An entry in the Peach Festival Poster Contest must be rectangular and have an area of 1200 square inches. Furthermore, it's length must be 20 inches longer than it's width. Find the dimensions.

Answer:

[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = x^2[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

There is not enough information to determine the mean, the median is 28.

There is not enough information to determine the mean absolute deviation, the interquartile range is 18

Step-by-step explanation:

The box plot given has a skewed distribution, this means that both the mean and median values are not the same. From a box plot, the median value Can be obtained as the point in between the box.

From the box plot given, the marked point in between the box is 28 cm

Hence, Median = 28 cm

The mean cannot be inferred from the skewed box plot.

There is also not enough information to determine the mean absolute deviation ;

The interquartile range:

(Q3 - Q1)

Q3 = upper quartile, the endpoint of the box = 40

Q1 = the starting point of the box = 22

IQR = Q3 - Q1

IQR = 40 - 22 = 18

Answer:

d=10.45t

Step-by-step explanation:

The last one is the answer.

Hope this helps!

--Applepi101

Answer:

D) d=10.45t

Step-by-step explanation:

His distance(d) was 100. And his time(t) was 9.58 seconds.

So 100=9.58x

x≈10.44

The answer is D, because 10.45 is greater than 10.44.

I hope this helps!

Answer:

4*12*2

Step-by-step explanation:

it will be the right answer

Answer:

There are 6 boys in group.

Step-by-step explanation:

Since we have given that

Number of arrangement of 4 boys = 12 times the number of arrangement of 2 boys.

So, Let the number of boys in the group be 'x'.

So, Number of boys in the group will be

\begin{gathered}x=\frac{12\times 2}{4}\\\\x=\frac{24}{4}\\\\x=6\end{gathered}

x=

4

12×2

x=

4

24

x=6

Hence, there are 6 boys in the group.

hope it helps you a follow would be appreciated

Answer:

x = 105/16

Step-by-step explanation:

2/3x - 1 = 27/8

Add 1 to each side

2/3x - 1+1 = 27/8+1

2/3x = 27/8 + 8/8

2/3x = 35/8

Multiply each side by 3/2

3/2 * 2/3x = 35/8 *3/2

x = 105/16

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Answer:

  $562,500 per hour

Step-by-step explanation:

The cost will be a minimum where C'(x) = 0.

 C'(x) = 0.56x -0.7 = 0

  x = 0.7/0.56 = 1.25

The cost at that production point is ...

  C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625

The minimum production cost is $562,500 per hour for production of 1250 items per hour.

_____

Additional comment

This is different than the minimum cost per item. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.

Answer:

(a) 129600 J

(b) 81000 J

Step-by-step explanation:

The work done is given by the product of force and the displacement in the direction of force.

Force, F = 500 N

distance, d = 324 m

(a) friction force, f = 100 N

The work done is

W = (F - f) x d

W = (500 - 100) x 324

W = 129600 J

(b) Friction, f = 250 N

The work done is

W = (F - f) d

W = (500 - 250) x 324

W = 81000 J

Answer:

$4543.70

General Formulas and Concepts:

Pre-Algebra

Algebra I

Simple Interest Rate Formula: [tex]\displaystyle A = P(1 + rt)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

P = 3500

t = 6

r = 4.97% = 0.0497

Step 2: Find Interest

Answer:

10) Los ángulos en azul y rojo son llano y obtuso, respectivamente. (Respuesta: B)

11) Los ángulos agudo y recto están diferenciados por los colores morado y naranja, respectivamente. (Respuesta: C)

Step-by-step explanation:

Basándonos estrictamente en lo descrito en la figura, tenemos la siguiente clasificación por colores:

Agudo - Morado.

Plano o Recto - Naranja.

Obtuso - Rojo.

Llano - Azul.

Completo - Negro.

A continuación, se consigna las respuestas en forma de oración:

10) Los ángulos en azul y rojo son llano y obtuso, respectivamente. (Respuesta: B)

11) Los ángulos agudo y recto están diferenciados por los colores morado y naranja, respectivamente. (Respuesta: C)

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Answer:

  3

Step-by-step explanation:

AB is 1 unit long.

A'B' is 3 units long.

The scale factor is the ratio of these lengths:

  scale factor = A'B'/AB = 3/1 = 3

ABC is dilated by a factor of 3 to get A'B'C'.

Answer:

Kindly check explanation

Step-by-step explanation:

Since the triangle is right angled ; we can solve for x using Pythagoras :

x = hypotenus ; hence ;

x² = opposite² + adjacent²

x² = 15² + 8²

x² = 225 + 64

x² = 289

x = √289

x = 17

Using Trigonometry :

Sin D = side opposite D / hypotenus = 8/17

Cos D = side Adjacent D / hypotenus = 15 / 17

Tan D = side opposite D / Adjacent side = 8/15

Sin F = side opposite F / hypotenus = 15/17

Cos F = side Adjacent F / hypotenus = 8 / 17

Tan F = side opposite F / Adjacent side = 15/8

Answer:

= 1296x √ xy

Step-by-step explanation:

Apply exponent rule: a^b . a^c = a^b + c    3 . 3 = 3^ 1 + 1

= x . 3^1+1 √648x . 4y . 8

Add the numbers: 1 + 1 = 2

= x . 3^2 √648x . 4y . 8

= 3^2 . 144x √ xy

Refine

= 1296x √ xy

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Answer:

Step-by-step explanation:

If we let a, b, c represent tickets booked on airlines A, B, C, respectively, then we have ...

  a + b + c = 55

  a - b = 6

  -2b + c = 5

Using the last two equations to write expressions for a and c, we have ...

  a = b +6

  c = 5 +2b

These can be substituted into the first equation to give ...

  (b +6) +b +(5 +2b) = 55

  4b +11 = 55

  4b = 44

  b = 11

  a = b+6 = 17

  c = 5 +2b = 27

He booked 17 tickets on Airline A, 11 tickets on Airline B, and 27 tickets on Airline C.

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Answer:

  A)  (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it

Step-by-step explanation:

We want ...

  C(x)/x < 100

  (20x +160)/x < 100

  20 +160/x < 100 . . . . . separate the terms on the left

  160/x < 80 . . . . . . . subtract 20

  160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0

  x > 2 . . . . . . simplify

In interval notation this is (2, ∞).   matches choice A

__

Technically (mathematically), we also have ...

  160/80 > x . . . . and x < 0

which simplifies to x < 0, or the interval (-∞, 0).

If we include this solution, then choice C is the correct one.

_____

Comment on the solution

Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.

Answer:

36

Step-by-step explanation:

Total students un the contest = 84

Number of students who gave their speech yesterday:-

[tex] \frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21[/tex]

so 21 students gave their speech yesterday

= 63

Number of students who gave their speech today:-

[tex] \frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27[/tex]

Number of students who have given their speech:-

= 21 + 27

= 48

Number of students who still haven't given their speech :-

= total - 48

= 84 - 48

= 36

Answer:

The car will depreciate at a rate of 21.14% per year.

Step-by-step explanation:

Given that the value of a car will “depreciate” over time, and, for example, a car that was worth $ 24,000 when it was new, is being sold for $ 13,500 three years later, to determine the annual depreciation rate on this car the following calculation must be performed:

13,500 x (1 + X) ^ 1x3 = 24,000

13,500 x (1 + 0.2114) ^ 3 = 24,000

X = 21.14%

Therefore, the car will depreciate at a rate of 21.14% per year.

Hi there!

[tex]\large\boxed{x = 60^o}[/tex]

We know:

∠AGB ≅ ∠DGC because they are vertical angles. They both are 90°.

∠AGE ≅ FGC because they are vertical angles, equal 30°.

∠BGF ≅ ∠DGE are vertical angles, both equal x.

All angles sum up to 360°, so:

360° = 90° + 90° + 30° + 30° + x + x

Simplify:

360° = 240° + 2x

Subtract:

120°  = 2x

x = 60°

Answer:

13/16 miles per minute

Step-by-step explanation:

Take the miles and divide by the minutes

1/8 ÷ 2/13

Copy dot flip

1/8 * 13/2

13/16 miles per minute

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Answer:

  D.

Step-by-step explanation:

The linear portion of the curve is in the region x ≥ 2. The only function defined that way is the one in choice D.

Answer:

XW = 78

Step-by-step explanation:

Both triangles are similar, therefore based on triangle similarity theorem we have the following:

XW/XZ = VW/YZ

Substitute

XW/6 = 104/8

XW/6 = 13

Cross multiply

XW = 13*6

XW = 78

Answer:

R1 = 150 in = 12.5 ft

R2 = 170 in = 14.167 ft

H = 220 in = 18.333 ft

Volume of solid cylinder = Pi * R^2 * H

So the volume of a hollow cylinder must be V = Pi * H * (R2^2 - R1^2)

V = 3.142 * 18.33 * (14.17^2 - 12.5^2) = 2565 ft^3

.

Answer: x = (-3,3), y = (-5,5)

Step-by-step explanation:

Add both of the equations together, for [tex]3x^{2}+3y^{2} = 102[/tex]. Now we can divide both sides by 3, getting[tex]x^2+y^2=34[/tex]. we subtract the first equation from our equation we just got, getting [tex]y^2=25[/tex] y= (5,-5). once we plug that in, we get [tex]50+x^2 = 59[/tex], [tex]x^2 = 9[/tex] x = (-3,3)

Answer:

[tex]1/16[/tex]

Step-by-step explanation:

The formula for the sequence [tex]a_n=\frac{1}{2}^n[/tex] is used to find the [tex]n[/tex]th term of the sequence.

To find the fourth term, substitute [tex]n=4[/tex]:

[tex]a_4=\left(\frac{1}{2})\right ^4,\\a_4=\frac{1^4}{2^4}=\boxed{\frac{1}{16}}[/tex]

Answer:

1/16

Step-by-step explanation:

the nth term is

[tex]a_{n} = (\frac{1}{2} )^{n}[/tex]

the 4th term is found by substituting n=4

[tex]a_{4} =(\frac{1}{2} )^{4} = \frac{1^{4} }{2^{4} } = \frac{1}{16}[/tex]

Answer:

x=10

Step-by-step explanation:

Using the Rational Roots Test, we can say that the potential rational roots are

± (1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90).

Unfortunately, there doesn't really seem to be an easy way to figure out which numbers are actually roots outside of guess and check. Therefore, to solve this, we'll have to go through numbers until we hit something.

To make the process faster, I wrote a Python script as follows:

numbers = [1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90]

negative_numbers = [i * (-1) for i in numbers]

numbers = numbers + negative_numbers

for i in numbers:

   if (i**3 - 10*(i**2) + 9*i-90) == 0:

       print(i)

The result comes out as 10, meaning that 10 is our only rational root. Using the Factor Theorem, we can say that because 10 is a root, (x-10) is a factor of the polynomial. Using synthetic division, we can divide (x-10) from the polynomial to get

10 |   1     -10     9      -90

    |          10     0       90

    _________________

        1       0     9        0

Therefore, we can say that

(x³-10x²+9x-90)/(x-10) = (x²+0x+9), so

x³-10x²+9x-90 = (x-10)(x²+9)

As the only solution to x²+9=0 contains imaginary numbers, x=10 is the only solution to x³-10x²+9x-90 = (x-10)(x²+9) = 0