Pablo finished his history assignment in 3/4 hours. Then he completed his math assignment in 1/5 hours. What was the total amount of time Pablo spent doing these two assignments? Write your answer as a fraction in simplest form.

Answer:

$4.8 for sugar and $25 for butter.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

8 × 90 = 720

4 × 180 (half of 8, double of 90) = 720

2 × 360 (half of 4, double of 180) = 720

1 × 720 = 720

Answer:

90 degree angle because a right angle is always 90 degrees

Answer:

Step-by-step explanation:

complementary angle- adds to 90°

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Answer:

X/120=1/24

5/120=1/24 24×5=120

Step-by-step explanation:

Answer:

Eliminate the denominators of the fractions 120⋅x/200=120⋅2/41

Cancel the multiplied terms that are in the denominator 120

x=120⋅1/4

x=5

The answer is x=5

Answer:

Step-by-step explanation: C is 100 X is 10 IV is 4 since the smaller number is in the front so you subtract instead of add

C=100 3X=30 IV=4

100+30+4=134

CXXXIV=134

\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

Answer:

To calculate XYZ Company's total assets minus liabilities, you would need to add up all of the assets listed on the balance sheet and then subtract the sum of all the liabilities.

In this case, the total assets would be $45,000 + $41,000 + $134,000 = $220,000. The total liabilities would be $55,000 + $56,000 + $50,000 = $161,000.

So, the total assets minus liabilities would be $220,000 - $161,000 = $59,000.

Step-by-step explanation:

Answer:

3²-5

Step-by-step explanation:

(3-2²)+5=4

3²-5=4

Answer:

D

Step-by-step explanation:

First off, lets simplify (3-2^2)+5 = -1+5 = 4

We will need to  find an expression that will equal to 4

lets try 1, 5-2^2 = 1, 1 =\ 4

Alright, lets try 2, 2^2 -5 = -1, -1=\5

Now lets try 3, 5 - 3^2 = -4, -4=\4

So by process of elimination we can say that D is correct by I will show you why it is correct. 3^2 -5 = 4, 4=4

If you have any questions ask me.

Hope it helped :)

Answer:

The y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Step-by-step explanation:

To solve this question, we need to plug in x = 0 into the given equation and simplify. We get:

y = 6(0 - 1/2)(0 + 3) y = 6(-1/2)(3) y = -9

Therefore, the y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Step-by-step explanation:

√z is defined only when z >= 0

Therefore √x - 1 is defined only when (x - 1) >= 0, x >= 1.

The only graph that shows the domain x >= 1 is graph Y.

The statement refers to the way that symbols are represented in sequences, a common practice in formal language theory, by employing a notation that makes symbols a part of the sequence.

In formal language theory, a language is often defined as a set of strings over an alphabet. By representing any alphabetic sequence of symbols as a single string using the notation outlined in the statement, we are able to recognise the language that comprises that sequence as a collection of strings. A subset of the language having all possible strings over the alphabet (a, b, and c) is the set of strings abc, which may be used to represent the language including the sequence (a, b, and c). So, this notation offers an easy approach to discuss languages and the sequences that make up such languages.

Hence, the statement relates the symbols and sequences.

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Answer:

Step-by-step explanation:

Answer:

\(k = 6.74 * 10^{-5}\)

Step-by-step explanation:

Given

\(F\ \alpha\ \frac{m * M}{r^2}\) --- The variation

\(F = 675; m = 125; M = 225; r = 0.0530\)

Required

Determine the constant of proportionality (k)

\(F\ \alpha\ \frac{m * M}{r^2}\)

Express as an equation

\(F = k\frac{m * M}{r^2}\)

Multiply both sides by \(r^2\)

\(Fr^2 = km * M\)

Make k the subject

\(k = \frac{Fr^2}{m * M}\)

Given that: \(F = 675; m = 125; M = 225; r = 0.0530\)

We have:

\(k = \frac{675* 0.0530^2}{125 * 225}\)

\(k = \frac{1.896075}{28125}\)

\(k = 0.000067416\)

This can be represented as:

\(k = 6.74 * 10^{-5}\)

Answer:

it's so simple

Step-by-step explanation:

20°+74°+x°=180°

x°=180°-94

x°= 86°

Answer:

C

Step-by-step explanation:

All sides make a cube

Answer:

D

Step-by-step explanation:

\(16+15+14=45\) - the total number of balls

\(|\Omega|=45\cdot44=1980\)

a)

\(A\) - blue, then yellow is selected

\(|A|=15\cdot14=210\\\\P(A)=\dfrac{210}{1980}=\dfrac{7}{66}\approx10.6\%\)

b)

 A - red, then red is selected

\(|A|=16\cdot15=240\\\\P(A)=\dfrac{240}{1980}=\dfrac{4}{33}\approx12.1\%\)

Answer:

n = 1

n = - 1

n = - 1/5

n = - 25

Step-by-step explanation:

We are to obtain the value if n in the given equations :

1.)

n - 13 = - 12

To find, n ;

Add 13 to both sides

n - 13 + 13 = - 12 + 13

n = 1

2.)

n/5 = - 1/5

Multiply both sides by 5

n/5 * 5 = - 1/5 * 5

n = - 1

3.)

-5n = 1

Divide both sides by - 5

-5n/-5 = 1/-5

n = - 1/5

4.)

n + 15 = - 10

Subtract 15 from both sides :

n + 15 - 15 = - 10 - 15

n = - 25

Answer:

D.

Step-by-step explanation:

Given: Dimensions of a rectangular prism are \(7.5\,\,inches,3\,\,inches\,,\,11.5\,\,inches\)

To find: total surface area of the rectangular prism in square inches

Solution:

Length of the rectangular prism (l) = 7.5 inches

Breadth of the rectangular prism (b) = 3 inches

Height of the rectangular prism (h) = 11.5 inches

Total surface area of the rectangular prism = 2(lb+bh+hl)

= \(2(7.5\times3+3\times11.5+11.5\times7.5 )\)

\(2(7.5\times3+3\times11.5+11.5\times7.5 )=2(22.5+34.5+86.25)\\=2(143.25)\\=286.5\,\,square \,\,inches\)

So, option D is correct

Answer:

D! I got it correcttt

Step-by-step explanation:

The calculated area of the triangle is 38.30 square units

From the question, we have the following parameters that can be used in our computation:

The triangle

The area of the triangle is calculated as

Area = 1/2absin(c)

Where

a = b = 10

c = 50 degrees

Using the above as a guide, we have the following:

Area = 1/2 * 10 * 10 * sin(50 degrees)

Evaluate

Area = 38.30

Hence, the area of the triangle is 38.30 square units

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The Interpretatiom of the equation is that;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

The algebra word problem can be solved by using variables to denote certain parameters I'm the question.

The general form of equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

We are given the equation:

$25w + $65

This equation represents the amount of money Kelly will have saved after some amount of weeks.

Thus;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

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The polynomial of degree 4, P(x), can be written as a product of linear factors in the form of P(x) = a(x-4)²(x-0)(x+4) where a is a constant.

Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.

To find the value of a, we can use the point (5,18) which is given. Since P(5) = 18, we can substitute 5 for x in the equation and solve for a. This gives us a (5-4)²(5-0)(5+4) = 18, and we can solve for a = 18/120 = 0.15. Therefore, the formula for P(x) is P(x) = 0.15(x-4)²(x-0)(x+4).

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Area of rectangle is,

A = 45 units²

And, Perimeter of rectangle is,

⇒ P = 28 units

We have to given that;

Vertices of rectangle are,

⇒ (- 4, - 5)  

⇒ (-4, 0)

⇒ (5, 0)

⇒ (5, - 5)

Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, Length of rectangle is distance between (- 4, - 5) and (- 4, 0).

Which is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (- 4 + 4)² + (0 + 5)²

⇒ d = √ 25

⇒ d = 5

And,  Width of rectangle is distance between (- 4, 0) and (5, 0).

Which is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (- 4 - 5)² + (0 - 0)²

⇒ d = √ 81

⇒ d = 9

Thus, Area of rectangle is,

A = L x W

A = 5 x 9

A = 45 units²

And, Perimeter of rectangle is,

⇒ P = 2 (L + W)

⇒ P = 2 (5 + 9)

⇒ P = 2 × 14

⇒ P = 28 units

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The graph shows the lines of two equations, a blue line and a red line.

Note that to solve a system of equations graphically, we would need to identify the point at which they both intersect.

The lines of these two equations intersect at the point where x = -3 and y = 1

ANSWER:

The correct answer is option B

Answer

The missing length is 10

Step-by-step explanation:

Represent the missing length with x

The sides of the given shape are directly proportional.

Mathematically:

(15 + x) to (12 + 8) and x to 7

Represent as a ratio:

\((15 + x) : (12 + 8) = x : 8\)

\(15 + x : 20= x : 8\)

Convert to fraction

\(\frac{15 + x}{20} = \frac{x}{8}\)

Cross Multiply:

\((15 + x)*8 = 20 * x\)

\(120 + 8x = 20x\)

Collect Like Terms

\(20x - 8x = 120\)

\(12x = 120\)

Solve for x

\(x = \frac{120}{10}\)

\(x = 10\)

The length of the missing side is 10

Answer:

171 > 117

Step-by-step explanation:

171 is greater than 117 meaning the alligator is eating the bigger number, 171.

Answer:

20 lbs of sugar per gallon as time goes to infinity

Step-by-step explanation:

Because of the statement ... as time goes to infinity...I am inclined to approach this problem using derivatives and limits

Let the amount of sugar in the tank at any time t(in minutes) be

\(S(t) \;lbs/gal\)

We have \(S(0) = 0\)  since the initial quantum of water has zero sugar

The inflow rate of sugar is given as 3  gal/min and each gallon contains 0.2 lbs of sugar
\therefore The rate of sugar increase in the tank n lbs/gal
= 0.2 lbs /gal \times 3 gal/min

=  0.6 lbs/min

Outflow rate = 3 gal/min
At any time t, the tank contains 100 gal
The amount of sugar at time t = \dfrac{S(t)}{100} lbs/gal

Therefore the outflow rate of sugar = 3 gal/min \times \dfrac{S(t)}{100} lbs/gal

= 0.03S(t) lb/min

The net rate is given by inflow rate - outflow rate

= 0.6 - 0.03S(t)

In calculus terms the net rate =  \(\dfrac{dS(t)}{dt}\)

Therefore
\(\dfrac{dS(t)}{dt} = 0.6 - 0.03S(t)\)

\(\dfrac{dS(t)}{dt} - 0.03S(t) = 0.6\\\\\)    (1)

A trick to solving differential equations of this type is to use the method of integrating factors

In general,  if we have a differential equation of the type
\(\dfrac{dy}{dx} + Py = Q\\\\\)
where P and Q are functions only of x

then the integrating factor is \(e^{\int\ {P} \, dx }\)

which you use to multiply both sides of the differential equation first

In equation (1) above,

y = S(t) which well simply write as S for convenience

Writing S' for \(\dfrac{dS(t)}{dt}\) for convenience we get equation (1) as

\(S' + 0.03S =0.6\)   (2)

From the above we see that P in the generalized differential equation corresponds to 0.03

Therefore the integrating factor is
\(\mbox {\large e^{\int 0.03dt} = e^{0.03t}}\)

Multiply equation (2) throughout by this integrating factor to get

\(\mbox{\large e^{0.03t} S' + 0.03S e^{0.03t} = 0.6 e^{0.03t} }\)

The left side is nothing but the first derivative of \(\mbox{\large (e^{0.03t}S) }\\\\\)
\(= \mbox{\large (e^{0.03t}S)'\\\\}}\)

Integrating both sides we get

\(\mbox{\large e^{0.03t}S = 0.06 \int e^{0.03t}dt}\\\\\)    (3)

\(\textrm{By using the fact that $\int e^{ax} dx = \dfrac{e^{ax}}{a} + C$}:\\\\\mbox{\large \int e^{0.03t}dt} = \dfrac{e^{0.03}}{ 0.03}} + C\\\\\)  

Therefore equation (3) becomes
\(e^{0.03t}S = 0.06 \cdot \dfrac{e^{0.03}}{0.03}} + C\\\\e^{0.03t}S = 0.06 \cdot 33.333 \cdot e^{0.03} + C\\\\e^{0.03t}S = 20 \cdot e^{0.03} + C\\\)

Dividing by \(e^{0.03} \textrm{ (same as multiplying by $e^{-0.03}$) both sides}\):

\(S = 20 + Ce^{-0.03t}\\\\\textrm{Plugging back S(t):}\\\\S(t) = 20 + Ce^{-0.03t}\\\)

We are asked to find the level of sugar content as t ⇒ ∞

At t = 0, S(t) = 0; there is no sugar content

S(0) = 0 = 20 + Ce⁰

0 = 20 + C
C = -20

\(S(t) = 20 -20e^{-0.03t}\\\\\)

As t ==>  ∞
we get

\(\lim _{x\to \infty }S\left(t\right)=\:\lim _{x\to \infty }\left(20\:-\:20e^{-0.03t}\right)=\:\:20\:-\:0\:=\:20\)

Therefore as time goes to infinity the eventual sugar content
= 20 lbs/gallon

The answer is just -infinite