each letter of the alphabet is written on a piece of paper and put in a hat. if a piece of paper is chosen at random, what is the probability that it will be a vowel? the number of favorable outcomes is . the number of possible outcomes is . so p(vowel)

fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1 , ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05 are the required functional estimations of a given representations.

However, we can estimate the partial derivatives with respect to x (fv) and y (ft) at the point (40,20) using the definition of partial derivatives:

fv = ∂f/∂x ≈ (f(40+h,20) - f(40,20))/h

where h is a small increment in the x direction. Similarly,

ft = ∂f/∂y ≈ (f(40,20+k) - f(40,20))/k

where k is a small increment in the y direction.

To estimate fv(40,20) and ft(40,20), we need to choose small values of h and k and evaluate the function at the corresponding points. Let's say h = 0.1 and k = 0.05:

fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1

ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05

We can then use these estimates to approximate the value of f(40.1,20.05) using the first-order Taylor approximation:

f(40.1,20.05) ≈ f(40,20) + fv(40,20)0.1 + ft(40,20)0.05

Note that this is an approximation and may not be very accurate if the function is highly nonlinear or has discontinuities. However, it can give us a rough idea of the value of f(40,20) and how it changes with small variations in x and y.

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An important advantage of experiments over observational studies is that experiments can control for lurking variables to have a stronger case for causation. Another advantage is that experiments can isolate the effects of a specific treatment.

What is an experiment?

An experiment is a scientific study that is designed to test a hypothesis or investigate a cause-and-effect relationship between variables. Experiments allow researchers to manipulate one variable (independent variable) and observe the effect on another variable (dependent variable) while controlling for other variables that may affect the outcome (lurking variables).

What are observational studies?

Observational studies are research designs that observe and collect data from participants without manipulating any variables. In observational studies, the researchers only observe and record what happens naturally without intervening in any way. Observational studies are used when experiments are not feasible or ethical.

What are the advantages of experiments over observational studies?

Experiments have several advantages over observational studies. Some of the advantages include:

Control over variables: Experiments allow researchers to control for variables that may affect the outcome by manipulating one variable (independent variable) and keeping all other variables constant. This helps researchers to establish a cause-and-effect relationship between variables.

Isolation of specific effects: Experiments can isolate the effects of a specific treatment by comparing outcomes between treatment groups and control groups. This helps researchers to determine the effectiveness of the treatment with a high degree of accuracy.

Similarity between treatment groups: Experiments can ensure that approximately the same number of subjects is assigned to each treatment group, thereby minimizing the effects of individual differences on the outcome. This increases the statistical power of the study and reduces the likelihood of obtaining spurious results.

Control of extraneous variables: Experiments can control for lurking variables (extraneous variables) that may affect the outcome by manipulating one variable (independent variable) and keeping all other variables constant. This helps researchers to establish a strong case for causation.

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Answer:

To find the volume of a prism, you need to multiply the area of the base by the height of the prism. Here are the steps:

Identify the shape of the base of the prism. It could be a rectangle, square, triangle, hexagon, or any other polygon.

Find the area of the base of the prism. The formula for finding the area of different shapes are:

Rectangle: A = length x width

Square: A = side x side

Triangle: A = (base x height) / 2

Hexagon: A = (3 x √3 x side²) / 2 (where side is the length of one of the sides of the hexagon)

Determine the height of the prism. This is the perpendicular distance between the two parallel bases.

Multiply the area of the base by the height of the prism. The formula is:

Volume = Area of Base x Height

For example, if the base of the prism is a rectangle with length 4 cm and width 5 cm, and the height of the prism is 10 cm, the volume of the prism would be:

Volume = 4 cm x 5 cm x 10 cm

= 200 cubic cm

Therefore, the volume of the prism is 200 cubic cm.

The simplified algebraic expression for the perimeter of the yard is 28m+10x, and if x=3m, then the perimeter is 58m.

The simplified algebraic expression for the perimeter of the yard is 28m+10x, and if x=3m, then the perimeter is 58m.

In the given figure, the yard is in the shape of a rectangle with dimensions (4x - 6) m and (2x + 3) m. The perimeter of a rectangle is the sum of the lengths of all four sides, which can be expressed as:

Perimeter = 2(Length + Width)

Perimeter = 2(4x - 6 + 2x + 3) m

Perimeter = 2(6x - 3) m

Perimeter = 12x - 6 m

So, a simplified algebraic expression for the perimeter of the yard is 12x - 6 m.

To find the perimeter in meters when x = 3 m, substitute x = 3 into the algebraic expression for perimeter:

Perimeter = 12(3) - 6 m

Perimeter = 30 m

Therefore, the perimeter of the yard when x = 3 m is 30 meters.

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Answer: the train got a head start

Step-by-step explanation:

the train got a head start

the probability that the difference between the sample mean and the true population mean will not exceed 0.5 inch is 0.9544

We can use the central limit theorem to approximate the distribution of the sample mean. Since the sample size is large (n=100), the sample mean follows approximately a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size (i.e., 2.5/sqrt(100) = 0.25).

Let X be the sample mean, then we want to find P(|X - μ| ≤ 0.5), where μ is the population mean.

Using the standard normal distribution, we can standardize X as follows:

Z = (X - μ) / (σ / sqrt(n)) = (X - μ) / 0.25

So we want to find P(|Z| ≤ 2), where Z follows a standard normal distribution.

Using a standard normal distribution table or calculator, we find that P(|Z| ≤ 2) = 0.9544.

Therefore, the probability that the difference between the sample mean and the true population mean will not exceed 0.5 inch is 0.9544

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Answer:

Range = Highest number -Lowest number

= 13-2=11

Answer:

11

Step-by-step explanation:

Highest number = 13

Lowest number = 2

Range = highest number - lowest number

Range = 13 - 2 = 11

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━

hope it helps⸙

Using trigonometry, we can determine that the length of the support wire is approximately 91.7 meters, by using the tangent function of the angle and solving for the hypotenuse of the right triangle formed by the tower, the support wire, and the ground.

The correct option is (c). A graphical method of representing the sample points of an experiment is a dot plot.

Dot plot is a graphical method of representing the sample points of an experiment. In a dot plot, each point represents an observation in the sample, and the points are placed on a number line.

A stem-and-leaf display is another graphical method of representing the sample points of an experiment. In a stem-and-leaf display, the digits in the observation are separated into two parts, with one part representing the "stem" and the other representing the "leaf."

A bar chart is a graphical method of representing data that uses bars to represent different categories or values.

A tree diagram is a graphical method of representing a series of events or outcomes.

Therefore, option (c) dot plot is the graphical method of representing the sample points of an experiment.

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Answer:

[tex]744x100=7,440[/tex]

Step-by-step example

all to do this is to 744x10

and it would help if you got this simple answer I hope this helps:D

Step-by-step explanation:

Without seeing the graph, it's difficult to determine the exact solution to the system of equations. However, the point of intersection between the two lines represents a solution that satisfies both equations. To find the x-coordinate of this point, you can use algebraic methods, such as substitution or elimination, to solve for the value of x.

the rate of change of the distance between the car and Hartville is:

dd/dt = (111*48)/sqrt(48477) ≈ 25.63 mph

We can use the Pythagorean theorem to determine the distance between the car and Hartville at any time. Let's call this distance "d".

At the start of the trip, d = [tex]\sqrt{(186^2 + 0^2) }[/tex]= 186 miles.

After traveling 111 miles due east, the car will have traveled for t = 111/48 = 2.3125 hours. During this time, the car will have moved north by a distance of 2.3125 * 0 = 0 miles, and east by a distance of 2.3125 * 48 = 111 miles.

Now, we can use the chain rule to find the rate of change of d with respect to time:

[tex]d^2 = x^2 + y^2[/tex]

Differentiating both sides with respect to time, we get:

2d(dd/dt) = 2x(dx/dt) + 2y(dy/dt)

where x and y are the east and north distances traveled by the car, respectively.

Since the car is traveling due east, dy/dt = 0. Also, at the instant when the car is 111 miles east of Hartville, x = 111 and y = 186.

Substituting these values, we get:

2d(dd/dt) = 2111(48) + 2186(0)

Simplifying:

dd/dt = (111*48)/d

At the instant when the car is 111 miles east of Hartville, we have:

d = [tex]\sqrt{(48477)}[/tex]

So the rate of change of the distance between the car and Hartville is:

dd/dt = (111*48)/[tex]\sqrt(48477)[/tex] ≈ 25.63 mph

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Answer:

Step-by-step explanation:

E(lh girls) [tex]=0.2\times 320=64[/tex]

E(lh boys) [tex]=0.1 \times 250 =25[/tex]

Estimated total left handed students [tex]=64+25=89[/tex]

Answer:

x = 65° , y = 115° , z = 65°

Step-by-step explanation:

consecutive angles in a parallelogram are supplementary , then

x + 115° = 180° ( subtract 115° from both sides )

x = 65°

opposite angles in a parallelogram are congruent , then

y = 115° and z = x = 65°

Answer:

See below!

Step-by-step explanation:

So,

So,

y + x = 180°

115 + x = 180

x = 180 - 115

Again,

z = x (Opposite angles)

So,

[tex]\rule[225]{225}{2}[/tex]

The algebraic expression for the particle's velocity vₓ at a later time t is v(t) = ct²/2m +v₀ₓ.

Given that,

c = speed of light

t = time

v₀ₓ = initial velocity of particle

m = mass of particle

Velocity and acceleration are related through time. Acceleration is the rate of change of velocity, which is represented graphically as the slope of the velocity vs. time line. Velocity can be represented as the area underneath an acceleration vs. time line.

Newton's second law declares that an object having mass m will accelerate due to a net force (F) will accelerate at a rate of:

α = F/m

Therefore, the function that describes the acceleration at any point in time of the particle is:

α(t)=ct/m

The velocity function is the integral of the acceleration function, so we get:

v(t)= ∫ct/m dt

= ct²/2m +C

where the constant C is the initial velocity of the particle at time t=0. Therefore, the velocity function representing the velocity at any point in time is:

v(t) = ct²/2m +v₀ₓ

Therefore, the algebraic expression for the particle's velocity vₓ at a later time t is v(t) = ct²/2m +v₀ₓ.

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Lori will receive a semiannual interest of $950 from the bond with a face value of $20,000 and a coupon rate of 9.5%, which will mature in 20 years.

To calculate the semiannual interest that Lori will receive from the bond, we need to use the following formula:

Semiannual interest = (Coupon rate x Face value) / 2

Substituting the given values, we get:

Semiannual interest = (9.5% x $20,000) / 2

Semiannual interest = ($1,900) / 2

Semiannual interest = $950

Therefore, Lori will receive a semiannual interest of $950 from the bond. This means that she will receive a total of $1,900 in interest every year until the bond matures in 20 years.

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Every student may take on any part, and no student may take on more than one role. Hence, it is feasible to have 45 different casts.

In contrast, there are various techniques to select r things from a set of n objects and arrange these r objects in permutations.

The permutations formula itself states that selection should come first (nCr), followed by arrangement (r).

the given :

10 students are working on a skit,

2 different roles. each role can be played by anyone

n = 10

r = 2

nPr = nCr x r!

nCr = n!/r!(n-r)!

so,

nCr = 10!/2!(10-2)!

nCr = 10x9/2x1

nCr = 45

so, the 45 different casts are possible

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Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. -1/4 can be expressed as a ratio of -1 and 4, so it is a rational number.

An irrational number cannot be stated using fractions, whereas a rational number can be expressed as the ratio of two integers with the denominator not equal to zero. Irrational numbers are non-terminating and non-recurring, whereas rational numbers have terminating digits.

Rational numbers contain the integer 0. It is not illogical to think that 0 is a number.

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Alien is an extraterrestrial species or a hypothetical species that lives beyond the planet Earth. They are beings from other planets that can travel in spacecraft. They are often depicted as having unique or supernatural powers that are beyond those of humans. The question given is about an alien species that leaves its planet to explore other planets. We are given the information that 120 aliens have left planet zenith over the past 3 years. We need to write an expression to model the change in aliens per year on planet zenith. We can write the following expression:Change in aliens per year = Total number of aliens left / Number of yearsThe total number of aliens left in the past 3 years is 120. Therefore,Total number of aliens left = 120Number of years = 3Substituting the values in the above expression, we get:Change in aliens per year = 120 / 3Change in aliens per year = 40 aliens per yearThe expression to model the change in aliens per year on planet zenith is 40 aliens per year. This means that 40 aliens are leaving planet zenith each year to explore other planets in the universe.

The average change in aliens per year can be calculated using the above expression. The change in aliens per year is 40 aliens. Hence, every year 40 aliens are leaving planet Zenith to explore other planets in the universe.

To model the change in aliens per year on planet Zenith, an expression can be formed from the given data. Let's look into the steps to model the change in aliens per year on planet zenith.

Step 1: We are given that 120 aliens have left planet zenith over the past 3 years.

Step 2: To find the change in aliens per year, we can divide the total number of aliens who left the planet over the past 3 years by the number of years.

Change in aliens per year = (120 aliens) / (3 years)

Step 3: Simplifying the above expression we get,Change in aliens per year = 40 aliens per year

Therefore, the expression to model the change in aliens per year on planet Zenith is 40 aliens per year. This implies that every year 40 aliens are leaving planet Zenith to explore other planets in the universe.

Evaluation: As per the given problem, 120 aliens have left planet Zenith over the past 3 years.

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Answer: 2+ 2

Step-by-step explanation:

no problem

The slice for apple will have an angle of 60 degrees, the slice for banana will have an angle of 90 degrees, the slice for guava will have an angle of 30 degrees, and the slice for grapes will have an angle of 180 degrees.

A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice is proportional to the quantity it represents. Pie charts are commonly used in business, media, and other fields to represent percentages, ratios, and proportions. They are useful for quickly understanding the relative sizes of different categories or groups in a dataset.

Here,

To create a pie chart from the given data, we first need to calculate the angle of each slice of the pie chart. To do this, we use the following formula:

Angle for a slice = (Frequency of the category ÷ Total frequency) × 360°

Using the given data, we can calculate the angle of each slice as follows:

Angle for apple = (12 ÷ 72) × 360° = 60°

Angle for banana = (18 ÷ 72) × 360° = 90°

Angle for guava = (6 ÷ 72) × 360° = 30°

Angle for grapes = (36 ÷ 72) × 360° = 180°

Now, we can draw a circle and divide it into 12 parts (each representing 30 degrees). Then, we can draw the slices of the pie chart using the angles we calculated above.

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The answer is k = 1/5, which represents the constant of proportionality between y and x in the equation y = x/5.

What is proportion?

Proportion is a mathematical concept that describes the equality of two ratios. In other words, it is a statement that two ratios or fractions are equal.

To determine if the equation y = x/5 represents a proportional relationship, we need to check if there is a constant of proportionality between y and x.

If there is a constant of proportionality, then we can write y = kx, where k is the constant of proportionality. In other words, the ratio of y to x is always the same constant value.

To find the constant of proportionality for the equation y = x/5, we can rearrange the equation as:

y/x = 1/5

This means that the ratio of y to x is always 1/5. Therefore, there is a constant of proportionality, which is 1/5.

So, the equation y = x/5 represents a proportional relationship, and the constant of proportionality is 1/5.

Therefore, the answer is k = 1/5, which represents the constant of proportionality between y and x in the equation y = x/5.

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(a) The probability that there is exactly one car and exactly one bus during a cycle is 0.020.

(b) The probability that there is at most one car and at most one bus during a cycle is 0.105.

(c) The probability that there is exactly one car during a cycle is 0.100, and the probability that there is exactly one bus during a cycle is 0.200. The probability that there is exactly one car is also 0.050.

(a) To find the probability that there is exactly one car and exactly one bus during a cycle, we need to look at the cell in the table where x = 1 and y = 1. This cell has a probability of 0.020. Therefore, the probability that there is exactly one car and exactly one bus during a cycle is 0.020.

(b) To find the probability that there is at most one car and at most one bus during a cycle, we need to add up the probabilities of the cells where either x = 0 or x = 1, and either y = 0 or y = 1. These cells are

x = 0, y = 0: 0.025

x = 0, y = 1: 0.010

x = 1, y = 0: 0.050

x = 1, y = 1: 0.020

Adding up these probabilities, we get

0.025 + 0.010 + 0.050 + 0.020 = 0.105

Therefore, the probability that there is at most one car and at most one bus during a cycle is 0.105.

(c) To find the probability that there is exactly one car during a cycle, we need to add up the probabilities of the cells where x = 1. These cells are

x = 1, y = 0: 0.050

x = 1, y = 1: 0.020

x = 1, y = 2: 0.030

Adding up these probabilities, we get

0.050 + 0.020 + 0.030 = 0.100

Therefore, the probability that there is exactly one car during a cycle is 0.100.

To find the probability that there is exactly one bus during a cycle, we need to add up the probabilities of the cells where y = 1. These cells are

x = 0, y = 1: 0.010

x = 1, y = 1: 0.020

x = 2, y = 1: 0.050

x = 3, y = 1: 0.060

x = 4, y = 1: 0.040

x = 5, y = 1: 0.020

Adding up these probabilities, we get

0.010 + 0.020 + 0.050 + 0.060 + 0.040 + 0.020 = 0.200

Therefore, the probability that there is exactly one bus during a cycle is 0.200.

Finally, the probability that there is exactly one car can also be obtained by summing the probabilities of the cells in the first row of the table

0.025 + 0.010 + 0.015 = 0.050

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So, the correct option is: The median is the best measure of center because there are outliers present.

A line plot is a type of graph that is used to display data along a number line. In a line plot, each data point is represented by a dot or mark placed above the corresponding value on the number line. Line plots are commonly used to represent small to moderate-sized data sets, especially those with discrete values or categories. The line plot typically consists of a horizontal line, called the axis, representing the numerical values of the data, with marks or dots above the line indicating the frequency or count of each value in the data set. Each mark or dot is placed directly above the value on the number line that it represents.

Here,

Since the data in the graph is skewed to the right, there are outliers present. Outliers are data points that are significantly different from the other values in the data set. Therefore, the median is the most appropriate measure of center to represent the data in the graph because it is less affected by outliers compared to the mean.

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Answer: A - (-5, 43)

Step-by-step explanation:

3cm is the length of the third side.

Given that an obtuse triangle with area 12 has two sides of lengths 4 and 10.

To find the length of the third side, we can use the formula for the area of a triangle; Area of a triangle = 1/2 × base × height, where base and height are perpendicular to each other.

Considering 4 and 10 as the base and height of the triangle respectively, the area of the triangle will be;

Area of the triangle = 1/2 × 4 × 10Area of the triangle

= 20 cm²

But given that the area of the triangle is 12 cm².

Thus, 20 cm² = 1/2 × 4 × 10 ⇒ length of the third side = 3 cm

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Answer:

x = 8

y = 12

Step-by-step explanation:

m∠A = sin⁻¹(9/15) = 36.87⁰

cos36.87 = y/15

y = 15(cos36.87) = 12

sin36.87 = 12/(12+x)

12 + x = 12/(sin36.87)

x = 12/(sin36.87) - 12 = 8

Answer:

x ≤ 55/7

Step-by-step explanation:

7x - 5 ≤ 50

7x ≤ 55

x ≤ 55/7