[tex]\left\{\frac{1}{2^n}\:+\:\frac{\left(-1\right)^n}{n+1}\::\:n\:\:N\right\}[/tex]
Find max, min, sup and inf

Answer:

75=x

Step-by-step explanation:

Answer:

The distance between points (4, -2) and (4,4) on a coordinate plane is 6 units. This is because the two points lie on the same vertical line, where the x-coordinate remains constant at 4. To find the distance between them, we simply need to subtract their y-coordinates: 4 - (-2) = 6. Therefore, the distance between the two points is 6 units.

Answer:2.86.

Step-by-step explanation:

We can use the geometric distribution to solve this problem. The geometric distribution models the number of trials needed to achieve the first success in a sequence of independent trials with a constant probability of success.In this case, the probability of success (the teacher tripping over the cords) is 0.35. Therefore, the expected value or mean of the geometric distribution is 1/0.35 ≈ 2.86.So, on average, students need to wait for 2.86 periods until the teacher trips over the cords in her classroom.Therefore, the answer is 2.86.

Answer: b

Step-by-step explanation:

A function relating these variables is D(x) = 10 + 2x,

D(9) = 28, meaning after 9 hours of snowfall,

An independent variable is a variable that is manipulated or controlled by the researcher in an experiment to observe its effect on the dependent variable. It is the variable that is changed deliberately to see how it affects the outcome of the experiment.

The independent variable, x, represents the number of hours since snow began falling,

and the dependent variable is the total amount of snow on Jace's lawn because the amount of snow depends on the number of hours since it began to snow.

A function relating these variables is D(x) = 10 + 2x, where D(x) is the total amount of snow on Jace's lawn in inches after x hours of snowfall.

So, D(9) = 28, meaning after 9 hours of snowfall, Jace will have a total of 28 inches of snow on his lawn.

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Therefore , the solution of the given problem of unitary method comes out to be you can purchase 30 sausage and 70 pepperoni pizzas to serve at your birthday party.

To complete the assignment, make use of the tried-and-true fundamental technique, the actual variables, and any insightful knowledge you gain from the general and detailed questions. In response, customers might be given another opportunity to sample the products. We will miss out on substantial expression gains in programming comprehension if these changes don't take place.

Here,

Let's use "p" for the quantity of pepperoni pizzas and "s" for the quantity of sausage pizzas. Finding p and s values that meet the requirements is necessary.

In light of the information provided:

One pepperoni pizza costs $8.

One sausage pizza costs $6.

100 pizzas are required.

Budget total: $740

To reflect the stated conditions, we can construct the following system of equations:

=> p + s = 100 (1)

=> 8p + 6s = 740 (2)

=> 8p + 8s = 800 (3)

=> 8p + 6s - (8p + 8s) = 740 - 800

=> -2s = -60

=> s = (-60)/(-2)

=> s = 30

=> p + 30 = 100

=> p = 100 - 30

=> p = 70

With a $740 budget, you can purchase 30 sausage and 70 pepperoni pizzas to serve at your birthday party.

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Answer:

To solve this problem using cylindrical coordinates, we need to express the integrand and the limits of integration in terms of cylindrical coordinates. In cylindrical coordinates, a point in 3D space is represented by the radius (r), the angle (theta), and the height (z), where:

x = r cos(theta)

y = r sin(theta)

z = z

The volume element in cylindrical coordinates is given by:

dV = r dr dtheta dz

Now we can write the integral as:

∫∫∫W(x^2+y^2)dV = ∫∫∫W(r^2) r dr dtheta dz

The limits of integration are given by:

0 ≤ z ≤ 2 (since the region of integration is between z=0 and z=2)

0 ≤ r ≤ 5 (since the region of integration is within the circle of radius 5 in the xy-plane)

0 ≤ theta ≤ 2π (since the region of integration extends throughout the entire circle in the xy-plane)

Therefore, we can write the integral as:

∫∫∫W(r^2) r dr dtheta dz

= ∫0^2 ∫0^5 ∫0^2 (r^2) r dz dr dtheta

Integrating with respect to z first, we get:

∫0^2 ∫0^5 ∫0^2 (r^2) r dz dr dtheta

= ∫0^2 ∫0^5 [(r^2) r (2-0)] dr dtheta

= 2 ∫0^5 (r^3) dr ∫0^2 dtheta

= 2 (1/4) (5^4) (2)

= 1250

Therefore, the value of the integral is 1250.

The correct answer is an option (A) 144.5 pounds per year, which is the closest value to the calculated average yearly growth rate of the elephant.

The term "average" refers to a measure of central tendency that represents the typical or typical value in a set of data.

Growth rate refers to the rate at which a quantity or value increases or decreases over time. It is often expressed as a percentage or a proportion and is used to measure the change in a particular variable relative to its initial value.

According to the given information:

To find the average yearly growth rate of the elephant, we can use the formula for calculating growth rate:

Growth Rate = ((Ending Value - Starting Value) / Number of Years)

In this case, the starting weight of the elephant is 220 pounds and the ending weight is 870.25 pounds. The number of years is 4.5 (since the growth occurred over 4.5 years).

Plugging these values into the formula, we get:

Growth Rate = ((870.25 - 220) / 4.5)

Simplifying the numerator, we get:

Growth Rate = 650.25 / 4.5

Dividing, we get:

Growth Rate ≈ 144.50 pounds per year

So, the correct answer is option (A) 144.5 pounds per year, which is the closest value to the calculated average yearly growth rate of the elephant.

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We can set up a proportion using the given ratio:

Weight on Earth : Weight on Planet X = 5 : 12

Let's let x be the weight of the elephant on Planet X. We can substitute the given weight on Earth to solve for x:

3800 : x = 5 : 12

We can cross-multiply to get:

3800 * 12 = 5 * x

Simplifying the right side, we get:

45600 = x * 5

Dividing both sides by 5, we get:

x = 9120

Therefore, the weight of the elephant on Planet X is 9120 pounds.

Answer: 11

Step-by-step explanation: To find the value of (fog)(-1), we first need to find the value of g(-1), which means plugging -1 into the equation for g(x):

g(x) = x² – 5x - 5

g(-1) = (-1)² – 5(-1) - 5

g(-1) = 1 + 5 - 5

g(-1) = 1

Now we need to find (fog)(x) by plugging g(x) into f(x) and simplifying:

f(x) = -x - 12

fog(x) = f(g(x))

fog(x) = f(x² – 5x - 5)

fog(x) = -(x² – 5x - 5) - 12

fog(x) = -x² + 5x + 17

Finally, we can find (fog)(-1) by plugging -1 into the equation for fog(x):

fog(x) = -x² + 5x + 17

(fog)(-1) = -(-1)² + 5(-1) + 17

(fog)(-1) = -1 - 5 + 17

(fog)(-1) = 11

Therefore, the value of (fog)(-1) is 11.

Answer:

False

Step-by-step explanation:

The formula for the area of a circle is A = pi • r^2

Answer: False

Step-by-step explanation: A = [tex]\pi[/tex] [tex]r^{2}[/tex]

We would need to study 678 families to determine the market preference for baby shampoo brands with a 96% confidence level and 4% margin of error, given that there are 12,000 families with babies in the sector of interest.

To calculate the sample size needed to determine the market preference for baby shampoo brands, we can use the formula:

n = [(Z^2 * p * q) / E^2]

where:

n = sample size

Z = Z-score for the desired level of confidence (in this case, 1.96 for a 96% confidence level)

p = proportion expected (in this case, 0.12 or 12%)

q = 1 - p

E = margin of error (in this case, 0.04 or 4%)

Substituting these values into the formula, we get:

n = [(1.96^2 * 0.12 * 0.88) / 0.04^2] = 677.16

Since we cannot have a fraction of a family, we round up the sample size to 678 families. Therefore, we would need to study 678 families to determine the market preference for baby shampoo brands with a 96% confidence level and 4% margin of error, given that there are 12,000 families with babies in the sector of interest.

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Answer:

Step-by-step explanation:

64 - 16= 48

[tex]\sqrt{48}[/tex]

[tex]\sqrt{3*16}[/tex]

4[tex]\sqrt{3}[/tex]

Answer:

Center= -4,8

Radius=7

Step-by-step explanation:

Adding 5 bonus points to each test grade in Mrs. Matthew's class will increase the mean, median, and mode of the scores by 5 points each.

The addition of 5 bonus points to each test grade will affect the mean, median, and mode in the following ways:

So, in conclusion, adding 5 bonus points to each student's test score will raise the mean, median, and mode of the scores by 5 points each.

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Based on the question, Xavier earned a commission of $270 on the last week.

Commissions is known to be a form of variable-pay remuneration that is said to be made for services given or products sold.

Note that from the question, Xavier earns a 15% commission on all washing machine he sells, so he sold four $450 machines last week.

So, the he total sale of the four machines is:

4 x $450 = $1,800

Since Xavier's commission is 15% of $1,800, it will be calculated as :

Commission = 15% x $1,800

                  = 0.15 x $1,800

                     = $270

Hence, Xavier earned a commission of $270 last week.

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Answer:

To find -5u, we simply need to multiply each component of u by -5:

-5u = -5<-9, 2> = <(-5)(-9), (-5)(2)> = <45, -10>

Therefore, -5u is equal to the vector <45, -10>.

Thus, the length of walk way around the filed is the perimeter of the right triangle which is found as: 206.023 m .

The quickest approach to determine a triangle's perimeter is to sum up all of its sides' lengths, but you must first determine each side's length if you don't already know it.

The walk way around the filed is the perimeter of the right triangle.

walk way = base + height + hypotenuse

walk way = B + P + H

base B = 80 - 10 = 70 m

Altitude P = 70 - 20 = 50 m

For the hypotenuse H , use the Pythagorean theorem:

H² = B² + P²

H² = 70² + 50²

H² = 4900 + 2500

H² = 7400

H = 86.023

So,

walk way = B + P + H

walk way = 70 + 50 + 86.023

walk way = 206.023 m

Thus, the  walk way around the filed is the perimeter of the right triangle which is found as: 206.023 m .

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Answer:

Okay, let's think through this step-by-step:

• Janelle Monae obtained a $3,500 loan at 8.5% interest for 1 year.

• 8.5% interest for 1 year = 8.5% of $3,500 = $297.50 in interest

• The loan amount ($3,500) plus interest ($297.50) = $3,797.50 total paid back

•Monthly payments = $3,797.50 / 12 months = $285.55

• So the interest amount in the first payment is $297.50 (calculated above as 8.5% of the $3,500 loan amount)

The choices do not match this:

A. $297.50 - This is the correct choice. This is the interest amount paid over the full loan.

B. $291.67 - This is too low. Calculated interest over 1 year at 8.5% is $297.50.

C. $24.79 - This is way too low. The interest amount due is $297.50 per the working.

D. $35.00 - This is also too low and does not make sense based on the loan details provided.

In summary, to find the interest in just the first payment, we calculate:

Interest over full loan ($297.50) / Number of payments (12) = $24.79

So the interest amount in just the first monthly payment is $24.79.

But the total interest paid over the life of the loan (1 year) is $297.50.

Does this help explain the steps and reasoning? Let me know if any part of the working or explanation is unclear. I can also provide additional examples if needed.

Let me know if you have any other questions!

Step-by-step explanation:

Juan's claim is plausible based on the given function because the maximum height of the ball is 62.875 feet, which is higher than the 50-foot light tower.

To prove that Juan hit the ball over the 50-foot light tower, we need to find the maximum height of the ball using the given function h(x) = -16x^2 + 60x + 4 and show that the maximum height is greater than 50 feet.

The maximum height of the ball occurs at the vertex of the parabolic function h(x), which is given by the formula x = -b/2a, where a = -16 and b = 60.

Substituting these values into the formula, we get:

x = -b/2a = -60/(2*(-16)) = 1.875

So the ball reaches its maximum height after 1.875 seconds. To find the maximum height, we can substitute this value of x into the original function h(x):

h(1.875) = -16(1.875)^2 + 60(1.875) + 4 = 62.875

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Answer:

Step-by-step explanation:

Parallel lines would never intersect no matter how long the lines go on for because they have the same slope. That will always be true.

It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.

We have,

Let's start by assigning variables to unknown quantities.

Let m be the time it takes for Mike to wash the car alone (in minutes).

We know that Stephanie takes 17 minutes to wash the car alone, so her rate of work is 1/17 car per minute.

Working together, their combined rate of work is 1/8.24 car per minute.

Using the formula:

(rate of work) = (amount of work) / (time)

we can set up the following equation to represent the work they do together:

1/8.24 = (1 car) / t

where t is the time it takes them to wash the car together.

We can also set up a similar equation for Stephanie's work alone:

1/17 = (1 car) / (t + x)

where x is the extra time it takes Mike to wash the car alone.

Since they are working on the same car, the amount of work done in both cases is the same, so we can set the two equations equal to each other and solve for x:

1/8.24 = 1/(t + x) + 1/17

Multiplying both sides by the least common multiple of the denominators (8.2417(t+x)).

17*(t+x) + 8.24*(t+x) = 8.24*17

Simplifying.

25.24t + 17x = 139.68

We also know that Mike's rate of work is 1/m car per minute.

Since we know the combined rate of work when they work together, we can set up another equation:

1/m + 1/17 = 1/8.24

Multiplying both sides by the least common multiple of the denominators (8.2417m).

178.24m + 8.2417m = 8.2417m + m8.24m

Simplifying.

141.08m = 139.68

Solving for m.

m = 0.989

Therefore,

It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.

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Answer:

This is a right angle

Step-by-step explanation:

There is a square inside of the triangle.

The area and the perimeter of the given parallelogram are 36.792 mm² and 24.28 mm respectively.

In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides.

The confronting or opposed sides and the opposing angles of a parallelogram are of equal length.

There are four distinct types of parallelograms, including three distinct types.

Rhombuses, parallelograms, squares, and rectangles are the four types.

So, the given image itself tells that the given figure is a parallelogram.

The area of the given parallelogram is:
A = b*h

A = 6.3*5.84

A = 36.792 mm²

The perimeter of the given parallelogram:

P = 2(a+b)

P = 2(6.3+5.84)

P = 24.28 mm

Therefore, the area and the perimeter of the given parallelogram are 36.792 mm² and 24.28 mm respectively.

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The graph that shows the solution to the system of linear inequalities is the Graph D.

Here, we are given first inequality as:

Y > -1/3x + 2

The graph of this inequality is a dotted straight line( since the inequality is strict) that passes through (6,0) and (0,2) with shaded region away from the origin ( since it fails zero test)

Second inequality is given by:

y > 2x - 3

The graph of this inequality is a dotted straight line( since the inequality is strict) that passes through (3/2,0) and (0,-3) with shaded region away towards the origin ( since it passes zero test). On plotting it's graph, we get the solution.

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Answer:

The mean of the numbers 5, 3, 6, x, 9, and 10 is given as 7.

To find the value of x, we can use the formula for the mean:

mean = (sum of all the numbers) / (number of numbers)

In this case, we have:

7 = (5 + 3 + 6 + x + 9 + 10) / 6

Multiplying both sides of the equation by 6, we get:

42 = 33 + x

Subtracting 33 from both sides of the equation, we get:

x = 9

Therefore, the value of x that makes the mean of 5, 3, 6, x, 9, and 10 equal to 7 is 9.

Answer:

[tex] \frac{468}{14.4} = \frac{d}{16.8} [/tex]

[tex]32.5 = \frac{d}{16.8} [/tex]

[tex]d = 546[/tex]

Wyatt can drive 546 miles on a full tank (16.8 gallons) of gas.

The quadratic equation in standard form can be written as:

y = x² - 10

Remember that for a quadratic equation whose solutions are x₁ and x₂, the quadratic can be written as:

y = (x - x₁)*(x - x₂)

Here the solutions are:

x = √10

x = -√10

Then we can write:

y = (x+  √10)*(x - √10)

Expanding that we will get:

y = x² + √10x - √10x + √10*-√10

y = x² - 10

That is the quadratic.

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