.

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

As a check, we see that c+s = 3+1 = 4, showing that he bought 4 cones total.

Also,

1.75c + 1.3s = 1.75*3 + 1.3*1 = 6.55

indicating he spent $6.55 total for the four cones. This matches with what the instructions tell us, so the answer is confirmed.

Answer:

Step-by-step explanation:

\(\left \{ {{c+s=4} \atop {1.75c+1.3s=6.55}} \right.\)

1.75c + 1.75s = 1.75 × 4 ........ (1)

1.75c + 1.3s = 6.55 ........ (2)

(1) - (2)

0.45s = 0.45 ⇒ s = 1

c + 1 = 4 ⇒ c = 3

[ 3 ] chocolate  [ 1 ] strawberry

The example that illustrates the difference between statistical significance and practial significance is

In a survey arranged by school-authority of a district on participation in sports by school-going boys and girls, it is found that 60% of boys and 57% of girls participate in outdoor sports. Thus the survey shows a 3% difference between school-going boy-participants and girl-participants in outdoor sports. Now the point is how much significance this 3% difference has statistically as well as practically. Statistical significance of this 3% depends upon the size of data used in determining the percentage of boys and girls participate in sports. If a sufficiently big sample size is used then the difference is statistically significant, and if a very small sample size is used then the difference is statistically insignificant. Thus bigger the sample size more is the statistical significance of a computed figure.

On the other hand practical significance of this 3% difference arises if decision is made or action is taken or needs to be taken on the basis of this 3% difference. If cost permits, the authority may consider promoting girl students participation in sports in order to bring about more gender parity in outdoor sports. In this case the 3% difference though small, may be practically significant.

Statistical significance is a measure of whether your research findings are meaningful. It is concerned with whether a research result is due to chance or sampling variability. Where, practical significance is concerened with wheteher the result is useful in the real world.

Therefore, the example that illustrates the difference between statistical significance and practial significance is

In a survey arranged by school-authority of a district on participation in sports by school-going boys and girls, it is found that 60% of boys and 57% of girls participate in outdoor sports. Thus the survey shows a 3% difference between school-going boy-participants and girl-participants in outdoor sports. Now the point is how much significance this 3% difference has statistically as well as practically. Statistical significance of this 3% depends upon the size of data used in determining the percentage of boys and girls participate in sports. If a sufficiently big sample size is used then the difference is statistically significant, and if a very small sample size is used then the difference is statistically insignificant. Thus bigger the sample size more is the statistical significance of a computed figure.

On the other hand practical significance of this 3% difference arises if decision is made or action is taken or needs to be taken on the basis of this 3% difference. If cost permits, the authority may consider promoting girl students participation in sports in order to bring about more gender parity in outdoor sports. In this case the 3% difference though small, may be practically significant.

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a. The chart did not maintain consistent scaling

b. The graph is not the appropriate graph type to display such data

c.  The display had inaccurate or distorted visual representations

When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.

The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.

So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.

It also advisable to make use of  clear and accurate labeling with descriptive titles and units of measurement.

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Explanation: A linear function would be a diagonal line from left to right either moving up or down in direction. An exponential function would be a straight line on the x axis from left or right until it reaches y axis, then a sharp curve up or down. A quadratic function would be a U shape either facing up or down.

Linear equation: y = mx + b
Exponential equation: y = abˣ
Quadratic function: y = axˣ + bx + c

The graph listed in the picture would be a quadratic function according to the explanation.

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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A polygon having seven sides and seven angles is called a heptagon. Seven straight sides and seven corners, or vertices, make up a heptagon. It's also referred to as a "septagon" at times.

A seven-sided polygon is called a heptagon. A closed figure with seven vertices, it is. Another name for a heptagon is a septagon.

There are various sorts of hexagons, depending on the angles and diagonals.

Regular and Irregular Heptagons

Concave and Convex Heptagon

The following are some heptagon's characteristics:

(1) The inner angles of a heptagon add up to 900 degrees.

(2) A heptagon's outside angles add up to 360 degrees.

(3) The internal angle of a normal heptagon measures approximately 128.57 degrees.

(4) The size of a typical heptagon's central angle is roughly 51.43 degrees.

(5) There are fourteen diagonals in a heptagon.

(6) Convex heptagons are another name for regular heptagons.

(7) A heptagon has a total of five triangles.

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Answer:

Step-by-step explanation:

ok so we organize it by:

9, 12, 13, 14, 14, 18, 19, 22, 22, 23, 42

so we eliminate 42 and so we cross out one from the left side and one from the right side and we repeat that and we find the center which is any number between 14-18

Answer:

50 meters above the ground. Then, it drops 65 meters into an underground tunnel.What is the elevation of the tunnel relative to the ground

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

khan show me the steps

Compute the above expression to find the balance in the account after 3 years.

What is Balance?

Balance refers to the amount of money or value in an account or financial statement. It represents the remaining funds or assets after deducting any liabilities, expenses, or withdrawals. In the context of banking or personal finance, the balance is the total amount of money available in an account at a specific point in time.

To compute the balance in the account after a specified period of time using compound interest, we can use the formula:

\(A = P(1 + r/n)^(nt),\)

where:

A is the final account balance,

P is the principal amount (initial investment),

r is the annual interest rate (expressed as a decimal),

n is the number of compounding periods per year,

t is the number of years.

For the first scenario:

Principal amount (P) = $15,000

Annual interest rate (r) = 6% = 0.06 (as a decimal)

Number of compounding periods per year (n) = 4 (quarterly compounding)

Number of years (t) = 8

Using the formula:

\(A = 15000(1 + 0.06/4)^(4*8)\)

Compute the above expression to find the balance in the account after 8 years.

For the second scenario:

Principal amount (P) = $23,000

Annual interest rate (r) = 5% = 0.05 (as a decimal)

Number of compounding periods per year (n) = 365 (daily compounding)

Number of years (t) = 3

Using the formula:

\(A = 23000(1 + 0.05/365)^(365*3)\)

Compute the above expression to find the balance in the account after 3 years.

Perform the calculations to obtain the final balances in the accounts after the specified periods of time, rounding to the nearest cent as needed.

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Answer:

8

Step-by-step explanation:

24/3 = 8

The mapping representing a rotation of 270 degree clockwise about the origin is (x, y) -----> (-y, x)

We use the rotation of 90 degree to find the mapping of 270 degrees.

The rotation of 270 degree clockwise is same as the anticlockwise rotation of 90 degrees about the origin.

So the mapping of 270 degree clockwise rotation is exactly the mapping of 90 degree anti clockwise rotation.

Now the mapping of 90 degree anti clockwise rotation is  (x, y) -----> (-y, x).

So the mapping representing a rotation of 270 degree clockwise about the origin is (x, y) -----> (-y, x)

This implies that a point (x, y) on the co-ordinate plane becomes (-y, x) after a clockwise 270 degree rotation.

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Answer:

m=7/4

Step-by-step explanation:

The average cost per mile for a one-day, 200-mile trip with a rented car that costs $60/day and gets 20 miles/gallon, with gasoline costing $2/gallon, is $0.35/mile.

To calculate the total cost of the trip, we need to first calculate how much gasoline the car will consume. For a 200-mile trip, the car will use 10 gallons of gasoline (200 miles / 20 miles per gallon). The cost of the gasoline will be $20 (10 gallons x $2 per gallon).

Adding the cost of renting the car ($60) to the cost of gasoline ($20), the total cost of the trip is $80. To calculate the average cost per mile, we divide the total cost of the trip by the number of miles traveled. Therefore, the average cost per mile for the one-day, 200-mile trip is $0.40 per mile ($80 total cost / 200 miles).

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The maximum interest rate that can be charged during the fifth year is 6.75%. The correct option is the third option c. 6.75%

From the question, we are to determine the maximum interest rate that can be charged during the fifth year

A 2/1 ARM means that the interest rate is fixed for the first two years and then adjusts annually based on a specified index plus a margin. The "2/10 cap" means that the interest rate can only increase or decrease by a maximum of 2 percentage points each year, and can never be more than 10 percentage points higher than the initial rate.

Since the initial rate is 2.75%, the maximum rate that can be charged during the fifth year is:

2.75% + (2 x 2%) = 6.75%

Hence, the maximum interest rate that can be charged during the fifth year is 6.75%.

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The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

To determine the critical path of the project, we need to find the longest path of activities that must be completed in order to finish the project on time. This is done by calculating the earliest start time (ES) and earliest finish time (EF) for each activity.

Starting with activity A, ES = 0 and EF = 4. Activity B can start immediately after A is complete, so ES = 4 and EF = 7. Activity C can start after A is complete, so ES = 4 and EF = 6. Activity D can start after B is complete, so ES = 7 and EF = 9. Finally, activity E can start after C and D are complete, so ES = 9 and EF = 11.

The variance for each activity is also given, which allows us to calculate the standard deviation and determine the probability of completing the project on time. The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

Using the expected durations and variances, we can calculate the standard deviation of the critical path. This information can be used to determine the probability of completing the project on time.

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The decimal expansion of the given fraction is 0.0208. Therefore, the correct answer is option D.

The given fraction is 13/625.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, the decimal expansion is 13/625 = 0.0208

So, the number of places of decimal are 4.

Therefore, the correct answer is option D.

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The acceleration acquired by the object of mass 12 Kg and is pushed with a force of 12 N, is given by 5/3 m/s².

We know that from the first law of Newton's Law that,

F = m*a

where 'F' is applied force; 'm' is mass of object and 'a' is acceleration.

Let the acceleration acquired by the object be 'A'.

Mass of the object is (m) = 12 Kg

The force applied (F) = 20 N

So from Newton's First Law of Motion we get,

F = m*a

20 = 12*A

A = 20/12

A = 5/3

Hence the acceleration will be 5/3 m/s².

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The question is in another language. The question is in English will be -

''What is the acceleration acquired by an object that has a mass of 12 Kg and is pushed with a force of 20N?''

4/7 is probability a two-way table to model this chance process.

What are examples and probability?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

                                The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

No events getting thick crust pizza and getting pizza with mushrooms are not disjoint as we can have pizza that has thick crust and mushroom both.

No events are not independent as

P(thick and having mushroom) is not equal to P(thick crust)*P(having mushroom)

P( thick and having mushroom) = 2/7

P(thick crust) = 3/7

P( having mushroom) = 4/7

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Answer:

$3

Step-by-step explanation:

(80-62) ÷ 3