help im clueless i wasn't at school the day we learned this ​

Given that, r(t) = <2t + 2, 4t - 4, 5t + 14> .Here, we need to find the unit tangent vector T and the curvature k for the following parameterized curve.To find unit tangent vector T, we first find the magnitude of r'(t) by the following formulae;

\(|r'(t)| = \sqrt{(2)^2 + (4)^2 + (5)^2} = \sqrt{45}\)r'(t) = <2, 4, 5>Now, we find the unit tangent vector T at point t by the following formulae;T(t) = r'(t) / |r'(t)|\(T(t) = \frac{<2, 4, 5>}{\sqrt{45}} = \left\langle \frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}, \frac{5}{\sqrt{45}} \right\rangle\)Hence, the unit tangent vector T is \(T(t) = \left\langle \frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}, \frac{5}{\sqrt{45}} \right\rangle\)To find the curvature k of the parameterized curve,

we first find the magnitude of the acceleration vector r''(t) by the following formulae;\(|r''(t)| = \sqrt{(0)^2 + (0)^2 + (0)^2} = 0\)Now, we find the curvature k of the parameterized curve at point t by the following formulae;k(t) = |r''(t)| / |r'(t)|^3k(t) = 0 / (45)^(3/2)Hence, the curvature k of the parameterized curve is 0. Answer: The unit tangent vector T is \(T(t) = \left\langle \frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}, \frac{5}{\sqrt{45}} \right\rangle\) and the curvature k of the parameterized curve is 0.

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The correct statements are:

1. If the product AB = 0 (zero matrix), then either A = 0 or B = 0.

4. BC = CB.

Explanation:

1. If the product of two matrices AB equals the zero matrix, it implies that at least one of the matrices A or B (or both) must be the zero matrix for the product to result in zero.

4. The statement BC = CB states that the order of multiplication of matrices B and C does not affect the resulting matrix. This property holds true for matrices of any size as long as the dimensions are compatible for matrix multiplication.

The other statements are not necessarily true in general:

2. Both BC and CB being square matrices is not guaranteed. The product of two matrices can result in a square matrix only if the number of columns of the first matrix is equal to the number of rows of the second matrix. In this case, B has 3 columns and C has 2 rows, so BC and CB are not square matrices.

3. The matrix A + BC is not defined since the addition of matrices requires them to have the same dimensions. In this case, A is a 2×2 matrix, while BC is a 2×3 matrix, so they cannot be added together.

5. The statement A = A12​ = I2​ implies that matrix A is equal to the 2×2 identity matrix I2​. However, this is not necessarily true as the given information does not provide any details about the values or properties of matrix A.

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False.Compared to sampling, conducting a census is typically more time-consuming and more expensive. A census involves gathering data from an entire population, which can be a time-intensive and costly process.

It requires reaching out to and collecting information from every individual or unit in the population, which can be logistically challenging and resource-intensive.

In contrast, sampling involves selecting a subset, or a sample, from the population and collecting data from that sample. Sampling allows for estimating characteristics of the population with a smaller time and cost investment compared to a census.

By selecting a representative sample, one can make inferences about the population as a whole without the need to survey or collect data from every individual or unit.

Therefore, sampling is generally considered to be a more efficient and cost-effective method compared to conducting a census.

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Step-by-step explanation:

Take a picture and repost

Answer:

(5,2)

Step-by-step explanation:

(5,2) is the same distance from the lone as point N

Answer:

N(2,5)

Step-by-step explanation:

Researchers must use experiments to determine whether causal relationships exist between variables.

Researchers use experiments to determine causative relationships between variables. A causative relationship exists when a change in one variable (the cause) leads to a change in another variable (the effect).

Experiments allow researchers to manipulate the cause and observe the effect while controlling for other factors that could influence the relationship.

For example, if a researcher is interested in examining the relationship between smoking and lung cancer, they would conduct an experiment where they randomly assign participants to either a smoking or a non-smoking group.

The researcher would then collect data on the incidence of lung cancer in each group while controlling for other factors that might influence the relationship, such as age, gender, and socioeconomic status.

By randomly assigning participants to the smoking and non-smoking groups, the researcher can be confident that any differences in lung cancer incidence are due to the effect of smoking and not due to differences in the participants.

This type of experiment is called a randomized controlled trial and is considered the gold standard for determining causative relationships.

Experiments are essential in determining causative relationships between variables because they help to establish a cause-and-effect relationship and avoid confounding (when the relationship between two variables is observed because of a third variable that affects both).

In addition, experiments can also provide information about the direction and strength of the relationship between variables.

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--The given question is incorrect; the correct question is

"Researchers must use experiments to determine whether ______ relationships exist between variables."--

The exclamation point in the middle of a yellow triangle is a warning icon that may be seen on a variety of gadgets and software, including Windows PCs and Android smartphones.

It often serves as a signal for a problem or issue that needs addressing. Depending on the context in which it occurs, a symbol's precise meaning may change.

On a Windows computer, for instance, it can mean that a device driver needs to be updated, but on an Android phone, it might mean that a system update or an app has a bug that needs to be fixed.

Investigate the origin of the alert and take the necessary steps to resolve any problems that could be impacting your system or device.

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The coordinate for the R' is (3, -4) if the R(-4, 3) is reflected in the line y = x option (D) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have:

Image of R(-4, 3) after a reflection in the line y = x

The rule for the reflection over y = x is:

(x, y) = (y, x)

(-4, 3) = (3, -4)

Thus, the coordinate for the R' is (3, -4) if the R(-4, 3) is reflected in the line y = x option (D) is correct.

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The ratio for the length of grey to red to bule is 4:9:3.

Ratio is the relation between two numbers which shows how much bigger one quantity than another. Ratio show how many times one contain show the other one.

According to the question

The given data are -

Grey = 0.8m

Red = 1.8 m

Bule = 0.6 m

By solving these we can get -

=0.8:1.8:0.6

=0.8×10:1.8×10: 0.6×10

=8:18:6

By simplifying it we can get

4:9:3.

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The 'x' coordinate is negative and 'y' coordinate is positive.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

We know that :

π = 180

Therefore,

3π/4 = (3×180)/4 = 3 × 45

3π/4 = 135

In second quadrant, we have negative value if x coordinate and positive value of y coordinate.

Hence, the angle lies in the second quadrant. Second quadrant is enclosed by the negative x axis and positive y axis.

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Answer:

x is negative, and y is positive.

Step-by-step explanation:

The answer above is correct.

Answer:

1,359

Step-by-step explanation:

3% of 45,300 is 1,359

Answer:

85

Step-by-step explanation:

Consecutive numbers are numbers that follow each other in order. The two consecutive numbers are 42 and 43.

42+43=85

Answer:

42 & 43

Step-by-step explanation:

Let the two consecutive numbers be x and x+1 .

Here it is given that the sum of two consecutive numbers is 85.

So we get the equation,

x + (x+1) = 85

We get,

x + x + 1 = 85

2x + 1 = 85

Transposing +1 to RHS,

2x = 85 - 1

2x = 84

Transposing 2 to RHS,

x = 84 ÷ 2

Therefore, we get x = 42

Therefore, the two numbers are x and x+1, so they are: 42 and 43.

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Answer:

1.) The 1ˢᵗ three term is (-32), (-7) and 18

2.) The 1ˢᵗ three term is 127, 106 and 85

Step-by-step explanation:

Here,

First Term = a₁ = - 32

Common Difference = (d) = 25

Now, For 1ˢᵗ three term,

n = 1

a₁ = - 32

n = 2

aₙ = a + (n - 1)d

a₂ = (-32) + (2 - 1) × 25

a₂ = (-32) + 1 × 25

a₂ = (-32) + 25

a₂ = -7

n = 3

aₙ = a + (n - 1)d

a₃ = (-32) + (3 - 1) × 25

a₃ = (-32) + 2 × 25

a₃ = (-32) + 50

a₃ = 18

Thus, The 1ˢᵗ three term is (-32), (-7) and 18

Here,

First Term = a₁ = 127

Common Difference = (d) = -21

Now, For 1ˢᵗ three term,

n = 1

a₁ = 127

n = 2

aₙ = a + (n - 1)d

a₂ = 127 + (2 - 1) × (-21)

a₂ = 127 + 1 × (-21)

a₂ = 127 - 21

a₂ = 106

n = 3

aₙ = a + (n - 1)d

a₃ = 127 + (3 - 1) × (-21)

a₃ = 127 + 2 × (-21)

a₃ = 127 - 42

a₃ = 85

Thus, The 1ˢᵗ three term is 127, 106 and 85

-TheUnknownScientist

As per the information provided, a = 4√3/3 + 4, b = 4 - 4√3/3 the answer can be calculated with optimization method. it will be as follows:

Sum of a and b is 8, we get

a+b=8

b=8−a

Now, let x=a−b

Then we get,

\(x=a−(8−a) \\ x=2a−8 \\ x+8=2 \\ 1 \div 2x+4=a

\)

we use this to answer to solve for b

\(b=8−a \\ =8−(1 \div 2x+4) \\ =4−1 \div 2x

\)

Now we use the product of two numbers and its difference. This can be expressed as:

\(a⋅b⋅x=(1 \div 2x+4)(4−1 \div 2x) \\ x=2 {x}^{2} − \frac{1}{4} {x}^{3} +16x−2x^{2} \\ =−14x^{3} +16x

\)

Thus, this expression that we need to maximize. Take the derivative, set it equal to zero, and solve for x

\(−3 \div 4x ^{2} +16=0 \\ 16 =3 \div 4 x ^{2} \\ 643=x \\ 28√3 \div 3=x\)

Now for us to check that this is a maximum, we have to note that the second derivative is

\(−3 \div 2x

\\ At \\

x=8√3 \div 3

\)

the second derivative is −4√3. Since this number is negative, the point is a maximum.

Now we must find the values of a and b for this x. We have to use the relationship

\(a=1 \div 2x+4\)

\(a=1 \div 2 \times 8√3 \div 3+4 \\ =4√3 \div 3+4\)

now we use the relationship b=8−a

\(b=8−(4√3 \div 3+4) \\ =4−4√3 \div 3\)

The first step in determining a function's maximum or minimum value is differentiating it. Then, set this derivative to zero and conduct the computation.

x. This will reveal the location of a function's maximum or minimum, but it won't reveal which.

Take the second derivative to get more details. A local maximum occurs when both the first and second derivatives are negative. You have a local minimum when both the first derivative and the second derivative are zero.

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The number of hours (x*) so that 83.40% of the packages are delivered in less than x* hours is 101.58.

This can be done by using the standard normal distribution table or calculator as follows:

z-score = inverse Norm(0.8340)

            = 0.95

Using the formula for z-score,

z = (x - μ) / σ

where μ = 83.18 hours and σ = 19.26 hours.

Substituting the values in the above formula, 0.95 = (x - 83.18) / 19.26

Multiplying both sides by 19.26,0.95 × 19.26

                                         = x - 83.1818.40

                                         = x - 83.18

Adding 83.18 to both sides, x = 101.58

Therefore, the number of hours (x*) so that 83.40% of the packages are delivered in less than x* hours is approximately 101.58 hours.

Rounding this off to 2 decimal places then 101.58 hours, which is reported as 101.58.

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Answer:

Step-by-step explanation:

The standard equation for a parabola is \(y=x^2\)

The given equation is: y = 2(x+2)(x-2)

The given equation is factored out. Since it is factored, we can set each x expression to zero, to solve for the x intercepts.

x+2 = 0

-2      -2

x = -2

x-2 = 0

+2     +2

x = 2

We can therefore graph, (-2, 0) and (2, 0), because we know that it is the x intercepts of the given quadratic function.

to find the vertex, you will take both x intercepts, divide them by two, and that will get you the x cooridnate. Following that you can plug in that value as x into the equation solve for the y coordinate.

\(\frac{(-2 + 2)}{2} = 0\\\\x=0\\y = 2(x+2)(x-2)\\\\y = 2(0+2)(0-2)\\y=-8\\\\vertex = (0, -8)\)

finally graph that point and create the parabola shape. If you'd like to make your parabola more accurate, you can always make a t chart of x and y values. and plug in x values into the equation to find the other y values.

I've attached a graph of the given parabola.

(a) The probability of observing a sample proportion of defective chips of 0.127 or less is approximately 0.063.

(b)The probability of observing a sample proportion within this range is approximately 0.982.  

What is the probability of collecting a sample of 212 computer chips and observing a sample proportion of defective chips of 0.127 or less, assuming a true proportion of defective chips of p = 0.1?

The probability of observing a sample proportion of defective chips of 0.127 or less, given a true proportion of p = 0.1 and a sample size of 212, is approximately 0.063. This probability can be calculated using the binomial distribution formula, taking into account the sample size, the observed proportion, and the true proportion of defective chips.

(a) To calculate the probability of observing a sample proportion of defective chips of 0.127 or less, given a true proportion of p = 0.1 and a sample size of n = 212, you can use the binomial distribution. The formula for calculating this probability is:

\(P(X\leq x)=\sum^x_{i=0}[(^nC_i) * p^i * (1-p)^{n-i}]\)

In this case, x = 0.127 * 212 = 26.924 (rounded to the nearest integer). Using R or Desmos, you can calculate the probability as follows:

\(P(X\leq 26)=\sum^x_{i=0} [(^{212}C_i) * (0.1)^i * (0.9)^{212-i}]\)

The result is approximately 0.063.

(b) To calculate the probability of observing a sample proportion of defective chips that is within two standard errors of the true population proportion, you need to calculate the standard error first. The standard error (SE) for a sample proportion is given by:

\(SE = \sqrt{\frac{(p * (1-p)}{ n}\)

In this case, p = 0.1 and n = 212. Calculate the standard error using this formula:

\(SE = \sqrt{\frac{(0.1 * (1-0.1)}{212}\)

The result is approximately 0.0169.

Next, you need to find the range within two standard errors of the true population proportion, which is (p - 2SE, p + 2SE).

Calculate this range:

Lower bound = 0.1 - 2 * 0.0169

Upper bound = 0.1 + 2 * 0.0169

The lower bound is approximately 0.0662, and the upper bound is approximately 0.1338.

To calculate the probability of observing a sample proportion within this range, you can use the cumulative distribution function (CDF) of the normal distribution. Using R or Desmos, you can calculate this probability as follows:

P(Lower bound ≤ X ≤ Upper bound) = P(X ≤ Upper bound) - P(X ≤ Lower bound)

The result is approximately 0.982.

Therefore,

(a) The probability of observing a sample proportion of defective chips of 0.127 or less is approximately 0.063.

(b)The probability of observing a sample proportion within this range is approximately 0.982.  

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=6000\left(1+\frac{0.035}{1}\right)^{1\cdot 4}\implies A=6000(1.035)^4\implies A\approx 6885\)

The cubic feet of space in the given tent is 150 cubic feet. The formula to calculate the volume of a triangular prism is: V = 1/2 * b * h * l Where V is the volume of the triangular prism b is the base of the triangle h is the height of the triangle l is the height of the triangular prism.  

Now we have to calculate the volume of a tent shaped like a triangular prism using the given measurements. According to the given data, The height of the triangular prism is 6 feet. The height of the entrance triangle is 3.5 feet. The base of the entrance triangle is 4.5 feet. So, the area of the entrance triangle = 1/2 * base * height = 1/2 * 4.5 * 3.5 = 7.875 square feet. The area of the base triangle = 1/2 * base * height = 1/2 * 4.5 * 6 = 13.5 square feet. Now, the volume of the triangular prism can be found by multiplying the area of the base triangle by the height of the triangular prism: V = 13.5 * 6 = 81 cubic feet. Now, the total volume of the tent will be the sum of the volume of the triangular prism and the entrance triangle: V(total) = V(prism) + V(triangle) = 81 + 7.875 = 88.875 cubic feet (rounded to three decimal places)Thus, the cubic feet of space in the given tent is 150 cubic feet (approx).  

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Answer: it might be the answer in the picture sorry if im wrong

Step-by-step explanation:

Answer:

area = 11 17/21 cm²

Step-by-step explanation:

area = length x width

area = 2 2/7 x 5 1/6 = 16/7 x 31/6 = 496/42 = 11 34/42 = 11 17/21 cm²

Answer:

V=100.53 inch³

Step-by-step explanation:

V=πr²h

V=22/7 x 2 x 2 x 8

V=100.53 inch³

A system of two linear equations in two variables that has infinite solutions will produce one line superimposed on the other line. This implies that both lines coincide. The correct option is d.

Linear equations are algebraic equations that can be used to represent straight lines on a graph. Linear equations are equations with two variables that can be represented on a graph as a straight line.

The general form of the linear equation is y = mx + b.

This form of the equation is used to represent the line on the graph.

A system of two linear equations in two variables represents two lines on the same graph. These lines are created by using two linear equations that are plotted on the same graph. Each line on the graph represents an equation in the system. The point where the two lines intersect represents the solution to the system of linear equations.

If the two equations in a system of linear equations in two variables represent the same line, then the system of equations will have infinite solutions. This is because both equations represent the same line, and there are an infinite number of points on that line that can be considered as solutions. This is the only case where a system of linear equations in two variables will have infinite solutions.

If we have a system of two linear equations in two variables that has infinite solutions, we would see one line superimposed on the other line. This implies that both lines coincide.  The correct option is d.

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To find the sum of a finite sequence using the integrator/accumulator function in the z-domain, we can follow these steps:

1. Given the finite sequence x[n] = {1, 3, 6}, where n starts at 0.

2. We need to convert the sequence from the time domain to the z-domain. In the z-domain, the sequence will be represented by a z-transform.

3. The z-transform of a sequence x[n] is defined as X(z) = Σ(x[n] * z^(-n)), where Σ represents the summation from n = -∞ to n = ∞.

4. In our case, the sequence x[n] starts at n = 0. Therefore, we need to rewrite the z-transform formula by shifting the index appropriately.

5. Shifting the index by k = 0, we have X(z) = Σ(x[n] * z^(-n)) = Σ(x[k] * z^(-k)), where Σ represents the summation from k = 0 to k = ∞.

6. Plugging in the values of the sequence x[k] = {1, 3, 6}, we have X(z) = 1 * z^0 + 3 * z^(-1) + 6 * z^(-2).

7. To find the sum of the sequence, we need to evaluate the z-transform at z = 1. In other words, we substitute z = 1 in X(z).

8. Evaluating X(z) at z = 1, we have X(1) = 1 * 1^0 + 3 * 1^(-1) + 6 * 1^(-2).

9. Simplifying the expression, we get X(1) = 1 + 3 + 6 = 10.

10. Therefore, the sum of the given finite sequence x[n] = {1, 3, 6} is 10 when evaluated using the integrator/accumulator function in the z-domain.

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Answer: 4,000,000, it’s like 2000, but 2000 times

Answer: 4000000

Step-by-step explanation:

Answer:

B. supplementary angles

Step-by-step explanation:

The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer: A.

Step-by-step explanation:

Two