Take a stick of unit length and break it into three pieces, choosing the break point at random. (The break points are assumed to be chosen simultaneously). What is the probability that the three pieces can be used to form a triangle?

Answer:

896 apples

Step-by-step explanation:

We need to order this data to solve the problem. "X" will be the total number of apples he collected.

"He gave the first guard half of his apples and 1 apple more". Mathematically:

[tex]Guard 1 = \frac{X}{2}+1\\[/tex]

"To the second guard, he gave half his remaining apples and 1 more". Mathematically:

[tex]Guard2 = \frac{X}{4}+1[/tex]

"He did the same to each of the remaining five guards". Mathematically:

[tex]Guard3to7 = \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]

Now we need to calculate "X" (total number of apples he collected). Let's sum all of the data above, that's our "X":

[tex]X= \frac{X}{2}+1 + \frac{X}{4}+1 + \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]

Solving this equation results in X = 896 apples.

Answer:

134.375 - 12.5 - 6 = 115.875

The area of the rug that can be seen after covering love seat and entertainment center is 115.875 square feet.

A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.

Given that,

The length of rug in living room = 12¹/₂ feet = 25 /2 feet.

And the width of rug = 10 ³/₄ feet= 43 /4 feet.

The area of the rug = width x length = 25/2 x 43 / 4 = 1075 / 8 = 134.375 square feet.

Also given that,

A love seat having area =  12¹/₂ square feet.

And area of entertainment center = 6 square feet

Area covered by love seat and entertainment center = 12.5 + 6 = 18.5 square feet

The remaining area that can be seen = 134.375 - 18.5 = 115.875 square feet.

The required area is 115.875 square feet.

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Answer:13

Step-by-step explanation: Six down to zero. Then zero up to seven.

Answer:

  y = 8x + 3

Step-by-step explanation:

The slope-intercept form of the equation of a line is ...

  y = mx + b

Putting 8 where m is, and 3 where b is, we get ...

  y = 8x + 3

_____

Yes, it's really that simple.

The equation of the line with a slope of 8 and a y-intercept of 3 is y = 8x + 3. This is found by substituting the given values into the slope-intercept formula, which is y = mx + b.

In Mathematics, the slope-intercept form of a linear equation is given by the formula y = mx + b, where 'm' represents the slope of the line and 'b' represents the y-intercept of the line. So, for the question, since the given slope, m = 8, and the y-intercept, b = 3, you can substitute these values into the formula to get the equation of the line. This results in the equation y = 8x + 3.

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Answer:

This is cluster sampling.

Step-by-step explanation:

American Airlines randomly selects 110 flights during a certain week and surveys all passengers on the flights.

This is a type of cluster sampling.

This type of sampling is done by dividing the population into different groups and a simple random sample of clusters is selected from the population.

The solution of the expression (6x – 5 + 4x²) + (2x - 2) will be;

⇒ 4x² + 8x - 7

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (6x – 5 + 4x²) + (2x - 2)

Now, Solve the expression is solve as,

⇒ (6x – 5 + 4x²) + (2x - 2)

⇒ 6x – 5 + 4x² + 2x - 2

⇒ 4x² + 6x + 2x - 5 - 2

Solve common terms,

⇒ 4x² + 8x - 7

Therefore,

The solution of the expression (6x – 5 + 4x²) + (2x - 2) will be;

⇒ 4x² + 8x - 7

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Explanation:

All of the points must be contained within a circle that will circumscribe an equilateral triangle of area 1. (We refer to this as the inscribed triangle.) Any points on the circle that do not form an equilateral triangle will form a triangle with an area less than 1. Likewise for any points within the circle.

The circle can be circumscribed by an equilateral triangle whose side length is double that of the inscribed triangle. Since the side length is double, the circumscribing triangle will have an area 2² = 4 times that of the inscribed triangle.

The inscribed triangle has an area of 1, so the circumscribing triangle must have an area of 4.

Answer:

1/18

Step-by-step explanation:

We are considering that we have 2 dices with 6 faces each (so, the probability to gettig any face in any dish is 1/6). To get an 11, we only have two ways to obtain it:

Dice 1= 6 and Dice 2 =5

or

Dice 1= 5 and Dice 2 =6

So, the probability of the event is given as:

P(Dice1=5 ∧ Dice2=6) ∪ P(Dice1=6 ∧ Dice2=5) = P(Dice1=5) x P(Dice2=6) + P(Dice1=6) x P(Dice2=5) = 1/6 x 1/6 + 1/6 x 1/6 = 1/36 + 1/36 = 2/36 = 1/18.

As 1/18 = 0,055, and 0,055 > 0,05, we consider the event as not significative (according to the definition of significance in the sentence).

Answer:

When you throw a dice, the total number of options that you can get is the product of the number of options for each dice, this means that the total number of combinations is:

c = 6*6 = 36 combinations.

Now, the combinations where the dice add to 11 are:

5 in one dice and 6 in the other.

6 in one dice and 5 in the other.

so out of 36 combinations, we have 2 options where we have an 11.

then the probability is the combinations that add to 11 divided by the total number of combinations:

p = 2/36 = 1/18 = 0.056

the probability is greater than 0.05, so it is significant.

Answer:

5x - y = 27

Step-by-step explanation:

Slope is the direction of line and it is calculated as,

[tex]Slope = \frac{y-y_{1}}{x-x_{1}} [/tex]

where (x₁, y₁) is any two points on the line.

Here, we have given that

Slope = 5  and (x₁, y₁) = (5, -2)

∴  [tex]5 = \frac{y-(-2)}{x-5} [/tex]

⇒ 5(x - 5) = y + 2

⇒ 5x - 25 = y + 2

⇒ 5x - y = 27

Hence, the equation of a line is: 5x - y = 27

Answer:

The answer to your question is:

a) ∠FGH = 34°

b) ∠HGI = 34°

c) ∠FGI = 68°

Step-by-step explanation:

We know that GH bisects ∠FGI

a) Find ∠FGH

∠ FGH = 5x - 6

∠ HGI = 6x -14

                      ∠ FGH = ∠ HGI

                     5x - 6   =  6x - 14

                    5x - 6x = -14 + 6

                          -1x = - 8

                            x = 8

∠ FGH = 5(8) - 6

            = 40 - 6

            = 34°          

b) m∠HGI = 6(8) -14

                = 48 - 14

                =  34°          

c) m∠FHI =  ∠ FGH + ∠ HGI

                = 34 + 34

               = 68°    

Answer:

1st car is 6mph 2nd car is 100mph

Step-by-step explanation:

ans to first car is in the question

and just subtract total travelled distance of car 1 after 2.5 hours. then subtrct it from the total distance and with the remaining distance solve for speed of other car which is distance over time.

The speed of the slower car is 52 mph, and the speed of the faster car is 52 mph + 6 mph, which equals 58 mph. This was calculated using the relationship between speed, distance, and time.

Let's denote the speed of the slower car as v miles per hour (mph), which means the faster car will have a speed of (v + 6) mph. Since they are travelling in opposite directions, their speeds add up when determining how far apart they will be over a period of time.

Combined speed = v + (v + 6) = 2v + 6 mph

After 2.5 hours, they are 275 miles apart. Using the formula for distance, which is Distance = Speed ×Time, we have:

Distance = (2v + 6) × 2.5

275 miles = (2v + 6) × 2.5

Solving for v, we divide both sides by 2.5:

110 = 2v + 6

Now, subtract 6 from both sides:

104 = 2v

Finally, divide by 2 to find the speed of the slower car:

v = 52 mph

Therefore, the speed of the slower car is 52 mph, and the faster car is 52 mph + 6 mph, which equals 58 mph.

Answer:

[tex]p=\left \{ {{15.99,m[tex]\leq[/tex]130} \atop {15.99+0.09*(m-130),m>130}} \right.[/tex]

Step-by-step explanation:

We will have a partial funcion to define an expression for the monthly phone charge, because we have a condition that changes the monthly cost.

For months under 130 minutes, there will not be any additional charge other that tha base monthly cost, so the expression for the months under 130 minutes will be the monthly fee.

For months over 130 we will have the same information than above, but we have to add a fee for every minute over 130 minutes. To find the amaunt of minutes over 30 minutes we will just subtract 130 to the amount of minutes used: (m-130). Then we will multiply that number times the cos of each minute over 130 minutes: 9*(m-130). Finally we will add the basic phone fee: 15.99 + (0.09*(m-130)).

Now we set the conditions and use the correct notation for a partial function and we get:

[tex]p=\left \{ {{15.99,m[tex]\leq[/tex]130} \atop {15.99+0.09*(m-130),m>130}} \right.[/tex]

given the equation is written in text so the signs and operators are weird, i don't understand the question but an inverse of any function can be found by switching f(x) or y with x.

For example if f(x) = 3x, then the inverse is x = 3y or y=x/3

Final answer:

The inverse of the function [tex]f(x) = \sqrt[3]{7x - 21} - 3[/tex] is found by first expressing the function as [tex]y = \sqrt[3]{7x - 21} - 3,[/tex] then isolating x, and finally expressing x in terms of y, resulting in the inverse function[tex]f^{-1}(y) = \frac{(y + 3)^3 + 21}{7}.[/tex]

Explanation:

To find the inverse of the function [tex]f(x) = \sqrt[3]{7x-21} - 3,[/tex]  we want to solve for x in terms of y. First, we replace f(x) with y to get [tex]y = \sqrt[3]{7x-21} - 3.[/tex] We then solve for x using the following steps:

Add 3 to both sides of the equation to get[tex]y + 3 = \sqrt[3]{7x-21}.[/tex]

Raise both sides to the power of 3 to eliminate :[tex](y + 3)^3 + 21 = 7x.[/tex]

Finally, divide by 7 to isolate x, so[tex]x = \frac{(y + 3)^3 + 21}{7}.[/tex]

Thus, the inverse function is [tex]f^{-1}(y) = \frac{(y + 3)^3 + 21}{7}.[/tex]

Step-by-step explanation:

By the problem we know that our events are:

[tex]A=[/tex]A batch is formed from two different lots.

[tex]B=[/tex]A batch requires additional processing.

So, according to that:

a) [tex]P(A)=3%=0.03[/tex]

Because P(A) and [tex]P(A^{'} )[/tex] are complementary events

b) [tex]P(A^{'} )=1-P(A)=1-0.03=0.97=97%[/tex]

Because of the problem, we know that:

c) [tex]P(B/A)=0.4=40%[/tex]

and,

d) [tex]P(B/A^{'} )=0.05=5%[/tex]

From the formula

e) P(A ∩ B)= P(A)*P(B/A)=[tex](0.03)*(0.4)=0.012[/tex]

f) P(A ∩ B')=P(A)-P(A ∩ B)=[tex]0.03-0.012=0.018[/tex]

And, finally

g) P(B)=P(B/A)*P(A)+P(B/A')*P(A')=[tex](0.4)*(0.03)+(0.05)(0.97)=0.0605[/tex]

(a)Probability of P(A) = 0.03  (b)Probability ofP(A')  = 0.97.(c) Probability of P(B|A) = 0.40 (d) Probability of P(B|A') = 0.05 (e) Probability of P(A ∩ B) = 0.012. (f)Probability of P(A ∩ B') =  0.03 - 0.012 = 0.018. (g) Probability ofP(B) = 0.0605.

Let's determine the various probabilities step-by-step for the given scenario.

       Given: P(A) = 0.03 (3% of all batches).

        P(A') = 1 - P(A) = 1 - 0.03 = 0.97.

       Given: P(B|A) = 0.40 (40% of such batches).

        Given: P(B|A') = 0.05 (5% of such batches).

        P(A ∩ B) = P(B|A) * P(A) = 0.40 * 0.03 = 0.012.

        P(A ∩ B') = P(A) - P(A ∩ B) = 0.03 - 0.012 = 0.018.

       P(B) = P(B|A) * P(A) + P(B|A') * P(A') = (0.40 * 0.03) + (0.05 * 0.97) =    0.012 + 0.0485 = 0.0605.

Answer:

For this question there appears to be absolutely no association. The points are all over the place and there is not consistent factors at play here.

Answer:

Actual Perimeter = 100 km

        Actual Area = 625 km²

Step-by-step explanation:

A scale drawing of a square has a side length of 5 millimeters.

The drawing has a scale of 1 mm : 5 km (which represents 1 mm is equal to 5 km)

We need to find the actual measurement of 5 mm square on scale.

                1 mm = 5 km

               5 mm = 5 × 5 km

                          = 25 km

The actual length of the side of square is 25 km

Now, we find the perimeter and area of the square.

                                 = 4 × 25

                                = 100 km

                                        = 25 × 25

                                        = 625 km²

Hence, The actual perimeter is 100 km and area of the square is 625 km²

If the orbit of the Moon around Earth is circular and the 1 revolution takes 27.3 days, the linear speed of the moon is 2291.94335 miles/hour.

The speed with which an object moves in a linear path is known as its linear speed.

The following are given:

The mean distance of the moon from Earth (r) is [tex]2.39\times10^5[/tex] miles.

The total distance covered by the moon in 1 revolution is 2πr.

The time taken for 1 revolution by the moon (T) is 27.3 days.

It is known that there are 24 hours in a day.

So, 27.3 days = 27.3 × 24 hours

The linear speed(v) of the moon can be calculated by dividing the distance covered by the time taken to complete a revolution as follows:

[tex]v = \dfrac{2\pi r}{T}[/tex]

   [tex]=\dfrac{2\times3.14\times2.39\times10^5}{27.3\times24}\\= 2291.94335\ miles/ hour[/tex]

Therefore, the linear speed of the moon is 2291.94335 miles/hour.

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To find the linear speed of the Moon, we calculate its circumference and divide it by the time taken for one revolution. The linear speed of the Moon is approximately (2π(2.39x10^5)) / (27.3 x 24) miles per hour.

To find the linear speed of the Moon, we first need to calculate its circumference. The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, the radius is the mean distance of the Moon from Earth, which is 2.39x10^5 miles. So, the circumference is 2π(2.39x10^5) miles.

To find the linear speed, we need to divide the circumference by the time it takes for the Moon to complete one revolution around Earth. Since each revolution takes 27.3 days, we need to convert that to hours. There are 24 hours in one day, so 27.3 days is equal to 27.3 x 24 hours. Finally, we divide the circumference by the time to get the linear speed in miles per hour.

Therefore, the linear speed of the Moon is approximately (2π(2.39x10^5)) / (27.3 x 24) miles per hour.

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Answer: There are 151,200 ways the members can be appointed.

Step-by-step explanation:

Since we have given that

Number of eligible candidates = 10

Number of remaining spots available = 6

Here, rank matters.

so, we will use "Fundamental theorem of counting or by Permutation":

So, Number of different ways the members can be selected is given by

[tex]^{10}P_6=10\times 9\times 8\times 7\times 6\times 5\\\\=151,200[/tex]

Hence, there are 151,200 ways the members can be appointed.

The number of different ways the president can appoint the members of the cabinet given that order matters and there are 10 eligible candidates for the remaining 6 positions is 151,200.

The question is asking for the number of different ways the six remaining cabinet positions can be filled, given that there are ten eligible candidates and rank matters. This scenario is an example of a permutation problem in combinatorics, a subfield of mathematics. A permutation is an arrangement of objects in a specific order. If rank matters, this means that the order in which the candidates are chosen for the cabinet positions is important. In this case, the formula for permutations is applicable. The formula for permutation when there are 'n' items available (10 eligible candidates) and 'r' items are chosen (6 positions) is given by nPr = n! / (n-r)!. Substituting these values, we have 10P6 = 10! / (10-6)!. After performing the calculation, we find there are 151,200 different ways in which the president can appoint the members of the cabinet.

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Answer:

The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.

Step-by-step explanation:

The scenario that is most likely to be shown in the graph is:

The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.

We can see that the initial calories are 50 as shown in the graph.

When x=0 the value on the y-axis is 50.

And this value is increasing by 100 units.

Answer:

The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.

Choice D.

Step-by-step explanation:

Answer:

Self-fulfilling prophecy

Step-by-step explanation:

According to my research on studies conducted by various psychologists, I can say that based on the information provided within the question this is an example of a Self-fulfilling prophecy. This is defined as a phenomenon of when an individual believes something will happen a certain way, and that event ends up happening only because the individual changed their behaviors and actions causing it to happen. Which is what Jenna did with her statistics class.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

Self-fulfilling prophecy

Step-by-step explanation:

A  self-fulfilling prophecy is the social and psychological phenomenon that, when exposed to a personal belief,  a person will change its conduct or behaviour in order to confirm or make real that particular belief in order to   avoid cognitive dissonance or the fact of being wrong.

Jenna believes she is bad in statistics. But that belief, which is not really or necessarily true, makes her change her behaviour and not study or abandon her effort to become better at statistics, which at the same time makes her perform badly in statistics in the future. This reinforcing loop maintains the belief and prophecy going in time.

Answer:

Han used a convenience nonrandom sampling approach

Step-by-step explanation:

The convenience nonrandom sampling approach consists in collecting a sample just because it is convenient. This means that the subjects are easy to select.

Han did precisely this, he went to the teacher's lounge and surveyed the faculty present there. He did not put any further effort like, for example, wait for more teachers to have a larger sample or make sure the ratio between female and male teachers was the same.

Answer:  it is B.) 7,000,000

Step-by-step explanation:

Answer:

The answer to your question is: $ 3.92 / kg

Step-by-step explanation:

Data

Lean ground beef cost = $1.78

price of 1 kg = ?

Equivalence  1 kg = 2.2 lbs

Process (rule of three)

                                 $1.78  -------------------   1 pounds

                                    x      -------------------    2.2 pounds

                       x = 2.2(1.78) / 1 = $ 3.92 / kg

Answer:

55 children's tickets

Step-by-step explanation:

Let the number of adult tickets sold  = a

Let the number of children tickets sold = c

As per the statement "The adult tickets were sold four times as many as children's tickets".the equation will be

a = 4c ----- (1)

As per second statement "the prices of the tickets for adults and children are $10 and $5 respectively."

The total price of the adult tickets = 10a

the total price of the children tickets = 5c

total tickets were sold for = $2,475

So the equation will be

10a + 5c = 2,475 ------(2)

Now substitute the the value of a from equation (1) to equation (2).

10(4c) + 5c = 2,475

40c + 5 c = 2,475

45c = 2,475

c = [tex]\frac{2475}{45}[/tex]

c = 55

The number of children's tickets 55.

Final answer:

To find the number of children's tickets sold in a spaghetti dinner event with given total sales and ticket prices, set up and solve the relevant equations step by step.

Explanation:

Given:

Total ticket sales for a spaghetti dinner = $2475

Adult ticket price = $10

Children's ticket price = $5

Number of adult tickets sold = 4 times the number of children's tickets sold

To find: Number of children's tickets sold

Step-by-Step Solution:

Let the number of children's tickets sold be x

Number of adult tickets sold = 4x

Write the equation: 5x + 10(4x) = 2475

Solve for x to find the number of children's tickets sold

x = 55

Answer:

q.1 quarter mile

q.2 half mile

:)

addition!

Step-by-step explanation:

Answer:

Transformation is the altering of shapes using different operations.

Step-by-step explanation:

The different operations of transformation are translation, reflection, and rotation.

Step-by-step explanation: A transformation is when we change the position or size of a given figure.

In part a, notice that we can flip the triangle on the left over the following line to the position of the triangle on the right. When we flip a figure over a line to create a mirror image, the new image is called a reflection. Therefore, the transformation shown in part a is called a reflection.

In part b, notice that we can turn the triangle on the top to the position of the triangle on the bottom. When we turn a figure to a new position, it's called a rotation. Therefore, the transformation in part b is a rotation.

In part c, notice that we can slide the triangle on the left to the position of the triangle on the right. When we slide a figure to a new position, it's called a translation. Therefore, the transformation in part c is a translation.

In part d, notice that the triangle on the left has been reduced in size to form the triangle on the right. When we reduce or increase the dimensions of a figure while maintaining its shape, the new image is called a dilation. Therefore, the transformation in part d is a dilation.

the answer is b)  5/3    1/3

                           x       y

Answer:

The answer to your question is: 3.7 hours

Step-by-step explanation:

Kam can make 72 cookies/ 3 hours

Madison can make 120 cookies/4 hours

Time to make 200 cookies together = ?

First, calculate the number of cookies make per hour

Kam            72 ---------------- 3

                   x   ----------------  1 hour

  x = 72/3 = 24 cookies/h

Madison

             120 -------------   4 hours

               x ---------------      1 hour

x = 120 / 4 = 30 cookies

Now we write and equation where "t" will be time

         24t + 30t = 200      and solve it

         54t = 200

        t = 200/54

        t = 3.7 hours

The time taken by both of them will be 3.7 hours.

The ratio of two numbers a and b can be written as a : b = a/b.

The ratio of two quantities is the unit rate of one quantity with respect to the other.

The given problem can be solved as follows,

The number of cookies made by Kam in 1 hour = 72/3 = 24.

The number of cookies made by Madison in 1 hour = 120/4 = 30.

The total number of cookies made by them in one hour = 30 + 24 = 54.

The time taken to make 200 cookies is the ratio of 200 and 54 as given below,

Time taken by both to make 200 cookies = 200/54 = 3.7 hours.

Hence, Kam and Madison would take 3.7 hours to make the cookies together.

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Answer:

Either B or D.

Step-by-step explanation:

I consider both options valid. It all depends on how the employer is keeping track of time, ie if the pay "ticks" every 60 minutes, or an employee is allowed to clock in half hours.

Will I be able to work 30 and a half hour for example? If I'm allowed to, D.

If I have to work multiple of 60 minutes, B.

Answer:

The answer is D

Step-by-step explanation: