Two coins are tossed. Assume that each event is equally likely to occur.
​a) Use the counting principle to determine the number of sample points in the sample space.
​b) Construct a tree diagram and list the sample space.
​c) Determine the probability that no tails are tossed.
​d) Determine the probability that exactly one tail is tossed.
​e) Determine the probability that two tails are tossed.
​f) Determine the probability that at least one tail is tossed.
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Part 1
​a) There​ is/are ______sample​ point(s) in the sample space.

Answer:

Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4. Associative property of addition: Changing the grouping of addends does not change the sum

The percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.

[tex]V = r^2h[/tex] , where r is the radius of the cylinder's base, h is its height, and (pi) is a mathematical constant corresponding roughly to 3.14159, gives the volume of a cylinder.

To solve this problem, we need to calculate the volumes of the two containers and then determine how much of Container B is empty after the water from Container A is transferred to it.

The volume of a cylinder is given by the formula  [tex]V = \pi r^2h[/tex] , where r is the radius of the base and h is the height of the cylinder.

Container A has a radius of  [tex]4[/tex] feet and a height of 18 feet, so its volume is:

[tex]V(A) = \pi (4^{2} )(18) = 288\pi[/tex] cubic feet

Container B has a radius of 5 feet and a height of 15 feet, so its volume is:

[tex]V(B) = \pi (5)^2(15) = 375\pi[/tex]  cubic feet

When the water from Container A is transferred to Container B, the volume of water in Container B will be:

V(water in [tex]B) = V(A) = 288\pi[/tex] cubic feet

The total volume of Container B is 375π cubic feet, so the volume that is empty after the transfer is:

V(empty in  [tex]B) = V(B) - V(water in B) = 375\pi - 288\pi = 87\pi[/tex] cubic feet

To find the percentage of Container B that is empty, we need to divide the volume that is empty by the total volume of Container B and then multiply by 100:

Percent empty [tex]= (V(empty in B) / V(B)) \times 100[/tex]

[tex]= (87\pi / 375\pi) \times 100[/tex]

[tex]= 23.2[/tex]%

Therefore, the percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.

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Answer: your answer would be A.

Mr. Mensah will pay 247.5 each month to the social security fund because 5.5% of 4500 is 247.5.

The total monthly salary of Mr. Mensah is 4500.

He is required to pay 5.5% of his salary into a social security fund.

Now, we have to find the amount he has to pay each month into the social security fund.

To find that, we need to find the value of 5.5 percent of 4500.

4500 ×5.5/100

45×5.5

247.5

Therefore, 5.5% of 4500 is 247.5.

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Answer:

I can tell

Step-by-step explanation:

Ok so to help you understand it do you see the button that says video? Yeah, click it. A video will pop up and explain it to you! :)

The distance from which the sprinkler can spread water is  4.37 feet

To determine the value, we need to know the area of the circle.

The formula for the area of a circle is expressed as;

A = πr²

Given that the parameters are;

Substitute the values, we have;

15 = 3.14r²

Divide both sides by the coefficient, we get;

r² = 4. 77

find the square root of both sides, we get;

r = 2. 19 feet

But note that the formula for diameter is given as;

Diameter = 2radius

Diameter = 2(2.19)

multiply the values

Diameter = 4.37 feet

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Answer:

Step-by-step explanation:

I'm sorry, but there isn't enough information to solve for the missing side of a triangle with just the perimeter given as 8x-6. We would need at least one more piece of information, such as the lengths of the other sides or angles of the triangle.

Since Q is the midpoint of NP, we know that NQ = QP. Similarly, we know that RS is the midpoint of OP, so we have RS = SO.

Let's label the length of QS as x. Then, we know that QR = 2x and SR = 3x.

To find the perimeter of triangle NOP, we need to find the lengths of NO, OP, and NP.

Using the Pythagorean Theorem, we can find that:

NO^2 = NQ^2 + OQ^2

NO^2 = (QP)^2 + (SO)^2

NO^2 = (x)^2 + (2x)^2

NO^2 = 5x^2

NO = x√5

Similarly, we can find that:

OP^2 = OQ^2 + PQ^2

OP^2 = (SO)^2 + (QP)^2

OP^2 = (3x)^2 + (x)^2

OP^2 = 10x^2

OP = x√10

Finally, we know that NP = NO + OP, so:

NP = x√5 + x√10

NP = x(√5 + √10)

To find the perimeter of NOP, we add up the three sides:

Perimeter of NOP = NO + OP + NP

Perimeter of NOP = x√5 + x√10 + x(√5 + √10)

Perimeter of NOP = x(2√5 + 2√10)

Perimeter of NOP = 2x(√5 + √10)

We can substitute the value we found for QS, which is x, to get:

Perimeter of NOP = 2(5 + 2√10)

Perimeter of NOP = 10 + 4√10

Therefore, the perimeter of triangle NOP is 10 + 4√10 units.

The unit rate that relates the two quantities of distance and volume of gas is:

U = 30 miles per gallon.

To do so, we can find the unit rate.

This would say how many gallons are consumed to drive a unit of distance, or which distance can you drive with one gallon.

Here we have the values:

10 gallons and 300 miles.

Then the unit rate is the quotient between these:

300miles/10 gallons = 30 miles per gallon

This says that with one gallon of gas you can travel 30 miles.

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The evaluations are:

i. 11!  = 39916800

ii. 24! = 2.045 x 10^37

Expansion by factorial is a method of expanding a given number from 1 to the number given. An example is given thus;

5! = 5 x 4 x 3 x 2 x 1!

   = 120

To evaluate the given expressions;

a. 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1!

       = 39916800

Also,

b. 24! = 24 x 23 x 22 x 20 x ........ x 5 x 4 x 3 x 2 x 1!

          = 204484017332398 x 10 ^23

          = 2.045 x 10^37

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Answer:

D

Step-by-step explanation:

- 4( [tex]\frac{3}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ) = - 15 ← distribute parenthesis by - 4

- 6x + 2 = - 15 ( subtract 2 from both sides )

- 6x = - 17 ( divide both sides by - 6 )

x = [tex]\frac{-17}{6}[/tex] , that is

x = [tex]\frac{17}{6}[/tex]

The calculated R2 value is 0.621, indicating that 62.1% of the variability in tumor growth can be explained by the linear regression model.

In statistics, the coefficient of determination, denoted by R2, is a measure of how well the regression line fits the data. It represents the proportion of the variance in the dependent variable (y) that is predictable from the independent variable (x).

To calculate R2, we use the formula R2 = SSR/SST, where SSR is the sum of squares of regression and SST is the total sum of squares.

From the given data, SSR = 568.5 and SST = 914.8. Thus, R2 = 568.5/914.8 = 0.621, rounded to three decimal places.

This means that 62.1% of the variability in the tumor growth can be explained by the linear regression model. The remaining 37.9% of the variability is unexplained and may be due to other factors not included in the model.

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The equation that represent the number of bracelets b and the number of rings r is 6b + 8r > 600 and 2b + 4r < 275, hence, option A is correct.

Let b represent the number of bracelets and r represent the number of rings that Marisol makes. Marisol plans to sell each bracelet for $6 and each ring for $8. So the amount she earns from selling bracelets is 6b and the amount she earns from selling rings is 8r.

The craft fair committee charges a $25 fee to sell at the fair. So Marisol's total earnings after paying the fee is 6b + 8r - 25. It costs Marisol $2 to make a bracelet and $4 to make a ring. So the total cost of making b bracelets and r rings is 2b + 4r. To make a profit, Marisol's earnings must be greater than her costs,

6b + 8r - 25 > 2b + 4r

Simplifying this inequality, we get,

4b + 4r > 25

We also know that Marisol wants to sell at least $600 in jewelry. This can be expressed as,

6b + 8r > 600

Finally, Marisol wants to spend less than $300 for supplies and the fee. This can be expressed as,

2b + 4r + 25 < 300

Simplifying this inequality, we get,

2b + 4r < 275

Therefore, the system of inequalities that represents the situation is,

6b + 8r > 600

4b + 4r > 25

2b + 4r < 275

where b represents the number of bracelets and r represents the number of rings that Marisol makes.

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she needs to clean 15 uniforms to break even

Answer:

Step-by-step explanation:

f(x)=2x

note: putting anything in the f(x) parentheses replaces x in the function with that value

so,

f(-3) = 2(-3) = -6

f(0) = 2*0 = 0

f(2) = 2(2) = 4

the cruising speed of the blue whale is approximately 3.16 meters per second.

What are  velocity?

a velocity is a unit of measurement for the Distance an object travels in a

the predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by

dividing the total Distance traveled by the journey time.

In this case, we know the mass of the blue whale (m = 170,000 kg) and its kinetic energy (KE = 890,000 J), but we need to solve for its velocity (v).

Rearranging the formula, we get:

v = √(2 * KE / m)

Plugging in the values we know, we get:

v = √(2 * 890000 J / 170000 kg)

Simplifying this expression, we get:

v = √10 = 3.16 m/s

Therefore, the cruising speed of the blue whale is approximately 3.16 meters per second.

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Answer:

a) (1/2)(5)(CD) = 20 cm^2

5CD = 40, so CD = 8 cm

b) (1/2)(12)(8) = 48 cm^2

The probability of drawing a pink case on the first draw is 30/80.

Probability is a branch of mathematics that deals with the measurement and analysis of random phenomena. It is the study of the likelihood or chance of an event occurring. It involves analyzing and predicting the likelihood of certain outcomes based on the available information and the rules of probability theory. Probability is used extensively in various fields, including statistics, physics, finance, engineering, and computer science, among others.

In the given question,

The probability of drawing a pink case on the first draw is 30/80. Since the cases are not replaced, the probability of drawing a pink case on the second draw is 29/79 (there are now 29 pink cases left out of 79 total cases). Similarly, the probability of drawing a pink case on the third draw is 28/78. Therefore, the probability of drawing three pink cases in a row is:

(30/80) * (29/79) * (28/78) = 0.0412 or about 4.12%.

So, the probability that the first three cases are all pink is 0.0412 or about 4.12%.

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There is higher variability of y with large values of x.

There is a non linear relation between x and y.

We observe from figure b that for lower values of x the residuals are negative and as the values of x increases the residuals become positive but are distributed very close to the zero line.

Again for the extremely high values of x the residuals become negative following a decreasing non linear trend. Hence, from the residual plot we can conclude that the relation between x and y is a non linear one. Hence, the correct option is fourth option i.e, There is a non linear relation between x and y.

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for the first question  answer is 35 , which we can clearly see its pointing 35 degree in the protractor  .second question is incomplete

what is protractor ?

To measure an angle using a protractor instrument, follow these steps:

Place the protractor on the angle: Place the flat side of the protractor on one of the angle's sides, making sure that the vertex (the point where the two sides of the angle meet) is at the center of the protractor.Align the protractor with the angle: Make sure the protractor is aligned with the angle you want to measure. The zero-degree mark on

In the given question,

for the first question  answer is 35 , which we can clearly see in the protractor  

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Answer:

4x - 1 > 15

4x > 16

x > 4

The solution set is all numbers greater than 4.

The calculated area of the triangle is 7.5 square inches

From the question, we have the following parameters that can be used in our computation:

The triangle with the following dimensions

base = 6 inches

height = 2.5 inches

Using the above as a guide, we have the following:

Area = 1/2 * base * height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 6 * 2.5

Evaluate

Area = 7.5

Hence, the area of the triangle is 7.5 square inches

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The surface area of the pyramid is approximately 74.24 square inches.

What is a pyramid?

A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a single point called the apex. The most common type of pyramid is a square pyramid, which has a square base and four triangular faces.

To find the surface area of the pyramid, we need to find the area of each of the four triangular faces and the area of the square base, and then add them up.

The area of each triangular face can be found using the formula:

Area = (1/2) * base * height

where the base is one of the sides of the square base and the height is the slant height of the pyramid.

The slant height of the pyramid can be found using the Pythagorean theorem:

slant height² = height² + (1/2 * base)²

where the height is the height of the pyramid, which is given as 7 inches, and the base is 4 inches.

height = 7 in.

base = 4 in.

slant height² = 7² + (1/2 * 4)² = 49 + 4 = 53

slant height = √53 ≈ 7.28 in.

Now we can find the area of each triangular face:

Area = (1/2) * base * height = (1/2) * 4 * 7.28 ≈ 14.56 in^2

There are four triangular faces, so the total area of the triangular faces is:

4 * 14.56 = 58.24 in²

The area of the square base is:

Area = side² = 4² = 16 in²

Finally, we can find the surface area of the pyramid by adding up the area of the triangular faces and the area of the square base:

Surface Area = 58.24 + 16 = 74.24 in²

Therefore, the surface area of the pyramid is approximately 74.24 square inches.

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The bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.

(162,000 - 2x) is invested in mortgages.

The annual income earned from the bond investment is:

0.09x

The annual income earned from the CD investment is:

0.07x

The annual income earned from the mortgage investment is:

0.10(162,000 - 2x) = 16,200 - 0.20x

The total annual income earned from the investments is:

0.09x + 0.07x + 16,200 - 0.20x = 14,650

Simplifying and solving for x, we get:

-0.04x + 16,200 = 14,650

-0.04x = -1,550

x = 38,750

Therefore, the bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.

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To find the probability of winning the lottery game, we can use the formula for combinations:

nCk = n! / (k! * (n - k)!)

where n is the total number of choices (22 in this case) and k is the number of choices we make (6 in this case).

So, the number of possible combinations of six numbers from 22 is:

22C6 = 22! / (6! * 16!) = 13,983,816

Therefore, the probability of winning the lottery game is 1 in 13,983,816.

The expected value of playing the lottery game can be calculated as follows:

Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)

Expected value = (1/13,983,816 * $40,000) - (13,983,815/13,983,816 * $1)

Expected value = $0.5709

This means that on average, the player can expect to win about 57 cents per game played. However, it is important to note that this is just an average and the actual outcome of any single game can vary widely.

Based on the data given in the table, B. Median for both coffee shops because the data distribution is not symmetric

It is better to describe the centers of distribution in terms of the median rather than the mean for both coffee shops because the data distribution is not symmetric.

The median is a better measure of central tendency in this case because it is not influenced by outliers or extreme values, which may exist in the data.

The mean, on the other hand, is sensitive to outliers and may not provide an accurate representation of the data distribution.

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The total carbon dioxide emission over a period of 7 years will be 5,13,183 kilotons.

Considering the carbon emissions follow an exponential rate then

A(t)=A₀(1-r)^t

where A₀ is the initial value, and r is the decay rate as a decimal.

For the given problem A₀ =80000 kilotons and emissions will decrease at the rate of 2.5% per year therefore, r=0.025

The general equation for emission becomes

[tex]A(t)=80000(1-0.025)^t[/tex]

[tex]A(t)=80000(0.975)^t[/tex]

To calculate total emissions for 7 years it is calculated as follows

[tex]I=\int\limits^{7}_0 {A(t)} .dt=\int\limits^{7}_0 {80000(0.975)^tdt}[/tex]

[tex]I=80000(0.975)^t/ln (0.975)\left \{ {{t=7} \atop {t=0}} \right.[/tex]

I=5,13,183Kilotonnes

Hence, the total emission of 5,13,183 kilotons of carbon dioxide would be emitted over the course of the 7-year period.

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Answer:

Step-by-step explanation:

After organizing the data, the researcher must present them so they can be understood by those who will benefit from reading the study. The most useful method of presenting the data is by constructing statistical charts and graphs. There are many different types of charts and graphs, and each one has a specific purpose.

This chapter explains how to organize data by constructing frequency distributions

and how to present the data by constructing charts and graphs. The charts and graphs

illustrated here are histograms, frequency polygons, ogives, pie graphs, Pareto charts,

and time series graphs. A graph that combines the characteristics of a frequency distribution and a histogram, called a stem and leaf plot, is also explained.

Section 2–2 Organizing Data 35

2–3

Objective

Organize data using

frequency

distributions.

1

2–2 Organizing Data

Suppose a researcher wished to do a study on the number of miles that the

employees of a large department store traveled to work each day. The researcher

first would have to collect the data by asking each employee the approximate distance the

store is from his or her home. When data are collected in original form, they are called

raw data. In this case, the data are

1 2 6 7 12 13 2 6 9 5

18 7 3 15 15 4 17 1 14 5

4 16 4 5 8 6 5 18 5 2

9 11 12 1 9 2 10 11 4 10

9 18 8 8 4 14 7 3 2 6

Since little information can be obtained from looking at raw data, the research

Answer:

c

Step-by-step explanation:

its ez

The solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.

(a) For f(x) = 0

We set the function equal to zero and solve for x:

f(0) = sec²x - 1 = 0

sec² x = 1

Taking the square root of both sides, we get:

sec x = ±1

Recall that sec x = 1/cos x = cos⁻¹ x

Therefore

x = cos⁻¹ (1) = 0 (using calculator or table)

x = cos⁻¹(-1) = pi

Therefore, the solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.

(b) For f(x) > 0

To get the positive values of x, we can start by factoring f(x):

f(x) = sec²x - 1 = (sec x + 1)(sec x - 1)

Since the square of the secant function is always positive, we have:

f(x) > 0 if and only if (sec x + 1)(sec x - 1) > 0

There are two cases to consider:

sec x + 1 > 0 and sec x - 1 > 0

sec x + 1 < 0 and sec x - 1 < 0

For case 1, we have:

sec x > -1 and sec x > 1

Since secant is always positive, we have sec x > 1.

For case 2, we have:

sec x < -1 and sec x < 1 (This is not possible)

(c) For f(x) < 0

By using the factored form of f(x) from part (b), we can find the values of x where f(x) is negative.

f(x) < 0 if and only if (sec x + 1)(sec x - 1) < 0

There are two cases to consider:

sec x + 1 > 0 and sec x - 1 < 0

sec x + 1 < 0 and sec x - 1 > 0

For case 1, we have:

sec x > 1 and sec x < -1 (not possible)

For case 2, we have:

sec x < -1 and sec x > 1

Since secant is always positive, this case is not possible either.

Therefore, there are no solutions to f(x) < 0 over the interval [0, 2pi).

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