5(-2x-1)-5x+2=27
Solve for x

The equivalent expressions among the given options are (I) I, II, and III. The expressions cos θ, cos (-θ), and sin (-θ)/tan (-θ) are all equivalent.

In trigonometry, cosine is an even function, meaning that cos (-θ) is equal to cos θ. This property holds true for any value of θ.

Similarly, sine and tangent are odd functions, meaning that sin (-θ) and tan (-θ) are equal to -sin θ and -tan θ, respectively. Therefore, sin (-θ)/tan (-θ) is equivalent to -sin θ/-tan θ, which simplifies to sin θ/tan θ.

Hence, all three expressions, cos θ, cos (-θ), and sin (-θ)/tan (-θ), represent the same trigonometric value and are equivalent to each other.

Therefore, the correct option is (I) I, II, and III.

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Answer:

I have no idea

Step-by-step explanation:

people are weird

the function has no holes, taht means the domain is ALL REAL NUMBERS!

Answer:

x = 2

Step-by-step explanation:

To solve for x, isolate it by dividing both sides of the equations by 5.

5x / 5 = 10 / 5

x = 2

Answer:

x = 2

Step-by-step explanation:

5x = 10

Divide both sides by 5.

x = 2

Answer:310.45

Step-by-step explanation:

An equation that shows the relationship between the two angle measure is 3x + 2 = 180 and the value of x is 59.

Let us consider the two supplementary angles with measures (x + 1) and (2x + 1). Since they are supplementary angles, we know that their sum is equal to 180 degrees. We can write this relationship between the two angle measures as an equation:

(x + 1) + (2x + 1) = 180

Simplifying this equation, we get:

3x + 2 = 180

Now, we can solve for x by isolating it on one side of the equation. To do this, we can subtract 2 from both sides of the equation:

3x = 178

Finally, we can solve for x by dividing both sides of the equation by 3:

x = 59.33

Therefore, we should round the value of x to the nearest whole number, which is 59.

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To check if the sampling distribution is normal, we need to determine the appropriate variable in the dataset and then identify the criteria to assess the normality of the distribution.

To check if the sampling distribution is normal, we would typically examine the shape and symmetry of the histogram. A bell-shaped and symmetrical histogram is indicative of a normal distribution. However, this does not specifically address the conditions for checking the normality of a sampling distribution.

The best choice for checking the normality of a sampling distribution is to verify that np > 10 and n(1-p) ≥ 10. Here, n represents the sample size, and p represents the probability of success for a particular event or variable. This condition ensures that there are a sufficient number of successes and failures in the sample, which allows for the application of the central limit theorem and the assumption of a normal distribution for the sampling distribution.

The other options presented in the question (n ≥ 30, np > 10 and n(1-p) > 10, p > 30) do not specifically address the conditions necessary for assessing the normality of the sampling distribution.

Therefore, the correct choice for checking the normality of a sampling distribution is that np > 10 and n(1-p) ≥ 10.

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\(\textbf{Heya !}\)

use the slope-formula:-

\(\sf{\cfrac{y2-y1}{x2-x1}}\)

put-in the values

\(\sf{\cfrac{-2-1}{1-(-3)}}\)

\(\sf{\cfrac{-3}{1+3}}\)

\(\sf{\cfrac{-3}{4}\)

\(\sf{-\cfrac{3}{4}}\)

`hope it's helpful to u ~

To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

Rearranging the equation, we get n = PV/RT.

Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.

Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.

To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:

1. Recall the ideal gas equation: PV = nRT

2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).

3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):

  n/V = (1.524 g/L) / (22.4 L/mol)

4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):

  M = (n/V) * (RT/P)

5. Substitute the values and solve for M:

  M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)

6. Calculate the molecular weight of the gas:

  M ≈ 32.0 g/mol

Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

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Answer:

3^2  = 9

(-4+5)^2-11+2^3 = -2

-2/9 or -9/2 ... re-read question is 3^2 dividing into (-4+5)^2-11+2^3

or the other way around... I think that there is a missing word...

3^2 "divided into"

vs 3^2 "divided by"

Step-by-step explanation:

Hello :)

We know that :

30g of cornflakes ⇒ 2.5g of fat

320g of cornflakes ⇒ xg of fat

x = 320 * 2.5 ÷ 30 ≈ 26.7 g of flat

Have a nice day!

Answer:

the answer is -36.125

Step-by-step explanation:

The first five elements generated by the recursion formula are 4, 4, 4, 4, 4. (Correct choice: 4)

In this question we know a recursion formula, which has to be checked to determine the characteristics of the first five elements:

t₁ = 4

t₂ = 2 · 4 - 4

t₂ = 4

t₃ = 2 · 4 - 4

t₃ = 4

t₄ = 2 · 4 - 4

t₄ = 4

t₅ = 2 · 4 - 4

t₅ = 4

The first five elements generated by the recursion formula are 4, 4, 4, 4, 4. (Correct choice: 4)

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The given statement to prove is: A ∧ B, A → C, B → D ⊢ C ∧ D.TFL stands for Truth-Functional Logic, which is a formal system that allows us to make deductions and prove the validity of logical arguments.

The steps to prove the given statement using basic TFL are as follows:1. Assume the premises to be true. This is called the assumption step. A ∧ B, A → C, B → D.2. Apply Modus Ponens to the first two premises. That is, infer C from A → C and A and infer D from B → D and B.3. Conjoin the two inferences to get C ∧ D.

4. The statement C ∧ D is the conclusion of the proof, which follows from the premises A ∧ B, A → C, and B → D. Therefore, the statement A ∧ B, A → C, B → D ⊢ C ∧ D is true, which means that the proof is valid in basic TFL. Symbolically, the proof can be represented as follows:

Premises: A ∧ B, A → C, B → DConclusion: C ∧ DProof:1. A ∧ B, A → C, B → D (assumption)2. A → C (premise)3. A ∧ B (premise)4. A (simplification of 3)5. C (modus ponens on 2 and 4)6. B → D (premise)7. A ∧ B (premise)8. B (simplification of 7)9. D (modus ponens on 6 and 8)10. C ∧ D (conjunction of 5 and 9).

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The rigid motion that verifies the congruence of two triangles using the Side-Angle-Side (SAS) criterion is the combination of a translation and a rotation.

To establish congruence between two triangles using the SAS criterion, we need to show that the triangles have two corresponding sides and the included angle equal in measure. This can be achieved through a specific rigid motion, which preserves the shape and size of the triangles.

The first step in the rigid motion is a translation. Translation involves moving the entire triangle along a straight line without altering its shape or size. By sliding one triangle along the plane, we can place the corresponding sides of the two triangles in the same position.

The second step is a rotation. A rotation is a transformation that turns the triangle around a fixed point, called the center of rotation. By rotating one triangle around its center, we can align the corresponding angles of the two triangles. By combining the translation and rotation, we ensure that the sides and the included angle of the two triangles match, verifying their congruence using the SAS criterion.

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The equation of the plane containing the point (4, -2, 3) and parallel to the plane 3x - 7z = 12 is 3x - 7z = -9.

To find the equation of the plane containing the point (4, -2, 3) and parallel to the plane 3x - 7z = 12, we can follow these steps:

1. Parallel planes have the same normal vector. In this case, the normal vector is given by the coefficients of x and z in the original equation (3, 0, -7).

2. Since the plane we're trying to find passes through the point (4, -2, 3), we can substitute the coordinates of this point into the equation ax + by + cz = d, where (a, b, c) is the normal vector.

Plugging in the values, we get:
3(4) + 0(-2) - 7(3) = d
12 - 21 = d
d = -9

3. Now, we can write the equation of the plane using the normal vector and the value of d we found:
3x - 7z = -9

So, the equation of the plane containing the point (4, -2, 3) and parallel to the plane 3x - 7z = 12 is 3x - 7z = -9.

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Answer:

The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.

Step-by-step explanation:

a)

Let 'x' be the total number of students in Mrs. Hayko's class.

One-third of the students walk to school: (1/3)x.

The remaining students who do not walk to school: (2/3)x.

Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.

Simplify to find the fraction of students taking the bus: (8/15)x.

b)

Consider different values for 'x' to find a whole number of students taking the bus.

Start with a small number, such as x = 15.

Calculate the number of students taking the bus using (8/15)x.

If the result is a whole number, it's a possible class size.

Repeat with different values of 'x' until a whole number is obtained.

The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.

The expression 2x/(x + 3) + (2 - x)/(2x + 1) can be rewritten with a common denominator and simplified.

To find the common denominator, we need to factorize the denominators and identify their shared factors. The first denominator, x + 3, cannot be factored further. However, the second denominator, 2x + 1, can be written as (2x + 1) = 2(x + 3) - 5.

Now, we can rewrite the expression using the common denominator of (x + 3)(2x + 1):

2x/(x + 3) + (2 - x)/(2x + 1) = (2x * 2 - x * (x + 3))/((x + 3)(2x + 1))

Expanding the numerator:

= (4x - x^2 - 3x)/((x + 3)(2x + 1))

Combining like terms:

= (4x - x^2 - 3x)/(2x^2 + 7x + 3)

Simplifying further:

= (-x^2 + x)/(2x^2 + 7x + 3)

Therefore, the simplified expression with a common denominator is (-x^2 + x)/(2x^2 + 7x + 3).

In this explanation, the keywords "common denominator" and "simplify" are bolded in the main answer, while in the supporting answer, the keywords "factorize" and "numerator" are bolded.

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Answer:

hm

Step-by-step explanation:

The value of x for the given quadratic expression is x = 5 ± √11.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is 3(x-5)²=33. The value of x will be calculated as,

3(x-5)²=33

(x - 5 )² = 11

(x - 5 )  = ±√11

x = 5 ± √11

Therefore, the value of x for the given quadratic expression is x = 5 ± √11.

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Answer:

Option C

Step-by-step explanation:

Check the attached photo.

Answer:

i m insha i no the z=7and jehdbxh jsjzhwj

dj dad nen

The HCF of 10125 and 7425 is 675, obtained by prime factorization and identifying the common factors.

To find the highest common factor (HCF) of 10125 and 7425, we can use the method of prime factorization.

Step 1: Prime factorize both numbers.

10125 = 3 × 3 × 3 × 5 × 5 × 5 × 3

7425 = 3 × 3 × 3 × 5 × 5 × 11

Step 2: Identify the common prime factors.

The common prime factors between 10125 and 7425 are 3 and 5.

Step 3: Find the minimum exponent for each common prime factor.

The minimum exponent for 3 is 3 (from 10125) and 3 (from 7425).

The minimum exponent for 5 is 3 (from 10125) and 2 (from 7425).

Step 4: Multiply the common prime factors raised to their minimum exponents.

HCF(10125, 7425) = 3^3 × 5^2 = 27 × 25 = 675.

Therefore, the highest common factor of 10125 and 7425 is 675.

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In general, different refrigerants should not be mixed or recovered into the same cylinder.

Different refrigerants have unique chemical compositions and properties that make them incompatible with one another. Mixing different refrigerants can lead to unpredictable reactions, loss of refrigerant performance, and potential safety hazards. Therefore, it is generally recommended to avoid recovering different refrigerants into the same cylinder.

When recovering refrigerants, it is important to use separate recovery cylinders or tanks for each specific refrigerant type. This ensures that the refrigerants can be properly identified, stored, and recycled or disposed of in accordance with regulations and environmental guidelines.

The refrigerant recovery process involves capturing and removing refrigerant from a system, storing it temporarily in dedicated containers, and then transferring it to a proper recovery or recycling facility. Proper identification and segregation of refrigerants during the recovery process help maintain the integrity of each refrigerant type and prevent contamination or cross-contamination.

To maintain the integrity and safety of different refrigerants, it is best practice to recover each refrigerant into separate cylinders. Mixing different refrigerants in the same cylinder can lead to complications and should be avoided. Following proper refrigerant recovery procedures and guidelines helps ensure the efficient and environmentally responsible management of refrigerants.

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The number of different refrigerants that may be recovered into the same cylinder is zero.

When it comes to refrigerants, it is important to understand that different refrigerants should not be mixed together. Each refrigerant has its own unique properties and should be handled and stored separately. mixing refrigerants can lead to chemical reactions and potential safety hazards.

The recovery process involves removing refrigerants from a system and storing them in a cylinder for proper disposal or reuse. During the recovery process, it is crucial to ensure that only one type of refrigerant is being recovered into a cylinder to avoid contamination or mixing.

Therefore, the number of different refrigerants that may be recovered into the same cylinder is zero. It is essential to keep different refrigerants separate to maintain their integrity and prevent any adverse reactions.

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The equilibrium quantity can be found by setting the demand equal to the supply and solving for x.

This gives x = 2716. The producer surplus at the equilibrium quantity can be found by calculating the area between the supply curve and the equilibrium price (which is found by substituting x=2716 into either the demand or supply function). This gives a producer surplus of $3285.64.
The equilibrium quantity occurs when the demand function, d(x), equals the supply function, s(x). Therefore, we can set d(x) = s(x):
2312/√x = 2√x
To solve for x, multiply both sides by √x, which gives:
2312 = 2x
Now, divide both sides by 2:
x = 1156 items
To find the producer surplus at the equilibrium quantity, we need the difference between the total revenue and the total cost. The total revenue can be found by multiplying the equilibrium quantity (x) by the supply function, s(x):
Total revenue = 1156 * 2√1156 = $4612
The total cost can be found by integrating the supply function:
Total cost = ∫2√x dx from 0 to 1156 = (4/3)x^(3/2) evaluated from 0 to 1156 = $3468
The producer surplus is the difference between the total revenue and the total cost:
Producer surplus = $4612 - $3468 = $1144

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Justin must drive at least 67.2 miles per hour (rounded to one decimal place) to average 64 miles per hour for the whole trip, including the 15-minute stop

To average 64 miles per hour for the whole trip, Justin must complete the 144-mile distance and the 15-minute stop in a total of 144 minutes (2 hours and 24 minutes) or less.

If we subtract the 15 minutes stop from the total time, Justin will have to cover the 144 miles in 129 minutes (2 hours and 9 minutes) or less.

To determine the required speed, we can use the formula:

\(speed = \frac{distance }{time}\)

So,  \(speed = \frac{144 miles}{129 minutes}=1.12 miles per minute\)

To convert this to miles per hour, we can multiply by 60:

1.12 miles per minute x 60 minutes per hour = 67.2 miles per hour

Therefore, Justin must drive at least 67.2 miles per hour (rounded to one decimal place) to average 64 miles per hour for the whole trip, including the 15-minute stop.

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Answer:

x≤−3 or x>−1

Step-by-step explanation:

Combine like terms

Isolate your variable x

Answer:

x<-3 or x>1

Step-by-step explanation:

you would just subtract 1 from both sides on the first one so you get 5x<-15 which can be x<-3 and for the second one -4x+6<10 subtract 6 so you get -4x<4 and divide by -4 which is x>1

Answer:

-6

Step-by-step explanation: