Numerical Analysis and differential equation( please help with Q21 the polynomial p2(x) = 1 − 1 2 x2 is to be used to approximate f (x) = cos x in [−1 2 , 1 2 ]. find a bound for the maximum error)

To prove that Z = {[b² | c=b] | b, c ∈ ℝ} is a subspace of ℝ²x², we need to show that Z satisfies the three properties of a subspace.

To prove that Y = {A ∈ ℝ²x² | A is an upper triangular matrix} is not a subspace of ℝ²x², we only need to show that it fails to satisfy one of the three properties.

For Z to be a subspace of ℝ²x², it needs to satisfy closure under addition, closure under scalar multiplication, and contain the zero vector.

1. Closure under addition: Let A = [b₁² | c₁=b₁] and B = [b₂² | c₂=b₂] be two matrices in Z. Their sum, A + B, is [b₁² + b₂² | c₁ + c₂ = b₁ + b₂]. Since b₁ + b₂ is a real number, A + B is also in Z. Hence, Z is closed under addition.

2. Closure under scalar multiplication: Let A = [b² | c=b] be a matrix in Z, and k be a scalar. The scalar multiple kA is [k(b²) | k(c) = kb]. Since kb is a real number, kA is also in Z. Therefore, Z is closed under scalar multiplication.

3. Contains the zero vector: The zero vector in ℝ²x² is the matrix [0 0 | 0 = 0]. This matrix satisfies the condition c = b, so it is in Z.

Thus, Z satisfies all the properties and is a subspace of ℝ²x².

For Y to be a subspace of ℝ²x², it needs to satisfy the three properties mentioned earlier. However, Y fails to satisfy closure under addition since the sum of two upper triangular matrices may not always be an upper triangular matrix. Hence, Y is not a subspace of ℝ²x².

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We can see that the computed z value lies inside the non-rejection region. Hence, we cannot reject the null hypothesis based on the evidence on hand.Therefore, the correct option is B. Based on the evidence on hand that the computed z statistic - 0.91 lies outside the rejection region, we cannot reject the null hypothesis.

The given values for the problem are: n = 74, p = 5/74, Po = 10%.

The significance level is given by alpha = 0.05 (given in the problem).

The null hypothesis and alternate hypothesis are as follows:H0: p = 0.10 Ha: p < 0.10.

The formula to calculate the z-statistic is given by:z = [tex](p - Po) / √[(Po(1 - Po))/n].[/tex]

Substituting the given values,z = [tex](5/74 - 0.10) / √[(0.10(0.90))/74] = -0.9138.[/tex]

Using the standard normal distribution table, the critical value for z at alpha = 0.05 for a left-tailed test is -1.645.

The computed z value is -0.9138 and the critical value at alpha = 0.05 is -1.645.

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Answer:

G. 32

Step-by-step explanation:

32 x 335 = 10720

16,100 - 10720 = 5380/190 = 28.3157894737

275 x 32 = 8800

18,800 - 8800 = 10,000/400 = 25 (This is the closer).

30 x 335 = 10,050

16,100 - 10,050 = 6050/190  = 31.8421052632

30 x 275 = 8250

18,800 - 8250 = 10550/400 = 26.375 (Same reason why it does't work)

25 x 335 = 8375

16,100 - 8375 = 7725/190 = 40.6578947368

25 x 275 = 6875

18,800 - 6875 = 11925/400 = 29.8125

24 x 335 = 8040

16,100 - 8040 = 8060/190 = 42.4210526316

24 x 275 = 6600

18,800 - 6600 = 12200/400 = 30.5

Answer:

10 times

Step-by-step explanation:

1km=1000m

3*1000=3000m

3000/300=10

you will need to run 10 times around the field

Given a point on the terminal side of an angle, (9, 12), we can find the exact value of the cosecant (csc) of the angle. The exact value of csc(θ) is 13/9.

To find the exact value of csc(θ), we need to use the given point (9, 12) on the terminal side of angle θ.

The cosecant function (csc) is defined as the reciprocal of the sine function (sin). Since the sine of an angle is given by the ratio of the opposite side to the hypotenuse in a right triangle, we can determine the value of csc(θ) by calculating the ratio of the hypotenuse to the opposite side.

In this case, the coordinates of the point (9, 12) represent the lengths of the sides of a right triangle. The opposite side is 12 and the hypotenuse is the length of the hypotenuse is the distance from the origin (0, 0) to the point (9, 12), which can be calculated using the Pythagorean theorem.

Using the Pythagorean theorem, we find that the hypotenuse is √(9^2 + 12^2) = √(81 + 144) = √225 = 15.

Therefore, the exact value of csc(θ) is the reciprocal of the sine of the angle θ, which is 13/9.

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Answer:

g(x) = x+5

Step-by-step explanation:

Given that,

[tex]f(x)=x^4+5x^3-3x-15[/tex]

[tex]q(x) = (x^3-3)[/tex]

We need to find the polynomial. We know that, Euclid division lemma states that

[tex]f(x)=q(x)\times g(x)+r(x)[/tex]

Where

f(x) is dividend

g(x) is the poynomial

q(x) is quotient

r(x) is remainder

So,

[tex]x^4+5x^3-3x-15=(x^3-3)\times g(x) +0\\\\g(x)=\dfrac{x^4+5x^3-3x-15}{(x^3-3)}\\\\g(x)=x+5[/tex]

So, the polynomial is (x+5).

Answer: its C

Step-by-step explanation: i just took the test

Answer:

25 and 135

Step-by-step explanation:

you see that the small square equals 90

Answer:

Step-by-step explanation:

Answer:

25.3

Character minimum

Answer:

stay calm

Step-by-step explanation:

stay calm

The total cost next year will be: $10,613.10

Solving:

The total cost of this year

Simply just add up everything that has been given which wouold give you 10,405

The total cost of next year

multiply the total cost of this year by 1.02 to find what the cost would be with a 2% increase which should give you 10,613.1

Answer:9

Step-by-step explanation:

The expression COSX + Sinx - tanx can be simplified by combining trigonometric identities.

We can use the trigonometric identities to simplify each term in the expression:

COSX + Sinx:

We know that sin(x) = cos(π/2 - x). Therefore, we can rewrite Sinx as Cos(π/2 - x):

COSX + Cos(π/2 - x)

tanx:

We know that tanx = sinx / cosx. Therefore, we can rewrite tanx as sinx/cosx:

sinx / cosx

Now, let's combine the terms:

COSX + Cos(π/2 - x) - sinx / cosx

Using the sum-to-product formula for cosine (Cos(A + B) = CosA * CosB - SinA * SinB), we can rewrite the expression as:

CosX * Cos(π/2) - SinX * Sin(π/2) - sinx / cosx

Since Cos(π/2) = 0 and Sin(π/2) = 1, the expression simplifies to:

0 - 1 - sinx / cosx = -1 - sinx / cosx

Therefore, the simplified expression is -1 - sinx / cosx.

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The required annual sales for stocked items A, B, and C would be $1,300, $1,560, and $3,250, respectively.

To calculate the required annual sales for each stocked item, we need to consider the turnover ratio and the maximum stock level. The turnover ratio indicates how many times the stock is sold and replaced within a year.

Given that the turnover ratio requirement is 2.6 per year, we can calculate the required annual sales for each item by multiplying the turnover ratio with the maximum stock level.

For item A, the maximum stock level is $1,000, and the required annual sales would be 2.6 times $1,000, which equals $2,600.

Similarly, for item B, the maximum stock level is $1,200, and the required annual sales would be 2.6 times $1,200, which equals $3,120.

For item C, with a maximum stock level of $2,500, the required annual sales would be 2.6 times $2,500, which equals $6,500.

However, since the average stock is assumed to be one-half the maximum stock, we need to adjust the required annual sales accordingly. The average stock for each item would be $500 for A, $600 for B, and $1,250 for C. Therefore, the required annual sales for A would be $2,600 minus $500, which equals $1,300. For B, it would be $3,120 minus $600, which equals $1,560. And for C, it would be $6,500 minus $1,250, which equals $3,250.

In summary, the required annual sales for items A, B, and C would be $1,300, $1,560, and $3,250, respectively.

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Complete Question is:

Jamie was surveying students about their use of the new computer lab in a school. Which question in the survey is a STATISTICAL QUESTION?

A.) How qualified is the trainer at the computer lab?

B.) Where is the computer lab located in the school?

C.) What is the number of learning stations at the computer lab?

D.) How many class projects did you complete using the computer lab?

Answer:

D.) How many class projects did you complete using the computer lab?

The answer is D because the question is directly related to the use of their new computer lab and the number of projects the students have completed in the computer lab. This is directly related to the survey since it is carried out for the students using computer lab.

Scatter plot

Box plot

Dot plot

To compare bite strength to weight for different carnivores, scatter plot, box plot, and dot plot are appropriate representations.

Scatter plot: A scatter plot can show the relationship between bite strength and weight by plotting each carnivore as a data point. The x-axis can represent weight, the y-axis can represent bite strength, and each point on the plot represents a different carnivore. This allows for visualizing the overall trend or pattern between the two variables.

Box plot: A box plot can display the distribution of bite strength and weight for different carnivores. It provides information about the median, quartiles, and any outliers in the data. By comparing the box plots for different carnivores, we can assess the variations in bite strength relative to weight.

Histogram: A histogram is not appropriate in this case because it represents the distribution of a single variable, such as bite strength or weight, and does not directly compare the two variables.

Table: A table can present the bite strength and weight data for different carnivores, but it does not provide a visual comparison or representation of the relationship between the two variables.

Dot plot: A dot plot can show the individual data points of bite strength and weight for each carnivore. Each dot represents a carnivore, and by comparing the position and density of dots, we can observe the relationship between bite strength and weight.

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Answer:

32

Step-by-step explanation:

The shapes are the same except for the direction so i think it would be 32

Answer:

32°

Step-by-step explanation:

quadrilateral ABCD is similar to quadrilateral WXYZ

Corresponding angles of similar polygons are congruent. We are told the two quadrilaterals are similar, so the pairs of corresponding angles are congruent.

You know angles are corresponding according to the statement of similarity is written.

quadrilateral ABCD is similar to quadrilateral WXYZ

The vertices are listed in the same order in both polygons showing which angles are corresponding.

<A corresponds to <W

m<W = m<A = 32°

Answer: 32°

The equation y = (0.9)t - 4 can be rewritten in the form y = a(1 - r)t, where a = -4 and r = 0.1. This represents exponential decay.

In the equation y = (0.9)t - 4, the term (0.9)t represents the exponential part, where the base is 0.9. By rewriting it in the form y = a(1 - r)t, we can identify the values of "a" and "r" that correspond to the given equation.

In this case, "a" is the initial value, which is -4. The negative value indicates a downward shift or decrease from the initial value. The term (1 - r) represents the remaining portion after each time interval. By comparing the given equation to the general form, we find that r = 0.1, which signifies a decay rate of 10%.

Overall, the equation y = (0.9)t - 4 represents exponential decay because the value of "r" is less than 1 (0.1) and "a" is negative (-4). This indicates a decreasing trend as time (t) increases.

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The solutions of the equation `tan(2x)-sin(x)=0` in the interval `[0, 2)` are:`x = 2πk ± 2arctan(√[(3+√5)/2]) ± 2arcsin(√[(1-cos(x))/2])` where `k` is an integer and `cos(x) = 1-2sin²(x/2)`

Given, `tan(2x)-sin(x)=0`.We can use the half-angle formula to solve this equation in the interval `[0, 2)` and obtain the solutions. The half-angle formula for tangent is: `tan(θ/2)= sin(θ)/(1+cos(θ))`The half-angle formula for sine is: `sin(θ/2)=±√[(1-cos(θ))/2]`Using the half-angle formula for tangent:`tan(2x)-sin(x)=0`Substituting `sin(x)` in terms of `tan(θ/2)`, we get:`tan(2x)-2tan(x/2)/(1+tan²(x/2))=0`Multiplying both sides by `1+tan²(x/2)`, we get:`tan(2x)(1+tan²(x/2))-2tan(x/2)=0`Simplifying this equation further using the double-angle formula for tangent:`(2tan(x/2)/(1-tan²(x/2)))(1+(2tan²(x/2))/(1-tan²(x/2))) - 2tan(x/2) = 0`

Multiplying both sides by `(1-tan²(x/2))`, we get:`2tan(x/2)(1+tan²(x/2)) - 2tan²(x/2) - (1-tan²(x/2))(2tan²(x/2)) = 0`Simplifying this equation, we get:`tan⁴(x/2) - 3tan²(x/2) + 1 = 0`This is a quadratic equation in `tan²(x/2)`.Solving this quadratic equation, we get:`tan²(x/2) = (3±√5)/2`Taking square root of both sides, we get:`tan(x/2) = ±√[(3±√5)/2]`We know that, `tan(x/2) > 0` in the interval `[0, 2)` since `x` lies in this interval. Therefore, we take the positive square root. We get:`tan(x/2) = √[(3+√5)/2]`Using the formula for sine, we get:`sin(x/2) = ±√[(1-cos(x))/2]`We know that, `sin(x/2) > 0` in the interval `[0, 2)` since `x` lies in this interval.

Therefore, we take the positive square root. We get:`sin(x/2) = √[(1-cos(x))/2]`Therefore, the solutions of the equation `tan(2x)-sin(x)=0` in the interval `[0, 2)` are:`x = 2πk ± 2arctan(√[(3+√5)/2]) ± 2arcsin(√[(1-cos(x))/2])`where `k` is an integer and `cos(x) = 1-2sin²(x/2)`

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In a right triangle ABC that is inscribed in a circle, the shortest height of the triangle is the altitude drawn from the right angle to the hypotenuse. This height, denoted as 'h', is perpendicular to the hypotenuse and divides it into two segments.

The altitude is also the shortest distance between the hypotenuse and the opposite vertex (the vertex not on the hypotenuse). The property of a right triangle inscribed in a circle is that the hypotenuse is the diameter of the circle, and the other two sides are radii of the circle.

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The key difference is that the Bernoulli distribution models a single trial, while the binomial distribution models multiple trials and focuses on the number of successes in those trials. The binomial distribution is an extension of the Bernoulli distribution to multiple trials.

The main difference between the binomial distribution and the Bernoulli distribution lies in the number of trials involved.

Bernoulli Distribution:

The Bernoulli distribution is a discrete probability distribution that models a single trial or experiment with two possible outcomes: success or failure. It is characterised by a single parameter, often denoted as p, which represents the probability of success. The outcome of each trial is independent of other trials, and it is represented by a random variable that takes the value 1 for success and 0 for failure.

Binomial Distribution:

The binomial distribution is also a discrete probability distribution that models multiple independent Bernoulli trials or experiments. Each trial is identical, and it has two possible outcomes: success or failure, just like the Bernoulli distribution. However, the binomial distribution considers the number of successes (k) in a fixed number of trials (n). It is characterised by two parameters: the probability of success (p) and the number of trials (n).

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Answer:

f(x) is flipped, and each point is moved 3 units to the left and 2 units up

Step-by-step explanation:

Answer:

1620 degrees.

Step-by-step explanation:

In a polygon the number of sides = the number of angles.

Each external angle = 360 / 11 = 32 8/11 degrees.

Each internal angle = 180 - 32 8/11 = 147 3/11 degrees

So sum = 147 3/11 * 11

= 1617 + 3

= 1620 degrees.

Answer:

It's 1620°

Hope it helps

Step-by-step explanation:

Hint:>

( The sum of the interior angle (S),

The the sides of the polygon (n).)

Then use this formula :

S=180°(n-2)

= 180°(11-2)

= 180°(9)

= 1620°

The product of 8(cos 17° + i sin 170°) and 7(cos 42° + i sin 439°) can be expressed as -336 + 94i.

To find the product of two complex numbers, we multiply their magnitudes and add their angles. Let's break down the given complex numbers. The first complex number, 8(cos 17° + i sin 170°), has a magnitude of 8 and an angle of 17°. The second complex number, 7(cos 42° + i sin 439°), has a magnitude of 7 and an angle of 42°.

To find the product, we multiply the magnitudes: 8 * 7 = 56. To determine the angle, we add the angles: 17° + 42° = 59°. Now we have the complex number 56(cos 59° + i sin θ). However, we need to convert the angle to the standard range of 0° to 360°. In this case, 59° is already within that range.

Therefore, the product of the given complex numbers is 56(cos 59° + i sin θ), where θ is the angle in the standard range. To evaluate this expression, we can use trigonometric identities to find the cosine and sine of 59°, or use a calculator. The result is approximately -336 + 94i, which represents the product in rectangular form.

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The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.

To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.

Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.

Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:

y - 2 = (1/2)(x - 4).

Simplifying this equation, we find:

y - 2 = (1/2)x - 2.

Rearranging the terms, we obtain:

y = (1/2)x.

Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).

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Answer is C. {(6,-2), (6.0), (6,2), (6,4)}

Step-by-step explanation:

Your welcome

The equilibrium vector for the transition matrix is [0.4, 0.2667, 0.3333].

The transition matrix given is:

0.70 0.10 0.20 0.10 0.75 0.15 0.10 0.35 0.55

'To find the equilibrium vector, we need to multiply the transition matrix by a vector of constants that would make the equation valid. The value of this vector of constants is given by:

(P-I)x = 0

Where P is the transition matrix and I is the identity matrix. The value of x is the equilibrium vector.

Let's write the augmented matrix:

(P-I|0) = 0.70-1 0.10 0.20 0.10 0.75-1 0.15 0.10 0.35 0.55-1

After subtracting the identity matrix from the transition matrix, we get the augmented matrix.

Using the Gauss-Jordan elimination method, we get 1 -0.08 -0.4-0.12 1 -0.28-0.18 -0.12 1

After row reducing the augmented matrix, we get the following equations:

x1 - 0.08x2 - 0.4x3 = 0-0.12

x1 + x2 - 0.28x3 = 0-0.18x1 - 0.12

x2 + x3 = 0

Solving these equations, we get

x1 = 1.2

x2 = 0.8

x3 = 2.

Using x1, x2, and x3 values, we can determine the equilibrium vector:

x = [1.2/3, 0.8/3, 2/3]

Simplifying the vector, we get the equilibrium vector as:

x = [0.4, 0.2667, 0.3333]

Thus, the equilibrium vector is [0.4, 0.2667, 0.3333].

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Answer

4z+5=

4*7+5=33

33

Step-by-step explanation: