Classify the following into finite and infinite set
(i) The set of months in a year
(ii)The set of stars in the galaxy
(iii)The set of even integers
(iv)The set of odd integers
(v)The set of alphabets

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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Answer:

Step-by-step explanation:

4*2*6=48a

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

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 amount on compound interest is $ 96,685,319.07

The amount on compound interest is given by A = P(1 + r)ⁿ where P = principal amount, r = interest rate and t = time

To find the amount on compound interest given that

So, substituting the values of the variables into the equation, we have that

A = P(1 + r)ⁿ

A = $3830(1 + 0.66)²⁰

A = $3830(1.66)²⁰

A = $3830(25244.21)

A = $ 96,685,319.07

The amount is $ 96,685,319.07

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The general form of the function is:

y = A sin(Bx - C) + D

To determine the specific values of A, B, C, and D that satisfy the given conditions, we can use the following steps:

Period: The period of a sinusoidal function is given by 2π/B, where B is the coefficient of x in the argument of the sine function. In this case, the period is 8, so we have:

2π/B = 8

Solving for B, we get:

B = π/4

Phase shift: The phase shift of a sinusoidal function is given by C/B, where C is the constant inside the argument of the sine function. In this case, the phase shift is -2, so we have:

C/B = -2

Substituting B from step 1, we get:

C/(π/4) = -2

Solving for C, we get:

C = -π/2

Amplitude and vertical shift: The range of the function is given as -12 ≤ y ≤ -4. The amplitude of a sinusoidal function is half the distance between its maximum and minimum values. In this case, the amplitude is:

(amplitude) = (maximum - minimum)/2 = (-4 - (-12))/2 = 4

The vertical shift of the function is given by the constant term D. Since the minimum value of the function is -12, we have:

D + (amplitude) = -12

Substituting the value of the amplitude from above, we get:

D + 4 = -12

Solving for D, we get:

D = -16

Therefore, the function of the form y = A sin(Bx - C) + D that has period 8, phase shift -2, and the range -12 ≤ y ≤ -4 is:

y = 4 sin(π/4 x + π/2) - 16

According to the compound interest concept the total cost of the land today is $89,306.64, $86,249.94, $83,693.44 respective to the discount percentage.

To calculate the PV of the second payment of $48,000 due in three years, we need to use the formula for the present value of a single sum:

PV = FV / (1 + r)ⁿ

where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.

Using the given information, the FV is $48,000, the discount rate is 4%, 6%, or 8%, depending on the question, and the number of periods is three. Using a financial calculator, Excel, or present value tables, we can calculate the PV of the second payment:

For a discount rate of 4%:

PV = $48,000 / (1 + 0.04)³ = $41,306.64

For a discount rate of 6%:

PV = $48,000 / (1 + 0.06)³ = $38,249.94

For a discount rate of 8%:

PV = $48,000 / (1 + 0.08)³ = $35,693.44

Next, we need to add the PV of the second payment to the initial payment of $48,000 to get the total cost of the land today:

For a discount rate of 4%:

Total cost = $48,000 + $41,306.64 = $89,306.64

For a discount rate of 6%:

Total cost = $48,000 + $38,249.94 = $86,249.94

For a discount rate of 8%:

Total cost = $48,000 + $35,693.44 = $83,693.44

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Answer: Broken Math Problem

Step-by-step explanation:

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

Step-by-step explanation:

Answer:

3,000

Step-by-step explanation:

v = lwh

v = (25)(10)(12)

v = 3000

Helping in the name of Jesus.

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:

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 number of different committees that can be formed is 495

From the question, we have the following parameters that can be used in our computation:

People = 12

Committee = 4

These can be represented as

n = 12 and r = 4

The number of different committees that can be formed is

Number = nCr

So, we have

Number = 12C4

Evaluate

Number = 495

Hence, the committee are 495

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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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Answer:

The length of the arc intercepted by a central angle of 3 radians in a circle of radius 76 is 228 and the length of the arc intercepted by a central angle of 2 radians in a circle of radius 15 is 30.

Explain:

The following formula determines the length of an arc that a circle's central angle intercepts:

Arc length is equal to (central angle / 2) 2r r r

where r denotes the circle's radius. We can determine the length of the two arcs using the following formula:

For the first circle, with a radius of 76 and a center angle of 3 radians:

Arc length = 3 x 76 = 228

Therefore, in a circle with a radius of 76, the length of the arc that is intercepted by a central angle of 3 radians is 228.

For the second circle, whose radius is 15, and whose center angle is 2 radians:

Arc length = 2 x 15 = 30

As a result, the length of the arc in a circle with a radius of 15 is 30 when it is intercepted by a central angle of 2 radians.

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The graph of the equation x² + y - 36 = 0 is symmetric with respect to the y-axis and the origin, but not with respect to the x-axis.

x² + y - 36 = 0

Symmetry with respect to the x-axis:

Replace y with -y: x² - y - 36 = 0

This equation is not equivalent to the original equation, so the graph is not symmetric with respect to the x-axis.

Symmetry with respect to the y-axis:

Replace x with -x: (-x)² + y - 36 = 0

Simplifying, we get x² + y - 36 = 0, which is equivalent to the original equation.

Therefore, the graph is symmetric with respect to the y-axis.

Symmetry with respect to the origin:

Replace x with -x and y with -y: (-x)² + (-y) - 36 = 0

Simplifying, we get x² + y - 36 = 0, which is equivalent to the original equation.

Therefore, the graph is symmetric with respect to the origin.

Hence, the graph of the equation x² + y - 36 = 0 is symmetric with respect to the y-axis and the origin, but not with respect to the x-axis.

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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: 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.

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 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 function f(x) = 3x/(x-9) has a vertical asymptote at x=9, a horizontal asymptote at y=3 as x->±∞, and a horizontal asymptote at y=-3 as x->±∞.

To identify the asymptotes and state the end behavior of the function f(x) = 3x/(x-9), we need to analyze the behavior of the function as x approaches positive and negative infinity.

First, let's look at the denominator of the fraction, which is x-9. This means that the function has a vertical asymptote at x=9, as the denominator approaches zero at that point. This vertical asymptote divides the x-axis into two regions, x<9 and x>9.

Now let's consider the behavior of the function as x approaches positive infinity. In this case, the numerator grows faster than the denominator, and the function approaches a horizontal asymptote at y=3. To see this, we can use the limit definition:

lim (x->∞) f(x) = lim (x->∞) 3x/(x-9) = lim (x->∞) 3(1/(1-9/x)) = 3

Similarly, as x approaches negative infinity, the function also approaches a horizontal asymptote at y=-3. Again, we can use the limit definition to confirm this:

lim (x->-∞) f(x) = lim (x->-∞) 3x/(x-9) = lim (x->-∞) 3(1/(1-9/x)) = -3

Therefore, the function f(x) = 3x/(x-9) has a vertical asymptote at x=9, a horizontal asymptote at y=3 as x->±∞, and a horizontal asymptote at y=-3 as x->±∞.

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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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An appropriate assignment of digits to the outcomes for a simulation of this random process would be:

Option 1: Let 0 and 1 = the student is enrolled in the nursing program. Let 2-5 = the student is not enrolled in the nursing program. Skip the digits 6, 7, 8, 9, and 0.

This option assigns two digits, 0 and 1, to represent the two possible outcomes: a student is either enrolled in the nursing program (outcome 1) or not enrolled (outcome 2-5). The digits 2-5 represent the non-nursing program outcomes, and the digits 6-9 and 0 are skipped.

Option 1 is appropriate because it assigns a unique digit to each possible outcome, and the skipped digits are not relevant to the simulation. Additionally, the proportion of digits assigned to each outcome (2 out of 10) corresponds to the proportion of students in the nursing program (20%).

Answer:

1375

Step-by-step explanation:

16*3*29 = 1392

1392-17 =1375

Answer:

Step-by-step explanation:

Quadrant II

A is in Quadrant I   then you count counterclockwise

B quadrant II     (2)

C Quadrant III    (3)

D Quadrant VI   (4)

Roman numerals are used to for quadrant number

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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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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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 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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