A number decreased by 19,
divided by -6, is no more than 5.'
ality:

Answers

Answer 1

Answer:

Fifteen less than twice a number35% of n4/17 of nSubtract y from 5Subtract 5 from yadd|sumof x and|to 8x added to 3x subtracted from 20p added to tp subtracted from tmultiply x and 825 divided by a numberquotient of ten and a number decreased by twothe sum of 4 and a number divided by 104 times a number plus 5 times the same numbert is atleast 10 and at most 22divide 8 by xdivide x by 93 groups of wx is no less than 25The product of w and 5 is less than 21w more than 47 times the sum of x and ytake away 4 from 3 times dtwice the sum of a number and 3


Related Questions

. Joe makes a one-time deposit of $5,000.00 to open an interest-bearing savings account for his newborn grandson, Tyler. The table shows the expected balance of the account, , when Tyler is t years old. Age in years, Balance in dollars, 0 5,000.00 2 5,030.08 4 5,060.34 6 5,090.78 8 5,121.41 10 5,152.21 12 5,183.21 14 5,214.39 Consider five intervals representing periods of t years during which the account balance, , changed. Order the intervals from greatest to least average rate of change.

Answers

The greatest average rate of change occurs during the interval from 12 to 14 years, and the least average rate of change occurs during the interval from 0 to 2 years.

What is the rate of change?

The rate of change is defined as the change in value with the rest of the other factor is called the rate of change.

Here,
To determine the average rate of change for each interval, we need to find the change in balance and divide by the change in time. We can then compare the values to determine the intervals with the greatest and least average rates of change.

Interval 0 to 2: Change in balance = 5,030.08 - 5,000.00 = 30.08; Change in time = 2 - 0 = 2. The average rate of change = 30.08/2 = 15.04.

Similarly,

Interval 2 to 4:  The average rate of change = 15.13.

Interval 4 to 6:  Average rate of change = 15.22.

Interval 6 to 8: Average rate of change= 15.32.

Interval 8 to 10: Average rate of change = 15.40.

Interval 10 to 12: Average rate of change = 15.50.

Interval 12 to 14:  The average rate of change = 15.59.

Ordering the intervals from greatest to the least average rate of change, we have,

Interval 12 to 14: 15.59

Interval 10 to 12: 15.50

Interval 8 to 10: 15.40

Interval 6 to 8: 15.32

Interval 4 to 6: 15.22

Interval 2 to 4: 15.13

Interval 0 to 2: 15.04

Therefore, the greatest average rate of change occurs during the interval from 12 to 14 years, and the least average rate of change occurs during the interval from 0 to 2 years.

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If point a is located at ( 2,-3) and there are 10 points between a and b what could be the possible coordinated for point b

Answers

The possible coordinates for point B could be (12, 4) if each coordinate increment is 1.

To find the coordinates of point B given that there are 10 equally spaced points between point A and point B, we need to determine the distance between the two points and divide it by 10 to find the increment for each coordinate.

Let's assume the coordinates of point B are (x, y).

The x-coordinate increment would be the difference between the x-coordinates of point B and A divided by 10:

Δx = (xB - xA) / 10

The y-coordinate increment would be the difference between the y-coordinates of point B and A divided by 10:

Δy = (yB - yA) / 10

Substituting the known values:

Δx = (xB - 2) / 10

Δy = (yB - (-3)) / 10

Since we have 10 equally spaced points between A and B, we can calculate the coordinates of point B by multiplying the increments by the number of points from A:

xB = 2 + 10 * Δx

yB = -3 + 10 * Δy

Now we can calculate the possible coordinates for point B using these formulas.

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The radius of a cone is 3 cm and the surface area is 81pi cm squared. Find the slant height of this cone.

Answers

24cm

1) We can find out the slant height of that cone by making use of the following:

\(\begin{gathered} R=3 \\ A=\pi r\mleft(s+r\mright) \\ \end{gathered}\)

2) Plugging into that we can write out:

\(\begin{gathered} 81\pi=3\pi(s+3) \\ \frac{81\pi}{3\pi}=\frac{3\pi(s+3)}{3\pi} \\ 27=s+3 \\ 27-3=s \\ s=24 \end{gathered}\)

Hence, the slant height is 24 cm

My pigg y bank has only pennies and nicklels in it , and 2/7 of the coins are nickel If i remove 84 pennies then 1/3 of the remening are pennies 1} suppose there are initially p pennies and n nickels in the pigy bank write an equation using the fact that 2/7 of the coins initially in the

Answers

Answer:

There are 105 pennies in the piggy bank.

There are 42 nickels in the piggy bank.

Step-by-step explanation:

there are:

p pennies in the piggy bank

n nickels in the piggy bank

Then we can define T, the total number of coins, as:

T = p + n

We know that 2/7 of the total number of coins are nickels.

This can be written as:

n = (2/7)*T = (2/7)*(n + p)

And if we remove 84 pennies, 1/3 of the remaining coins are pennies.

This can be written as:

p - 84 = (1/3)*(n + p - 84)

Then we have a system of two equations:

n = (2/7)*(n + p)

p - 84 = (1/3)*(n + p - 84)

Let's solve the system, to do it, we first need to isolate one of the variables in one of the equations.

We can isolate n in the first one, to get:

n = (2/7)*(n + p) = (2/7)*n + (2/7)*p

n - (2/7)*n = (2/7)*p

n*(5/7) = (2/7)*p

n = (7/5)*(2/7)*p = (2/5)*p

n = (2/5)*p

Now we can replace this in the other equation:

p - 84 = (1/3)*(n + p - 84)

p - 84 = (1/3)*( (2/5)*p + p - 84)

Let's solve this for p

p - 84 = (1/3)*( (7/5)*p - 84)

3*(p - 84) = (7/5)*p - 84

3p - 252 = (7/5)*p - 84

3*p - (7/5)*p = 252 - 84

(15/5)*p - (7/5)*p = 168

(8/5)*p = 168

p = (5/8)*168 = 105

There are 105 pennies in the piggy bank.

And we know that:

n = (2/5)*p = (2/5)*105 = 42

There are 42 nickels in the piggy bank.

X+2 is a factor of x^3- kx^2 +3x+7k. Find the value of k.

Answers

Answer:  k = 14/3

Explanation:

If x+2 is a factor of the other polynomial mentioned, then x = -2 is a root of that polynomial.

This means plugging x = -2 into the cubic expression will have it result in zero.

x^3- kx^2 +3x+7k = y

(-2)^3- k*(-2)^2 +3*(-2)+7k = 0

-8 - 4k - 6 + 7k = 0

3k - 14 = 0

3k = 14

k = 14/3

Chuck Sox makes wooden boxes in which to ship motorcycles. Chuck and his three employees invest a total of 30 hours per day making the __________. boxes.

Answers

The original productivity is 4 boxes/ hour. the new productivity is 7.33 boxes/hour, the unit increase in productivity is 3.33 boxes/hour, the percentage increase in productivity is 83.25%

Let's call the original productivity "P1" and the new productivity "P2".

P1 = 120 boxes / 30 hours = 4 boxes/hour

P2 = 220 boxes / 30 hours = 7.33 boxes/hour

The unit increase in productivity is P2 - P1 = 7.33 - 4 = 3.33 boxes/hour

The percentage increase in productivity is (P2 - P1) / P1 * 100% = (3.33 / 4) * 100% = 83.25%.

So, we conclude that original productivity of boxes is 4 boxes/ hour,  the new productivity is 7.33 boxes/hour, the unit increase in productivity is 3.33 boxes/hour, and the percentage increase in productivity is 83.25%.

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_______ The given question is incomplete, the complete question is given below:-

Chuck Sox makes wooden boxes in which to ship

motorcycles. Chuck and his three employees invest a total of 30

hours per day making the 120 boxes.

1) What is their productivity?

2) Chuck and his employees have discussed redesigning the process

to improve efficiency. If they can increase the rate to 220 boxes

per day, what will be their new productivity?

3) What will be their unit increase in productivity per hour?

4) What will be their percentage change in productivity?

It cost $32 per day to rent a medium-sized car plus $0.25 for each mile driven over 150 miles the equation that represents this situation is y= 0.25x + 32 where y represents the total cost of renting a car and x represents the number of miles driven over 150 miles

It cost $32 per day to rent a medium-sized car plus $0.25 for each mile driven over 150 miles the equation

Answers

Answer:

a) 0.25 stands for 25 cents per mile

b) 32 stands for $32 just to rent the car

Step-by-step explanation:

Select the correct answer from each drop-down menu. five people buy individual insurance policies. according to the research, the probability of each of these people not filing a claim for at least 5 years is . the probability that all 5 have not filed a claim after 5 years is , and the probability that exactly 3 will have filed a claim after 5 years is .

Answers

The correct answer is 0.033.

1) P(after 5 years, all 5 file no claim) \(= 0.132\)

2) P(exactly three claims filed after five years) \(= 0.033\)

Explanation in detail:

1) We're told that the chances of each of these folks not submitting a claim for at least 5 years are 2/3.

As a result, for all five of them

P(all 5 file no claim after 5 years) = \((2/3)^5 = 0.1317 ≈ 0.132\) is the probability.

2) Because the chance of each not submitting a claim in the previous 5 years is 2/3,

After 5 years, the likelihood of each making a claim is \(1 - 2/3 = 1/3\).

As a result, P(exactly three file claim after five years) \(= (1/3)^3 ≈ 0.037\).

What is probability ?

Probability is synonymous with possibility. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also utilized in probability distribution, in which you will learn about the possible results of a random experiment. To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.

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I NEED HELP WITH THIS WILL MARK BRAINLIEST!

I NEED HELP WITH THIS WILL MARK BRAINLIEST!

Answers

Answer:

y=-2/5x-6

Step-by-step explanation:

The line crosses the y axis at -6 so the y intercept is -6. The line of the graph goes down 4 and right 10 so the slope is -4/10 which is equal to -2/5 when simplified.

Answer:

y= -2/5x -6

Step-by-step explanation:

The slope is 2/5, because slope is rise over run, and the two points rise 2, and run 5. The y intercept is -6, because the line crosses the y axis at -6. Slope intercept form is y= mx+b, where x and y are the points, and slope is m, and b is y intercept. So the equation is y= 2/5x -6. HOPE THIS HELPS!! :D This is a negative slope too, so the slope is negative.

LINEAR Equations HELP ASAP

LINEAR Equations HELP ASAP

Answers

Answer: D) -4/3

Step-by-step explanation:

Slop can be represented as \(\frac{rise}{run}\).  This equation rises -24 units then runs 18.  Thus, the slope is -24/18, or -4/3.

Hope it helps <3

Answer:

-4/3.

Step-by-step explanation:

To get the slope, you do the rise over the run.

In this case, the rise is going to be -24, since the track is falling. The run will be 18.

-24 / 18 = -12 / 9 = -4/3

Hope this helps!

can someone help me ASAP

can someone help me ASAP

Answers

Answer:

8/9 n-3

Step-by-step explanation:

YO ITS I-READY DIAGNOSTIC COOOL

The graph of a proportional relationship contains the point (8,4). What is the corresponding equation? Enter your answer as a fraction in simplest form by filling in the boxes.


y= — x

The graph of a proportional relationship contains the point (8,4). What is the corresponding equation?

Answers

Given:

The graph of a proportional relationship contains the point (8,4).

To find:

The corresponding equation.

Solution:

If y in directly proportional to x, then

\(y\propto x\)

\(y=kx\)        ...(i)

Where, k is the constant of proportionality.

The graph of a proportional relationship contains the point (8,4).

Putting x=8 and y=4 in (i), we get

\(4=k(8)\)

\(\dfrac{4}{8}=k\)

\(\dfrac{1}{2}=k\)

Putting \(k=\dfrac{1}{2}\) in (i), we get

\(y=\dfrac{1}{2}x\)

Therefore, the required equation is \(y=\dfrac{1}{2}x\).

a. What was the average annual return on large-company stock from 1926 through 2016 in nominal terms? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What was the average annual return on large-company stock from 1926 through 2016 in real terms? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answers

The average annual return on large-company stock from 1926 through 2016 in nominal terms was approximately 10.07%. This means that, on average, investors who held large-company stocks saw their investments grow by 10.07% each year before adjusting for inflation.

b. The average annual return on large-company stock from 1926 through 2016 in real terms, after adjusting for inflation, was approximately 6.88%. This takes into account the impact of inflation on the purchasing power of the returns. While the nominal return of 10.07% may seem higher, the real return of 6.88% reflects the actual increase in wealth that investors experienced during this period.

The difference between the nominal and real returns can be attributed to the effects of inflation. Inflation erodes the purchasing power of money over time, meaning that the same amount of money can buy fewer goods and services in the future. By adjusting for inflation, we get a more accurate measure of the true growth of investments in terms of real value. Therefore, while the nominal return may seem more impressive, it is important to consider the real return to understand the actual increase in wealth over the long term.

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What does the size of stiffness matrix depend on?

Answers

the size of the stiffness matrix depends on the number of degrees of freedom and the type of elements used in the analysis. It is an important tool in structural mechanics and engineering for analyzing the behavior and performance of structures under different loading conditions.

In structural mechanics and engineering, the stiffness matrix is a mathematical representation of the stiffness of a structure, which relates the forces and displacements of the structure. The size of the stiffness matrix depends on several factors, including the number of degrees of freedom and the type of elements used in the analysis. The number of degrees of freedom (DOF) in the system determines the size of the stiffness matrix. DOF refers to the number of independent displacements or rotations that a structure can undergo in response to external forces. For example, a simple beam structure might have two DOF (vertical displacement and rotation), while a more complex structure such as a truss or frame might have many more DOF. The size of the stiffness matrix also depends on the type of elements used in the analysis. Different types of elements have different degrees of freedom and stiffness properties, which affect the size and shape of the stiffness matrix. For example, a truss element has two DOF and a constant axial stiffness, while a beam element has four or six DOF and variable stiffness properties that depend on its geometry and material properties.

In summary, the size of the stiffness matrix depends on the number of degrees of freedom and the type of elements used in the analysis. It is an important tool in structural mechanics and engineering for analyzing the behavior and performance of structures under different loading conditions.

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Which numbers are the means of the proportion shown

Which numbers are the means of the proportion shown

Answers

\(\bold{{Answer}}\)

B.2.And30

What is the means of a proportion?

1 : harmonious relation of parts to each other or to the whole : balance, symmetry. 2a : proper or equal share each did her proportion of the work. b : quota, percentage. 3 : the relation of one part to another or to the whole with respect to magnitude, quantity, or degree : ratio.

A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."

please correct me if im wrong

Answer:

D

Step-by-step explanation:

Given the proportion

\(\frac{a}{b}\) = \(\frac{c}{d}\)

Then a and d are the extremes of the proportion

and b, c are the means of the proportion

Then for

\(\frac{2}{3}\) = \(\frac{20}{30}\)

3 and 20 are the means → D

What is this? Please help me find the answer

What is this? Please help me find the answer

Answers

Answer:

You can buy 4 Pizzas

Step-by-step explanation:

if you think carefully the devilery fee is still $7

because even how many pizzas you odered,the devilery man can deliver them all together

divide the spare change with the price of each pizza.

55÷12=4 r.7

4×12= 48

$48 dollars for 4 pizzas and $7 for the delivery.

48+7=55

thus he bought 4 pizzas

Answer:

thats math solution u need to answer it

write additive and multiplicative inverse of19/-6 and-2/3

Answers

Answer:

Additive inverse of 19/-6 is 19/6

Additive inverse of -2/3 is 2/3

Multiplicative inverse of 19/-6 is -6/19

Multiplicative inverse of  -2/3 is  3/-2 (also written as -3/2)

Step-by-step explanation:

(a) The additive inverse of a number is that number that when added to it gives 0.

For example, the additive inverse of x is -x.

This is because adding -x to x gives 0. i.e

x + (-x) = 0

In other words, the additive inverse of a number is the negative of that number.

Given:

(i) 19/-6

The additive inverse of 19/-6 is the negative of 19/-6 which is -(19/-6).

-(19/-6) then gives 19/6

Therefore, the additive inverse of 19/-6 is 19/6

(ii) -2/3

The additive inverse of -2/3 is the negative of -2/3 which is -(-2/3).

-(-2/3) then gives 2/3

Therefore, the additive inverse of -2/3 is 2/3

(b) The multiplicative inverse of a number is that number that when multiplied by it gives 1.

For example, the multiplicative inverse of y is 1/y.

This is because multiplying y by 1/y gives 1. i.e

y x (1/y) = 1

In other words, the multiplicative inverse of a number is the reciprocal of that number.

Given:

(i) 19/-6

The multiplicative inverse of 19/-6 is the reciprocal of 19/-6 which is 1/(19/-6).

1 / (19/-6) then gives -6/19

This is found by just swapping the numerator(19) and the denominator(-6)

Therefore, the multiplicative inverse of 19/-6 is -6/19

(ii) -2/3

The multiplicative inverse of -2/3 is the reciprocal of -2/3 which is 1/(-2/3).

1 / ( -2/3) then gives  3/-2

This is found by just swapping the numerator(-2) and the denominator(3)

Therefore, the multiplicative inverse of  -2/3 is  3/-2 (also written as -3/2).

PLeassssse HELPPPP!!!

PLeassssse HELPPPP!!!

Answers

Answer:

B i believe is the answer

Step-by-step explanation:


In Exercise 4, find the surface area of the solid
formed by the net.

In Exercise 4, find the surface area of the solidformed by the net.

Answers

Answer:

3. 150.72 in²

4. 535.2cm²

Step-by-step Explanation:

3. The solid formed by the net given in problem 3 is the net of a cylinder.

The cylinder bases are the 2 circles, while the curved surface of the cylinder is the rectangle.

The surface area = Area of the 2 circles + area of the rectangle

Take π as 3.14

radius of circle = ½ of 4 = 2 in

Area of the 2 circles = 2(πr²) = 2*3.14*2²

Area of the 2 circles = 25.12 in²

Area of the rectangle = L*W

width is given as 10 in.

Length (L) = the circumference or perimeter of the circle = πd = 3.14*4 = 12.56 in

Area of rectangle = L*W = 12.56*10 = 125.6 in²

Surface area of net = Area of the 2 circles + area of the rectangle

= 25.12 + 125.6 = 150.72 in²

4. Surface area of the net (S.A) = 2(area of triangle) + 3(area of rectangle)

= \( 2(0.5*b*h) + 3(l*w) \)

Where,

b = 8 cm

h = \( \sqrt{8^2 - 4^2} = \sqrt{48} = 6.9 cm} (Pythagorean theorem)

w = 8 cm

\(S.A = 2(0.5*8*6.9) + 3(20*8)\)

\(S.A = 2(27.6) + 3(160)\)

\(S.A = 55.2 + 480\)

\(S.A = 535.2 cm^2\)

what is the answer to 5

what is the answer to 5

Answers

Answer:

6

Step-by-step explanation:

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Answer:

5x+7=2x+4

3x+7=4                 (subtract 2x)

3x = 4-7                (subtract 7)

3x = -3                  (divide)

x = -3/3

x = -1

Can someone please help me solve this? or at least explain how I would go about solving this?​

Can someone please help me solve this? or at least explain how I would go about solving this?

Answers

Answer:

find the probaillity of each one.

Step-by-step explanation:

What is the probability that a randomly chosen player is a freshman or a senior, p(a or b)? show work.

Answers

The probability that a randomly chosen player is a freshman or a senior is 0.6666 or approximately 66.66%.

In probability, p(a or b) denotes the probability that event a or event b or both of them will occur.

The formula for this is: p(a or b) = p(a) + p(b) - p(a and b)

Where p(a) represents the probability of event a, p(b) represents the probability of event b and p(a and b) represents the probability of both events occurring.

If there is no overlap between the two events, i.e., p(a and b) = 0,

then the formula simplifies to: p(a or b) = p(a) + p(b)

Let p(f) be the probability that a randomly chosen player is a freshman and p(s) be the probability that a randomly chosen player is a senior.

Then, the probability that a randomly chosen player is a freshman or a senior is given by: p(f or s) = p(f) + p(s) - p(f and s)

Now, we need to find the values of p(f), p(s) and p(f and s).

Let's start with p(f).

From the given data, we know that there are 24 freshmen out of a total of 60 players: p(f) = 24/60 = 0.4

Similarly, we can find p(s):p(s) = 16/60 = 0.2666 (rounded to four decimal places)

To find p(f and s), we need to know how many players are both freshmen and seniors.

Since this is not given in the problem, we cannot find this value.

However, we can assume that there are no players who are both freshmen and seniors, i.e., p(f and s) = 0With this assumption,

we can find p(f or s):p(f or s)

= p(f) + p(s) - p(f and s)

= 0.4 + 0.2666 - 0

= 0.6666 (rounded to four decimal places)

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If Paula divides her pencils among three friends and herself, everyone gets the same number of pencils. If Paula divides her pencils among
five friends and herself, everyone will get the same number of pencils.
How many pencils could Paula have?
A 28
B. 30
C. 42
D. 48

Answers

C.28 I guess if is not then sorry

Tina wrote the equations 3 x minus y = 9 and 4 x + y = 5. What can Tina conclude about the solution to this system of equations?

Answers

Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

Enrique predicts that he can make additional money from sales of accessories and services for computer products sold by his store. The table at the right shows predicted percent returns for such sales. For example, if the store makes x dollars selling computer products, Enrique predicts the store will make 0.05x dollars from selling accessories. Part A In January and February of this year, the store made $2,500 from sales of accessories and services. Let x represent the amount the store will make from sales of computer products from March through December. Write an equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year. If Enrique predicts sales from accessories and services for the entire year will be $5,000, about how much money must be made from computer product sales from March through December? Explain.

Answers

Answer:

Following are the solution to this question:

Step-by-step explanation:

x was its full computer product revenue from March to December.  In january and february, the revenue towards products and services before x quantities for computer product revenues will happen between March to December is $2,500.  

Whenever x quantity is sold, then 0.05x quantity was sold for supplies and equipment.  

The sum of accessories to sell should be calculated, indeed, year-round.  

It helps us to split into two parts  

y = accessory sales in January and February + accessories sales in March and December  

Use item 2  

y = $2,500 + March to December accessories sale  

Now use sections 1 and 3  

y = $2,500 + 0.05x

The above equation rewriting gives  

y = 0.05x + $2,500 (a)  

This formula is compared with a standard y = mx+c interrupt slope  

We got a pitch of 0.05 and a pitch of $2,500.

Can someone help with question 1 please

Can someone help with question 1 please

Answers

Answer: B

Step-by-step explanation:

The answer is B because of the equal sign in the middle meaning that both the sin and cos are equal

The answer is B since you are equally putting it.

You’re writing a novel.If you write 5 pages every 2 days,how long will it take you to write a 250 page novel?

Answers

Answer:

100 days

Step-by-step explanation:

You know that you write at a speed of 5 pages every 2 days. In order to write a 250 page novel, you're going to have to to write 250/5 = 50 *2 = 100 days.

100 days
Because 5x50 is 250 which is the amount of pagesand 2x50 is 100 which is the amount of days

what are some ratios that are equivalent to these ratios 5:2, 10:4, or 15:6,

Answers

Answer:

5:2- 10:4, 15:6, 50:20

10:4- 20:8, 30:12, 100:40

15:6- 30:12, 45:18, 150:60

Step-by-step explanation:

Hope This Helps

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starting at one vertex of a cube, and moving randomly from vertex to adjacent vertices, what is the expected number of moves until you reach the vertex opposite from your starting point

Answers

The given question requires the determination of the expected number of moves until we reach the vertex opposite from our starting point by moving randomly from vertex to adjacent vertices.

Let E denote the expected number of moves. If we are starting at a vertex of the cube, then there are three vertices adjacent to it. Let E1 denote the expected number of moves needed to reach the vertex opposite the starting vertex, given that our first move is to an adjacent vertex. Let E2 denote the expected number of moves needed to reach the vertex opposite the starting vertex, given that our first move is not to an adjacent vertex.                                                                          From the vertex, we have three possible choices for the first move.                                                                                                                     From the next vertex, we have two possible choices for the next move (since one of the adjacent vertices was our starting point). After that, we have only one move left to reach the opposite vertex, giving a total of 3 + 2 + 1 = 6 moves. Thus E1 = 6. From the vertex, we have three possible choices for the first move. From the next vertex, we cannot move back to the starting vertex, but there is still one adjacent vertex to avoid. Thus, we have two choices for the second move. After that, we have only one move left to reach the opposite vertex, giving a total of 3 + 2 + 1 = 6 moves. Thus, E2 = 6. Now we can find E using the law of total probability and the above information. We have E = (1/3)E1 + (2/3)E2E = (1/3)6 + (2/3)6E = 6

Therefore, the expected number of moves, until we reach the vertex opposite from our starting point, is 6.

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Simplify the radical √√189².
O 3√2d
O 20³√3
Od√180
3d+√2a

Answers

Answer:

The first step is to simplify the double radical.

√√189² = √(189²) = √(189*189) = √(35281)

Now, we simplify the radical by finding the prime factorization of 35281:

35281 = 189² = (189)(189) = (363)(363) = (3²*63²)

So, we can simplify the radical as:

√35281 = √(3²63²) = 3√(63²) = 3√(6363) = 3√3969 = 3√(31323) = 3√(3²1323) = 3*63 = 189

Therefore, √√189² = √(189*189) = √35281 = 189

Step-by-step explanation:

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