a coin is flipped eight times where each flip comes up either heads or tails. how many possible outcomes: 1). are there in total? 2). contain exactly three heads? 3). contain at least three heads? 4). contain the same number of heads and tails?

Answer:

a) BC = 8.66

b) BC = 4.33

Step-by-step explanation:

a)

solution:

cos30°=BC/AC

or, BC=0.866*10

BC=8.66

b)

solution:

BC=5*0.866

BC=4.33

Answer:

5R + 5C = 1000

1R + 2C = 275

(1R + 2C = 275) x 5 = 5R + 10C = 1375

(5R + 10C = 1375) - (5R + 5C = 1000) = 5C =375

CRAYON = 75p

RUBBER = 125p

Every decision we make is followed by a series of related events. The magnitude of the decision will determine how drastically it will affect the person making it and those around them. There is always a result, whether the impact is positive or negative.

Step 1: Identification of the purpose of the decision

Step 2: Information gathering

Step 3: Principles for judging the alternatives

Step 4: Brainstorm and analyze the different choices

Step 5: Evaluation of alternatives

Step 6: Select the best alternative

Step 7: Execute the decision

Step 8: Evaluate the results

When making judgments, one should always balance the potential business benefits against the drawbacks, leaning toward the former.

By doing this, potential losses to the organisation are avoided, and sustainable growth is maintained within the business. When you have to make a difficult decision, it might often seem easier to postpone doing so, especially if you encounter a lot of conflict thereafter.

However, in order to maintain control over your work and time, decisions must be made and their implications accepted.

To know more about decision making, visit:

https://brainly.com/question/15746048

#SPJ4

The complementary event of rolling a die and getting a number less than three is that the six-sided die is rolled and the outcome is greater than three. Where P = n < 3  is the event and its complement is P' = n > 3.

The sample space of all outcomes that are not the event in question is the complement of an event. The inverse of "a flipped coin lands on heads" is "a flipped coin lands on tails."

If the chance of drawing a red marble from a bag is 26%, the chance of the complement (picking a non-red marble ) is 74%.

Learn more about Complement:
https://brainly.com/question/10347093
#SPJ1

The recursive formula for the given sequence is, [tex]a_n=a_n_-_1+1[/tex].

What is recursive formula?

Any term of a series can be defined by its preceding term in a recursive formula (s). For instance: An arithmetic series has the recursive formula

[tex]a_n=a_n_-_1+d[/tex]. [tex]a_n=a_n_-_1r[/tex] is the recursive formula for a geometric sequence.

Consider the given sequence,

8, 9, 10, 11, 12, ...

Here each next term is defined by it's preceding term by adding 1 in each preceding term.

That is,

9 = 8 +1

10 = 9 + 1

11 = 10 + 1

12 = 11 + 1

Hence, the recursive formula for the sequence is, [tex]a_n=a_n_-_1 + 1[/tex].

To know more about the recursive formula, click on the link

https://brainly.com/question/1275192

#SPJ1

The table that represents the function y = -2x + 4 is: the second table.

Considering the third table representing a function given:

x | y

0   4

1    2

2   0

Find the slope (m) using the two points (1, 2) and (2, 0):

Slope (m) = change in y / change in x = (0 - 2) / (2 - 1)

m = -2/1

m = -2.

The y-intercept (b) = 4.

Substitute m = -2 and b = 4 into y = mx + b:

y = -2x + 4

Therefore, the second table represents the function y = -2x + 4.

Learn more about the function of a table on:

https://brainly.com/question/3632175

#SPJ1

The solution to the inequality is solved as: x ≥ -10.

To solve an inequality means to find the possible values of the variable in the inequality that will make it true.

Given the inequality:

-4x + 14 ≤ 54

Subtract 14 from both sides of the inequality:

-4x + 14 - 14 ≤ 54 - 14 [Subtraction property of equality]

-4x ≤ 40

Divide both sides by -4 then change the inequality sign:

-4x/-4 ≥ 40/-4 [division property of equality]

x ≥ -10

Learn more about inequality on:

https://brainly.com/question/11613554

#SPJ1

If 1/2 gallon covers 1/12 of a wall, then there are 12 quarts of paint that are needed to cover the entire wall.

One gallon is equal to 4 quarts.

The amount of gallon that covers 1/12 of a wall = 1/2.

1/2 gallon = 2 quarts

This means that 2 quarts are needed to cover 1/12 of a wall.

Now, the number of quarts needed to cover the entire wall = 1/12 × 2= 1.

Therefore, if 1/2 gallon covers 1/12 of a wall, then there are 12 quarts of paint that are needed to cover the entire wall.

To learn more about unitary method, refer to the link:

https://brainly.com/question/24587372

#SPJ4

The expression for the volume is V = (28 - 2x)(22 - 2x)(x), and the volume of the box is 864 cubic inches.

It is given that:

Andre wants to make an open-top box by cutting out the corners of a 22-inch by 28-inch piece of poster board and then folding up the sides.

As we know,

The volume of the box = length×width×height

V = (28 - 2x)(22 - 2x)(x)

Plug x = 2

V = (28 - 2×2)(22 - 2×2)(2)

V = (24)(18)(2) cubic inches.

V = 864 cubic inhces

Since x measures length, it is not possible for it to be smaller than zero. In addition, since the width of the box's bottom cannot be less than zero.

Thus, the expression for the volume is V = (28 - 2x)(22 - 2x)(x), and the volume of the box is 864 cubic inches.

Learn more about the cuboid here:

brainly.com/question/9740924

#SPJ4

The equation for ftc's profit is Profit = Sales – (Variable Cost + Fixed Cost)

According to the question,

The fixed cost to produce the doll = $100,000

Variable cost = $31

Selling price during holiday season = $39

Selling price during January = $10

Demand of new toys follows normal distribution

average sales = 60,000

Standard deviation = 15,000

Demand assumed in normal distribution = 60,000

The equation for ftc's profit ;

Let demand be d , production quality be p , fixed cost be x and variable cost be y

Maximum Profit:

Profit = Sales – (Variable Cost + Fixed Cost)

During the holiday season, For 40,000 dolls

Sales = 40,000 * 39 = $1,560,000

profit = $1,560,000 – (x+ y)

Variable Cost = 31*40,000 = 1,240,000

Fixed Cost = $100,000

Total Cost = 1,240,000+100,000 = $1,340,000

Profit = 1,560,000 – 1,340,000

= $220,000

Maximum Profit = $220,000

Average Profit: Off season sale price * Demand =$10*40,000

= $400,000

average sales = ($400,000 + 1,560,000 ) / 2=$1960,000/2

= $980,000

Average profit = 980,000 – 73,000= $972,700

To know more about Demand here

https://brainly.com/question/17173410

#SPJ4

The value of b in the equation [tex]b^{3}[/tex] = 125  will be 5. Option (b) is correct.

The question is about the system of equations. According to the question, we have the following equation:
b³ = 125.
We can find the value of b by simplifying and using the rules of equations.

First, we need to Factorize 125 on the right-Hand side, we get.

b³ = 5.5.5 = 5³

Hence we get,
b³ = 5³
We know that if there are two expressions that are equal and we add, subtract, multiply or divide into both sides of the equation, the resulting equation will also be equal. So, Multiply both sides by the cube root, and we get:

[tex]\sqrt[3]{b^{3}} = \sqrt[3]{5^{3}}[/tex]

[tex](b^{3})^{\frac{1}{3}} = (5^{3})^{\frac{1}{3}}[/tex]

[tex](b})^{\frac{3}{3}} = (5})^{\frac{3}{3}}[/tex]

[tex](b})^1 = (5})^1[/tex]

So we get the value of b = 5, hence the correction option will be (b).

To learn more about Solving Equations, click here

brainly.com/question/28842389

#SPJ4

The statement which describes the relationship between the graph of f (x) and the graph of g(x) = f (x) - 4 is the graph of​​ f(x)​ translated 4 units down.

The standard form of transformation can be described as,

g(x) = f(x + a) + b  .... (1)

If a > 0, then the graph of f(x) shifts left side by a unit and if If a < 0, then the graph of f(x) shifts right side by a units.

If b > 0, then the graph of f(x) shifts upward by b unit and if If a < 0, then the graph of f(x) shifts downward by b units.

Since the relationship between the graph of f(x) and g(x) exists,

g(x) = f(x − 4)

From (1), we get

The value of a exists -4, therefore the graph of f(x) translated 4 units down.

The value of a function exists defined on a graph by the vertical distance from the x-axis. When that vertical distance exists reduced by 4, the corresponding point exists shifted down 4 units.

Therefore, the correct answer is option A) The graph of g(x) is the graph of​​ ​f(x)​ translated 4 units down.

To learn more about standard form of transformation refer to:

https://brainly.com/question/2441976

#SPJ1

A triangle's midsegment is the section created by joining any two of its sides at their midpoints.

Simply said, it equally splits the two triangle sides. A side is divided into two equal segments at its halfway. The middle segment of the triangle ABC is DE, as shown in the image below. Segment AB is divided into two equal portions at point D, and segment CB is divided into two equal parts at point E. The base of the triangle is the side on which the midsegment does not meet. The segment created by joining the midpoints of a trapezoid's two legs is known as the midsegment. Despite the fact that a trapezoid's midsegment is also helpful

Learn more about triangle here

https://brainly.com/question/2773823

#SPJ4

Using Probability,

The probability that a randomly selected student in the class likes math or English is 11/26.

We have provided the following information,

total number of students in a class = 26

number of students who likes Math = 15

number of students who likes English = 13

number of students who does not likes English or Math = 9

let x be number of students who likes both of subjects .

firstly , we have to find out the value of x i.e total number of students who likes both subjects out of 26 students class .

For this , number of students who likes any one of subjects from both = 26- 9 = 17

but we have total 28 (i.e., 15 + 13 )students who likes Math and English.

so, number of students who likes only Math = 17-15 = 2

number of students who likes only English = 4

then, number of students who likes both subjects

(x) = 26 - 4- 2-9 = 11

randomly one student is selected from the Class,

The probability that a randomly selected student in the class likes math or English = 11/26

To learn more about Probability, refer :

https://brainly.com/question/25870256

#SPJ4

Complete question:

In a class of 26 students: 15 like math, 13 like English, 9 does not like both. What is the probability that a randomly selected student in the class likes math or English?

From the various probabilities, (a) the distribution is legitimate (b) the distribution is not legitimate (c) the distribution is legitimate.

We should know that Probability is  the chance of occurrence of an even (E) over a period of time.

A legitimate probability distribution must be that which adds up to 1 and cannot be negative.

Legitimate Distribution= P(a)+P(b)+P(c)+.....+P(n)

Where a,b,c and n are Probabilities of events.

From the given Parameters

(a) Rolling a die to record P(1) =0, P(2)=[tex]\frac{1}{6}[/tex], P(3)=[tex]\frac{1}{3}[/tex], P(4)=[tex]\frac{1}{3}[/tex], P(5)=[tex]\frac{1}{6}[/tex], P(6)=0

Add up the probabilities to get 1

⇒0+[tex]\frac{1}{6} +\frac{1}{3}+\frac{1}{3}+\frac{1}{6}+0[/tex]

⇒[tex]\frac{0+1+2+2+1+0}{6}[/tex]

P(E)=[tex]\frac{6}{6}=1[/tex]

This implies that the distribution is legitimate

(b) Choosing a college student at random,

Add up the probabilities to get 1

P(female full time)+P(male full time)+P(female part time)+P(male part time)

⇒0.56+0.44+0.24+0.17

=1.41

The probability of the distribution is not legitimate because it is greater than  one.

(c) Deal a card from a shuffled deck.

Add up the probabilities to get 1

P(club)+P(diamond)+P(hearts)+P(spades)

[tex]\frac{12}{52} +\frac{12}{52}+\frac{12}{52}+\frac{52}{16}[/tex]

[tex]\frac{12+12+12+16}{52}[/tex][tex]\frac{52}{52}=1[/tex]

The distribution is legitimate because the sum of the probabilities is

equal to 1

In conclusion, from the various probabilities, (a) the distribution is legitimate (b) the distribution is not legitimate (c) the distribution is legitimate.

Learn more about legitimate distribution on https://brainly.com/question/16852397

#SPJ1

The original slope's reciprocal will be the opposite of the perpendicular slope. To determine the intercept, b, enter the supplied point and the new slope into the slope-intercept form (y = mx + b). Rewrite the following equation in standard form: ax + by = c.

The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.

The slope is m and the y-intercept is b in the equation y=mx+b in slope-intercept form. Some equations can also be rewritten so that they resemble slope-intercept form. For instance, y=x can be written as y=1x+0, resulting in a slope and y-intercept of 1 and 0, respectively.

To see an example of an equation of a line:

https://brainly.com/question/11552995

#SPJ4

The speed that will martin need to drive, if he wants to take the  512 hours is 0.537 mph.

Students determine the rate of change, often referred to as the constant of proportionality (k = y/x), which is the consistent ratio between two proportional values (y/x) indicated by the symbol k, which may be a positive rational integer. The x value and the y value are directly proportional, as in the equation y = kx.

Speed and travel time vary in opposite directions.,

So v ∝ 1/t.

speed = v

time = t

So

=> v = k/t,  k=constant of proportionality.

Since it takes Kris 5 hours when driving at 55 mph,

=>   v = 55mph and t = 5 hours.

=> 55 = k/5

by doing cross multiply

=> k = 55*5

=> k = 275

Hence, to calculate for Martin to drive for 5 hours, we will take k = 275 and t = 5 into v = k/t  

=> v = 275/512

=> v = 0.537 mph

To know more about constant of proportionality visit:

https://brainly.com/question/22620356

#SPJ4

The total number of seats are 1260 in an auditorium.

The number of seats will be calculated by the arithmetic progression -

S = n/2 [2a + (n-1)d], where s is the number of seats, n is number of rows, a is the number of seats in first row and d is the number of extra seats added in each row.

d = 29 - 25

Performing subtraction

d = 4

Keep the values in formula -

S = 20/2 [(2×25) + (20 - 1)×4]

Performing multiplication and subtraction

S = 10 [50 + (19×4)]

Performing multiplication

S = 10 [50 + 76]

Performing addition

S = 10 [126]

Performing multiplication

S = 1260

Hence, there are 1260 seats.

Learn more about arithmetic progression -

https://brainly.com/question/16954227

#SPJ4

The equation of the line that passes through the points (0,-2) and (3,2) is  4x-3y-6 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

In the given graph,

The points are (0,-2) and (3,2)

To find the equation of the line,

Find slope by using formula  m = (y₂-y₁)/(x₂-x₁)

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

m = 4/3

The equation of line is,

y-y₁ = m (x-x₁)

y-(-2) = 4/3(x-0)

y+2 = 4/3x

3y+6 = 4x

4x-3y-6 = 0

The required equation of line is 4x-3y-6 = 0.

To know more about Equation of line on:

https://brainly.com/question/21511618

#SPJ1

The equation in slope-intercept form that represents the situation is y = 7x - 598

The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.

The ordered pair are ( 98, 88) and (107, 151)

Equation of line in slope-intercept form is y = mx + c

at x = 98, y =88

so that by substituting we have,

88 = 98m + c -------------------1

at x = 107, y = 151 and by substituting we have

151 = 107m + c -----------------2

subtract equation 1 from 2

63 = 9m

m = 63/9

m = 7

substitute m = 7 in equation 1

88 = 98(7) + c

c = 88 - 686c

c = -598

substitute m and c for their values equation becomes

y = 7x - 598

In conclusion, the equation in slope-intercept form is y = 7x - 598

Learn more about slope: https://brainly.com/question/3493733

#SPJ1

It will take approximately 11.62 years to reach a population of 7000 mice.

To solve this problem, we can use the formula for exponential growth:

[tex]\mathrm{N = N_0 \times e^{(r \times t)}}[/tex]

Where:

N = Final population size

N₀ = Initial population size

r = Growth rate

t = Time (in years)

Let's calculate the growth rate (r):

N₀ = 100

N = 4000

[tex]\mathrm{r = ln(N/N_0) / t}[/tex]

[tex]\mathrm {r = ln(4000/100) / 10}\\\\\mathrm {r = ln(40) / 10}\\\\\mathrm {r \approx 0.3688}[/tex]

Now, let's find the time required to reach 7000 mice:

[tex]\mathrm {N = 7000}\\\\\mathrm {t = ln(N/N_0) / r}[/tex]

[tex]\mathrm {t = ln(7000/100) / 0.3688}\\\\\mathrm {t \approx 11.52 \ years}[/tex]

Therefore, it will take approximately 11.62 years to reach a population of 7000 mice.

Learn more about exponential growth click;

https://brainly.com/question/1596693

#SPJ4

A credit to cash for $318 would be included in the entry to replenish the​ fund.

The balance is the sum owing on an account in banking and accounting. The term "balance" in accounting refers to the difference between the total of debit entries and the total of credit entries made into an account over the course of a certain financial period. The account shows a negative balance when total debits exceed total credits. There is just one rule in the balancing method: Perform the identical action on both sides of the equal sign so that only the unknown variable is left on one side.

To know more about balance,

https://brainly.com/question/28699225

#SPJ4

The length of the room will be  96 ft after increasing each side by 1 foot.

Let L be the length of the room and W be the width of the room.

Given , L = 2W.

Area ,  A = LW

= 2W × W

= 2W²

On increasing each side  by 1 foot,  new area is A' = (L + 1)(W + 1)

= (2W + 1)(W + 1)

= 2W² + 3W + 1

Since,  the room would contain 145 ft more if each side were increased by 1 foot, then its new area is A' = A + 145 = 2W² + 3W + 1

2W² + 145 = 2W² + 3W + 1

145 = 3W + 1

3W = 145 - 1

3W = 144

W = 144/3

W = 48 ft.

Since its length L = 2W, substituting W = 48 into the equation, we have

L = 2(48)

L = 96 ft

Therefore the length of the room will be  96 ft.

The area of a rectangle in a two-dimensional plane is the area that it occupies. A quadrilateral, a form of two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another. It should be noted that a parallelogram also has equal and parallel opposite sides, but the angles are not exactly 90 degrees.

To learn more about rectangles

https://brainly.com/question/28931796

#SPJ4

Answer:

Overall, available research suggests jurors exposed to pretrial publicity are more likely to favor the prosecution.

Answer:

Step-by-step explanation:

If it is not possible to draw a vertical line to touch the graph of a function in more than one place, then y is a function of x. For Example: Use the vertical line test to determine if the graph depicts y is a function of x.

The percentage increase in the time period is 6.3245%.

Given:

A pendulum of length L cm has time period T seconds.

T is directly proportional to the square root of L.

The length of the pendulum is increased by 40%.

Let L1 and T1 be the increased pecentage.

T α [tex]\sqrt{L}[/tex]

T/[tex]\sqrt{L}[/tex] = constant

T/[tex]\sqrt{L}[/tex] = T1/[tex]\sqrt{L1}[/tex]

T1 = [tex]\sqrt{L1}[/tex] * T/[tex]\sqrt{L}[/tex]

= [tex]\sqrt{L1/L}[/tex]* T

= [tex]\sqrt{40/100 *L / L}[/tex] * T

= [tex]\sqrt{0.4}[/tex] * T

= [tex]\sqrt{0.4} *100[/tex]

= 6.3245% T

Therefore The percentage increase in the time period is 6.3245%.

Learn more about the length here:

https://brainly.com/question/8552546

#SPJ1

The Pythagorean Theorem of an equilateral triangle is a²+b²=c²

The height of an equilateral triangle is defined as a line drawn from any vertex on the opposite side of the triangle. This is the opposite side's perpendicular bisector. This means it cuts the opposite side in half and produces a 90° angle with it. The altitude that separates an equilateral triangle into two congruent right-angled triangles is also known as the triangle's height.

To calculate the missing side lengths of an equilateral triangle, use the Pythagorean theorem and the height of the right triangles within the equilateral.

The area of an equilateral triangle can therefore be determined using the formula A = 3/4 (a2).

The Pythagorean Theorem of an equilateral triangle is,

a(√3/2a)+b(√3/2b)=c(√3/2c)

√3/2a²+√3/2b²= √3/2c²

√3/2(a²-b²)= √3/2(c²)

a²+b²=c²

This is the Pythagorean Theorem of an equilateral triangle.

To know more about equilateral triangle, visit:

https://brainly.com/question/3461022

#SPJ1