solve the equation
x/2-2=4+1/2

Answer: The width of the rectangular window is 53 cm.

Step-by-step explanation:

We know that the area of a rectangle is given by the formula:

Area = Length x Width

Substituting the given values, we have:

3816 cm² = 72 cm x Width

To solve for the width, we can divide both sides by 72 cm:

Width = 3816 cm² ÷ 72 cm

Width = 53 cm

Therefore, the width of the rectangular window is 53 cm.

The given system of equations above is graphed in the xy -plane, then the x-coordinate of the intersection point (x, y) is -1.0625.

What is the system of equations?

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.

There are different methods to find the solution of a system of two equations in two variables, but one common one is to use elimination or substitution. Here, we will use substitution.

From the first equation, we can isolate x in terms of y by adding 1.5y to both sides and dividing by 2.4:

2.4x - 1.5y = 0.3

2.4x = 1.5y + 0.3

x = (1.5/2.4)y + 0.3/2.4

x = 0.625y + 0.125

Now we substitute this expression for x into the second equation and solve for y:

1.6x + 0.5y = −1.3

1.6(0.625y + 0.125) + 0.5y = −1.3

1.0y = −1.8

y = −1.8/1.0

y = −1.8

Finally, we substitute this value of y back into either equation to find the corresponding x-coordinate:

x = 0.625y + 0.125

x = 0.625(-1.8) + 0.125

x = −1.0625

Therefore, the x-coordinate of the intersection point (x, y) is -1.0625.

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Answer:

D) x = 1,200 + 1,200(0.025)(9)

In this equation, 1,200 is the initial deposit, 0.025 is the decimal representation of the annual interest rate, and 9 represents the time period in months. The multiplication of 0.025 and 9 gives the proportion of interest earned in 9 months, which is then multiplied by the initial deposit and added to it to give the total amount in the account after 9 months.

Simplifying the equation:

x = 1,200 + (1,200)(0.025)(9)

x = 1,200 + 270

x = 1,470

Therefore, there would be $1,470 in the account after 9 months

Answer:

We can use the formula for the area of a rectangle to solve this problem. Let's assume that the length of the top of the bookcase is L and the width is b. Then, we can write:

L × b = 300

Solving for b, we get:

b = 300 / L

Since we don't know the length L, we cannot find the exact value of b. However, we can use the given information to make an estimate. Let's say that the length of the bookcase is 60 inches. Then, we have:

b = 300 / 60 = 5

So, if the length of the bookcase is 60 inches, the width needs to be at least 5 inches to accommodate Bria's soap carving collection. However, if the length is different, the required width will also be different.

a. The cοmplement οf the given angle is 38 degrees.

b. The supplement οf the given angle is 128 degrees

Twο angles are said tο be cοmplementary if their measurements sum up tο 90 degrees. They are, in οther wοrds, angles that "cοmplete" οne anοther tο create a right angle. As an illustratiοn, if οne angle is 30 degrees, its cοunterpart is 60 degrees.

Twο angles are said tο be supplementary if their sums equal 180 degrees. They are, in οther wοrds, angles that "cοmplete" οne anοther tο create a straight line. If οne angle is 120 degrees, fοr instance, its cοmplement is 60 degrees.

Given the measure οf the angle is 52 degrees.

The cοmplement οf the angle is, when it is added with a angle and the result is 90.

Thus,

90 - 52 = 38

The supplement οf an angle is when the result οf additiοn is 180 degrees.

Thus,

180 - 52 = 128

Hence, the complement of the given angle is 38 degrees. b. The supplement of the given angle is 128 degrees

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Answer:

Answer:

Step-by-step explanation:

y=cos2x

y1=-2sin2x=2cos(2x+π/2)

y2=-2*2sin (2x+π/2)=2²cos(2x+π/2+π/2)=2²cos(2x+2*π/2)

y3==2²*-2sin(2x+2*π/2)=2³cos(2x+2*π/2+π/2)=2³cos(2x+3π/2)

......................................................................................................

y45=2^{45}cos(2x+45π/2)

The possible values of TP in isosceles triangle are between 5.5 and infinity.

Let TP = x. Then we have:

TI = TP = x (isosceles triangle)

PI = TP - PI = x - 7 (isosceles triangle)

PO = TP + OP = x + 11 (triangle inequality)

Using the fact that the sum of any two sides of a triangle must be greater than the third side, we have:

x + x > 11 --> x > 5.5

x + 11 > x --> 11 > 0

x + 7 > 5 --> x > -2

Therefore, the possible values of x are between 5.5 and infinity. The sum of all possible values of x is infinity since there is no upper bound on the possible values.

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_____The given question is incomplete, the complete question is given below:

Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What is the sum of all possible lengths for TP?

The value of f⁻¹(3) is 1/3. The value of f⁻¹(12) is -14/3. The complete table is:

X 0 1 2

f(x) 2 5 8.

A function is a mathematical rule that assigns a unique output or value for each input or value in a set. It is a relationship between two sets of numbers, called the domain (input) and range (output), such that each input value is associated with exactly one output value. A function is usually denoted by a letter such as f, and its input is represented by x, while its output is represented by f(x). The concept of a function is a fundamental one in mathematics and has many applications in various fields, including physics, engineering, economics, and more.

Here,

To find the values of f(x), we substitute the given values of x in the function f(x) = 3x + 2:

X 0 1 2

f(x) 2 5 8

To find f⁻¹(3), we first replace f(x) with 3 in the equation f(x) = 3x + 2:

3 = 3x + 2

Solving for x, we get:

x = 1/3

Therefore, f⁻¹(3) = 1/3.

To find f⁻¹(-12), we replace f(x) with -12 in the equation f(x) = 3x + 2:

-12 = 3x + 2

Solving for x, we get:

x = -14/3

Therefore, f⁻¹(-12) = -14/3.

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To remove the y-term in  the given linear equation in two Variable multiply the equation by 4 then add these two equations.

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. Yet, there are two solutions to a linear equation with two variables.

According to given question;

5X+8y=5   ……..eqn 1.

3x-2y=3    ………eqn 2.

Multiply by 4 in the eqn 2.

We get

12x-8y=12 ……..eqn 3 .

When we add eqn 1 and eqn 3 we get ;

17x =17

X =1

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After eliminating the y-term in the given equations i.e 5x+8y=5 and

3x-2y=3, The solution to the system of equations is x = 1, y = 0.

The elimination method is the technique used to solve systems of linear equations. It involves adding or subtracting equations in a system to eliminate one variable and find the value of the other variable.

To eliminate the y-term in these equations, you can multiply the second equation by 4, which will give you:

12x - 8y = 12

Now, you can add this equation to the first equation:

5x + 12x + 0y = 5 + 12

Simplifying the left side gives you 17x, and simplifying the right side gives you 17. So, you have the equation:

17x = 17

Solving for x gives you x = 1.

Now that you have found the value of x, you can substitute it into one of the original equations to solve for y. Using the first equation, you get:

5(1) + 8y = 5

Simplifying this equation gives you:

8y = 0

Solving for y gives you y = 0.

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Answer:

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

There are 3 of 3's  and 2 of 5's out of 12 sides.

The probability of rolling either 3 or 5 is:

Answer:

36

9

1/4

Step-by-step explanation:

hope I helped ya :]

Answer:

12075

Step-by-step explanation:

Simply multiply both terms together

483 x 25 = 12075

Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.

The above statement is True.

In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.

A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.

Sometimes the term linear function has the same meaning as linear map, but not in analysis.

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Triangle ADE has a surface area of 75 cm².

Triangle area determination. Use the equation area = 1/2 * base * height to determine a triangle's surface area. Decide which side will serve as the triangle's base, then calculate the triangle's height from that base.

Using similarity to determine y's value

AD/BD = AE/BE

y/(a-x) = y/x

yx = y(a-x)

x = a/2

This fact can be used to determine the height of the trapezoid:

h = √(BC² - [(AB-DC)/2]²)

= √(10² - [2²]²)

= 8

Now that we know how long MD is, we can:

As a result of the triangles ADE and BDE's resemblance, we can now determine the value of y:

y/BD = AE/BE

y/(a-x) = y/x

yx = y(a-x)

x = a/2

Substituting x = a/2 and BD = AB - DC = 10 - 6 = 4, we get:

y/4 = AE/(a/2)

y = 2AE/a

Substituting y = 2AE/a in the above equation, we get:

(2AE/a)/4 = AE/(a/2)

AE = (a/2)²/2

We may now apply the triangle's area formula, ADE:

Area of ADE = (1/4) x y x (a+b)

= (1/4) x 2AE/a x (a+b)

= (1/8) x (a²/2) x (a+b)

= (1/16) x a² x (a+b)

Substituting a = 10 and b = 6, we get:

Area of ADE = (1/16) x 10² x (10+6)

= 75 cm².

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Two radicals are said to be radicals if they have the same indices and the radicand.

In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:

3√(pq) → pq is the radicand

√(a+b) → a + b is the radicand

4√15 → 15 is the radicand

A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.

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Complete question:

Type the correct words in the blanks:

Two radicals are said to be radicals if they have the same               and the radicand.

Answer:

150 cm2

Step-by-step explanation:

Given side of cube's area = 25. Since Side's a square,

Edge^2 = 5^2 = 5 cm

Total surface area: 6*a² = 6*5*5 = 150 cm2

Caludia needs to pay 2917.6128 as a payment of compound interest capital+interest.

What is compound interest?

compound interest is interest on principal + interest and this denotes to the addition of interest to the principal amount of a loan or deposit.

Capital(p) = $6400

Rate of interest(r) = 11%

Years(n) = 3

The general formula of compound interest is [tex]A= p(1+\frac{r}{100}})^n[/tex].

Now

[tex]A= 6400(1+\frac{11}{100}})^3\\A=6400 \times \frac{111}{100} \times \frac{111}{100} \times \frac{111}{100}\\A= 8752.8384[/tex]

The entire amount (Capital+interest) is equal to $8752.8384.

If we take 1 year as a period then Claudia needs to pay [tex]\frac{8752.8384}{3}\\=2917.6128[/tex]

Therefore, Claudia needs to pay 2917.6128 as a payment of compound interest capital+interest.

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When coffee beans sell for $5 per pound, producers supply 9 million pounds. This indicates that at a higher price, producers are willing to supply a larger quantity of coffee beans.

This means that at a lower price, producers will supply a smaller quantity of coffee beans. Conversely, when the price of coffee beans increases to $15 per pound, producers supply 40 million pounds.

The relationship between price and quantity supplied is a fundamental concept in economics. When prices are lower, producers may not have enough incentive to produce and supply goods. On the other hand, when prices are higher, producers may have more incentive to produce and increase their supply. This is often referred to as the law of supply.

Understanding this relationship is important for businesses and policymakers to make informed decisions about pricing and production. By analyzing market trends and the behavior of producers, they can adjust prices to maintain a balance between supply and demand. For example, if prices are too high, it may lead to a surplus of goods that cannot be sold, while prices that are too low may result in shortages or supply constraints.

In conclusion, the relationship between price and the supply of coffee beans reflects a broader economic principle that is essential for understanding how markets work. By examining the supply curve, we can gain insights into how producers respond to changes in price, and use this information to make informed decisions about pricing and production.

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Answer:

3n squared+n+2

Answer:

the nth term of the sequence is 2n² + 4T

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Step-by-step explanation:

he sequence represents a quadratic function, the nth term of the sequenceis 2n² + 4 

The nth term of a quadratic sequence is :an² + bn + c c = zeroth term ; a = second difference ÷ 2

From the sequence :First difference = 6, 10, 14, 18Second difference = 4, 4, 4

 First difference between terms in position 1 and 0 :6 - 4 = 2 

Zeroth term = First term in sequence - 2 = 6 - 2 = 4a = 4/2 = 2

Plugging the values into the equation :2n² + bn + 4 Using the 2nd term :n = 22(2)² + 2b + 4 = 128 + 2b + 4 = 12 2b = 12 - 12 2b = 0b = 0

Hence, the nth term of the sequence is 2n² + 4

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It involves selecting 35 candies from a bag containing 20 strawberry, 20 cherry, and 10 orange Starburst candies. X is the number of strawberry candies selected. X has a hypergeometric distribution, with possible values from 0 to 20. P(X > 18) is 0.0125, and probability mass function P(X = 3) is 0.0783. The expected value of X is 14, and the variance of X is approximately 5.67.

X has a hypergeometric distribution with parameters M=40 (20+20), N=50 (20+20+10), and n=35.

X can take on values from 0 to 20, since there are only 20 strawberry candies in the bag.

Using the cumulative distribution function for the hypergeometric distribution, we have P(X > 18) = 0.0125.

Using the probability mass function for the hypergeometric distribution, we have P(X = 3) = 0.0783.

The expected value of X is E[X] = np = 35(20/50) = 14.

The variance of X is Var[X] = np(1-p)(N-n)/(N-1) = (35)(20/50)(30/49)(40/49) ≈ 5.67.

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Answer:

Step-by-step explanation:

Solve for x

(x-14)+(2x+8)= 180

3x-14+8=180

3x-6=180

3x=186

x=62degrees

Solve for y

(7y-15)+62=180

7y+47=180

7y=180-47

7y=133

y=19degrees

If a whole number has a whole number square root, it means that there exists a number that you can multiply by itself to get that number.

Let us understand this statement by taking example, the whole number 9 has a whole number square root, which is 3. This means that 3 multiplied by itself gives 9: 3 x 3 = 9. Similarly, the whole number 16 has a whole number square root, which is 4. This means that 4 multiplied by itself gives 16: 4 x 4 = 16.

However, not all whole numbers have whole number square roots. For example, the whole number 2 does not have a whole number square root, which means that there is no whole number you can multiply by itself to get 2. In this case, we would say that 2 is an "irrational" number, because its square root is not a whole number or a fraction of whole numbers.

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The workload of the resource is 20.5 units.

To calculate the workload of a resource that serves different flow unit types, one must know the amount of flow units, the processing time for each flow unit, and the number of resources available. This is best calculated using Little's Law, which states that the average number of flow units in a system is equal to the average rate of flow units multiplied by the average time they spend in the system.

For example, if a resource is serving 3 flow unit types, A, B and C, with 10, 8 and 5 units respectively, and a processing time of 2 minutes, 1 minute and 3 minutes respectively, with 2 resources available, the workload can be calculated as follows:

Workload = (10*2 + 8*1 + 5*3) / 2

       = 41 / 2

       = 20.5 units

Therefore, the workload of the resource is 20.5 units.

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Complete question

What are the flow unit types that the resource is serving?

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

A = the final amount (6700 dollars)

P = the principal amount (5500 dollars)

r = the annual interest rate (4.5% or 0.045)

n = the number of times the interest is compounded per year (once annually)

t = the time period (in years) for which the money is invested

Substituting these values in the formula, we get:

6700 = 5500(1 + 0.045/1)^(1t)

Dividing both sides by 5500, we get:

1.21818181818 = 1.045^t

Taking the logarithm (base 10) of both sides, we get:

t = log(1.21818181818) / log(1.045)

Solving this equation using a calculator, we get:

t ≈ 4.4

Therefore, the person must leave the money in the bank for approximately 4.4 years (to the nearest tenth of a year) until it reaches 6700 dollars.

Answer:

The total number of ways to choose 2 students from a class of 16 is given by the combination formula:

C(16,2) = 16! / (2! * (16-2)!) = (1615) / (21) = 120

This means there are 120 possible pairs of students that could be drawn.

The probability of you and your best friend being chosen is the number of ways that you and your friend can be selected divided by the total number of possible pairs. There is only 1 way to select you and your best friend out of the class of 16, so the probability is:

P(you and your best friend are chosen) = 1/120

Therefore, the probability that you and your best friend will be chosen is 1/120. Option (B) is the correct answer.

Answer:

The probability of choosing one specific student out of 16 is 1/16. After one student is chosen, there are 15 students left, so the probability of choosing the second specific student out of the remaining 15 is 1/15. The probability of both events happening is the product of the probabilities: (1/16) x (1/15) = 1/240. However, there are two ways that the students can be chosen (your friend first, then you or you first, then your friend), so we need to multiply the probability by 2: 2 x (1/240) = 1/120. Therefore, the probability of you and your best friend being chosen is 1/120. Answer: 1/120.

The polynomial's value is Degree: 2 (because x has a maximum power of 2), Degree: 2 (since x has a maximum power of 2), and Degree: 1 (since x has a maximum power of 1).

A polynomial is an equation made up of exponents, constants, and variables that is combined using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).

Expanding the provided expression, we obtain: Polynomial 1

6x2 + 2x - 24x - 8 = (x-4)(6x+2) = 6x2 - 22x - 8

When we condense the phrase, we get:

3

(3x² - 11x - 4)

Level: 2

Amount of terms: 1

2nd polynomial:

(7x² + 3x) Degree: (21x2 - 12) = 7x2 + 3x - (21x2 + 12) = -14x2 + 3x + 12 2 (because the maximum power of x is 2)

Polynomial 3: 2(-10x2 + 18x + 13) + 4(5x2 + 9x + 7) = 20x2 + 36x + 28 - 20x2 + 36x + 26 = 72x + 54

Grade: 1

There is one term.

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Answer:

C: 8, 9, 10

Step-by-step explanation:

Answer:

4.5y

subtract 2.9y from 7.4y, and you get 4.5y

Answer: an = 128 * (1/4)^n

Step-by-step explanation:

The given sequence is not an arithmetic or geometric sequence, but we can try to find a pattern using algebra. Let's assume that the formula for the nth term is of the form:

an = a * b^n

where a and b are constants to be determined. We can find these constants by using the first two points:

a * b^1 = 32 (when n = 1)

a * b^2 = 8 (when n = 2)

Dividing the second equation by the first, we get:

b^1 = (8/32) / (1/2) = 1/4

Substituting this value of b in the first equation, we get:

a * (1/4)^1 = 32

a = 128

Therefore, the formula for the nth term is:

an = 128 * (1/4)^n

We can check this formula using the other given points:

a2 = 128 * (1/4)^2 = 8

a3 = 128 * (1/4)^3 = 2

a4 = 128 * (1/4)^4 = 0.5

So the formula holds for all the given points.