PROBLEM SOLVING WITH TREND LINES

2. 75

2. 50

Part I: The scatter plot at the left shows the

cost of gas per gallon during certain years.

Use the scatter plot to answer questions 1-5.

2. 25

2. 00

2017-1970 = ?

1. 75

1. 50

PRICE OF GAS PER GALLON ($)

1. 25

Y=0. 05(?) +0. 25

1. 00
. 75
. 50
. 25

5

10

15 20 25 30 35 40 45 50

YEARS (SINCE 1970)

The value of x must be x = 18, assuming that K is a point on the segment JL.

Here we have a segment JL, such that K is a point between J and L.

Here we know that the lengths are:

JK = x + 7

KL = 3x + 25

JL = 7x - 22

We know that the sum of the two first ones should be equal to the total segment:

JK + KL = JL

Then we can write the equation:

x+ 7 + 3x + 25 = 7x - 22

Solving this for x.

4x + 32 = 7x - 22

32 + 22 = 7x - 4x

54 = 3x

54/3 = x = 18

that is the value of x.

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Answer:

A)  [tex]15x^2+22x+8[/tex]

B)  Degree 2, Quartic Expression

C)  The dimensions of the rectangle are polynomials. When multiplied together, the area of the rectangle is also a polynomial.

Step-by-step explanation:

A)  The formula for area of a rectangle is Area = L * W. The length and width are represented by (3x+2) and (5x+4). So we can say that

[tex]Area = (5x+4)(3x+2)[/tex]

Use FOIL to multiply the the polynomials. First, Outside, Inside, Last

[tex]Area = (5x)(3x) + (5x)(2) + (3x)(4) + (2)(4)\\Area = 15x^2 + 10x + 12x + 8\\Area = 15x^2 + 22x + 8[/tex]

The expression that represents the area of the rectangle is

[tex]15x^2 + 22x + 8[/tex].

B)  The degree of the expression is 2, because two is the highest power of x. The classification of the expression is quadratic because the graph of the expression is a parabola.

Degrees vs. Classification

Degree 0:  Zero Polynomial or Constant

Degree 1:  Linear (line)

Degree 2:  Quadratic (parabola)

Degree 3: Cubic

Degree 4: Quartic

...

C)  Closure property for polynomials applies to addition, subtraction, and multiplication. It means that the result of multiplying two polynomials will also be a polynomial. Part A demonstrates polynomial closure under multiplication because the dimensions of the rectangle are polynomials and so is the area.

The algebraic property that can be used to rewrite 3x ⋅ (7y ⋅ 4) as (3x ⋅ 7y) ⋅ 4 is the associative property of multiplication.

The associative property of multiplication states that the grouping of factors in a multiplication expression does not affect the result. In other words, the order in which the multiplication operations are performed does not change the final answer. Thus, we can rearrange the multiplication expression by grouping 3x and 7y together using the associative property and then multiply the product by 4 to get the same result. This property is very useful in simplifying and solving multiplication expressions with multiple factors.

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Here is an example table for tracking the flowers stocked in the flower shop, based on the information provided in Question 4, Part I:

A flower is the reproductive structure found in flowering plants.

Flower Type Color Initial Quantity

Roses          Red 50

Roses          Pink 30

Tulips         Yellow 25

Tulips          Red 20

Lilies         White 40

Lilies          Pink 15

In this table, each row represents a specific flower type and color, and the initial quantity of that flower type and color that the shop stocks. This table can be used to track inventory levels and monitor when certain types and colors of flowers need to be restocked.

Additional columns can be added as needed to track other information, such as supplier information, purchase dates, or prices.

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The equation p = 8.50h allows us to calculate Eric's pay for any number of hours worked.

An equation is a mathematical statement that shows the equality of two expressions or quantities. It typically contains variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Equations are often used to solve problems and find unknown values.

Here,

Eric's pay is $8.50 per hour, so we can write:

p = 8.50h

where p is his pay and h is the number of hours worked.

Let's take an example, if Eric works for 20 hours, we can substitute h = 20 into the equation to find his pay:

p = 8.50(20)

p = 170

So Eric's pay for working 20 hours is $170.

Similarly, if Eric works for 40 hours, we can substitute h = 40 into the equation:

p = 8.50(40)

p = 340

So Eric's pay for working 40 hours is $340.

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The formula would be: =BINOM.DIST(3,9,0.25,TRUE) + BINOM.DIST(2,9,0.25,TRUE) + BINOM.DIST(1,9,0.25,TRUE) + BINOM.DIST(0,9,0.25,TRUE). Probability of this outcome is 0.372.

The probability of drawing at most three spade cards when drawing nine cards with replacement from a standard 52-card deck is 0.628. This probability was calculated using the binomial distribution formula in Microsoft Excel. The formula takes into account the number of trials (nine), the probability of success (drawing a spade card), and the number of successes desired (at most three). The result shows that there is a relatively high likelihood of drawing at least four spade cards, as the probability of this outcome is 0.372.

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The equivalent expressions are:

(30/12)*k + (4/12)*k + 1-  3/4

(34/12)*k - 1/4

So here we have the expression:

(5/2)*k + 1 + (1/3)*k - 3/4

An equivalent expression is an expression that can be rewritten into this one.

If we simplify the expression we will get:

(5/2)*k + (1/3)*k + 1-  3/4

(15/6)*k + (2/6)*k + 1/4

(17/6)*k + 1/4

The equivalent expressions are then:

(30/12)*k + (4/12)*k + 1-  3/4  (this is like our second step).

(34/12)*k - 1/4 (just multiply the fraction by 2 in the denominator and numerator)

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The equivalent expressions of 5/2k + 1 + 1/3k - 3/4 are

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

5/2k + 1 + 1/3k - 3/4

Express the fractions to have equal denominators

So, we have

30/12k + 1 + 4/12k - 3/4 ---- this is represented by option (a)

Evaluate the like terms

34/12k + 1/4 ---- this is represented by option (d)

The above are the expressions equivalent to 5/2k + 1 + 1/3k - 3/4

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Commission is usually calculated as a percentage of the selling price of a product or service. Therefore, the correct answer is option B, where the commission is calculated as (percent commission) x (selling price). For example, if the commission rate is 5% and the selling price is $100, the commission earned would be $5, calculated as follows:

Commission = (5%)( $100) = $5

This means that the salesperson or agent would earn $5 in commission for selling the product or service at a price of $100. The commission rate can vary depending on the type of product or service and the agreement between the parties involved.

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Answer:

3.06 cm^2/sec

Step-by-step explanation:

Since the shape is a cube, all sides have equal lengths, 6 cm  The rate of increase of 0.025cm/s [Note: I assume the unit should be cm/s, not cms'].

See the attached spreadsheet calculation.  Starting at time = 0 sec, the initial area is 36 cm^2.  Each second adds 0.025 cm to each side length,.

We can express this change in length as an equation:

Initial Length (6cm) + (x seconds)*(0.025 cm/s)

So for 10 second, l = 6 cm + 0.25cm or 6.25cm

--

The area is also changing with time.  At 0 seconds, the area is (6cm)^2 or 36 cm^2.  At 10 seconds, the area is (6.25cm)*(6.25cm) or 39.06 cm^2.

The area increased from 36 cm^2 to 39.06 cm^2 in 10 seconds.  That is a change rate of ((39.06 - 36 cm^2)/(10 sec):

 ((39.06 - 36 cm^2)/(10 sec)

 ((3.06 cm^2)/(10 sec)

3.06 cm^2/sec

Answer:

Mario's heart beats 112 times per minute.

To find out, we can use the following equation:

Heart rate = number of beats / time

Since we're given that Mario's heart beats 28 times in 1/4 minute, we can set up the equation like this:

Heart rate = 28 / 1/4

To divide by a fraction, we can multiply by its reciprocal:

Heart rate = 28 x 4/1

Heart rate = 112

Therefore, Mario's heart rate is 112 beats per minute.

Answer:

[tex]14in^2[/tex]

Step-by-step explanation:

Volume of a rectangluar prism = Length x Width x Height

Volume, Length, and Width is given now we can solve for Height, y

[tex]V = l * w * h[/tex]

[tex]3in^3 = 1in * 1in* h[/tex]

[tex]h = 3in[/tex]

Surface area of a rectangular prisim is A = 2(wl +hl +hw)

A = [tex]2(1in * 1in + 3in * 1in + 3in * 1in)\\2(1 in^2+ 3 in^2+ 3in^2)\\2(7in^2)\\14in^2[/tex]

Hope this helps!

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A sequence An is defined recursively by the equation aₙ = 0.5( aₙ₋₁ + aₙ₋₂ ) for n ≥ 3

First five terms of this sequence are 14, 14, 14, 14, 14 respectively.

A sequence is an ordered list of numbers. Like 1,2,3,.... The three dots implies to continue forward by following the pattern. Each number in the sequence is called a term. We have a sequence 'aₙ' and it is defined as aₙ = 0.5( aₙ₋₁ + aₙ₋₂ ) for n≥ 3 and

First term of sequence, a₁ = 14

second term of sequence, a₂ = 14

We have to determine value of first five terms of sequence.

Third term of sequence, n = 3

a₃ = 0.5( a₂ + a₁ )

=> a₃ = 0.5( 14 + 14)

=> a₃ = 0.5 × 28 = 14

Forth term of sequence, n = 4

a₄ = 0.5( a₃ + a₂ )

=> a₄ = 0.5( 14 + 14 ) = 14

Fifth term of sequence, n= 5

a₅ = 0.5( a₄ + a₃ )

=> a₅ = 0.5( 14+ 14) = 14

Hence, required terms are obtained and sequence is 14,14,14,14,..... ( constant sequence).

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Complete question:

A sequence, An is defined recursively by an = 0.5(an-1 + an-2) for n ≥ 3, where a1 = 14 and a2 = 14. Find the first five terms of the sequence.

The exact volume of the cylinder is 192π cubic inches

The volume of a cylinder can be calculated using the formula:

V = πr²h

where V is the volume, r is the radius, and h is the height.

Given the radius r = 8 inches and the height h = 3 inches, we can substitute these values into the formula to get:

V = π(8²)(3)

V = π(64)(3)

V = 192π

So the exact volume of the cylinder is 192π cubic inches. Since this is an exact answer, we can leave it in terms of π, or we can use a calculator to get a numerical approximation of V

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Answer:

The Area of the Triangle = 81.77

Step-by-step explanation:

Using the Formula for the Area of the Triangle given two sides and the included angle between them

Then the Area = [tex]\frac{1}{2} *13*15*sin(57)=81.77[/tex]

Hope it is Helpful

The present ages of the child and woman are 4 and 16, respectively.

A quadratic equation is a polynomial equation of second degree in one variable. It has the structure:

ax² + bx + c = 0

where the variable x and the constants a, b, and c. There may be one, two real solutions to a quadratic equation or two complex solutions. They are helpful in finding the roots of polynomials and other parabolic shape-related problems, such as projectile motion. Quadratic equations can be solved using a variety of strategies, including factoring, completing the square, and the quadratic formula.

Let us suppose the current age of the child = x.

The current age of the woman is 4x.

5 years ago, the age of the child = x - 5.

The age of the woman was 4x - 5.

Thus,

(x - 5)(4x - 5) = 175

4x² - 25x + 20 = 0

4x² - 25x + 20 = 0

(4x - 5)(x - 4) = 0

x = 5/4 or x = 4.

We can discard the first solution, as it implies a negative age for the woman.

Therefore, the present ages of the child and woman are 4 and 16, respectively.

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If the volume of a right cone is 3,525, then the height of the cone is approximately 5 units.

We can use the formula for the volume of a cone to solve for the height of the cone:

V = (1/3)πr²2h

where V is the volume of the cone, r is the radius (half of the diameter), and h is the height of the cone.

Given that the diameter of the cone is 30 units, the radius is 15 units. Substituting this and the volume V = 3525, we get:

3525 = (1/3)π(15)²2h

3525 = 225πh/3

h = 3(3525)/(225π)

h ≈ 5

Therefore, the height of the cone is approximately 5 units.

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a)  approx 0.562$$

When playing backgammon, the doubling cube is an important feature that allows players to increase the stakes of the game. Imagine playing with a "tripling cube" instead, with faces of 3, 9, 27, 81, 243, and 729. Using the analysis given for the doubling cube, we can compute the probability of winning above which a triple should be accepted.To determine the probability of winning above which a triple should be accepted, we need to use the formula derived from the analysis of the doubling cube:$$P_w = \frac{q^2}{1-2q^2}$$where Pw is the probability of winning, and q is the probability of losing. We can substitute 1-q for p, the probability of winning, to get:$$P_w = \frac{(1-p)^2}{1-2(1-p)^2}$$Now, we need to modify this formula to account for the tripling cube. If we triple the current stakes, then we have effectively tripled the value of the doubling cube. In other words, if the current stakes are 1, then the value of the tripling cube is 3. If the current stakes are 2, then the value of the tripling cube is 9. More generally, if the current stakes are n, then the value of the tripling cube is 3^n. Using this information, we can modify the formula as follows:$$P_w = \frac{q^{3^n}}{1-2q^{3^n}}$$. This is the formula we need to use to compute the probability of winning above which a triple should be accepted. We can solve for q using the quadratic formula:$$q = \frac{1\pm\sqrt{1-4(1-2P_w)(-P_w^{3^n})}}{2}$$The value of q we want is the smaller one, because we want to compute the probability of losing. Once we have q, we can substitute it into the formula for Pw to get the probability of winning above which a triple should be accepted. Example Suppose we have a backgammon game with a current stake of 4, and we are considering accepting a triple from our opponent. Using the formula above, we can compute the probability of winning above which a triple should be accepted as follows:$$n = \log_3{3^2} = 2$$$$P_w = \frac{q^{3^2}}{1-2q^{3^2}}$$$$q = \frac{1-\sqrt{1-4(1-2P_w)(-P_w^{3^2})}}{2}$$$$q = \frac{1-\sqrt{1-8P_w^9}}{2}$$$$q = \frac{1-\sqrt{1-8(0.5)^9}}{2}$$$$q \approx 0.515$$$$P_w = \frac{q^{3^2}}{1-2q^{3^2}}$$$$P_w = \frac{(0.515)^9}{1-2(0.515)^9}$$$$P_w \approx 0.562$$. Therefore, if we have a probability of winning greater than 0.562, then we should accept the triple.

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Step-by-step explanation:

2.1 Factoring 3x2-2x-23

The first term is, 3x2 its coefficient is 3 .

The middle term is, -2x its coefficient is -2 .

The last term, "the constant", is -23

Step-1 : Multiply the coefficient of the first term by the constant 3 • -23 = -69

Step-2 : Find two factors of -69 whose sum equals the coefficient of the middle term, which is -2 .

-69 + 1 = -68

-23 + 3 = -20

-3 + 23 = 20

-1 + 69 = 68

The volume of the top half of the cone (in terms of π) is 4π whose height is 6 inches and radius is 4 inches.

The volume of the top half of the cone (in terms of π) is 4π whose height is 6 inches and radius is 4 inches.

It is a physical quantity that is typically expressed in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

When the cone is sliced in half by a horizontal plane, the resulting cross-section is a circle with radius 2 inches. This circle has half the diameter of the original base of the cone, which means that it has half the area. We can use this fact to find the volume of the top half of the cone.

The original cone has height 6 inches and radius 4 inches, so its volume is given by:

V = (1/3)π(4²)(6) = (1/3)π(96) = 32π

When the cone is sliced in half, the top half has volume equal to half the volume of the original cone that lies above the horizontal plane. The height of this top half can be found using similar triangles: the radius of the top half is half the radius of the original cone, so the height of the top half is half the height of the original cone. Therefore, the height of the top half is 3 inches.

The radius of the top half is given as 2 inches, which means that its volume is:

V = (1/3)π(2²)(3) = (1/3)π(12) = 4π

Therefore, the volume of the top half of the cone (in terms of π) is 4π.

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Answer:

To evaluate this expression, we need to follow the order of operations, which is commonly remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction):

1. Start with any operations inside parentheses. There are no parentheses in this expression.

2. Evaluate any exponents. There are no exponents in this expression.

3. Evaluate multiplication and division, from left to right. In this expression, we have:

7 + (35/3) + 5 - (7 + (35/3) / (3 - 5))

= 7 + (35/3) + 5 - (7 + (11.67) / (-2))

= 7 + (35/3) + 5 - (7 - 5.835)

= 7 + (35/3) + 5 + 5.835 - 7

= 15.835 + (35/3) - 7

4. Finally, evaluate addition and subtraction, from left to right:

15.835 + (35/3) - 7

= 15.835 + 11.67

= 27.505

Therefore, the value of the expression is 27.505.

Step-by-step explanation:

Step-by-step explanation:

M=4-3/6-8

=1/-2

=-0.5

midpoint=4+3/2=6+8/2

=7/2=14/2

=3.5=7

(7;3.5)

Therefore , the solution of the given problem of equation comes out to be  y = 0.5x²- 3

The foundation of a model of linear regression is the equation y=mx+b. The inclination is B, and the y-intercept is m. Although it is true that y and y are separate parts, the the above sentence is frequently referred to as a "mathematics problem with two variables". Y=mx+b is the formula for a singular system of equations, where m denotes the gradient and b the y-intercept. The equation is Y=mx+b, where m denotes slopes and b denotes the y-intercept.

Here,

=> x  y

  -4  5

   -2  -1

   0  -3

    2  -1

To find : the equation which passes through the point

=> y = 0.5x²- 3

We can see,

=> y = 0.5(-4)² - 3

=> y = 8 -3

=> y =5

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Answer:

2)

3x + 13 = 16

3x + 13 + (-13) = 16 + (-13)

3x = 3

3x / 3 = 3 / 3

x = 1

3)

2x / 2 = 20 / 2

x = 10

Activity 3:

1) x = 13, m‹O = 137°

2) x = 5, PG = 18

Step-by-step explanation:

The surface area οf the cοne is 578.1 square feet.

An οbject's surface area is the tοtal area that all οf its surfaces οccupy. The fοrmulas we will learn in this pοst make it simple tο determine the variοus surface areas that variοus 3D shapes in geοmetry have. There are twο grοups fοr the surface area:

1. Surface area οf the lateral Surface that is curved.

2. Surface area οverall

In the questiοn,

We knοw that fοr a cοne οf radius R and slant height H the surface area is given by the fοrmula:

S = π×R^2 + π×R×(H)

with pi = 3.14

On the diagram we can see that H = 19.3ft, and the diameter οf the base is 14 ft, then the radius is:

R = 14ft/2

= 7ft

Replacing these values in the fοrmula abοve we will get:

S = 3.14×(7ft) ² + 3.14×7ft×(19.3ft)

= 578.1 ft²

Sο, the cοrrect οptiοn is the secοnd οne.

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The complete question is:

Which is closest to the surface area of the figure below? 1463.8 m2 1463.8 m squared 578.1 m2 578.1 m squared 923.2 m2 923.2 m squared 3692.6 m2

Answer:

1.     m∠1 = 60° because angle ∠1 and the 60° angle are vertical angles

2.    ∠1 and ∠2 are adjacent.

3.    m∠2 = 180° - 60°

Step-by-step explanation:

m∠2 is not equal to 60° because it is the complementary angle of the one labeled 60°. Therefore, m∠2 = 30°. m∠2 can be determined by the information given. m∠1 ≠ m∠2 because m∠1 = 60° and m∠2 = 30°

Answer: it represent the hours it took

Step-by-step explanation:

Answer:

Answer

Step-by-step explanation:

Step-by-step explanation:

The zeros and their multiplicities of the function are 1/([tex]\sqrt{3}[/tex],-1/[tex]\sqrt{3}[/tex],-3,3 and 1,1,1,1.

The value which satisfy the polynomial. that is on substituting the value in the polynomial will give 0.

To find the zeros of the function, we need to solve the equation f(x) = 0. We can do this by factoring the polynomial using the difference of squares formula:

[tex]\begin{aligned} f(x)&=9 x^{4}-82 x^{2}+9 \ &= (3x^2 - 1)(3x^2 - 9) \ &= 3(x-\frac{1}{\sqrt{3}})(x+\frac{1}{\sqrt{3}})(x-3)(x+3) \end{aligned}[/tex]

From this factorization, we can see that the zeros of the function are:

x = 1/([tex]\sqrt{3}[/tex],-1/[tex]\sqrt{3}[/tex],-3,3

Therefore, the zero of f is (1/3, -1/3, 3, -3). To determine the multiplicities of each zero, we can look at the degree of each factor.

For the factors (x - 3) and (x + 3), we have a degree of 1, which means that each of these zeros has multiplicity 1.

For the factor (x - 1/√3), we have a degree of 1 as well, which means that this zero also has multiplicity 1.

For the factor (x + 1/√3), we have a degree of 1, which means that this zero also has multiplicity 1.

Therefore, the zeros and their multiplicities of the function are 1/([tex]\sqrt{3}[/tex],-1/[tex]\sqrt{3}[/tex],-3,3 and 1,1,1,1.

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Answer:

3y-16

y-5=x

4x-y+4

4(y-5)-y+4

4y-20-y+4

3y-16  

Answer:

4

Step-by-step explanation:

(is the equation below x - 7 or x +7, I am working with x + 7)

9+ (2x - 6) is equivalent to x + 7

9 + (2x - 6) = x + 7

Open the bracket

9 + 2x - 6 = x + 7

2x + 3 = x +7

Subract 3 from both sides

2x = x + 4

Subtact x from both sides

X = 4

Confirm if the equation in the question is x +7 or x - 7

Answer:

47.6 inches

Step-by-step explanation:

diameter is just double the radius

23.8×2= 47.6 inches