The height, hh, of a plant (in inches) ww weeks since it was planted is represented by the equation h=1.2w+3h=1.2w+3. How many weeks ( round up to the nearest whole number) will it take the plant to reach one foot? ( Hint: convert feet to inches.) Answer value

Answers

Answer 1

Answer:

It will take 8 weeks for the plant to reach one foot.

Step-by-step explanation:

The equation is:

\( h = 1.2w + 3 \)

Where:

h: is the height = 1 foot

w: is the time in weeks =?

We can convert feet to inches as follows:

\( 1 feet = 12 inches \)

\( h = 1 ft*\frac{12 in}{1 ft} = 12 in \)

Hence, the number of weeks is:

\( w = \frac{h - 3}{1.2} = \frac{12 - 3}{1.2} = 7.5 = 8 \)

Therefore, it will take 8 weeks for the plant to reach one foot.

I hope it helps you!                                


Related Questions

The equation ý = 135.23x - 245, 121.9 predicts the population of a town in year x.
According to the equation, what was the town's population in 2001?
Enter your answer in the box. Round to the nearest whole number.

Answers

The population of the town in the year 2001 according to the equation; ý = 135.23x - 245 is; 270,350.

What is the population of the town in the year 2001?

since the given equation is;

ý = 135.23x - 245

Therefore, in year 2001; the population, y is;

y = 135.23 (2001) - 245

y = 270,595.23 - 245

y = 270,350.23

y = 270,350 (nearest whole number).

Ultimately, the population of the town in 2001 is; 270,350.

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3' - '2' + 'm' / 'n' is ________.

Answers

The expression "3' - '2' + 'm' / 'n'" is invalid because it combines character literals and arithmetic operations. The expression "3' - '2' + 'm' / 'n'" is not valid in most programming languages.

It attempts to mix character literals ('3', '2', 'm', 'n') with arithmetic operations (-, +, /), which is not meaningful. In programming languages, characters are typically represented using character literals enclosed in single quotes.

While arithmetic operations are performed on numerical values. The expression should be revised to ensure that the operations are performed on numerical values rather than character literals.

For example, if 'n' and 'm' represent numerical values, the expression could be written as "3 - 2 + m / n" to perform arithmetic operations correctly.

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The value of a piece of land in a town is increasing every year . Its value, in dollars, t years after 1970 and until 2001 can be modeled by the function 31, 000(1.001) ^ t . What is the domain of the function ?
A. All whole numbers greater than or equal to 1971 and less than or equal to 2001 .
B. All real numbers greater than or equal to 1971 and less than or equal to 2001 .
C . All non - negative real numbers less than or equal to 31.
D. All whole numbers less than or equal to 31

Answers

Answer:

D. All whole numbers less than or equal to 31

Step-by-step explanation:

The x value in this situation is the number of years after 1970 and until 2001.

This means that the domain will be the number of years after 1970 and until 2001.

Since the situation calculates the value of land in years after 1970, the domain will start at 0. Since it is until 2001, which is 31 years after 1970, the domain will go up to 31.

So, the domain will include all whole numbers less than or equal to 31.

The correct answer is D. All whole numbers less than or equal to 31

The domain of the function is a real number from 1971 to 2001. Then the correct option is B.

What is an exponent?

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

The value of a piece of land in a town is increasing every year.

Its value, in dollars, in t years after 1970 and until 2001 can be modeled by the function

\(\rm y = 31, 000(1.001) ^ t\)

Then the domain of the function will be

All real numbers are greater than or equal to 1971 and less than or equal to 2001.

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Solve for x: 3x - 5 = 2x + 6​

Answers

Answer:

3x - 5 = 2x + 6  

Step one- Subtract 2x to isolate the variable  

X – 5 = 6  

 

Step two- Add 5 to continue to isolate the variable  

X = 11  

 

Your answer is      x = 11  

 

Hopefully this helps! Feel free to mark brainliest!

Answer: x=11

Step-by-step explanation:

3x-5=2x+6

+5. +5

3x=2x+11

-2x -2x

x=11

22. y =x-v over b solve for x

Answers

Answer:

See Below

Step-by-step explanation:

y = \(\frac{x-v}{b}\)

Isolate x

First step, multiply both sides by b to get rid of fraction

y(b) = x - v

+v          +v

y(b) +v = x

Hope this helps!=)

Help me please........

Help me please........

Answers

Answer:

A

Step-by-step explanation:

By the Pythagorean Theorem, you know that:

\(2^2+5^2=c^2\)

Therefore, the correct answer is choice A. Hope this helps!

Answer: choice A

Step-by-step explanation:

Based on the pythagorean theorem which states

\(a^{2} +b^{2} =c^{2}\)

c being the hypotenuse

so 2^2+5^2=c^2

and c would equal \(\sqrt{29}\)

If f(1) = 0, what are all the roots of the function f (x) = x cubed + 3 x squared minus x minus 3? Use the Remainder Theorem.
x = –1, x = 1, or x = 3
x = –3, x = –1, or x = 1
x = –3 or x = 1
x = –1 or x = 3

Answers

Answer:

x = –3, x = –1, or x = 1

Step-by-step explanation:

when I put -3.-1,or 1 as x I get 0

Remainder Theorem Way :

x^3-3x^2-x-3

x^2 (x+3) -1(x+3) = 0

(x^2 -1) (x+3) = 0

(x+1) (x-1) (x+3) = 0

x= 1 x= -1 x= -3

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Answer:

its b

Step-by-step explanation:

cause I took test

identify the solution of the compound inequality x − 2 > 4 or 5x ≥ 35 and the graph that represents it.

Answers

To find the solution of the compound inequality x − 2 > 4 or 5x ≥ 35, we need to solve each inequality separately and then combine their solutions using the OR operator.

Solving x − 2 > 4, we add 2 to both sides to get x > 6.
Solving 5x ≥ 35, we divide both sides by 5 to get x ≥ 7.

The solution of the compound inequality x − 2 > 4 or 5x ≥ 35 is the set of all values of x that satisfy at least one of the inequalities, which is x > 6 or x ≥ 7.

To graph this solution, we draw a number line and mark the points 6 and 7 with open circles (because they are not included in the solution). Then we shade the region to the right of 6 and/or to the right of 7, as shown below:

<---o---o=========>
6   7

The open circles indicate that 6 and 7 are not included in the solution, because x can be any value greater than 6 or any value greater than or equal to 7, but not both at the same time.

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the problem is x > 6 or x ≥ 7. To explain this solution, we need to solve each inequality separately and then combine the results.

First, we solve x − 2 > 4 by adding 2 to both sides to get x > 6.

Next, we solve 5x ≥ 35 by dividing both sides by 5 to get x ≥ 7.

To combine the results, we take the union of the two solutions, which gives us x > 6 or x ≥ 7. This means that any value of x that is greater than 6 or equal to 7 will satisfy the original compound inequality.

The graph that represents this solution is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.

the solution to the compound inequality x − 2 > 4 or 5x ≥ 35 is x > 6 or x ≥ 7, and the graph that represents it is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.

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Find the principal that will yield a simple interest of Rs 9000 in 5 years at a rate of 6% per annum.

Answers

9514 1404 393

Answer:

  ₹ 30000

Step-by-step explanation:

The simple interest formula is ...

  I = Prt . . . . . . principal P invested at rate r for t years

Fill in the values you know, and solve for the one you don't know.

  9000 = P(0.06)(5)

  9000/0.30 = P = 30000

The principal that will give ₹9000 in interest is ₹30000.

A =?

P= 9000

t = 5 yrs

r = 6% = 0.06

A = p(1+r)^t

A = 9000(1+0.06)⁵

A = 9000× 1.338

A = 12044 Rs.

pls help asap if you can!!!!

pls help asap if you can!!!!

Answers

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

What are alternate interior angles

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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The statement says that you’ve triggered the penalty apr so that it has now increased to 28. 99%. What action triggered this?.

Answers

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

You failed to make the minimum payment by the due date. This is an action that can result in a message that "you've triggered the Penalty APR so that it has now climbed to 28.99%."

A charge APR is a charge that can be applied if you don't pay your bills on time. It may be set up so that future transactions may be subject to a penalty APR that is higher than the card's standard rate.

If the minimum payment was not made by the due date, Penalty APR would be applied.

But if the card also has a penalty APR and you trigger it, you will likely lose that promotional offer. Federal consumer protections that limit penalty APRs don't apply to small-business credit cards. That means issuers can be more punitive, such as applying penalty APRs sooner than 60 days after not making payments.

Therefore,

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

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Mr. Hawkins is covering a wall with wallpaper. The room measures 14 feet by 12 feet in a rectangular shape. Each square foot of wallpaper costs $2.90. What is the cost of adding wallpaper to the room?​

Answers

Answer:

The total cost of adding wallpaper to the room is 487.20

determine the probability that the first child of clara and charles will be a boy with both albinism and hemophilia.

Answers

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%. Albinism and hemophilia are both recessive genetic conditions, meaning that both parents must have the recessive gene in order for a child to be born with either condition. Since neither Clara nor Charles have either condition, the probability that their first child will be a boy with both albinism and hemophilia is 0%.

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.

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munozkatia07 This is for you to get 6/5 brainliests

Answers

Answer:

What do you need help with?

Step-by-step explanation:

Valerie ran three and one-fourth laps yesterday, and her coach wants her to run two and one-half times that many laps today. how many laps will she need to run today? choose the expression needed to solve the problem.

Answers

Valerie needs to run \(8\frac{1}{8}\) laps.

What are mixed fractions?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

You can divide any fraction into two pieces. These are the denominator and numerator. A improper fraction is one in which the numerator is greater than the denominator. The numerator must then be multiplied by the denominator by the students. They will then receive a specific form of a fraction. That is referred to as a mixed fraction.

Given,

Number of laps valerie ran = \(3\frac{1}{4}\) laps

Number of times her coach wants her to run = \(2\frac{1}{2}\) times

Therefore,

total number of laps she needs to run = \(3\frac{1}{4} \times 2\frac{1}{2}\)

                                                               \(= \frac{13}{4} \times \frac{5}{2}\)

                                                               \(= \frac{65}{8}\) laps

                                                               \(=8\frac{1}{8}\) laps.

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Joseph paints ornaments for a school play. Each ornament is made up of two identical​ cylinders, as shown. All surfaces of each cylinder must be painted. How many cans of paint does he need to paint 75 ​ornaments?
PLEASE HELP ME BIG GRADE!!!!!!!!!

Joseph paints ornaments for a school play. Each ornament is made up of two identical cylinders, as shown.

Answers

Number of cylindrical cans of paint does he need to paint 75 ​ornaments is 20.

What is the Surface Area of a Cylinder?

The total area that the cylinder's curved surface and round bases enclose is referred to as its surface area. The cylinder's total surface area consists of the curving surface as well as the areas of the two bases, each of which is shaped like a circle. A cylinder is a 3D solid object made up of two circular bases connected by a curving face.

Surface Area of Cylinder = 2πrh+2πr²

where , r is radius of cylinder=4.6cm

H is height of cylinder=2*6.5cm=13cm

A=2×π×4.6×13+2×π×4.6²≈508.68668cm²

Total Number of cans of paint needed to paint 75 ​ornaments=75×508.68668

/1900=20.

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Use the following information for problems 4-6.The mean weight of a domestic house cat is 8.9 pounds, with a standard deviation of 1.1 pounds.The distribution of domestic house cat weights can reasonably be approximated by a normal distribution.What percentage of domestic house cats weigh less than 7.8 pounds?What percentage of domestic house cats weigh more than 11.1 pounds?A domestic house cat weighing 9 pounds is in what percentile?Use the following information for problems 7-9.An article in a health magazine suggested getting a dog in order to increase time spent walking (for exercise). A researcher for the article found that the distribution of time spent walking by dog-owners was approximately normally distributed with a mean of 38 minutes per day. She also found that 84% of dog-owners spend less than 45 minutes walking per day.Find the standard deviation (in minutes) for daily walking time among dog-owners.Construct a normal distribution curve that displays all relevant data for this scenario.How long would a dog-owner need to walk in a day to be ranked in the 99th percentile?Using any research tools at your disposal, find 3 real-world examples of variables that are, in fact, normally distributed.

Answers

In order to solve this question, we need to use the z-score z of value x, belonging to a normal distribution with mean μ and standard deviation σ.

z is defined as:

\(z=\frac{x-\mu}{\sigma}\)

In this problem, we have, in pounds:

μ = 8.9

σ = 1.1

PART 1

So, the percentage of domestic house cats that weigh less than 7.8 pounds is:

\(P(x<7.8)=P(z<\frac{7.8-8.9}{1.1})=P(z<-1)\)

And from a z-score table, we have:

\(P(z<-1)=0.15866\)

Therefore, the percentage of domestic house cats that weigh less than 7.8 pounds is approximately 0.1587 or 15.87%.

PART 2

The percentage of domestic house cats that weigh more than 11.1 pounds is 1 minus the percentage of them that weigh less than that:

\(\begin{gathered} P(x>11.1)=1-P(x<11.1) \\ \\ P(x>11.1)=1-P(z<\frac{11.1-8.9}{1.1})=1-P(z<2) \\ \\ P(x>11.1)=1-0.97725=0.02275 \end{gathered}\)

Therefore, the percentage of domestic house cats that weigh more than 11.1 pounds is approximately 0.0228 or 2.28%.

PART 3

The domestic house cat weighing 9 pounds is in percentile P(x<9):

\(P(x<9)=P(z<\frac{9-8.9}{1.1})=P(z<0.09091)=0.53622\cong0.54\)

Therefore, a domestic house cat weighing 9 pounds is in the 54th percentile.

solve the following linear program: max 3x 2y s.t. 2x 2y < 8 a 3x 2y < 12 b 1x 0.5y < 3 c x,y > 0 what is the optimal solution for this lp model?

Answers

To solve the given linear program, we'll use the simplex method. Let's label the constraints as (a), (b), and (c).

The objective function is: max 3x + 2y

Subject to the constraints:

(a) 2x + 2y < 8

(b) 3x + 2y < 12

(c) x + 0.5y < 3

(d) x, y > 0

We need to convert the inequalities into equations:

(a) 2x + 2y = 8

(b) 3x + 2y = 12

(c) x + 0.5y = 3

We can rewrite constraint (c) as: 2x + y = 6 for convenience in the calculations.

Z | -3 | -2 | 0 | 0 | 0 | 0 |

s1 | 2 | 2 | 1 | 0 | 0 | 8 |

s2 | 3 | 2 | 0 | 1 | 0 | 12 |

s3 | 2 | 1 | 0 | 0 | 1 | 6 |

The initial tableau represents the maximization problem, with the objective function coefficients in the Z row, the variables x, y, and the slack/surplus variables (s1, s2, s3) in the columns, and the right-hand side values in the b column.

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In an office, there are 75 women and 125 men .Find the ratio of
the number of men to the number of women.

Answers

Given:

In an office, there are 75 women and 125 men.

To find:

The ratio of the number of men to the number of women.

Solution:

We have,

Number of men = 125

Number of women = 75

The ratio of the number of men to the number of women is:

\(\text{Required Ratio}=\dfrac{\text{Number of men}}{\text{Number of women}}\)

\(\text{Required Ratio}=\dfrac{125}{75}\)

\(\text{Required Ratio}=\dfrac{5}{3}\)

\(\text{Required Ratio}=5:3\)

Therefore, the ratio of the number of men to the number of women is 5:3.

Susan’s partial construction is below.

What should the next step be if you are constructing the angle bisector through point Z?
A. Increase the compass to almost doublw the width to create another arc from point Z.
B. From Z, draw a line that crosses the arc.
C. Without changing the width of the compass, repeat the drawing process from point B, making the two arcs cross each other at a new point called K.
D. Close the compass and use a straight edge to draw a line from the midpoint of the arc to point Z.

Susans partial construction is below.What should the next step be if you are constructing the angle bisector

Answers

THE ANSWER IS D I THINK

The next step in constructing the angle bisector through point Z is Increasing the compass to almost double the width to create another arc from point Z.

Option A is the correct answer.

What is an angle bisector?

It is the line that bisects an angle into two equal halves.

We have,

When constructing an angle bisector with a compass and a straightedge, the first step is to draw arcs through both legs of the angle centered at the vertex of the angle.

Now,

From the figure,

The next step to construct an angle bisector through point Z is to draw arcs on points A and B with Z as the vertex.

This is similar with

Increasing the compass to almost double the width to create another arc from point Z.

Thus,

Increasing the compass to almost double the width to create another arc from point Z is the next step to make an angle bisector through point Z.

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A circle with radius of 2 cm sits inside a
11 cm x 12 cm rectangle.
What is the area of the shaded region?
Round your final answer to the nearest
hundredth.
11 cm
2 cm
12 cm
cm2

A circle with radius of 2 cm sits inside a11 cm x 12 cm rectangle.What is the area of the shaded region?Round

Answers

Answer:

119.4cm^2

Step-by-step explanation:

Area of rectangle = 132cm^2

Area of circle = 12.6cm^2

Shaded region = 132cm^2 - 12.6cm^2 = 119.4cm^2

How many more minutes can mate car travel per gallon of gas then jenna's car

Answers

Mate's car can travel approximately 5 more minutes per gallon of gas compared to Jenna's car.

To determine how many more minutes Mate's car can travel per gallon of gas compared to Jenna's car, we would need additional information about the fuel efficiency or miles per gallon (MPG) for each car.

Fuel efficiency is typically measured in terms of miles per gallon, indicating the number of miles a car can travel on a gallon of gas.

To calculate the difference in travel time, we would also need to know the average speed at which the cars are traveling.

Once we have the MPG values for Mate's car and Jenna's car, we can calculate the difference in travel time per gallon of gas by considering their respective fuel efficiencies and average speeds.

If Mate's car has a fuel efficiency of 30 MPG and Jenna's car has a fuel efficiency of 25 MPG, we can calculate the difference in travel time by comparing the distances they can travel on a gallon of gas.

Let's assume both cars are traveling at an average speed of 60 miles per hour.

For Mate's car:

Travel time = Distance / Speed

= (30 miles / 1 gallon) / 60 miles per hour

= 0.5 hours or 30 minutes.

For Jenna's car:

Travel time = Distance / Speed

= (25 miles / 1 gallon) / 60 miles per hour

= 0.4167 hours or approximately 25 minutes.

Without specific information about the MPG values and average speeds of the cars, it is not possible to provide an accurate answer regarding the difference in travel time per gallon of gas between Mate's car and Jenna's car.

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the volume of a sphere is decreasing at a constant rate of 3 cubic centimeters per second. at the instant when the radius of the sphere is decreasing at a rate of 0.25 centimeter per second, what is the radius of the sphere?

Answers

As the volume of the sphere is decreasing at a constant rate of 3 cm³/s, the radius of the sphere is 0.98 cm

The volume of the sphere is given by:

V = 4/3. πr³

Where:

r = radius.

Take the derivative with respect to t

dV/dt = 4. πr² dr/dt

Data from the problem:

dV/dt = 3 cm³/s

dr/dt = 0.25 cm/s

Plug these parameters into the equation:

3 = 4. πr² (0.25)

πr² = 3

r² = 3/π

r = sqrt (3/π) = 0.98 cm

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DuBois used descriptive statistics (among other research methods) to explore the social condition of African-Americans. Among the statistics he presented we find... Select one: a. ...numbers of African-Americans in cities versus rural areas. b. ...property ownership (including real estate) by African-Americans. c. ...changing proportions of the African-American population as compared to the total population of the United States. d. All of the above. e. None of the above

Answers

Among the statistics he presented we find: D. All of the above.

What is a case study?

In Psychology and Statistics, a case study can be defined as a research methodology that typically involves the use of a descriptive research technique to obtain an in-depth analysis about an individual, group of people, or phenomenon.

Based on the information provided about the social condition of African-Americans by W.E.B. DuBois using descriptive statistics, we can logically deduce the following:

"Numbers of African-Americans in cities versus rural areas."

"Property ownership (including real estate) by African-Americans."

"Changing proportions of the African-American population as compared to the total population of the United States."

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3.
For what value of x will 3x + 4 = x-6 be a true
statement?
A. x = -5
B. x=-
C. r= -1
D. x =
x=-

3.For what value of x will 3x + 4 = x-6 be a truestatement?A. x = -5B. x=-C. r= -1D. x =x=-

Answers

Answer:

A

Step-by-step explanation:

3x +4 = x-6

3x -x = -6 -4

2x = -10

x = -10/2 = -5

x^2+11x+30 ?????????????????????

Answers

Solution:

X^2+11x+30

=X^2+(6+5)x+30

=X^2+6x+5x+30

=X(x+6)+5(x+6)

=(X+6)(x+5).

So,the answer is (x+6)(x+5).

Which expression is equivalent to
1/2(2n + 6)
A- 1/2 + 2n + 6
B- 2 1/2n + 6 1/2
C- n + 6
D- n +3

Answers

Answer:

D

Step-by-step explanation:

=(1/2)*2n+(1/2)*6

=n+3

Answer:

D

Step-by-step explanation:

=(1/2)*2n+(1/2)*6

=n+3

I need help with steps on how to solve and how to get the answer

I need help with steps on how to solve and how to get the answer

Answers

two rectangles to be similar, their sides have to be proportional (form equal ratios). The ratio of the length should equal the ratio of the width.

thus,

\(\begin{gathered} \frac{12}{x}=\frac{6}{10} \\ 12\cdot10=6x \\ 120=6x \\ x=\frac{120}{6} \\ x=20 \end{gathered}\)

Therefore x=20.

There are three numbers for the combination to the store's safe. The first number is 17. The next one two numbers can be multiplied together to give a product of 28 . What are all of the possibilities for the other two numbers? Write your answers as multiplication equations, and then write all the possible combinations to the safe.

Answers

Answer:

7*4=2814*2=28factors of 28 are 1,2,4,7,14,28

Step-by-step explanation:

if correct mark brainliest plz

also Merry Christmas

If I1 ⊇ I2 ⊇ .... In ⊇... is a nested sequence of intervals and if In = [an; bn], show that a1 ≤ a2 ≤ ....... ≤ an ≤ ........ and b1 ≤ b2 ≤..... bn ≤ ......

Answers

The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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