Find the 10th term of the arithmetic sequence in which 12 and d = 9.1.​

It should be noted that the factored form of the expression w³ - 8w² + 12w is w(w - 6)(w - 2).

First, we look for common factors that can be factored out of all the terms. In this case, we can factor out w:

w(w² - 8w + 12)

Now, we need to factor the quadratic expression w² - 8w + 12. We're looking for two numbers that multiply to 12 (the coefficient of the constant term) and add up to -8 (the coefficient of the linear term).

By trying different combinations, we can find that -6 and -2 satisfy these conditions:

w(w - 6)(w - 2)

Therefore, the factored form of the expression w³ - 8w² + 12w is w(w - 6)(w - 2).

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The slope-intercept form of the equation of each line is  y=-x+4.

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Based on the given information, person C would take 600 minutes to finish the job by himself.

Let's break down the steps to find out how long it would take person C to finish the job by himself.

1. Determine the rate at which person A completes the job. We can find this by dividing the total job by the time it takes person A to complete it: 1 job / 100 minutes = 1/100 job per minute.

2. Similarly, determine the rate at which person B completes the job: 1 job / 120 minutes = 1/120 job per minute.

3. When person A and person B work together, we can add their rates to find the combined rate: (1/100 job per minute) + (1/120 job per minute) = (12/1200 + 10/1200) = 22/1200 job per minute.

4. After 40 minutes of working together, person C joins them, and together they finish the job in an additional 10 minutes. So the total time they take together is 40 minutes + 10 minutes = 50 minutes.

5. Calculate the total job done by person A and person B working together: (22/1200 job per minute) * (50 minutes) = 22/24 = 11/12 of the job.

6. Since person C helped complete 11/12 of the job in 50 minutes, we can calculate the rate at which person C works alone by dividing the remaining 1/12 of the job by the time taken: (1/12 job) / (50 minutes) = 1/600 job per minute.

7. Now we can find how long it would take person C to finish the job by himself by dividing the total job (1 job) by the rate at which person C works alone: 1 job / (1/600 job per minute) = 600 minutes.

Therefore, it would take person C 600 minutes to finish the job by himself.


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It would take c approximately 3.75 minutes to finish the job by himself. To find out how long it would take c to finish the job by himself, we need to first calculate how much work a and b can do together in 40 minutes.

Since a can finish the job in 100 minutes, we can say that a completes \(\frac{1}{100}\)th of the job in 1 minute. Similarly, b completes \(\frac{1}{120}\)th of the job in 1 minute.

So, in 40 minutes, a completes \(\frac{40}{100}\) = \(\frac{2}{5}\)th of the job, and b completes \(\frac{40}{120}\) = \(\frac{1}{3}\)rd of the job.

Together, a and b complete 2/5 + 1/3 = 6/15 + 5/15 = 11/15th of the job in 40 minutes.

Since a, b, and c complete the entire job in an additional 10 minutes, we can subtract 11/15th of the job from 1 to find out how much work c did in those 10 minutes. This comes out to be 1 - 11/15 = 4/15th of the job.

Therefore, c can complete 4/15th of the job in 10 minutes.

To find out how long it would take c to complete the whole job by himself, we can set up a proportion:

    (4/15) / x = 1 / 1

Cross-multiplying gives us:

    4x = 15

=> x = 15/4 = 3.75 minutes.

Therefore, it would take c approximately 3.75 minutes to finish the job by himself.

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Answer:

x⁴-196x³+9204x²+32200x+40000

Step-by-step explanation:

(x+2)(x+2)×(x-100)(x-100)=

(x²+4x+4)×(x²-200x+10000)=

(x⁴-200x³+10000x²+4x³-800x²+40000x+4x²-800x+40000)

=x⁴-196x³+9204x²+32200x+40000

x⁴-196x³+9204x²+32200x+40000

Answer:

30°, 60° and 90°

Step-by-step explanation:

Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.

Note that a right angled triangle is made up of two acute angles and a right angled (90°)

Let's get one of the acute angles first

If Arccos (√3/2)=β

β = cos^-1 √3/2

β = 30°

This shows that one of the acute angles is 30°

To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.

90+30+x = 180

120+x = 180

x = 180-120

x = 60°

All the angle measurement for the right angled triangle are 30°, 60° and 90°

A characteristic of the classical approach to probability include the following: D. probabilities assume outcomes of an experiment are equally likely.

In Science, an experiment is a scientific investigation which typically involves the process of manipulating an independent variable (the cause), in order to determine or measure the dependent variable (the effect).

In Mathematics and statistics, an expected value is sometimes referred to as the long-term mean (average) of a discrete random variable, E(X) and it can be calculated by taking the weighted average of all the outcomes of the discrete random variable with respect to their probabilities.

In this context, we can logically deduce that a characteristic of the classical approach to probability is that most times probabilities assume outcomes (results) of an experiment are equally likely.

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Answer:

10 meters.

Step-by-step explanation:

The area of a rectangle formula is width multiplied by length. So, to find the length of the pool, simply divide the width from the area.

90/9=10

The length of the pool is 10 meters.

Hope this helps!

If not, I am sorry.

Answer:

X = 14

Step-by-step explanation:

30 = 5x + 2

25         60

multiply both sides by 60

1800/25 = 5x + 2

Multiply both sides by 25

1800 = 25 (5x + 2)

1800 = 125x + 50

  -50.            -50

1750 = 125x

divide both sides by 125

14 = x

Answer:

x=14

Step-by-step explanation:

Similar Shapes

Two figures that have the same shape are said to be similar.

If two figures are similar, the ratios of the lengths of their corresponding sides are equal.

We are given two similar shapes and the lengths of two corresponding sides:

25 corresponds to 30

60 corresponds to 5x+2

According to the definition:

\(\displaystyle \frac{5x+2}{60}=\frac{30}{25}\)

Multiplying by 60*25:

\(25(5x+2)=60(30)\)

Operating:

\(125x+50=1800\)

Subtracting 50:

\(125x=1800-50=1750\)

Dividing by 125:

\(x = 1750/125 =14\)

x=14

Answer: a and c

Step-by-step explanation:

I know it’s not b but isn’t adjacent angel two angels?

Correct me if I’m wrong

Chloe runs her air conditioner for a total of 4 months, or 120 days. Chloe spends $176.40 per year on utility bills for the air conditioner during the four hottest months.

The reason for this expense is the need for cooling during these months, and the cost associated with running the air conditioner for 7 hours per day at a rate of $0.21 per hour.

To calculate the annual cost of running Chloe's air conditioner, we need to consider the number of hours per day, the cost per hour, and the number of days the air conditioner is used.

1. First, let's determine the total number of hours the air conditioner runs during the four hottest months:
7 hours/day * 30 days/month * 4 months = 840 hours

2. Now, we can calculate the total cost by multiplying the number of hours by the cost per hour:
840 hours * $0.21/hour = $176.40

At 7 hours per day, that's a total of 840 hours of use. At a cost of 21 cents per hour, Chloe spends 0.21 x 840 = $176.40 per year on utility bills for her air conditioner.

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The value of |EE| at P(/ 6 , 0.1, 2) is  |20^(-0.5)(cos(5/6) ax + cos(5/6)ay)|.

To find the magnitude |EE| at point P, we substitute the coordinates of P (x, y, z) into the expression for EE and calculate the magnitude using the Pythagorean theorem.

Given EE = 20^(-5y)(cos(5x) ax + cos(5x)ay), we evaluate it at P(/6, 0.1, 2):

|EE| = |20^(-5y)(cos(5x) ax + cos(5x)ay)|

Substituting the coordinates of P, we have:

|EE| = |20^(-5(0.1))(cos(5(/6)) ax + cos(5(/6))ay)|

Simplifying further:

|EE| = |20^(-0.5)(cos(5/6) ax + cos(5/6)ay)|

To find a unit vector in the direction of E at point P, we divide the vector EE by its magnitude |EE|.

Unit vector in the direction of E at P = EE / |EE|

Substituting the values, we have:

Unit vector in the direction of E at P = (20^(-5y)(cos(5x) ax + cos(5x)ay)) / |EE|

Finally, to find the equation of the direction line passing through point P, we use the parametric form of the line equation, which is:

(x - x₀) / a = (y - y₀) / b = (z - z₀) / c

where (x₀, y₀, z₀) is the given point on the line and (a, b, c) is the direction vector. In this case, the direction vector is the unit vector in the direction of E at point P. Substitute the values of P and the direction vector into the equation, and simplify if necessary to obtain the equation of the line passing through P.

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The value of |EE| at P(/ 6 , 0.1, 2) is  |20^(-0.5)(cos(5/6) ax + cos(5/6)ay)|.

To find the magnitude |EE| at point P, we substitute the coordinates of P (x, y, z) into the expression for EE and calculate the magnitude using the Pythagorean theorem.

Given EE = 20^(-5y)(cos(5x) ax + cos(5x)ay), we evaluate it at P(/6, 0.1, 2):

|EE| = |20^(-5y)(cos(5x) ax + cos(5x)ay)|

Substituting the coordinates of P, we have:

|EE| = |20^(-5(0.1))(cos(5(/6)) ax + cos(5(/6))ay)|

Simplifying further:

|EE| = |20^(-0.5)(cos(5/6) ax + cos(5/6)ay)|

To find a unit vector in the direction of E at point P, we divide the vector EE by its magnitude |EE|.

Unit vector in the direction of E at P = EE / |EE|

Substituting the values, we have:

Unit vector in the direction of E at P = (20^(-5y)(cos(5x) ax + cos(5x)ay)) / |EE|

Finally, to find the equation of the direction line passing through point P, we use the parametric form of the line equation, which is:

(x - x₀) / a = (y - y₀) / b = (z - z₀) / c

where (x₀, y₀, z₀) is the given point on the line and (a, b, c) is the direction vector. In this case, the direction vector is the unit vector in the direction of E at point P. Substitute the values of P and the direction vector into the equation, and simplify if necessary to obtain the equation of the line passing through P.

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The appropriate critical value is -1.88 and the decision is to fail to reject the null hypothesis.

The null hypothesis (H0) states that the new drug is not superior to the one commonly prescribed. The alternative hypothesis (H1) states that the new drug is superior to the one commonly prescribed. We use the level of significance (α) as 0.03.

Given that:

The test statistic can be calculated using the following formula:

\(Z = (x - np) / \sqrt{(np(1 - p))}\)

Substituting the values, we get:

\(Z = (68 - 100(0.6)) / \sqrt{(100(0.6)(0.4)} )\)

Z = -1.86

The critical value of the z-distribution for a one-tailed test at a 0.03 level of significance is -1.88. Since -1.86 is not less than -1.88, we fail to reject the null hypothesis (H0). Therefore, there is not sufficient evidence to conclude that the new drug is superior to the one commonly prescribed at a 0.03 level of significance.

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a) Let x represent the number of pounds of seed needed per acre. From the information given, It takes 60 pounds of seed to completely plant a 10-acre field. Thus, we have the following equations

60 = 10

x = 1

By crossmultiplying, we have

10x = 60

x = 60/10

x = 6

6 pounds of seed are needed per acre

b) Let x represent the number of hours of bike use that a customer gets per dollar. From the information given, it costs $17 to rent a bike for 3 hours.

Thus, we have the following equations

17 = 3

1 = x

By crossmultiplying, we have

17x = 3

x = 3/17

x = 0.17647

Rounding to the nearest hundredth,

the number of hours of bike use that a customer gets per dollar is 0.18

Answer:3.6

Step-by-step explanation:

Step 1: Calculate

We calculate the square root of 13

√13 = 3.60555127546399

Step 2: simplify

Reduce the tail of the answer above to two numbers after the decimal point which is :

3.60

Step 3: Round

Round 3.60 so you only have one digit after the decimal point to get the answer:

3.6

Written in Standard Form: 5u^(2)v^(2)+5u^(2)u+4uv^(2)-4uv

Simplified: 5u^(2)v+4uv^(2)+5u^(2)v^(2)-4uv

Brainliest or a thank you please this took me a while to type :)) <3

Given the following relationship dQ = (∂T/∂E)_V dT + [(∂V/∂E)_T + P]dV

To prove the relationship between heat transfer (dQ) and changes in temperature (dT) and volume (dV) using the internal energy (E) as a function of state E(T, V), we need to differentiate E with respect to T and V.

The first step is to express the total differential of E using the chain rule:

dE = (∂E/∂T)_V dT + (∂E/∂V)_T dV

where (∂E/∂T)_V represents the partial derivative of E with respect to T at constant V, and (∂E/∂V)_T represents the partial derivative of E with respect to V at constant T.

Now, let's rearrange the equation to isolate dQ:

dQ = (∂E/∂T)_V dT + (∂E/∂V)_T dV

To relate dQ to the given partial derivatives, we need to consider the first law of thermodynamics:

dQ = dE + PdV

where P is the pressure.

Substituting dE + PdV into the equation above:

dQ = (∂E/∂T)_V dT + (∂E/∂V)_T dV + PdV

Now, we can rearrange the terms to match the desired relationship:

dQ = (∂E/∂T)_V dT + [(∂E/∂V)_T + P]dV

This matches the relationship stated:

dQ = (∂T/∂E)_V dT + [(∂V/∂E)_T + P]dV

Therefore, we have successfully proven the relationship between heat transfer (dQ) and changes in temperature (dT) and volume (dV) using the internal energy (E) as a function of state E(T, V).

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Answer:

number 1. answer 3x+6

number 2. answer 2r-8

number 3. answer 4y+8

number 4. answer 24-6x

Hello.

The Distributive Property states that

a(b+c)=ab+ac

Let's use this formula to simplify our expressions.

3(x+2)=3x+6

2(r-4)=2r-8

4(y+2)=4y+8

6(4-x)=24-6x

I hope it helps.

Have an awesome day.

\(\boxed{imperturbability}\)

By identifying the maximum value (75) and the minimum value (59) in the data set, we can determine the range, which is 16 inches .

The range of a data set measures the spread or variability of the data. It is calculated by subtracting the minimum value from the maximum value. In this case, the minimum value is 59 (the shortest height) and the maximum value is 75 (the tallest height) in the given data set.

Range = Maximum value - Minimum value

Substituting the values, we have:

Range = 75 - 59 = 16

Therefore, the range of the given data set is 16. This means that the heights of the students in the high school class range from a minimum of 59 inches to a maximum of 75 inches, with a difference of 16 inches between them.

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The advantages of graphing calculator, It has been demonstrated that using graphing calculators effectively in the classroom may improve students' grasp of mathematical ideas, encourage them to approach problems at a higher level, and increase their test scores.

The equations can be entered into the graphing calculator in standard form or slope intercept form. Even if the intersection is a decimal, the calculator accurately locates it. You may quickly alter the window's settings to be able to view the system's answer wherever it may be.

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The given statement would be False.

What is Mean and Median ?

Mean: A data set's mean (average) is calculated by summing all of the numbers in the set and then dividing by the number of values in the set. Median: When a data collection is ordered from least to largest, the median is the midway value.

If there are a few very small values in a data set compared to the rest of the data, the median will be larger than the mean.

The median is the middle value in a set of data and is not affected by extreme values, while the mean is the average of all values in the data set and is influenced by extreme values.

Therefore, The given statement would be False.

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i would say its the first one

A point estimate (mean) for the average height of all people at the place where you work is 62.26

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.

Given,

Number of observations =  20

Mean = sum of all observation / number of observations

Mean =  66 +65 +66+ 67+ 62+ 70+ 69+ 68+ 71+ 78+ 61+ 62.5+ 64+ 64.2+ 64.3+ 58+ 60+ 63+ 65+ 66.2 / 20

Mean = 1245.2 / 20 = 62.26

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An equation for the distance between the friends after time (t) in hours is c = 4t√125.

In order to determine an equation for the distance between the friends after an amount of time (t) in hours, we would create a mental image of a right-angled triangle because they both head in the opposite (North) and adjacent (East) direction.

Therefore, the distance between them after t hours represent the hypotenuse of a right-angled triangle, which can be calculated by using Pythagorean theorem.

Next, we would determine the distance covered by each friend:

For the first friend (North), we have:

Distance, a = speed × time

Distance, a = 40t

For the second friend (East), we have:

Distance, b = speed × time

Distance, b = 20t

By applying Pythagorean theorem, the distance between the friends after an amount of time (t) is given by:

Distance, c² = a² + b²

Distance, c² = (40t)² + (20t)²

Distance, c² = 1600t² + 400t²

Distance, c² = 2000t²

Distance, c = √(16 × 125t²)

Distance, c = √16t² × √125

Distance, c = 4t√125

Note: The prime factorization of 2000 is 2⁴ × 5³ = 16 × 125.

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The exact length of the polar curve r = 5cos(theta) over the interval 0 ≤ theta ≤ pi/2 is 5π/2 units

To find the length of the polar curve r = 5cos(theta) over the interval 0 ≤ theta ≤ pi/2, we can use the following formula:

L = ∫[a,b] sqrt[r^2 + (dr/dθ)^2] dθ

where a and b are the initial and final values of theta over the interval, and r and (dr/dθ) are the polar equation and its derivative with respect to theta.

First, we need to find the derivative of r with respect to theta:

dr/dθ = -5sin(theta)

Then, we can substitute r and (dr/dθ) into the formula:

L = ∫[0,π/2] sqrt[(5cos(theta))^2 + (-5sin(theta))^2] dθ

Simplifying under the square root:

L = ∫[0,π/2] sqrt[25(cos^2(theta) + sin^2(theta))] dθ

L = ∫[0,π/2] 5 dθ

L = 5θ ∣ [0,π/2]

L = 5(π/2 - 0)

L = 5π/2

Therefore, the exact length of the polar curve r = 5cos(theta) over the interval 0 ≤ theta ≤ pi/2 is 5π/2 units.

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Answer:

3 7/12

Step-by-step explanation:

Answer:

is 3 7/12 that last one D

Step-by-step explanation:

if you take and do 1/6 - 3/4 you get 0.58 and when you convert 7/12 to a decimal you get 0.58 so 18-15 is 3 and then your fraction is 7/12 with you answer being D.3 7/12

Answer: a) To find the equation of line PS, we first need to find the slope of the line L1 which is given by:

slope = (y2 - y1) / (x2 - x1)

= (3 - 5) / (-2 - 0)

= 2/2

= 1

Since PS is parallel to L1, it also has the same slope. We can now use the point-slope form of the equation of a line to find the equation of PS, using the point P(1,2):

y - y1 = m(x - x1)

y - 2 = 1(x - 1)

y - x + 2 = 0

Therefore, the equation of line PS is y - x + 2 = 0.

b) To find the coordinates of S, we know that S lies on line PS and also on the line passing through points (6,4) and P(1,2). Let's call the coordinates of S as (x,y). Since S lies on line PS, we know that y - x + 2 = 0. We can also use the slope formula to find the slope of line PS:

slope_PS = (y - 2) / (x - 1)

Since PS is parallel to line L1, we know that slope_PS = 1. Therefore, we can write:

(y - 2) / (x - 1) = 1

y - 2 = x - 1

y = x + 1

Now, we can use the fact that S also lies on the line passing through points (6,4) and P(1,2). This line has the equation:

(y - 4) / (x - 6) = (2 - 4) / (1 - 6)

(y - 4) / (x - 6) = -2/-5

(y - 4) / (x - 6) = 2/5

We can solve for y in terms of x:

y - 4 = (2/5)(x - 6)

y = (2/5)x - 8/5 + 4

y = (2/5)x + 6/5

Now, we can set the two equations for y equal to each other, since they both represent the y-coordinate of point S:

x + 1 = (2/5)x + 6/5

Solving for x, we get:

x = 2

Substituting x = 2 into either of the equations for y, we get:

y = 3

Therefore, the coordinates of S are (2,3).

c) To find the coordinates of Q, we can use the fact that PQ is parallel to SR and PS is parallel to QR. This means that PQRS is a parallelogram and its opposite sides are parallel. Since we know the coordinates of P and S, we can find the coordinates of Q and R by adding or subtracting the appropriate vector from P and S.

The vector that we need to add to P to get Q is the same vector that we need to add to S to get R, which is given by the displacement vector PS = <5,1>. Therefore:

Q = P + PS

= <1,2> + <5,1>

= <6,3>

Therefore, the coordinates of Q are (6,3).

d) To find the equation of line L2 which is the perpendicular bisector of line QR, we first need to find the midpoint of QR. The midpoint formula is given by:

midpoint = [(x1 +)]

We can then find the midpoint of QR using the midpoint formula:

midpoint of QR = ((-4 + 1)/2, (7 + 4)/2) = (-1.5, 5.5)

So the slope of L2 is the negative reciprocal of the slope of QR:

slope of L2 = -1/slope of QR = -(7-5)/(1+4) = -2/5

We can use the point-slope form of the equation of a line to find the equation of L2. We know that L2 passes through the midpoint of QR, so we can use the point (-1.5, 5.5):

y - 5.5 = (-2/5)(x + 1.5)

Simplifying and rearranging, we get:

y = (-2/5)x + 7.5

Therefore, the equation of line L2 is y = (-2/5)x + 7.5.

Answer:

Net change means the differnce between the before result and the after result. You would subtract the numbers, but if you have a gain(the before result smaller than after result) you would do its absolute value. If it's a loss(the before result bigger than after result) you would put a negative behind its absolute value.

e.g. if 2019 had $1 net worth and 2020 had $2 net worth, since 2>1 it would be |2-1| = 1. If 2019 had $2 net worth and 2020 had $1 net worth, since 1<2 there would be a - |2-1| = -1 net change.

However, if there is no change it would be just 0.

Answer:

A,B and D

A: y= 2x -3/2

B: y =2x-4

C:y=2x-5

same gradient y=mx+c

m=2

Answer:

Step-by-step explanation:

The angle and its supplementary angle have a difference of 15.8°. To find the measures, we need to solve an equation.

Let's assume the measure of the angle is x°. The measure of its supplementary angle would be (180° - x°). According to the given information, x° = (180° - x°) - 15.8°.

Simplifying the equation, we have:
x° = 180° - x° - 15.8°
2x° = 164.2°
x° = 82.1°

Therefore, the angle measures 82.1° and its supplementary angle measures (180° - 82.1°) = 97.9°. The difference between these angles is indeed 15.8°, as stated in the problem.

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When making economic decisions, a traditional economy looks to cultural traditions, beliefs, and other tenets.

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