How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the batoon. All balloons have a temperature gauge in the crown. Suppose that 55 readings (for a balloon in equilibrium) gave a mean temperature of x-97°C. For this balloon, -18°C. (a) Computea 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium (Round your answers to one decimal place.) lower mit 'C "C upper limit (b) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, de you expect that the balloon will go up or down? Explain It will go down because hot air will make the balloon fal It will go up because hot air will make the balloon fall O will go down because hot air will make the balloon rise It will go up because hot air will make the balloon rise Need Help?

Hey there! I'm happy to help!

We want to find how much paper we need to make the cup. So, we need to find the surface area of the cylinder, which is basically the "walls and floors" of the cup. So, this is the circle on the bottom and the surrounding stuff that goes up. There is no circular top to this cup, which will be important when finding the total area of paper.

So, first we need to find how much paper we need to make the bottom circle. The formula for the area of a circle is A=πr². This r represents the radius, or the distance from the center of the circle to the edge. We are given that the cup is 3 cm completely across, and the radius is be half of that, so the radius is 1.5 cm. Let's find the area. We will use 3.14 for π.

π×1.5²=7.065

Now, we need  to find the area of the walls of the cup. The wall is a rectangle that is basically wrapped around the circle. The height of the rectangle is the height of the cup and the length of the rectangle is the circumference (perimeter) of the bottom circle because the length of the rectangle wraps completely around the circle.

First, let's find the circumference of the circle. The circumference is the diameter (distance across the circle, so 3 cm) multiplied by π. We will use 3.14 for π.

3π=9.42

So, this means that the long side of the rectangle is 9.42 cm, and now we multiply this by the height.

9.42×6.4=60.288

Now, we add the rectangle area and the bottom circle area.

60.288+7.065=67.353

But, they want us to round to the nearest centimetre, so we will just say 67 square centimetres.

An important thing to note is that this is not  the area of a normal cylinder (one with a top and a bottom circle) because it is a cup so it does not have a top. If you have a cylinder with a top and a bottom, you would just multiply the area of the circle by two, so then you have the top and bottom. If that were the case, the area of our cylinder would be 74 cm with the numbers we have been given here.

Have a wonderful day!

Answer:

1 is your answer.........

99% of people consumed less than 54.3 gallons of bottled water. The probability that someone consumed more than 30 gallons of bottled water is 0.512. The probability that someone consumed less than 30 gallons of bottled water is 0.488.

a. Probability that someone consumed more than 30 gallons of bottled water = P(X > 30)

Using the given mean and standard deviation, we can convert the given value into z-score and find the corresponding probability.

P(X > 30) = P(Z > (30 - 30.3) / 10) = P(Z > -0.03)

Using a standard normal table or calculator, we can find the probability as:

P(Z > -0.03) = 0.512

Therefore, the probability that someone consumed more than 30 gallons of bottled water is 0.512.

b. Probability that someone consumed between 30 and 40 gallons of bottled water = P(30 < X < 40)

This can be found by finding the area under the normal distribution curve between the z-scores for 30 and 40.

P(30 < X < 40) = P((X - μ) / σ > (30 - 30.3) / 10) - P((X - μ) / σ > (40 - 30.3) / 10) = P(-0.03 < Z < 0.97)

Using a standard normal table or calculator, we can find the probability as:

P(-0.03 < Z < 0.97) = 0.713

Therefore, the probability that someone consumed between 30 and 40 gallons of bottled water is 0.713.

c. Probability that someone consumed less than 30 gallons of bottled water = P(X < 30)

This can be found by finding the area under the normal distribution curve to the left of the z-score for 30.

P(X < 30) = P((X - μ) / σ < (30 - 30.3) / 10) = P(Z < -0.03)

Using a standard normal table or calculator, we can find the probability as:

P(Z < -0.03) = 0.488

Therefore, the probability that someone consumed less than 30 gallons of bottled water is 0.488.

d. 99% of people consumed less than how many gallons of bottled water?

We need to find the z-score that corresponds to the 99th percentile of the normal distribution. Using a standard normal table or calculator, we can find the z-score as: z = 2.33 (rounded to two decimal places)

Now, we can use the z-score formula to find the corresponding value of X as:

X = μ + σZ = 30.3 + 10(2.33) = 54.3 (rounded to one decimal place)

Therefore, 99% of people consumed less than 54.3 gallons of bottled water.

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Answer:

1/3

Step-by-step explanation:

sample space includes 12 outcomes:

blue, green, yellow for 1, 2, 3, and 4

P(blue) = 4/12 or 1/3

Answer:

Each 13 scoops of ice cream

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

f(x)=27

y=27(x)

x=1

y=27

Answer:

Step-by-step explanation:

then simplify

Answer:

5,425.92

Step-by-step explanation:

multiply 12×12

then mulitply 144×3.14×12

The number of solutions for the system of equations is given as follows:

Zero.

The system of equations for this problem is defined as follows:

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

From the image presented at the end of the answer, the two graphs never intersect, and hence the number of solutions to the system of equations is of zero.

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The set of all numbers of the form a+b*sqrt(2), where a and b are integers, is countable.

This can be proven by first showing that sqrt(2) is irrational, which implies that the function f(a; b) = a + b*sqrt(2) is one-to-one and onto from the set Z Z = {(a,b)} to the set of numbers {a+b*sqrt(2)}.

This reduces the proof to showing that Z Z is countable. Z Z is a subset of Z x Z and Z x Z is countable, as it can be put into a one-to-one correspondence with the set of natural numbers. Thus, there is a bijection between Z x Z and the set of numbers {a+b*sqrt(2)}, which implies that the set of numbers a+b*sqrt(2) is countable.

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a. 2.0405 x 10^7

b. 2.0202 x 10^-2

c. 3.450 x 10^-1

d. 1.1111 x 10^-5

e. 1.0101 x 10^2

f. 9.0650 x 10^-2

a. To convert 20405000 to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 2.0405, and since we moved the decimal point 7 places to the left, we multiply by 10^7. Therefore, 20405000 can be expressed as 2.0405 x 10^7.

b. To convert 0.0202020 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 2.0202, and since we moved the decimal point 2 places to the right, we multiply by 10^-2. Therefore, 0.0202020 can be expressed as 2.0202 x 10^-2.

c. To convert 0.3450 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 3.450, and since we moved the decimal point 1 place to the right, we multiply by 10^-1. Therefore, 0.3450 can be expressed as 3.450 x 10^-1.

d. To convert 0.000011111 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 1.1111, and since we moved the decimal point 5 places to the right, we multiply by 10^-5. Therefore, 0.000011111 can be expressed as 1.1111 x 10^-5.

e. To convert 101010 to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 1.01010, and since we moved the decimal point 2 places to the left, we multiply by 10^2. Therefore, 101010 can be expressed as 1.0101 x 10^2.

f. To convert 0.090650 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 9.0650, and since we moved the decimal point 1 place to the right, we multiply by 10^-1. Therefore, 0.090650 can be expressed as 9.0650 x 10^-2.

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The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.

The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.

To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.

The modified code for binary search in descending order would look like this:

public static int binarysearch2(int[] list, int key) {

   int low = 0;

   int high = list.length - 1;

   while (high >= low) {

       int mid = (low + high) / 2;

       if (key > list[mid])

           high = mid - 1;

       else if (key < list[mid])

           low = mid + 1;

       else

           return mid;

   }

   return -1; // Not found

}

By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.

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Answer:

16 kids

Step-by-step explanation:

50-2=48

48/3=16

The probability that two men will be selected from the first set and two women will be selected from the second set is 3/10 * 2/3, or 1/5.

The probability of selecting two men from the first set is 3/4. This is because there are 3 men in the first set and the probability of selecting one is 1/4. Since we need to select two, the probability of selecting both is 3/4 multiplied by itself, or 3/4 x 3/4. The probability of selecting two women from the second set is 2/3. This is because there are 2 women in the second set and the probability of selecting one is 1/3. Since we need to select two, the probability of selecting both is 2/3 multiplied by itself, or 2/3 x 2/3. The probability of selecting two men from the first set and two women from the second set is then 3/4 x 3/4 x 2/3 x 2/3, which is equal to 3/10 x 2/3, or 1/5.

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Use parentheses that may or may not contain parameters directly after the function name to invoke the function.

As part of GAIA, the AI created for Project Zero Dawn in reaction to the Faro Plague, the subordinate functions are a part. The Faro Swarm's deactivation and the planet's terraforming are all objectives of Project Zero Dawn, and they are all accomplished through their extensive suite of subfunctions, each of which is dedicated to a particular purpose.

There are nine supporting roles.

A top engineer on the Zero Dawn project known as an Alpha created each of the nine subordinate functions. They were supported by a project development team made up of professionals in their industry who were well-known throughout the world.

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We will find that there are 5 outcomes where the sum of the numbers on the dice adds up to 6.

We want to see how many outcomes are there where the sum of the two dice is equal to 6. Each dice has 6 outcomes, which are:

{1, 2, 3, 4, 5, 6}

For rolling two dice with 6 outcomes each, the total number of outcomes is:

6*6 = 36

For rolling two dice, we can use the notation:

dice 1,  dice 2

And we can also write the sum, so we will only look at the outcomes where the sum is 6.

dice 1,  dice 2,  Sum

1            5          1 + 5 = 6

5           1           5 + 1 = 6

2           4           2 + 4 = 6

4           2            4 + 2 = 6

3           3            3 + 3 = 6

So there are 5 outcomes where the sum is equal to 6, so the correct option is B

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Answer:

C

Step-by-step explanation:

the other guy explains it better, but i took the quiz, so I can confirm

Each car on Mabel's train is a little less than half a foot long i.e., 3/8 feet long, or 0.375 feet long. This is solved by using simple mathematical operations.

To find the length of each car on Mabel's train, we can use the formula:

Total length of train = length of one car × number of cars

We are given that Mabel's train has 8 cars and is 3 feet long, so we can substitute those values into the formula and solve for the length of one car:

3 = x × 8

where x is the length of one car.

To solve for x, we can divide both sides by 8:

3/8 = x

Therefore, each car on Mabel's train is 3/8 feet long, or 0.375 feet long.

In other words, each car is a little less than half a foot long.

To help visualize this, imagine dividing the 3-foot length of the train into 8 equal parts. Each part would be 3/8 feet long, which is the length of one car. So when Mabel puts all 8 cars together, they form a train that is 3 feet long.

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The equation that shows the relationship between x, the number of minutes, and y, the price, is y = 0.15x. In this equation, y represents the price and x represents the number of minutes.

The equation implies that the price (y) is directly proportional to the number of minutes (x), with a proportionality constant of 0.15.

This means that for every unit increase in the number of minutes, the price will increase by 0.15 units. Similarly, for every unit decrease in the number of minutes, the price will decrease by 0.15 units.

The equation y = 0.15x represents a linear relationship between the price and the number of minutes. It indicates that the price changes linearly with respect to the number of minutes. This type of relationship is useful in scenarios such as calculating the cost of a service based on the duration.

It's important to note that the other equations x = 0.154, x = 9y, and y = 9x do not represent a direct relationship between the number of minutes and the price. Instead, they indicate different mathematical relationships or conversions between the two variables.

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Answer:

The Last box. (y=1/2x-4)

Step-by-step explanation:

The formula is y=mx+b
b is the interception point on the y axis.
So the -4 is where the line crosses on the y axis.
mx is how many spaces it goes up or down.
If you look the box goes up or down twice then left or right once.

So that's your answer, hope this helps.

Therefore, it will take approximately 13.7 years for the population to double.

a. To determine the growth rate, you need to calculate the percentage increase in population. The formula for growth rate is:

Growth Rate = (New Value - Old Value) / Old Value * 100

Using the given values, we have:

Growth Rate = (1577 - 1500) / 1500 * 100
Growth Rate = 77 / 1500 * 100
Growth Rate ≈ 5.13%

b. To write a general equation for the population, you can use the formula:

p(t) = p(0) * (1 + r/100)^t

where p(t) is the population at time t, p(0) is the initial population, r is the growth rate, and t is the number of years.

c. To estimate the population in 2010, we need to find the population at time t = 2010 - 2000 = 10 years. Using the general equation from part b, and substituting the given values:

p(10) = 1500 * (1 + 5.13/100)^10
p(10) ≈ 1500 * (1.0513)^10
p(10) ≈ 1500 * 1.6436
p(10) ≈ 2465.4

Therefore, the estimated population in 2010 is approximately 2465.

d. To find out how many years it will take for the population to double, we need to solve the equation:

2 * p(0) = p(0) * (1 + r/100)^t

Simplifying the equation, we have:

2 = (1 + r/100)^t

Taking the logarithm of both sides, we get:

log(2) = t * log(1 + r/100)

Finally, solving for t, we have:

t = log(2) / log(1 + r/100)

Substituting the growth rate from part a, we have:

t = log(2) / log(1 + 5.13/100)
t ≈ log(2) / log(1.0513)
t ≈ 13.7 years

Therefore, it will take approximately 13.7 years for the population to double.

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Two vectors in ℝ⁴ are orthogonal if their dot product is zero.

Two vectors in ℝ⁴ are said to be orthogonal if their dot product is zero. The dot product of two vectors measures the similarity or alignment between them. When the dot product is zero, it signifies that the vectors are perpendicular to each other and do not share any common direction.

Geometrically, orthogonality between two vectors in ℝ⁴ means that they are linearly independent and span different directions in four-dimensional space. It implies that there is no projection of one vector onto the other, and they are completely perpendicular to each other.

The concept of orthogonality is fundamental in many areas of mathematics, physics, and engineering. In linear algebra, orthogonal vectors play a crucial role in defining orthogonal bases and orthogonal projections. They also have applications in vector calculus, where they are used to define gradients and normal vectors. In physics, orthogonal vectors are relevant in studying forces, velocities, and geometric transformations. Overall, understanding orthogonality is essential for analyzing vector relationships and geometric properties in multi-dimensional spaces.

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Answer:

8

Step-by-step explanation:

If you go along the x-axis to 9 and go up till it  meets the blue line and go left you will reach the integer 8 so f(9)=8

The probability is approximately 0.9167 or 91.67%.

To find the probability that the sum of two dice numbers does not exceed 10, we need to determine the favorable outcomes (sums less than or equal to 10) and the total possible outcomes when rolling two dice.

There are 36 possible outcomes when rolling two dice because each die has six faces (1, 2, 3, 4, 5, and 6), and the total number of outcomes is obtained by multiplying the number of outcomes for each die (6 * 6 = 36).

Now let's determine the favorable outcomes (sums less than or equal to 10):

When the sum is 2: There is only one combination (1 + 1).

When the sum is 3: There are two combinations (1 + 2 and 2 + 1).

When the sum is 4: There are three combinations (1 + 3, 2 + 2, and 3 + 1).

When the sum is 5: There are four combinations (1 + 4, 2 + 3, 3 + 2, and 4 + 1).

When the sum is 6: There are five combinations (1 + 5, 2 + 4, 3 + 3, 4 + 2, and 5 + 1).

When the sum is 7: There are six combinations (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1).

When the sum is 8: There are five combinations (2 + 6, 3 + 5, 4 + 4, 5 + 3, and 6 + 2).

When the sum is 9: There are four combinations (3 + 6, 4 + 5, 5 + 4, and 6 + 3).

When the sum is 10: There are three combinations (4 + 6, 5 + 5, and 6 + 4).

Adding up the favorable outcomes, we get: 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 = 33.

Therefore, the probability that the sum of the two dice numbers does not exceed 10 is given by:

Probability = Favorable outcomes / Total outcomes = 33 / 36 = 11/12 ≈ 0.9167.

So, the probability is approximately 0.9167 or 91.67%.

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To differentiate the function f(x) = qx + r/sx + t, where q, r, s, and t are constants, the derivative is given by f'(x) = q - (r/s) * (1/x^2).

To differentiate the given function, we need to apply the rules of differentiation. Let's break down the steps:

1. Differentiate qx with respect to x: Since q is a constant, the derivative of qx is simply q.

2. Differentiate r/sx with respect to x: We can rewrite r/sx as r * (s * x)^(-1). Applying the power rule of differentiation, the derivative of (s * x)^(-1) is (-1) * (s * x)^(-1 - 1) * s = -s/x^2.

3. Differentiate t with respect to x: Since t is a constant, the derivative of t with respect to x is 0.

4. Combining the derivatives obtained from the previous steps, we have f'(x) = q - (r/s) * (1/x^2).

Therefore, the derivative of the given function f(x) = qx + r/sx + t, where q, r, s, and t are constants, is f'(x) = q - (r/s) * (1/x^2).

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The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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Answer:

y=10x-15

Step-by-step explanation:

with the points given you know x=2 and y=5

make a new point called (x,y)

now use the formula (y-5)/(x-2)=10 (10 being the gradient)

y-5 = 10(x-2)

y-5=10x-20

add 5 to both sides

y-5+5=10x-20+5

y=10x-15

Since we're given a point and a slope, we can write

the equation of this line using the point-slope formula.

The point-slope formula is shown at the top of the image below.

The given point, (2,5), represents (x1,y1).

Now plug in the information to get the equation below.

Now you can distribute the 10.

Then add 5 to both sides.

You will end up with the equation y = 10x - 15 as your answer.

9514 1404 393

Answer:

  n = 5/2

Step-by-step explanation:

Given

  5/2(4n -10) +4 = 2/3(6n -9)

  5(2n -5) +4 = 2(2n -3) . . . . . . . simplify a bit

  10n -25 +4 = 4n -6 . . . . . . . . . eliminate parentheses

  6n = 15 . . . . . . . . . . . . . . . . . . . add 21-4n

  n = 15/6 = 5/2

The value of n that makes the equation true is n = 5/2 = 2.5.

The four numbers that satisfy the given conditions are 13, 13, 13, and 19.

Let's represent the three equal numbers as x. We know that one of the numbers is a multiple of 19, so we can write it as 19y, where y is a positive whole number.

According to the given information, the four numbers add up to 96:

x + x + x + 19y = 96

Since the three equal numbers are represented as x, we can simplify the equation:

3x + 19y = 96

To find the values of x and y, we need to use trial and error or solve the equation using a systematic approach.

Let's start by trying different values of y and see if we can find a combination that satisfies the equation:

For y = 1:

3x + 19(1) = 96

3x + 19 = 96

3x = 96 - 19

3x = 77

x = 77/3 (not a whole number)

For y = 2:

3x + 19(2) = 96

3x + 38 = 96

3x = 96 - 38

3x = 58

x = 58/3 (not a whole number)

For y = 3:

3x + 19(3) = 96

3x + 57 = 96

3x = 96 - 57

3x = 39

x = 39/3

x = 13

So, one of the numbers is 13, and the other three numbers (since they are equal) are also 13.

Therefore, the four numbers that satisfy the given conditions are 13, 13, 13, and 19.

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Answer:

21 songs are rap songs

Step-by-step explanation:

1/4=7 so 7+7=14+7=21+7=28=(7x4=28-7=21)

Answer:

21 songs

Step-by-step explanation:

Let's figure out how many are R&B songs first.

We know that 1/4 of the 28 total songs are R&B. Remember that in mathematics, "of" usually means to multiply, so we multiply 1/4 by 28:

1/4 * 28 = 7 songs

So, 7 songs are R&B. This means that since the rest are rap, we can subtract 7 from the total 28:

28 - 7 = 21 songs

Step-by-step explanation: