Homework Set 6: Problem 2 Previous Problem Problem List Next Problem a(u, v) x = u-20, y = 6u - 8v implies 2(x, y) = Preview My Answers Submit Answers

Answer:

The missing number: 6

The property used: Distributive Property of Multiplication

Explanation:

Given the below;

The below shows an example of the distributive property of multiplication;

Applying the distributive property in the given equation, we can see that;

So the missing number is 6 and the equation can be written as;

Answer:

u + 15

Step-by-step explanation:

Since we don't know the value of u, we have to put the equation like this.

Hope I helped :)

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When rolling a number cube one time, there are several things that are true. Here are three options:

1. The outcome will be a whole number between 1 and 6: Since the number cube has faces numbered from 1 to 6, rolling it one time will result in one of these whole numbers.

2. Each face has an equal chance of landing face-up: The number cube is designed in such a way that each face has an equal probability of landing face-up when rolled. This means that the chances of rolling a 1, 2, 3, 4, 5, or 6 are all the same.

3. The outcome is independent of previous rolls: Rolling the number cube one time does not depend on or affect any previous rolls. Each roll is considered an independent event, so the previous outcome does not influence the next roll.

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The effort needed to move an object along a curve that is specifically oriented. F(x, y) = (y, x) on the parabola y = 6x² from (0,0) to (2,24) is 48.

A bowl-shaped object is defined as having a curve at the surface created by the intersection of a cone and a plane that is perpendicular to a straight line. Another definition of a curve is one created when a moving point moves such that its distance from a fixed point equals its distance from a fixed line. A quadratic function is known in this form as its standard form. A parabola is a U-shaped curve that represents the quadratic function on a graph.

The given parabola is,

y = 6x²

Here consider x=t

Then,

y=6t²(0≤t≤z)

The work done by F(x, y) would be:

W=\(\int\limits^_c\)F.dr

=\(\int\limits^_c\)(\(y_{i} +x_{j}\))(d\(x_{i}\)+d\(y_{j}\))

=\(\int\limits^_c\)y dx + x dy

=\(\int\limits^2_0\)((6t²)(1)+(t)(12t))dt

=\(\int\limits^2_0\)18t²dt

=48

Therefore, the effort needed to move an object along a curve that is specifically oriented. F(x, y) = (y, x) on the parabola y = 6x² from (0,0) to (2,24) is 48.

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the series is convergent from x = -1 (left end) to x = 1 (right end).

To find the interval of convergence for the power series ∑n=1 to infinity of \(n^{(1/3)} * x^n\), we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. Mathematically, the ratio test can be expressed as:

lim┬(n→∞)⁡〖|(\(a_{(n+1)}/a_n)\)|〗 < 1

Let's apply the ratio test to the given series:

\(a_n = n^{(1/3)} * x^n\)

\(a_{(n+1)} = (n+1)^{(1/3)} * x^{(n+1)}\)

Taking the ratio of consecutive terms:

|a_(n+1)/a_n| = |((n+1)^(1/3) * x^(n+1)) / (n^(1/3) * x^n)|

Simplifying the expression:

\(|a_{(n+1)}/a_n| = |(n+1)^{(1/3)} * x / n^{(1/3)}|\)

Taking the limit as n approaches infinity:

lim┬(n→∞)⁡〖\(|(a_{(n+1)}/a_n)\)|〗 = lim┬(n→∞)⁡〖|\((n+1)^{(1/3)} * x / n^{(1/3)}|\)〗

Using the properties of limits, we can simplify the expression further:

lim┬(n→∞)⁡〖|(a_(n+1)/a_n)|〗 = lim┬(n→∞)⁡〖\(|(1 + 1/n)^{(1/3)} * x|\)〗

= 1 * |x|

= |x|

We know that |x| < 1 for convergence. Therefore, the interval of convergence for the given power series is -1 < x < 1.

To determine the left endpoint of the interval of convergence, we substitute x = -1 into the series:

∑n=1 to infinity of \(n^{(1/3)} * (-1)^n\)

This is an alternating series. When n is odd, the terms of the series will be positive, and when n is even, the terms will be negative. The series converges by the Alternating Series Test.

the left endpoint of the interval of convergence is x = -1.

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Info given

We have a total of people given (82). We also know that we have 54 children of under 12 years and under some children were under 3 years

We define x as the number of children under 3 years.

We want to find C for the total cost. We don't have the unitary prices but we can assume it as C1 (over 3 and lower than 12) and C2(adults) for children and adults.

Solution:

With C the total amount collected and C1 and C2 described above.

Based on the information in the graph, it can be inferred that the sport with the most players and followers is cricket.

To make a bar graph with the information in the table, we must take into account the categories (watch and participate), the different sports and the data that correspond to each category and each sport.

Once we understand this data, we need to set the parameters of the graph. On one axis we put the reference of the different values and on the other axis we put the different sports. Additionally, we must take into account that we must make two bars for each sport and that they represent the individuals who participate and the individuals who watch.

According to the above, the graph would look like this:

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The total product average product and marginal product are important to operate efficiently and maximize profits. Option D is the correct answer.

Being able to calculate the total product, average product, and marginal product is important for businesses to operate efficiently and maximize profits.

The total product is the overall output produced by a business, while the average product is the output per unit of input, and the marginal product is the change in output resulting from a change in input.

These calculations can help businesses optimize their production processes by identifying the most efficient levels of input and output.

By maximizing their output while minimizing their input costs, businesses can increase their profitability and gain a competitive advantage in the market.

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The question is -

Being able to calculate the total product average product and the marginal product is important:

a. for determining demand and supply.

b. when filing taxes.

c. to keep competition in check.

d. to operate efficiently and maximize profits.

The curve is defined by x = 4t^2 + 3 and y = t^8. To find the equation of the tangent line and the value of d^2y/dx^2 at the point where t is given. Therefore, the value of d^2y/dx^2 at the given point is 7.

The tangent line equation can be found by using the point-slope form of a line. The second derivative of y with respect to x is also calculated using the chain rule and substituting the value of t.

We are given that x = 4t^2 + 3 and y = t^8. To find the equation of the tangent line at a specific point, we need to differentiate y with respect to x using the chain rule:

dy/dx = dy/dt / dx/dt

Using the power rule of differentiation, we get:

dy/dt = 8t^7

dx/dt = 8t

Substituting the value of t at the given point, we get:

dy/dx = (8t^7) / (8t) = t^6

At the given point, we can find the value of t and then calculate the value of dy/dx. For simplicity, we assume that t = 1. Therefore, dy/dx = 1^6 = 1.

Next, we need to find the equation of the tangent line using the point-slope form of a line:

y - y1 = m(x - x1)

where (x1, y1) is the point of tangency and m is the slope of the tangent line.

Substituting the values of x1, y1, and m, we get:

y - t^8 = (dy/dx)(x - 4t^2 - 3)

y - 1 = (x - 4t^2 - 3)

Therefore, the equation of the tangent line is y = x - 4t^2 + 4.

Finally, we need to find the second derivative of y with respect to x using the chain rule:

d^2y/dx^2 = d/dx (dy/dx)

d^2y/dx^2 = d/dt (dy/dx) / dx/dt

Using the power rule of differentiation, we get:

d^2y/dt^2 = 56t^6

dx/dt = 8t

Substituting the value of t at the given point, we get:

d^2y/dx^2 = (56t^6) / (8t) = 7t^5

Again, assuming that t = 1, we get d^2y/dx^2 = 7. Therefore, the value of d^2y/dx^2 at the given point is 7.

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Answer:

3,293 yards are more than a mile

Step-by-step explanation:

1 mile is 1,760 yards. Thereby, we know that 3,293 is more than 1,760.

Answer: 3,293 yards is more than a mile since a mile is 1,760 yards

Step-by-step explanation:

2 miles are 3,520 yards which can further prove that 1 mile is way less the 3,293 yards

Hope this helped

Answer:

A

Step-by-step explanation:

I just took the quiz

Iota is an imaginary unit number that is denoted by i and the value of iota is \(i=\sqrt{-1}\)

Letter A represent \(z^{3}\)

Given that, z = 1 - i

Now finding  \(z^{3}\) ,

                    \(z^{3}=(1-i)(1-i)(1-i)\\\\=(1+i^{2-2i} )(1-i)\\\\=1+i^{2}-3i-i^{3}+2i^{2}\\\\=1-1-3i+i-2\\\\=-2-2i\)

In given diagram, it is observed that Point A is  \(-2-2i\).

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Answer:

20 > -1

Step-by-step explanation:

Well 20 is a positive integer that is 20 units from 0 whereas -1 is a negative integer that is 1 unit behind zero.

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

To solve the inequality y + 7 ≤ -1, we need to isolate the variable y on one side of the inequality sign.

Starting with the given inequality:

y + 7 ≤ -1

We can begin by subtracting 7 from both sides of the inequality:

y + 7 - 7 ≤ -1 - 7

y ≤ -8

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

In the context of a number line, all values to the left of -8, including -8 itself, will make the inequality true. For example, -10, -9, -8, -8.5, and any other value less than -8 will satisfy the inequality. However, any value greater than -8 will not satisfy the inequality.

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The following question may be like this:

What is a solution of the inequality shown below? y+7≤-1

bottom was cut off a bit its 4=b

I'm pretty sure you have to write how much they are

Pink heart is 2

Green square is 2

Blue moon 1

Answer:

Pink Heart = 2 Green Square = 6  Blue Moon = 4

Step-by-step explanation:

h ( h x g) = (b x g) = 24    left side of table

2 (2 x  3)  = (4 x 6) = 24   right side of table

h(h x g ) = 2(2 x 3) = (4 x 6) = (b x g) = 24   equivalent outcomes

The length of the stick was 7.55 cm.

Given that,

initial speed of bug is given by, v=0.65 m/s

m refers to the mass of bug.

Mass of stick is given by, M= 10m

I refers to the moment of inertia of bug and stick together about the end of the stick.

ω refers to the angular velocity of the bug and stick immediately after collision.

L refers to length of stick

Stick can be considered rod.

Now, moment of inertia about end of a rod is given by = 1/3 ML²

From angular momentum conservation theory we can get,

total initial angular momentum = total final angular momentum

mvL = Iω

mvL = [mL² + 1/3 ML²] ω

mvL = [mL² + 1/3 (10m) L²] ω

0.65 L = 4.333 L²ω

L = 0.15/ω

ω = 0.15/L

Change in vertical position center of mass of rod is given by,

H = L/2 [1 - cos θ]

Change in vertical position of bug after reaching max height is given by,

h = L [1 - cos θ]

From energy conservation law we can conclude that,

Rotational kinetic energy immediately after collision = Potential energy of bug and stick system at max height .

(1/2) [mL² + 1/3 ML²] ω² = mgh + MgH

(1/2) [mL² + 1/3 (10m) L²] ω² = m(gh + 10gH)

2.167 L²ω² = g (h + 10H)

2.167 L² (0.15/L)² = g [L [1 - cos θ] + 5L [1 - cos θ]] (Substituting the relations from previous)

(2.167) (0.15)² = 6 (9.8) L (1 - cos 8.5)

L = 0.0755 m (Rounding off to nearest fourth decimal places)

L = 7.55 cm

Hence the length of the stick was 7.55 cm.

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The question is incomplete. The complete question will be -

Answer:

dteps

Step-by-step explanation:

answer

Answer:

35.00

Step-by-step explanation:

Sin(B)/b = Sin(A)/b

a* Sin(B) = b Sin(A)

b = a * Sin(B)/ Sin(A)

Plug in --> Get answer

The value of b is 34.75.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

From the law of sin,

Sin 29.8/c = Sin 34.5/22 = Sin B/b

Now,

The sum of the angles in a triangle is 180.

So,

∠A + ∠B + ∠C = 180

34.5 + ∠B + 29.8 = 180

∠B = 180 - (34.5 + 29.8)

∠B = 115.7

Now,

Sin 34.5/22 = Sin B/b

0.57/22 = Sin 115.7/b

0.57/22 = 0.90/b

b = (0.90 x 22) / 0.57

b = 34.74

Thus,

The value of b is 34.75.

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The statement "confidence intervals are useful when trying to estimate unknown statistics" id True.

Confidence intervals are valuable tools for estimating unknown statistics. When dealing with limited data, it is often impossible to determine the true value of a population parameter with absolute certainty. Confidence intervals provide a range of plausible values within which the true parameter is likely to fall.

A confidence interval consists of two components: a point estimate and a margin of error. The point estimate is the best guess of the parameter's value based on the available data, while the margin of error reflects the uncertainty associated with the estimate. By specifying a confidence level, typically expressed as a percentage (e.g., 95% confidence interval), we can quantify the level of confidence we have in capturing the true parameter within the interval.

Confidence intervals allow researchers and decision-makers to make informed conclusions about population parameters while acknowledging the inherent uncertainty. They provide a range of plausible values, taking into account sampling variability and the variability of the data. Confidence intervals also facilitate hypothesis testing, as they help determine whether a hypothesized value falls within the interval.

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Internal validity explains the association between binge-watching tv and irritability.

In the context of a specific study, internal validity refers to how strongly a piece of evidence supports a claim regarding cause and effect. It is one of the most crucial characteristics of scientific research and a crucial idea when considering evidence more generally.

The extent to which alternative explanations for a study's findings (often, sources of systematic error or "bias") can be ruled out is a measure of its internal validity. In contrast, external validity measures how well data support judgments made regarding other situations (that is, the extent to which results can be generalized).

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Answer:

I don't know

Step-by-step explanation:

my previous answer was wrong

Answer:

As while decimal figures which have unique numbers such as pi are irrational numbers, decimal numbers which have repeating numbers such as 0.36363 are rational numbers. Which means that 0.363636 is a prime example of a rational number that is not an integer.

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Main Answer:The points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on and the Vertical tangent  are (0, π/2), (0, 3π/2), (0, 5π/2),so on.

Supporting Question and Answer:

How do we find points on a curve where the tangent line is horizontal or vertical?

To find points on a curve where the tangent line is horizontal or vertical, we need to determine the values of θ (or any parameter) that correspond to those points. This can be done by analyzing the derivatives of the curve equation and identifying the conditions under which the derivative is zero or undefined. Horizontal tangent lines occur when the derivative with respect to θ is zero, while vertical tangent lines occur when the derivative with respect to r is undefined or infinite.

Body of the Solution:To find the points on the curve r = 8 cos θ where the tangent line is horizontal or vertical, we need to determine the values of θ that correspond to those points.

  Differentiating r = 8 cos θ with respect to θ, we get:

dr/dθ = -8 sin θ

Setting dr/dθ = 0, we have:

-8 sin θ = 0

Since sin θ = 0 when θ is an integer multiple of π, the values of θ that give a horizontal tangent line are: θ = 0, π, 2π, 3π, ...

For each value of θ, we can find the corresponding value of r by substituting it back into the equation r = 8 cos θ.

   Differentiating r = 8 cos θ with respect to r, we get:

dθ/dr = -1 / (8 sin θ)

For a vertical tangent line, sin θ must be equal to zero, which occurs when θ is an integer multiple of π.

Therefore, the values of θ that give a vertical tangent line are: θ = π/2, 3π/2, 5π/2, ...

Again, for each value of θ, we can find the corresponding value of r by substituting it into the equation r = 8 cos θ.

Combining the values of θ and their corresponding values of r, we have: Horizontal tangent: (8, 0), (-8, π), (8, 2π), (-8, 3π), ... Vertical tangent: (0, π/2), (0, 3π/2), (0, 5π/2), ...

Final Answer:Thus, the points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on, while the points where the tangent line is vertical are (0, π/2), (0, 3π/2), (0, 5π/2), and so on.

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The points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on and the Vertical tangent  are (0, π/2), (0, 3π/2), (0, 5π/2),so on.

To find points on a curve where the tangent line is horizontal or vertical, we need to determine the values of θ (or any parameter) that correspond to those points. This can be done by analyzing the derivatives of the curve equation and identifying the conditions under which the derivative is zero or undefined. Horizontal tangent lines occur when the derivative with respect to θ is zero, while vertical tangent lines occur when the derivative with respect to r is undefined or infinite.

To find the points on the curve r = 8 cos θ where the tangent line is horizontal or vertical, we need to determine the values of θ that correspond to those points.

Horizontal tangent line: A horizontal tangent line occurs when the derivative of r with respect to θ is equal to zero.

 Differentiating r = 8 cos θ with respect to θ, we get:

dr/dθ = -8 sin θ

Setting dr/dθ = 0, we have:

-8 sin θ = 0

Since sin θ = 0 when θ is an integer multiple of π, the values of θ that give a horizontal tangent line are: θ = 0, π, 2π, 3π, ...

For each value of θ, we can find the corresponding value of r by substituting it back into the equation r = 8 cos θ.

Vertical tangent line: A vertical tangent line occurs when the derivative of θ with respect to r is undefined or infinite.

  Differentiating r = 8 cos θ with respect to r, we get:

dθ/dr = -1 / (8 sin θ)

For a vertical tangent line, sin θ must be equal to zero, which occurs when θ is an integer multiple of π.

Therefore, the values of θ that give a vertical tangent line are: θ = π/2, 3π/2, 5π/2, ...

Again, for each value of θ, we can find the corresponding value of r by substituting it into the equation r = 8 cos θ.

Combining the values of θ and their corresponding values of r, we have: Horizontal tangent: (8, 0), (-8, π), (8, 2π), (-8, 3π), ... Vertical tangent: (0, π/2), (0, 3π/2), (0, 5π/2), ...

Thus, the points on the given curve where the tangent line is horizontal are (8, 0), (-8, π), (8, 2π), (-8, 3π), and so on, while the points where the tangent line is vertical are (0, π/2), (0, 3π/2), (0, 5π/2), and so on.

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Answer:

1

Step-by-step explanation:

because its the only one where if you run a line down the y axis it only crosses the line at one point

No, the shop did not meet the sales target to sell a mean of 65 umbrellas per month.

The Mean is 63.67.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

From the graph,

The number of umbrellas sold.

Jan = 54

Feb = 84

Mar = 72

April = 94

May = 52

June = 26

The mean of the number of umbrellas.

= (54 + 84 + 72 + 94 + 52 + 26) / 6

= 382 / 6

= 63.67

Thus,

The mean for the first six months is 63.67.

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Answer:

yes its is

Step-by-step explanation:

4x2+11x -20 = -212

-212 / 4 = -53

The standard deviation of X is approximately 1.715.

The standard deviation of a binomial distribution with parameters n and p is given by the formula:

σ = sqrt(np(1-p))

where

n is the sample size and

p is the probability of success.

In this case, n = 15 and p = 0.33, so we have:

σ = sqrt(15 * 0.33 * (1 - 0.33)) = 1.715 (rounded to three decimal places)

Therefore, the standard deviation of X is approximately 1.715.

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Answer:

7 Hours

Step-by-step explanation:

Because it takes Ryan 10hrs to finish the job, and with both Ryan and Molly it takes 3hrs to finish the job, so subtract 10 minus 3 and you get 7, therefore it takes Molly 7hrs to finish the job

Hope it's right

Answer:

X  = 1.2

Step-by-step explanation:

-2(3x + 7) = -2(1 + 8x)

-6x - 14 = -2 - 16x

+16x              +16x

10x - 14 = -2

     +14    +14

10x = 12

10  =   10 = 1.2

(x = 1.2)