Don, Eric, and Finn line up in random order for the cafeteria line. What is
the probability that they line up from front to back in alphabetical order?*
A- 15.2%
B- 16.6%
C-18.2%
D-21.8%

Answer: Each lateral face would have an area measuring 11.32 square metres.

(2) The total lateral area is 40.88 square metres.

Step-by-step explanation: A three-sided triangular prism as stated in the question would have triangular faces on all sides and since the one in the question is described as a hollow triangular pyramid, we can safely conclude that each surface is a flat/plane shape. Also, each of the triangular surfaces has a base length of 4 metres and a slant height of 6 metres. The surface area is given as

Area of a triangle =  1/2 * base * height

However, the height given is the slant height. Therefore to calculate the vertical height, we shall apply the Pythagoras' theorem, which means the triangular surface would have to be divided into two halves by a perpendicular line that splits the base length into two equal sides. This results in a right angled triangle with the hypotenuse measuring 6 metres and one of the two other sides measuring 2 metres. We now have

AC² = BC² + AB²

Where AC is the hypotenuse 6, BC is one of the other sides 2, and AB is the unknown (slant height).

6² = 2² + AB²

36 = 4 + AB²

Subtract 4 from both sides of the equation

32 = AB²

Add the square root sign to both sides of the equation

√32 = √AB²

5.66 = AB

The area of the triangular surface now becomes;

Area = 1/2*base*height

Area = 1/2 x (4 x 5.66)

Area = 1/2 x 22.64

Area = 11.32 metres²

The total of all three surfaces would be derived as

Surface areas = 11.32 x 3

Surface areas = 33.96 metres²

For the base area, with all three sides measuring 4 metres each, the area would be derived but first we need to calculate the slant height first.

With a line drawn perpendicular to one of the sides, we now have a right angled triangle with the hypotenuse as 4, one of the sides as 2, and the other side unknown (slant height).

AC² = AB² + BC²

4² = 2² + BC²

16 = 4 + BC²

Subtract 4 from both sides of the equation

12 = BC²

Add the square root sign to both sides of the equation

√12 = √BC²

3.46 = BC

The area of the base triangle now becomes;

Area = 1/2*base*height

Area = 1/2 x (4 x 3.46)

Area = 1/2 x (13.84)

Area = 6.92

The total lateral area would now become

Lateral area = Surface area + Base area

Lateral area = 33.96 + 6.92

Lateral area = 40.88 metres²  

Answer:

12 and 36 on edge

Step-by-step explanation:

Answer: 1.8

Step-by-step explanation:

The division, 18 divided by 10 gives 1.8.

Division is one of the basic arithmetic operations in mathematics. It is the opposite of multiplication.

18 divided by 10 means that we are dividing a group of 18 objects into 10 equal groups. That is:

18/10 = 1.8

Note: Since we are dividing by 10, we can move the position of the decimal point to the left by one step.

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Answer:

200

Step-by-step explanation:

A=b×L

A=20×10

A=200

Answer:

Like a square, a rectangle has lines that are perpendicular to two other lines. This means it also has four right angles.

Step-by-step explanation:

Answer:

a right triangle

Step-by-step explanation:

Answer:

D. 80

Step-by-step explanation:

edge 2021

The perimeter of the parallelogram LMNO is 80 cm

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given that, in a parallelogram LMNO, the length of L M is 22 cm and the length of M N is 18 cm.

Perimeter of a parallelogram = 2(sum of two adjacent sides)

= 2(18+22)

= 2×40

= 80

Hence, the perimeter of the parallelogram LMNO is 80 cm

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Answer:

V=Bh so Volume = π4.0 2 16.0 = 804.25

Step-by-step explanation:

Answer:

x=3  y=2

Step-by-step explanation:

2x-y=4

7x+3y=27

Multiply the first equation by 3

3(2x-y)=4*3

6x - 3y+12

Add this to the second equation to eliminate y

6x -3y = 12

7x+3y=27

---------------------

13x +0y = 39

Divide each side by 13

13x/13 = 39/13

x = 3

Now find y

2x-y =4

2(3) -y = 4

6-y=4

Subtract 6 from each side

6-y-6 = 4-6

-y = -2

y=2

Answer:

13.5% probability of a meerkat living between 12.3 and 14.2 years.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 10.4

Standard deviation = 1.9

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above the mean.

Between 12.3 and 14.2 years.

12.3 = 10.4 + 1.9

So 12.3 is one standard deviation above the mean.

50% of the measures are above the mean. Of those, 68% are within 1 standard deviation of the mean.

14.2 = 10.4 + 2*1.9

So 14.2 is two standard deviations above the mean.

50% of the measures are above the mean. Of those, 95% are within 2 standard deviation of the mean.

0.5*0.95 - 0.5*0.68 = 0.135

13.5% probability of a meerkat living between 12.3 and 14.2 years.

Answer:

100

Step-by-step explanation:

100+90+85+95+80= 450,

450/5=90

She has to earn on her next assignment to attain an average of 90 for grade 100.

The average is the middle value of the given data set and is calculated by adding up all the numbers and dividing the result by the total quantity of figures added.

Amy’s current grades for her assignments in math class are 85, 90, 95, and 80.

Let x be the grade she has to earn on her next assignment to attain an average of 90.

The grade does she have to earn on her next assignment to attain an average of 90 is;

[tex]\rm Average =\dfrac{Sum \ of \ all \ grades}{Number \ of \ grades}\\\\ 90 =\dfrac{x+90+85+95+80}{5}\\\\ 90 \times 5 = x+350\\\\450=x+350\\\\x =450-350\\\\x=100[/tex]

Hence, she has to earn on her next assignment to attain an average of 90 for grade 100.

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Answer: -5

Step-by-step explanation:

Answer:

-5 is right

Step-by-step explanation:

Answer:

A =41.81

Step-by-step explanation:

Since this is a right angle, we can use trig functions

sin A = opp/ hypotenuse

sin A = 4/6

SinA = 2/3

Take the inverse sin of each side

sin^-1 (sin A) = sin^-1 (2/3)

A =41.8103149

To the nearest hundredth

A =41.81

To find the surface area of a prism (or any other geometric solid) we open the solid like a carton box and flatten it out to find all included geometric forms. To find the volume of a prism (it doesn't matter if it is rectangular or triangular) we multiply the area of the base, called the base area B, by the height h.

This info should help you.

Answer:

94

Step-by-step explanation:

the area of the 3 x 5 face is used 4 times rather than twice

Answer:

There are many different types of equations we can use to allow x to equal 19! Below are some examples :) See if you can come up with some on your own based off of these examples:

        x = 19.......................................There's one for you :)

        x - 4 = 15..................................Add 4 to both sides

         x = 19

Answer:

45

Step-by-step explanation:

y = 5 * (1/2)^x

Step-by-step explanation:

This is an exponential function

y =ab^x

where a is the initial value ( where x = 0)

a = 5

y = 5 * b^x

Pick a point to determine b

(1,2.5)

2.5 = 5 * b^1

2.5 = 5 *b

Divide each side by 5

2.5/5 = b

b = 1/2

y = 5 * (1/2)^x

Answer: 12km

Step-by-step explanation:

2cm=3km

2x4=8

3x4=12

Final answer:

The real-life distance between two points that are 8 cm apart on a map, with a map scale of 2 cm = 3 km, is 12 km. This is calculated using a proportion based on the given scale ratio.

Explanation:

The question asks how to calculate the real-life distance between two points that are 8 cm apart on a map, given that 2 cm on the map are equal to 3 km in real life. To solve this, we can use a proportion where 2 cm on the map corresponds to 3 km of actual distance. The scale ratio is therefore 2 cm : 3 km. If the points are 8 cm apart on the map, we set up the proportion as follows:

We cross multiply to find x:

So, the real-life distance between the two points is 12 km.

Answer:

Step-by-step explanation:

x= -2

2x² - 5x + 6 = 2(-2)² - 5*(-2) + 6

                  = 2*4 + 10 + 6

                   = 8 + 10 + 6

                  = 24

Answer:

c

Step-by-step explanation:

The function that has a vertex at (2, -9) is;

C: f(x) = (x - 5)(x + 1)

The formula for x-coordinate of a vertex is;

x = -b/2a

The correct function is Option C with f(x) = (x - 5)(x + 1).

We will expand to get;

f(x) = x² -5x + x - 5

f(x) = x² - 4x - 5

Putting 2 for x gives;

f(2) = 2² - 4(2) - 5

f(2) = -9

Also, x = -b/2a = -(-4)/(2*1) = 2

Thus, it is proved that option C has it's vertex at 2, -9

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Answer:

4

Step-by-step explanation:

Answer:

382.5

Step-by-step explanation:

9x10=90

9x9=81

13.5x9=121.5

9x10=90

180+81+121.5= 382.5

There are two triangles.

Area of a triangle = 1/2 x 10 x 9 = 45 square in.

45 x 2 = 90 square inches

One side is 9 x 9 = 81 square inches.

One side ix 10 x 9  = 90 square inches.

One side = 9 x 13.5 = 121.5 square inches.

Total surface area = 90 + 81 + 90 + 121.5 = 382.5 square inches.

Answer:

Step-by-step explanation:

A - C = ( -2, 9) - (- 2 -3) 

= ( 0, 12) 

AC = 12 

B - C = (7 - 3) - ( - 2 -3) 

= (9, 0) 

BC = 9 

ABC is a right -angled triangle with AC as the hypotenuse 

AC = sqrt( 9^2 + 12^2) 

= sqrt(81 + 144) 

= srqt(225) 

= 15 

Perimeter = 12 + 9 + 15 

= 36 units 

 So the answer is 36 units

Answer:

Step-by-step explanation: A - C = ( -2, 9) - (- 2 -3) 

= ( 0, 12) 

AC = 12 

B - C = (7 - 3) - ( - 2 -3) 

= (9, 0) 

BC = 9 

ABC is a right -angled triangle with AC as the hypotenuse 

AC = sqrt( 9^2 + 12^2) 

= sqrt(81 + 144) 

= srqt(225) 

= 15 

Perimeter = 12 + 9 + 15 

= 36 units 

 So the answer is 36 units

Joy's approach to sampling art at the gallery, by examining 2 pieces per artist, can be representative if the selections span the artists' exhibited range. However, the representativeness might be limited if artists have a wide variety of styles or themes not captured by just two pieces.

Joy, by examining 2 pieces of art by each artist at the art show, attempts a representative sampling of the gallery's overall offerings. Whether this approach yields a representative sample depends on a few key factors. Primarily, the diversity and range of the artists' works on display must be considered. If each artist displays a wide variety of work and Joy's selections span this variety, her sample could offer a fair representation of the gallery's exhibition. However, if the artists have a vast body of work with significant variations in style, theme, or period not captured by just two pieces per artist, Joy's sample may not accurately represent the entire collection.

Furthermore, the extent to which the selected works reflect the artists’ core themes or periods plays a critical role in determining representativeness. Assuming each artist's work on display has an equal chance of being selected and Joy chooses pieces that span the artists' exhibited range, the sample can be somewhat representative. Nonetheless, a truly comprehensive view would likely require examining a greater number or a more strategically chosen set of artworks.

Joy’s examination provides valuable insights, but for a truly representative view of the gallery, additional observations or data would be beneficial.

Let’s explore the concept of representative samples in the context of Joy’s art gallery experience.

1. Understanding Representative Samples:

o A representative sample is a subset of a larger population that accurately reflects the characteristics of the entire population. In this case, the population consists of all the art pieces displayed in the gallery.

o When we say a sample is “representative,” it means that the selected pieces adequately capture the diversity and essence of the entire collection.

2. Joy’s Situation:

o Joy closely examined 2 pieces of art by each artist. Since each artist had an equal number of pieces on display, Joy effectively observed a balanced representation of the artists’ work.

o By examining multiple pieces from each artist, Joy has a better chance of encountering a variety of styles, themes, and techniques.

3. Likelihood of Representativeness:

o Given that Joy looked at 2 pieces from each artist, we can consider this sample as potentially representative.

o However, there are a few factors to consider:

 Artistic Diversity: If the artists’ styles are vastly different, the sample may not fully represent the entire gallery’s range.

 Number of Artists: If there are only a few artists in total, the sample might be less representative.

 Gallery Size: The larger the gallery, the more challenging it is to capture full representativeness with a limited sample.

4. Conclusion:

o While Joy’s sample is a good start, it’s essential to recognize its limitations.

o To determine true representativeness, we’d need more information about the total number of artists, the overall collection size, and the diversity of artistic approaches.

In summary, Joy’s examination provides valuable insights, but for a truly representative view of the gallery, additional observations or data would be beneficial.

Answer: X=7

Step-by-step explanation: Use the formula (b/2)^2 in order to create a new term. Solver for X by using this term to complete the square.

X=7

Answer:

20

Step-by-step explanation:

The volume of a cone is given as:

[tex]V = \frac{1}{3} \pi r^2 h[/tex]

where r = radius

h = height

The volume of the cone is 540π and its radius is 9.

This implies that:

[tex]540 \pi = \frac{1}{3} \pi * 9^2 * h\\\\h = \frac{540 * 3}{81} \\\\h = 20[/tex]

The height of the cone is 20.

Answer:

The answer is 20 bro

Step-by-step explanation:

Answer:

2 + 2  =4

2 * 2 = 4

so, 2 + 2 = 2 * 2

Step-by-step explanation:

2 + 2  =4

2 * 2 = 4

so, 2 + 2 = 2 * 2

Yes, 2 PLUS 2 the same answer as 2 TIMES 2. The explanation is given.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

Expression,

2 PLUS 2 and 2 TIMES 2

In numerator form,

2+2 = 4

2 x 2 = 4

Multiplication is a mathematical arithmetic operation.

It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Therefore, solution of 2 PLUS 2 and 2 TIMES 2 is 4.

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Final answer:

When two number cubes are rolled, the events of rolling the same number and getting an odd sum are mutually exclusive, as one excludes the possibility of the other occurring.

Explanation:

Two events are considered mutually exclusive if the occurrence of one event excludes the possibility of the other event occurring simultaneously. When examining whether the events of rolling two number cubes are mutually exclusive, we look at two particular events:

   The numbers rolled are the same.

   The sum of the numbers rolled is odd.

Two number cubes can simultaneously show the same number, which would be an even number (since the pairs would be (2,2), (4,4), or (6,6)) and not lead to an odd sum. Therefore, if we roll the dice and get two numbers that are the same, we cannot get an odd sum. This means that these two events cannot happen at the same time, so the correct answer is:

A. Yes because if one event occurs, the other can't occur.

Answer: The height of the monitor is 12 inches.

Step-by-step explanation:

First, you need to acknowledge the Pythagorean Theorum,

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

You already have the c and the b , so you just have to plug them in to find a!

This is what it looks like when you substitute:

a² + 16² = 20²

Then, simplify.

a² + 256 = 400

Now, to isolate the variable, you have to move 256 to the other side. This, of course, means it changes from a positive to a negative number.

a² = 400 - 256

a² = 144

Now, you have to remove the square root from a. But, don’t forget, what you do to one side, you have to do to the other side. So, your equation will now look like this:

√a²  = √144

The square root of a squared is obviously just a! And the square root of 144 is 12. Therefore, we now know that:

a = 12

So, the height of the monitor was 12 inches.

I believe you are looking for, intersecting.

Step-by-step explanation:

Step 1:  Convert miles to feet

1 mile = 5280 feet

1.5 * 5280

7920 feet

Answer:  7920 feet

Answer:

150 degrees

Step-by-step explanation:

HOPE THIS HELPED!

The measure of an angle between 0° and 360° coterminal with 510° is 150°. The difference between coterminal angles yields 360°.

The angles that share a common terminal side are said to be coterminal angles. So, the difference between those angles is 360°.

The given coterminal angle is 510°.

So, the reference angle = 510° - 360° = 150°

Thus, the angle is required as a measure of 150°.

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