Find the length of the curve described by r(t) = − sin 3ti + cos
3tj + 5tk for 0 ≤ t ≤ π/3

It is possible to use a relational operator and math operators in the same expression.

In programming, you can use relational operators (e.g., <, >, ==, !=) and math operators (e.g., +, -, *, /) together in the same expression. This is often used in conditional statements or loops to compare calculated values.

For example, consider the following expression:

`if (2 * 3) > (4 + 1)`

In this expression, we have math operators (*) and (+) and a relational operator (>). The math operations are evaluated first, resulting in:

`if (6) > (5)`

Then, the relational operator (>) is evaluated, and the expression becomes:

`if True`

The expression is true because 6 is greater than 5.

It is possible to use both relational operators and math operators in the same expression, which can be useful in various programming situations such as conditional statements or loops.

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Answer: 39 degrees Fahrenheit

-extend line out to where y-value is 57.
-based on the line of best fit, we can predict that if Malika sold 57 hot cocoas, the day’s high temperature would be 36 degrees F.

According to the given statement;

Amount is deducted from his pay per week for Medicare, which is taxed at 1.45 percent is $8.35

Gross pay is the sum of a person's earnings during a specific time period before any deductions are made. The calculation of gross pay does not take into account deductions for employer-provided health insurance, retirement plans, or compulsory taxes and Medicare contributions. Since it does not reflect a person's take-home pay, the gross pay definition is different from the one for net pay.

According to the given value;

Dalton's gross pay = 576

his medicare tax rate = 1.45% = 0.0145

the tax on his medicare = 0.0145 x 576 = $8.35

Hence,Amount is deducted from his pay per week for Medicare, which is taxed at 1.45 percent is $8.35

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Answer: $122.19

Step-by-step explanation:

Hi, to answer this, first we have to calculate the additional KB that Astrid used:

KB used- KB limit=

6,978-5,000 = 1,978

Then, the cost of the plan is equal to a fixed fee (49) plus the product of the number of additional KB over 5,000(x) and the cost per KB (0.037).

Cost = 49+ 0.037 x

Substituting x =1,978

C = 49+ 0.037 (1,978)

C =49+73.186

C=$122.19

Feel free to ask for more if needed or if you did not understand something.  

Answer: It will be (B)

Step-by-step explanation:

Answer:

\(f(x) = 5x - 2 \\ \\ \)

B ) Replace f ( x ) with f' ( x )

Answer:

buy =13

rent = 17

40=1.50 every hour is

41.5

43

44.5

46

47.5

49

50.5

52

....

2.00+ 1.50 an hour

3.5

7

10.5

14

17.5

21

...

Step-by-step explanation:

Answer:

Distributive property is when you multiply or add the numbers in the parentheses equally to the number outside the parentheses.

That probably isn't a good answer, here's what I found on google:

To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Step-by-step explanation:

I'll do #10 as an example:

(x-5)y

distribute the numbers-  y(x)-y(5)

without the parentheses-  yx-y5

you can't really get an answer by multiplying a number and a variable, or a variable and a variable, so you just leave them and take the parentheses.

Here's #11:

-4(2a-3b+c)

distribute the numbers-  (-4*2a)-(-4*3b)+(-4c)

solve-  -4*2= -8

-4*3= -12

-8a-(-12)b+4c

*I dunno how to use parentheses for negative numbers but what I did for distributing is pretty much the same thing

Hope this helps you.

Answer:

19/3 (6 1/3)

Step-by-step explanation:

Answer:

-30

Step-by-step explanation:

400-[200-{35+15-70(100/25)}]

400-[200-{35+15-70(4)}]

400-[200-{35+15-280}]

400-[200-{50-280}]

400-[200-{-230}]

400-[430]

-30

The Olap operations for a data warehouse of a train company contains information about train segments is performed in order to answer the queries with dimension hierarchies when needed.

OLAP operation for first case is Filter on the train dimension to select only Alstom trains. Filter on the departure station dimension to select only French or Belgian stations. Filter on the year dimension to select only 2012. Aggregate the number of kilometers measure across the selected dimensions

Dimension hierarchies for this case is Station dimension: Country > City > Station,  Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for the second case is Filter on the departure station and arrival station dimensions to select only trips that cross country borders. Filter on the year dimension to select only 2012. Aggregate the duration measure across the selected dimensions

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for third case is Filter on the departure station and arrival station dimensions to select only trips that involve Paris. Filter on the month dimension to select only July 2012. Aggregate the number of trips measure across the selected dimensions.

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for fouth case is Filter on the departure station and arrival station dimensions to select only trips that involve Belgian stations. Filter on the year dimension to select only 2012.Aggregate the duration measure across the selected dimensions. Calculate the average duration of the segments

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

OLAP operation for fifth case is Aggregate the number of passengers measure across all segments of each trip. Divide by the number of segments per trip to get the average number of passengers per segment

Dimension hierarchies for this case is Station dimension: Country > City > Station, Trip dimension: Year > Month > Day > Trip ID.

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Answer:

A is the answer

Step-by-step explanation:

Let's start solving this problem by getting first the price of getting 5 items. We have

We then get the amount to be discounted by multiplying the total cost of 5 items with the discount percentage. We have

We then subtract this amount to the total cost of buying the 5 items to get the final answer. We have

Answer: $46.76

W is a subset of span(w), and span(w) is closed under vector addition, scalar multiplication, and contains the zero vector, we know that w must also have these properties. Therefore, w is a subspace of v.

To show that a subset w of a vector space v is a subspace of v if and only if span(w) = w, we need to prove both directions of the equivalence:

First, we'll assume that w is a subspace of v. In this case, we know that w is closed under vector addition and scalar multiplication, and that it contains the zero vector.

To show that span(w) = w, we need to prove two things:

span(w) is a subset of w: This is true by definition of span(w) - every vector in span(w) can be written as a linear combination of vectors in w, so it must be in w as well.

w is a subset of span(w): This is also true, because every vector in w is itself a linear combination of vectors in w (namely, itself with a coefficient of 1), so it is also in span(w).

Therefore, we have shown that span(w) = w.

Next, we'll assume that span(w) = w. In this case, we know that every vector in w can be written as a linear combination of vectors in w. We need to show that w is closed under vector addition and scalar multiplication, and that it contains the zero vector.

Let u, v be two vectors in w, and let c be a scalar. Then we can write:

\(u = a1w1 + a2w2 + ... + anwn\)

\(v = b1w1 + b2w2 + ... + bnwn\)

where w1, w2, ...,\(wn\) are vectors in w, and a1, a2, ..., an, b1, b2, ...,\(bn\)are scalars.

Then, we have:

\(u + v = (a1+b1)*w1 + (a2+b2)*w2 + ... + (an+bn)*wn\)

which is a linear combination of vectors in w, so u + v is in w.

Also, we have:

\(cu = c(a1w1 + a2w2 + ... + anwn) = (ca1)w1 + (ca2)w2 + ... + (can)*wn\)

which is also a linear combination of vectors in w, so c*u is in w.

Finally, since w is a subset of span(w), and span(w) is closed under vector addition, scalar multiplication, and contains the zero vector, we know that w must also have these properties. Therefore, w is a subspace of v.

Therefore, we have shown both directions of the equivalence, and proved that a subset w of a vector space v is a subspace of v if and only if span(w) = w.

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The variable of interest in observational studies is not controlled. Option D is correct.

Observational studies are a type of study in which the researcher observes and records data without interfering with or manipulating the variables of interest. In observational studies, the researcher does not intervene or control the variables being studied, but instead, collects data by observing the natural behavior or characteristics of the study subjects.

Observational studies are useful in many fields, including medicine, psychology, sociology, and economics. They are often used to explore potential relationships between variables, to identify risk factors for diseases, to investigate the effectiveness of interventions, and to study social phenomena.

Observational studies have advantages and disadvantages. One advantage is that they can provide valuable information about real-world behavior and characteristics of individuals or groups. Therefore, it is important to carefully design and analyze observational studies to ensure that the results are accurate and reliable.

Hence, D.is not controlled is the correct option.

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Answer:

22.5 feet

Step-by-step explanation:

volume of a retangular shape: l*w*h

4.5*2.5*2=22.5

Answer:No

It won't fit

Step-by-step explanation:

This is due to the fact that 7.54545454545454... is larger than 7.5

No. The picture frame will not fit into a box that measures 7.5 inches on each side.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Length of picture frame = 7 6/11 = 7.54 inches

Length of Box = 7.5 inches

So, From the above as we can see length of the box is smaller than the length of the picture frame.

Hence, it would not fit.

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Answer:

Since the pole is in the shape of a cylinder, its volume can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length in this case). We are not given the radius, so we cannot calculate the exact volume. However, we can use an approximation assuming a reasonable radius.

Let's assume a radius of 1 foot. Then, the volume would be V ≈ π(1)²(15) = 15π ≈ 47.1 cubic feet.

The closest answer choice to this approximation is D) 141 ft². However, note that volume is measured in cubic units (feet cubed or ft³), not square units (feet squared or ft²). Therefore, none of the answer choices are in the correct units for the volume of a cylinder.

Answer:

Step-by-step explanation:

Initial amount = 500 mg

Elimination rate = 5.2% = 0.052 times per hour

This is the exponential decay and the equation would be:

General equation

Where

a is initial amount

b is rate of change

Here b=1-0.052=0.948

So equation

Answer:

m = - 2, c = 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

y + 2x = 3 ( subtract 2x from both sides )

y = - 2x + 3 ← in slope- intercept form

with m = - 2 and c = 3

The volume of Mrs. Wood's math building at West High School cannot be determined with the given information. Volume = length × width × height

The information provided only includes the height of the ceiling (10 feet) and the length of one side of the building (25 feet). However, to calculate the volume of a building, you need the dimensions of all three sides: length, width, and height.

In this case, we are missing the width and depth (or breadth) of the building. Without these measurements, it is not possible to determine the volume. To calculate the volume of a rectangular-shaped building, you multiply the length, width, and height.

If you have the missing dimensions, for example, if you know the width of the building is 20 feet and the depth is 30 feet, then you can calculate the volume using the formula: volume = length × width × height. However, as the width and depth are not provided in the given information, we cannot calculate the volume accurately.

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Answer:

A

Step-by-step explanation:

i to an odd power is 1 and i to an even power is -1 so you can see it is A

When a thesis test is being performed for a population mean, the probability of a type II error isn't dependent on the sample mean. Option B is the right answer.

A type II error occurs when a null thesis isn't rejected despite it being incorrect. It's worth noting that the threat of making a type II error is affected by several factors, including the sample size, the true population mean, the position of significance, and the variability of the data.

As a result, the larger the sample size, the lower the threat of making a type IIerror.The true population mean also has an impact on the liability of a type II error. As the difference between the true mean and the hypothecated mean grows, the threat of a type II error decreases.

The position of significance is also pivotal in determining the threat of a type II error. As the significance position increases, the threat of a type II error decreases.

So, the correct answer is B

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Increasing marginal productivity infers that extra units of capital and labor contribute more to yield, driving productive asset allotment. ∝ and ß < 1 expect reducing returns, adjusting with reality.

To appear that the generation work has to expand the marginal productivity of capital (in case ∝ > 1) and labor (on the off chance that ß > 1), we ought to take fractional subsidiaries with regard to each input calculation. For capital (K), the fractional subsidiary of the generation work is:

\(\dfrac{dy}{dK }= \alpha AK^{(\alpha-1)}L^\beta\)

Since ∝ > 1, (∝ - 1) is positive, which implies that the fractional subordinate \(\dfrac{dy}{dK}\) is positive. This shows that an increment in capital input (K) leads to an increment in yield (y), appearing to expand the marginal efficiency of capital.

Additionally, for labor (L), the fractional subordinate of the generation work is:

\(\dfrac{dy}{dL} = \beta AK^{\alpha}L^{(\beta-1)}\)

Since \(\mathbf{\beta > 1, (\beta-1)}\) it is positive, which implies that the halfway subordinate \(\dfrac{dy}{dL}\) is positive. This demonstrates that an increment in labor input (L) leads to an increment in yield (y), appearing to increase the marginal productivity

The economic importance of increasing marginal productivity is that extra units of capital and labor contribute more to yield as their amounts increment.  This suggests that the more capital and labor a firm employments, the higher the rate of increment in yield. This relationship is vital for deciding the ideal assignment of assets and maximizing generation effectiveness.

In most generation capacities, it is accepted that ∝ and ß are less than 1. This presumption adjusts with experimental perceptions and financial hypotheses.

In case ∝ or ß were more prominent than 1, it would suggest that the marginal efficiency of the respective factor increments without bound as the calculated input increments.

In any case, there are decreasing returns to scale, which suggests that as calculated inputs increment, the Marginal efficiency tends to diminish. Therefore, accepting ∝ and ß are less than 1 permits for more reasonable modeling of generation forms and adjusts with the concept of diminishing marginal returns.

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Answer:

1/2 x^2 = 450

Step-by-step explanation:

x is the greater number.

The other number is 1/2x.

1/2x * x = 450

1/2 x^2 = 450

The equation that can be used to find x which is the greater number is 1/2(x²) = 450

Word problems involving algebraic expression require the use of variables to interpret the problems and the use of arithemtic operations in solving the variables.

From the given information:

Let say:

However, the first number is half the second number

i.e y = x/2

So, we have:

(x/2) × x = 450

1/2(x²) = 450

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Answer: A≈1385.44m²

Step-by-step explanation:

A=πr2=π·212≈1385.44236m²