Find the domain of the vector function et r(t) = (cos(2t), In(t + 2),( et/(t-1))
a. (-2, 1) U (1, [infinity]0)
b. (-[infinity], 1) U (1, [infinity])
c. (-2, [infinity])
d. (-1,2) U (2, [infinity]0)
e. (-[infinity], -2) U (-2,00)

The robot moves in the positive direction along a straight line so that after t minutes its distance is s=6t^4 feet from the origin. (a) Find the average velocity of the robot over intervals 2, 4. We have the following data: Initial time, t₁ = 2 min.

Final time, t₂ = 4 min.The distance from the origin is given by s = 6t^4Therefore, s₁ = s(2) = 6(2^4) = 6(16) = 96 feet s₂ = s(4) = 6(4^4) = 6(256) = 1536 feet

We can find the average velocity of the robot over the interval 2, 4 as follows: Average velocity = (s₂ - s₁) / (t₂ - t₁)Average velocity = (1536 - 96) / (4 - 2)Average velocity = 1440 / 2Average velocity = 720 feet per minute(b) Find the instantaneous velocity at t=2.To find the instantaneous velocity at t = 2 min, we need to take the derivative of the distance function with respect to time. We have the distance function as:s = 6t^4 Taking derivative of s with respect to t gives the velocity function:v = ds / dt Therefore,v = 24t³At t = 2, the instantaneous velocity is:v(2) = 24(2)³v(2) = 24(8)v(2) = 192 feet per minute Therefore, the instantaneous velocity at t = 2 min is 192 feet per minute.

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Answer:

8

Step-by-step explanation:

Deer = snow flake = 4

4 + 4 + 4 = 12

Dear - 3 = 1

Snowman = 1

Tree = 8

8 + 1 (snowman) + 8 = 17

A group must consist of 73 people to guarantee that at least 7 were born in the same month of the year.

To guarantee that at least 7 people were born in the same month of the year, we can use the Pigeonhole Principle. The Pigeonhole Principle states that if n items are placed into m containers, with n > m, then at least one container must contain more than one item.

In this case, the "items" are people, and the "containers" are the months of the year. Since there are 12 months in a year, there are 12 containers. To guarantee that at least 7 people were born in the same month, we need to find the smallest number of people (n) that satisfies the Pigeonhole Principle.

First, let's consider placing 6 people in each of the 12 months. This would result in 72 people (6 x 12).

However, this scenario still doesn't guarantee that any of the months would have 7 people.

To ensure that at least one month has 7 people, we need to add 1 more person to the group, making the total 73 people (72 + 1).

Now, even in the worst-case distribution scenario, at least one month would have 7 people, satisfying the Pigeonhole Principle. Therefore, a group must consist of 73 people to guarantee that at least 7 were born in the same month of the year.

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Answer:

6100

Step-by-step explanation:

I think its 1600

Answer: 61219.444

Step-by-step explanation:

The decimal will go 3 times to the right on the nearest thousandths place.

~I hope I helped you! :)~

The relationship that is normally expressed as the quotient of one quantity divided by another is called a ratio

The relationship that is normally expressed as the quotient of one quantity divided by another is called a ratio. A ratio is a comparison of two numbers or measurements, and it can be written in different ways.

For example, if we have two quantities A and B, the ratio of A to B can be written as

A/B

A:B

"A is to B"

The ratio of A to B tells us how many times A is contained within B, or how many units of A we would need to have to match the amount of B.

Ratios are useful in many fields, such as finance, engineering, and science, where they are used to compare and analyze different quantities and their relationships.

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cos(a b) = 0.965 and sin(a b) = 0.674 .

sin a = 0.865

cos a = √(1 - sin² a)

cos a = sqrt(1 - 0.865²)

cos a = 0.502

Similarly, cos b = 0.529

sin b = √(1 - cos² b)

sin b = √(1 - 0.529²)

sin b = 0.854

Trigonometry identity

cos(a b) and sin(a b)

cos(a b) = cos ( 0.502 × 0.529 )

cos(a b) = cos 0.266

cos(a b)  = 0.965

Trigonometry identity

sin(a b) = sin (0.865 × 0.854 )

sin(a b) = sin (0.739)

sin(a b) = 0.674

Therefore, cos(a b) = 0.965 and sin(a b) = 0.674

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Answer:

18in

Step-by-step explanation:

Given data

Height h= 15 in

Area= 135 in^2

The expression for the area is given as

Area= 1/2 Base * Height

substitute

135= 1/2* Base*15

135= 7.5 Base

Base= 135/7.5

Base=  18 in

Hence the base is 18in

Answer:

x = 2

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4/1 or 4

y over x, and simplify

Answer:

1 by 2 is o

Step-by-step explanation:

so slope is 1 by 2 of o .

If one addend of x is c, the other addend is x-c.

An addend is a term that is added to another term to form a sum. In the equation x = c + (x-c) , c and (x-c) are the two addends that make up the sum x.

The reason why x-c is the other addend is that the sum of the two addends (c and x-c) must equal x.

In other words x = c + (x-c) can be simplified to x = c + x - c which is x = x

Therefore, If one addend of x is c, the other addend is x-c.

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Answer:

The answer is

$ 836.03 monthly payments.

It will take 112.5 minutes of time to reach a depth of 200 feet.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

From, The given information, Let 'x' be the time in minutes and 'y' be the depth in feet.

So, y ∝ x.

y = kx.

80 = 45k.

k = 16.9.

Now, When y = 200,

200 = (16/9)×x.

x = 112.5 minutes.

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Answer:

\(\frac{68}{65}\) or \(1\frac{3}{65}\) or 1.046

Step-by-step explanation:

To divide fractions: you keep the same fraction as it is, you change the divide sign to mutiplication, and you flip the numbers in the second fraction. Like so:

\(\frac{17}{5}\)×\(\frac{4}{13}\)

Then, just multiply across the top to get: 68.

Then, multiply across the bottom to get: 65.

Your answer will be \(\frac{68}{65}\), you can simplify it to a mixed number \(1\frac{3}{65}\), or to a decimal 1.046.

Answer:

\(\frac{221}{20}\\\\11\frac{1}{20}\)

Both fractions are the same, just different ways of expressing the value.

Step-by-step explanation:

1. Approach

To divide fractions, one must remember how to do so. First, one will reciprocate the second fraction. Reciprocating essentially means switching the places of the numerator and denominator. The numerator is the part of the fraction that is above the fraction bar, and the denominator is the part below. One will switch the places of these two numbers. Next, one will change the division sign to a multiplication sign. Finally, one will multiply the two fractions, multiply the numerator by the numerator, and the denominator by the denominator. Finally one will simplify by removing a common factor that both the numerator and the denominator of the new fraction have.

2. Solving

\(\frac{17}{5}\) ÷ \(\frac{13}{4}\)

Reciprocate, and change sign;

\(\frac{17}{5} * \frac{4}{13}\)

Multiply,

\(\frac{17}{5}*\frac{13}{4}\\\\= \frac{221}{20}\)

Convert to improper fractions;

\(11\frac{1}{20}\)

Answer:

\(D.\ 3328\ ft^3\)

Step-by-step explanation:

Given

Volume of baby pool = 52ft³

Required

Determine the volume of the medium pool

Volume of a cylinder is calculated as:

\(V = \pi r^2h\)

Hence, the volume of the baby pool is:

\(\pi r^2h = 52\)

where r and h are the radius and height of the baby pool

Represent the height and radius of the medium pool as H and R

From the given parameters in the question

\(H = 4 * h\) and \(R = 4 * r\)

\(H = 4 h\) and \(R = 4 r\)

The volume of the medium cylinder is calculated as

\(Volume = \pi R^2H\)

Substitute 4h for H and 4r for R

\(Volume = \pi (4r)^2(4h)\)

Open bracket

\(Volume = \pi (4r) * (4r) * (4h)\)

\(Volume = \pi 16r^2 * (4h)\)

\(Volume = \pi 16r^2 * 4h\)

Collect like terms

\(Volume = \pi r^2 * h * 4 * 16\)

\(Volume = \pi r^2 h * 64\)

Recall that \(\pi r^2h = 52\)

So, the expression becomes

\(Volume = 52 * 64\)

\(Volume = 3328\)

Hence, the medium pool can hold \(3328ft^3\) of water

The error Justin made in his calculation is "He should have added the values in the numerator before dividing by 2".

The correct answer choice is option B

(x + y + 5) / 2

Where,

x and y are his parents’ current heights in inches,

Mom’s height = 54 inches

Dad’s height = 71 inches

Substitute into the expression

(71 + 54 + 5) / 2

= 130/2

= 65 inches

Justin's work:

( 71 + 54 + 5 ) / 2

= 71 + 27 + 5

= 103 inches

Therefore, Justin should have added the numerators before dividing by 2.

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Answer:

B

Step-by-step explanation:

The total change in position is represented by a number with a magnitude of 155 feet.

Hope this helps!

xoxo,

cafeology

Answer:

8

Step-by-step explanation:

Zeroes in the end are not significant figures. They're "place holders".

So 80 only has one significant figure (often written as sig fig).

Info related to the question

True, a data warehouse allows users to specify certain dimensions or characteristics.

In a data warehouse, dimensions represent the different aspects or characteristics by which data can be categorized or analyzed. These dimensions can include various attributes or variables that provide context and organize the data.

Users of a data warehouse can specify these dimensions based on their analytical needs and the nature of the data being stored.

For example, in a sales data warehouse, common dimensions may include product, customer, time, and location.

By specifying these dimensions, users can slice and dice the data based on different criteria and gain insights from various perspectives.

By defining dimensions, users can navigate through the data warehouse and perform multidimensional analysis using tools such as OLAP (Online Analytical Processing).

Dimensions provide a structure for organizing and querying data in a way that facilitates analysis and reporting.

In summary, a data warehouse allows users to specify dimensions or characteristics that help organize and analyze the data stored in the warehouse. These dimensions provide a framework for users to navigate and explore the data from different perspectives.

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The length of OP is √(3) and the Pythagorean Theorem is used to find it.

A theorem is a statement that has been proven to be true based on rigorous mathematical reasoning and evidence. It is a fundamental concept in mathematics and plays a central role in building the structure of mathematical knowledge. Theorems are often used as a basis for further mathematical analysis and the development of new theories and applications.

The length of OP can be found using the Pythagorean Theorem.

By the Pythagorean Theorem, we know that:

MN² + NO² = MO²

Since angle MNP is congruent to angle ONP, we know that triangles MNP and ONP are similar. Therefore, we can set up a proportion:

MN/NP = ON/NP

Simplifying this proportion, we get:

MN = ON

Substituting this into the equation for MO², we get:

MN²  + NO²  = MO²

2(MN² ) = MO²

Since MP is given as 2, we can use the Pythagorean Theorem in triangle MOP to find OP:

MO² = MP² + OP²

2(MN²) = MP² + OP²

2(MN²) - MP² = OP²

2(2²) - 1² = OP²

3 = OP²

OP = √3

Therefore,

The length of OP is √(3) and the Pythagorean Theorem is used to find it.

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Answer:

-2

Step-by-step explanation:

I thought of the number 4

Divide 4 by 2

2

2 - 4 = -2

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Answer:

12-4=8

Step-by-step explanation:

12-4 = 8

Answer:

8.11

Step-by-step explanation:

4+4+7+13+12+9 = 49

divide that by 6

========================================================

Explanation:

Sort the data set to go from {4,4,7,13,12,9} to {4,4,7,9,12,13}

Next, cross off the first and last items to get this smaller set: {4,7,9,12}

Repeat the last step to get this even smaller set: {7,9}

We can see that 7 & 9 are tied for the middle most positions. Add them up and divide by 2 to find the midpoint

(7+9)/2 = 16/2 = 8

The median is 8

The nominal rate to plug in will be 0.085.

Given to us, the nominal rate is 8.5%,

The value to plug into your equation,

The equation can be simple interest or compound interest in both cases the value of the nominal rate to the plugin will be the same.

Thus, the nominal rate is 8.5% can be written as

\(\begin{aligned}Nominal rate&= 8.5\%\\&= \dfrac{8.5}{100} \\&= 0.085\end{aligned}\)

Hence, the nominal rate to plug in will be 0.085.

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Answer:

m<B= 52

Step-by-step explanation:

2x - 30 + 3x + 10 + 7x + 32 = 180

12x + 12 = 180

12x = 168

x = 14

m<B= 3x + 10

3(14) + 10

52

The area of kite ADCB based on the information will be s 49.5 units².

Given that ADCB is a kite, we know that AD = DC and AB = BC. We also know that AD = 5 units and that CD is perpendicular to the x-axis. This means that the x-coordinate of C must be 8, since the x-coordinate of D is 3 and AD = 5 units. The y-coordinate of C must be 0, since CD is perpendicular to the x-axis and the y-coordinate of D is 5. Therefore, the coordinates of C are (8, 0).

The area of a kite is equal to the product of the diagonals, divided by 2. In this case, the diagonals are AC and BD. The length of AC is 11 units, and the length of BD is 9 units. Therefore, the area of kite ADCB is:

= (11 * 9) / 2

= 49.5 units².

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Answer:

option 1

Step-by-step explanation:

you multiply the numerators and the denominators which gets you 4^1/8

An expression is defined as a set of numbers, variables, and mathematical operations. The given exponential function when simplified will result in 4^(1/8). The correct option is A.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given exponential expression can be simplified as shown below.

\((4^{\frac14})^{\frac12}\)

Using the exponential property (mᵇ)ˣ = mᵇˣ,

= \(4^{\frac14 \times \frac12}\)

= \(4^{\frac18}\)

Hence, the given exponential expression when simplified will result in 4^(1/8).

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To solve for \(V_2\) in the equation \(M_1 \cdot V_1 = M_2 \cdot V_2\) with the given values \(M_1 = 22.7\), \(V_1 = 2.70\), and \(M_2 = 5.24\), we can rearrange the equation to isolate \(V_2\). The solution for \(V_2\) is approximately 12.1.

To explain the solution further, we start with the equation \(M_1 \cdot V_1 = M_2 \cdot V_2\) and the given values: \(M_1 = 22.7\), \(V_1 = 2.70\), and \(M_2 = 5.24\).

Rearranging the equation to solve for \(V_2\), we divide both sides of the equation by \(M_2\): \(\frac{{M_1 \cdot V_1}}{{M_2}} = V_2\).

Substituting the given values, we have \(\frac{{22.7 \cdot 2.70}}{{5.24}}\), which can be evaluated to find \(V_2 \approx 12.1\).

This calculation is based on the principle of the dilution formula, which states that the initial concentration and volume of a solution are equal to the final concentration and volume when diluted. By rearranging the equation and plugging in the given values, we can determine the unknown volume, \(V_2\), in the equation. The resulting value of 12.1 indicates the volume required to achieve the desired concentration in the dilution process.

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To solve for \(V_2\) in the equation \(M_1 \cdot V_1 = M_2 \cdot V_2\) with the given values \(M_1 = 22.7\), \(V_1 = 2.70\), and \(M_2 = 5.24\), we can rearrange the equation to isolate \(V_2\). The solution for \(V_2\) is approximately 12.1.

To explain the solution further, we start with the equation \(M_1 \cdot V_1 = M_2 \cdot V_2\) and the given values: \(M_1 = 22.7\), \(V_1 = 2.70\), and \(M_2 = 5.24\).

Rearranging the equation to solve for \(V_2\), we divide both sides of the equation by \(M_2\): \(\frac{{M_1 \cdot V_1}}{{M_2}} = V_2\).

Substituting the given values, we have \(\frac{{22.7 \cdot 2.70}}{{5.24}}\), which can be evaluated to find \(V_2 \approx 12.1\).

This calculation is based on the principle of the dilution formula, which states that the initial concentration and volume of a solution are equal to the final concentration and volume when diluted. By rearranging the equation and plugging in the given values, we can determine the unknown volume, \(V_2\), in the equation. The resulting value of 12.1 indicates the volume required to achieve the desired concentration in the dilution process.

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Answer:

37°

Step-by-step explanation:

(4x + 2)° = 150° [Vertically Opposite Angles]

=> 4x = 150 - 2

=> 4x = 148

\( = > x = \frac{148}{4} \)

=> x = 37° (Ans)

Angle (4x+2)° and angle 150° are vertically opposite angles so, their measures will be equal.

Which means :

\( =\tt 4x + 2 = 150\)

\( =\tt 4x = 150 - 2\)

\( = \tt4x = 148\)

\( =\tt x = \frac{148}{4} \)

\(\hookrightarrow \: \color{plum}x = 37\)

Let us check whether or not we have found out the correct measure of x by placing 37 in the place of x:

\( =\tt 4 \times 37 + 2 = 150\)

\( = \tt148 + 2 = 150\)

\( =\tt 150 = 150\)

Since the measures of both the angles are equal we can conclude that we have found out the correct value of x.

Thus, the value of x in this figure = 37

Therefore, the correct option is (A) 37.