The cost of a set of 4 tires is $192. What is the cost per tire?

Answer:

5b is the coefficent.

A coefficent is an integer multiplied by a variable. 5 is being multiplied by b.

5(b)

Answer:

Option (D)

Step-by-step explanation:

Length of arc AB in a circle O = 105°

Radius (AO) of the circle = 6 cm

Since, measure of an arc = central angle formed by the arc

Length of arc = \(\frac{\theta}{360}(2\pi r)\)

Where θ = central angle = 105°

r = radius of the circle = 6 cm

By substituting these values in the formula,

m(arc AB) = \(\frac{105}{360}(2\pi \times 6)\)

                = 10.9956

                ≈ 11.0 cm

Therefore, option (D) will be the answer.

In summary, we have determined that the exact solution to the given initial value problem involves a challenging integral. However, we can approximate the solution numerically or explore alternative methods to find an appropriate solution.

To solve the given initial value problem, we'll use an integrating factor to simplify the equation and then apply the initial condition.

The given differential equation is:

y' + y*cos(t) = 2/(sin(2t))

Step 1: Find the integrating factor.

The integrating factor is given by the exponential of the integral of the coefficient of y, which is cos(t):

μ(t) = e^(∫ cos(t) dt)

=\(e^{(sin(t))}\)

Step 2: Multiply both sides of the differential equation by the integrating factor μ(t):

\(e^{(sin(t))}\) * y' + \(e^{(sin(t))}\) * y * cos(t) = 2/(sin(2t)) * \(e^{(sin(t)}\)

Step 3: Recognize the left side as the derivative of the product of y and the integrating factor:

d/dt (\(e^{(sin(t))} * y) = 2/(sin(2t)) * e^{(sin(t))}\)

Step 4: Integrate both sides with respect to t:

∫ d/dt (\(e^{(sin(t))}\) * y) dt = ∫ (2/(sin(2t)) * \(e^{(sin(t))}\) dt

\(e^{(sin(t))}\) * y = ∫ (2/(sin(2t)) * \(e^{(sin(t)))}\) dt

Step 5: Evaluate the integral on the right side:

At this point, finding an exact solution requires solving the integral, which can be quite challenging. However, we can still make progress using an approximate numerical method or an approximation technique such as series expansion.

Let's use a numerical method to approximate the solution.

Step 6: Apply the initial condition y(0) = 1.

Substituting t = 0 and y = 1 into the equation e^(sin(t)) * y = ∫ (2/(sin(2t)) * e^(sin(t))) dt, we get:

\(e^{(sin(0)) }\)* 1 = ∫ (2/(sin(2*0)) * \(e^{(sin(0))}\)) dt

1 = ∫ (2/0) dt

The integral on the right side is undefined, which suggests that the initial value problem does not have a unique solution. This can happen in certain cases, and it requires further analysis or alternative methods to find an appropriate solution.

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The first ordered pair is (850, 162.65), indicating that at a price of $162.65 per ounce, the daily demand of Virbog is 850 ounces. The second ordered pair is (1450, 132.05), indicating that at a price of $132.05 per ounce, the daily demand of Virbog is 1450 ounces.

These ordered pairs represent the relationship between the quantity demanded and the price per ounce of Virbog. It shows how the demand for Virbog changes with respect to its price.

The first ordered pair indicates that as the price per ounce increases to $162.65, the quantity demanded decreases to 850 ounces. The second ordered pair indicates that as the price per ounce decreases to $132.05, the quantity demanded increases to 1450 ounces. This information can be used to analyze the demand curve for Virbog and study its price elasticity.


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\(\sf\huge{Answer :-}\)

\(\implies\sf{ {2}^{4x} = 78 } \\ \implies\sf{ ({2}^{4})^{x} = 78 } \\ \implies\sf{ {16}^{x} = 78 } \\ \: \: \: \: \: \: \: \: \: \: \: \implies\sf{ x = log_{16}(78) } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies\sf{x = 1.5713505547\: } \\\implies\sf{x = 1.57}\)

The mean absolute deviation for the data-set is given as follows:

2.86.

The mean of the data-set is given as follows:

(10 + 11 + 13 + 18 + 17 + 14 + 8)/7 = 13.

The deviations of the data-set are given as follows:

3, 2, 0, 5, 4, 1, 5.

Hence the MAD is given as follows:

(3 + 2 + 0 + 5 + 4 + 1 + 5)/7 = 2.86.

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Answer:

339.3 cubic inches

Step-by-step explanation:

SA (cyl) = 2πr² + 2πrh

SA = 2(3²)π + 2(3)(15)π

SA = 18π + 90π

SA = 108π

SA ≈ 339.3 in³

a+b+c=68

b-3=a

c-5=b

now just solve the system of equations, substitue so that there are only b's in the equation:

a+b+c=68

(b-3) + b + (b+5) = 68

3b=66

b=22

Therefore Barbara is 22

The required age of barbar is 22 years.

Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old.  How old is Barbara to be determined.

In mathematics, it deals with numbers of operations according to the statements.

Let the age of Alice, Barbara and Carol are a, b and c.

Age Alice is 3 years younger than Barbara,

a = b - 3     - - - -(1)

Age Barbara is 5 years younger than Carol

b = c - 5

c = b + 5     - - - -(2)

Together the sisters are 68 years old i.e.

a + b +c =68

From equation 1 and 2

b - 3 + b + b +5 = 68

3b + 2 = 68

3b = 66

b  = 33

Thus, the required age of barbar is 22 years.

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Answer:

14 feet or 182 feet

Step-by-step explanation:

Let the height of the pole be x

Distance from the bottom of the pole to the anchor point = (x - 62)

Length of the wire = (36 + x)

From Pythagoras theorem;

(36 + x)2 =  + (x - 62) 2

1296 + 72x +  x2 = x2 + x2 - 124x + 3844

collecting like terms;

72x + 124x  + x2 - 2x2 + 1296 - 3844 = 0

196x - x2 - 2548  = 0

Rearranging the quadratic equation;

x2 - 196x + 2548 =0

(x−14)(x−182)=0

x = 14 feet or 182 feet

Hence, the height of the pole is 14 feet or 182 feet

An argument in which the reasons support the conclusion so that the conclusion follows from the reasons offered is called a valid argument.

In logic and critical thinking, an argument consists of two main components, premises and a conclusion.

The premises are statements or reasons put forth as evidence or support for the conclusion.

The conclusion is the statement that is being asserted or inferred based on the premises.

A valid argument is one in which the logical relationship between the premises and the conclusion is such that if the premises are true.

Then the conclusion must also be true.

In other words, the conclusion logically follows from the premises.

When an argument is valid, it means that the truth or validity of the premises guarantees the truth or validity of the conclusion.

It does not necessarily mean that the premises are true in reality, but rather that if they were true, the conclusion would be true as well.

Here is an example to illustrate a valid argument,

Premise 1

All mammals are warm-blooded animals.

Premise 2

Dogs are mammals.

Conclusion,

Therefore, dogs are warm-blooded animals.

In this example, if we assume that the premises are true, the conclusion logically follows.

The truth of Premise 1 establishes that all mammals are warm-blooded, and Premise 2 identifies dogs as mammals.

This implies, the conclusion that dogs are warm-blooded animals logically follows from the given premises.

A valid argument can still have false premises or a false conclusion.

The validity of an argument simply relates to the logical relationship between the premises and the conclusion.

Rather than the truth or accuracy of the statements themselves.

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Answer:

y = -3x -7

Step-by-step explanation:

Subtract 21 and it would be 3y - 9x -21 = 0

Then divide by three and simplify

So your answer would be y = -3x - 7

Answer: use the radious

Step-by-step explanation:

Answer:

6a + 12b + 18c

Step-by-step explanation:

6 (a +2b+3c)

Distribute

6a + 6*2b + 6*3c

6a + 12b + 18c

If the Sahas were reading a best-sellingnovel as a family. The person who read the greatest fraction and who read the same fraction of the book is: A. Maddie read the greatest; Mr. Saha and Mrs. Saha read the same.

Fraction of each are:

Mr. Saha - 2/6

Mrs. Saha - 1/3

Maddie - 3/4

George - 2/3

Now let find the person who read the greatest and same fraction

Mr. Saha - 2/6 = 0.33

Mrs. Saha - 1/3 = 0.33

Maddie - 3/4 = 0.75

George - 2/3 =0.66

So,

Mr. Saha - 2/6 = 0.33 ( Same fraction)

Mrs. Saha - 1/3 = 0.33 (Same fraction)

Maddie - 3/4 = 0.75  (Greatest fraction)

Therefore the correct option is A.

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The complete question is:

The Sahas were reading a best-selling novel as a family. They checked in with each other to see how much of the book each had read.

Fraction Read:

Mr. Saha - 2/6

Mrs. Saha - 1/3

Maddie - 3/4

George - 2/3

Who read the greatest fraction and who read the same fraction of the book.

answer choices

Maddie read the greatest; Mr. Saha and Mrs. Saha read the same.

Mr. Saha read the greatest; Maddie and George read the same.

Mrs. Saha read the greatest; Mr. Saha and Mrs. Saha read the same.

George read the greatest; Maddie and Mr. Saha read the same.

The correct probabilities are P(at least two tails) = 0. 5 and P(at least one heads) = 0. 875.

Let's calculate the probabilities based on the given sample space:

Total number of outcomes (sample space) = \(2^{3}\) = 8

P(one tails):

From the sample space, there are four outcomes that have exactly one tails: HTT, THT, TTH, TTT.

So, P(one tails) = 4/8 = 0.5

P(three heads):

From the sample space, there is only one outcome that has three heads: HHH.

So, P(three heads) = 1/8 = 0.125

P(one heads and two tails):

From the sample space, there are three outcomes that have one heads and two tails: HHT, HTH, THH.

So, P(one heads and two tails) = 3/8 = 0.375

P(at least two tails):

From the sample space, there are four outcomes that have at least two tails: TTH, THT, HTT, TTT.

So, P(at least two tails) = 4/8 = 0.5

P(at least one heads):

From the sample space, there are seven outcomes that have at least one heads: HHH, HHT, HTH, THH, THT, TTH, TTT.

So, P(at least one heads) = 7/8 = 0.875

Therefore, the correct probabilities are:

P(one tails) = 0.5

P(three heads) = 0.125

P(one heads and two tails) = 0.375

P(at least two tails) = 0.5

P(at least one heads) = 0.875

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Answer:

1115.49 feet

Step-by-step explanation:

To convert meters to feet, multiply 340 meters by 3.281 because there are approximately 3.281 feet in 1 meter.

340*3.281= 1115.49

D. not continuous at X=0

if you trace the function you'll find a jump in the graph. To be continuous the line can't have any breaks in it. In this example, it's discontinuous when X=0

The value of the expression 3 cubed minus 2 cubed is 19.

Cubing a number means multiplying it by itself three times. The expression for "3 cubed" can be written as 3³, which means 3 raised to the power of 3. Similarly, "2 cubed" is written as 2³. Cubing is a mathematical operation that involves raising a number to the power of 3. When a number is cubed, it is multiplied by itself twice.

Simplifying the expression:

3³ = 3 × 3 × 3 = 27

2³ = 2 × 2 × 2 = 8

Substituting the values back into the expression:

27 - 8 = 19

So,  "3 cube minus 2 cube" =  19.

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Answer: The total cost of the fences=$165.6

Step-by-step explanation:

Let a = the length of the side if the square.

The perimeter of the square is 60 ft

                                   4a = 60ft

divide both sides by

                                  4a = 60/4

                                    a = 15 ft

The garden is surrounded by two fences, one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside

Expand to get:

                               4*a + 4(a + 2*3)

Replace a with 15 to get:

                         =  4*15 + 4(15 + 6) 60 + 4(21) 60+84

                         = 144ft

The cost of the fence is $1.15 per foot

The cost of 144 ft fence will be:

                       = 144*1.15

                       = $165.6

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 y = -3/5x - 123/5 is slope-intercept form .

What is an explanation of the slope-intercept form?

Point = ( 1,24 )

slope = -3/5

the equation in standard form of the line that passes through the point

               y - y₁ = m ( x - x₁)

                y - 24 = -3/5 ( x - 1)

             5 (y - 24) = -3( x - 1 )

                5y -    120 = -3x + 3

                 5y = -3x + 3 + 120

                 5y = -3x + 123

                 y = -3/5x - 123/5

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Answer:

70%

Step-by-step explanation:

Volume of container A

50.27 * 17 = 854.6cm^3

Volume of container B

113.1 * 11 = 1244.1 cm^3

percent of Container B that is full after the pumping is complete

=

\( \frac{854.6}{1244.1} \times 100\)

= 68.69%

Answer: 5/6÷2/3

5/6×3/2

=5/4

5/4 cups of strawberries makes 1 litre of smoothie

To find the derivative of base e, we first need to know the definition of the natural logarithm function, which is defined as the inverse of the exponential function.

The exponential function with base e is denoted by e^x, and the natural logarithm function is denoted by ln(x).

The derivative of the natural logarithm (base e) function is an important concept in calculus, as it helps us understand how the logarithm changes as the input (or the base) changes.

ln(x) is the logarithm to the base e of x, meaning that e^(ln(x)) = x. Therefore, the natural logarithm of x is the value of y such that e^y = x.

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The explicit formula for the given sequence is:

an = 39 + (n-1)7, where n is the position of the term in the sequence.

The given sequence is an arithmetic sequence where each term is obtained by adding a common difference 'd' to the preceding term.

To find the explicit formula for this sequence, we need to find the value of 'd' and the first term 'a1'.

We can find the common difference 'd' by subtracting any two consecutive terms in the sequence.

Let's subtract the second term from the first term:

46 - 39 = 7

This means the common difference 'd' is 7.

To find the first term 'a₁', we can substitute any of the given terms in the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n-1)d

Let's use the first term of the sequence, which is 39, and substitute n = 1 and d = 7:

39 = a₁ + (1-1)7

39 = a₁

So the first term of the sequence is 39.

Now we can write the explicit formula for the nth term of the sequence:

an = 39 + (n-1)7

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To determine whether the set S is linearly independent or linearly dependent.The set is linearly independent. This is because the only way to make a linear combination of vectors equal to the zero vector is to have all the coefficients equal to zero.

A linear combination of vectors is the sum of a scalar multiple of each vector in the set. We must check if the equation a(-2,2,4) + b(1,9,-2) + c(2,3,-3) = (0,0,0) has only the trivial solution, i.e., a=b=c=0. This gives us the system of equations,-2a + b + 2c = 01a + 9b + 3c = 02a - 2b - 3c = 0We can solve the system of equations by using Gauss-Jordan elimination. The augmented matrix for the system is:[-2 1 2 0][1 9 3 0][2 -2 -3 0]Let's use elementary row operations to simplify the matrix.

We can swap the first and second rows since the first element in the second row is 1.[1 9 3 0][-2 1 2 0][2 -2 -3 0]We can then add twice the first row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][-2 1 2 0][0 16 3 0]We can then add nine times the first row to the second row to eliminate the leading coefficient in the second row.[1 9 3 0][0 17 15 0][0 16 3 0]We can then add -16/17 times the second row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][0 17 15 0][0 0 -117/17 0]We see that the only solution is a=0, b=0, and c=0. Therefore, the set S is linearly independent.

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To match the equations in Column I with the correct first step for solving them in Column II, we need to identify the appropriate algebraic manipulation for each equation.

Equation (a) is 2x + 3 = 5. The correct first step for solving this equation is to subtract 3 from both sides to isolate the term with x, resulting in 2x = 2.

Equation (b) is √(x + 5) = 9. The correct first step for solving this equation is to square both sides of the equation, eliminating the square root, resulting in x + 5 = 81.

Equation (c) is (x + 5)^(5/2) = 32^(2/3). The correct first step for solving this equation is to raise both sides of the equation to the power 2/3, resulting in (x + 5)^(5/2)^(2/3) = 32.

Equation (d) is (x + 5)^(-6) = 0. The correct first step for solving this equation is to take the reciprocal of both sides, resulting in 1/(x + 5)^6 = 0.

Equation (e) is √(x(x + 5)) = -6. The correct first step for solving this equation is to square both sides of the equation, eliminating the square root, resulting in x(x + 5) = 36.

Matching the equations with their correct first steps:

(a) - Subtract 3 from both sides

(b) - Square both sides

(c) - Raise both sides to the power 2/3

(d) - Take the reciprocal of both sides

(e) - Square both sides

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Step-by-step explanation:

y =-5

5x-6y=40

5x-6(-5)=40

5x+30=40

5x=40-30

x=10/5

x=2

Answer:

The value of x is 2 and y is -5

Step-by-step explanation:

Here, y = - 5 and 5x - 6y = 40 are two given equations.

Substitution Method:

y = - 5 ...(1)

5x - 6y = 40 ...(2)

Now, put the value of y = - 5 in equation (2) we get,

5x - 6y = 40

5x - 6(-5) = 40

5x - (-30) = 40

5x + 30 = 40

Now, Subtract 30 from both side

5x + 30 - 30 = 40 - 30

5x = 10

Now, Divide by 5 from both side

5x ÷ 5 = 10 ÷ 5

x = 2

Thus, The value of x is 2 and y is -5

5x - 6y = 40

5(2) - 6(-5) = 40

10 - (-30) = 40

10 + 30 = 40

40 = 40

Hence, L.H.S = R.H.S

-TheUnknownScientist

The midpoint of the line segment with endpoints (-1, -6) and (4, 5) is (3/2, -1/2).

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the coordinates:

((x1 + x2)/2, (y1 + y2)/2)

In this case, the endpoints are (-1, -6) and (4, 5), so we can plug in the values:

((x1 + x2)/2, (y1 + y2)/2) = ((-1 + 4)/2, (-6 + 5)/2)

Simplifying this expression, we get:

((x1 + x2)/2, (y1 + y2)/2) = (3/2, -1/2)

Therefore, the midpoint of the line segment with endpoints (-1, -6) and (4, 5) is (3/2, -1/2).

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Answer:

Step-by-step explanation:

To determine the ordered pairs formed from combining a term in Pattern A with its corresponding term in Pattern B, we need to find the terms that have the same position in each pattern.

Pattern A: 1, 4, 7, 10, 13

Pattern B: 5, 13, 17, 17, 13

The ordered pairs formed by combining a term in Pattern A with its corresponding term in Pattern B are:

(1, 5)

(4, 13)

(7, 17)

(10, 17)

(13, 13)

Therefore, the correct answers are:

(10, 17)

(1, 5)

(7, 13)

(4, 13)

(13, 17)

Note that (1, 4) is not a correct answer, since 4 is not the corresponding term in Pattern B for the first term (1) in Pattern A.