If you take any positive integer and apply the following infinitely:
If the number is even, divide by two
If the number is odd, multiply by 3 and add 1

Will every integer eventually fall back down into the 4, 2, 1 loop, or is there a positive integer that never falls down into that loop?

the area of one of the isosceles triangles formed by cutting the square by a diagonal is 25√(7) square cm.

Find the area of triangle?

To find the area of one of the isosceles triangles formed by cutting the square by a diagonal, we can use the fact that the area of a triangle is given by the formula:

A = (1/2)bh

where A is the area of the triangle, b is the base, and h is the height.

In this case, the base of the isosceles triangle is one of the sides of the original square, which is 10 cm. The height can be found by using the Pythagorean theorem, since the diagonal of the square and the height of the isosceles triangle form a right triangle:

d² = h² + (10/2)²

where d is the length of the diagonal, which can be found using the Pythagorean theorem:

d² = 10² + 10² = 200

d = √(200) = 10√(2)

Substituting this value for d in the first equation, we get:

(10√(2))² = h²+ (10/2)²

200 = h² + 25

h²= 175

h = √(175) = 5√(7)

Now we can use the formula for the area of a triangle to find the area of one of the isosceles triangles:

A = (1/2)(10)(5√(7))

A = 25√(7) square cm

Therefore, the area of one of the isosceles triangles formed by cutting the square by a diagonal is 25√(7) square cm.

To know more about Area visit :-

https://brainly.com/question/17335144

#SPJ1

The vertical intercept in this context refers to the height at which the object is positioned when time is equal to zero.

Based on the information,, we can see that the vertical intercept is at a height of 1000 meters.

In terms of the context, this means that at the beginning of the experiment or measurement, the object was positioned at a height of 1000 meters above the ground.

This could represent the initial position of an object that is being dropped or launched from a certain height, or the starting altitude of an aircraft or spacecraft.

In this case, the vertical intercept in this context refers to the height at which the object is positioned when time is equal to zero.

Learn more about intercept on;

https://brainly.com/question/29155562

#SPJ1

Answer:

Census

Step-by-step explanation:

It's a census because it provides meaningful information to the person who is collecting it. The meaningful information being the height

Answer:

Census

Step-by-step explanation:

The other guy already said it.

If we want to choose 6 objects out of 14 objects and the order does not matter, then the number of ways we can do this is 3003.

The number of ways you can select or organize objects is defined by formulas of permutation and combination. Choosing one or the other depends on whether the order matters (permutation) or not (combination). In this case, as the order does not matter, the general formula is:

C  = n! / r! (n-r)!

In this formula, n is the total of items and r is the total I need to select. Let's then solve it:

C= 14! / 6! (14! - 6!)

C = 14! / 6! 8!

C= 14 x 13 x 12 x 11 x 10 x 9 / 6 x 5 x 4 x 3 x 2

C= 7 x 13 x 11  x 3  

C= 3003

Note: This question is incomplete; here is the missing section;

How many ways can this be done, if the order of the choices does not matter?

Learn more about combinations in https://brainly.com/question/19692242

#SPJ1

Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if you have two angles that are supplementary, the sum of their measures is 180 degrees.

Supplementary angles can be adjacent or non-adjacent. Adjacent supplementary angles are two angles that share a common vertex and side, but whose non-shared sides form a straight line. Non-adjacent supplementary angles are two angles that are not next to each other, but whose sum is equal to 180 degrees.

Given that x + y = 180

If y = 56 degrees

x = 180 - 56

x = 124

Learn more about supplementary angles:https://brainly.com/question/13045673

#SPJ1

The probability that the casino's total profit will exceed $1000 is very close to zero.

The probability of winning a bet on red in American roulette is 18/38, and the probability of losing is 20/38.

Therefore, the expected profit for the casino on each bet is:

E(profit per bet) = (18/38) x ($1) + (20/38) x (-$1) = -$0.0526

The variance of the profit per bet can be calculated as follows:

Var(profit per bet) = (18/38) x ($1 - (-$0.0526))^2 + (20/38) x (-$1 - (-$0.0526))^2 = $0.921

The standard deviation of the profit per bet is the square root of the variance, which is approximately $0.960.

The expected profit for the casino from 25000 bets is:

E(total profit) = 25000 x (-$0.0526) = -$1315

The standard deviation of the total profit is the square root of the variance multiplied by the number of bets, which is approximately $305.46.

To find the probability that the casino's total profit will exceed $1000, we can standardize the distribution of the total profit as follows:

z = (1000 - (-$1315)) / $305.46 = 9.48

Using a standard normal table or calculator, we can find that the probability of a standard normal variable exceeding 9.48 is essentially zero.

Learn more about probability here: https://brainly.com/question/24756209

#SPJ1

if we take 200(origin amount) as the 100%, what's 92 off of it in percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 200 & 100\\ 92& x \end{array} \implies \cfrac{200}{92}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 50 }{ 23 } ~~=~~ \cfrac{ 100 }{ x }\implies 50x=2300\implies x=\cfrac{2300}{50}\implies x=46[/tex]

Answer:

The sum of the first 19 terms of the arithmetic sequence 2, 3, 4, 5, ... is 209.

To find the sum of the first 19 terms of the arithmetic sequence 2, 3, 4, 5, ..., we need to use the formula for the sum of an arithmetic sequence:

Sₙ = n/2 (a₁ + aₙ)

where Sₙ is the sum of the first n terms of the sequence, a₁ is the first term of the sequence, aₙ is the nth term of the sequence, and n is the number of terms we want to sum.

In this case, a₁ = 2 (the first term of the sequence), aₙ = 2 + (n - 1) = n + 1 (the nth term of the sequence), and n = 19 (we want to sum the first 19 terms of the sequence).

Therefore, we can plug these values into the formula and get:

S₁₉ = 19/2 ˣ (2 + 19 + 1)

= 19/2 ˣ 22

= 209

So the sum of the first 19 terms of the arithmetic sequence 2, 3, 4, 5, ... is 209.

To know more about sum visit:

https://brainly.com/question/13013054?

#SPJ1

Answer:a=4

Step-by-step explanation:

The total cost of this balloon mortgage is $288,513.13.

What is a mortgage?

When you and a lender enter into a mortgage, the lender is granted the power to seize your property if you are unable to pay back the loan amount plus interest. To purchase a property or borrow money against the value of a home you currently own, you can use a mortgage loan.

Here, we have

Given: $195,000 25/7 balloon 7.2% annual rate Monthly Payment: $1,403.20 Balloon Payment: $170,644.33

We have to find the total cost of this balloon mortgage.

Monthly payment = 1403.20 which happens for 7 years (7*12 Months)

The total monthly payment for 7 years = 1403.20*7*12 = 117,868.80

Ballon payment =170,644.33 (Given)

Total cost of the balloon payment = 117,868.80 + 170,644.33 = 288,513.13

Hence, the total cost of this balloon mortgage is $288,513.13.

To learn more about the mortgage the given link

https://brainly.com/question/28472132

#SPJ1

Answer:

Step-by-step explanation:

=√((x2 – x1)² + (y2 – y1)²)

=√((8 – 1)² + (9 – 2)²)

=√((7)² + (7)²)

=√(49 + 49)
=√(2 • 49)

=7√2

Divide the line segment into 7 parts equally:

=(7√2)/7

=1√2

Multiply to 6 and 1 to get 6:1 ratio:

= 6(1√2)

= 6√2

Final Answer: 6√2 and √2.

Plot and character development can help you predict a novel’s theme by hinting at ideas about what the conflict is and how the main characters are likely to deal with it.

What is plot?

The sequence of events in a book, movie, or other narrative where each event has an influence on the subsequent one in accordance with the law of cause and effect is known as the plot. The causal events of a narrative can be conceived of as a collection of occurrences linked together by the connector "and so." Plots can be simple—like in a traditional ballad—or complicated and intertwined, with each element occasionally referred to as a subplot or imbroglio.

To learn more about plot from the given link

https://brainly.com/question/1345709

#SPJ1

The circumference of a circle with a diameter of 21 cm is 65. 94cm

The equation for the formula that is used to determine the circumference of a circle is expressed as;

C = 2πr

Such that the parameters are enumerated as;

Also, the formula for calculating the radius of a circle is expressed as;

Radius = Diameter/2

Substitute the value

Radius = 21/2 = 10. 5cm

Substitute the value for circumference

Circumference = 2 × 3.14 × 10. 5

Find the value

Circumference = 65. 94cm

Learn about circumference at: https://brainly.com/question/14283575

#SPJ1

Answer:

Option B

Step-by-step explanation:

To find the standard deviation, we need to follow these steps:

1) Find the mean of the data set.

2) Calculate the difference between each data point and the mean.

3) Square each difference.

4) Find the average of the squared differences.

5) Take the square root of the average to get the standard deviation.

First, we find the mean of the data set:

Mean = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6 = 46.4 / 6 = 7.73

Next, we calculate the difference between each data point and the mean:

| 7.2 - 7.73 | = 0.53

| 8.9 - 7.73 | = 1.17

| 2.7 - 7.73 | = 5.03

| 11.6 - 7.73 | = 3.87

| 5.8 - 7.73 | = 1.93

| 10.2 - 7.73 | = 2.47

Then, we square each difference:

0.53^2 = 0.2809

1.17^2 = 1.3689

5.03^2 = 25.3009

3.87^2 = 14.9569

1.93^2 = 3.7249

2.47^2 = 6.1009

Next, we find the average of the squared differences:

(0.2809 + 1.3689 + 25.3009 + 14.9569 + 3.7249 + 6.1009) / 6 = 8.62

Finally, we take the square root of the average to get the standard deviation:

sqrt(8.62) = 2.93

Therefore, the standard deviation of the data set is 2.93, which is option B.

According to the model, the recommended amount of sleep for a 25-year-old person is equal to 6.75 hours of sleep.

In Mathematics and Statistics, a line of best fit is also referred to as a trend line and it can be defined as a statistical or analytical tool that is typically used by researchers and mathematicians in conjunction with a scatter plot, in order to determine whether or not there is any form of association and correlation between a data set.

Based on the scatter plot, we can logically deduce that a linear equation which represents the line of best fit include the following:

y = -0.25x + 13

For a 25 years old person, the recommended hours of sleep can be calculated as follows;

y = -0.25x + 13

y = -0.25(25) + 13

y = -6.25 + 13

y = 6.75 hours of sleep.

Read more on line of best fit here: brainly.com/question/12284501

#SPJ1

Answer:

90

Step-by-step explanation:

There are 30 days in November, so 3 x 30 = 90.

We must add the relevant components of each of the three vectors, X1, X2, and X3, in order to resultant vector the final vector XR, which has the components (1, -5)m.

R = A + B. Equation 2 To create the resultant vector, opposing vectors are subtracted from one another. R is the resulting vector in this case, and the column B is directed in the opposite direction to a vector A.

We must add the relevant components of each of the three vectors, X1, X2, and X3, in order to resultant vector the final vector XR, which has the components (1, -5)m.

To find the resultant vector, we need to add the corresponding components of the three given vectors. So, we have:

XR = X1 + X2 + X3

XR = (-2,0) m + (0,-5) m + (3,0) m

XR = (-2+0+3, 0+(-5)+0) m

XR = (1, -5) m

Therefore, the resultant vector XR is (1, -5) meters.

To know more about resultant vector visit:

brainly.com/question/20426452

#SPJ1

Complete question -

Add the following three vectors to find the resultant vector, XR:

X1 = (-2,0)m, X2= (0,-5,)m, x3 = (3,0)m

Answer:

The terms 2x and -5x are like terms.

Step-by-step explanation:

Like terms are terms that have the same variable(s) raised to the same power(s). In this case, both 2x and -5x have the same variable "x" raised to the same power "1". The only difference between them is the coefficient, which is 2 for 2x and -5 for -5x. However, the coefficients do not affect whether two terms are like or unlike terms.

So, because 2x and -5x have the same variable raised to the same power, they are like terms.

Answer:

(9), (11), ( ) and (9,11) is your correct answer.

Answer: $5.00

Step-by-step explanation:

The cost of a 6-mile ride is made up of three components: a base fare of $1.25, a distance charge of 50 cents per mile, and a waiting charge of 30 cents per minute for the time spent eating at stoplights.

The distance charge for a 6-mile ride is:

6 miles x $0.50/mile = $3.00

The waiting charge for 2.5 minutes at 30 cents per minute is:

2.5 minutes x $0.30/minute = $0.75

So the total cost of the ride is:

$1.25 (base fare) + $3.00 (distance charge) + $0.75 (waiting charge) = $5.00

Therefore, a 6-mile taxi ride with 2.5 minutes of waiting time at stoplights costs $5.00.

The cubic function family includes the function G(x).

A collection of functions known as the cubic function family may be written as [tex]f(x) = ax3 + bx2 + cx + d,[/tex]  where a, b, c, and d are constants. Cubic functions can have one, two, or three real roots because of their odd degree (3). Real-world phenomena like population growth and decline are frequently modelled using these functions. The coefficient of x3 in the following function [tex]G(x) = -x3 is -1,[/tex]  which is a constant. This function belongs to the family of cubic functions since it may be written in the typical form of a cubic function. As a result, G(x) has a single real root and is a cubic function.

learn more about functions here:

https://brainly.com/question/12431044

#SPJ11

Answer:

Step-by-step explanation:

Alan made an error in assuming that the distance between -8 and 3 on the x-axis is the same as the distance between -8 and the y-axis, and between 3 and the y-axis. This is not necessarily true, as the distance between two points on a coordinate plane is given by the Pythagorean theorem:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the actual distance between points A and B:

distance = sqrt((3 - (-8))^2 + (-4 - (-4))^2)

distance = sqrt(11^2 + 0^2)

distance = sqrt(121)

distance = 11

So the actual distance between points A and B is 11 units.

Therefore, Alan's error was assuming that the distance between A and B is simply the difference in the x-coordinates, which is not the case.

The male with an associate degree has a yearly median income of $36,432.

The median income means an income amount that divides a population into two equal groups, half having an income above that amount, and half having an income below that amount

The weekly income of a male with an associate degree is $759. We have 4 weeks in a month, and 12 months in a year. So, the yearly median income is:

= 4 *12 * $759

= $36,432

Therefore, the male with an associate degree has a yearly median income of $36,432.

Read more about median income

brainly.com/question/16488054

#SPJ1

Answer:

If a class has 2/3 girls.

Lets ask ourselves, what does this mean?

It means that 2/3 of the class are girls and therefore 1/3 of the class are boys. I.e. for every 2 girls in the class there is 1 boy in the class.

Therefore the ratio of girls to boys is

2 : 1