A SCHOOL HAS 320 GIRLS AND 250 BOYS

THE PROBABILITY THAT A GIRL IS LEFT-HANDED IS 0.2
THE PROBABILITY THAT A BOY IS LEFT-HANDED IS 0.1

ESTIMATE THE NUMBER OF LEFT-HANDED STUDENTS IN THE SCHOOL

The probability that X will be at least 2 is 0.5940 and the probability that X will be between 2 and 4 (inclusive) is 0.3010.

The Poisson distribution is given by the formula:

\(P(X = k) = (e^{(-\lambda)} * \lambda ^k) / k!\)

where λ is the expected value or mean of the distribution.

In this case, we are given that E(X) = 2.4, so λ = 2.4.

Using a Poisson probability calculator, we can find:

P(X > 2) = 1 - P(X ≤ 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

= \(1 - [(e^{(-2.4)} * 2.4^0) / 0! + (e^{(-2.4)} * 2.4^1) / 1! + (e^{(-2.4)} * 2.4^2) / 2!]\)

= \(1 - [(e^{(-2.4)} * 1) + (e^{(-2.4)} * 2.4) + (e^{(-2.4)} * 2.4^2 / 2)]\)

= 1 - 0.4060

= 0.5940 (rounded to four decimal places)

Therefore, the probability that X will be at least 2 is 0.5940.

Using a Poisson probability calculator, we can find:

P(2 < X < 4) = P(X = 3) + P(X = 4)

= \((e^{(-2.4)} * 2.4^3 / 3!) + (e^{(-2.4)} * 2.4^4 / 4!)\)

= 0.2229 + 0.0781

= 0.3010 (rounded to four decimal places)

Therefore, the probability that X will be between 2 and 4 (inclusive) is 0.3010.

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dy/dx = (sin(x) - y) / (x - cos(y)).This is the expression for dy/dx obtained through implicit differentiation of the given equation.

To find dy/dx using implicit differentiation, we differentiate both sides of the equation with respect to x. Let's go step by step:Differentiating the left-hand side:

d/dx(xy) + d/dx(cos(x)) = d/dx(sin(y))

Using the product rule, we have:

x(dy/dx) + y + (-sin(x)) = cos(y) * dy/dx

Rearranging the equation to isolate dy/dx terms:

x(dy/dx) - cos(y) * dy/dx = sin(x) - y

Factoring out dy/dx:

(dy/dx)(x - cos(y)) = sin(x) - y

Finally, we can solve for dy/dx by dividing both sides by (x - cos(y)):

dy/dx = (sin(x) - y) / (x - cos(y))

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the volume of the silo is approximately 11,657.88 cubic meters.

To find the volume of the silo, we need to calculate the volumes of the cylinder and the cone separately, and then add them together.

The radius of the base of the silo is half the diameter, so it's 10 meters / 2 = 5 meters.

The height of the cylinder is given as 27 meters. Since the height of the cone is half the height of the cylinder, the height of the cone is 27 meters / 2 = 13.5 meters.

The volume of a cylinder is calculated using the formula:

Volume of Cylinder = π * radius^2 * height

Plugging in the values, we get:

Volume of Cylinder = π * 5^2 * 27 = 3375π cubic meters (approximately 10,598.07 cubic meters)

The volume of a cone is calculated using the formula:

Volume of Cone = (1/3) * π * radius^2 * height

Plugging in the values, we get:

Volume of Cone = (1/3) * π * 5^2 * 13.5 = 337.5π cubic meters (approximately 1059.81 cubic meters)

Adding the volumes of the cylinder and the cone, we get:

Volume of Silo = 3375π + 337.5π = 3712.5π cubic meters (approximately 11,657.88 cubic meters)

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The number of pages that are in the book is 1 31/45 pages.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, Tyler reads 2/15 pages on Monday 1/3 on Tuesday and 2/9 on Wednesday and 3/4 on thursday .and has 14 pages left on friday how many pages are in the book.

The fraction for pages will be:

= 2/15 + 2/9 + 1/3 + 3/4 + 1/4

= 2/15 + 5/9 + 1

= 6 / 45 + 25/45 + 1.

= 1 31/45

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Complete question

tyler reades 2/15 pages on monday 1/3 on tuesday and 2/9 on wendsday and 3/4 on thursday .and has 1/4 pages left on friday how many pages are in the book

Answer:

inverse operations is with oppisite operations that undo each other.

open circle is circle not filled in to show that the point is a border value and is not included as part of the solution set.  

like terms is terms that have the same varible raised to the same exponent.

ordered pair is a group of two numbers written in the form (x, y) where the x value represents a horizontal position.

the last one numeric expressions is an expression involving only constants

Step-by-step explanation:

Answer:

inverse operations is with oppisite operations that undo each other.

open circle is circle not filled in to show that the point is a border value and is not included as part of the solution set.  

like terms is terms that have the same varible raised to the same exponent.

ordered pair is a group of two numbers written in the form (x, y) where the x value represents a horizontal position.

the last one numeric expressions is an expression involving only constants

Step-by-step explanation:

Answer:  option B

(B) y ≤ 1/3x – 4 <========+ 100%

Step-by-step explanation:

The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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C. True, because to use the Law of Sines, at least two sides must be known.

The Law of Sines is a trigonometric rule that relates the sides and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

To use the Law of Sines, at least two sides and the angle opposite one of them (or two angles and one side) must be known.

Therefore, the statement "The Law of Sines can be used to solve triangles where three sides are known" is false, as it is not necessary to use the Law of Sines to solve a triangle where all three sides are known.

In summary, the correct answer is C. True, because to use the Law of Sines, at least two sides must be known.

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According to the information presented in this video, all of the following activities are likely to occur in the information requirements determination​ (IRD) phase of systems analysis except beta testing.

According to the information presented in this video, all of the following activities are likely to occur in the information requirements determination (IRD) phase of systems analysis except beta testing. The IRD phase of the systems analysis process is used to determine information requirements for the system being developed. The IRD process identifies what information is needed to support business functions and operations.

The activities that are carried out during the IRD phase of the systems analysis process include: Reviews of paper-based forms and reports Interviews with system users Observation of system use Meetings with the development team Therefore, the answer is option C. Beta testing is not a part of the IRD phase of systems analysis.

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Answer:

a

Step-by-step explanation:

If a bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. The height of the 7th bounce of the ball is 0.7.

Given data:

First bounce = 3.75 feet

Successive bounce = 79% or 0.79%

Bounce = 7

Now let determine the height of thee 7th bounce of the ball using this formula

Height =  First bounce  × (Successive bounce) ^ Number of bounce

Let plug in the formula

Height = 3.75 × (0.79 ) ^7

Height  = 0.7

Therefore the height is 0.7.

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Answer:

F-50=B

also chill

P/6=2 is for the next problem

Step-by-step explanation:

the only question I see is : "what is the area of the puddle, when the employees arrive at 7 am ?".

well, in that case, it had rained for 4 hours with the hole in the roof (from 3am to 7am).

4 hours = 4×60 = 240 minutes.

that means the radius of the puddle grew to

240×0.1 = 24 cm

therefore the area of the puddle was

pi×r² = pi×24² = 576pi = 1,809.557368... cm² ≈

≈ 1,810 cm²

Answer:

720/60

=12

Yepz

Step-by-step explanation:

Hope it helps

Answer:

It's True

Step-by-step explanation:

1 minute = 60 words

then how many words in 12 minutes?

So, Multiply 12 with 60

12 × 60 = 720

Thus, 720 words can be type in 12 minutes

-TheUnknownScientist

37.5 degrees

we know angled like this always have 180 degrees total between the 2. which means we can set up a little equation to solve for x. The equation is (3x+22)+(x-4)= 180. Initially we can take the solid numbers (22 and -4) and get rid of them by taking them to the 180. 180- 22 is 158. 158 + 4 is 162. now we have 3x + x = 162. we combine like terms. means we end up with 4x =162. We now divide by 4 which means we get 40.5. Now we know x is 40.5. Now dbc is just 40.5- 4 which is 37.5.

The measure of angle ∠DBC is,

⇒ ∠DBC = 35.5°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Point D is in the interior of ∠ABC.

And, ∠ABD = (3x + 22)°

⇒ ∠DBC = (x - 4)°

Clearly, Both angle make a linear pair.

Hence, We get;

⇒ ∠ ABD + ∠DBC = 180°

⇒ (3x + 22) + (x - 4) = 180°

⇒ 3x + 22 + x - 4 = 180

⇒ 4x + 18 = 180

⇒ 4x = 180 - 18

⇒ 4x = 162

⇒ x = 162/4

⇒ x = 40.5

Hence, The measure of angle ∠DBC is,

⇒ ∠DBC = (x - 4)°

⇒ ∠DBC = (40.5 - 4)°

⇒ ∠DBC = 35.5°

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The straight-line distance from the wilderness area to the Morrisons' campsite is approximately 5 miles.

To find the straight-line distance from the wilderness area to the Morrisons' campsite, we can use the Pythagorean theorem.

Let's consider the campsite as the origin (0, 0) on a coordinate plane. The wilderness area is located 3 miles due north and 4 miles due east from the campsite. Therefore, its coordinates are (4, 3).

Using the Pythagorean theorem, the straight-line distance d is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates of the campsite (0, 0) and the wilderness area (4, 3) into the formula, we get:

d = √((4 - 0)² + (3 - 0)²)

= √(4² + 3²)

= √(16 + 9)

= √25

= 5

Therefore, the straight-line distance from the wilderness area to the Morrisons' campsite is approximately 5 miles.

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Answer:

n is 68 and m is 44

Step-by-step explanation:

Answer:

The program in Python is as follows:

age = int(input("Age: "))

if age>=13 and age <=19:

   print("Teenager")

else:

   print("Not a teenager")

Step-by-step explanation:

This gets input for age

age = int(input("Age: "))

This checks if age is between 13 and 19 (inclusive)

if age>=13 and age <=19:

If yes, the age is teenage

   print("Teenager")

If otherwise, the age is not teenage

else:

   print("Not a teenager")

(a) The type of bias in the survey is non-response bias

(b) The bias can be remedied by increasing the response rate, using follow-up methods, analyzing respondent characteristics, employing alternative survey methods, and utilizing statistical techniques such as weighting or imputation.

(a) Determining the type of bias in the survey:

The survey exhibits nonresponse bias.

Nonresponse bias occurs when the individuals who choose not to respond to the survey differ in important ways from those who do respond, leading to a potential distortion in the survey results.

(b) Suggesting a remedy for the bias:

One possible remedy for nonresponse bias is to increase the response rate.

This can be done by providing incentives or rewards to encourage participation, such as gift cards or entry into a prize draw.

Following up with nonrespondents through phone calls, emails, or personal visits can also help improve the response rate.

Additionally, comparing the characteristics of respondents and nonrespondents and adjusting the results based on any identified biases can help mitigate the bias.

Exploring alternative survey methods, such as online surveys or telephone interviews, may reach a different segment of the population and improve the representation.

Statistical techniques like weighting or imputation can be used to adjust for nonresponse and minimize its impact on the survey estimates.

Therefore, nonresponse bias is present in the survey, and remedies such as increasing the response rate, follow-up methods, analysis of respondent characteristics, alternative survey methods, and statistical adjustments can be employed to address the bias and improve the accuracy of the survey results.

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Based on the given circle with secants HIJ and LKJ, the length of HI to the nearest tenth is equal to 46.3 units.

In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to this circle, we have the following:

LJ × KJ = IJ × HI

37 × 15 = 12HI

555 = 12HI

HI = 555/12

HI = 46.3 units.

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The approximate distance between Khloe and school is given by 18.78 miles.

Representing Khloe's movements on a coordinate plane.

Let us assume that Khloe's starting point (her school) is at the origin (0,0).

She walks 20 miles due west,

which means she moves 20 units to the left on the x-axis. Her new position is (-20,0).

She then walks 8 miles due north,

which means she moves 8 units up on the y-axis.

Her new position is (-20,8).

Finally, she walks 3 miles due east,

which means she moves 3 units to the right on the x-axis.

Her new position is (-17,8).

Distance between Khloe's final position and her starting point (the school),

Use the Pythagorean theorem,

Distance = √((change in x)^2 + (change in y)^2)

⇒Distance = √((-17-0)^2 + (8-0)^2)

⇒Distance = √(289 + 64)

⇒Distance = √353

⇒Distance ≈ 18.78 miles

Therefore, Khloe is approximately 18.78 miles away from her school.

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Answer: d

Step-by-step explanation:

Note that the distance to the tower and the height of the tower create a right triangle at the base of the tower.  The equation to find the height of a right triangle is to multiply the length times the tangent of angle β.

Given:

b = a · tanβ

tan(30°) = √3/3

Step 1:  Solve

b = (30/1) · (√3/3)

b = (30 · √3) / (1 · 3)

b = (30√3) / (3)

b = 10√3

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer:

16

Step-by-step explanation:

let x be the unknown

1/8x =16/8

1/8x =2

x=8×2

x=16

The value of 1/8 times equals 16/8 will be 16.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that 1/8 times, what equals 16/8. Let x be the unknown. Let the unknown number be x. The value of x will be calculated as below:-

1/8x =16/8

1/8x =2

x=8×2

x=16

Therefore, the value of 1/8 times equals 16/8 will be 16.

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Answer:

The focus of the ellipse are;

(-12·√(10), -8) and (12·√(10), -8)

Step-by-step explanation:

The given equation for the ellipse is presented as follows;

\(\dfrac{x^2}{46} + \dfrac{(y + 8)^2}{26} = 1\)

From the general equation of the ellipse, we have;

\(\dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1\)

The focus of the ellipse are, (h - c₁, k) and (h + c₁, k)

By comparison, we get;

h = 0, k = -8, a = 46, b = 26

We have;

c² = a² - b²

c² = 46² - 26² = 1440

c = 12·√(10)

The focus of the ellipse are therefore;

(0 - 12·√(10), -8) = (-12·√(10), -8), and (0 + 12·√(10), -8) = (12·√(10), -8).

Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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The slope(m) of the line that passes through the points (1, −3) and (3, −5) is m = -1.

The slope of a line determines the inclination of the line with the positive x-axis.

The slope of the line passing through (x1, y1) and (x2, y2) is given by m =(y2 - y1) / (x2 - x1)

Given that,

Here, (x1, y1) = (1, −3) and (x2, y2) = (3, −5)

m = (y2 - y1) / (x2 - x1)

m = [-5 - (-3)] / [3 - 1]

m = [-5 + 3] / [2]

m = [-2] / 2

m = -1

Slope = m = -1

Thus, The slope(m) of the line that passes through the points (1, −3) and (3, −5) is m = -1.

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