The box plot below represents the lengths, in inches, of fish a group of friends caught.
What is the interquartile range of the data?

Step-by-step explanation:

in such problems with just equations we always need to have the main (optimization) equation or condition, and then usually some constraint equations.

the constant equations allow us typically to express one variable through another, until we have only one variable for the optimization equation. then we find the zeros of the first derivative of that functions and find the needed maximum or minimum if needed via the second derivative.

now if we have inequalities, it is even easier, I think.

we find the corners of the shaded area that must contain our minimum or maximum by finding the intersections of the delimiter lines. the optimum must be one of the corners.

and then we try the coordinates of the different corners in the optimization equation and see, which one delivers the highest or lowest value. and we are done.

a.

x + y <= 240

y >= 4x

b.

500x + 450y = profit

theoretically we have 3 corners to test

(0, 0)

(0, 240)

(48, 192)

(0, 0) is clearly the minimum, profit 0.

(0, 240) gives

450×240 = $108,000

(48, 192) gives

500×48 + 450×192 = 24000 + 86400 = $110,400

that is the maximum.

so, the farmer makes the most profit under the given constraints, if he plants 48 acres corn and 192 acres sprouts.

Answer:

hope you can understand

Answer:

Surface area of cube = 6x²

surface area of cube = surface area of sphere

it means that 6x²=4πr²

x²=

[tex] \frac{4\pi {r}^{2} }{6} = \frac{4 \pi9}{6} = \frac{4\pi3}{2} = 6\pi[/tex]

[tex]x = \sqrt{6\pi} [/tex]

[tex] \sqrt{6\pi} = \sqrt{k\pi} [/tex]

[tex]6\pi = \pi \: k[/tex]

[tex]k = 6[/tex]

Answer:

5.71%

Step-by-step explanation:

1.75 kg = 1750 gm ( 1kg = 100gm)

So if the corrected weight is to the nearest gram, the bag can weigh ± 1 gm from the corrected weight

So the error is 1/1750 = 1 /1750 x 100 % = 5.71%

Using it's concept, it is found that the range of fat grams for the five sandwiches is of 24 grams.

It is given by the difference of the highest value by the lowest value in the data-set.

In this problem, the sandwich with the least fat has 9 grams and the one with the most has 33 grams, hence the range is given by:

R = 33 - 9 = 24 grams.

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t - 7

hope it helps...!!!

The area of the trapezoid will be 32.5 square feet. Then the volume of the geometry will be 341.25 cubic feet.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The figure is shown.

Then the volume of the given geometry will be

Volume = Area of the trapezoid × Height

Then the area of the trapezoid will be

[tex]\rm Trapezoid \ area = \dfrac{1}{2} \times (8 + 5) \times 5\\\\\\Trapezoid \ area = 32.5 \ ft^2[/tex]

Then the volume of the geometry will be

Volume = 32.5  × 10.5

Volume = 341.25 cubic ft.

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Using proportions, it is found that one mechanic could assemble 5 bicycles in 8 hours, and it would take 40 hours to assemble 25 bicycles.

The equation is: b = 0.625t.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, two mechanics can assemble 10 bicycles in 8 hours. How many bicycles could one mechanic assemble in 8 hours? Hence the rule of three is given by:

2 mechanics - 10 bicycles.

1 mechanic - x bicycle.

Applying cross multiplication:

2x = 10 -> x = 5 bicycles in 8 hours.

Hence the equation for the number of bicycles in t hours of a single mechanic is given by:

b = 5/8t = 0.625t.

For 25 bicycles, we have that:

25 = 0.625t.

t = 25/0.625.

t = 40 hours.

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Answer:
No

Step-by-step explanation:

Replace x with the given c value to get y = 5 + 2 which becomes y = 7

Since y is 3 in the given solution and not 7 it cannot be a solution.

Answer:

8 Square meters

Step-by-step explanation:

plus the 6m and 2m this meters is both side , so add that then it'll become 8 Square meters

or multiply the 6m and 2m it'll become 12m

Answer:

248 with remainder 5

Step-by-step explanation:

thats it

The potential at the center of the sphere is the same as the potential at the surface. Then the correct option is B.

The amount of labor required to move a unit signal from one part to another is defined as the potential difference between any two points.

If the conducting sphere contains a positive charge distributed uniformly over its surface

The charge inside the sphere is zero, so the electric field inside the sphere is zero

Hence potential is same ( E = - dV/dr)

The potential at the center of the sphere is the same as the potential at the surface.

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Replace x in the equation of f(x) and solve:

f(0) = sqrt(0) = 0

F(49/9) = sqrt(49/9) = 7/3

Put values get answer

x=0

x=49/9

The solution to this system of equations is: The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options. (Option C).

It means that if the number of hours worked is above 20, then it is more profitable to utilize the $20/hour rate.

Recall that the contractor has two options for billing a completed job. They are:

Let us fix x hours to be required for completing the project:

Note that:
The total amount recievable per contract is $500 while working on a retail basis, it will cost $25x.

Stating this mathematically, e have

25x < 500 when x < 20.

This mean that

25x < 500 when x < 20.

Then we find that by I contract he would get 500 $ but by II choice he would get 25x dollars

We find that

25x<500 if x<20

This suggests that a $500 flat rate is preferable if the number of hours done is fewer than 20.

Hence the correct answer is Option C.

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Answer:

C

Step-by-step explanation:

just took the test

Answer:

100.53

Step-by-step explanation:

V=πr2h

3=π·42·6

3≈100.53096

Hope this helps! please mark me brainliest :)

Volume =  

1  πr2h

3

=  

1 ×π×42×7

3

=  117.28612573402 centimeters^3

The table that represents the graph described is Table A - A 2-column table with 6 rows. Column 1 is labeled x - 0, 1, 2, 3, 4, 5. Column 2 is labeled y = 2x - 3 with -3, -1, 1, 3, 5, 7.

In order to solve this, look for the table that has x and y values that tally with the points on the graph.

The points on the graph are:

(0, -3), (1, -1), (2, 1), (3, 3), (4, 5), and (5, 7).

When you look at the first table, you see that the first x value corresponds with the y value of the first point on the graph. The second point on the graph of (1, -1) is also the same as the first table's x and y values.

In conclusion, option A is correct.

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Answer:

Its A

Step-by-step explanation:

Answer:

Trinomial.

Step-by-step explanation:

Note how much terms there are in the given expressions:

Term 1: [tex]3x^{2}y^{4}\[/tex]

Term 2: [tex]5x[/tex]

Term 3: [tex]1[/tex]

Note each meaning of the terms:

Monomial: Having only one term.

Binomial: Having two terms.

Trinomial: Having three terms.

Polynomial: Typically used to describe expressions with 4 or more terms.

In this case, there are only 3 terms, and so your answer is Trinomial.

~

Answer:

4.64 ft

Step-by-step explanation:

75 % = .75

11 * .75^3 = 4.64 ft

Answer:

x = 40°

Step-by-step explanation:

In circle with center O.

Answer:

Mike now has zero cups of rice

Step-by-step explanation:

1) 7x - 5x + 15 - x

2) 2x + 15 -x

3) x + 15

Answer:

x+15

Step-by-step explanation:

pemdas first you do parenthesis and since yo odn't know x then you move on to exponents and if thats not in there then you go to multiplication and any number thats next toa parenthesis without a sign in between them has to be multiplied so -5 times 5 equals -5x and you also have to multiply -5 by negative 3 which is +15 because negative times negative equals positive and -x is still in there so since it's only one x it's equal to -1x and -1x +-5x equals -6x and now 7x-6x equals x+15

Answer:

y=log(pi divide by 2)exponent ×

it's approximately 2.5...i hope this helps

The value of the x-coordinate of point D is,

⇒ 2.5

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

Graph of a function is shown.

And, A point D is shown in graph.

Now, By graph we get;

Coordinate of D is,

D = (2.5, - 1.5)

Hence, We get;

x - coordinate of D = 2.5

y - coordinate of D = - 1.5

Thus, The value of the x-coordinate of point D is,

⇒ 2.5

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Answer:

1 hour and 55 minutes.

Step-by-step explanation:

3:00 to 4:00 is 1 hour. 4:00 to 4:55 is 55 minutes. 1 hour + 55 minutes = 1 hour and 55 minutes.

Answer:  59.690260418206

The result is approximate. Round that value however you need to.

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

Explanation:

For a circle with radius r = 142.5, the full distance around the edge (aka perimeter aka circumference) is found by using the formula below.

C = 2*pi*r

C = 2*pi*142.5

C = 895.353906273091

That value is approximate. I used my calculator's stored value of pi to get the most accuracy possible.

That value of roughly 895 represents the distance around a full circle of that radius, but we only want a 24 degree pizza slice.

In other words, we want 24/360 = 1/15 of the full perimeter

(1/15)*895.353906273091 = 59.690260418206

Answer:

59.69 units

Step-by-step explanation:

TOTAL circumference of this circle = pi * d = pi * 2r = 895.354

  now you  want 24 degrees of the entire 360 degrees

       24/ 360   *    895.354 = 59.69 units

Answer:

69 children, 57 adults

Step-by-step explanation:

Let a = number of adults and c = number of children.

a + c = 126---------------->4a + 4c = 504

4a + 2.25c = 383.25-->4a + 2.25c = 383.25

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

1.75c = 120.25

c = 69, a = 57

Answer:

15.6205 (15.62)

Step-by-step explanation:

The distance between two points with coordinates (-9,-8) and (1,4) is:

15.62 units

(actual is 15.6205)

(results are in decimal form, rounded to the nearest 100th)

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

Find the mean, median, mode and range for the following data set. 1, 3, 5, 9, 8, 5, 8, 6

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and How to solve:-}}}[/tex]

In order to find the mean of a data set, we add all the numbers in the data set and add them, then we divide by how many there are:-

[tex]\bigstar[/tex] On simplification,

[tex]\bigstar[/tex] Now, divide by 8, because there are 8 numbers in the data set:-

[tex]\bold{\dfrac{45}{8}\:;written\:as\:decimal\Longrightarrow5,625}}}[/tex]

We've found the mean, but we also need to find the median, mode, and range!

The median is the number in the middle, but we should first arrange the data from least to greatest:-

1, 3, 5, 5, 6, 8, 8, 9

Now pick the number in the middle, which is:-

5,6. There are 2 numbers in the middle!

So what we do is we find the mean of the two numbers in the middle:-

5+6=11

11/2     [tex]\Longleftarrow[/tex] median

Now, we don't need to find the mean anymore - the mode and range don't require the mean.

The median requires the mean only when there's an even amount of numbers in the data set.

The mode of a dataset is the number we see the most.

Here we see the number 1 once, the number 3 once, the number 5 appears twice, 6 appears one time only, 8 appears twice and, last but not least, 9 appears once.

So this data set has two modes - 5 and 8.

In order to find the range, we take the smallest number (1) and subtract it from the largest number (9), which results in

8 (range)

[tex]\rule{300}{1}[/tex]

Answer:

mean=

5.625

median=5.5

mode=5and8

Step-by-step explanation:

mean=1+3+5+5+6+8+8+9/8

45/8

5.625

median=1,3,5,5,6,8,8,9

5+6/2

11/2

5.5

mode=

5and8

Answer:

Mean= [tex]\frac{11+9+11+15+17+13+17}{7}[/tex]

        =13.28 ≈13

For median arrange in ascending or descending order. i am arranging in ascending order

9,11,11,13,15,17,17

cancel from left and right until one number is left

median=13

Answer: I belive it’s C sorry if it’s wrong

Step-by-step explanation: because if you rotate it it will swap sides making it A,B