Help ASAP please!! Find the length of the missing side. If necessary, round to the nearest tenth.


Options:


58



20.5



841



29

Answer:

m= 6 or m= 8. I'm not sure if its multiple choice, but that's what I got.

Answer:

m=6,8

Step-by-step explanation:

Answer:

The probability that the balls are the same color is [tex]\frac{175-7x}{250}[/tex] where x is the number of blue balls in the second urn

Step-by-step explanation:

Let's call x the number of blue balls in the second urn. Since there are 25 ball in this urn, the number of red balls would be 25 - x.

Now, we're looking for the probability that the balls are the same color, this means, that both balls are either blue OR red. (since we're using "or", this gives us the clue that we will sum up both probabilities.

1) P(both balls are the same color) = P(both balls are blue) + P( both balls are red).

2) Now we will find what is the probability that both balls are blue (this will be a multiplication since we need that ball 1 is blue AND ball 2 is blue:

P(both balls are blue) = P(ball 1 is blue) x P(ball 2 is blue)

P(both balls are blue) = [tex](\frac{3}{10} )(\frac{x}{25} )[/tex] = [tex]\frac{3x}{250}[/tex]

3) To find what is the probability that both balls are red, the process is similar than when both are blue.

P(both balls are red) = P(ball 1 is red) x P(ball 2 is red)

P(both balls are red) = [tex](\frac{7}{10} )(\frac{25-x}{25} )[/tex]= [tex]\frac{175-7x}{250}[/tex]

4) Going back to 1) and substituting:

P(both balls are the same color) = [tex]\frac{3x}{250} +\frac{175-7x}{250} \\ \\ = \frac{3x-7x+175}{250} \\ \\=\frac{175-4x}{250}[/tex]

Final answer:

The probability that the balls are the same color is 17/40.

Explanation:

The probability that the balls are the same color is 17/40.

To calculate this, we need to find the probabilities of both balls being red and both balls being blue and then add them together.

Probability of both balls being red: (7/10) * (26/35) = 182/350

Probability of both balls being blue: (3/10) * (9/35) = 27/350

Finally, add the two probabilities: 182/350 + 27/350 = 209/350 = 17/40

Answer:

  Any of 7,111,777 or 7,333,555 or 7,555,333 or 7,777,111.

Step-by-step explanation:

The first digit must be 7. The sum of the unknown digits is then 31-7 = 24. Since this represents 3 pairs of digits (a thousands period digit and a units period digit), each pair must total 24/3 = 8.

There are two ways that odd numbers can total 8: 1+7 = 3+5 = 8. Since there is no restriction on the digits other than they must be the same in any period and they must be odd, there are 4 ways the 2 pairs of digits can be arranged into a number:

Answer:

Equation of tangent of curve at x = 36:    

1)[tex]y = \frac{x}{12} + 3[/tex] 

2[tex]y = \frac{-x}{12} - 3[/tex]     

Step-by-step explanation:

We are given the following information:

[tex]y = \sqrt{x}[/tex]

Value of curve when x =  36:

[tex]y = \sqrt{36} = \pm 6[/tex]

Thus, [tex]y = \pm6[/tex], when x = 6.

Slope of curve, m =

[tex]\frac{dy}{dx} =\frac{d(\sqrt{x})}{dx}=\frac{1}{2\sqrt{x}}[/tex]

At x = 36,

slope of curve =

[tex]\frac{1}{2\times \sqrt{36}}\\\\m=\frac{1}{12},\frac{-1}{12}[/tex]

Equation of tangent of curve at x = 36:

[tex](y-y_1) = m(x-x_1)[/tex]

[tex]= (y-(\pm 6)) = (\pm\frac{1}{12} )(x - 36)[/tex]

Thus, equation of tangents are:

1)

[tex](y-6) = \frac{1}{12}(x-36)\\12(y-6) = x-36\\y = \frac{x}{12} + 3[/tex]

Comparing to [tex]y = mx + c[/tex], we get [tex]m = \frac{1}{12}[/tex] and [tex]c =3[/tex]

2)

[tex](y+6) = \frac{-1}{12}(x-36)\\12(y+6) = -x+36\\y = \frac{-x}{12} - 3[/tex]

Comparing to [tex]y = mx + c[/tex], we get [tex]m = \frac{-1}{12}[/tex] and [tex]c =-3[/tex]

Final answer:

The equation of the tangent line at x = 36 for the curve y = sqrt(x) is y = 1/12x + 3, found by using the slope of 1/12 and solving for the y-intercept c, which is 3.

m = 1/12

c = 3

Explanation:

To find the equation of the tangent line at x = 36 for the curve y = sqrt(x), we first identified that y = 6 when x = 36 and computed the slope of the curve, which is 1/12 at x = 36.

Using the slope-intercept form of a line, y = mx + c, where m is the slope, and c is the y-intercept, we can substitute m = 1/12 and the point (36, 6) to solve for c.
Substituting into the slope-intercept equation gives us 6 = (1/12)\(36) + c.

Solving for c, we find that the y-intercept c = 3.

Thus, the equation of the tangent line is y = 1/12x + 3.

Answer:

The answer to your question is: Henry gets £ 78

Step-by-step explanation:

Data

Henry = H

Gavin = G

Jim = J

Henry + Gavin + Jim = £ 130

H = 2G

G = 3J

Process

Write an equation in terms of G

                                H + G + J = 130

                               2G + G + G/3 = 130

Solve it for G

                            3( 2G + G + G/3 = 130)

                            6G + 3G + G = 390

                             10G = 390

                                 G = 390 / 10

                                 G = £39  

                           H = 2G = 2(39)

                                    H = £78

                                   J = G/3

                                   J = 39/3

                                   J = £13                        

Final answer:

By setting up and solving algebraic equations, we find that Henry receives £78, which is twice the amount that Gavin receives and six times the amount that Jim receives from the total sum of £130.

Explanation:

Let's solve the problem by denoting Jim's share of the money as x. According to the problem, Gavin gets triple the amount of money that Jim gets, which means Gavin gets 3x. Henry gets twice as much as Gavin, so he gets 2(3x) or 6x. The total amount of money is £130 and the sum of their shares is x + 3x + 6x = 10x. Setting up the equation:

10x = £130,

we find that x, Jim's share, is £130/10 = £13. Gavin's share is 3 times Jim's: 3 × £13 = £39, and Henry's share is 6 times Jim's: 6 × £13 = £78. So Henry gets £78.

After 22 s, the car has velocity

[tex]v=\left(1.7\dfrac{\rm m}{\mathrm s^2}\right)(22\,\mathrm s)=36.4\dfrac{\rm m}{\rm s}[/tex]

In this time, it will have traveled a distance of

[tex]\dfrac12\left(1.7\dfrac{\rm m}{\mathrm s^2}\right)(22\,\mathrm s)^2=411.4\,\mathrm m[/tex]

Over the next 29 s, the car moves at a constant velocity of 36.4 m/s, so that it covers a distance of

[tex]\left(36.4\dfrac{\rm m}{\rm s}\right)(29\,\mathrm s)=1055.6\,\mathrm m[/tex]

so that after the first 51 s, the car will have moved 1467 m.

After the 29 s interval of constant speed, the car's negative acceleration kicks in, so that its velocity at time [tex]t[/tex] is

[tex]v(t)=36.4\dfrac{\rm m}{\rm s}+\left(-5.8\dfrac{\rm m}{\mathrm s^2}\right)t[/tex]

The car comes to rest when [tex]v(t)=0[/tex]:

[tex]36.4-5.8t=0\implies t=6.3[/tex]

That is, it comes to rest about 6.3 s after the first 51 s. In this interval, it will have traveled

[tex]\left(36.4\dfrac{\rm m}{\rm s}\right)(6.3\,\mathrm s)+\dfrac12\left(-5.8\dfrac{\rm m}{\mathrm s^2}\right)(6.3\,\mathrm s)^2=114.2\,\mathrm m[/tex]

so that after 57.3 s, the total distance traveled by the car is 1581.2 m, or about 1.6 km.

Answer:

The number of child tickets sold was 43 and the number of adult tickets sold was 20

Step-by-step explanation:

Let

x ----> the number of child tickets sold

y ----> the number of adult tickets sold

we know that

[tex]x=3y-17[/tex] -----> equation A

[tex]8x+12y=584[/tex] ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

The solution is the point (43,20)

see the attached figure

therefore

The number of child tickets sold was 43 and the number of adult tickets sold was 20

Answer:

Number of child tickets sold = 43

Number of adult tickets sold = 20

Step-by-step explanation:

Let the number of child ticket be c and number of adult ticket be a,

Given that the number of $8 child tickets is 17 less than 3 times the number of $12 adult tickets,

      c = 3a - 17

        3a - c = 17 ----------------------eqn 1

The theater received $584

That is

       8 c + 12 a = 584 ----------------------eqn 2

  eqn 2 /4

       2 c + 3 a = 146 ----------------------eqn 3

eqn 3 - eqn 1 gives

             2 c + 3 a - (3a - c) = 146 - 17

               3 c = 129

                   c = 43

Substituting in eqn 1    

           3 x a - 43 = 17

            3a =  60

               a = 20

Number of child tickets sold = 43

Number of adult tickets sold = 20

Answer:

100 blocks.

Step-by-step explanation:

Let x represent number of blocks built by Gage.

We have been given that Colton was 5 times as fast at building the castle than Gage, so number of blocks built by Colton would be [tex]5x[/tex].

We are also told that it takes 120 blocks to build the castle. Since Colton and Gage were building a castle together, so number of blocks built by both will be equal to 120.

[tex]x+5x=120[/tex]

[tex]6x=120[/tex]

[tex]\frac{6x}{6}=\frac{120}{6}[/tex]

[tex]x=20[/tex]

Number of blocks built by Colton: [tex]5x=5\cdot 20=100[/tex].

Therefore, Colton had build 100 blocks.

Answer:

The actual area of the park is 21,600 miles square.

Step-by-step explanation:

Step 1: Calculate the area of the park

Area of rectangle = Length x width

Length = 4 inches

Width = 6 inches

Scale factor is given as, 1 inch = 30 miles.

So, converting the length and width in miles by using the scale factor, we get

Length = 4 * 30 = 120 miles

Width =  6 * 30 = 180 miles

The formula of finding the area of an rectangle is:

Area = length x width

By putting the values in equation, we get

Area = 120 x 180

Area = 21,600 miles square

Therefore, the actual area of the park is 21,600 miles square.

Answer:

  32 mi @ N77°E

Step-by-step explanation:

The route of travel forms legs of a right triangle, so the final distance (d) from harbor can be found using the Pythagorean theorem:

  d² = 28² +16² = 784 +256 = 1040

  d = √1040 ≈ 32.249 . . . miles

___

The angle (α) added to the original N47°E bearing can be found using the fact that opposite and adjacent sides are given. So, they can tell you the tangent of the angle:

  tan(α) = 16/28

  α = arctan(16/28) ≈ 29.74°

Then the bearing to the final position is ...

  47° +29.74° = 76.74°  . . . . . east of north

Rounded to whole numbers, the final position from harbor is ...

  32 miles @ N 77° E

Answer:

P ( 500<X<650 ) = 0.8577

Step-by-step explanation:

Since μ=572 and σ=51 we have:

P ( 500<X<650 ) = P ( 500−572< X−μ<650−572 )

[tex]\RightarrowP ( \frac{500-572}{51} < \frac{x-\mu}{\sigma} < \frac{650-572}{51})[/tex]

⇒ P ( 500<X<650 ) = P ( −1.41<Z<1.53 )

Now, Using the standard normal table to conclude that:

P ( −1.41< Z <1.53 ) = 0.8577

Final answer:

Approximately 85.77% of Indiana tenth-grade students scored between 500 and 650 on the English/language arts ISTEP exam, as calculated by converting the given scores to z-scores and finding the proportion within the standard normal distribution.

Explanation:

To find the proportion of Indiana tenth-grade students who scored between 500 and 650 on the English/language arts exam, given that the ISTEP scores are approximately normal with a mean (μ) of 572 and a standard deviation (σ) of 51, we can use the standard normal distribution.

First, we'll convert the scores to z-scores using the formula z = (X - μ) / σ where X is the score.

Then we'll look up these z-scores in a standard normal distribution table or use a calculator with normal distribution functions to find the proportion of students whose scores fall between these two z-scores. The table or calculator will provide us with the areas under the curve to the left of each z-score.

Let's assume the area to the left of z=-1.41 is approximately 0.0793 (7.93%) and to the left of z=1.53 is approximately 0.937 (93.7%). To find the proportion between 500 and 650, we'll subtract the smaller area from the larger one:

Proportion = Area to the left of z=1.53 - Area to the left of z=-1.41 = 0.937 - 0.0793 = 0.8577 or 85.77%

Therefore, approximately 85.77% of the students scored between 500 and 650 on the ISTEP English/language arts exam.

Answer:

20

Step-by-step explanation:

8/2 = 4

4 * 5 = 20

Answer:

  Jon can plot the ratio of 5 to 6 on a graph (5, 6), then move up 6 and right 5 to find the next frame size, and then keep the same rate to find other points.

Step-by-step explanation:

A line from the origin to the point (5, 6) has a slope of 6/5. To find other points on the same line, one would need to continue to rise 6 units for each run of 5 units to the right.

The only answer choice that appropriately matches (x, y) values to rise/run values is the one shown above.

_____

Comment on this answer

The slope of the line described in this answer is 6/5, which seems appropriate for a frame that is 6 inches high and 5 inches wide. However, I would call this a plot of the ratio 6 to 5, rather than the ratio 5 to 6.

Answer:

Jon can plot the ratio of 5 to 6 on a graph (5, 6), then move up 6 and right 5 to find the next frame size, and then keep the same rate to find other points.

i hope this helps!

Answer:

3t + 35 = 6

subtract 35 from both the sides of the equation

3t + 35 - 35 = 6-35

3t = -29

t = - 29/3

Step-by-step explanation:

Answer:

-29/3

Step-by-step explanation:

3t+35=6

3t=6-35

3t=-29

t=-29/3

Answer:

The answer is E. Impossible to determine

Step-by-step explanation:

Normally, you would find the Confidence interval of a normal sample by using

X(-+) Z* Sigma/n

Where x is the mean, sigma the standard deviation n the size of the sample and z the value  determined by your confidence interval size of 95%

.However, this approximation of a confidence interval may only be used for a sample if the number of observations is at least 30 or above.  When we have less observations than 30 we must use the standard deviation of the populations. But we only have a sample standard deviation so its not adequate or possible to determine CI the true mean of the population with such a small sample size.

Answer:

Third option given

Step-by-step explanation:

On a coordinate plane, a parabola opens to the right with a vertex at (0, 0).

use the following x values to plot the associated y values on the x-y plane:

If x = 0,  then [tex]y=\sqrt{0}  =0[/tex]

If x = 1,  then [tex]y=\sqrt{1}  =1[/tex]

If x = 4,  then [tex]y=\sqrt{4}  =2[/tex]

If x = 9,  then [tex]y=\sqrt{9}  =3[/tex]

Join the points and you will find a branch of a parabola opening to the right.

Answer:

The Answer is D

Step-by-step explanation:

on e2020 its the last graph

Answer:

  1071.30 per month

Step-by-step explanation:

The multiplier each year is 1 + .03 = 1.03. After 6 years, the cost has been multiplied by that factor 6 times, so has been multiplied by 1.03⁶ ≈ 1.194052.

  $897.20 × 1.194052 ≈ $1071.30

The typical family of four should expect to spend $1,056.27 per month for food six years from now.

1. Calculate the inflation factor using the formula: [tex]\( (1 + \text{inflation rate})^{\text{number of years}} \).[/tex]

  - Inflation rate = 3% or 0.03

  - Number of years = 6

  - Inflation factor = [tex]\( (1 + 0.03)^6 = 1.191016 \)[/tex]

2. Multiply the current monthly food expenditure by the inflation factor to find the expected expenditure six years from now.

  - Current expenditure = $897.20/month

  - Expected expenditure = $897.20 × 1.191016 = $1,056.27/month

Therefore, the typical family of four should expect to spend $1,056.27 per month for food six years from now if inflation occurs at a rate of 3% per year.

Genghis Khan's army organizational structure can be used to calculate the total number of men under him: For an army of 10,000 soldiers, the total is 11,110 men; for an army of 5,763 soldiers, it is 6,404 men.

To solve both parts of the student's question, we use the military organizational structure implemented by Genghis Khan that is based on the 'decimal' system. We start with the lowest level groups of 10 soldiers and move up in orders of magnitude (10, 100, 1,000, and 10,000).

Part (a): Army of 10,000 soldiers

Groups of 10: There are 1,000 groups of 10 in an army of 10,000 soldiers.

Leaders of 10: Each group of 10 has 1 leader, resulting in 1,000 leaders of 10.

Groups of 100: 1,000 leaders of 10 make up 100 groups of 100 (because 1,000/10 = 100).

Leaders of 100: There are 100 leaders of 100.

Groups of 1,000: 100 leaders of 100 make up 10 groups of 1,000 (because 100/10 = 10).

Leaders of 1,000: There are 10 leaders of 1,000.

Adding it all together: 10,000 soldiers + 1,000 leaders of 10 + 100 leaders of 100 + 10 leaders of 1,000 = 11,110 total men under the command of Khan for an army of 10,000.

Part (b): Army of 5,763 soldiers

Groups of 10: There are 576 full groups of 10 and 1 incomplete group (with 3 soldiers), resulting in 577 groups.

Leaders of 10: There are 577 leaders of 10.

Groups of 100: 577 leaders of 10 make up 57 full groups of 100 and 1 incomplete group (with 7 leaders of 10), resulting in 58 groups.

Leaders of 100: There are 58 leaders of 100.

Groups of 1,000: 58 leaders of 100 make up 5 full groups of 1,000 and 1 incomplete group (with 8 leaders of 100), resulting in 6 groups.

Leaders of 1,000: There are 6 leaders of 1,000.

Adding it all together: 5,763 soldiers + 577 leaders of 10 + 58 leaders of 100 + 6 leaders of 1,000 = 6,404 total men under the command of Khan for an army of 5,763 soldiers.

Answer:

[tex]x=(c-60)/85[/tex]

Step-by-step explanation:

we have

[tex]c=85x+60[/tex]

Solve for x

That means -----> isolate the variable x

subtract 60 both sides

[tex]c-60=85x+60-60\\c-60=85x[/tex]

Divide by 85 both sides

[tex](c-60)/85=85x/85\\(c-60)/85=x[/tex]

Rewrite

[tex]x=(c-60)/85[/tex]

Answer:

The range of g(x) is y > 0

The ranges of f(x) and h(x) are different from the range of g(x)

Step-by-step explanation:

we have

[tex]f(x)=-(\frac{6}{11})^{x}[/tex]

[tex]g(x)=(\frac{6}{11})^{-x}[/tex]

[tex]h(x)=-(\frac{6}{11})^{-x}[/tex]

Using a graphing tool

see the attached figure

Verify each statement

case A) The range of h(x) is y > 0.

The statement is false

The range  of h(x) < 0

case B) The range of g(x) is y > 0.  (Note the statement is The range of g(x) is y > 0 instead of  The domain of g(x) is y > 0)

The statement is true (see the attached figure)

case C) The ranges of f(x) and h(x) are different from the range of g(x)

The statement is true (see the attached figure)

Because

The ranges of f(x) and h(x) are y < 0

and

The range of g(x) is y > 0

case D) The domains of f(x) and g(x) are different from the domain of h(x)

The statement is false

The domain of the three functions is the same

Answer:

OPTION C.The ranges of f(x) and h(x) are different from the range of g(x).

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let "e" and "a" represent the speeds of Elvira and Aletheia, respectively. Then the total distance they cover is ...

  distance = speed × time

  (1/2)e + (2/3)a = 3.1

And the relationship between their speeds is ...

  e - a = 0.6

__

To solve this system, we can double the first equation and subtract the second to get ...

  2(1/2e +2/3a) -(e -a) = 2(3.1) -(0.6)

 7/3a = 5.6 . . . . . . . . . . simplify

  a = (3/7)(5.6) = 2.4 . . . multiply by 3/7

  e = a +0.6 = 3.0 . . . . . Elvira's speed is 0.6 mph more than Aletheia's

Elvira's walking speed is 3.0 miles per hour; Aletheia's is 2.4 miles per hour.

Answer:

The answer to your questions is: 25 new teachers

Step-by-step explanation:

Data

# of students = 2000

ratio = 3:80 teachers to students

New teachers = ?

Process

I suggest to use rule of three to solve this problem

                     3 teachers ----------------  80 students

                      x                ----------------  2000 students

                  x = (2000 x 3) / 80 = 75 teachers

               Number of initial teachers = 75

The ratio change to 1:20

                     1 teacher -------------------  20 students

                     x             -------------------   2000 students

                     x = (2000 x 1) / 20

                    x = 100 teachers

Number of new teachers = 100 - 75 = 25

Answer:

Step-by-step explanation:

Probability of getting the newspaper on his front porch = P(A) = 0.64

Probability of finding the newspaper on his  lawn = P(B) =? (We don't know, this is what we have to find.)

Total probability = 1

Formula, P(A) + P(B) = 1

Let's put all values in this formula,

              0.64 + P(B) = 1

              P(B) = 1 - 0.64

              P(B) = 0.36

Thus, the probablity that Mr. Johnson finds his newspaper on his lawn is 0.36 or 36%.

Answer:

y= (h(6)-h(4))/2x +C

Where C=-2*h(6)+3*h(4)

Step-by-step explanation:

The secant line is the line that meets a function (in this case h(x) ) in two points, so we have to apply the ecuation of a straigt line that meets two points:

y-y1 = (y2-y1)/(x2-x1) * (x-x1)

In this case X1=4 , x2=6, y1 = h(4) and y2= h(6)

So

y-h(4)= 1/2 (h(6)-h(4)) * (x-4)

y-h(4)= 1/2 (h(6)-h(4)) x- 2 *(h(6)-h(4))

y-h(4)= 1/2 (h(6)-h(4)) x- 2 (h(6) + 2h(4))

y= 1/2 (h(6)-h(4)) x- 2 h(6) + 2h(4) + h(4)

y= 1/2 (h(6)-h(4)) x- 2 h(6) + 3h(4)

Good Luck!

*****************************************************************************

Dont forget to rate my answer if it was helpful!

Answer:

He is correct.

Step-by-step explanation:

Because a linear system in three variables means that they have solutions if the all three have points in common in R3 space. But, in the case that they don't have any solution mean the opposite, they don't have points in common in R3 space.

In a linear system, variables must be related through common points. So, graphically, you should draw intersecting geometrical places in order to show the intersections, wich are the common results or points that are the solutions of the linear system.

A linear system of equation in three variables has no solution is the correct statement.

" Linear equation is defined as the equation whose variables with highest degree one."

According to the question,

Given statement,

A linear system of equation in three variables has no solution.

Verification:

Consider a example of linear system of equation with three variables

[tex]2x-4y +z=3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)[/tex]

[tex]8x-2y+ 4z=7 \ \ \ \ \ \ \ \ \ \ \ \ \ (2)[/tex]

[tex]-4x+y -2z=-14\ \ \ \ \ \ \ \ \ \ (3)[/tex]

Solve linear equation to get the solution

Multiply [tex](3)[/tex] by [tex]2[/tex] and add it to [tex](2)[/tex],

[tex]\ \ 8x-2y+ 4z=7\\\\-8x+2y-4z =-28[/tex]

we get,

[tex]0x+0y + 0z = -21[/tex]  which is not possible and has no solution.

Hence, linear system of equation has no solution is the correct statement.

Learn more about linear equation here

brainly.com/question/11897796

#SPJ2

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

First term = 13

Increase each time = 20

Number of clients = 25

So, it forms an arithmetic progression:

So, 25 th term would be

[tex]a_{25}=a+(n-1)d\\\\a_{25}=13+(25-1)\times 20\\\\a_{25}=13+24\times 20\\\\a_{25}=13+480\\\\a_{25}=493[/tex]

Hence, list would look like 13,33,............493.

Therefore, Option 'D' is correct.

Answer:

2 stations with 7 of jugs of water and 10 of sports drink in each station

Step-by-step explanation:

Lets start with the jugs of water, to have the same amount in each station you need have a number of station that divide for 14 the remainder or "left over" equal to 0, or in other words multiple of 14 in the interval 1 to 14

multiples of 14 : 1, 2, 7 and 14

so you can have

1 station with 14 jugs of water

2 stations with 7 jugs of water each

7 stations with 2 jugs of water each

14 station with 1 jugs of water each

Now we need to do the same for the 20 jugs of sports drink

multiple of 20 in the interval 1 to 20: 1,2,4,5,10 and 20

so you can have:

1 station with 20 jugs of sports drink

2 stations with 10 jugs of sports drink

4 stations with 5 jugs of sports drink

5 station with 4 jugs of sports drink

10 station with 2 jugs of sports drink

20 stations with 1 jugs of sports drink

So we have that both cases, water and sport drinks have coincidence of 1 or 2 stations, and the maximum of both is 2 stations with 7 jugs of water and 10 of sports drink each

Final answer:

To determine the greatest number of refreshment stations that can be set up, we find the greatest common divisor (GCD) of 14 jugs of water and 20 jugs of sports drink, which is 2. Therefore, the committee can set up 7 refreshment stations with 1 jug of water and 2 jugs of sports drink at each.

Explanation:

The committee has 14 jugs of water and 20 jugs of sports drink and wants to set up the greatest number of refreshment stations along the marathon course without any beverages left over. To find this solution, we need to determine the greatest common divisor (GCD) of the two quantities of jugs because each station must have the same combination of jugs of water and sports drink.

First, list the factors of each number:

Factors of 14: 1, 2, 7, 14

Factors of 20: 1, 2, 4, 5, 10, 20

The largest common factor is 2, which means the refreshment stations can have a combination of 1 jug of water and 2 jugs of sports drink. So, the committee can set up 7 refreshment stations (14 jugs of water / 2 per station = 7 stations; and 20 jugs of sports drink / 2 per station = 10 stations, but limited by the smaller number of jugs of water).

Answer:

Production has increased 20/day

Step-by-step explanation:

In the first scenario production is 500/day and productivity 25 set/hour. After the changes, production is 600/day and 25 set/hour.

So productivity remains the same, nevertheless, as there are more productive hours per day, production raises, in this case the can be calculated as (New Production-Old Production)/Old Production=(600-500)/500=100/500=0.2=20%.

As productivity remains the same, you do not ge more sets/shift, as shifts are shorter (8 instead of hours, so you get 200/shift instead of 250/shift). The rest of the option is false as productivity remains constant

Answer:

The answer to your question is: 5/8

Step-by-step explanation:

data

5/14 divided by 4/7

Process

                        [tex]\frac{5}{14\\}[/tex]

                        [tex]\frac{4}{7}[/tex]

multiply 5 and 7 and the result is the numerator

multiply 14 and 4 and the result is the denominator

                            (5 x 7) / ( 14 x 4)

                            35 / 56

                            5 / 8              simplify both numerator and denominator