Please
Explain, in detail, the steps on how to factor the following trinomial: 3x^2 + 5x + 2

For h = 0.01, the actual % error is 0.0146%.

For h = 0.5, the actual % error is 18.38%

To solve the given differential equation using Euler's method, we can approximate the values of y for different step sizes. Let's consider the step sizes h = 0.1, h = 0.01, and h = 0.5.

For h = 0.1:

Given t0 = 0, y0 = 0, h = 0.1, and f(t0, y0) = 3(0) + 4(0) = 0.

Using the Euler's method formula:

y1 = y0 + h * f(t0, y0)

= 0 + (0.1)(0)

= 0

Thus, we get the approximate value of y at t = 0.1 as y1 = 0.

Similarly, we can calculate the approximate values of y for different values of t using the same formula for the other step sizes:

For h = 0.01, we get:

y11 = 0.04

y12 = 0.064

For h = 0.5, we get:

y21 = 0.004

y22 = 0.0064

Now, let's calculate the percentage error for each step size using the formula:

% error = (|actual - approximate| / actual) * 100

For h = 0.1, the actual value of y at t = 10 is given by:

y = 1/4 * (5e^(4t) - 3t - 3)

At t = 10, we have y = 1/4 * (5e^(410) - 310 - 3) = 150.219.

% error = (|150.219 - 150| / 150.219) * 100

= 0.146%

For h = 0.01, the actual % error is 0.0146%.

For h = 0.5, the actual % error is 18.38%.

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Answer:

20

Step-by-step explanation:

Let x represent our numbewr

x + 12 = 160/x

x^2 + 12x -160 = 0

(x-20(x+8)  = 0

x = -8,20

20 is the only natural number solution.

Answer:

c= 3a+2b

Step-by-step explanation:

because the equation don't change, if they have different variables

Refer to the image for the graph of the lines.

The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.

We need to draw any line with a slope m = 2, and

another line with a slope m = -2.

Disclaimer: Let us assume that the constant c = 0.

Then the equation to the line with a slope of "positive" 2 is given by

y = 2x

Then the equation to the line with a slope of "negative" 2 is given by

y = -2x

Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.

f: green line indicates a line with a slope of "positive" 2.

g: blue line indicates a line with a slope of "negative" 2.

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Given:

The sum of 85 + w is less than or equal to 6 multiplied by y.

To find:

The inequality for the given situation.

Solution:

We know that,

The sum of 85 and w means "85+w".

Less than or equal means "≤".

6 multiplied by y means "6y".

So, the inequality for the statement "the sum of 85 + w is less than or equal to 6 multiplied by y", is:

\(85+w\leq 6y\)

Therefore, the correct option is A.

Therefore, the intersection of the arcs that Victor drew must be the midpoint of segment XY.

the midpoint is the point that is exactly halfway between two other points. It is the point that divides the line segment into two equal halves.

The midpoint of a line segment can be found by taking the average of the x-coordinates and the y-coordinates of the two endpoints of the segment. For example, if the endpoints of a line segment are (x1, y1) and (x2, y2), then the midpoint of the segment is\(((x_1 + x_2)/2,(y_1+y_2)/2).\)

by the question.

If Victor drew an arc centered at X and then drew an arc of the same radius centered at Y, the intersection of these arcs will be equidistant from X and Y. This is because the points on the arcs are all a fixed distance away from their respective centers.

Since Victor is drawing a perpendicular segment to XY, the intersection of the arcs he drew will be the midpoint of XY. This is because the perpendicular segment will divide XY into two equal segments, and the intersection of the arcs is equidistant from X and Y.

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Get in terms of y

-7x + 3y = 24

3y = 7x + 24

y = 7x/3 + 8

Notice this is in form y = mx + b

m is slope

7/3 is being multiplied by x, therefore that is the slope because this is in that form.

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Answer:

D. 29

Step-by-step explanation:

just did the test and got it correct. Edmentum, Plato.

Answer:

3.50

Step-by-step explanation:

1.25 x 2 = 2.50

2.50 + 4.50 = 7

7 / 2 = 3.50

Hope this helps!

The number of trees saved by this process is 68trees

A rate is a ratio in which the two terms being compared have different units.For example, *

3 guest to a table. Rates often use the word per. Therefore we can say 3guest per table.

Similarly I tonne of recycled office paper save 17trees.

If 1 tonne = 2000pounds

then 2000pounds save 17trees

therefore 1 pound will save 17/2000 trees

8000 pounds will therefore save 17/2000× 8000

= 17×4= 68 trees

Therefore 8000pounds of recycled office paper will save 68 trees.

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If the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

As we know that,

Statustical significance refers to claim that a result from data generated by testing or experimentation is likely to be attributable to specific cause.

Sample size is the total number of individuals or items that comprise a sample.

And, the variance is a descriptive statistic, which falls under the category of a measure of spread.

The circumstance in which a very small treatment effect can be found to be significant is best described by option A: If the sample size big and the sample variance is small.

A large sample size will increase the probability that the results of a statistical test will yield significant results. This is why most statistical tests are accompanied by a measure of effect size. A statistically significant result associated with a very large sample size, will likely have a small effect size, an undesirable result for a researcher, as it implies one of the only reasons significant results were obtained was due to the large sample, not necessary the magnitude of the experimental effect.

Likewise, if variance is small, this will also increase the probability that the results of a statistical test will yield significant results. Variance is simply another word in statistics for the error. A decrease in error will lead to an increased probability of obtaining significant results, hence the idea that a small amount of variance will lead to an increased probability of significant results.

Hence, if the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

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Answer:

104 swimmers

Step-by-step explanation:

ratio is 8:1

8 : 1

x : 13

x = 8 multiplied by 13

swimmers = 104

Answer:

the GCF is 3x^3

Step-by-step explanation:

Identifying the greatest common factor of an expression like this one involves finding the GCF of each term  when the terms are placed side by side:  the GCF of -15x^3 and 6x^4 is 3x^3, because 3 and x^3 are the largest factors of their type (constant, power of x) that will divide evenly into -15x^3 and 6x^4.

The end result is 3x^3(-5, 2x).  Once again, the GCF is 3x^3.

Step-by-step explanation:

25 miles / 40 minutes is the reference speed.

speed is always expressed in distance/time.

for different distances the ratio of rate between distance and time must be the same, if the speed is truly the same.

so,

25 miles / 40 minutes = 40 miles / x minutes

x minutes × 25 miles = 40 minutes × 40 miles

x minutes = 40 minutes × 40 miles / 25 miles =

= 40 minutes × 8/5 = 8×8 = 64 minutes

the ostrich will need 64 minutes for 40 miles.

It will take the Ostrich 64 minutes to run 40 miles, at the same speed

The distance-time ratio is given as:

Distance : Time = 25 miles : 40 minutes

When the distance is 40 miles, the ratio equation becomes

40 miles : Time = 25 miles : 40 minutes

Express as fraction

\(\frac{Time}{40} = \frac{40}{25}\)

Multiply both sides by 40

\(Times = \frac{40}{25} * 40\)

Solve for times

\(Time =64\)

Hence, it will take 64 minutes to run 40 miles

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The equation of the parabola using vertex form in the graph is given as; y = (-19/9)(x + 3)².

For the given question;

The curve on the graph in the vertex form is defined by the the equation;

y = a( x – h) 2 + k

Where, (h,k) are the vertex of the curve.

From the graph.

Vertex (h,k) = (-3, 0)

Point = (x, y) = (0, -19)

Put the values in the curve.

y = a( x – h)² + k

-19 = a( 0 – (-3))² + 0

Solving.

a = -19/9

Now, the put the value of a in the equation of parabola.

y = (-19/9)(x + 3)² + 0

y = (-19/9)(x + 3)²

Thus, the equation of the parabola in the graph is given as; y = (-19/9)(x + 3)².

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Answer:

y = -2x + 9

Step-by-step explanation:

The slope of the line can be found from 2 points.

(y2-y1)/(x2-x1)

7-3/1-3

4/-2

= -2

-2 is the slope.

The y-intercept is 9.

The equation of a line is y=mx+b.

m is the slope, and b is the y-intercept.

y = -2x + 9

we have

The sum of two numbers is 92. One eighth of the first number plus one third of the second number is 19. Find the numbers.​

Let

x ------> first number

y -----> second number

the algebraic expression that represent this situation is

x+y=92 ------> equation A

(1/8)x+(1/3)y=19

Multiply both sides by 24

3x+8y=456 ------> equation B

solve the system of equations

Isolate teh variable x in the equation A

x=92-y ------> equation C

substitute equation C in equation B

3(92-y)+8y=456

solve for y

276-3y+8y=456

5y=456-276

5y=180

y=36

Find the value of x

x=92-36

x=56

therefore

the numbers are 56 and 36

The variable x has a value of - 6 according to direct variation model.

There are two variables x and y, which are related to direct variation model, whose expression is defined below:

y = k · x

Where k is the constant of proportionality.

If we eliminate the constant of proportionality, then we find the following relationship:

y₁ / x₁ = y₂ / x₂

If we know that x₁ = 3, y₁ = - 9 and y₂ = 18, then the value of x₂ is:

x₂ = x₁ · (y₂ / y₁)

x₂ = 3 · [18 / (- 9)]

x₂ = 3 · (- 2)

x₂ = - 6

The missing value of variable x is - 6.

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Answer:

8

it's the prefix to the variable

Step-by-step explanation:

Answer:

Step-by-step explanation:

8

y = 29 - 0.75x (option C)

The initial amount of gallons of diesel fuel = 29 gallons

Rate of consumption of fuel = 0.75 gallons per hour

we write the above information in the form of a liear equation:

y = mx + c

m = rate of consumption of fuel = 0.75 gallons per hour

c = intial amout of diesel fuel = 29

SInce, we are using up the fuel, it means the initial amount will be reducing every hour.

Our rate of consumption will be negative.

The equation becomes:

y = - 0.75x + 29

y = 29 - 0.75x (option C)

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Answer:

−x^15+8x+7

Step-by-step explanation:

Answer:

− ( x 15 − 8 x− 7 )

From: iOE Your friend :) :D *Be awesome Be You*

"A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. " For the question "Are the conditions for inference met?" we say No, the 10% condition is not met. This is further explained below.

Generally, the confidence interval is simply defined as a predetermined interval across which some parameter has a certain chance of falling

In conclusion, with a resultant confidence interval of; confidence interval ( -8.373, -3.627) For the hypothesis test question "Are the inference requirements met?" Our company is certain that the 10% threshold has not been reached.

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On factorizing the polynomial 3m²-9 we get 3(m²-3).

The factor of polynomial is defined as the process of expressing the polynomial as a product of two or more polynomials.

For Example : the factors of x²-16 are (x+4)(x-4).

In the given question we need to factor

3m²-9

here 9 can be written as 3*3

rewriting the above equation we get

3m²-3*3

As both the terms contain 3 we can take 3 common from both the terms ;

taking 3 common from each term we get ,

=3(m²-3)

Therefore , On factorizing 3m²-9 we get 3(m²-3) .

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To begin, let's define some of the terms mentioned in the question. A random variable (RV) is a variable whose possible values are outcomes of a random phenomenon.

A non-negative RV is a random variable that can only take non-negative values (i.e. values greater than or equal to zero).

A variable is a quantity or factor that can vary in value.

Now, let's look at the problem at hand.

We are given that G is an uniform random variable on [-t,t]. This means that the probability distribution of G is uniform over the interval [-t,t].

We are also given that X is a non-negative RV that is independent of G. This means that the probability distribution of X is not affected by the values of G.

Finally, we are asked to show that for any t >= 0, it holds:

(smoothing Markov)

To prove this, we can use the definition of conditional probability.

P(X > x | G = g) = P(X > x, G = g) / P(G = g)

By independence, we know that P(X > x, G = g) = P(X > x) * P(G = g).

Since G is a uniform RV, we know that P(G = g) = 1 / (2t) for any g in [-t,t].

So, we can simplify the equation as:

P(X > x | G = g) = P(X > x) * (2t)

Now, we can use the law of total probability to find P(X > x), which is the probability that X is greater than x:

P(X > x) = ∫ P(X > x | G = g) * P(G = g) dg

where the integral is taken over the interval [-t,t].

Substituting in the equation we derived earlier, we get:

P(X > x) = ∫ P(X > x) * (2t) * 1/(2t) dg

Simplifying, we get:

P(X > x) = 2 * ∫ P(X > x) dg

Now, we can use the definition of expected value to find E(X):

E(X) = ∫ x * f(x) dx

where f(x) is the probability density function of X.

Using the same logic as before, we can find the probability that X is greater than or equal to t:

P(X >= t) = 2 * ∫ P(X >= t) dg

Substituting this into the original equation, we get:

(smoothing Markov)

Therefore, we have shown that for any non-negative RV X which is independent of G and for any t >= 0, it holds that:

(smoothing Markov)

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Answer:D(38) I think

Step-by-step explanation:

a. The ANOVA table does not provide any information about the number of age classes. Therefore, it cannot be determined from the given table how many age classes were there.

b. The ANOVA table does not provide any information about the age-sex combination or the number of observations for each combination. Therefore, it cannot be determined from the given table how many observations were made for each age-sex combination.

c. The ANOVA table provides information about the sources of variation and their respective sum of squares, degrees of freedom, and mean squares. From this table, it can be concluded that the interaction between factors and error have a significant effect on the response variable, territory size. However, the table does not provide any information about the effect size or the direction of the effect. To draw any conclusions about the relationship between the factors and the response variable, further analysis such as post-hoc tests or effect size calculations would be required.

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