You are among 100 people attending a charity fundraiser at which a large-screen TV will be given away as a door prize. To determine who wins, 99 white balls and 1 red ball have been placed in a box and thoroughly mixed. The guests will line up and, one at a time, pick a ball from the box. Whoever gets the red ball wins the TV, but if the ball is white, it is returned to the box. If none of the 100 guests gets the red ball, the TV will be auctioned off for additional benefit of the charity a) What is the probability that the first person in line wins the TV? b) You are the sixth person in line. What is the probability you win the TV? c) Find the probability that it takes at least 10 people for the TV to be won. d) What is the probability that the charity gets to sell the TV because no one wins. e) Where would you want to be in line in order to maximize your chances of winning?

The value of z such that 7% of the area under the standard normal curve lies to the right of z is approximately -0.4

To find the value of z such that 7% of the area under the curve lies to the right of z, we need to find the value of z such that 43% of the area lies to the left of z.

This value of z is known as the 43rd percentile of the standard normal curve.

We can use a table of the standard normal distribution, also known as the z-table, to find the value of z corresponding to the 43rd percentile.

According to the z-table, the value of z corresponding to the 43rd percentile is approximately -0.4

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A. The top cycle in this case is a -> b -> c -> a.

B. The agenda that wins the candidate is:

First vote:

a vs b -> a wins

Second voice:

versus. c -> a wins

The agenda that Candidate B wins is:

First vote:

b vs c -> b wins

Second Voice:

b vs a -> b wins

The agenda that Candidate C wins is:

First vote:

c vs a -> c wins

Second Voice:

c vs b -> c wins

C. Using the Borda count system, the candidates' scores are as follows:

a:

18 points (6 points from voter 1, 4 points from voter 2, and 8 points from voter 3)

b:

18 points (4 points from voter 1, 6 points from voter 2, and 8 points from voter 3)

c:

18 points (6 points from voter 1, 8 points from voter 2, and 4 points from voter 3)

d:

12 points (8 points from voter 1, 4 points from voter 2, and 0 points from voter 3)

e:

12 points (4 points from voter 1, 8 points from voter 2, and 0 points from voter 3)

f:

12 points (8 points from voter 1, 0 points from voter 2, and 4 points from voter 3)

g:

6 points (4 points from voter 1, 0 points from voter 2, and 2 points from voter 3)

Therefore, candidates a, b, and c tie for first place with 18 points each.

D. No, the Borda count winner is not the Condorcet winner, because the Condorcet winner is the candidate who would win in a majority rule vote against every other candidate. In this case, candidate c is the Condorcet winner, because c beats a and b in majority rule votes.

E. The candidate with the worst score in the Borda count is  g of 6 points.

F. If a candidate fails, the original worst candidate may no longer be the worst. In this case, if candidate g fails, the remaining candidates will have the following results:

a:

15 points (Voters 1 to 5 points, Voters 2 to 4 points, Voters 3 to 6 points)

b:

15 points (Voters 1 to 4 points, Voters 2 to 5 points, Voters 3 to 6 points)

c:

15 points (Voters 1 to 5 points, Voters 2 to 6 points, Voters 3 to 4 points)

Day:

10 points (voters 1 to 6 points, voters 2 to 4 points, voters 3 to 0 points)

e:

10 points (voters 1 to 4 points, voters 2 to 6 points, voters 3 to 0 points)

f:

10 points (voters 1 to 6 points, voters 2 to 0 points, voters 3 to 4 points)

In this case, g's 6-point score is not included in the calculation, so candidate g is no longer last.

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The slope of the line determined by the points (-3,2) and (2,-2) is -0.8. The slope of a line is a measure of the steepness of the line.

To find the slope of a line given two points, you can use the formula:

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

Plugging in the coordinates of the two points given, we get:

slope = (-2 - 2) / (2 - (-3))

= -4 / 5

= -0.8

So, the slope of the line determined by the points (-3,2) and (2,-2) is -0.8.

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The probability that someone is in the right job and the test is then wrong is 0.195.

The probability that the employee is in the wrong job and the test predicts that he is in the right job is 0.105.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In

The probability that he is in the right job is 0.65, so the probability he is in the wrong job is 0.35, and similarly, the probability that the test is inaccurate is 0.3.  Thus, the probability that someone is in the right job and the test is then wrong is:

= 0.65*0.3

= 0.195

The probability that someone is in the wrong job and the test is right is:

= 0.35 × 0.3

= 0.105.

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The measure of the central angle in degrees subtended by an arc of length 5 meter is 71.61 degrees

The radius of the circle = 4 meters

The circumference of the circle = 2πr

Where r is the radius of the circle

The value of π = 3.14

The circumference of the circle = 2π × 4

= 8π

The arc length = 5 meters

Consider the x as the central angle

The proportion of central angle and circumference will be

5/8π = x radiance / 2π

Cross multiply the terms

x × 8π = 5 × 2π

x = 10π / 8π

x = 5/4 radiance

Convert radiance to degrees

We know

1 radiance = 180/π degrees

5/4 radiance = 5/4 × 180/π degrees

= 71.61 degrees

Therefore, the central angle is 71.61 degrees

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The time management skill and amount of work done is an example of positive correlation.

Correlation or dependency pertains to any statistical link involving two random variables or bivariate data, whether causal or not. Although the term "correlation" can refer to any form of link, in statistics it is most usually used to refer to the degree to which two variables are statistically linearly associated.

The link between the heights of parents and their children, as seen in the enough that demand curve, and the correlation between the price of an item and the quantity of items that buyers are willing to acquire are examples of dependent phenomena.

The Pearson product-moment correlation coefficient (PPMCC), sometimes known as "Pearson's correlation coefficient," is the most commonly used measure of two-value dependency.

It is computed by dividing the covariance ratio of the two variables in our numerical dataset by the square root of their variances. The covariance of the two variables is simply divided by the product of their standard deviations in mathematics. The coefficient was calculated by Karl Pearson from Francis Galton's similar but slightly different idea.

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Answer:

A and B

Step-by-step explanation:

It is transformed fro a to a' by shift left of 7 and down 3    T(-7,-3)

Additive Property of Equality justifies the second line in the  3x + 2 = 8

3x+ 2 - 2 = 8 - 2 solution.

What is Multiplicative Property of Equality?

When we multiply on both sides of an equation then the equation is remain same.

Distributive property: a(b + c) = ab + ac in other words the product of a number with sum of two numbers is equal to the sum of product first two numbers and "first and third" numbers.

Associative property: (a + b) + c = a + (b + c): If we shift the parenthesis then the result will remain the same.

Given equation is

3x+2=8

The second step is 3x + 2 - 2 = 8 - 2.

The additive inverse of 2  is -2.

-2 is added in second step. Thus Additive Property of Equality is used.

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The forecast for 2012 was 980.

From 2004 to 2013 there are 10 years, if we include the initial year. Hence, 2013 must be year 9. Therefore, 2012 must be year 8 (check the attached image to get a better understanding of this logic, in case it's needed). With this information, take the value of 8, substitute it by x in the formula and calculate:

[tex]Sales(8) = 100 - 10x + 15x^{2} \\ \\Sales(8) = 100 - 10(8) + 15(8)^{2}\\ \\Sales(8) =980[/tex]

The forecast for 2012 was 980.

In a line When the line is parallel to the x-axis, the slope is zero. The first set of coordinates' slope will be 0.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,where (x₂,y₂) and (x₁,y₁) are the coordinates of any point on the line of slope.

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

1. For the first slope, the given coordinates are;

(-3,2), (-1,2), (1,2) and (3,2).

Now, if we take the first and the last point to calculate the slope of the line, we will get,

m =  (y₂- y₁) / (x₂ - x₁)

m = (2-2) / (3+3) = 0

Thus, the slope of the line is 0.

2. For the second slope, the given coordinates are;

(-3,3), (-1,1), (1,-1) and (3,-3).

Now, if we take the first and the last point to calculate the slope of the line, we will get,

m =  (y₂- y₁) / (x₂ - x₁)

m = (-3-3) / (3+3) = -1

Thus, the slope of the line is -1.

3. For the third slope, the given coordinates are

(-5,-5), (0,0) and (5,5).

Now, if we take the first and the last point to calculate the slope of the line, we will get,

m =  (y₂- y₁) / (x₂ - x₁)

m = (5+5) / (5+5) = 1

Thus, the slope of the line is 1.

4. For the fourth slope, the given coordinates are

(-2,5), (-2,0) and (-2,5)

Now, if we take the first and the last point to calculate the slope of the line, we will get,

m =  (y₂- y₁) / (x₂ - x₁)

m = (-2+2) / (5-5) = ∞

Thus, the slope of the line is undefined.

Therefore, the slope of the first pair of coordinates will have no slope or zero slopes.

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The value of the variables x and y according to the given representation as required are; 3 and -1 respectively.

It follows from the task content that the values of the variables x and y are to be determined according to the given representation.

Since the given representation is;

x( 1, 1 ) + y( 2, -1 ) = ( 1, 4 )

The system of equations which correctly represents the situation is;

x + 2y = 1..........(i)

x - y = 4............(ii)

By subtracting equation (ii) from equation (i); we have;

2y - (-y) = 1 - 4

3y = -3

y = -3 / 3

y = -1.

On this note, by substitution into the equation (ii);

x - (-1) = 4

x + 1 = 4

x = 4 - 1

x = 3.

On this note, the values of x and y as required in the task content are; 3 and -1 respectively.

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Using the completing square method, the value of (C) x = ±√5 - 2.

A quadratic polynomial of the form ax2+bx+c can be transformed to the form in elementary algebra by using the "completing the square" method for certain values of h and k.

In other words, the quadratic expression is completed by inserting a perfect square trinomial.

So, we have:

x² + 4x = 1

The x-coefficient terms must be divided by two:

4/2 = 2

Square:
2² = 4

Add 4 on both sides as follows:

x² + 4x + 4 = 1 + 4

x² + 4x + 4 = 5

Transform into perfect squares:

(x + 2)² = 5

Both sides of the square root:

x + 2 = ±√5

x = ±√5 - 2

Therefore, using the completing the square method, the value of (C) x=±√5-2.

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Complete question:
Solve x2 + 4x = 1 for x by completing the square.

a. x = −3

b. x = −1

c. x equals plus or minus the square root of 5 minus 2

d. x equals plus or minus square root of 5 plus 2

Answer:

is c correct?

Step-by-step explanation:

Answer:

-5 ≤ y < ∞.

Step-by-step explanation:

The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = |x| − 5, we can first consider what happens when x is positive. In this case, the absolute value of x is just x, so the function becomes f(x) = x − 5. For example, if x = 6, then f(x) = 6 - 5 = 1. We can do this for any positive value of x to find the y-values that the function produces when x is positive.

Next, we can consider what happens when x is negative. In this case, the absolute value of x is -x, so the function becomes f(x) = -x - 5. For example, if x = -6, then f(x) = -6 - 5 = -11. We can do this for any negative value of x to find the y-values that the function produces when x is negative.

We can then combine the y-values that the function produces when x is positive and negative to find the range of the function. Since the function produces all y-values greater than or equal to -5 when x is positive and all y-values less than or equal to -5 when x is negative, the range of the function is -5 ≤ y ≤ ∞.

Therefore, the correct answer is -5 ≤ y < ∞.

Answer:

Step-by-step explanation:

When graphed they intersect at (2, 5)

Answer:

y = - 0.4x -6

Step-by-step explanation:

The slope-intercept form of a line equation is

y = mx + b

where m is the slope and b the y-intercept where the line crosses the y axis.

From the figure it is clear that the line passes through (0, -6) and therefore the y-intercept is -6

To compute the slope, find another  convenient point on the line. Compute the ratio of change in y values(called rise) to the change in x values(called run). This will be the slope

We see that point (10, -10) has been identified on the graph.(Any of the 4 identified points will do, I just chose this)

So two points to consider are (0, -6) and (10, -10)

Change in y values = rise = -10 - (-6) = 1- + 6 = -4

Change in x values = run = 10 - 0 = 10

So slope m = -4/10 = -0.4

Equation of line is y = -0.4x -6

Answer: 0.06

Step-by-step explanation:

The value of the fraction, negative 5 and 1 over 7 ÷ negative 7 and 3 over 4 is 144/217

A fraction can be described as the part of a whole element or value.

The different types of fractions are;

Examples of proper fractions; 2/4, 5/6, 7/9

Examples of improper fractions; 4/2, 3/2, 6/5

Examples of mixed fractions; 2 1/4, 4 6/7, 8 1/2

Examples of simple fractions; 1/ 3, 3/4, 1/2

Now, from the information given, we have;

Convert into improper fractions

-36/7 ÷ -31/4

take inverse of the divisor and multiply

-36/ 7 × 4/-31

-144/-217

144/217

Hence, the value is 144/217

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Answer: -433.15

Step-by-step explanation:

he's id debt and has to pay off the 433.15 later on.

Answer:

The McQuires' account is currently overdrawn by $483.15.

Step-by-step explanation:

If the McQuires' account balance was $750 on Friday and they wrote a check for $1,183.15 on Saturday, then the balance would be 750 - 1,183.15 = -$433.15 after the check cleared. Since the bank charges a $50 overdraft fee, the final balance in the McQuires' account would be -$433.15 - $50 = -$483.15. The McQuires' account is currently overdrawn by $483.15.

10% condition is not met in this case because here sample size if 10% of the population is taken = 20.

Standard deviation decreases if 10% condition is violated.

10% condition states that the sample size we are working with must not exceed the population size. It is mostly useful when we are working with samples which are not independent.

If we use the 10% condition even with samples which are not actually independent, this condition will make it seem independent.

(a) Here population size = 200

Sample size = 50

If the 10% condition is met, sample size = 10% of population size

                                                                  = 0.10 × 200

                                                                  = 20

Sample size has exceeded the 10% condition.

(b) Standard deviation measures how much the set of values differ from      it's mean value.

Violating 10% condition increases the sample size which in turn decreases the standard deviation.

Hence the 10% condition has not met in this case as the sample size is larger. Standard deviation decreases if 10% condition is violated.

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The required probability is P(X≥3) =0.3234

The average number of winning tickets that the woman buys each month is 2.

The binomial probability distribution is a discrete type of probability distribution with two parameters, n, and p. The probability mass function of the distribution is used to get the required probability. The average value of the winning number is the expected value of the binomial distribution.

The probability mass function of the binomial distribution is defined as:

[tex]P(X=x)=\frac{n}{x} p^{x} (1-p)^{n-x} , x =0,1,2,3,....,n.[/tex]

Given that,

n = 20

p = 0.10

The required probability is P(X≥3)

P(X≥3) = 1-P(X<3)

P(X≥3)= 1-P(X=0)-P(X=1)-P(X=2)

P(X≥3)= 1- 0.1216- 0.270- 0.285

P(X≥3) = 0.3234

The mean of the distribution is defined as μ=n*p= 20*0.10= 2

The average number of winning tickets that the woman buys each month is 2.

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Suppose that the relation G is defined as follows G={(-6, -4), (5, -4), (1, 5) give the domain and range of G in set notation

domain {-6, 5, 1}

range {-4, -4, 1}

In mathematics, set notation is essentially a list of numbers, things, or results. Curly brackets, often known as braces, are used for set notation.

The items included between brackets are referred to as elements of a set and are not required to be in any particular order.

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

in the given relation, G={(-6, -4), (5, -4), (1, 5)}

the first figure in the parenthesis is the domai whilel the next is the range

hence domain = -6, 5, and 1 while range is -4, -4, and 5

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The area of the shaded region - [tex]\int\limits^\frac{5\pi }{4} _\frac{3\pi }{4}[/tex] [tex]cos^{2}[/tex] 2θ dθ

Determine α, β and f(θ).

To determine α and β, imagine a clock dial that turns counter-clockwise around the origin. The shaded area must be passed over by the dial. Place the dial in its starting position, and find the angle it makes with the horizontal axis, this angle is α. Do the same for the dial's end position, this angle [tex]\beta[/tex] .

To find f(θ), this equals r.

     α= [tex]\frac{3\pi }{4}[/tex]

      β= [tex]\frac{5\pi }{4}[/tex]

​     f(θ)=r=cos2θ

we know the integration formula,

A = [tex]\int\limits^\alpha _\beta[/tex] f (θ )² dθ

Hence, the area of the shaded region:

A =    [tex]\int\limits^\frac{5\pi }{4} _\frac{3\pi} {4} \,[/tex]  [tex]cos^{2}[/tex] 2θ dθ

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The number of violent crimes committed in a city on a given day in a random sample of 90 days is a discrete random variable.

A random variable refers to a numerical quantity that is obtained by a random experiment. A random variable is known as discrete if it has either a finite or a countable number of possible values while it is called continuous if its possible values contain a whole interval of numbers. Hence, a discrete random variable refers to a variable that can take any whole number values as outcomes of a random experiment. It is a variable whose value is obtained by counting. Probability distributions are used to illustrate the values of discrete random variables. A discrete random variable is also known as a stochastic variable. Examples of a discrete random variable are a binomial random variable and a Poisson random variable. As the number of crimes committed in a city can only take discrete values such as 40 crimes, 50 crimes and cannot be 40.5 crimes, it is a discrete random variable.

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Answer:

$19.56

Step-by-step explanation:

$4.89 per pound times the number of pounds to be purchased (4).

so 4(4.89)=19.56

A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution and he value of the test statistic for your Z-test is 3.1111

Given :

You are a writer for the school newspaper and are suspicious of the claim. To test it, you decide to perform a hypothesis test. To do so, you choose a random sample of 160 students who visited the site looking for a roommate. Of the students surveyed, 48 said they found a match their first time using the site.

we know that ,

z = x - μ / σ

= 160 - 48 / 36

= 112 / 36

= 3.1111

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Answer:

add one black and one white marble

Step-by-step explanation:

you have to make bag b equivalent to a 2:3 ratio.

add 1 to 5 to make it divisible by 2

divide 6 by 2

=3

multiply 3 by 3 to get a 2:3 ratio

=9

subtract initial marbles

9-8=1

Answer:

2 hrs

Step-by-step explanation:

d / r = time

40 mi  / 20 m/hr = 2 hrs

A number line is plotted below:

A number line, used to represent the real numbers visually in early mathematics, is a drawing of a graduated straight line. It is presumptively true that each real number and each point on a number line relate to one another. A line with carefully marked, equally spaced-out points on it is frequently used to represent integers. Despite the fact that the image only displays the integers from -3 to 3, the line contains all real numbers, going on forever in both directions, as well as numbers that fall in between the integers. Especially when negative numbers are involved, it is frequently used as a teaching tool for basic addition and subtraction.

The number line is properly known as the real number line in advanced mathematics and can also be referred to as a real line.

A number line is plotted below:

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Answer:

48 ft

Step-by-step explanation:

The height i the scale drawing is 4 in and the length is 8 in which is twice the height

The actual school has a height of 24 ft so the length is twice the height here = 24 x 2 = 48 ft

The mirror needs to be at location C.

What is congruency of triangles?

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

When two figures resemble one another in terms of size and shape, this is what mathematics refers to as congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables. Congruent triangles have equal comparable sides and angles.

It is given, height of Kiran is 5.8ft and that of Statue of Liberty is 305 ft.

Let the position of the mirror be at C.

Height of Kiran is AB, which is 5.8ft.

Height of Statue of Liberty is ED, which is 305 ft.

Thus, the triangles EDC and ABC are congruent.

The distance from Kiran to the mirror is BC and the distance between mirror to Statue of Liberty is CD.

Attached below is an image for reference.

Hence the mirror needs to be at location C.

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