Assuming two hikers begin at a trail start, which scenarios must be true based on the table? Check all that apply.

Melissa and Corey started on different trails.
Melissa hiked up the trail for a longer period of time than Corey.
Melissa and Corey crossed paths between 60 and 90 minutes.
Corey began his descent before Melissa.
As Melissa’s time increased from 0 to 60 minutes, her elevation decreased.

The percentage decrease would be 70 percent.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

The price of an item has dropped to 27$ today. Yesterday it was 90.

90 - 27 = 63

The percentage decrease;

63 / 90 x 100= 70%

Hence, The percentage decrease would be 70 percent.

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The length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft

Length of each scarf = Total length of scarf / Number of friends

= 39.9 ft / 7

= 5.7 ft

Therefore, the length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft

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Answer:

I think the best answer is 143

Answer: The player expects to lose 184.21 dollars.

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

Explanation:

X = net winnings in dollars

Ignore the "28" because it's really not that relevant here. All we care about is the probability 1/38 which is the probability of winning money. The probability of losing money is 1 - (1/38) = 37/38. Put another way: there's 1 way to win, and 37 ways to lose.

If the player wins, then they walk away with 7+245 = 252 dollars

If the player loses, then their "winnings" is -7

So either X = 252 or X = -7 are the only two options.

Let's form a table showing those options with their corresponding probabilities.

[tex]\begin{array}{|c|c|} \cline{1-2}X & P(X)\\\cline{1-2}252 & 1/38\\\cline{1-2}-7 & 37/38\\\cline{1-2}\end{array}[/tex]

Now multiply each X value and P(X) value across the rows.

252*(1/38) = 6.631579

-7*(37/38) = -6.815789

These values are approximate.

[tex]\begin{array}{|c|c|c|} \cline{1-3}X & P(X) & X*P(X)\\\cline{1-3}252 & 1/38 & 6.631579\\\cline{1-3}-7 & 37/38 & -6.815789\\\cline{1-3}\end{array}[/tex]

Add up the results of the third column

6.631579 + (-6.815789) = -0.18421

This represents the net winnings for any average spin of the wheel. The player unfortunately expects to lose, on average, about $0.18421 or 18.421 cents per spin.

Do this 1000 times and the player should expect to lose about

1000*(0.18421) = 184.21 dollars

Keep in mind that due to the random nature of roulette wheel, the player may get lucky or their luck may be worse than what is described. The idea is that over the long run, the average should be somewhat close to losing 184.21 dollars.

Another way to think of it could be to have 1000 players doing the same game (rather than have 1 person play the same game 1000 times). Some players may get lucky, while others may not get so lucky. But their collective average should be losing that $184.21

Answer:

0.462

Step-by-step explanation:

1km=1000m

so to get from metres to kilometres you divide by 1000

so 462÷1000=0.462

Answer:

  5/6 mile

Step-by-step explanation:

The formula for the area of a rectangle can be used with the given values to write an equation for the length of the farmland.

__

Here is the equation for the area of a rectangle.

  A = LW . . . . . area is the product of length and width

When we fill in the area and width, we have ...

  5/9 mi² = L(2/3 mi) . . . . . equation for the length of the farmland

Solving this equation gives ...

  L = (5/9)/(2/3) mi . . . . . . . . divide by the coefficient of L

  L = (5/9)/(6/9) mi = 5/6 mi . . . . . perform the division

The length of Sandra's farmland is 5/6 mile.

Answer:

• f(g(x)) =  [tex]\sqrt{x^{2} + 1}[/tex]  + 8

• g(f(x)) = 16[tex]\sqrt{x}[/tex] + x + 65

Step-by-step explanation:

• f(g(x)) = f(x² + 1)

         = [tex]\sqrt{x^{2} + 1}[/tex]  + 8

• g(f(x)) = g([tex]\sqrt{x + 8}[/tex] )

            = [tex](\sqrt{x } + 8)^{2}[/tex] + 1

            =  x + 16[tex]\sqrt{x}[/tex] + 64 + 1

            = 16[tex]\sqrt{x}[/tex] + x + 65

Given:

The given equation is 5y=3x-5

Find: Draw the graph

Explanation:

It is given that 5y=3x-5. Substitute x=0 into the given equation we have

[tex]5y = 3x - 5[/tex]

[tex]5y = 3(0) - 5[/tex]

[tex]5y = - 5[/tex]

[tex]y=-1[/tex]

Now, substitute x=5 into the given

equation we have

[tex]5y = 3(5)-5[/tex]

[tex]5y = 15-5[/tex]

[tex]5y = 10[/tex]

[tex]y = 2[/tex]

The points are (0,-1) and (5,2).

Therefore, the required graph is

Hence, the required graph is obtained.

There are 10,080 different ways in which the friends can seat on the circular table.

There are 9 friends, such that two of them need to be separated by exactly two people.

Because the table is circular, we can consider the first position as the position where Bob is.

Now let's count the number of options for each of the other 8 positions. (counting to the left).

The next two positions have 7 and 6 options respectively (as these can be taken by any of the other 7 friends)

For the next seat, we could seat Anna or one of the remaining 5 friends.

Let's assume we seat Anna there, then for each of the next positions, we will have, respectively, 5, 4, 3, 2, 1 options.

The total number of combinations is given by the product between the numbers of options, so we have:

C = 7*6*5*4*3*2*1

But we also need to consider the case where Anna is on the first position (and Bob on the third), so we just need to add a factor equal to 2.

C = 2*(7*6*5*4*3*2*1) = 10,080

There are 10,080 different ways in which the friends can seat on the circular table.

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Answer:

sum of all sides

Step-by-step explanation:

x1y2 + x3y3 + x1y1

Answer:

i think the answe is. y=0x-6

Answer:

12.5%

Step-by-step explanation:

1/8 × 100% = 12.5%

So 9f you multiply an eighth by one hundred percent and simplify accurately you'll get 12.5%

Answer:

-7 is -7 units away from zero. Its opposite is 7 from zero.

Step-by-step explanation: Count from 0 how many digits away it is

Answer:

amount of coloured fabric in mm = 48

amount of white fabric in mm = 12

ratio = white fabric : coloured fabric = 12 : 48 = 1:4

The height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have:

A tunnel is constructed with a semi-elliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet.

2a = 60 (width of the tunnel is 60 feet)

a = 30

And the maximum height at the center of the tunnel is 25 feet

b = 25

Let's assume the center of the ellipse is at the origin.

So the equation of the ellipse:

[tex]\rm \dfrac{x^2}{30^2}+\dfrac{y^2}{25^2}=1[/tex]

Now plug x = a - 5 = 30 - 5 = 25

[tex]\rm \dfrac{25^2}{30^2}+\dfrac{y^2}{25^2}=1[/tex]

After solving:

[tex]\rm \dfrac{y^2}{25^2}=1-\dfrac{25}{36}[/tex]

[tex]\rm y^2=\dfrac{6875}{36}[/tex]

y = ±13.819 ≈ ±13.82

Height cannot be negative

y = 13.82 feet

Thus, the height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

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If a polyhedron has a volume of 35 cm cube and is dilated by a factor of 5/2 then the volume of dilated polyhedron will be 50.6 cm cube.

Given Volume of polyhedron=35 cm cube . Factor from which is dilated 5/2.

If the polyhedron is dilated by factor 5/2 then the volume of the polyhedron will change by the cube of that  factor because when it is dilated by factor its material also increases.

Volume =35[tex]cm^{3}[/tex]

After dilation

Volume=35+[tex](5/2)^{3}[/tex]

=35+15.625

=50.625

After Rounding nearest to thousand we will get 50.6 [tex]cm^{3}[/tex].

Hence after dilation the volume which is 35 cm cube will change from 35 to 50.6[tex]cm^{3}[/tex].

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The English phrase of the obtained equation is 12 times z subtracted by 3. The obtained equation after solving is 12z -23

Simplifying means making something easier to do or comprehend, as well as making something less difficult.

Given data;

z be the unknown number

Given conditions;

1. The difference between a number and −23.

2.−23 is equal to the product of the number and 13.

The mathematical form of the given phrase is;

⇒ z - (-23) = z × 13

⇒z+23 = 13z

⇒12z -23

The English phrase of the obtained equation is 12 times z subtracted by 3.

Hence the simplification of the given expressions is 12z -23.

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If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

Using this formula

Margin of error=Standard deviation×Mean

Let plug in the formula

Margin of error=205 × 9.5%

Margin of error = 19.475

Margin of error = 19.5 (Approximately)

Therefore If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.

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The median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a box and whisker plot shown in the picture.

From the box plot, the line between the box ends represents the median of the data.

The median = 40

The least number of smartphones distributed = 33

Q3 = 48

Thus, the median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.

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Answer:

They are not parallel

Step-by-step explanation:

original equation

10x + 3y = -3

subtract 10x

3y = -10x - 3

divide by 3

y = -10/3x - 1

original equation

5x - 4y = -3

subtract 5x

-4y = -5x-3

divide by -4

y = 5/4x + 3/4

the slopes are not equal to each other (5/4x and -10/3x) so they are not parallel

Answer:

P=2l+2W

if l=12 and W=8

then,

P=2L+2W

=2.18+2.8

=36+16

=52

Considering the multiplication of mixed fractions, [tex]\frac{21}{6}[/tex] or 3.5 hours was sunny that day.

To multiply mixed fractions, it is necessary to transform these fractions into improper fractions. To do this, the whole part is multiplied by the denominator of the fraction that accompanies it. The result of the multiplication is added to the numerator of the fraction that accompanies it, and it will be the denominator of the new fraction, while the denominator remains the same.

After transforming the mixed fractions to be multiplied into improper fractions, they are multiplied. To do this, it is necessary to multiply the numerators of the two fractions, and the denominators of the fractions. If the resulting product needs to be simplified to lowest terms, divide the numerator and denominator by common factors.

On a day in winnipeg with 10[tex]\frac{1}{2}[/tex] h of daylight, it was sunny for [tex]\frac{1}{3}[/tex] of that time. This is:

10[tex]\frac{1}{2}[/tex] h × [tex]\frac{1}{3}[/tex]

Solving:

10[tex]\frac{1}{2}[/tex] h × [tex]\frac{1}{3}[/tex] = [tex]\frac{10x2+1}{2}[/tex] × [tex]\frac{1}{3}[/tex] =  [tex]\frac{21}{2}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{21x1}{2x3}[/tex]= [tex]\frac{21}{6}[/tex]= 3.5

Finally, [tex]\frac{21}{6}[/tex] or 3.5 hours was sunny that day.

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Answer:

8/3

Step-by-step explanation:

4 x 2 = 8, so (4 × 2)/2 = 8/3.

Answer:

The total number of registered doctors in this year are 307345.

Step-by-step explanation:

Let the total number of doctors who registered in this year are x

Given that the total number of female doctors in total registered doctors are 54400

According to the question 17.7 percent of the total registered doctors are the female doctors

Hence the total number of  registered doctors who are females are 17.7% of x

which is written as 17.7*x÷100

According to the question 17.7x÷100= 54400

as we are given that the total number of female doctors are 54400

now

17.7x = 54400×100

x= 54400×100÷17.7

x= 307344.633 ≈ 307345

Therefore there are 307345 doctors who registered that year.

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The grades and gender is 29/59

It is a branch of mathematics that deals with the occurrence of a random event.

Given:

              A              B             C              Total

Male       20            13            7                 40

Female    9               2            8                 19

Total        29            15            15               59

Total candidates who have A grade = 20+9 = 29

So, the probability that the student got an A

= 29/59

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Answer:

B. 47 7/12

Step-by-step explanation:

=126 1/4 - 78 2/3

Change the two mix fraction to improper fractions.

= 505/4 - 236/3

= 1515-944/12

= 571/12

= 47 7/12

Answer:

Option C.  [tex]g(x)=(\frac{1}{3}x)^2[/tex]

Step-by-step explanation:

Given a function to start with, extra operations that are done outside of the given function, cause vertical transformations, whereas operations that are done inside of the function cause horizontal transformations.

Transformations on the outside

Ex. [tex]g(x)=(x^2)-3[/tex]  is subtracting 3 outside, so its transformation is vertical.

Transformations on the inside

Ex. [tex]g(x)=(x-7)^2[/tex] is subtracting 7 inside, so its transformation is horizontal.

For any function, stretches or compressions occur by multiplying by positive numbers larger or smaller than 1.

Multiplying by numbers larger than one, quantities get larger, and multiplying by a positive number less than one, quantities get smaller.

For example, [tex]\$10*2 = \$20[/tex], but [tex]\$10*\frac{1}{2} = \$5[/tex]

For transformations, this intuition needs a small modification:

Multiplying on the outside

When multiplying outside of the function, things outside happen normally, and since it is happening outside, it is in a vertical direction.

Ex. Multiplying outside by 3, things get larger (stretch) vertically to 3 times as much as (300% of) normal (away from a height of zero).

Multiplying outside by [tex]\frac{1}{2}[/tex] , things get smaller (compress) vertically down to [tex]\frac{1}{2}[/tex] as much as (50% of) normal (toward a height of zero).

"g" is lower than "f", so it may have been compressed vertically (see alternative solution at end).

Looking at the only options with multiplication outside (A & B), option B multiplies by 3 (greater than 1), so it would stretch "f" even taller.

Option A, does compress "f" vertically (by 1/3), but doesn't compress it enough to arrive at the point (3,1) defined on function "g". Note ordered pair (3,1) on "g", meaning when you input "3", you get out "1".  

Putting 3 into the "f" function, f(3)=9.  Since one-third (the transformation in Option A) of 9 is 3, not 1, Option A doesn't compress "f" enough.

Multiplying on the inside

When multiplying inside, transformations happen horizontally, and inside things happen "backwards".

So, if multiplying inside by 4, (...normally things get bigger...) things actually get smaller (compressed) horizontally, reduced to 1/4 (the reciprocal of 4) the size (toward a horizontal distance of zero).

If multiplying by a number less than one (but positive), like [tex]\frac{1}{3}[/tex] , (...things normally get smaller...) things will actually get larger (stretch) in the horizontal direction out to triple (the reciprocal of [tex]\frac{1}{3}[/tex]) as much as normal.

Looking options C & D (where multiplication happens inside), both have multiplication by a positive number less than one (... normally would make things smaller...), which will stretch "f" out horizontally.

Looking at the red point (3,1), the blue function does have a height-matched point at (1,1).

Measuring horizontal distances, (3,1) is 3-units from the y-axis, whereas (1,1) is only 1-unit away.  Thus, the "g" is 3 times as far as "f", meaning a horizontal stretch outward by 3.

Answer C multiplies inside by [tex]\frac{1}{3}[/tex], so it actually makes things 3 times bigger horizontally.

The correct answer is option C.

To verify, from (3,1), put 3 into the option C g(x) --  it gives "1" as an output.

[tex]g(x)=(\frac{1}{3}x)^2\\g(3)=(\frac{1}{3}(3))^2\\g(3)=(1)^2\\g(3)=1\\[/tex]

This function could have been compressed vertically to obtain the red graph.

Note that f(3)=9.

The point (3,1), on the red function, is only at a height of 1 ... 1/9th the height of the blue function.  We could compress the "f" vertically by 1/9th to transform the blue function into the red function.

Vertical transformations come from operations outside, and outside things behave "normally", so to vertically compress by 1/9th, just multiply on the outside by 1/9th.

Thus, an alternative answer to transform f(x) to g(x) is [tex]g(x)=\frac{1}{9}(x^2)[/tex]

Two last things:

Simplifying this function we just obtained we get [tex]g(x)=\frac{1}{9}x^2[/tex]

Returning to the function that we chose for our answer in option C, [tex]g(x)=(\frac{1}{3}x)^2[/tex]

[tex]g(x)=(\frac{1}{3}x)(\frac{1}{3}x)[/tex]

[tex]g(x)=\frac{1}{9}x^2[/tex]

Note that the transformation answer for this problem (Option C) and our alternative solution both simplify and match perfectly, so they both represent the same end result.

By applying definite integrals and integration rules, the area bounded between the curves f(x) = x² and g(x) = -(x+2)² + 4 is equal to 8 square units.

The points of intersection between the two curves are (x, y) = (0, 0) and (x, y) = (-2, 4). The curve is f(x) = x² and upper curve is g(x) = -(x+2)² + 4. The area between the two curves is defined by this definite integral:

[tex]A = \int\limits^{0}_{-2} {f(x) - g(x)} \, dx[/tex]

[tex]A = \int\limits^{0}_{-2} {f(x)} \, dx - \int\limits^{0}_{-2} {g(x)} \, dx[/tex]

[tex]A = \int\limits^0_{-2} {[-(x+2)^{2}+4]} \, dx -\int\limits^0_{-2} {x^{2}} \, dx[/tex]

[tex]A = -\frac{(x+2)^{3}}{3}|_{-2}^{0} + 4\cdot x|_{-2}^{0}-\frac{x^{3}}{3}|_{-2}^{0}[/tex]

[tex]A = - \frac{2^{3}}{3} + 0 + 4\cdot [0 - (-2)] - 0 + \frac{(-2)^{3}}{3}[/tex]

[tex]A = -\frac{8}{3} + 8 -\frac{8}{3}[/tex]

A = 8

By applying definite integrals and integration rules, the area bounded between the curves f(x) = x² and g(x) = -(x+2)² + 4 is equal to 8 square units.

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