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The position of an object is determined as  (¹/₃ ln |1 + t³| + 2)i + (- ¹/₂cos(2t) + 3 )j.

None of above is the correct answer.

The position of an object is defined as the product of velocity of the object and the time of motion of the object.

So to obtain the position of the particle, we will integrate the velocity of the particle as follows;

The velocity is given as;

v(t) = t²i/(1 + t³)  +  sin 2t j

Integrate i component as;

Let u = 1 + t³

du/dt = 3t².

dt = du / (3t²)

∫ t²/(1 + t³) dt =∫ (1/u) x (t²/3t²) du

= (1/3) ∫ (1/u) du

= (1/3) ln |u| + C

= (1/3) ln|1 + t³| + C

Integrate j component as follows;

∫ sin(2t) dt = - ¹/₂cos(2t) + C

∫ v(t) dt = (1/3) ln|1 + t³|)i - ¹/₂cos(2t)j

So finally, we add the initial position of 2i + 3j, as follows;

x = (¹/₃ ln |1 + t³| + 2)i + (- ¹/₂cos(2t) + 3 )j

So none of the options matches this solution, the closet is B.

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Answer:

The universal set is the set of all elements that can possibly belong to either set A or set B. To find the least possible universal set for A and B, we need to combine all the elements from both sets while avoiding duplicates.

The combined set of A and B is {a, b, k, s, u, y, t, p, l, m}. Therefore, this is the least possible universal set for A and B.

Step-by-step explanation:

The universal set is the set of all elements that can possibly belong to either set A or set B. To find the least possible universal set for A and B, we need to combine all the elements from both sets while avoiding duplicates.

The combined set of A and B is {a, b, k, s, u, y, t, p, l, m}. Therefore, this is the least possible universal set for A and B.

The probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train is 0.5 or 50%.

To calculate the probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train from the terminal to the rental car and long term parking center, we need to find the probability of each event separately and then add them together.

The probability of waiting less than 2 minutes can be calculated as the ratio of the time interval from 0 to 2 minutes (2 minutes) to the total time interval of 8 minutes;

P(waiting less than 2 minutes) = (2 minutes) / (8 minutes) = 0.25

The probability of waiting more than 6 minutes can be calculated as the ratio of the time interval from 6 to 8 minutes (2 minutes) to the total time interval of 8 minutes;

P(waiting more than 6 minutes) = (2 minutes) / (8 minutes) = 0.25

Now, to find the probability of waiting less than 2 minutes or more than 6 minutes, we can add the two probabilities together;

P(waiting less than 2 minutes or more than 6 minutes) = P(waiting less than 2 minutes) + P(waiting more than 6 minutes)

= 0.25 + 0.25

= 0.5

Therefore, the  probability of waiting less than 2 minutes or more than 6 minutes will be 0.5 or 50%.

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Answer:

To find the prism with a volume between 38 and 48 cubic inches, we need to calculate the volume of each prism and then compare it to the given range.

Prism A:

Number of cubes in prism A = 4 x 5 x 2 = 40

Volume of each cube = 1 cubic inch

Volume of prism A = Number of cubes x Volume of each cube = 40 x 1 = 40 cubic inches

Prism B:

Number of cubes in prism B = 3 x 4 x 3 = 36

Volume of each cube = 1 cubic inch

Volume of prism B = Number of cubes x Volume of each cube = 36 x 1 = 36 cubic inches

Prism C:

Number of cubes in prism C = 4 x 4 x 1 = 16

Volume of each cube = 1 cubic inch

Volume of prism C = Number of cubes x Volume of each cube = 16 x 1 = 16 cubic inches

Prism D:

Number of cubes in prism D = 4 x 4 x 6 = 96

Volume of each cube = 1 cubic inch

Volume of prism D = Number of cubes x Volume of each cube = 96 x 1 = 96 cubic inches

Therefore, the prism with a volume between 38 and 48 cubic inches is prism A, since its volume is 40 cubic inches which falls within the given range.

Step-by-step explanation:

Answer:

Prism A:

Number of cubes in prism A = 4 x 5 x 2 = 40

Volume of each cube = 1 cubic inch

Volume of prism A = Number of cubes x Volume of each cube = 40 x 1 = 40 cubic inches

Prism B:

Number of cubes in prism B = 3 x 4 x 3 = 36

Volume of each cube = 1 cubic inch

Volume of prism B = Number of cubes x Volume of each cube = 36 x 1 = 36 cubic inches

Prism C:

Number of cubes in prism C = 4 x 4 x 1 = 16

Volume of each cube = 1 cubic inch

Volume of prism C = Number of cubes x Volume of each cube = 16 x 1 = 16 cubic inches

Prism D:

Number of cubes in prism D = 4 x 4 x 6 = 96

Volume of each cube = 1 cubic inch

Volume of prism D = Number of cubes x Volume of each cube = 96 x 1 = 96 cubic inches

Therefore, the prism with a volume between 38 and 48 cubic inches is prism A, since its volume is 40 cubic inches which falls within the given range.

Step-by-step explanation:

The height from the ground to the top of the ladder is 61. 28 feet

First, we need to know that their are six different trigonometric identities.

These identities includes;

From the information given, we have that;

the height of the ladder that is leaning against the house = 80 feet

This the hypotenuse side

The angle of elevation is 50 degrees

Then, the opposite side is the height from the ladder = x

Using the sine identity, we have;

sin 50 = x/80

cross multiply the values

x = 61. 28 feet

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Answer:

y + 3 = - 9(x - 2)

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 )

y = - 9x - 1 ← is in slope- intercept form

with slope m = - 9

• Parallel lines have equal slopes

then slope of parallel line is m = - 9

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

m = - 9 and (a, b ) = (2, - 3 ) , then

y - (- 3) = - 9(x - 2) , that is

y + 3 = - 9(x - 2)

The surface area of a right square pyramid if the area of the base is 169 cm² and the slant height of the pyramid is 13 cm is 507 cm².

We know that the area of the square base is 169 cm², so we can solve for the length of one side.

To find the length, we use the formula for the area of a square:

Area = length x length

169 = length²

Taking the square root of both sides, we get:

length = √169

        = 13 cm

Now we can use the formula for the surface area of a square pyramid:

Surface area = area of base + (1/2)perimeter of base x slant height

The perimeter of the base is 4 times the length of one side, so it is:

perimeter of base = 4 x length = 4 x 13 cm = 52 cm

Plugging in the values we have:

Surface area = 169 cm² + (1/2)(52 cm)(13 cm)

Surface area = 169 cm² + 338 cm²

Surface area = 507 cm²

Therefore, the surface area of the right square pyramid is 507 cm².

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The measure of WY using trigonometric identities is 5.4405.

We have,

Using trigonometric identities,

tan 33 = YW/√70

Now,

√70 = 8.37

tan 33 = 0.65

Substituting,

0.65 = YW/8.37

YW = 0.65 x 8.37

YW = 5.4405

Thus,

The measure of WY is 5.4405.

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The distance from Kimberly's house to Marilyn's house = 12.04 mi

Let us assume that A be the angle at Kimberly's house, B represents the angle at Bobby's house and S represents the angle at Marilyn's house.

Let a, b, c represents the sides(distance between two houses) opposite to angles A, B and C.

Using sine rule to triangle ABC,

sin A/a = sin B/b = sin C/c

Consider equation,  

sin A/a = sin B/b

sin(63°) / 14 = sin(50°) / b

b = (0.766 × 14) / 0.891

b = 12.04 mi

Thus, the required  distance between Kimberly's house and Marilyn's house = 12.04 mi

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The value of the radius of the cone is, 5 inches

We have to given that;

The volume of a cone is 35π cubic inches.

And, the height is 4.2 inches.

Now, We know that;

Volume of cone is,

V = πr²h/3

Hence, We get;

35π = π × r² × 4.2 / 3

105 = 4.2r²

r² = 105/4.2

r² = 25

r = 5 inches

Thus, The value of the radius of the cone is, 5 inches

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The  vector-valued function is continuous at t=2,

are

A vector-valued function, is described as a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.

We are required  to check if the limit of the function as t approaches 2 exists and is equal to the value of the function at t=2, in order to determine if the  vector-valued function is continuous at t=2.

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The  algebraic expression represents loga 75 is st²

An algebraic expression is an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

The statement reads:

loga 2=r,

loga 3=s, and

loga 5=t

Log 75 Log(3*5*5)

That log3*log5*log5

= s*t*t = st²

Therefore the expression is st²

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Answer:translation, 12^2+35^2, squre root the answer, thgen add it to 12

Step-by-step explanation:

In the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.

We have a right triangle with an unknown angle θ (measured in degrees), the opposite side length of 16 units, and a hypotenuse length of 21 units. We're given the formula for calculating the sine of an angle:

sin(θ) = opposite / hypotenuse

By substituting the values we know, we get:

sin(x) = 16 / 21

x = sin⁻¹(16 / 21)

x ≈ 49.6°

Therefore, in the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.

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The value of ||w - u || = 3 sqrt 2

Given:

u = 2i - 3j

w = - i - 6j

w - u = ( - i - 2i ) + ( - 6j - (-3j))

w - u = - 3i - 3j

|| w - u || = sqrt [ - 3^2 + - 3^2 ]

||w - u || = 3 sqrt 2

The concept of a radical in mathematics refers to the symbolic representation (√) of finding the roots of an expression or a number.

The widely known and frequently used kind is the square root (√), which reveals a positive value that, when multiplied by itself at once, generates the radicand.

Other forms may include cube roots (∛) or fourth roots (∜). To simplify radicals, one can factor out those factors within it that result in perfect cubes or squares from their corresponding radicands.

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Answer: x^2 + 0x + 19/5 = 0

Step-by-step explanation: The initial step involves the equation -4x - 19 = x, which can be simplified by performing the operation of subtracting x from both sides.

The given equation can be represented as -5x - 19 = 0 in standard algebraic form, where 'x' denotes the unknown variable.

The process of combining similar or like terms leads to the consolidation of terms that share the same variable and corresponding exponents.

The given expression, 5x - 19 = 0, can be rewritten in an academic manner as a linear equation. Specifically, this expression represents a linear equation in one variable, where x is the unknown. The equation can be solved to find the value of x that satisfies it. This can be done through various methods, such as isolation of x, substitution, or using algebraic properties. The solution of this equation is x = 19/5, which can be verified by plugging it back into the original equation and observing its validity.

In order to render this equation in a standard format, it is imperative to eliminate the fixed element present on the left-hand side. The aforementioned task can be accomplished by simultaneously augmenting 19 to each side of the equation.

The equation 5x = 19 can be expressed in an academic manner as a linear equation with one variable. Specifically, it states that there is a value, x, that when multiplied by the constant factor of 5, results in a final product of 19. This equation could be used as a starting point for further mathematical analysis or application, such as solving for the specific value of x or incorporating it into a larger system of equations.

The left-hand side of the expression contains the linear term and the constant term, while the right-hand side is equal to 0. In order to express this equation in a standardized form, it is necessary to perform division by a factor of negative five to isolate the variable x.

The numerical value of the variable x is equivalent to negative nineteen divided by five, expressed as x = -19/5.

The standard form of the quadratic equation can be expressed as follows:

The mathematical expression, x + 19/5 = 0, may be restated in a formal academic style as follows: "The equation is of the form x + 19/5 = 0."

In order to determine the coefficients of the squared and constant terms, it can be observed that the coefficient of the squared term equates to 1 by virtue of the squared exponent of x, while the constant term evaluates to 19/5. This analytical approach yields the appropriate identification of the relevant coefficients in the given equation. Henceforth, the standard format for the quadratic equation is expressed as follows:

The equation in question is x^2 + 0x + 19/5 = 0.

Answer:

3,000

Step-by-step explanation:

v = lwh

v = (25)(10)(12)

v = 3000

Helping in the name of Jesus.

Answer:

The answer is the second choice.

Step-by-step explanation:

The slope is rise over run, which is 3/-1, which is -3, which goes before the x. The line hits the y axis at -1, so it is -3x–1

The simple interest after 4 years with the given principal and rate is $120.

Given that, principal =$600, rate=5% and time=4 years.

We know that, simple interest=(Principal×Rate×Time)/100.

Simple interest = (600×5×4)/100

= $120

Therefore, the simple interest after 4 years with the given principal and rate is $120.

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190 percent. you can find this by dividing the numerator by denominater

Answer:

190%

Step-by-step explanation:

19/10 = 19 ÷ 10 = 1.9

1.9 x 100 = 190%

The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.

Buying the car is more expensive than leasing by $13,600 over the 5-year period.

We have,

To calculate the cost of leasing the car, we first need to determine the total amount paid over the lease term:

= (Monthly payment x Number of months) + Down payment

= ($473 x 60) + $2,420

= $28,780

To determine the cost of buying the car, we first need to calculate the total loan amount:

= Cost of car - Down payment + Residual value

= $34,000 - $5,000 + $16,400

= $45,400

Now,

Total loan cost = (Monthly payment x Number of months) + Down payment

Total loan cost = ($623 x 60) + $5,000

Total loan cost = $42,380

So,

The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.

To determine which option is less expensive, we can subtract the cost of leasing from the cost of buying:

Cost of buying - Cost of leasing = $42,380 - $28,780

Cost of buying - Cost of leasing = $13,600

So,

Buying the car is more expensive than leasing by $13,600 over the 5-year period.

Thus,

The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.

Buying the car is more expensive than leasing by $13,600 over the 5-year period.

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The variables to the parallelogram OPQR are;

1. coordinates of points M is (1, 2.5)

2. The length of PQ is 4

3. The length of QR is 5.4

4. The length of PM is 3.9

5. The length of OM is 2.7

6. The perimeter of the parallelogram OPQR is approximately  18.8

7. if m ∠QMR = 120° m ∠ QMP = 60°

8. If m ∠ QRO = 80°  m ∠ROP =  100°

To calculate for every listed length of parallelogram OPQR it will be helpful to list all the coordinate for this diagram and they are;

O (0, 0)

p (-2, 5)

R (4, 0)

Q (2, 5)

To find for M, we could just get it from the diagram by looking at the points for x and then y. This is (1, 2.5). You can also calculate it like this

Mx = (Px + Rx)/2 = (-2 + 4)/ 2 = 2/2 = 1

My = (Py + Ry)/2 = ( 5 + 0)/2 = 2.5

To calculate for the length of any side, we say

LPQ = √(Qx -Px)² + (Qy - Py)² = √(2 - -2)² + (5-5)² = √8 = 4

LQR = √(Rx -Qx)² + (Ry - Qy)²

LPM = √(Mx -Px)² + (My - Py)²

LOM = √(Mx -Mx)² + (Oy - My)²

if m∠QMP = 180° - m∠QMR = 180° - 120° = 60°

The question below is as seen in the pictures provided.

The diagonals of parallelogram OPQR intersect at point M.

What are the coordinates of points M?

Find PQ

Find QR

Find PM

Find OM

Find permeter of parallelogram OPQR

if m ∠QMR = 120° what is m ∠ QMP

If m ∠ QRO = 80°  what is m ∠ROP

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Answer:

116

Step-by-step explanation:

The time required for the amount to double and triple are 19.53 and 30.95 respectively.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

[tex]f(t) = P_{0}e^{rt}[/tex]

Where:

Based on the information provided above, we can reasonably infer and logically deduce that a function for the time required for the amount to double is given by;

[tex]2(1500) = 1500e^{0.0355t}\\\\3000= 1500e^{0.0355t}\\\\2=e^{0.0355t}[/tex]

Taking the natural log (ln) of both sides of the equation, we have:

0.0355t = ln(2)

Time, t = 19.53

Similarly, a function for the time required for the amount to triple is given by;

[tex]3(1500) = 1500e^{0.0355t}\\\\4500= 1500e^{0.0355t}\\\\3=e^{0.0355t}[/tex]

Time, t = 30.95

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The total number of employees in the company is 560.

The total number of employees in the company is calculated as follows;

the true average number of cups of coffee consumed per employee during the workweek is 10.2 ± 0.6 cups.

maximum = 10.8 cups/employee

minimum = 9.6 cups/employee

The minimum number of employees is calculated as;

n_m = 6,048 cups / 10.8

n_m = 560

The maximum number is calculated as;

n_max = 6,048 cups/9.6

n_max = 630

Based on the error margin, we take the minimum number.

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Answer:

D

Step-by-step explanation:

A dot plot would be the best representation for this data, because the number of scores reported individually is small and a dot plot is ideal for displaying individual data points.

The correlation coefficient which best matches the data plotted on the graph is 0.25, the correct option is C.

We are given that;

The graph of different values of x

Now,

we can see that there is a weak positive linear relationship between x and y, as the points are scattered around a slightly upward-sloping line. The closer the points are to the line, the stronger the correlation. The farther the points are from the line, the weaker the correlation. Hence, we can expect the correlation coefficient to be a small positive number, less than 1.

Therefore, by correlation coefficient the answer will be 0.25.

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