1.28/2.26 step by step explanation

The actual length of the house is 30 feet.

What is a scale factor?

A scale factor resembles a unit scale in several ways. It is a ratio that assesses the relationship between scale and real dimensions. Because it doesn't provide any specified units, it differs.

It is given that:

Width of the kitchen = 4 inches.

Length of the kitchen= 6 inches.

It is also given that the actual width of the house is equal to 20 feet.

Now we have to find the length of the house:

The proportion will be:

[tex]\frac{4}{6} =\frac{20}{Length} \\Length=\frac{20*6}{4} \\Length=30feet[/tex]

Therefore the actual length of the house is 30 feet.

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The length of the side is 12 units in simplest radical form with a rational denominator.

A triangle is said to be equilateral if all of its sides and angles are equal. An equilateral triangle is also known as an equiangular triangle since each of its angles has a value of 60 degrees.

Given:

The triangle given in the image is an equilateral triangle.

That means the angle measure of the triangle is 60° each.

And all the sides are equal.

To find the value of x:

Sin(60/2)° = opposite/ hypotenuse.

Sin30° = x/6

x = 6/Sin30°

[tex]x = \frac{6}{1/2}[/tex]

x = 6(2)

x = 12

Therefore, the value of x is 12 units.

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The complete question:

The triangle below is equilateral. Find the length of the side in simplest radical form with a rational denominator.

The image is given below.

Answer:

To estimate the number of seventh-graders who attend summer camp, we can use the sample proportion of 30 out of 200 students.

Let's call the population proportion of seventh-graders who attend summer camp "p".

The sample proportion can be estimated as:

p = 30/200 = 0.15

To estimate the number of seventh-graders in the entire school who attend summer camp, we can multiply the population size by the sample proportion:

Estimated number of seventh-graders attending summer camp = p * population size = 0.15 * 780 = 117

So, about 117 seventh-graders in the school are expected to attend summer camp.

Answer:

117 seventh-graders in the school are expected to attend summer camp.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can use the formula for the future value of an annuity to find the amount you'll have in the account at the end of Year 6. An annuity is a series of equal payments made at equal intervals of time, and the future value of an annuity is the amount you'll have in the future if you invest those payments and earn a given rate of interest.

The formula for the future value of an annuity is:

FV = PMT * (((1 + r)^n - 1) / r)

where:

FV = future value of the annuity

PMT = annual payment amount

r = annual interest rate as a decimal

n = number of payments

In this case:

PMT = $1,500

r = 0.05

n = 6

Plugging in the values:

FV = $1,500 * (((1 + 0.05)^6 - 1) / 0.05)

FV = $1,500 * (1.328867 - 1) / 0.05

FV = $1,500 * 0.328867 / 0.05

FV = $1,500 * 6.577340

FV = $9,865.61

So, the amount in the account at the end of Year 6 will be $9,865.61. To find the last payment, we subtract this amount from the desired future value of $10,000:

$10,000 - $9,865.61 = $134.39

Therefore, your last payment will be $134.39.

Answer:

Step-by-step explanation:

The floor-to-ceiling clearance is 7 ft 5 in, which is equal to 7 * 12 + 5 = 89 inches.

We need to construct 8 shelves, each of which is 1 inch thick, so the total thickness of the shelves is 8 * 1 = 8 inches.

We also need to leave an equal space between each shelf and the next, the top shelf and the ceiling, and the bottom shelf and the floor. So, there will be 7 equal spaces in total (6 between shelves and 1 between the bottom shelf and the floor).

Therefore, the space between each shelf and the next will be (89 - 8) / 7 = 11 inches.

Here's a step by step solution:

Calculate the total height of the room in inches: 7 ft 5 in = 7 * 12 + 5 = 89 inches.

Calculate the total thickness of all the shelves: 8 shelves * 1 inch/shelf = 8 inches.

Deduct the thickness of the shelves from the height of the room to find the total space available: 89 inches - 8 inches = 81 inches.

Divide the total space available by the number of spaces (7) to find the space between each shelf and the next: 81 inches / 7 = 11 inches.

The value of x at the point of intersection is given as follows:

x = -1.

We must test for both definitions of the second function, and find which solution is in the correct range.

For the first definition, the solution is given as follows:

2x + 1 = x

2x - x = -1

x = -1.

-1 is less than 1, hence x = -1 is one solution to the system of equations.

For the second definition, the solution is given as follows:

2x + 1 = -x + 2

3x = 1.

x = 1/3.

Which is less than one, while the function is defined for values greater than 1, hence it is an extraneous solution.

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The given expression can be written in a single radical as q³ .   [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]. The solution has been obtained by solving the radical expressions.

What are radical expressions?

An expression which contains a square root is referred to as a radical expression. The 'V'-shaped portion of the radical sign will have a superscript number when it is used to represent any root other than a square root.

We are given √q³ [tex]\sqrt[3]{q^{8} }[/tex].

On simplifying the expression, we get

⇒√q² . q [tex]\sqrt[3]{q^{3} . q^{3} . q^{2} }[/tex]

⇒q . √q . q² .  [tex]\sqrt[3]{ q^{2} }[/tex]

⇒q³ . √q  [tex]\sqrt[3]{ q^{2} }[/tex]

⇒q³ . [tex]\sqrt[]{ q^{\frac{1}{2} + \frac{2}{3} } }[/tex]

⇒q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]

Hence, the given expression can be written  in a single radical as q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex].

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The g-intercept of the function g(n) is 0.

The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.

What is a function?

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range), such that each input is related to exactly one output.

To find the g-intercept of a function, we need to determine the value of g when n = 0. So, to find the g-intercept of the function g(n) = 2n⁴+ 20 n³ + 42n², we can simply substitute n = 0 into the function:

g(0) = 2(0)⁴ + 20 (0)³ + 42(0)² = 0

Therefore, the g-intercept of the function g(n) is 0.

To find the n-intercepts of a function, we need to determine the values of n for which g(n) = 0. In other words, we need to solve the equation 2n⁴+ 20 n³ + 42n² = 0.

We can factor out a common factor of 2n² to simplify the equation:

2n²(n² + 10n + 21) = 0

This equation is true when either 2n² = 0 (which implies n = 0), or when n² + 10n + 21 = 0. The quadratic equation n² + 10n + 21 = 0 can be factored as (n + 3)(n + 7) = 0, so its solutions are n = -3 and n = -7.

The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.

Hence,

The g-intercept of the function g(n) is 0.

The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.

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Answer:

  45°

Step-by-step explanation:

Given a polygon with an interior angle of 135°, you want to know the measure of the corresponding exterior angle.

At any given vertex of a polygon, the interior and exterior angles are supplementary:

  exterior angle = 180° - interior angle

  exterior angle = 180° -135°

  exterior angle = 45°

Answer: The sum of the interior angles of a regular polygon can be found using the formula:

(n-2)180°, where n is the number of sides of the polygon.

Let's call the number of sides of the polygon "s".

We know that one of the interior angles is 135°, so we can set up an equation using the formula for the sum of the interior angles:

s * 135° = (s-2)180°

Expanding the right side of the equation:

s * 135° = (s-2) * 180°

s * 135° = s * 180° - 360°

Solving for s:

135° = 180° - 360°/s

135° = 180° - 2 * 180°/s

135° = 180° - 2 * (180°/s)

180° - 135° = 2 * (180°/s)

45° = (180°/s)

So, s = 180° / 45° = 4 sides.

The size of one exterior angle can be found by subtracting each interior angle from 360°:

360° - 135° = 225°.

Therefore, one exterior angle of the polygon is 225°.

Step-by-step explanation:

The number of students who either play hockey or football is given by the equation n ( A ∪ B ) = 45 students

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the total number of students in the class be n ( U ) = 50 students

Let the number of students who play hockey be n ( A ) = 20 students

Let the number of students who play football be n ( B ) = 35 students

Let the number of students who play hockey and football n ( A ∩ B ) = 10

So , from the set theory n(A∪B) = n(A) + n(B) - n(A⋂B)

Substituting the values in the equation , we get

The number of students who play hockey or football = 20 + 35 - 10

On simplifying the equation , we get

The number of students who play hockey or football = n( A ∪ B ) = 45 students

And , the number of students who do not play hockey or football is given by the equation = n ( U ) - n ( A ∪ B )

On simplifying the equation , we get

The number of students who do not play hockey or football = 50 - 45 = 5 students

Hence , the number of students who play hockey or football is 45 students

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300 people read neither​ of the papers.

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. It is a fundamental theory in mathematics and can be used as a foundation for all other areas of mathematics.

Total population n(ξ) = 5000

Number of people reading Concord, n(C) = 2800

Number of people reading Guardian, n(G) = 2300

Number of people reading both = n(C ∩ G)] = 400

Number of people reading any of the newspaper = n(C ∪ G)] = n(C) + n(G) - n(C ∩ G) = 2800 + 2300 - 400 = 4700.

Number of people reading none of them is equal to = Total population - Number of people reading any of the newspaper = 5000 - 4700 = 300

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Answer: A tangent to the x-axis means that the y-coordinate of the point of tangency is 0. So, we can find the possible values of d by setting y = 0 and solving for x:

0 = x^3/3 + 7x^2/2 + 10x + d

This is a cubic equation, so it can be solved using various methods such as factoring, completing the square, or using a numerical method such as the Newton-Raphson method. If the equation can be factored or the method used is numerical, there might be multiple possible values of d. If the method used is completing the square, there would be only one possible value of d.

However, without a specific method, it's not possible to find the exact value(s) of d. The possible values of d will depend on the specific solution method used to solve the equation.

Step-by-step explanation:

Answer: 12.8 cm

Step-by-step explanation:

Multiply 3.2 by the scale of 4 to get 12.8.

The polynomial function of degree 4 is,

⇒ f (x) = 5 (x + 3)² (x - 3)²

Relation between set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.

Given that;

Zeroes of function is,

⇒ -3 (multiplicity 2) and 3 (multiplicity 2),

And, It passes through the point (-4,245).

Now, The polynomial function of degree 4 is,

⇒ f (x) = A (x - (- 3))² (x - 3)²

⇒ f (x) = A (x + 3)² (x - 3)²

Since, It passes through the point (-4,245).

Hence, Put x = - 4, y = 245

⇒ 245 = A (- 4 + 3)² (- 4 - 3)²

⇒ 245 = A (- 1)² (- 7)²

⇒ 245 = A × 49

⇒ A = 245/49

⇒ A = 5

Thus, The polynomial is,

⇒ f (x) = A (x + 3)² (x - 3)²

⇒ f (x) = 5 (x + 3)² (x - 3)²

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The surface area of hexagonal prism A is 9√3x² cm². We are given that hexagonal prism B is the image of hexagonal prism A after dilation by a scale factor of 2.

Therefore, all corresponding sides of prism A and prism B are in the ratio of 1:2. Let the side length of the base of hexagonal prism A be 'x'. Then, the side length of the base of hexagonal prism B is '2x'.

We know that the surface area of hexagonal prism B is 172 cm². Using the formula for the surface area of a hexagonal prism, we can write:

172 = 2(3√3)(2x)^2 + 6(2x)h

where h is the height of hexagonal prism B.

Simplifying this equation, we get:

172 = 24√3x² + 12xh

Dividing both sides by 12, we get:

14.33 = 2√3x² + h

Now, since hexagonal prism B is a dilation of hexagonal prism A by a scale factor of 2, the height of hexagonal prism A is half the height of hexagonal prism B. So, the height of hexagonal prism A is h/2.

Using the formula for the surface area of a hexagonal prism, we can write:

SA(A) = 2(3√3)x² + 6x(h/2)

Substituting h/2 for the height of hexagonal prism A, we get:

SA(A) = 2(3√3)x² + 3xh

Substituting 2√3x² + h/2 for h, we get:

SA(A) = 2(3√3)x² + 3x(2√3x² + h/2)

SA(A) = 6√3x² + 3√3x² + (3/2)xh

Substituting 2√3x² for h in the above equation, we get:

SA(A) = 6√3x² + 3√3x² + (3/2)x(2√3x²)

SA(A) = 9√3x²

Therefore, the surface area of hexagonal prism A is 9√3x² cm².

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The statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.

In relation to the original function f, the inverse function is denoted by the symbol f⁻¹, and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function.

We know that inverse of function is NOT the reciprocal of f. The composition of the function f and the reciprocal function f inverse gives the domain value of x.

Hence, the statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.

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Tony m,ay or may not afford the car insurance

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

Yearly pay = $8300 (approximated)

Insurance = 1/30 of his rounded yearly pay

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

Insurance= 1/30 * $8300

Evaluate

Insurance=  $276.7

Additional information about Tony's expenses and financial situation are needed to determine if he can afford the monthly car insurance or not.

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The value of delta such that the statement is true is:

δ = 0.0002

We want to find δ such that:

if |x -3| < δ, then |5x - 15| < ε

So we have two absolute value inequalities to work with.

With ε = 0.001

If we take the second inequality and replace epsilong, we will get:

|5x - 15| < 0.001

We can take 5 as a common factor on the left side to get:

5*|x - 3| < 0.001

Dividing both sides by 5 gives:

|x - 3| < 0.001/5

|x - 3| < 0.0002

Then the value of delta is 0.0002.

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The length of line segment DL of the system of similar triangles is 4√3. The length of line segment BD of the system is √3.

Two triangles are similar if they have congruent angles and if their sides are not congruent though proportional. The statement of the problem can be described by following equations:

Proportion formula

AD / BD = DL / AD

DL = 4 · BD

Then, we find the formula for line segment DL:

AD / BD = 4 · BD / AD

AD² = 4 · BD²

BD = √(AD / 2)

If we know that AD = 6, then the length of line segment DL:

BD = √3

DL = 4√3

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Answer:

x= -5

Step-by-step explanation:

4(x + 3) = -8

4x + 12 = -8

4x = -20

x = -5

The value of x in the proportion equals 50.

Proportion is referred to as a part, share, or number considered in comparative relation to a whole. Proportion can be defined as when two ratios are equivalent, they are in proportion. It is an equation or statement used to show that two ratios or fractions are equal.

In proportion, if two sets of numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol  ":" or "=".

16/50 = x/156.25

x = 156.25 x 16 / 50

x = 2500 / 50

x = 50

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Banks and other financial institutions may offer cash loans for reasons like revenue generation and marketing

Banks and other financial institutions may offer cash loans to people who did not apply for them for several reasons which include

Other reasons include:

Risk management, Customer convenience, Mistakes/Errors

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The percent of the world's total production of bikes that is contributed by United States is 0.65%.

Production refers to the process of combining different inputs, both material and immaterial, to produce output. Ideally, this output will be a valuable good or service that adds to people's utility.

Data

Number of bikes produced by US = 815,000 bikes.

Number of bikes produced by the world population = 126 million bikes.

The percent of the world's total production of bikes that is contributed by U.S will be:

= (0.815/126) × 100

= 0.00646825396 * 100

= 0.65%.

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The system of equations which has infinitely many solutions as required to be determined is; Choice D; 2x + y = 5 and 4x + 2y = 10.

By the standards of linear geometry, two equations have infinitely many solutions when their graphs coincide and in which case, they have the same slope and y-intercept.

Therefore, the system of equations which satisfy the said criterion is; 2x + y = 5 and 4x + 2y = 10.

Ultimately, the correct answer is; Choice D; 2x + y = 5 and 4x + 2y = 10.

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The mean of the sampling distribution is given as follows:

37.827 millimeters.

The mean of the sampling distribution is obtained using the Central Limit Theorem.

The mean of the sampling distribution is the same as the population mean, hence it is given as follows:

37.827 millimeters.

(on the problem, we are given the population mean).

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Answer:

PR and SQ have the same midpoint.

Step-by-step explanation:

PR and SQ have the same midpoint.

Answer:

Step-by-step explanation:

To find the base of the exponential function F(x) = b^x, we need to use the information that its graph contains the point (1/3, 2). We can use this information to solve for b.

Since the graph passes through the point (1/3, 2), we can set x = 1/3 and y = 2 in the equation F(x) = b^x:

b^(1/3) = 2

Taking the cube root of both sides, we get:

b = (2)^3 = 8

So the base of the exponential function F(x) = b^x is b = 8, which means the correct answer is C) 8.

The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

What is meant by continuous compounding?

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.

Given,

rate per period  = 3%

Principal amount = $1000

Compounding is done after 1,5 and 20 years.

But we are asked to find the amount after continuous compounding after 1 year.

The formula of the amount after continuous compounding is:

[tex]A = Pe^{rt}[/tex]

where A = amount after continuous compounding

        r = rate of period

     t = time period

    P  = principal amount

[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45

Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]

n = times it compounds per year = 365

r = 0.03

AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]

                                  = 3.04%

Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

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The dual problem of the primal problem "Maximize Z = 7X1 + 5X2, Subject to X1 + 2X2 ≤ 6, 4X1 + 3X2 ≤ 12, X1, X2 ≥ 0" is:

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Greater than (or greater than or equal to), less than (or less than or equal to), or not equal to signs are used in place of the equal sign.

Minimize Z = 6Y1 + 12Y2

Here

Y1 + 4Y2 ≥ 7

2Y1 + 3Y2 ≥ 5

Y1, Y2 ≥ 0

(b) The dual problem of the primal problem "Maximize Z = 3X1 + 4X2, Subject to 5X1 + 4X2 ≤ 200, 3X1 + 5X2 ≤ 150, 8X1 + 4X2 ≥ 80, X1, X2 ≥ 0" is:

Minimize Z = 200Y1 + 150Y2

Subject to:

4Y1 + 5Y2 ≥ 3

5Y1 + 3Y2 ≥ 4

4Y1 + 8Y2 ≤ -80

Y1, Y2 ≥ 0

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"Your question is incomplete, probably the complete question/missing part is:"

Write the dual of following problems:

(a) Maximize Z = 7X1 + 5X2

Subject to:

X1 + 2X2 ≤ 6

4X1 + 3X2 ≤ 12

X1, X2 ≥ 0

(b) Maximize Z= 3X1 + 4X2

Subject to:

5X1 + 4X2 ≤ 200

3X1 + 5X2 ≤ 150

8X1 + 4X2 ≥ 80

X1, X2 ≥ 0

Answer: To verify the identity, we need to convert both sides into sines and cosines and see if they are equal.

Starting with the left side:

cotx = 1/tanx

So,

cotx - tanx = 1/tanx - tanx

Using the identity tan^2x = sec^2x - 1, we get

cotx - tanx = (sec^2x - 1) / tanx

Expanding the right side using the definition of cscx and sinx, we get:

cotx - tanx = secx(1/sinx - 2sinx)

So,

cotx - tanx = secx(cscx - 2sinx)

Since both sides are equal, we can conclude that the identity is verified.

Step-by-step explanation: