what is the square root of 81

(a) The cardinality of A is 37.

The set A is defined as {2, 3, 4, 5, ..., 38}, which is a set of consecutive integers. To find the cardinality of A, we count the number of elements in the set. We can do this by subtracting the smallest element from the largest element and then adding 1:

|A| = 38 - 2 + 1 = 37

Therefore, the cardinality of A is 37.

(b) The cardinality of A is 16.

The set A is defined as the set of all complex numbers of the form a + bi, where a and b are integers such that -1 ≤ a ≤ 2 and -2 ≤ b ≤ 1. To find the cardinality of A, we count the number of elements in the set.

The set of possible values for a is {-1, 0, 1, 2}, and the set of possible values for b is {-2, -1, 0, 1}. Therefore, the set A has 4 × 4 = 16 elements.

Alternatively, we can write out all the elements in the set:

A = {-1 - 2i, -1 - i, -1, -1 + i, 0 - 2i, 0 - i, 0, 0 + i, 1 - 2i, 1 - i, 1, 1 + i, 2 - 2i, 2 - i, 2, 2 + i}

Therefore, the cardinality of A is 16.

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Answer:

11.72sq.m

Step-by-step explanation:

Area of the shaded region = Area o triangle - Area of the semicircle

Area of triangle = 1/2 * base * height

Area of triangle = 1/2 * 6 * 6

Area of triangle = 3 * 6

Area of triangle = 18sq. m

Area of semicircle = πr²/2

r is the radius =  2m

Area of semicircle = π(2)²/2

Area of semicircle = 2(3.14)

Area of semicircle = 6.28sq. m

Area of the shaded region = 18 - 6.28

Area of the shaded region = 11.72sq.m

Answer:

He sliced it diagonally or at an angle.

Step-by-step explanation:

He sliced it diagonally (or at an angle) because the horizontal cross-section of a cylinder is a circle and the vertical cross-section of a cylinder is a rectangle, an oval is between a rectangle and a circle.

Answer:

D. 50

Step-by-step explanation:

50-54 is 30

55-59 is 20

Answer: x^5/x^1 = x^4

y^2/y^2 = 1

so

x^4

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The measure of ∠F in the regular nonagon is 140 degrees.

In a regular nonagon, all angles have the same measure since it is a regular polygon. To find the measure of ∠F, we need to divide the sum of the interior angles of a nonagon by the number of sides.

The sum of the interior angles of a polygon can be found using the formula:

Sum of interior angles = (n - 2) * 180 degrees

where n represents the number of sides.

For a nonagon with 9 sides, the sum of the interior angles is:

Sum of interior angles = (9 - 2) * 180 degrees = 7 * 180 degrees = 1260 degrees.

Since all angles in a regular nonagon have the same measure, we can find the measure of ∠F by dividing the sum of the interior angles by the number of sides:

Measure of ∠F = Sum of interior angles / Number of sides = 1260 degrees / 9 = 140 degrees.

Therefore, the measure of ∠F in the regular nonagon is 140 degrees.

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Step-by-step explanation:

The 2-point backward difference formula for approximating the derivative of a function at a point x0 is graphically represented by the slope of the line connecting the points (x0 - h, f(x0 - h)) and (x0, f(x0)), where h is a positive value.

The 2-point backward difference formula is a numerical method used to approximate the derivative of a function at a specific point. To understand its graphical interpretation, consider a function f and a point x0 on its graph. The formula involves calculating the slope of a line that connects two points on the graph. The first point is (x0 - h, f(x0 - h)), which corresponds to a slightly shifted x-value from x0, denoted as x0 - h, and its corresponding y-value is f(x0 - h). The second point is (x0, f(x0)), representing the original point on the graph. The value of h is chosen to be positive, indicating that the first point is to the left of the second point. By calculating the slope of the line connecting these two points using the familiar slope formula, rise over run, we obtain an approximation of the derivative of the function at x0 using the 2-point backward difference formula.

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Answer:

y = x2 − 500x + 60,000

Step-by-step explanation:

area of the fenced-in section = length • width

y  = (x − 200)(x − 300)

= x² − 300x − 200x + 60,000

= x² − 500x + 60,000

Step-by-step explanation:

En la vida diaria estamos rodeados de figuras geométricas como los polígonos y las circunferencias;alguno ejemplos son los siguientes:  las ventanas,las puertas,el reloj de pared,un balón,los vasos de cocina,las llantas de una bicicleta,un automóvil,etc.

Si necesitamos pintar la sala de nuestra casa,debemos saber exactamente la cantidad de pintura que vamos a necesitar ,para eso debemos calcular el área exacta  del  tramo de pared.

Si necesitamos acabar con la maleza de nuestra jardin ,debemos saber exactamente cual es el área de nuestro jardín ,para aplicar el volumen o la proporción exacta del plaguicida.

Conocer el área de un terreno o lote nos da una idea de lo grande que es y del valor que tiene, por eso es importante saber cómo obtener el área.

Answer:

97.6 cm³

Step-by-step explanation:

Volume of plastic object :

Volume of cylinder - volume of cone

From. The diagram. :

Radius, r = diameter /2 = 4/2

Volume of cylinder = pi*r²h

V = 22/7 * 2² * 8 = 100.53096 cm³

Volume of cone = 1/3*pi*r²h

V = 1/3 * 22/7 * 2² * 8

V = 2.9321531 cm³

(100.53096 - 2.9321531) cm³

= 97.598 cm³

= 97.6 cm³

Answer: A is 70 B is 45 and C is 50

Step-by-step explanation:

Answer:

Scott spent $53.25 on lattes last month.

Step-by-step explanation:

To find how much Scott spent in total, multiply the number of lattes bought by the cost of each latte:

15 × 3.55

53.25

Answer:

I hope this helps but I do not really know what your school is like.

Step-by-step explanation:

Dear Friend,

I wish you could be here at my school, it is really a great school. Here everyone is so helpful, and you are sure to find lots of friends. The teachers don't care of your race, gender, or backround, or anyone. Everyone is so nice and caring. Also, their food is healthy and delicious, and they have different varieties of food each day so that you have to pick from. Did I also tell you that, safety is the number one thing that is on the list, they help remind you what you can do to stay safe, and they have top security with guards, cameras, locked gates, and drills. Also, during lunch or recess or lunch they have plenty of things you do, like they have benches for relaxing, basketball courts, and a big soccer field. Finally, bullying is not tolerated here. But, if there is anything that is bothering you, we beautiful amazing counselors that will help you through anything. So, I help this makes you want to come over here.

      -Sincerely,

               Your friend.

Answer:

$5367.54

Step-by-step explanation:

9000 = P(1 + .03/12)^207*

9000 = P×1.676744643

P = 5367.54

*207 = 12 x 17.25

Answer:

0.73001

Step-by-step explanation:

1 month = 730.01 hours

730.01 * $0.001

= 0.73001

Approximately 0.73 or 0.7.

Answer:

A slope of 2/3

Step-by-step explanation:

if you look at the line, starting at the y axis, then just count up 2 and over three, in other graphed lines, just start at the y axis and try to find where the line crosses a specific point, then calculate the rise/run.

3. After 10 minutes, the height of the water is 4 inches

Answer:

1) P(20) = 0

2) P(0) = 0

3) P(10) = 4

4) P(4) = 10

Step-by-step explanation:

We are told that the function P(t) denotes the height of the water in the bath tub.

At P(0) = 0, it means that after 0 minutes, there is no water in the bath tub.

1) If after 20 minutes, the bathtub is empty, then we can depict the function as; P(20) = 0

2) The bath tub starts out with no water. It means at 0 minutes, there was no water in the tub. Thus;

P(0) = 0

3) If after 10 minutes, the height of the water is to be 4 inches, then;

P(10) = 4

4) If the height is 10 inches after 4 minutes, then;

P(4) = 10

Answer:

3 seconds

Step-by-step explanation:

Complete question:

An object is dropped from a bridge and allowed to freefall to the ground. The height of the object over time can be modeled using h(t)=144-16t2. How many seconds will it take the object to reach the ground? 2 seconds 3 seconds 9 seconds 16 seconds

Given the height of an object modelled by the expression;

h(t)=144-16t²

The object will reach the ground when h(t) = 0

Substitute into the formula

0 = 144 - 16t²

-144 = -16t²

144 = 16t²

Swap

16t² = 144

t² = 144/16

t² = 9

Square root both sides

√t² = ±√9

t = ±3secs

Since the time cannot be negative, hence the object will reach the ground 3 seconds after

These probabilities are calculated based on the given probability mass function and represent the likelihood of specific events occurring with the random variable x.

P(x = 3) represents the probability of getting the value 3 from the random variable x. In this case, the probability is 1/4, which means there is a 1/4 chance of getting the value 3.

P(x < 4) represents the probability of getting a value less than 4 from the random variable x. Since all the values in the given probability mass function are less than 4, the probability is 1, indicating that it is certain to get a value less than 4.

P(x > 3) represents the probability of getting a value greater than 3 from the random variable x. In the given probability mass function, there are 3 values greater than 3 (1/4 + 3/8), so the probability is 3/8.

P(2 < x < 4) represents the probability of getting a value between 2 and 4 (exclusive) from the random variable x. In the given probability mass function, there are two values within this range (1/8 + 1/4), so the probability is 3/8.

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The line integral is -165/7.

The given line integral is ∫ ds, where is the line segment from (−1,0,2) to (1,−3,8).

The line integral is given by the following formula:

∫ (,,) ds = ∫_^ ((),(),()) ||'()|| d

Here,() = 2 − 1, () = −3, () = 6 + 2and a = 0 and b = 1.

We know that ds = ||'()|| d.

Let us find '() first.'() = 〈2,−3,6〉,

therefore, ||'()|| = √(2² + (−3)² + 6²) = 7

So, ds = 7dt.

We need to find the value of (,,) at each of the parameterizations, so let us find those next.

(,,) = = (−3)(6 + 2) = −18² − 6

Now we can compute the integral:

∫ ds=∫0^1(−18² − 6)7=−162/7 - 3/7= −(165/7)

Therefore, the value of the line integral is -165/7.

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Answer:

x = 26

Step-by-step explanation:

Therefore, there are 23,725 different groups of six members that can be selected from the twenty-three members of the Baltimore Mean Green tennis team.

In this scenario, we are interested in determining the number of different groups of members that can be selected from a total of twenty-three members to form a team of six.

Since the order of selection and specific positions within the team are not considered, we are dealing with combinations rather than permutations.

To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating binomial coefficients is:

Where n represents the total number of items or members (in this case, 23), and k represents the number of items or members to be selected (in this case, 6). The exclamation mark denotes the factorial operation.

Applying the formula, we can calculate the number of combinations as follows:

After performing the calculations, we find that the number of different groups of members that can be selected is:

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Answer:

24 A-(8+8)

Step-by-step explanation:

Answer: 4(6a-4) This is one equivalent expression of 24a-16.

The probability that among the students in the sample no more than 7 are female is approximately 0.982 or 98.2%.

To calculate the probability that no more than 7 students in the sample are female, we need to consider the binomial distribution.

The community college student body consists of 40% males, which means 60% are females.

We have a random sample of 8 students.

To get the probability, we can use the binomial probability formula:

P(X ≤ k) = Σ (n choose x) * p^x * (1-p)^(n-x)

Where:

n is the number of trials (sample size)

k is the number of successes (female students)

p is the probability of success (proportion of females in the population)

(n choose x) is the binomial coefficient

In this case:

n = 8 (sample size)

p = 0.6 (proportion of females in the population)

k can take the values 0, 1, 2, 3, 4, 5, 6, or 7

We need to calculate the sum of probabilities for each value of k:

P(X ≤ 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

Calculating each term using the binomial probability formula and summing them will give us the desired probability.

Note: The binomial probability formula assumes independent and identically distributed (i.i.d.) trials and a fixed probability of success.

The community college student body consists of 40% males, which means 60% are females.

We have a random sample of 8 students.

Let's calculate the probability:

P(X ≤ 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

To calculate each term, we use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Where:

n is the number of trials (sample size) = 8

k is the number of successes (female students)

p is the probability of success (proportion of females in the population) = 0.6

Let's calculate each term and sum them up:

P(X = 0) = (8 choose 0) * (0.6^0) * (0.4^8) = 0.1678

P(X = 1) = (8 choose 1) * (0.6^1) * (0.4^7) = 0.3579

P(X = 2) = (8 choose 2) * (0.6^2) * (0.4^6) = 0.3020

P(X = 3) = (8 choose 3) * (0.6^3) * (0.4^5) = 0.1463

P(X = 4) = (8 choose 4) * (0.6^4) * (0.4^4) = 0.0410

P(X = 5) = (8 choose 5) * (0.6^5) * (0.4^3) = 0.0068

P(X = 6) = (8 choose 6) * (0.6^6) * (0.4^2) = 0.0006

P(X = 7) = (8 choose 7) * (0.6^7) * (0.4^1) = 0.00003

Summing up the probabilities:

P(X ≤ 7) = 0.1678 + 0.3579 + 0.3020 + 0.1463 + 0.0410 + 0.0068 + 0.0006 + 0.00003 ≈ 0.982

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