Tonia has $375 in her savings account. She plans to deposit $80 each month for the next 12 months. At the end of the year, she will have an account balance of $1,335.

\(\cfrac{~~ 2-\frac{2 }{ x} ~~}{3-\frac{1}{x}}\implies \cfrac{ ~~ \frac{2x-2}{x} ~~ }{\frac{3x-1}{x}}\implies \cfrac{2x-2}{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{3x-1}\implies \cfrac{2x-2}{3x-1}\)

The commutative law of addition is also referred to as the law of cumulative addition and it states that if two numbers are added together, then, the outcome is equal to the addition of their interchanged position because addition is considered as a binary operation.

This ultimately implies that, the sum of addends would always be the same (equal) regardless of their arrangement in accordance with the commutative law of addition. Mathematically, the commutative law of addition can be represented using the following formula:

A + B = B + A.

In this context, we can reasonably infer and logically deduce that the given expression was rewritten using the commutative law of addition.

In conclusion, Line 1 says 3 + 4, which could be represented using dots as ••• + •••• for a total of 7 dots. Line 2 says 4 + 3, which could be represented using dots as •••• + ••• for a total of 7 dots.

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The ratio of radius of the small circle to radius of big circle is OP : OA

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

The circles

From the circles, we have the following parameters

Radius of big circle = OA

Radius o the small circle = OP

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

Ratio = Radius of small circle: Radius of the big circle

So, we have

Ratio = OP : OA

Hence, the ratio of the radii is OP : OA

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The university grew at an average percentage rate of approximately 15.36% per year.

1. In order to find the average percentage growth rate, we will use the formula for geometric mean growth rate:
Growth Rate = ((Ending Value / Starting Value)^(1 / Number of Years)) - 1
2. In this case, the starting value is 1,200 students, the ending value is 5,200 students, and the number of years is 10.
Growth Rate = ((5,200 / 1,200)^(1 / 10)) - 1
3. Calculate the values:
Growth Rate = (4.3333^(1 / 10)) - 1
Growth Rate = 1.1536 - 1
Growth Rate = 0.1536
4. Convert the decimal to a percentage:
Growth Rate = 0.1536 * 100 = 15.36%

Hence, Based on the geometric mean, the local university grew at an average percentage rate of approximately 15.36% per year over the 10-year period.

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Answer:

\(\sqrt{3}\) = m

Step-by-step explanation:

So we can say;

Tan(30) = m/3

=> Tan(30) * 3 = m

=> \(\sqrt{3}\) = m

Hope this helps!

Answer:

50 pennies, 10 dimes

Step-by-step explanation:

0.01p+0.01d=1.50

p=5d

(0.01)5d+0.10d-1.50

0.05d+0.10d-1.50

0.15d=1.50

d=1.50/0.15

d=10

p=5d

=5x10

p=50

Answer= 50 pennies, 10 dimes

An equation is formed of two equal expressions. Amber has 50 pennies and 10 dimes.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of pennies be represented by x, while the number of dimes is represented by y. Therefore, the statement "there are five times as many pennies as dimes" can be written as,

x = 5y

Now, since the sum of all the coins is $1.50, therefore, the sum can be written as,

0.01x + 0.1y = 1.50

0.01(5y) + 0.1y = 1.50

0.05y + 0.1y = 1.50

0.15y = 1.50

y = 10

Now, the value of x will be,

x = 5y

x = 5(10)

x = 50

Hence, Amber has 50 pennies and 10 dimes.

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The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

The given problem is:

min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0

The feasible region is as follows:

Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:

Now, let's check each option one by one:

a. 4x₁ + 2x₂ ≥ 20

The feasible region is the region above the line 4x₁ + 2x₂ = 20.

b. −6x₁ + 4x₂ ≤ 12

The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6

The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0

The feasible region is the region above the x-axis.

Now, check the point of intersection of the lines.

They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.

Therefore, we reject this point.

The other two points, (10,0) and (6,0) are in the feasible region.

Now, check the values of the objective function at these two points.

Objective function value at (10,0): 80

Objective function value at (6,0): 48

Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

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Answer:19,4 or 4,19

Step-by-step explanation: Let the width of the rectangle be 'w' in

According to the question length of the rectangle (l) is one inch less than five times it's width;

l = (5w - 1) in

Perimeter of rectangle = 46 inches

Formula of perimeter of rectangle = 2(Length + Width)

So,

Width of the rectangle (w) = 4 in

Answer:

a : 2 , b : 1 , c : 0 , d : 0

Step-by-step explanation:

a: 2

b: 1

c: 0

d:0

Answer:

d .

Step-by-step explanation:

I went over it in class .

Answer:

width is 12.5 inches

length is 37.5 inches

Step-by-step explanation:

x is width, 3x is length,

Complete question :

Miranda is braiding her hair then she will attach beads to the braids she wants 1/3 of the beads to be red if the greatest number of beads that will fit on the braid is 12 what other fraction could represent the part of the beads that are red?

Answer:

2 / 6

Step-by-step explanation:

Fraction of red beads on braid = 1/3

greatest number of braids = 12

Fraction of red beads = (1 /3) * 12 = 4 red beads

Thus implies that :

When greatest number of braids = 12

fraction of red beads) = (Number of red beads / greatest number of beads)

Fraction = 4 / 12

Divide by 2 = 2/6 (don't reduce to lowest term).

Answer:

D

Step-by-step explanation:

{(-2,1)(2,7)} that's my answer

A chart that compares three sets of values in a three-dimension chart is called surface.

A two-dimensional collection of points (flat surface), a three-dimensional collection of points with a curved cross section (curved surface), or the perimeter of any three-dimensional solid are all examples of surfaces in geometry.

A surface is typically a continuous boundary that separates two areas of a three-dimensional space. For instance, a sphere's surface divides its interior from its exterior, and a horizontal plane divides the half-planes above and below it. Despite the fact that regions they contain are three-dimensional and have a volume, surfaces are basically two-dimensional and have an area. Despite this, surfaces are frequently referred to by the names of the regions they surround. Differential geometry studies the characteristics of surfaces, particularly the concept of curvature.

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Answer:

b = 51

Step-by-step explanation:

b/27 = 17/9

27/9 = 3

We need to multiply the right side by 3/3 to get to the left

17/9 * 3/3

51/27

Answer:

0.80c

Step-by-step explanation:

'c' represents the original price.  20% off leaves 80% of c, which is the sales price:  0.80c

We can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

So, as we have the equation:

12x + 3 = 3(5x + 9)

Now, as we can see, Sadio took out 3 as common from LHS and RHS and solved the equation.

Which gave her the value of x as -8.

Amir, on the other hand, did not take out anything as common and directly multiply 3 with other terms in the brackets to solve the equation.

He also got -8 as the value of x.

Hence, we can conclude that yes both the ways of solving the equation is correct which is done by Sadio and Amir.

Therefore, we can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.

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9514 1404 393

Answer:

  -22

Step-by-step explanation:

The remainder theorem tells you the remainder will be f(-3), where -3 is the value of x that makes the binomial factor equal to zero.

  f(-3) = (-3)^3 +5 = -27 +5 = -22

The remainder when f(x) is divided by x+3 is -22.

_____

The attachment shows long division, with a remainder of -22.

Answer:

\(\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx = ln3\)

General Formulas and Concepts:

Pre-Calculus

Calculus

Derivatives

Derivative Notation

Trig Derivatives

Integrals

Integration Constant C

Integration Rule [Fundamental Theorem of Calculus 1]:                                        \(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Integration Property [Multiplied Constant]:                                                             \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Trig Integration

Logarithmic Integration

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle \int\limits^{\frac{2 \pi}{3}}_{\frac{- \pi}{3}} {\frac{sinx}{1 + cosx}} \, dx\)

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Step 3: Integrate Pt. 2

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

Unit: Integration

Book: College Calculus 10e

\(\huge\text{Hey there!}\)

\(\large\text{In order for you to SOLVE for THIS EQUATION you have to do is}\\\large\text{PEMDAS. Which simply means}\downarrow\)

\(\bullet\large\text{Parentheses}\\\bullet\large\text{Exponents}\\\bullet\large\text{Multiplication}\\\bullet\large\text{Division}\\\bullet\large\text{Addition}\\\bullet\large\text{Subtraction}\)

\(\large\text{Here is your steps to solving for your given equation}\downarrow\)

\(\large\text {4(3 + 4) + 6(9 - 1) - 8}\\\large\text{3 + 4 = 7}\\\large\text{4(7) + 6(9 - 1) - 8}\\\large\text{(9 - 1) = 8}\\\large\text{4(7) + 6(8) - 8}\\\large\text{4(7) = 28}\\\large\text{28 - 6(8) - 8}\\\large\text{6(8) = 48}\\\large\text{28 + 48 - 8}\\\large\text{28 + 48 = 76}\\\large\text{76 - 8 = \bf 68}\\\large\text{= \bf 68}\\\\\boxed{\boxed{\huge\text{Answer: \bf 68}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Step-by-step explanation:

⠀⠀⠀⠀⠀⠀⠀⠀⠀

Answer:

90

Step-by-step explanation:

We'll calculate these squares one by one, then add them together. First, let's work on \(1^{2}\). This is equivalent to 1 times itself two times, which is equal to 1, since 1 times 1 is 1.

Now, we'll look at \(2^{3}\). This is equal to 2 times 2 times 2, which is equal to 8. 2 times 2 is 4, times 2 is 8.

Finally, let's look at \(3^{4}\). This is equal to 3 times 3 times 3 times 3 - 3 times 3 is 9, times 3 is 27, times 3 is 81. So that's our last number.

What's 1 + 8 + 81? 1 + 8 is 9, and 81 + 9 is equal to 90. So that's the sum of the expression.

Hopefully that was helpful! If you have further questions, let me know.

Answer:

Step-by-step explanation:

1^2+2^3+3^4

(1 x 1) + (2 x 2 x 2) + (3 x 3 x 3 x 3)

1 + 8 + 81

9 + 81

90 is the answer

Awnser

8 gallons of cans

Answer:

Step-by-step explanation:

because x^2+bx-12 has two binomials factorts of the form (x+p) and (x+q)

=> x² + bx - 12 = (x+p)(x+q)

=> x² + bx - 12 = x² + (p+q)x + pq

=>  

The distance from the tree to the rope anchored to the ground is 5.3 ft

Pythagoras theorem:

where

c = hypotenuse

a and b are the other legs.

Therefore,

How far the tree is anchored to the ground is the adjacent side of the triangle. Therefore,

b² = 8² - 6²

b² = 64 - 36

b = √28

b = 5.29150262213

b = 5.3 ft

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Answer:

m=4/5

Step-by-step explanation:

Hope I helped ヾ(＾-＾)ノ

The range of rounds down nearest integer function is {-2,1,5} while domain is {-2.3,√2,4.6}.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

Given the rounds down nearest integer function INT(x)

x = -2.3,√2,4.6

Since the domain is the set of all x's values thus  {-2.3,√2,4.6} will be the domain.

For x = -2.3 ⇒ INT(-2.3) = -2

For x = √2 = 1.414 ⇒ INT(√2) = 1

For x = 4.6 ⇒ INT(4.6) = 5

So range  {-2,1,5}

Hence "The range of rounds down nearest integer function is {-2,1,5} while domain is {-2.3,√2,4.6}".

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Answer:

Upper Left

Bigger slopes means steeper lines.

Good luck!

Answer:

The caste system

Step-by-step explanation:

Buddhism does not believe in the caste system

Answer:

the caste system

Step-by-step explanation:

second option !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

We can simplify the linear equation until we get:

-4 = 2

Which is a false equation, this means that the equation has no solutions.

Here we have the following linear equation:

(1/3)*(6w - 12) = 2w + 2

To find how many solutions it has, let's try to solve it. We will do that by isolating the variable (w) in one side of the linear equation.

Expanding the left side we get:

(1/3)*6w + (1/3)*(-12) = 2w + 2

2w - 4 = 2w + 2

Subtracting 2w in both sides we get:

2w - 4 - 2w = 2w + 2 - 2w

-4 = 2

So we ended up with a false equation that does not depend on w, so there is no value of w such that the equation becomes true, then the linear equation has no solutions.

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Answer:

(a) T= 0.34r^3

(b) T= 73.44