given that 3p = 2m - 5q, express m in terms of p and q

The forecast value for time period 2 is 210, and the forecast error is -110 when the actual value is 100. Option B

To calculate the forecast value for time period 2, we substitute W = 2 into the regression equation:

y = 200 + W + 2W^2

= 200 + 2 + 2(2^2)

= 200 + 2 + 2(4)

= 200 + 2 + 8

= 210

Therefore, the forecast value for time period 2 is 210.

To calculate the forecast error, we compare the forecasted value with the actual value for time period 2. Given that the actual value is 100, the forecast error can be calculated as the difference between the actual value and the forecast value:

Forecast error = Actual value - Forecast value

= 100 - 210

= -110

Hence, the forecast error is -110.

Therefore, the correct answer is:

Forecast value = 210; forecast error is -110. So Option B is correct.

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The  smallest such $n$ is $12$.

To solve the problem, we can start by expanding $(n+r)^3$ and approximating it by ignoring the term $r^3$, since $r$ is small.

We  then want to find the smallest positive integer $n$ such that there exists a positive real number $r$ less than $1/1000$ satisfying the equation. We can try different values of $n$ starting from $n=1$ and incrementing by $1$ until we find a value of $n$ that works.

By  testing a few values, we find that $n=12$ works, giving us $1728 + 1296r + 324r^2$, which is less than $(12+1/40)^3$. Therefore, the smallest such $n$ is $12$.

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The value of x is 21.88

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

angle A is 27.2°, the opposite angle is 10 and the hypotenuse is x

therefore,

sin27.2 = 10/x

x( sin27.2) = 10

x = 10/sin27.2

x = 10/0.457

x = 21.88

Therefore the value of x is 21.88

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Answer:

The width is 2x+1

Step-by-step explanation:

10x^2 +5x

Divide this by 5x

10x^2 /5x = 2x

+

5x/5x =1

Add this together

2x+1

The width is 2x+1

Answer:

( 2x + 1 )

Step-by-step explanation:

10x^2 + 5x

it could also be;

5x (2x + 1)

so, the width is( 2x +1)

by using the condition for orthogonality between surfaces and applying it to the given equation  \(z^{2}\) = \(x^{2}\) + \(y^{2}\) and \(x^{2}\) + \(y^{2}\) + \(z^{2}\) = \(r^{2}\) are orthogonal at every point of intersection.

Let's consider the surfaces F(x, y, z) = 0 and G(x, y, z) = 0, where the gradients of F and G are non-zero at the point of intersection P. To prove that the surfaces are orthogonal at P, we need to show that their dot product, FxGx + FyGy + FzGz, is equal to zero at P.

The dot product of the gradients can be written as FxGx + FyGy + FzGz. If this expression evaluates to zero at P, it implies that the gradients are perpendicular, and therefore the surfaces are orthogonal at P.

Now, let's apply this result to the surfaces \(z^{2}\) = \(x^{2}\) + \(y^{2}\) and \(x^{2}\) + \(y^{2}\) + \(z^{2}\) = \(r^{2}\). Taking the gradients of these surfaces, we find that the dot product FxGx + FyGy + FzGz is equal to 2\(z^{2}\) + 2(\(x^{2}\) + \(y^{2}\) + \(z^{2}\)), which simplifies to 3\(z^{2}\) + 2(\(x^{2}\) + \(y^{2}\)).

Since this expression is equal to zero for all points (x, y, z) satisfying the equation of the second surface, \(x^{2}\) + \(y^{2}\) + \(z^{2}\) = \(r^{2}\), we can conclude that the surfaces \(z^{2}\) = \(x^{2}\) + \(y^{2}\) and \(x^{2}\) + \(y^{2}\)+ \(z^{2}\) = \(r^{2}\) are orthogonal at every point of intersection

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The given statement "non-linear quality constraints can sometimes be rewritten as linear constraints" is TRUE because this process, known as linearization, involves transforming non-linear expressions into equivalent linear expressions.

Linearization simplifies complex problems, allowing them to be solved using linear programming techniques. However, this may not always be possible for all non-linear constraints, and some trade-offs in accuracy might occur.

Linearization techniques, such as piecewise linear approximation or variable substitution, can be applied to rewrite non-linear constraints into linear ones, facilitating the use of linear programming methods for more efficient and tractable solutions.

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The median of this set is:

9

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result.

HAVE A NICE DAY!

Answer:

Step-by-step explanation:

Remark

You always have to put the data in order to answer a question like this one.

6 7 7 8 10 14 15

The median is the middle number. In this case it is 8. There are 3 numbers below 8 and 3 numbers above 8, so 8 is the median.

Answer: 8

The Poisson distribution becomes a good approximation to the Binomial distribution when the number of trials is large, the probability of success is small, and the expected number of successes is λ = np.

(a) The probability mass functions (PMF) of Bino(np) and Pos(np) with the parameters n = 100, p = 0.2,0.8 for the interval k [0, 100) can be plotted using the MATLAB functions binopdf and poisspdf.

(b) To show that Poisson distribution approximates Binomial distribution when n is large, p is small, and λ = np, we can use the Poisson approximation to Binomial distribution. Using the fact that n-k/k → 1 as n →[infinity], we can simplify the Binomial distribution to:

Bino(n,p) ≈ (np)^k e^(-np)/(k!)

By letting λ = np and replacing in the above expression, we get:

Bino(n,p) ≈ (λ/k)^k e^(-λ)/k!

This expression is the PMF of a Poisson distribution with parameter λ, which proves that Poisson distribution approximates Binomial distribution under the given conditions.

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Answer:

The mode is 78, which appears the most times (3).

The mode of the given data 62, 78, 84, 62, 72, 78, 54, 60, 78, 80 is 78.

The mode is the data that occurs most frequently, in the data set listed below 62, 78, 84, 62, 72, 78, 54, 60, 78, 80. We can see that the number 78 appears three times, which is more than any other value in the set when we look at the data.

Note: If multiple values occur with the same highest frequency, but in this case, 78 is the only mode, the data set may have multiple modes.

Thus, the mode of 62, 78, 84, 62, 72, 78, 54, 60, 78, and 80 data set is 78.

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Answer:

8.5 Yards

Step-by-step explanation:

Pythagorean Theorem: \(c = \sqrt{a^{2} +b^{2} }\)

a = 6

b = 6

Therefore: \(c = \sqrt{6^{2} +6^{2} }\) = 8.485

The path is 8.5 yards long

Answer:

happy to explain

Step-by-step explanation:

Algebra is an area in mathematics that uses variables, in the forms of letters and symbols, to act as numbers or quantities in equations and formulas. Geometry is an area in mathematics that studies points, lines, varied-dimensional objects and shapes, surfaces, and solids

The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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The probability that their first child will have kidney disease is 1/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we have

Both parents must be heterozygous to have a 1/4 chance of having an

affected child. Parent 2 is heterozygous (her father was homozygous recessive, but she has unaffected).

For the child to have the disease, both Parent 1 and Parent 2 would need to be heterozygous

There is a 50% chance of this for Parent 1 and a 100% chance of this for Parent 2 and then, there is a 25% chance that their first child will be affected:

50%× 100% × 25% = 12.5%

1/2 × 1/4 = 1/8

Hence, the probability that their first child will have kidney disease is 1/8.

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Answer:

$250*C + $180*G = $950

Step-by-step explanation:

Solving for G, it is G = (950 - 250C)/180

Solving for C, it is C = (950 - 180G)/250

Answer:

$10665,64

Step-by-step explanation:

S=19900*(1-(7,5/100))^8=10665, 64

Answer:10665.64

Step-by-step explanation: Exponential Functions:

y=ab^x

A= starting value = 19900

r=rate = 7.5%=0.075

Exponential Decay:

b=1-r=1-0.075=0.925  

Write Exponential Function:

y=19900(0.925)^x

Plug in time for x:

y=19900(0.925)^8

y= 10665.6404317  

Evaluate

y≈10665.64

The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

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The frictional force acting on the cylinder is F= (4.0N)i when a fishing line wrapped around a uniform solid cylinder exerts a constant, horizontal force on it of magnitude 12 app n.

Given that,

A fishing line wrapped around a uniform solid cylinder exerts a constant, horizontal force on it of magnitude 12 app n. The cylinder has a radius of 0.10 m, a mass of 10 kg, and rolls smoothly on the horizontal surface.

We have to find what is the cylinder being frictionally forced by.

We know that,

To ensure that the angular acceleration is positive, we make the unorthodox decision to treat the clockwise sense as positive (as is the linear acceleration of the center of mass, since we take rightward as positive). Applying the linear form of Newton's second law results in

(12 N)−f=Ma

Therefore, f=−4.0 N.

The friction force is discovered to point rightward with a magnitude of 4.0 N, or, in contrast to what we thought when formulating our force equation,

F= (4.0N)i

Therefore, The frictional force acting on the cylinder is F= (4.0N)i when a fishing line wrapped around a uniform solid cylinder exerts a constant, horizontal force on it of magnitude 12 app n.

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The set of variables that is most likely to have a cause-and-effect relationship is option C: the weight of a box and the postage rate we have to pay to ship the box to California.

Based on the given sets of variables, the set most likely to have a cause-and-effect relationship is:
B. The height of a person and the weight of a person

This is because there is a general correlation between a person's height and their weight, as taller individuals tend to have higher weights. While this is not an absolute rule, there is a stronger cause-and-effect relationship in this set compared to the other options.

This is because the weight of the box is a likely cause of the postage rate, as the heavier the box, the more postage we will have to pay to ship it. In options A and B, there may be a correlation between the variables, but it is less likely that there is a direct cause-and-effect relationship. In option D, the make of a car is not a likely cause of its mileage, as there are many other factors that can affect a car's mileage.

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Answer:-6 and 6

Both of these are 6 units away from 0 on a number line, though it would help more if you had choices but i believe this is the answer.

The area of the hexagonal head using each persons (Andre & Lin) method is;

Total Area using Lin's method = 93.6 ft²

Total Area using Andre's method = 93.6 ft²

From the image, a side of the hexagon is 6 inches. This means that all sides of each triangle will be also 6 inches.

Formula for area of a triangle = ¹/₂(base x height)

We see a perpendicular distance spanning from one end of the hexagon to the other end passing through the centre of the hexagon. It passes 2 triangles.

Thus, the height of one triangle = 10.4/2 ft = 5.2 ft

Area of one triangle =  ¹/₂ × 6 × 5.2 = 15.6 ft²

Thus, Area of hexagon = area of 6 triangles = 6 × 15.6 = 93.6 ft²

Let us first find the area of the rectangle;

Area of rectangle = length × width

Area of rectangle = 10.4 × 6 = 62.4 ft²

For the rectangle, we know three sides now which are;

10.4 ft, 6 ft, 6 ft but we don't know the height and as such we will use heron's formula to get the area of one triangle;

A = √s((s - a)(s - b)(s - c))

where; a,b and c are the 3 sides of the triangle

s = (a + b + c)/2

Thus; s = (10.4 + 6 + 6)/2 = 11.2 ft

Thus;

A = √11.2((11.2 - 10.4)(11.2 - 6)(11.2 - 6))

A = 15.6 ft²

There are 2 triangles and so Area of 2 triangles =2 × 15.6 = 31.2 ft²

Thus;

Total Area = 62.4 ft² + 31.2 ft²

Total Area = 93.6 ft²

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Answer:

y'=3x^2+34x+72

Step-by-step explanation:

I see this has no answer and it might be too late.

It's asking us to find dy/dx, after taking log of both sides and apply any useful properties of log.

Take log of both sides:

log(y)=log[x(x+8)(x+9)]

Apply product rule of logarithms on right:

log(y)=log(x)+log(x+8)+log(x+9)

Now differentiate both sides:

y'/y=1/x+1/(x+8)+1/(x+9)

Multiply both sides by y:

y'=y(1/x+1/(x+8)+1/(x+9))

Replace y with x(x+8)(x+9) -> this is from the given equation:

y'=x(x+8)(x+9)(1/x+1/(x+8)+1/(x+9))

Distribute:

y'=(x+8)(x+9)+x(x+9)+x(x+8)

Multiply/distribute some more:

y'=x^2+17x+72+x^2+9x+x^2+8x

Combine like terms:

y'=3x^2+34x+72

Answer:

42

Step-by-step explanation:

so 180-132 will give u top angle of triangle

which is 48 degrees

48+90+x=180

180-90-48=x

x= 42

Answer:

132

Step-by-step explanation:

its right angle = 90 degrees

plsu both angles

and minus answer by 180

The following are crucial factors in hypothesis testing:

In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.

Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.

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Answer: AC = sqrt 241 or 15.5

Step-by-step explanation:

Use the Pythagorean Theorem

4^2 + 15^2 = c^2

16 + 225 = c^2

241 = c^2

sqrt241 = c

The fraction form of 42% is 21/50.

Every fraction's numerator and denominator are split in half by a horizontal bar known as the fractional bar.

The denominator displays the number of pieces into which the whole has been divided. It is situated below the fractional bar in the lower part of the fraction.

The numerator indicates how many portions of the fraction are selected or displayed. It is located at the upper part of the fraction, above the fractional bar.

We have to write 42% into the simplest form fraction.

So, Explicit 42%

42 /100

Now, simplify the fraction by making it in its lowest form

42 /100

2 x 21/ 2x 50 = 21/50

Hence, the fraction is 21/50.

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Answer:

No, P(high school | GPA above 3.0) ≠ P(high school)

Step-by-step explanation:

Given

See attachment for table

Required

Determine if High school and GPA above 3.0 are independent

Let

\(H \to\) High school

\(G \to\) GPA above 3.0

For both events to be independent, the following must be true

\(P(H\ |\ G) = P(H)\)

From the table:

\(P(H) = \frac{H}{Total}\)

\(P(H) = \frac{60}{100} = 0.60\)

\(P(H | G) = \frac{H\ n\ G}{G}\)

\(P(H | G) = \frac{14}{40} = 0.35\)

The test for independence is as follows:

\(P(H\ |\ G) = P(H)\)

By comparison

\(P(H\ |\ G) \ne P(H)\)

i.e.

\(0.35 \ne 0.60\)

Hence, both events are not independent

Answer:

The number is 28.35

Step-by-step explanation:

45% of 36

\(\frac{x*y}{100}\)

= \(\frac{45*36}{100}\)

= \(\frac{2835}{100}\)

= 28.35