find the least common denominator for each pair of fractions

Answer:

[tex]x2 + 4x + 4 = 0 [/tex]

a) The total amount that you will have into the account is given as follows: $360,211.

b) The amount of money inserted into the account is of: $84,000.

c) The amount of interest earned is given as follows: $276,211.

The balance of an account is given as follows:

[tex]B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}[/tex]

The meaning of each parameter is given as follows:

The parameters for this problem are given as follows:

P = 200, r = 0.07, n = 12, t = 35.

Hence the balance will be given as follows:

[tex]B = \frac{200\left(\left(1 + \frac{0.07}{12}\right)^{420}-1\right)}{\frac{0.07}{12}}[/tex]

B = $360,211.

The amount inserted into the bank account is given as follows:

200 x 12 x 35 = $84,000.

Then the amount of interest is given as follows:

360211 - 84000 = $276,211.

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The total amount Jill paid for the curtains and comforter is, 216.25.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Jill was remodeling her bedroom she bought 4 curtains for 37 each and comforter for 68.25.

Now, The cost of 4 curtains = 4 × 37

                                           = 148

And, The cost of comforter = 68.25

Thus, The total amount jill paid for the curtains and comforter is,

⇒ 148 + 68.25

⇒ 216.25

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a) -32.06 (To the nearest hundredth)

b) -37.7 (To the nearest tenth)

c) 3.1 (To the nearest tenth)

d) 5.86  (To the nearest hundredth)

f) -4.33  (To the nearest hundredth)

g) 11.44  (To the nearest hundredth)

h) 62x + 45 = 38x + 79

i) 46y - 18 = -37y

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=), and shows the relationship between the variables present in the equation. Equations are used to model real-world problems and find solutions to various mathematical problems.

They can be solved for a specific variable by using various mathematical methods and techniques.

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Step-by-step explanation:

Given:

Present value =₹ 40000

Interest rate =6% per annum

Time =6 months

To find the amount we have the formula,

Amount (A)=P(1+(r/100))n

where P is present value, r is rate of interest, n is time in years

Now substituting the values in above formula we get,

∴A=40000(1+(6/4)/100) ²

⇒A=40000(1+3/200)²

⇒A=40000(203/200)²

⇒A=40000(203/200) ²

⇒A=203×203

⇒A=₹ 41209

∴ Compound interest =A–P

=41209–40000=₹ 1209

The inequality nature is discussed below.

Given is a inequality.

Assume the inequality to be -

ax + b > g

Now, if for the value of g = - 7, the expression - (ax + b) is greater than g       {for any specific value of x} then the inequality is said to be true.

Therefore, the inequality nature is discussed above.

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Answer:

Step-by-step explanation:

...........

Inserting plus or minus signs in Web Assign can be done in the following way Log into your Web Assign account.

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Answer:

Both Rachel and Erik are trying to estimate the area of the circular rug with a diameter of 8 ft. Rachel's estimate using the formula A = πr^2 is correct and is the standard way to find the area of a circle. Erik's method of dividing the circle into 12 parts and forming a parallelogram is also a creative way to estimate the area, but it may not be as accurate as Rachel's formula-based approach.

Step-by-step explanation:

The area of a circle can be calculated using the formula A = πr^2, where r is the radius of the circle. In this case, the diameter of the circle is 8 ft, so the radius can be calculated as r = 8/2 = 4 ft. Substituting the radius into the formula gives A = π x 4^2 = 16π.

Erik's approach of dividing the circle into 12 parts and forming a parallelogram is an estimation method that could be used to find the area of a circle. The idea is to divide the circle into equal parts, arrange them into a parallelogram shape, and find the area of the parallelogram. This will give an estimate of the area of the circle, but it may not be as accurate as using the formula A = πr^2.

The sequence 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30 has 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 of 2's

A number system is defined as a system of writing to express numbers.

The concept on skip counting by 2’s or twos is an essential skill to get the idea when we progress to learn the concept on counting to basic addition.

2=2×1

4=2×2=2 times

6=2×3=3 times

10=2×5=5 times

12=2×6= 6 times

14=2×7=7 times

16=2×8=8 times

18=2×9=9 times

20=2×10= 10 times

22=2×11=11 times

24=2×12=12 times

26=2×13=13 times

28=2×14=14 times

30=2×15=15 times

Hence, the sequence 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30 has 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 of 2's.

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The equation of the circle can be written as:

(x - 3)^2 + (y + 2)^2 = 16

We know that for a circle of radius R and the center is (a, b) can be written as:

(x - a)^2 + (y - b)^2  = R^2

Here we want to find the equation for a circle of radius of 4 units and a center at (3, -2), then the equation is:

(x - 3)^2 + (y -( - 2))^2 = 4^2

Now we can simplify that equation to get:

(x - 3)^2 + (y + 2)^2 = 16

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Answer:

i hope this help

Step-by-step explanation:

Statement Reason

Points A, B, and C form a triangle. Given

Let be a line passing through B and parallel to . Definition of parallel lines

∠3 ≅ ∠5 and ∠1 ≅ ∠4 Definition of corresponding angles in parallel lines

m∠1 = m∠4 and m∠3 = m∠5 Substitution of corresponding angles

m∠4 + m∠2 + m∠5 = 180° Angle addition and definition of a straight line

m∠1 + m∠2 + m∠3 = 180° Substitution.

The circumferance of the circle is 131.88 inches.

The circumferance of a circle is the length of the one - dimensional curve that encloses the circle's area. Mathematically -

C = 2πr

C = πd                                  ..... Eq { 1 }

Given is a circle with diameter of 42 inches.

We can write the circumferance as -

C = 3.14 x 42

C = 131.88 inches.

Therefore, the circumferance of the circle is 131.88 inches.

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The probability that all have type B​+ blood is 0.000286 The probability that none of the have type B​+ blood is 0.572898.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Given;

The probability that a person in the United States has type B​+ blood is 13​%.

Since four unrelated people in the United States are selected at random, we can say that each person is independent of the other to have B+ blood group;

Let X be the number of persons who have blood group B+ in the group of 4 persons;

X is Binomial with p = 0.13;

a) P(X = 4) = (0.13)4 = 0.000286

b) P(x =0) = (1 -0.13)¹ = 0.572898

Therefore, the probabilities will be 0.000286 and 0.572898

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The 5th term of the geometric sequence described by an = 5(1.5)-1 is 6.5

Geometric progression,  which is also called geometric sequence, is defined as a sequence with non-zero numbers where all of the terms after the first is determined by multiplying the previous one by a fixed, non-zero number that is termed the common ratio.

The general formula for a geometric sequence is given as;

an = ar^n-1

From the information given, we have that the nth term of the geometric sequence is expressed with the equation;

an = 5(1.5)-1

expand the bracket

an = 7.5 - 1

Now, subtract the value, we get;

an = 6.5

Hence, the value of the term of the geometric sequence is 6.5

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x = 2.67 is the solution to the equation -6x + (3)(2x) = 16.

What is the Algebraic Equations?

Algebraic equations are mathematical statements that describe a relationship between two or more variables, where one variable is expressed in terms of the others.

To solve the equation -6x + (3)(2x) = 16, we can simplify the expression on the left-hand side first:

-6x + (3)(2x) = -6x + 6x = 0x = 0

Next, we isolate the x term on one side of the equation by subtracting 16 from both sides:

0x = 0 - 16 = -16

Finally, we can solve for x by dividing both sides of the equation by -6:

x = -16 / -6 = 2.67 (rounded to two decimal places).

So, x = 2.67 is the solution to the equation -6x + (3)(2x) = 16.

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The solution to the equation is given as option C

The equation says [tex]\frac{6}{5}+\frac{3}{5}x[/tex]

we have to add the fractions

[tex]\frac{1 *6 +1*3x}{5}[/tex]

= 6 + 3x / 5

Hence the correct solution to the question here is option C because[tex]\frac{6+3x}{5} = \frac{3}{5}(2+x)[/tex]

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The different ways can the program select which students will answer the five questions will be 1,72,10,368.

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, Mrs. Mortlock uses a calculator program to select students at random to answer questions during class. Each of the 28 students in her class is equally likely to be chosen every time she runs the program.

Multiplication counting principle: If the first event could occur in m ways and the second event could occur in n ways, then the number of ways that the two events could occur in the sequence is m⋅n.

There are 28 students, and each of the 28 students is equally likely to be selected to answer each question among 5 questions.

First question: 28 ways

Second question: 28 ways

Third question: 28 ways

Fourth question: 28 ways

Fifth question: 28 ways

Use the multiplication counting principle.

Thus,

Combination = 28^5

Combination = 1,72,10,368

Therefore, The different ways can the program select which students will answer the five questions will be 1,72,10,368.

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The vertex of the absolute value function y = |3x - 9| is at (3, 0).

The actual name is the vertex, and to find the vertex we first need to find the value of x such that the argument of the absolute value part becomes zero, then we need to solve:

3x - 9 = 0

3x = 9

x = 9/3 = 3

x = 3

Now we can evaluate the absolute value function there:

y = |3*3 - 9|

y = 0

The vertex is at (3, 0).

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Answer:

what is the period of the sinusoidal function?

4

Step-by-step explanation:

You're welcome.

Option D is correct, the differentiate of the equation of x³+y³=1 is dy/dx=-x²/y²

A differential equation is an equation that contains one or more functions with its derivatives.

We have to differentiate the equation of x³+y³=1

Differentiate both sides

3x²+3y²dy/dx=0

3y²dy/dx=-3x²

Divide both sides by 3y²

dy/dx=-x²/y²

Hence, option D is correct, the differentiate of the equation of x³+y³=1 is dy/dx=-x²/y²

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The surface area of the cone with a slant height of 10ft and radius of 7ft is 373.7 ft²,

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The surface area of a cone is expressed as;

A = πrl + πr²

Where r is radius of the base, l is the slant height of the cone and π is constant pi ( π = 3.14 )

From the diagram;

Plug the given values into the above formula

A = πrl + πr²

A = ( 3.14 × 7 × 10 ) + ( 3.14 × (7)² )

A = ( 219.8 ) + ( 153.86 )

A = 373.7 ft²

Therefore, the surface area is 373.7 ft²

Option B) 373.7 ft² is the correct answer.

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Work Shown:

Complementary angles add to 90 degrees.

A+B = 90

(3x+18)+(2x+17) = 90

5x+35 = 90

5x = 90-35

5x = 55

x = 55/5

x = 11

Then we can determine each angle:

As a check: A+B = 51+39 = 90 to confirm the answer.

Answer: I understand that you're feeling overwhelmed. Let's try to solve this problem together.

To evaluate the function f(x) = -3x + 5 at a specific value of x, we substitute that value into the expression and simplify. For example, if we want to evaluate the function at x = 2:

f(2) = -3 * 2 + 5 = -6 + 5 = -1

So f(2) = -1. This means that the value of the function when x = 2 is -1.

If you have any other questions or concerns, I'm here to help!

Step-by-step explanation:

Answer: X divided by 5

               X/5

Step-by-step explanation:

if x is the cost of the dinner each person pays x divided by 5 because there are 5 people

The algebraic expression of the sum of 4 consecutive even numbers is 4y + 12.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as addition, subtraction, multiplications, division etc.

Therefore, let's represent the algebraic expression for the sum of 4 consecutive even numbers.

Even numbers are numbers which when divide by 2 has no remainders.

Therefore,

let

y = first even number

Hence, the expression is as follows;

y + y + 2 + y + 4 + y + 6

y + y + y + y + 2 + 4 + 6

4y + 12

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