The following product can be expanded into a power series with coefficients ak:

expression is given in attach file.

Find the coefficients ak in front of the individual xk terms for all k 2 N

When a double cone is sliced at the apex by a plane perpendicular to the base of the cone, the resulting conic section is a parabola.

Option B is the correct answer.

We have,

A parabola is a type of conic sect ion that can be defined as the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix).

In the case of slicing a double cone at the apex, the resulting conic section will have the characteristic shape of a parabola.

The slicing plane intersects both sides of the double cone, creating a curved shape that opens upward or downward, depending on the orientation of the cone.

The vertex of the parabola corresponds to the point of intersection of the slicing plane with the double cone.

Therefore,

When a double cone is sliced at the apex by a plane perpendicular to the base, a parabola is formed.

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The complete question:

Which degenerate conic is formed when a double cone is sliced at the apex by a plane perpendicular to the base of the cone?

A. Circle

B. Parabola

C. Ellipse

D. Hyperbola

Answer: 5 units^2

Step-by-step explanation:

You can deduce that the height of the triangle is 5. You use the pythagoreon theorem to find the missing distance. 5^2+x^2=7^2

X=sqrt24.

Using that info you find the area of the missing triangle. Getting 2.5sqrt24. Find the area of the combined triangles, (5*(2+sqrt25))/2.

you should get 5+2.5sqrt24. Then subtract the missing triangle to get 5.

Therefore, Zahid earned $1,001.16 in that particular week in hour and Samantha earned $1,237.50 in that particular week.

An hour is a unit of time measurement that represents a duration of 60 minutes or 3,600 seconds. It is commonly used to measure time in various contexts, such as work schedules, meetings, and appointments. The abbreviation for hour is "hr" or "h".

Given by the question.

For Zahid:

Regular wage per hour = $774.72 / 36 hours = $21.52/hour

Overtime wage per hour = 1.5 x $21.52 = $32.28/hour

Zahid worked 7 hours of overtime (43 - 36 = 7)

Zahid's earnings for the week would be:

Regular earnings = 36 hours x $21.52/hour = $775.20

Overtime earnings = 7 hours x $32.28/hour = $225.96

Total earnings = Regular earnings + Overtime earnings = $1,001.16

For Samantha:

Regular wage per hour = $962.50 / 35 hours = $27.50/hour

Overtime wage per hour = 2 x $27.50 = $55/hour

Samantha worked 5 hours of overtime (40 - 35 = 5)

Samantha's earnings for the week would be:

Regular earnings = 35 hours x $27.50/hour = $962.50

Overtime earnings = 5 hours x $55/hour = $275

Total earnings = Regular earnings + Overtime earnings = $1,237.50

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Answer:

Step-by-step explanation:

C.) P = 3(a+2)-4

The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

Growth of apple tree= 2feet

Now,

Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:

3(h+2) - 4 = p

Simplifying, we get:

3h + 2 = p

Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.

Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:

P = 3a + 6

This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:

P = 2a + 10

This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:

P = 3a + 2

Therefore, by equation the answer will be P=3(a+2)-4.

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Therefore, the initial value of the function is $1,852 and the rate of change is $12.18 per shirt. The initial value represents the cost of the shirts before any were purchased,

In mathematics, a function is a rule that assigns to each element in a set called the domain, a unique element in another set called the range. In other words, a function is a mathematical object that takes an input and produces a specific output, according to a specific set of rules or operations.

by the question.

et the initial value be represented by a and the rate of change by r.

The given information can be represented by the following equation:

a + 150r = 1,852

Since the flat-rate shipping cost is $25, the cost of the 150 shirts alone would be:

a + 150r - 25 = 1,827

The initial value, a, represents the cost of the shirts before any shirts were purchased. In this case, it would be the cost of the shirts if no shirts were purchased plus the flat-rate shipping cost of $25.

So, a = 1,827 + 25 = 1,852.

The rate of change, r, represents the increase in cost for each additional shirt purchased. In this case, it would be the cost of one shirt.

So, r = (1,852 - 25)/150 = 12.18.

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Answer:17.6 cm

Step-by-step explanation:

if you can see the graph it can be seen as 17.6 cm.

Answer:

The baristas secret formula beans cost per pound is $19.2.

Step-by-step explanation:

Given is that a barista mixes 12 lb of his secret-formula coffee beans with 15 lb of another bean that sells for $18 per lb.The cost of 1 pound of another bean as -$(15/18) = $(5/6)Assume that 1 pound of secret coffee costs ${x}. So, we can write -x + 5/6 = 20x = 20 - 5/6x = 19.2Therefore, the baristas secret formula beans cost per pound is $19.2.

Answer:

Find 5 rational numbers between 4/5 - and * 3/7

(a) Distance travelled in first 48 minutes = 40 km. (b)(i) Distance travelled in remaining journey = 30 km. (ii) Yes, Stanley arrived at Peter's house before 9:30 a.m. as he reached there at 9:28 a.m.

(a) To find the distance travelled for the first 48 minutes, we can use the formula:

distance = speed x time

The speed is 50 km/h and the time is 48/60 hours (since 48 minutes is 0.8 hours). So,

distance = 50 x 0.8

distance = 40 km

Therefore, Stanley travelled 40 km for the first 48 minutes of his trip.

(b) Let's use the formula for average speed:

average speed = total distance ÷ total time

We know that the total distance is the distance travelled in the first 48 minutes plus the distance travelled for the remaining journey. Let's call the distance for the remaining journey "d". We also know that the total time is 1 hour (60 minutes).

So,

70 = (40 + d) ÷ 1

40 + d = 70

d = 30

Therefore, the distance for the remaining journey is 30 km.

(i) To express the distance travelled for the remaining journey in terms of 1, we can use the formula we found in part (b):

d = 30 km

(ii) To find out if Stanley arrived at Peter's house before 9:30 a.m., we need to know the total time of his journey. We know that he left his home at 8:00 a.m. and his average speed was 70 km/h. So, the total distance he travelled is:

distance = speed x time

distance = 70 x time

We also know that the total distance is the distance for the first 48 minutes plus the distance for the remaining journey:

distance = 40 + 30

distance = 70 km

Therefore, the total time of his journey is:

time = distance ÷ speed

time = 70 ÷ 70

time = 1 hour

Since he arrived at Peter's house at 9:00 a.m. (1 hour after he left his home), we can conclude that he arrived before 9:30 a.m.

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so he got them for £10 all 24 bars, then he went and sold each for 50c, so hmmm 24 at £0.50 that's (24)(0.5) = 12, so he bought them for £10 and sold them for £12, he's got a surplus or profit of £2.

now, if we take 10(origin amount) as the 100%, what's 2 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 10 & 100\\ 2& x \end{array} \implies \cfrac{10}{2}~~=~~\cfrac{100}{x} \\\\\\ 5 ~~=~~ \cfrac{ 100 }{ x }\implies x=\cfrac{100}{5}\implies x=20[/tex]

Hello!

Given,

Perimeter of rectangle = 32 cm

Width = 7cm

Perimeter of a rectangle = 2 (l+b)

32cm = 2l + 2 (7cm)

32 cm = 2l + 14cm

32cm -14cm =2l

2l= 18cm

l = 9cm

Area of a rectangle = length × breadth

= 7cm × 9cm

= 63 cm^2

Answer:

C. (45+2+7)-(43+2+7) / 5+3

Step-by-step explanation:

To find the average rate of change of h(x) on the interval -3 ≤ x ≤ 5, we need to evaluate the following expression:

[h(5) - h(-3)] / (5 - (-3))

We have:

h(5) = 4(5) + 2 + 7 = 29

h(-3) = 4(-3) + 2 + 7 = -5

Substituting into the formula, we get:

[29 - (-5)] / (5 - (-3)) = 34 / 8 = 17 / 4

Therefore, the expression that gives the average rate of change of the function h(x) on the interval -3 ≤ x ≤ 5 is:

C. (45+2+7)-(43+2+7) / 5+3

Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Step-by-step explanation:

Step-by-step explanation:

after a little bit of thinking and experimenting we find that the function multiplied x by 6 and subtracts 2.

y = 6x - 2

formally, we find this by using the normal linear form

y = ax + b

and we use the given data points to find a and b.

4 = a×1 + b = a + b

10 = a×2 + b = 2a + b

so, by adding a on one side and adding 6 on the other side, we keep the balance.

therefore, a = 6

the first equation gives us then

4 = 6 + b

b = -2

and that's it.

so,

for x = 10 we get as output (y)

6×10 - 2 = 58

for x = n we get as output (y)

6n - 2

The required points are (0,2) and (0,-2) respectively.

The equation of the ellipse is 4x² + y² = 4. Find the points on the ellipse that are farthest away from the point (1,0). (Round your answers to the nearest hundredth.)Solution:The given equation of the ellipse is 4x² + y² = 4.Let (x, y) be a point on the ellipse.The square of the distance between (x, y) and (1,0) is given by:(x - 1)² + y²The maximum and minimum of (x - 1)² + y² occur at the same point where the maximum and minimum of [(x - 1)² + y²] is equal to the maximum and minimum of [4x² + y² - 4] and also where the gradient of both functions is perpendicular.Thus, we need to find the maximum and minimum of the function f(x, y) = (x - 1)² + y² subject to the constraint 4x² + y² = 4.Maximize and minimize the function f(x, y) subject to the constraint 4x² + y² = 4 using Lagrange multipliers.Let g(x, y) = 4x² + y² - 4 = 0 be the constraint equation.Let L be the Lagrange functionL(x, y, λ) = f(x, y) + λg(x, y)Therefore, L(x, y, λ) = (x - 1)² + y² + λ[4x² + y² - 4]Now differentiate L(x, y, λ) partially with respect to x, y and λ.Lx = 2(x - 1) + 8λxLy = 2y + 2λydL/dλ = 4x² + y² - 4 = 0From the equation dL/dλ = 0, we get4x² + y² = 4 ⇒ x²/1 + y²/4 = 1Thus, the ellipse can be represented as:x = cosθ; y = 2sinθwhere 0 ≤ θ ≤ 2πThus, Lx = 2(x - 1) + 8λx = 0⇒ 2cosθ - 2 + 8λcosθ = 0Ly = 2y + 2λy = 0⇒ 2sinθ + 2λ(2sinθ) = 0dL/dλ = 4x² + y² - 4 = 0⇒ 4cos²θ + 4sin²θ - 4 = 0⇒ cos²θ + sin²θ = 1∴ 4λsinθ + cosθ - 1 = 0Solving the equations obtained above, we get(1) θ = 0: (x, y) = (1,0)(2) θ = π: (x, y) = (-1,0)(3) θ = π/2: (x, y) = (0,2)(4) θ = 3π/2: (x, y) = (0,-2)The points on the ellipse that are farthest away from the point (1,0) are (0,2) and (0,-2).(0,2) has the largest y-value, and (0,-2) has the smallest y-value.Therefore, the required points on the ellipse are:(0, 2) (larger y-value)(0, -2) (smaller y-value)Hence, the required points are (0,2) and (0,-2) respectively.

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(a) μx  15.55 cubic feet. The standard deviation is the square root of the variance, i.e., θx = 1.881 cubic feet

The mean, or expected value, of x can be calculated as μx = Σ(xi * P(xi)) where xi are the possible values of x and P(xi) are their corresponding probabilities. Thus, μx = (13.40.2) + (15.80.5) + (19.3*0.3) = 15.55 cubic feet.

To calculate the standard deviation, we first need to calculate the variance, which can be obtained as θ²x = Σ((xi-μx)² * P(xi)). Thus, θ²x = ((13.4-15.55)²0.2) + ((15.8-15.55)²0.5) + ((19.3-15.55)²*0.3) = 3.54.

Therefore, the standard deviation is the square root of the variance, i.e., θx = √3.54 = 1.881 cubic feet (rounded to four decimal places).

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(A). The probability distribution of X is approximately normal because the sample size is large enough (n = 50) and the population proportion (p = 0.78) is not too close to 0 or 1.

(B) The mean of the approximately normal distribution is μ = np = 50 x 0.78 = 39, and the standard deviation is σ = sqrt(np(1-p)) = sqrt(50 x 0.78 x 0.22) = 3.22.

(C) To calculate the probability that 35 or fewer individuals need to standardize the value of X using the formula z = (X - μ) / σ. Then, z = (35 - 39) / 3.22 = -1.24 in the standard normal distribution table or using a calculator. The probability is approximately 0.1093 or 10.93%.

(D). The null hypothesis is H0: p = 0.78, and the alternative hypothesis is Ha: p < 0.78. The test statistic is z = (35/50 - 0.78) / sqrt(0.78 x 0.22 / 50) = -1.97, which has a p-value of 0.0244 or 2.44%.

Probability is a branch of mathematics that deals with the study of random events. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1. An event with probability 0 means it will never occur, while an event with probability 1 means it will always occur.

The calculation of probability involves analyzing the possible outcomes of an event and assigning a probability to each outcome based on its likelihood of occurring. The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in various fields, such as statistics, finance, engineering, and science, to make predictions and informed decisions.

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The exponential model for the population can be written as P = 20000 * 1.171^t, where P is the population after t years, 1.171 is the growth factor per year (100% + 17.1%), and 20000 is the initial population.

This equation assumes that the population grows continuously at a constant rate of 17.1% per year. It is an example of exponential growth, which means that the population increases at an increasingly faster rate over time.

Using this model, we can predict the population size at any point in the future. For example, after 5 years, the population would be P = 20000 * 1.171^5 = 41,992 organisms. It is important to note that this model is based on certain assumptions, such as unlimited resources and a constant growth rate, which may not always hold true in real-world scenarios.

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Answer: x = -2

Step-by-step explanation:

Since both equations are in the y-slope form,

we can use substitution for y in finding x.

Hence,

4x=x-6

4x-x=x-x-6

Subtract x from both sides to get x on one side and integer on one side.

[tex]\frac{3x}{3} =\frac{-6}{3}[/tex]

Divide 3 to find the value of x

x=-2

The 90% confidence interval for the average number of hours of sleep for working college students is between 6.15 and 6.85 hours.

Therefore, the answer is option (a) 6.15 and 6.85 hours.

A confidence interval is a statistical range of values within which we can be reasonably confident that the true value of a population parameter lies. It is commonly used in inferential statistics to estimate an unknown population parameter, such as a mean or a proportion, based on a sample from that population.

To calculate the 90% confidence interval for the average number of hours of sleep for working college students, we'll use the formula:

Confidence Interval = Sample Mean ± (Critical Value x Standard Error)

Where:

Sample Mean: 6.5 hours (the average number of hours of sleep)

Critical Value: t-value corresponding to a 90% confidence level with 100 degrees of freedom (101 students - 1)

Standard Error: Standard Deviation / Square Root of Sample Size

Let's plug in the values and calculate the confidence interval:

Standard Error = 2.14 / √101 ≈ 0.2139

Confidence Interval = 6.5 ± (1.660 x 0.2139)

Confidence Interval = 6.5 ± 0.3546

Lower Bound = 6.5 - 0.3546 ≈ 6.1454

Upper Bound = 6.5 + 0.3546 ≈ 6.8546

Rounding to the hundredths place, the 90% confidence interval for the average number of hours of sleep for working college students is between 6.15 and 6.85 hours.

Therefore, the answer is option (a) 6.15 and 6.85 hours.

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The algebraic representation of the statement subtract 4 times the positive square root of z from thrice of x is 4√z - 3x.

A mathematical expression is composed of term. A coefficient is an integer that is either multiplied by the variable it is associated with or put alongside the variable. A coefficient is, in other words, the numerical component of a phrase that contains both constants and variables. For instance, the coefficient in the expression 2x is 2.

The algebraic representation of the given statement is:

4 times the positive square root of z: 4√z

4 times the positive square root of z: 4√z - 3x

Hence, the algebraic representation of the statement subtract 4 times the positive square root of z from thrice of x is 4√z - 3x.

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The fraction and ratio that complete the equations in its simplest term is 5/6k and 2 : 9 respectively.

h : k = 5 : 6

h/k = 5/6

cross product

h × 6 = k × 5

6h = 5k

divide both sides by 6

h = 5/6k

Then,

2x = 9y

2/9 = x/y

2 : 9 = x : y

Ultimately, the simplest form of fraction and ratio which completes the equation is 5/6k and 2:9.

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Answer: 20

Step-by-step explanation:

Using the Pythagorean theorem, we know that:

c² = a² + b²

Substituting the given values, we get:

c² = 12² + 16²

c² = 144 + 256

c² = 400

Taking the square root of both sides, we get:

c = √400

c = 20

Therefore, the length of the hypotenuse in the right triangle is 20.

Answer:

Step-by-step explanation:

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Answer:

s= 6

Step-by-step explanation:

The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the

coefficient of friction and d is the stopping distance (in feet). The table shows the

coefficient of friction for different surfaces. You are driving 35 miles per hour on an

icy road when a deer jumps in front of your car. How far away must you begin to

brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO

UNITS NEEDED

Answer:

-130

Step-by-step explanation:

Over a year, the Blue Valley Glacier typically moves about the same distance as the Silver Lake Glacier, and Blue Valley has the same variability in its annual movement compared to Silver Lake.

The median annual movement of the Blue Valley Glacier is 300.2 feet, and the interquartile range is 14 feet.

The interquartile range indicates the spread of the data within the middle 50% of the data

So we know that the annual movement of the Blue Valley Glacier falls within a range of 300.2 ± 7 feet (i.e. 293.2 to 307.2 feet)

Similarly, the median annual movement of the Silver Lake Glacier is 300.4 feet, and the interquartile range is also 14 feet

So the annual movement of the Silver Lake Glacier also falls within a range of 300.4 ± 7 feet (i.e. 293.4 to 307.4 feet)

Since the ranges for both glaciers overlap and have the same size, we can conclude that they typically move about the same distance over a year, and that the variability in the annual movement of Blue Valley is comparable to that of Silver Lake.

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Green Circle's circumference is 138.16 metres.

Blue Circle's circumference is 69.08 metres.

The green circle has a radius of 22 metres.

The blue circle's diameter is 1/2. the green circle's radius is 12*22, or 11 metres.

The formula for circumference is C = 2r.

The Green circle's circumference is 2*3.14*22, or 138.16 metres.

The Blue Circle's circumference is 2 * 3.14 * 11 = 69.08 metres.

What is its diameter?

The circumference of a circle or other curved geometric object refers to its length. It is the boundary across any two-dimensional circular surface measured linearly in one dimension.

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Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same, he also know that he can earn 16 for each hour that he works at his aunt's store, therefore he needs to work 8 hours.

Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same,

therefore, we can say that 215 - 100 = 115

therefore, Mark now needs only 115 for him to buy sneakers and  now we need to find how many full hours do Mark need to work to buy sneakers:

therefore, we need to divide 115 by 16 to find out the hours he needs to work at his aunt's store:

115/16 = 7.2

we get 7.2 which also means 7 hours 20 mins but we need to find full hours Mark needs to work, that will be:

8 hours.

Therefore, we know that Mark needs to work 8 full hours for him to buy sneakers.

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The three examples of contracts are:

Contracts are legal agreements between two or more parties that involve the exchange of goods, services, or money. They can be classified as unilateral or bilateral, express or implied, executed or executory.

Here are three examples of contracts that a person can be a part of:

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