Conduct a survey with a minimum of 20 people. Complete the designed questionnaire in 1.2. Remind participants why you are doing survey and that their information will be kept confidential. Submit 20 original completed questionnaires.

Answers

Answer 1

Some of the tips which is used to conduct a survey are:

Determine the purpose of the survey and define the population of interest.Design the questionnaire and ensure that the questions are clear and concise.Select a sample from the population and distribute the questionnaire to the participants.Remind participants why you are conducting the survey and assure them that their responses will be kept confidential.

What is the need to conduct a survey (questionnaire)?

Conducting a survey is an important tool for gathering information from a large and diverse group of people. Its allows allow researchers to obtain data from a representative sample of the population, which can then be used to make informed decisions, identify trends, and measure changes over time.

Also important, its can provide insight into people's attitudes, beliefs, and behaviors, which can be valuable in developing marketing strategies, designing programs and policies, and making important decisions.

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Related Questions

Increase £16470.45 by 3.5%
Give your answer rounded to 2 DP

Answers

Step-by-step explanation:

"increase" means to take the original 100% and put an additional 3.5% of these 100% on top of it.

so, we have to calculate

100% + 3.5% of £16470.45

100% of £16470.45 = £16470.45 × 100/100

3.5% of £16470.45 = £16470.45 × 3.5/100

the sum is therefore

£16470.45 × (100/100 + 3.5/100) =

= £16470.45 × (1 + 0.035) = £16470.45 × 1.035 =

= £17,046.91575 ≈ £17,046.92

Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 JQK
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?

Answers

The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.

The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.

Actual count of K = 12 - 2 = 10

Total count of 6 and K = 7 + 10 = 17

The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:

Experimental probability = (frequency of K or 6) / (total number of draws)

Experimental probability = 17 / 100

Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

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I will mark you brainiest!

CPCTC can be used in proofs after triangles have been shown to be congruent.
A) True
B) False

Answers

Answer:

True.

Step-by-step explanation:

CPCTC is commonly used at or near the end of a proof, which asks the student to show that two angles or two sides are congruent. It means that once two triangles are proven to be congruent, then the three pairs of sides that correspond must be congruent and the three pairs of angles that correspond must be congruent.

Give the interval(s) on which the function is continuous.
g(t) = 1/√16-t^2

Answers

The function g(t) is defined as:

g(t) = 1/√(16-t^2)

The function is continuous for all values of t that satisfy the following conditions:

The denominator is non-zero:

The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].

There are no vertical asymptotes:

The function does not have any vertical asymptotes, because the denominator is always positive.

Thus, the function g(t) is continuous on the interval [-4,4].

A company has a fixed cost of $1277 each day to run their factory and a variable cost of $1.93 for each widget they produce. How many widgets can they produce for $2127?

Answers

The company can produce approximately 425 widgets for $2127.

What is cost function ?

The key concept used here is the concept of cost functions, which is an important concept in economics and business. A cost function is a mathematical function that expresses the total cost of production as a function of the level of output produced. In this case, the cost function is a linear function of the form C = a + bx, where C is the total cost, a is the fixed cost, b is the variable cost per unit, and x is the level of output.

Finding the number of widgets the company can produce given a fixed cost and a variable cost per widget :

To solve this problem, we can set up an equation that relates the total cost to the number of widgets produced.

Let x be the number of widgets produced.

The total cost C is given by:

C = fixed cost + variable cost

C = 1277 + 1.93x

We want to find the number of widgets produced for a total cost of $2127. So we can set up an equation:

2127 = 1277 + 1.93x

Subtracting 1277 from both sides gives:

850 = 1.93x

Dividing both sides by 1.93 gives:

x ≈ 439.9

Since we can't produce a fractional number of widgets, we need to round down to the nearest integer. Therefore, the company can produce approximately 425 widgets for $2127.

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59, 60, 61, 62, 63, 64, 65, and 66 Find the values of x for which the series converges. Find the sum of the series for those values of x. 59. § (-5)".z" n=1 Answer + 00 60. Σ(α + 2)" n=1 61. (x - 2)" 3" n=0 Answer + 62. (-4)" (x - 5) n=0 00 63. 2" ch NO Answer

Answers

The values of x for which the series converges is x ∈ (-1/5, 1/5). The sum of the series for those values of x is (-5x)/(1 + 5x).

The series is [tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex].

We can write this series as [tex]\Sigma^{\infty}_{n=1}(-5x)^n[/tex].

This is a infinite geometric series with first term a = -5x and common ration r = -5x.

It is convergent when

|r| < 1

|-5x| < 1

|-5| |x| < 1

5|x| < 1

Divide by 5 on both side, we get

|x| < 1/5

The series is convergent when x ∈ (-1/5, 1/5).

Sum of the series is

Sₙ = a/1 - n

Sₙ = (-5x)/{1 - (-5x)}

Sₙ = (-5x)/(1 + 5x)

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The complete question is:

Find the values of x for which the series converges. Find the sum of the series for those values of x.

[tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex]

To the nearest hundredth, what is the volume of the sphere? (Use 3.14 for pie.)

Answers

Therefore, the volume of the sphere to the nearest hundredth is 724,775.70 cubic millimeters.

What is volume?

Volume is a measurement of the amount of space occupied by a three-dimensional object. It is often expressed in units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or gallons (gal), depending on the context. The volume of a solid object can be calculated by multiplying its length, width, and height or using a specific formula depending on the shape of the object. For example, the volume of a rectangular box can be calculated as length x width x height, while the volume of a cylinder can be calculated as π x radius² x height. In general, volume is an important concept in many fields, including physics, chemistry, engineering, and architecture. It is often used to describe the capacity of containers, the displacement of fluids, and the amount of material used in construction or manufacturing.

Here,

The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is approximately 3.14.

Substituting the given value of the radius, we get:

V = (4/3) x 3.14 x 48³

V ≈ 724,775.68 cubic millimeters

Rounding this value to the nearest hundredth, we get:

V ≈ 724,775.68 ≈ 724,775.70 cubic millimeters (rounded to two decimal places)

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10 POINTS NEED HELP ASAP!!!! PLEASE HELP ME FIND THE AREA AND THE PERIMETER!!

Answers

The area of the composite shape using the area formula for the different shapes is 460.48ft².

What are composite shapes?

The area of composite shapes refers to the space occupied by any composite shape. A composite shape is a shape that is made by connecting a few polygons to form the required shape.

These figures or shapes can be built from a wide range of shapes, such as triangles, squares, quadrilaterals, etc. Divide a composite item into basic forms such a square, triangle, rectangle, or hexagon to get its area.

Now in the question,

First let us find the area of the semi-circle.

Area of semi-circle = πr²/2

= [3.14 × (16/2) ²]/2

= (3.14 × 8²)/2

= 200.96/2

= 100.48ft²

Now coming to the rectangle,

area of the rectangle = l × b

= 20 × 15

= 300ft²

Now for calculating the area of the triangle,

area = 1/2 × b × h

= 1/2 × 12 × 10

= 60ft²

Therefore, the area of the total figure = 100.48 + 300 + 60 = 460.48ft².

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g suppose x and y are two random variables. you don't know their distribution, but someone tells you e[x]

Answers

When x and y are independent variables with x having uniform distribution (0,1) and y having exponential distribution respectively, then e (X+Y) is 3/2, E(XY) is 1/2, E (x-y)2 is 4/3, and e (x2 e24) is -1/3 22etyx u (0,1) > Independent y exp (1) > Independent

The exponential distribution is a continuous probability distribution used in probability theory and statistics that frequently addresses the amount of time until a given event occurs. Events occur continually, independently, and at a steady average pace during this process.

E (x) = 0+1/2 = 1/2

v (x) = [1 – 0]2 / 12 = 1/12

E x2 = v (x) + [Ex]2

      = 1/12 + 1/4 = 1+3/12 = 4/12 = 1/3

E (y) = 1  v(y)=1  

E y2= 1+1= 2

Eety = ∫0etye-ydy  

Eety  =  ∫0e-y (1 – t)dy  

a : E (x+y) = E (x) + E(y)

      E (x+y) = 1/2+1 = 3/2

b: E (xy) = E (x) E(y) = 1/2 x 1 = 1/2

c: E (x+y)2 = E (x2 - 2xy+ y2)

 =  1/3 - 2 x 1/2 + 2

  = 1/3 + 1 = 4/3

d. E x2e24

= 1/3 x -1 = - 1/3

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You are playing a game with a friend. It costs you $2 to play. If you roll a 1 on a 6-sided die you win $4. If you roll a 2, 3, 4, 5, or 6 you win nothing and lose $2 the cost to play. Calculate the expected value for this game. How much should the player be willing to to pay to play this game and not lose money in the long run?

Answers

The player should be willing to pay up to $12 to play this game and not lose money in the long run.

How to calculate the expected value for this game.

First we need to multiply the probability of winning by the amount won and subtract the probability of losing by the amount lost.

The probability of rolling a 1 on a 6-sided die is 1/6, and the probability of rolling any other number is 5/6.

So, the expected value of the game is:

(1/6) x $4 - (5/6) x $2

= ($4/6) - ($10/6)

= -$1/3

This means that on average, for every game played, the player can expect to lose $1/3.

To find out how much the player should be willing to pay to play this game and not lose money in the long run, we can set the expected value equal to zero:

(1/6) x $4 - (5/6) x $2 = $0

Simplifying the equation, we get:

$4/6 = $10/6

Multiplying both sides by x, we get:

(1/6) x - $2 = 0

Solving for x, we get:

x = $12

Therefore, the player should be willing to pay up to $12 to play this game and not lose money in the long run.

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PLEASE HELPPPPP 30 POINTSSSS!

Answers

Answer:

the answer will be 117

Step-by-step explanation:

you need to multiply

Someone plezzz help me

Answers

Neither anushka nor lukas are correct as both of their calculations are wrong.

How are linear equations solved?

Basic arithmetic operations like addition, subtraction, multiplication, and division are used to isolate the variable on one side of a linear equation and solve it. The objective is to make the equation as simple as possible until the variable can be identified and its value calculated. In order to solve a linear equation, you must first combine like terms to simplify the expressions on both sides of the problem.

Then, you can use inverse operations to get rid of constants and coefficients. The value of the variable can be ascertained by solving for it once it has been isolated. By looking at the coefficients and constants of the equation, it can be established if the equation has no solution or infinite solutions. In various disciplines, such as science, engineering, and finance, linear equations are used to represent connections between variables.

2/5b + 1 = -11

2/5b = -12

b= -12 x 5/2

b = -30

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Find the missing length indicated

Answers

The value of x is 5

Define the term Similar triangles?

Triangles with the same shape but different sizes are said to be similar triangles. To be more specific, two triangles are comparable if their respective sides are proportionate and their corresponding angles are congruent.

Two triangles are similar if corresponding angles are congruent and corresponding sides are proportional.

from the below figure, both the triangles are similar, ∆ABC ≈ ∆EFB

By using Thales's theorem, the ratio of the sides of triangles are;

BE/EA = BF/FC

15/30 = x/10    

x = 5

Therefore the value of x is 5

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The ratio of triangle sides can be calculated using Thales' theory, and it is the value of x is 5

Define the term Similar triangles?

Similar triangles are those with the same shape but varying sizes. To be more precise, two triangles are comparable if their matching angles and respective sides are congruent.

If matching sides are proportional and corresponding angles are congruent, two triangles are similar.

Both triangles in the following figure are comparable ∆ABC ≈ ∆EFB

The ratio of triangle sides can be calculated using Thales' theory, and it is;

BE/EA = BF/FC

15/30 = x/10    

x = 5

Therefore the value of x is 5

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5) What is the probability of picking a vowel, replacing it
and then picking a consonant from the word "SLEEP"?

Answers

The probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is approximately 0.096 or 9.6%.

What is probability?

Probability is usually expressed as a number between 0 and 1, with 0 meaning that the event is impossible and 1 meaning that the event is certain.

According to question:

There are two vowels (E) and three consonants (S, L, P) in the word "SLEEP".

The probability of picking a vowel on the first draw is 2/5, because there are two vowels out of five letters total.

Since we replace the vowel we picked, the probability of picking another vowel on the second draw is also 2/5.

The probability of picking a consonant on the third draw is 3/5, because there are three consonants left out of five letters total.

Therefore, the probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is:

(2/5) x (2/5) x (3/5) = 12/125 or approximately 0.096 or 9.6%.

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d. Two judges in a beauty contest rank the ten competitors in the following order.

Do d. Two judges in a beauty contest rank the ten competitors in the following order.

Do the two judges appear to agree in their standard? the two judges appear to agree in their standard?

Answers

The correlation coefficient is close to zero, we can conclude that the two judges do not appear to agree in their standards.

What is correlation and causation in statistics?

Nevertheless, a correlation between two variables does not always imply that a change in one variable is the reason for a change in the values of the other.

There is a causal link between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.

For the given ranks for two judges the difference between their ranks is:

d: 0.0 4.0 -2.0 1.0 -0.5 1.5 -1.0 -1.0 0.5 2.0

Squaring the given distance we have:

d²: 0.0 16.0 4.0 1.0 0.25 2.25 1.0 1.0 0.25 4.0

Σd² = 29.75

The Spearman's rank correlation coefficient is given as:

ρ = 1 - (6Σd²)/(n(n²-1))

ρ = 1 - (629.75)/(10(10²-1))

ρ ≈ 0.03

Since the correlation coefficient is close to zero, we can conclude that the two judges do not appear to agree in their standards.

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The complete question is:

The Millers have hired an interior designer to decorate their family room. They want to have a 29" by 29" oil painting framed and incorporated in the design plan. If the designer chooses molding that is 4" wide and is priced at $3.65 per inch, how much will the molding cost (before tax)?

Answers

Answer: I really don't know i'm just trying to get a quest done sorry

Suppose a student takes mathematics and economics as subjects. He obtains the following marks on his tests 82% for maths and 89% for economics. Using the available information determine how the student performed relative to the rest of the class in each subject. Describe this in terms of where his z-scores lie on the normal distribution curve. In which subject did he perform better?

Information
Mathematics
Mean 68
Standard deviation 8

Economics
Mean 80
Standard deviation 6

Answers

Answer:

The student's z-score for mathematics is 0.75, which means that his score is 0.75 standard deviations above the mean. This puts him in the upper quartile of the class, indicating that he performed better than 75% of the class.

The student's z-score for economics is 1.5, which means that his score is 1.5 standard deviations above the mean. This puts him in the upper quintile of the class, indicating that he performed better than 80% of the class.

The student performed better in economics than in mathematics.

Express using algebra:
Z increased by 16%

Answers

Answer:

Let's start by expressing "Z increased by 16%" using algebra.

Let Z be the original value of some quantity.

To increase Z by 16%, we need to add 16% of Z to Z:

Z + 0.16Z

Simplifying this expression by factoring out Z, we get:

Z(1 + 0.16)

Combining like terms, we have:

Z(1.16)

Therefore, "Z increased by 16%" can be expressed algebraically as:

Z increased by 16% = Z(1.16)

Answer:

z(1.16)

Step-by-step explanation:

What percentage decrease in profits from 2021 to 2022 would imply that profits were equal in 2020 and 2022?

Answers

This means that in order for the profits in 2022 to match those in 2020, the profits in 2021 would also need to match those in 2020.

 [tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.

What does “mean profit” mean?

Profits for mesne. According to Section 2(12) C.P.C., the term “mesne profit” refers to any earnings that the person who is in wrongful possession of a piece of property has actually received or may obtain in the future. High Court of Telangana.

The earnings in 2022 must match the profits in 2020, hence we must choose the value of r such that:

[tex]P \times(1-r/100)^² = P[/tex]

By simplifying and dividing both sides by P, we obtain:

[tex](1-r/100)^² = 1[/tex]

Taking the square root of both sides, we get:

1-r/100 = ±1

Each time we solve for r, we obtain:

[tex]1-r/100 = 1[/tex] , which implies [tex]r = 0[/tex]

and

 [tex]1-r/100 = -1,[/tex] which implies [tex]r = 200[/tex]

We reject the [tex]r = 200[/tex] Option because a percentage drop cannot be larger than 100%.

Therefore,  [tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.

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which statemnt is ture when the dimensions of a two-dimensional figures are dilated by a scale factor of 2

Answers

When a shape is dilated, the size of the shape changes. The true statement is (d) The scale factor is 2.5.

Dilation:

Dilation is the process of changing the size of an object or shape by reducing or increasing its size by a specific scale factor. For example, a circle with a radius of 10 units shrinks to a circle with a radius of 5 units. Applications of this method are in photography, arts and crafts, sign making and more.

According to the Question:

How to determine the scale factor

In figure A, we have:

Length = 0.6

In figure B, we have:

Length =1.5

The scale factor is then calculated as:

K = 1.5/0.6

Dividing the equation:

k = 2.5

Hence, the true statement is (d) The scale factor is 2.5.

Complete Question:

The first figure is dilated to form the second figure. Which statement is true?

The scale factor is 0.4.

The scale factor is 0.9.

The scale factor is 2.1.

The scale factor is 2.5.

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A firm is a monopoly for the good it produces. Its average cost function is AC = 9+(3/10)q+30/q, where q is the quantity produced. The demand equation for its good is given by q = 40 - (4/3)p where p is the price.
(a) Find expressions, in terms of q, for the total revenue.
(b) What is the equation for the Total cost?
(c) Find the expression for profit. (d) Find the total output and revenue at the break even point.
(e) Find the profit when 20 units are produced.
(f) Find the profit when 7 units are produced.
(g) Find the output required to obtain a profit of RM100.​

Answers

The answer of the given question is (a) TR = p(40 - (4/3)p), or TR = 40p - (4/3)p² , (b)  TC = 9q + (3/10)q² + 30 , (c) π = 40p - (4/3)p² - 9q - (3/10)q² - 30 , (d) TR ≈ 342.67 , (e) the profit when 20 units are produced is approximately RM188.27 , (f)  the profit when 7 units are produced is approximately -RM24.44, indicating a loss , (g) the output required to obtain a profit of RM100 is approximately 8.78 units.

What is Equation?

An equation is  mathematical statement that asserts yhe equality of two expressions. It typically consists of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division, among others. Equations are often used to solve problems, to model real-world phenomena, and to describe mathematical relationships.

(a) The total revenue is given by TR = p x q. Substituting the demand equation q = 40 - (4/3)p, we get TR = p(40 - (4/3)p), or TR = 40p - (4/3)p².

(b) The total cost is given by TC = q x AC. Substituting the given average cost function, we get TC = 9q + (3/10)q² + 30.

(c) The profit is given by π = TR - TC. Substituting the expressions we found in parts (a) and (b), we get π = 40p - (4/3)p² - 9q - (3/10)q² - 30.

(d) At the break even point, the firm earns zero profit, so we set π = 0 and solve for q. Substituting the expression we found in part (a) for p, we get:

0 = 40p - (4/3)p² - 9q - (3/10)q² - 30

0 = 40(40/3 - (3/4)q) - (4/3)(40/3 - (3/4)q)² - 9q - (3/10)q² - 30

0 = 533.33 - 51.25q - 0.22q^2

Solving for q using the quadratic formula, we get:

q = (51.25 ± sqrt(51.25² - 4(-0.22)(533.33))) / 2(-0.22)

q ≈ 22.75 or q ≈ 206.58

We reject the solution q ≈ 206.58 because it is outside the relevant range of output, which is between 0 and 40. Therefore, the total output at the break even point is approximately 22.75 units. To find the total revenue at the break even point, we substitute q = 22.75 into the demand equation from part (a) and get:

p = (40/3) - (3/4)q

p ≈ 15.08

TR = p x q

TR ≈ 342.67

(e) To find the profit when 20 units are produced, we substitute q = 20 into the expression for profit we found in part (c) and get:

π = 40p - (4/3)p² - 9q - (3/10)q² - 30

π ≈ 188.27

Therefore, the profit when 20 units are produced is approximately RM188.27.

(f) To find the profit when 7 units are produced, we substitute q = 7 into the expression for profit we found in part (c) and get:

π = 40p - (4/3)p² - 9q - (3/10)q² - 30

π ≈ -24.44

Therefore, the profit when 7 units are produced is approximately -RM24.44, indicating a loss.

(g) To find the output required to obtain a profit of RM100, we set the profit equation equal to 100 and solve for q:

Profit = TR - TC

100 = pq - ACq

100 = (40-(4/3)p)*q - (9+(3/10)q+30/q)*q

100 = (40-(4/3)p - 9q - 3q²/10)

Multiplying by 10 and rearranging terms, we get a quadratic equation in q:

3q² + 91q - 310 = 0

Solving for q using the quadratic formula, we get:

q = (-91 ± sqrt(91² - 43(-310)))/(2*3)

q ≈ 8.78 or q ≈ -29.44

Since the quantity produced cannot be negative, the output required to obtain a profit of RM100 is approximately 8.78 units.

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Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch. (1 point)
help me pls D;​

Answers

The length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.

How to find the dimensions of rectangle?

Since the area of the soap carvings is 300 square inches, we want the top of the bookcase to have the same area. Let's assume the length of the top of the bookcase is "l" and the width is "b". Then we have:

Area of top of bookcase = lb

We want this area to be equal to 300 square inches. Therefore, we can write:

lb = 300

We are solving for "b", so we can rearrange this equation to solve for "b":

b = 300/l

Since we don't know the value of "l", we can't solve for "b" exactly. However, we can approximate it by assuming a value for "l". Let's say we assume that "l" is 20 inches. Then we can calculate "b" as follows:

b = 300/20 = 15

So if the length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.

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Christine has a six-sided dice numbered from 1 to 6. She rolled it a total of 50 times. It landed on an odd number 21 times. a) Work out the relative frequency of the dice landing on an odd number. Give your answer as a decimal. b) If the dice were fair, what would the theoretical probablity of it landing on an odd number be? Give your answer as a decimal. c) Is the dice definitely biased or definetely not biased, or is it impossible to tell? Write a sentence to explain your answer.

Answers

A) Relative frequency is number of times an event happened over total number of events:

Answer is 21/50 = 0.42

B) On a 6 sides die, there are 3 even numbers and 3 odd numbers, so the theoretical probability of landing on odd would be 3/6 = 0.50

C) Because the die has an equal amount of chance landing on even or odd, both are 3/6, then the dice is not biased.

Orlando skip the rope 125 times in 45 seconds write this as a unit rate

Answers

Answer:

g h hh h

Step-by-step explanation:

Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, compute the system's impulse response h[n] without using z-transforms.

Answers

Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, the impulse response of the system: h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]

To compute the impulse response h[n] of a linear time-invariant (LTI) system given its input-output relationship, we can use the convolution sum:

y[n] = x[n] * h[n]

y[n] = (1/2)*(x[n] + 2x[n-1] + 3x[n-2])

y[n] = (1/2)*(δ[n] + 2δ[n-1] + 3δ[n-2])

y[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]

Thus, the impulse response of the system is:

h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2],where δ[n] is the impulse signal.

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The Ford F-150 is the best selling truck in the United States.
The average gas tank for this vehicle is 23 gallons. On a long
highway trip, gas is used at a rate of about 3.2 gallons per hour.
The gallons of gas g in the vehicle's tank can be modeled by the
equation g(t)=23 -3.2t where t is the time (in hours).
a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?

Answers

a) The domain of the function is  [0, 7.1875], while the range is [0,23]. Considering the domain and the range, the graph of the function is given by the image presented at the end of the answer.

b) The trip had a duration of 5.1875 hours.

How to obtain the domain and the range of the function?

The function for this problem is defined as follows:

g(t) = 23 - 3.2t.

The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the domain is given as follows:

23 - 3.2t = 0

3.2t = 23

t = 23/3.2

t = 7.1875 hours.

The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].

The graph is a linear function between points (0, 23) and (7.1875, 0).

At the end of the trip there were 6.4 gallons left, hence the length of the trip is obtained as follows:

23 - 3.2t = 6.4

t = (23 - 6.4)/3.2

t = 5.1875 hours.

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2 bags of dog food. How many days will 3/4 last?

Answers

Answer:

3/4 of a bag of dog food will last 3 days.

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0.59°C and 0.88°C.

Answers

The probability of obtaining a reading between 0.59°C and 0.88°C is 0.7224 and 0.8106.

What is mean?

The sum of all possible values, weighted by the chance of each value, is equal to the mean of a discrete probability distribution of the random variable X. Each possible number of X must be multiplied by its probability P(x) before being added as a whole to determine the mean. In statistics, the mean is one measure of central trend in addition to the mode and median. The mean is simply the average of the numbers in the specified collection. It suggests that values in a specific data gathering are evenly distributed. In order to find the mean, the total values given in a datasheet must be added, and the result must be divided by the total number of values.

In this question, using the formula,

z-score = (x – μ) / σ

where:

x: individual data value

μ: population mean

σ: population standard deviation

for x=0.59

μ= 0

σ= 1

z-score= 0.59

Probability=0.7224

for x=0.88

z-score= 0.88

Probability=0.8106

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To effectuate such a transfer, the owner must follow certain legal procedures.
1. Execution
2. Delivery
3. Acceptance
4. Recording
- Transfer in real property is not always voluntary.
- May be without the knowledge of the owner
Or even in some cases, against his/her will

Answers

Transferring ownership of real property (land and buildings) can happen in a variety of ways, and it is not necessarily consensual.

A transfer can occur, for example, through eminent domain, in which the government takes private property for public use and compensates the owner for its worth. Transfers can also occur through foreclosure, which occurs when a borrower fails on a loan and the lender takes control of the property.

Regardless of the conditions, the legal steps for transferring ownership usually include execution, delivery, acceptance, and recording. The signing of a legal instrument that transfers ownership is referred to as execution. The transfer of custody or control of the property to the new owner is referred to as delivery. The new owner's agreement to accept the transfer is referred to as acceptance.

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Write the equation for a parabola with a focus at (2,2) and a directrix at x=8

Answers

Answer:

(y - 2)² = -12(x - 5)

Step-by-step explanation:

A parabola is a locus of points, which are equidistant from the focus and directrix;

Generic cartesian equation of a parabola:

y² = 4ax, where the:

Focus, S, is: (a, 0)

Directrix, d, is: x = -a

a > 0

Put simply, a is the horinzontal difference between the directrix and the vertex or between the vertex and focus;

Always a good idea to do a quick drawing of the graph;

We are the told the focus, F, is: (2, 2) and directrix, d, is: x = 8;

First thing to note, the vertex, or turning point will be in line with the focus vertically, i.e. they will share the same y-coordinate;

Horizonatally, it will be halfway between the focus and the directrix, i.e. halfway between 8 and 2;

Therefore, the vertex will be will be (5, 2);

We can also work out a:

a = 8 - 5 = 5 - 2

a = 3

Substituting this value of a into the generic cartesian equation:

y² = 4(3)x

y² = 12x

The focus and directrix will be:

S: (3, 0)

d: x = -3

Next thing to note, a parabola curves away from the directrix;

In this case, the directrix is x = 8, so the vertex will be the right-most point on the parabola, it will curve off to the left and the focus will also be to the left;

What we want to do is compare with y² = 12x;

This parabola, has a vertex (0, 0), which is the left-most point that curves off to the right and a focus also to the right;

Since we know the formula of this parabola, if we figure out how to transform it into the one in the question, we can find out it's equation;

What we should recognise first is that the parabola in the question is reflected in the y-axis, compared to y² = 12x;

So we apply the transformation that corresponds to this, i.e. use the f(-x) rule:

y² = 12(-x)

y² = -12x

Now the two graphs will have the same shape and orientation;

The focus and directrix will also be affected:

S: (-3, 0)

d: x = 3

Now, the only remaining difference would be the coordinates of the focus and directrix of the two graphs;

The focus of the graph in the question is 5 units to the right and 2 units upwards compared to the focus of y² = -12x;

The directrix is 5 units to the right of that of y² = -12x;

So we apply a translation transformation of 5 units right and 2 units up, like so:

(y - 2)² = -12(x - 5)

Replace y with (y - 2) to translate up 2 units;

Replace x with (x - 5) to translate 5 units right.

We know have a parabola with focus, (2, 2), directrix, x = 8 and vertex, (5, 2), i.e. the parabola in the question;

Hence, the equation of the parabola in the question is:

(y - 2)² = -12(x - 5)

It might seem a bit long and complicated to begin with, but can be done very quickly if you can get used to it.

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