Popular chocolate bar Toblerone is packaged in a triangular prism. Its cross-section is an equilateral triangle of side 3.6 cm and a perpendicular height of 3.1 cm. The length of the bar is 21 cm.

a. State the number of faces, vertices, and edges for this triangular prism.

b. Find the volume of the packaging. Show all your workings and include units in your final answer.

Answers

Answer 1

Answer:

a. The triangular prism has 5 faces, 9 vertices, and 12 edges.

b. To find the volume of the packaging, we need to multiply the area of the base (an equilateral triangle) by the height of the prism.

The area of an equilateral triangle with side length 3.6 cm is given by:

$A = \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4}(3.6\text{ cm})^2 \approx 5.270\text{ cm}^2$

So, the volume of the Toblerone packaging is:

$V = Ah = (5.270\text{ cm}^2)(21\text{ cm}) \approx 110.59\text{ cm}^3$

Therefore, the volume of the Toblerone packaging is approximately 110.59 cubic centimeters.


Related Questions

Vincent flipped three coins during a probability experiment. The outcomes of the first 40 trials are shown
Based on the information in the table, in how many of the next 120 trials will the outcome be exactly two of the coins showing heads? in the table.

Answers

Answer:

I'm sorry, but I cannot see the table you are referring to. However, I can explain the general approach to solving this type of problem.

When flipping a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads on any one flip is 1/2, and the probability of getting tails is also 1/2.

If Vincent has already flipped the coins 40 times and recorded the outcomes, we can use that information to estimate the probability of getting exactly two heads in the next 120 flips.

One way to do this is to find the proportion of the 40 trials that resulted in exactly two heads. Let's say that out of the 40 trials, 10 of them resulted in exactly two heads. Then the proportion of trials that resulted in two heads is:

10/40 = 1/4

This means that the probability of getting exactly two heads in one trial is 1/4.

To find the expected number of trials out of the next 120 that will result in exactly two heads, we can multiply the probability of getting two heads in one trial by the total number of trials:

(1/4) x 120 = 30

Therefore, we would expect that out of the next 120 trials, approximately 30 of them would result in exactly two heads. However, this is just an estimate based on the information given. The actual number of trials that result in exactly two heads could be more or less than 30 due to random variation.

in california, people use 63 btu of energy per home. this is 30% less than the national average. how many btu does an average american household use?

Answers

The national average for energy usage per home in BTU is approximately 90 BTU.

BTU stands for British Thermal Unit, which is the amount of energy required to raise the temperature of one pound of water by one degree Fahrenheit. It is used to quantify the amount of energy consumed by heating or cooling equipment.In California, people use 63 BTU of energy per home, which is 30% less than the national average. Therefore, to calculate the average BTU consumption for American households, we will use the following formula: National average BTU = California BTU / (1 - 30%)

Let's solve for the national average BTU: National average BTU = 63 BTU / (1 - 0.30)

National average BTU = 63 BTU / 0.70National average BTU = 90 BTU

Therefore, the average American household uses 90 BTU of energy per home.

Learn more about  percentages and linear equations:https://brainly.com/question/28654618

#SPJ11

A future interest usually exists in conjunction with which of the following real property interests at the time that it is the interest granted?

Answers

A future interest in real property typically exists in conjunction with a present interest in that same property at the time the future interest is granted.

What is a future interest?

Future interests are created when a property owner grants an interest in their property that will take effect at a later time, such as after their death or the expiration of a lease.

These interests are typically created in the form of a trust or a will, and they can be used to ensure that property is distributed according to the owner's wishes, to provide for the future needs of family members, or to protect property from creditors or other claims.

Examples of future interests include remainders, reversions, and executory interests.

Complete questin:

A future interest usually exists in conjunction with which of the following real property interests at the time that it is the interest granted?

1) future interest

2) protect property

3) both a and b

4) None of these

To know more about Interest:

https://brainly.com/question/13324776

#SPJ11

Bo and Erica are yoga instructors. Between the two of them, they teach 37 yoga classes each week. If Erica teaches 14 fewer than
twice as many as Bo, how many classes does each instructor teach per week?
OA. 19 Bo; 18 Erica
OB. 14 Bo; 23 Erica
OC. 21 Bo; 16 Erica
OD. 17 Bo; 20 Erica

Answers

Answer:

The correct answer is OD.

Step-by-step explanation:

To find how many classes each instructor teaches per week, you need to set up and solve a system of equations based on the given information. In other words,

Let x be the number of classes Bo teaches per week and y be the number of classes Erica teaches per week.

The first equation is based on the total number of classes they teach

x + y = 37

The second equation is based on the relationship between their numbers of classes

y = 2x - 14

To solve this system, you can use substitution or elimination methods. For example, using substitution, you can plug in y = 2x - 14 into the first equation and get

x + (2x - 14) = 37

Simplify and solve for x

3x - 14 = 37

So, Bo teaches 17 classes per week and Erica teaches 20 classes per week.

Answer:

A. 19 Bo; 18 Erica

Step-by-step explanation:

im good like that hehe

The solution to the equation -2(x + 11) = -8 is x = _

Answers

From the given information provided, the value of x for given solution of equation is -7.

An equation is a statement that shows the equality of two expressions. A solution of an equation is a value or values of the variable(s) that make the equation true.

Let's solve the equation step by step:

-2(x + 11) = -8

First, we can distribute the -2 to the term inside the parentheses:

-2x - 22 = -8

Next, we can add 22 to both sides of the equation to isolate the variable term:

-2x = 14

We can divide both sides of equation by -2 to solve for x:

x = -7

The solution to the equation -2(x + 11) = -8 is x = -7.

Learn more about solution here: brainly.com/question/24644930

#SPJ4

how do we ensure trigonometric functions compute values appropriately? what is the value of this expression?

Answers

We can ensure trigonometric functions compute values appropriately by validating the results against known values. In order to ensure that the argument is in a short interval surrounding a place where an approximation is highly accurate, one performs a range reduction prior to computing things like a cos or sin.

By comparing the results to established values, we can make sure trigonometric functions compute values correctly. As an example, if we wanted to validate the cosine of 45 degrees, we could compare the result to the known value of 0.707. If the computed value is within a small margin of error of the known value, then we can assume the trigonometric function is computing values appropriately.

In order to calculate functions like cos or sin, one must first perform a range reduction to make sure the input is inside a narrow range surrounding a point where an approximation is highly accurate. It is typically close to zero.

To learn more about trigonometric functions link is here

brainly.com/question/6904750

#SPJ4

The prisms are similar. What is the surface area of Prism B? Prism A is 10 m. Prism B is 6 m. Surface area = 880m2

Answers

Answer:

79.92m

Step-by-step explanation:

here you go hope this helps

traveling for 3 hr into a steady headwind, a plane flies 1650 mi. the pilot determines tha tflying with the same wind for 2 hr, he could make a trip of 1300. find the rate of the plane and the wind speed

Answers

The rate of the plane (in still air) is 600 miles per hour and the speed of the wind is 50 miles per hour.

Let's denote the rate of the plane (in still air) by p and the speed of the wind by w.

From the first part of the problem, we know that the plane flies 1650 miles in 3 hours against the headwind. This means that the effective speed of the plane (relative to the ground) was 1650/3 = 550 miles per hour slower than its speed in still air, i.e., p - w = 550.

From the second part of the problem, we know that the plane could make a trip of 1300 miles in 2 hours with the same wind. This means that the effective speed of the plane (relative to the ground) was 1300/2 = 650 miles per hour faster than its speed in still air, i.e., p + w = 650.

Now we have two equations with two unknowns, which we can solve using a system of equations. Adding the two equations, we get:

2p = 1200

Therefore, p = 600 miles per hour. Substituting this value into one of the equations, we get:

600 + w = 650

Therefore, w = 50 miles per hour.

Learn more about Speed here:

https://brainly.com/question/2004627

#SPJ4

explain what the p-value means in the given context. a state university wants to increase its retention rate of 4% for graduating students from the previous year. after implementing several new programs during the last two years, the university reevaluates its retention rate and comes up with a p-value of 0.075. using , what can we conclude?

Answers

In this context, the p-value represents the probability of observing the data or a more extreme result, assuming that the null hypothesis (the retention rate is still 4%) is true.

In other words, it measures the strength of evidence against the null hypothesis. A small p-value indicates that the observed result is unlikely to have occurred by chance alone, while a large p-value suggests that the null hypothesis cannot be rejected.

In this case, the calculated p-value of 0.075 suggests that there is some evidence to reject the null hypothesis that the retention rate is still 4%.

However, since the p-value is above the conventional threshold of 0.05, we cannot conclude with certainty that the new programs have significantly increased the retention rate. Instead, we can say that there is some indication that the programs may have been effective, but further investigation is needed to determine if this is true.

To learn more about p-value click on,

https://brainly.com/question/29675177

#SPJ4

An architect is designing a house. He wants the bedroom to have the dimensions of 10 ft by 6 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume of the bedroom. Solve on paper. Then check your work on Does doubling all three dimensions mean the den will have double the volume of the bedroom? Why or why not? Does doubling all three dimensions mean the den will have double the volume of the bedroom? No If he doubles all three dimensions, the den's volume will be more than double the volume of the bedroom.

Answers

Answer:

(2 x 10) x (2 x 6) x (2 x 7) = 3360ft³    <--    the den would be that
The volume:
10 x 6 x 7 = 420ft³       Volume = 8

ginas journal has a square cover with the side length shown. what is the perimeter of the journal? what is the area of the jouranl?

Answers

The given is of the square cover of Gina's journal with a side length of 24 cm. So the perimeter of the journal is  96 cm and the area of the journal would be 576 square cm.

If Gina’s journal has a square cover with a side length of 24 cm, then the perimeter of the journal would be 4 times the side length,

     Which is 4 x 24 = 96 cm.

To calculate the area of a square, you need to multiply the length of one of its sides by itself.

     The formula for the area of a square is,

      Area = Side x Side or Area = Side².

Therefore, the area of the journal would be the side length squared,  

      Which is  24 x 24 = 576 square cm.

Question: Gina's journal has a square cover with the side length shown as 24 cm. what is the perimeter of the journal? what is the area of the journal?

Learn more about the square cover area and perimeter at: https://brainly.com/question/25092270

#SPJ11

during the summer of 2018, coldstream country club in cincinnati, ohio collected data on 443 rounds of golf played from its white tees. the data for each golfer's score on the twelfth hole are contained in the datafile coldstream12. (round your answers to four decimal places.) (a) construct an empirical discrete probability distribution for the player scores on the twelfth hole.

Answers

Given information:

During the summer of 2018, Coldstream Country Club in Cincinnati, Ohio collected data on 443 rounds of golf played from its white tees. The data for each golfer's score on the twelfth hole are contained in the datafile coldstream12. (Round your answers to four decimal places.)

Construct an empirical discrete probability distribution for the player scores on the twelfth hole.

A probability distribution is a tabulation of probabilities for every outcome in a sample space. It is a summary of the probabilities for all possible values of a random variable. In statistics, there are two types of probability distributions: empirical and theoretical.

An empirical distribution is a frequency distribution of observed data. A theoretical distribution is a distribution that is derived from theory.

To construct the empirical probability distribution, we will use the following steps:

Step 1: Calculate the range of the data set, which is the difference between the maximum and minimum values. Range = Maximum value – Minimum value = 8 – 3 = 5.

Step 2: Divide the range by the number of intervals (or classes) desired. In this case, we will use 6 intervals. Interval size = Range / Number of intervals = 5 / 6 = 0.833333333.

Step 3: Determine the lower limit of each interval by subtracting the interval size from the minimum value.

Lower limit of first interval = Minimum value – Interval size = 3 – 0.833333333 = 2.166666667.

Lower limit of second interval = Lower limit of first interval + Interval size = 2.166666667 + 0.833333333 = 2.999999999 ≈ 3.

Lower limit of third interval = Lower limit of second interval + Interval size = 3 + 0.833333333 = 3.833333333.

Lower limit of fourth interval = Lower limit of third interval + Interval size = 3.833333333 + 0.833333333 = 4.666666666.

Lower limit of fifth interval = Lower limit of fourth interval + Interval size = 4.666666666 + 0.833333333 = 5.499999999 ≈ 5.

Lower limit of sixth interval = Lower limit of fifth interval + Interval size = 5 + 0.833333333 = 5.833333333.

Step 4: Count the number of data points that fall in each interval. The table below shows the frequency distribution for the data set.

Interval Lower Limit Upper Limit Frequency Relative Frequency

1 2.166666667   2.999999999  33     0.0745

2 3 3.833333333 93 0.2096

3 3.833333333 4.666666666 74 0.1669

4 4.666666666 5.499999999 56 0.1264

5 5.5 6.333333333 8 0.0180

6 5.833333333 6.666666666 4 0.0090

Total - - 268 1.0000

From the above table, the empirical discrete probability distribution is constructed.

To learn more about empirical, refer below:

https://brainly.com/question/30439049

#SPJ11

How much more interest do vour parents have to pay at the end of the first month because their (i point) rating 15 good rather than excellent?

Answers

The more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent is option (D) $19.02.

First, we need to calculate the sales tax on the mobile home purchase:

Sales tax = 4.2% of $89,000 = 0.042 x $89,000 = $3,738

The total cost of the mobile home including sales tax is

Total cost = $89,000 + $3,738 = $92,738

After making a down payment of $3,000, the amount to be financed is:

Amount financed = $92,738 - $3,000 = $89,738

To calculate the interest, we need to know the monthly interest rate. Let's assume the loan term is 30 years, which is 360 months. Then, the monthly interest rate for an excellent credit rating would be:

Monthly interest rate (excellent) = 4.75 / 1200 = 0.00396

And for a good credit score

Monthly interest rate (good) = 5.00 / 1200 = 0.00417

The interest for the first month for an excellent credit rating would be:

Interest (excellent) = $89,738 x 0.00396 = $355.33

And for a good credit rating:

Interest (good) = $89,738 x 0.00417 = $374.43

The difference in interest is:

Difference in interest = $374.43 - $355.33 = $19.02

Therefore, the correct option is (D) $19.02.

Learn more about credit score here

brainly.com/question/2272694

#SPJ4

The given question is incomplete, the complete question is:

Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment. How much more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent?

Secured Unsecured

Credit APR (%) APR (%)

Excellent 4.75 5.50

Good 5.00 5.90

Average 5.85 6.75

Fair 6.40 7.25

Poor 7.50 8.40

Options:

A) $29.39

B) $21.10

C) $18.71

D) $19.02

a bond is worth 100$ and grows in value by 4 percent each year. f(x) =

Answers

To represent the value of the bond after x years, we can use the function:f(x) = 100 * (1 + 0.04)^xwhere x is the number of years the bond has been held.The expression (1 + 0.04) represents the growth factor of the bond per year, since the bond grows in value by 4 percent each year. By raising this factor to the power of x, we obtain the cumulative growth of the bond over x years.Multiplying the initial value of the bond, 100$, by the growth factor raised to the power of x, gives us the value of the bond after x years. This is the purpose of the function f(x).

Solve for n: 8л = 56

Answers

n/8⋅л=56. You’re welcome!

n
8

л
=
56

8

л
=
5
6


Boom! There ya goooo

the phone calls to a computer software help desk occur at a rate of 3 per minute in the afternoon. compute the probability that the number of calls between 2:00 pm and 2:10 pm is: (a) exactly 25. (b) more than 25.

Answers

The probability that the number of phone calls between 2:00 pm and 2:10 pm is exactly 25 is 1/110,592,893.

To calculate this probability, use the Poisson distribution formula: P(x) = (e^-λ * λ^x) / x!, where λ = 3 x 10 = 30. Therefore, P(25) = (e^-30 * 30^25) / 25! = 1/110,592,893.

The probability that the number of phone calls between 2:00 pm and 2:10 pm is more than 25 is the sum of probabilities of all calls more than 25. That is, the probability is 1 - (e^-30 * (30^0 + 30^1 + 30^2 + ... + 30^25)) / (0! + 1! + 2! + ... + 25!).

By using the same Poisson distribution formula, the probability is 1 - 0.99988822 = 0.00011178.

To know more about Poisson distribution formula click on below link:

https://brainly.com/question/30388228#

#SPJ11

There are many cylinders with a radius of 6 meters. Let h represent the height in meters and v represent the volume in cubic meters. Write an equation that represents the volume, v , as a function of the height, h

Answers

The equation that represents the volume, v, as a function of the height, h is given as: V(h) = 36πh,

where h is the height in meters and V is the volume in cubic meters.

The volume of a cylinder can be calculated using the formula V=πr²h.

Here, we have a number of cylinders with a radius of 6 meters.

Let h represent the height in meters and v represent the volume in cubic meters.

To write an equation that represents the volume, v,

as a function of the height, h,

we can substitute the value of r (radius) with 6m in the formula of the cylinder’s volume,

V = πr²h.

So we get:

V = π(6m)²h

V = 36πh

This equation tells us that the volume of any cylinder with a radius of 6 meters can be expressed as 36πh,

where h is the height of the cylinder.

For similar question on cylinder’s volume.

https://brainly.com/question/27033747

#SPJ11

If the dartboard has a diameter of 14 inches and each number occupies 1/20 of the board, how much space does a single number occupy in square inches?​

Answers

Each number occupies 7.7 inches² of  the dartboard.

What is area?

In geοmetry, area is the amοunt οf space a flat shape, like a pοlygοn, circle οr ellipse, takes up οn a plane. The area οf a shape is always measured in square units. Tο find the area οf simple shapes like a square οr the area οf a rectangle, yοu οnly need its width, w, and length, l (οr base, b). The area is length times width:

First we need the area of the dartboard

Area = πr²

here r = d/2 = 14/2 = 7

Area of dartboard = πr²

[tex]$ \rm = \frac{22}{7 } \times 7 \times 7[/tex]

= 22 × 7

= 154 inches²

Now, its is said that each number occupies 1/20 of the board,

Then area of each number =  154 ×  1/20

                                             = 7.7 inches²

Thus, Each number occupies 7.7 inches² of  the dartboard.

learn more about area

https://brainly.com/question/27683633

#SPJ1

A rectangular garden plot has a length of 4 meters and a width of 3.5 meters. Jackson wants to put a fence around the garden. He also wants to install landscape fabric over the entire plot to prevent weeds. How much fencing will he need to buy? How much landscape fabric will he need to buy?

Answers

Using the formula of area and perimeter of the rectangle, the answers to both subparts are shown:

(A) The fencing required is 15 meters.

(B) The fabric required is 14m².

What is a rectangle?

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°).

A rectangle has equal and parallel opposite sides.

Four sides make up a rectangle, which has opposing sides that are parallel and of equal length.

It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees.

An example of a parallelogram with equal angles is a rectangle.

It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.

A square is a rectangle with four equally long sides.

(A) The required fencing:
Perimeter = 2(l+w)

Perimeter = 2(7.5)

Perimeter = 15

The fencing required is 15 meters.

(B) The landscape fabric required:

Area = l*w

Area = 4*3.5

Area = 14m²

The fabric required is 14m².

Therefore, using the formula of area and perimeter of the rectangle, the answers to both subparts are shown:

(A) The fencing required is 15 meters.

(B) The fabric required is 14m².


Know more about rectangles here:

https://brainly.com/question/25292087

#SPJ1

Oliver spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 6900 feet.
Oliver initially measures an angle of elevation of 16° to the plane at point A. At some
later time, he measures an angle of elevation of 27° to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest tenth of a foot if necessary.

Answers

Thus, the distance travelled by the airplane from point A to point B is found as:  1159.93 ft.

Explain about the angle of elevation?The angle from of the horizontal upward to an item is referred to as the angle of elevation. The line of sight of an observer will rise above the horizontal.The angle from horizontal downward to an item is referred to as the "angle of depression." The line of sight of an observer would fall short of the horizontal.

Let the distance travelled between A and B be 'x'.

Height h = 6900 feet.

The figure is attached.

Using the tan function:

tan Ф = opposite side/ hypotenuse

In right triangle BCE.

tan 27 = 6900 / y

y = 6900 / tan 27

y = 15281.80

In right triangle ACD

tan 16 = 6900 /(x + y)

x + y = 6900/tan 16

x = 26873.72 - 15281.80

x = 1159.93

Thus, the distance travelled by the airplane from point A to point B is found as:  1159.93 ft.

Know more about the angle of elevation

https://brainly.com/question/15580615

#SPJ1

now standardize this distance by dividing it by the population standard-deviation (or standard error). in other words, how many population-standard-deviations (or standard-error) away is your sample mean from the population mean?

Answers

Population-standard-deviations (or standard-error) away is your sample mean from the population mean is therefore (x - μ) / σ.

In order to standardize the distance, we must divide it by the standard deviation of the population (or standard error).How far the sample mean is from the population mean in terms of population-standard-deviations (or standard-error) can be determined by dividing it by the population standard deviation (or standard error). The equation for the same is as follows:
z = (x - μ) / σ
where,
z = standard score,
x = sample mean,
μ = population mean,
σ = population standard deviation.
for such more question on population mean

https://brainly.com/question/28103278

#SPJ11

Isla will deposit $800 in an account that earns 5% simple interest every year. Her sister Aven will deposit $750 in an account that earns 7% interest compounded annually. The deposits will be made on the same day, and no additional money will be deposited or withdrawn from the accounts. Which statement is true about the balances of the girls’ accounts at the end of 48 months?

Answers

To compare the balances of the two accounts, we need to calculate the future value of each account after 48 months.

For Isla's account with simple interest, the interest earned every year is:

$800 x 0.05 = $40

After 48 months (4 years), the interest earned is:

$40 x 4 = $160

So the balance of Isla's account after 48 months is:

$800 + $160 = $960

For Aven's account with compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

where A is the future value, P is the principal (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

For Aven's account, P = $750, r = 0.07, n = 1 (compounded annually), and t = 4. Plugging these values into the formula, we get:

A = $750(1 + 0.07/1)^(1 x 4) = $1039.14

Therefore, the statement "Aven's account will have a higher balance than Isla's account at the end of 48 months" is true.

what is the probability of rolling a sum less than or equal to 7 ? express your answer as a fraction or a decimal number rounded to four decimal places.

Answers

The probability of rolling a sum of 7 or less on two dice is 11/36. This can be expressed as a decimal number rounded to four decimal places as 0.3056.

We need to look at the possibilities when rolling two dice. Each die has six sides, which means the total number of outcomes when rolling two dice is 36. There are 11 combinations of two dice that produce a sum of 7 or less: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (3,1), (3,2). So, 11/36 can be simplified to 1/4, or 0.3056.

To understand this in a more visual way, you can draw a table and use colored dots to indicate the possible combinations. This will show you that out of 36 total possibilities, 11 of them produce a sum of 7 or less.

In summary, the probability of rolling a sum of 7 or less on two dice is 11/36, which can be expressed as a decimal number rounded to four decimal places as 0.3056.

For more such questions on Probability.

https://brainly.com/question/27279592#

#SPJ11

license plates are made using 2 letters followed by 2 digits. how many plates can be made if repetition of letters and digits is allowed?

Answers

The number of license plates that can be made if repetition of letters and digits is allowed is:

67,600

How to determine the number of plates when repeating the letters and numbers?

Can be found by multiplying the number of possibilities for each position.

License plates are made using 2 letters followed by 2 digits. In this case, repetition is allowed, which means that each of the 2 letters can be any of the 26 letters of the English alphabet, and each of the 2 digits can be any of the 10 digits from 0 to 9. Thus, the total number of possible license plates can be found by multiplying the number of possibilities for each position.

There are 26 choices for each of the two letter positions, and 10 choices for each of the two digit positions, so the total number of possible license plates is:

26 x 26 x 10 x 10 = 67,600

Therefore, there are 67,600 plates that can be made if repetition of letters and digits is allowed.

More informationa about Permutations and Combinations here: https://brainly.com/question/28065038

#SPJ11

3. Consider the following statement: For each positive real number r, if r2 = 18, then r is irrational (a) If you were setting up a proof by contradiction for this statement, what would you assume? Carefully write down all conditions that you would assume. (b) Complete a proof by contradiction for this statement.

Answers

(a) To set up a proof by contradiction for the statement "For each positive real number r, if r^2 = 18, then r is irrational," we will assume the opposite of the given statement. Specifically, we would assume that there exists a positive real number r such that r^2 = 18, and r is rational (not irrational).

(b) To complete the proof by contradiction, follow these steps:

1. Assume that there exists a positive real number r such that r^2 = 18, and r is rational.
2. Since r is rational, we can write it as a fraction a/b, where a and b are integers with no common factors other than 1 (i.e., a and b are coprime) and b ≠ 0.
3. We have r^2 = 18, so (a/b)^2 = 18.
4. Squaring both sides, we get a^2 / b^2 = 18.
5. Rearrange the equation: a^2 = 18b^2.
6. Since 18 is an even number, a^2 is also an even number, which implies that a is an even number (let's say a = 2k, where k is an integer).
7. Substitute a with 2k: (2k)^2 = 18b^2, which simplifies to 4k^2 = 18b^2.
8. Divide both sides by 2: 2k^2 = 9b^2.
9. Now, we see that the left side of the equation is an even number (2k^2), which implies that 9b^2 is also an even number. However, 9 is an odd number, so for 9b^2 to be even, b must be even.
10. Both a and b are even, which contradicts our original assumption that a and b are coprime (having no common factors other than 1).

Therefore, our assumption that there exists a positive real number r such that r^2 = 18 and r is rational leads to a contradiction. Thus, the original statement is true: for each positive real number r, if r^2 = 18, then r is irrational.

To know more about Rational and Irrational numbers:

https://brainly.com/question/17450097

#SPJ11

Solve (x – 3)2 = 49. Select the values of x. –46, -4, 10, 52.

Answers

Answer:

x = 10, -4

Step-by-step explanation:

(x – 3)² = 49

x - 3 = √49

x - 3 = ± 7

x = 10, -4

Looking at options,  10 and -4 is the answer.

iii) iv) 1 km 200 m - 500 m = 876 m + 1 km 500 m = v) 2 km 50 m - 950 m =I want answers my questions

Answers

The solution to the conversion of units are:

iii) 1 km 200 m - 500 m = 700 m

iv) 876 m + 1 km 500 m = 2km 376 m

v) 2 km 50 m - 950 m = 1 km 100 m

How to carry out conversion of units?

iii) We want to solve:

1 km 200 m - 500 m

From conversion factors, we know that:

1 km = 1000 m

Thus:

1 km 200 m = 1000m + 200 m = 1200 m

Thus:

1 km 200 m - 500 m = 1200 m - 500 m

= 700 m

iv) We want to solve:

876 m + 1 km 500 m

From conversion factors, we know that:

1 km = 1000 m

Thus:

876m = 0.876 km

1 km 500 m = 1.5 km

Thus:

876 m + 1 km 500 m = 0.876 km + 1.5 km

= 2.376 km or 2km 376 m

v) We want to solve:

2 km 50 m - 950 m

From conversion factors, we know that:

1 km = 1000 m

Thus:

2 km 50 m = 2.05 km

950m = 0.95 km

Thus:

2 km 50 m - 950 m = 2.05 km - 0.95 km

= 1.1 km or 1 km 100 m

Read more about Conversion of Units at: https://brainly.com/question/9032119

#SPJ1

are the following statements true or false? if false, correct the statement. a. the precision of your answer is determined by the largest place of significance when adding and subtracting.

Answers

The statement "the precision of your answer is determined by the largest place of significance when adding and subtracting" is False because The precision of your answer is determined by the number of decimal places when adding and subtracting.

For example, if one number is given to the nearest hundredth and the other is given to the nearest tenth, then the result should be given to the nearest tenth. This is because the tenths place is the largest place of significance in this case.

When adding and subtracting, it is important to take into account the precision of each number before adding or subtracting.

If one number is given to the nearest tenth and the other is given to the nearest hundredth, then the result should be given to the nearest hundredth, as the hundredths place is the largest place of significance.

The same applies for any other number of decimal places.

To know more about decimal places click on below link:

https://brainly.com/question/50455#

#SPJ11

Find the exact value of X.

Answers

In the given right angled triangle, using Pythagorean theorem, the value of x is 12.73 units.

What is Pythagorean theorem?

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the length of the squares on the other two sides add up to the length of the square whose side is the hypotenuse, or the side across from the right angle. This theory can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:

a² + b² =c²

What is Hypotenuse?

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.

In the given right angled triangle, using Pythagorean theorem,

x² = (9[tex]\sqrt{2}[/tex] )²+ (9[tex]\sqrt{2}[/tex] )²

x² = 81×2

x = [tex]\sqrt{162}[/tex]

x = 12.73 units

Therefore, the value of x will be 12.73 units.

To know more about Pythagorean Theorem, visit

https://brainly.com/question/343682

#SPJ1

The diameter of a softball is 3.8 inches. Estimate the volume within the softball. Round answers to the nearest
whole number and leave in the answer.
a. Volume: 73
b. Volume: 14
c. Volume: 9
d. Volume: 58

Answers

The volume of the ball is 9π (optionC)

What is volume of a sphere?

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center.

The ball takes the shape of the sphere. The volume of a sphere is therefore calculated as ;

V = 4/3 πr³

r = d/2 = 3.8/2 = 1.9

V = 4/3 × π × 1.9³

V = 27.44 π/3

V = 9π ( nearest whole number)

therefore the volume of the ball is 9π (nearest whole number)

learn more about volume of a sphere from

https://brainly.com/question/10171109

#SPJ1

Other Questions
When the antifungal agent myxothiazol is added to a suspension of respiring mitochondria, the QH2 / Q ratio increases. Where in the electron transport chain does myxothiazol inhibit electron transfer? which groups tend to have a higher than normal probability of dying themselves in the first year following the death of a spouse? g if the consumer price index increases from 129 to 153 then in percentage terms you would like to have a cost of living adjustment equal to how much? enter a number rounded to two decimal places. You deposit $1,000.00 in an account earning 3.44% interest compounded monthly. How much will you have in the account in 8 years? If you flipped a coin 550 times, how many times would you expect it to land on heads? leanne is 5 months old. chastity is 8 months old. dominique is 25 months old. which infant should show the most evidence of stranger anxiety? the mass of a single atom of an element which has only one stable isotope is 1.79*10^-22 grams. what is the atomic weight of the element explain why the lymphatic system is a one-way system, whereas the blood vascular system is a two-way system Pls help nonsence will be reported and banned offering 100 points!!! and brainiest An office building casts a shadow that is 15 feet long. A nearby tree casts a showdown that is 2/5 feet long. If the tree is 5 feet tall how tall is the office building. the cost allocation method most widely used because of its accuracy and ability to provide a detailed level of analysis is: What is the value of k?127.3 if income is 4,800, consumption is 3,500, government purchases is 1,000, and taxes minus transfers are 800, public saving is: a restaurant offers a special pizza with any 6 toppings. if the restaurant has 16 topping from which to choose, how many different special pizzas are possible? to qualify a column name, precede the name of the column with the name of the table, followed by a(n) . 7 x 10 the the power of -5 at 3:25 p.m., two trains left kalamazoo, michigan. one train traveled westward at a constant rate of kaia's firm took its distinctive competencies and used those when expanding into foreign markets. this provided them with the same firm-specific advantage it had in its original location. which strategic alternative for international business is kaia's firm using? If a 20-kilogram anvil is held 3 meters what is the potential energy? Find the surface area of a rectangular prism