HELPOOO QUIICKKK PLEASE 10 points

HELPOOO QUIICKKK PLEASE 10 Points

Answers

Answer 1

Answer:answer is 37

Step-by-step explanation:

2x+1=75

2x=75-1

2x=74

x=74/2

therefore, x=37


Related Questions

The length of ribbons found at a seamstress are listed.

3, 11, 11, 13, 13, 21

What is the appropriate measure of variability for the data shown, and what is its value?

The mean is the best measure of variability and equals 11.
The median is the best measure of variability and equals 11.5.
The range is the best measure of variability and equals 18.
The IQR is the best measure of variability and equals 2.

Answers

The appropriate measure of variability for the given data is the range, which is the difference between the maximum and minimum values in the dataset. In this case, the range is calculated as 21 - 3 = 18. The range provides a straightforward and intuitive measure of how spread out the data is. The other options (mean, median, and IQR) are measures of central tendency or spread and may not capture the full range of variability in this dataset. Therefore, the correct answer is C. The range is the best measure of variability, and its value is 18.

Joey wants to read 2,000 pages by the end of the summer. He has already read 1,250 pages. The rest of his reading will be spread over 5 weeks, and Joey wants to read the same number of pages each week. How many pages will he need to read each week?

Answers

Answer:

150 pages

Step-by-step explanation:

want to read 2,000 pages

already read 1,250 pages

Number of pages left to read

= 2000-1250

= 750

Rest of the reading spread over 5 weeks

wants to read same number of pages each week

Number of pages that need to be read each week over 5 weeks

= Number of pages left to read / total number of weeks

=750 / 5

= 150

He will need to read 150 pages a week.

14x² - 21x³ + 49x⁴

ayudenme porfavor​

Answers

no se

sólo lo hago esto para poder preguntar

please help!

The measure of angle J is 120⁰ and is supplementary to the measure of angle K. If the measure of angle K is 12 x , what is the value of x ?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.

Answers

Using the fact that the angles are supplementary, we can write and solve a linear equation to find that x = 5°.

How to find the value of x?

Remember that two angles are supplementary if the addition of their measures is equal to 180°.

Here we know that angles J and K are supplementary, then we know that:

J + K = 180°

Here we also know that:

J = 120°

K = 12x

So we can write a linear equation of the form:

120° + 12x = 180°

12x = 180° - 120°

12x = 60°

x = 60°/12 = 5°

x = 5°

We conclude that the value of x is 5°.

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-6+7y=8
Solve for y.

Answers

Answer:

y=2

Step-by-step explanation:

7y=14

y=2

-6+7y=8
7y=8+6
7y=14
dived both sides by 7
you get y=2
hope that helps!
-6+7y=8Solve for y.

Angle ADB and CD are straight lines. angle ADC = 5 x angle CDB Work out the size of angle ADC.

Angle ADB and CD are straight lines. angle ADC = 5 x angle CDB Work out the size of angle ADC.

Answers

Answer:

Step-by-step explanation:

Angle ADB and CD are straight lines. angle ADC = 5 x angle CDB Work out the size of angle ADC.

State the groups of shapes​

Answers

Answer:

The groups are round shapes, triangles, quadrilaterals, pentagons, and hexagons.

Step-by-step explanation:

The groups are round shapes, triangles, quadrilaterals, pentagons, and hexagons.

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds.  Find the weight per carton.​

Answers

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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3. The_____of an investment is measured by the variance or, more commonly, the standard deviation of its return.
A. total risk B. systematic C. risk diversified S. risk total return

Answers

The total risk of an investment is measured by the variance or, more commonly, the standard deviation of its return. Therefore, the correct answer option is: A. total risk.

What is risk management?

In Economics, risk management can be defined as a strategic process which involves the identification, evaluation, analysis and control of potential threats (risks) that are present in a business, project, or system, as an obstacle to its capital, revenues, success, and profits.

What is rate of return?

In Business management, rate of return can be defined as a net gain (profit) or loss that is associated with an investment over a specified period of time, and it is usually expressed as a percentage of the initial cost of an investment.

In conclusion, the standard deviation or variance of its return is typically used for measuring the total risk of an investment.

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What is the factorization of the trinomial below?

3x^3 + 6x^2 - 24x

A. 3x(x - 2)(x + 4)

B. 3x(x - 2)(x - 4)

C. 3(x - 2)(x + 4)

D. 3(x^2 - 2)(x + 4)

What is the factorization of the trinomial below? 3x^3 + 6x^2 - 24xA. 3x(x - 2)(x + 4)B. 3x(x - 2)(x

Answers

The correct answer is A

Need Trig Help plz Picture attached

Need Trig Help plz Picture attached

Answers

Option B is the correct answer

Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places​

Answers

Answer:

= 173.903t

Step-by-step Explanation:

The given equation is: f(t) = 227e^(b*t)

To convert it to the form f(t) = ab, we need to write it in the form of f(t) = a * e^(k*t), where a and k are constants.

Let's start by taking the natural logarithm (ln) of both sides:

ln(f(t)) = ln(227e^(b*t))

Using the properties of logarithms, we can simplify this to:

ln(f(t)) = ln(227) + ln(e^(b*t))

ln(f(t)) = ln(227) + b*t

Now, let's define a new constant, k = b, and rewrite the equation in terms of a and k:

ln(f(t)) = ln(a) + k*t

where a = 227 and k = -0.09

Taking the exponential of both sides, we get:

f(t) = e^(ln(a) + k*t)

f(t) = e^(ln(a)) * e^(k*t)

f(t) = a * e^(k*t)

Substituting the values of a and k, we get:

f(t) = 227 * e^(-0.09*t)

Therefore, the equation f(t) = ab is:

f(t) = 227e^(-0.09t) ≈ 173.903t (rounded to three decimal places)

15 POINTS
Using Pythagoras' theorem, calculate the length
of XY.
Give your answer in centimetres (cm) to 1 d.p.

15 POINTSUsing Pythagoras' theorem, calculate the lengthof XY.Give your answer in centimetres (cm) to

Answers

Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

Answer:
13.3cm
Step-by-step explanation:
The Pythagorean theorem is a^2+ b^2 = c^2
Plug the values into the equation.
7^2+ b^2 = 15^2
Simplify.
49 ÷ b^2 = 225
Subtract 49 from both sides.
b^2 = 176
Take the square root of both sides.
vb^2 = v176
b=13.266
b=13.3cm

Bookwork code: N84
This is a new version of the question Make sure you start now workings
Calculate the range, in centimetres (cm), of the following
lengths:
15 cm, 0.5 cm, 10.3 cm, 16.7 cm, 21 cm,
8.6 cm

Answers

The range, in centimetres (cm), of the following lengths is 20.5 cm

What is the range?

The difference between the lowest and highest numbers is referred to as the range. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

Given, 15 cm, 0.5 cm, 10.3 cm, 16.7 cm, 21 cm, 8.6 cm

So, the highest value of length = 21 cm

the lowest value of length = 0.5 cm

Then, range = the highest value - the lowest value

                    = 21 - 0.5 = 20.5 cm

Hence, the range, in centimetres (cm), of the following lengths is 20.5 cm

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Find the midpoint of CD with endpoints C (6,-9) and D (0,15)​

Answers

Answer:

1.5

Step-by-step explanation:

find x
a.204
b.90
c.78
d.102

find x a.204b.90c.78 d.102

Answers

Answer:

Hope you can understand my handwriting though

find x a.204b.90c.78 d.102

I need help with this math question (complex fractions and rational expressions). For the answer, I need a step-by-step explanation so I can understand it, thank you :) I tried putting it into Symbolab to understand it but that wasn't very helpful so I think human assistance would be more beneficial haha. \((\frac{(7x^{2} + 5x) }{x^{2} + 1 } ) - (\frac{5x}{x^{2} -6})\)

Answers

Answer:

can you type it out

Step-by-step explanation:

Given: The coordinates of rhombus WXYZ are W(0, 4b), X(2a, 0), Y(0, -4b), and Z(-2a, 0).
Prove: The segments joining the midpoints of a rhombus form a rectangle.
As part of the proof, find the midpoint of YZ.

Answers

The midpoint of segment YZ is (-a, -2b).

Given the coordinates of the rhombus WXYZ:

W(0, 4b)

X(2a, 0)

Y(0, -4b)

Z(-2a, 0)

Find the midpoint of YZ:

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the coordinates of Y and Z:

Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)

= (-a, -2b)

Therefore, the midpoint of segment YZ is (-a, -2b).

Show that the segments joining the midpoints are perpendicular:

To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.

Let's consider the segments joining the midpoints:

Segment joining the midpoints of WX and YZ:

Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)

Midpoint of YZ: (-a, -2b)

Slope of WX = (2b - 4b) / (a - 0) = -2b / a

Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a

The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.

Conclusion:

We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.

Additionally, the midpoint of segment YZ is (-a, -2b).

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Divide. Express your answer in simplest form. ○14 ○ 49 ○98 ○28​

Answers

Answer: 49

see below for work

Divide. Express your answer in simplest form. 14 49 98 28

Answer:

gang gang

Step-by-step explanation:

Marco wants to know how much the other students in his mathematics class study. He recorded the data he collected in
the following table.
Time spent studying per week (in hours)
2.0
5.0
1.0
2.5
2.5
3.5
0.0
4.5
2.5
4.0
3.5
3.0
2.0
1.5
4.0
2.0
0.5
3.0
1.0
3.0
3.5
1.5

1. Construct a histogram for the data.

Marco wants to know how much the other students in his mathematics class study. He recorded the data

Answers

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

I need help with pre calculus.

I need help with pre calculus.
I need help with pre calculus.
I need help with pre calculus.

Answers

Problem 1

Answer: Choice A.  (0,9)

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

Explanation:

The first task is to determine the function for f(x). Because it's linear, it's in the form y = mx+b. Let's find the slope m.

Select any two columns to pick out (x,y) points from the f(x) function. I'll pick the first two columns to select the points (-6,15) and (-4,11). Apply the slope formula to these two points to get...

m = (y2-y1)/(x2-x1)

m = (11-15)/(-4-(-6))

m = (11-15)/(-4+6)

m = -4/2

m = -2

Then use this m value along with any of the points of the table to determine the y intercept b. I'll use the point (-6,15)

y = mx+b

b = y-mx

b = 15-(-2)*(-6)

b = 15-12

b = 3

The y = mx+b equation becomes y = -2x+3 and that leads directly to the function f(x) = -2x+3.

Repeat all of those steps but do so for g(x) this time. I'll skip those steps over but you should get the function g(x) = 5x-6.

The y intercepts of f(x) and g(x) found were 3 and -6 respectively. Subtract those values to find the y intercept of h(x) = (f-g)(x) = f(x)-g(x).

So we get 3-(-6) = 3+6 = 9 which leads to the location (0, 9).

=========================================================

Problem 2

Answer: Choice Ax is any real number but x cannot equal -2, -1 or 1.

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

Explanation:

Through trial and error, the factor by grouping method, or using your graphing calculator, factor the denominator to get

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

The factors (x+2), (x+1) and (x-1) lead to the roots of x = -2, x = -1, and x = 1 in that order. Those three roots of g(x) will make g(x) = 0 and cause a division by zero error in the denominator. So we must kick out those three values from the domain. Every other real number is allowed in the domain. So that's how we get the notation for choice A. It starts off saying x is a real number. Then it goes onto say that -2, -1 and 1 aren't allowed.

So overall the domain is described as: "x can be almost any real number except x cannot be -2, cannot be -1, and it cannot be 1".

Side note: We don't involve the numerator function at all.

=========================================================

Problem 3

Answer: Choice B. 2x+1 and x-3

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

Explanation:

The height is x, which we can factor out like this

2x^3-5x^2-3x

2x^2*x - 5x*x - 3*x

x(2x^2-5x-3)

Effectively you would use the distribution rule in reverse.

Now let's factor the remaining expression in the parenthesis.

I'll use the factor by grouping method.

2x^2-5x-3

2x^2-6x+1x-3

(2x^2-6x) + (1x-3)

2x(x-3) + 1(x-3)

(2x+1)(x-3)

Therefore, the full factorization is

x(2x+1)(x-3)

which shows we have the dimensions of x, (2x+1) and (x-3). The order doesn't matter so we could easily have (2x+1) the length and (x-3) the width, or we could have it the other way around.

You can verify that (2x+1)(x-3) expands out to 2x^2-5x-3 using either the FOIL method or the box method.

Please help with this Algebra question

Please help with this Algebra question

Answers

Answer:

x = -2, y = -1, z = 1

Step-by-step explanation:

From (3), z = 2x + 5

From (2) y = (x - 2)/4

Sub them into (1):

5x - 6*(x - 2)/4 + 3(2x + 5) = -1

5x - 3x/2 + 3 + 6x + 15 = -1

19x/2 = -19

x/2 = -1

x = -2

y = (x - 2)/4 = (-2-2)/4 = -1

z = 2x + 5 = 2(-2) + 5 = 1

5.4 / 113.4

Pls show work

5.4 / 113.4Pls show work

Answers

Hopes this helps:

Answer: 21

Have a great day.
5.4 / 113.4Pls show work

on a separate sheet of paper, sketch the rectangle for each problem using any method round and estimate to check your answer problem 1 5 x 4,751

Answers

The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

What is rounding of a number?

Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.

The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.

2. 7 x 6000 = 42,000.

To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.

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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

What is rounding of a number?

The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.

In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.

Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.

2. 7 x 6000 = 42,000.

We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.

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can you please show me how you got the answer (50 points)

can you please show me how you got the answer (50 points)

Answers

Answer:

\(4x^{6}2y^{-2}\)

Step-by-step explanation:

We can use a property I like to call SEi-F. (Subtract Exponents in a Fraction)

But first, there is an exponent outside of the parentheses in both places. We can use the Power of Parentheses to simplify and then use the SEi-F.

We will start with the x in the numerator.

3*4 = 12

Now for the y in the numerator.

4*4 = 16

Our new numerator is \(4(2x^{12}y^{16})\)

We do need to simplify the numerator one more time to get rid of the 4 outside the parentheses.

We will start with x's coefficient.

2*4 = 8

Now for y's coefficient.

1**4 = 4

*y seems to have no coefficient, but if so, it has a coefficient of 1. This applies to other variables.

Our final simplified numerator is \(8x^{12}4y^{16}\).

Repeat with the denominator.

Try it yourself!

Make sure that when you finish, you finish the fraction.

After completing the denominator, your completed fraction should be:

\(\frac{8x^{12}4y^{16}}{4x^{6}2y^{18}}\)

Now we can use the SEi-F to complete the problem.

Start with x.

8x - 4x = 4x

12 - 6 = 6

The first term is \(4x^{6}\).

Now for y.

4y - 2y = 2y

16 - 18 = -2

The second term is \(2y^{-2}\)

The complete, simplified equation is \(4x^{6}2y^{-2}\).

I could be wrong on the answer, but the work should be correct.

Hope this helps. Have a nice day. Oh, and one more thing. Surprised I'm not stealing points?

In class, we developed the formula
(a) Use the formula (using appropriate substitutions) to find the closed form for ∑2
= 2
(b) Use the formula in the notes for ∑
= 13 to find the closed form expression form for

= 3 (assume a ≥ 1 and a ≤ b)
(c) In class, we developed the formula
Use this formula and some algebra to derive a closed form for the sum ∑
= 0( ― 1)2 ― 1
(d) Test your closed form solution in (c) to find the value of ∑3
= 0( ― 1)2 ― 1 and see if
it matches the manual computation of the 4 terms of the sum.

Answers

(a) The closed form for ∑2 is 2.

(b) The closed form expression for ∑3 is 24.

(c) The closed form for the sum ∑n = 0(― 1)² ― 1 is n(1 - n) / 2.

(d) The value of -3 matches the manual computation of the four terms.

Our closed form solution is correct.

To find the closed form for ∑2, we can use the formula for the sum of the first n terms of an arithmetic series:

∑2 = n(a + l) / 2

In this case, a = 2 (the first term) and l = 2 (the last term) since we are summing a series of 2's.

We also know that there is only one term, so n = 1.

Substituting these values into the formula, we have:

∑2 = 1(2 + 2) / 2

= 4 / 2

= 2

The formula for the sum of the first n terms of an arithmetic series is:

∑n = n(a + l) / 2

In this case, we have a = 3 (the first term), l = 13 (the last term), and n = 3 (the number of terms).

Substituting these values into the formula, we get:

∑3 = 3(3 + 13) / 2

= 3(16) / 2

= 48 / 2

= 24

The formula we developed in class is:

∑n = n(a + a + (n - 1)d) / 2

In this case, we have a = 0 (the first term) and d = -1 (the common difference).

Substituting these values into the formula, we get:

∑n = n(0 + 0 + (n - 1)(-1)) / 2

= n(0 - n + 1) / 2

= n(1 - n) / 2

To test the closed form solution for ∑3 = 0(― 1)² ― 1, we substitute n = 3 into the closed form expression we derived in part (c):

∑3 = 3(1 - 3) / 2

= 3(-2) / 2

= -6 / 2

= -3

Now, let's manually compute the sum of the first four terms of ∑3 = 0(― 1)² ― 1:

0(― 1)² ― 1 + 1(― 1)² ― 1 + 2(― 1)² ― 1 + 3(― 1)² ― 1

= 0 - 1 - 2 - 3

= -6

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Simplify fully

8n

10n

Answers

Answer:

The answer is 4/5

Step-by-step explanation:

Simplify the expression.

Hoped this helped!

Brainly, please?

Answer: 4/5

Step-by-step explanation: 8n/10n

8/10

4/5

Find the measure of the indicated angle in each triangle.

A)37

B)63

C)80

D)180

Find the measure of the indicated angle in each triangle.A)37B)63C)80D)180

Answers

m∠U = 80°

total interior angle in a triangle is 180°

m∠U + 37° + 63° = 180°

m∠U = 180° -  63° - 37°

m∠U = 80°

m<U be x

Apply angle sum property

\(\\ \rm\rightarrowtail x+37+63=180\)

\(\\ \rm\rightarrowtail x+100=180\)

\(\\ \rm\rightarrowtail x=80\)

Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options. y = –Three-fourthsx + 1 3x − 4y = −4 4x − 3y = −3 y – 2 = –Three-fourths(x – 4) y + 2 = Three-fourths(x + 4)

Answers

Answer:

The equation of the parallel  line to the given equation is

3 x-4 y = -4    and

The equation of the parallel  line to the given equation is

\(y = 1 + \frac{3 x}{4}\)

Step-by-step explanation:

Explanation:-

Given equation of the line 3 x -4 y = 7 and given point ( -4 , -2 )

The equation of the parallel line to the given equation is

3 x - 4 y = k

it is passes through the point ( -4 , -2)

3 (-4) - 4 ( -2) = k

-12 +8 = k

k = -4

The equation of the parallel  line to the given equation is

3 x- 4 y = -4

Dividing '4' on both sides , we get

\(\frac{3 x-4 y}{-4} = 1\)

\(\frac{-3 x}{4} +y =1\)

\(y = 1 + \frac{3 x}{4}\)

Conclusion:-

The equation of the parallel  line to the given equation is

3 x- 4 y = -4

and

The equation of the parallel  line to the given equation is

\(y = 1 + \frac{3 x}{4}\)

   

Answer:

the answer is b and d edge 2021

Step-by-step explanation:

I am finished taking the test got a 100%

Problem 2:

Priya is walking down a long hallway. She walks halfway and stops. Then, she walks half of the remaining distance, and

stops again. She continues to stop every time she goes half of the remaining distance.

1. What fraction of the length of the hallway will Priya have covered after she starts and stops two times?

2. What fraction of the length of the hallway will Priya have covered after she starts and stops four times?

3. Will Priya ever reach the end of the hallway, repeatedly starting and stopping at half the remaining distance? Explain

your thinking.

Answers

Answer:

The answers to the questions about problem 2 are:

The fraction of the length after Priya stops two times is 3/4.The fraction of the length after Priya stops four times is 15/16.Priya will never reach the end of the hallway.

Step-by-step explanation:

The explanation about each answer is below:

1. In the first stop, Priya has walked half of the total length, and there would still be half the hallway, however, when she stops the second time, she has walked the half of the half, I mean:

\(\frac{1}{2}/2=\frac{1}{4}\)

If you add the two values you obtain the total distance traveled by Priya:

\(\frac{1}{2}+\frac{1}{4}= \frac{3}{4}\)

And the distance traveled in two stops is 3/4 of the total length of the hallway.

2. With four stops the system is the same, we know with two stops Priya travels 3/4 of the hallway, now with the third stop, she will travel half of the remaining distance:

\(\frac{1}{4}/2=\frac{1}{8}\)

And in the fourth stop she will travel half of the remaining, I mean:

\(\frac{1}{8}/2=\frac{1}{16}\)

Now, we add all the values of the distances obtained:

\(\frac{3}{4}+\frac{1}{8}+\frac{1}{16}= \frac{15}{16}\)

So, the distance traveled by Priya in the fourth stop is 15/16 of the total length of the hallway.

3. How we know, the numbers are infinite, in the same forms the distances, by this reason, how the problem says that Priya walks just half of the distance, she will never reach the end because despite she has very near of the end, she will continue walking just half and ever smaller distances.

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