Question: QUESTIONS In a data set, the interquartile range is 18, and the third quartile is 95. What is the value that corresponds to the 25th percentile?

Answer: The first answer choice

AKA: y = -1.74x + 46.6

Step-by-step explanation:

The solutions to the quadratic equation by factoring 12x² - 12x + 3 = 0 are x = 1/2.

To solve the quadratic equation 12x² - 12x + 3 = 0 by factoring, we need to find two binomials whose factors multiply to give the quadratic equation.

Let's begin by multiplying the coefficient of x² (12) and the constant term (3). We get 12 × 3 = 36.

Now, we need to find two numbers that multiply to 36 and add up to the coefficient of x (-12). In this case, the numbers are -6 and -6 because (-6) × (-6) = 36, and (-6) + (-6) = -12.

Using these numbers, we can rewrite the middle term of the quadratic equation:

12x² - 6x - 6x + 3 = 0

Now, let's group the terms:

(12x² - 6x) + (-6x + 3) = 0

Factor out the greatest common factor from each group:

6x(2x - 1) - 3(2x - 1) = 0

Notice that we have a common binomial factor, (2x - 1), which we can further factor out:

(2x - 1)(6x - 3) = 0

Now, we can set each factor equal to zero and solve for x:

2x - 1 = 0    or    6x - 3 = 0

Solving the first equation, we add 1 to both sides:

2x = 1

Divide both sides by 2:

x = 1/2

Solving the second equation, we add 3 to both sides:

6x = 3

Divide both sides by 6:

x = 1/2

Therefore, the solutions to the quadratic equation 12x² - 12x + 3 = 0 are x = 1/2.

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Answer:

Step-by-step explanation:

it’s 9.55 au

Saturn is 9.57 au  far from the sun

Kepler's third law, also called the law of periods, states that the square of the orbital period is proportional to the cube of its mean distance R.

Let time period of earth = T (e)

Time period of Saturn will be = T(s) = 29.5 T(e)

(since , it is given that Saturn orbits every 29.5 years )

distance of earth from sun = r(e) = 1.5 * \(10^{11}\) m

distance of Saturn from the sun = r(s) = ?

using Kepler's third law

\(T^{2}\) is directly proportional to \(r^{3}\)

\(T(s)^{2}\)/\(T(e)^{2}\) = \(r(s)^{3}\) / \(r(e)^{3}\)

r(s) = r(e) \((T(s) / T(e))^{2/3}\)

r(s) = 14.32 * \(10^{11}\) m = 9.57 au

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Answer:

96.8a thats what I got

Step-by-step explanation:

hope this helps

To find the displacement when t = 0, t = 1/4, and t = 1/2, we can substitute the given values of t into the equation y(t) = 4 cos(8t).

Let's calculate the displacements:

1. When t = 0:

y(0) = 4 cos(8 * 0) = 4 cos(0) = 4 * 1 = 4 centimeters

2. When t = 1/4:

y(1/4) = 4 cos(8 * 1/4) = 4 cos(2) ≈ 4 * (-0.41) ≈ -1.64 centimeters

3. When t = 1/2:

y(1/2) = 4 cos(8 * 1/2) = 4 cos(4) ≈ 4 * (-0.65) ≈ -2.60 centimeters

Therefore, when t = 0, the displacement is 4 centimeters; when t = 1/4, the displacement is approximately -1.64 centimeters; and when t = 1/2, the displacement is approximately -2.60 centimeters.

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We need 144 men to build the house in 12 days working 13 hours a day.

Let M be the number of men needed to build the house in 12 days working 13 hours a day.

140 x 10 x 16 = M x 13 x 12

Simplifying the equation, we get:

22400 = 156M

Dividing both sides by 156, we get:

M = 144.1

An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.

Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.

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The expression obtained by simplifying is 3\(x^{3}\) + 17\(x^{2}\) + 21x - 9.

What is an expression?

A mathematical expression consists of its own components, at least two additional variables or integers, and one or more arithmetic operations.

We are given an expression as

(\(x^{2}\) + 6x + 9) (3x - 1)

Now, for simplifying the expression, we will multiply the terms.

So, we get

⇒ (\(x^{2}\) + 6x + 9) (3x - 1)

⇒ 3\(x^{3}\) - \(x^{2}\) + 18\(x^{2}\) - 6x + 27x - 9

Now, by combining the like terms, we get

⇒ 3\(x^{3}\) + 17\(x^{2}\) + 21x - 9

Hence, the expression obtained by simplifying is 3\(x^{3}\) + 17\(x^{2}\) + 21x - 9.

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Question: Simplify the following

(x² + 6x + 9) (3x - 1)

Answer:

The range of this quadratic function is

-infinity < y ≤ 2.

The distance between the given 2 points using the distance formula is 4√2.

So, the Distance formula: \(d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)

Substitute values in the distance formula as follows:
\(d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\\d=\sqrt{\left(0-(-4)\right)^2+\left((-2)-2\right)^2}\\d=\sqrt{\left(4\right)^2+\left(-4\right)^2}\\\\d=\sqrt{16+16}\\d=\sqrt{32}\\\\d=\sqrt2*2*2*2*2\\d=2*2\sqrt2\\\\d=4\sqrt2\)

Therefore, the distance between the 2 points is 4√2.

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Answer: 3 boxes

Step-by-step explanation:

6 x 5 = 30

36(closest multiple of 12 to 30) divided by 12 = 3

Answer:

2.5 boxes

Step-by-step explanation:

So, if each friend wants 5 cookies then you would multiply 6*5 which =30. Then you would divide 30 by 12 boxes which = 2.5. So you need 2.5 boxes or 3 if they need to be whole.

Answer:

$4.53 or $12.13

Step-by-step explanation:

You need to solve the equation 150 = -6x2 + 100x - 180. I can subtract 150 from both sides and use the quadratic formula to find x = 4.53 and 12.13. This means that if the store sells soccer balls for $4.53 or $12.13, it will earn a daily profit of $150.

Answer:

k = 18

Step-by-step explanation:

6(3k + 15) − 16k = 7k

Distribute

18k +90 - 16k = 7k

Combine like terms

2k + 90 = 7k

Subtract 2k from each side

2k+90-2k = 7k -2k

90 = 5k

Divide by 5

90/5 = 5k/5

18 = k

Answer:

\(k = 18\)

Step-by-step explanation:

\(6(3k + 15)- 16k = 7k \\ 18k + 90 - 16k = 7k \\ 18k - 16k - 7k = - 90 \\ - 5k = - 90 \\ \frac{ - 5k}{ - 5} = \frac{ - 90}{ - 5} \\ k = 18\)

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The area of the region common to the interiors of the cardioids r = 1 + cosθ and r = 1 - cosθ is (π + 2)/4.

We can find the area of the region common to the interiors of the cardioids by setting the two equations equal to each other and solving for θ. This will give us the values of θ that define the boundaries of the region. We can then integrate the area enclosed between the two curves over those boundaries.

1 + cosθ = 1 - cosθ

2cosθ = 0

cosθ = 0

θ = π/2, 3π/2

So the boundaries of the region are θ = π/2 and θ = 3π/2.

To find the area of the region, we can integrate the area enclosed between the two curves over these boundaries:

A = 2 ∫[0, π/2] (1 + cosθ) / 2 × dθ

Note that we multiply by 2 to account for the area in the other half of the region, between θ = 3π/2 and θ = 2π, which is symmetric.

Simplifying the integrand:

A = ∫[0, π/2] (1 + cosθ) / 2 × dθ

= (1/2) ∫[0, π/2] (1 + cosθ) dθ

= (1/2) (∫[0, π/2] dθ + ∫[0, π/2] cosθ dθ)

Evaluating the integrals:

A = (1/2) (θ ∣[0, π/2] + sinθ ∣[0, π/2])

= (1/2) (π/2 + sin(π/2) - 0 - sin(0))

= (1/2) (π/2 + 1)

= (π + 2) / 4

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Answer:

x√3 = 5√ 3

x = 5√ 3 / √ 3

x= √ 3(5√ 3 / √ 3)

x= 15/3

b= 5

5x2 =10

a=10 and b=5

Answer: 3(11-7) +4 (-8)= -20

Step-by-step explanation: I took the test

The expression yx = k shows inverse proportionality. the statement is true

The expression is

yx = k

The inverse proportionality states that the value of one quantity will increase when the value of another quantity decreases  or vice versa,

The inverse proportionality represented in the form of

y ∝ 1/x, here the value of y decreases when the value of x increases or vice versa

Here the given expression is

yx = k

Move the x to right hand side

y = k/x

We can write as
y = k × (1/x)

where k is the constant term

Therefore

y ∝ 1/x

Which is inverse proportionality

Hence, the expression yx = k shows inverse proportionality, the statement is true

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5 more than a number is greater or equal to 27

The "number" can be represented as x.

\(\boxed{x+5\geq 27}\)

Answer: the absolute value is 18

Step-by-step explanation:

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Answer:

3(3a-6b+7c)

Step-by-step explanation:

9a-18b+21c=3(3a-6b+7c)

The transformations applied to the parent function involve horizontal compression and horizontal translation, resulting in steeper and shifted graphs.

To obtain the graphs of f(x) = √√-3 and g(x) = √-3, we need to understand the transformations applied to the parent function y = √x.

Starting with the parent function y = √x, the first transformation applied to f(x) is the square root (√) of the input, which is denoted as y = √x. This transformation compresses the graph horizontally, causing it to become steeper.

The second transformation applied to f(x) is another square root (√) operation, resulting in y = √√x. This transformation further compresses the graph horizontally, making it steeper than the graph of y = √x. Additionally, since the original input for x is negative (-3), the square roots of negative numbers are imaginary. Therefore, the graph of f(x) = √√-3 will not be defined for any real values of x.

In the case of g(x) = √-3, the parent function y = √x is transformed by replacing the variable x with -3. This shifts the graph horizontally to the left by 3 units.

However, since the square root of a negative number is undefined in the real number system, the graph of g(x) = √-3 will also not be defined for any real values of x.

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The third measurement of the park is approximately 624.42 ft.

To find the third measurement of the park, we need to use the properties of a right triangle and apply the Pythagorean theorem.

Let's label the measurements as follows:

The length of the department store building = 610 ft (let's call it A)

The length of the bank = 140 ft (let's call it B)

The third measurement of the park (the unknown side) = C

According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we have:

A^2 + B^2 = C^2

Substituting the known values:

610^2 + 140^2 = C^2

370,810 + 19,600 = C^2

390,410 = C^2

To find C, we take the square root of both sides:

C = √390,410

C ≈ 624.42 ft

As a result, the park's third measurement is roughly 624.42 feet.

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It would require 2257920 blocks to construct the great pyramid.

Given,

Side of  base of pyramid = 756 ft = \(\frac{756}{3}\) = 252 yard

height of pyramid = 480 ft = \(\frac{480}{3}\) = 160 yard

volume of 1 block which is used to construct pyramid = 1.5 cubic yard

Volume of pyramid can be determined by formula,

\(Volume\ of\ pyramid\ =\ \frac{1}{3}*area\ of\ base*height\)

At first,

area of base=side x side = 252x252= 63504 square yard

now,

\(Volume\ of\ pyramid\ =\ \frac{1}{3}*area\ of\ base*height\\\\Volume\ of\ pyramid\ = \frac{1}{3}*63504*160\\\\Volume\ of\ pyramid\ = \frac{1}{3}*10160640\\\\Volume\ of\ pyramid\ = 3386880\ cubic\ yard\)

Now, the number of blocks required to construct the pyramid will be,

\(Number of blocks =\frac{3386880}{1.5}=2257920\)

Thus, the number of blocks required to construct the great pyramid is 2257920.

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Your question is incomplete, please complete the question

Step-by-step explanation:

×/21 x ×/21 = 7× x/21

x= 1/3

The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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The item that is not an item in the income statement is b. Furniture & Fixture as it is considered a fixed asset and is reported on the balance sheet instead.

The income statement, also known as the profit and loss statement, provides a summary of a company's revenues, expenses, gains, and losses over a specific period. It helps to assess the financial performance of a business. The income statement typically includes various items such as revenues, cost of goods sold, operating expenses, interest income or expense, and other gains or losses.

a. Discount allowed is a revenue item that represents the discounts given to customers as an incentive for early payment or other reasons. It is usually reported as a deduction from sales revenue.

c. Furniture & Fixture is not typically included in the income statement. Instead, it is considered a non-operating or non-recurring item and is generally classified as a fixed asset on the balance sheet. Fixed assets represent long-term investments made by a company for its operations.

d. Discount received is also not an item in the income statement. It represents the discounts received by a company from its suppliers for early payment or other reasons. Similar to discount allowed, it is usually reported as a deduction from the respective expense account.

In summary, b. Furniture & Fixture is the item that is not included in the income statement. It is considered a fixed asset and is reported on the balance sheet instead.

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Answer:

\(x = 32.637075718 cm^2\)

Step-by-step explanation:

\(cos(40\textdegree) = \frac{25}{x}\\\\x = 25/cos(40\textdegree)\\x = 32.637075718 cm^2\)

Answer: w=20/3

Step-by-step explanation: start by multiplying -3/2 by 2 and multiply -10 by 2 as well. you would get -3w = -20. divide both sides by -3 and you’ll get 20/3.

Answer:

AED 972

Step-by-step explanation:

Area of the wall = 9² = 81 m²

each m² costs AED 12

so 81 m² will cost 12×81 = AED 972

Answer:

2

Step-by-step explanation:

calculato

Answer:

a) function 1

b) function 4

Step-by-step explanation:

function 1 has a y-int of 4

function 2 has a y-int of 1

function 3 has a y-int of -5

function 4 has a y-int of -2

A least steep graph will have the smallest slope (disregarding negatives)

1: m= 4

2: m= -4

3: m= 2

4: m= -1