Factor.

x²(x + 2) + 9(x + 2) =

The least common multiple ( LCM ) is A = 3c

Given data ,

Let the three numbers be represented as c , 3c and 3

Now , The prime factorization of each number is:

c: c

3c: 3 * c

3: 3

The LCM is the product of the highest power of each prime factor. In this case, the highest power of c is c, and the highest power of 3 is 3. Therefore, the LCM is:

LCM = c * 3 = 3c

Hence , the LCM of c, 3c, and 3 is 3c

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Area of the figure is 402.8 ft².

We have,

Rectangle area = Length x Width

Area of sector = π r² x angle / 360

Now,

There are two rectangles and one sector.

So,

Area of one rectangle.

= 8 x 2

= 16 ft²

Area of another rectangle.

= 5 x 2

= 10 ft²

Area of the sector.

= π x r² x {360 - (150 + 90 + 90)}

= 3.14 x 2² x 30

= 376.8 ft²

Now,

The area of the figure.

= 16 + 10 + 376.8

= 402.8 ft²

Thus,

The area of the figure is 402.8 ft².

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Answer:

Step-by-step explanation:

You want the height of a 150 lb person with a BMI of 25, and the weight of a 61-inch person with a BMI of 25. BMI is (weight·703/height²).

The equation is already solved for height. You only need to fill in the given numbers:

  [tex]H(w)=\sqrt{\dfrac{703w}{b}}\\\\H(150)=\sqrt{\dfrac{703\cdot150}{25}}\approx\boxed{64.9\quad\text{inches}}[/tex]

Solving the equation for weight, we have ...

  [tex]b=\dfrac{703w}{h^2}\qquad\text{given}\\\\w=\dfrac{bh^2}{703}\qquad\text{divide by the coefficient of $w$}[/tex]

Using the given values in this equation, we find the weight to be ...

  [tex]w=\dfrac{25\cdot61^2}{703}\approx\boxed{132.3\qquad\text{pounds}}[/tex]

Justification:

(1) BP | Premise

(2) (RDP) | Premise

(3) RD B | Modus Ponens (1), (2)

(4) ROP | Premise

(5) T | Modus Ponens (3), (4)

T | Conclusion (the desired statement to be proved)

The given proof is presented in the format of a deductive argument, where each line represents a statement that either follows logically from previous statements (i.e., by a rule of inference) or is assumed to be true (i.e., a premise). The objective of the proof is to demonstrate that the conclusion, represented by the symbol "/T", is a logical consequence of the premises.

The justification column of the proof provides an explanation of why each statement in the argument is true or valid. In this proof, the first four lines are premises that are assumed to be true, and their justifications are simply labeled as "Premise". The last two lines of the proof represent the application of a rule of inference called modus ponens, which states that if we have two statements A and A -> B, we can infer B. The justification for line 3 is modus ponens with lines 1 and 2 as antecedent and consequent respectively, and the justification for line 5 is modus ponens with lines 3 and 4 as antecedent and consequent respectively.

The conclusion of the proof, represented by "/T", is reached by applying modus ponens with lines 3 and 4 as antecedent and consequent respectively. The conclusion follows logically from the premises and the application of the modus ponens rule, which justifies the truth of the conclusion. Therefore, we can conclude that the argument is valid, and the conclusion can be accepted as true.

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An information that is needed to conclude that line segment EF is the bisector of ∠DEG include the following: m∠FEG ≅ ∠DEF.

In Mathematics and Geometry, an angle bisector simply refers to a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

By applying the angle bisector theorem, we can reasonably infer and logically deduce the following congruent angles;

m∠FEG ≅ ∠DEF (definition of angle bisector).

In conclusion, m∠FEG ≅ ∠DEF is the required information that proofs that line segment EF is the angle bisector of ∠DEG

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Answer:

7.7

Step-by-step explanation:

Find the third angle that is not given:

180 - (120 + 37) = 23.

Draw a line that cuts the 120 degree angle and makes two 90 degree angles with the opposite side. We will call this line h.

You can find the length of h by using sine of 37 degrees. We get:

sin(37 deg) = h/5

h = 3.01

Because we have already found the third angle, 23 degrees, we can use sine of 23 degrees to find the missing side length (x):

sin(23 deg) = 3.01/x

x = 7.7

Answer is 7.7

The location of the center and the radius will be (-1.5. -2) and 3, respectively. Thus, the correct option is A.

Given that:

Equation: (x + 1.5)² + (y + 2)² = 9

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

Compare the equation, then we have

Center: (-1.5, -2)

Radius: r² = 9 ⇒ r = 3

Thus, the correct option is A.

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The required amount of rent be $4,850.19.

The original rent of apartment per month = $1700

And the interest = 11%

Time = 10 years.

To determine the apartment's rent during the tenth year:

Rent is calculated as Initial = Rent x [tex](1 + Increase Rate )^{year}[/tex] .

We plug the values and compute the rent for the tenth year using the provided data,

Rent = $1700 x (1 + 0.11)¹⁰

Rent = $1700 x 2.85

Rent = $4,850.19

Thus,

The apartment's rent in the tenth year would be about $4,850.2 per month.

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Hello!

It's a division.

17  I  6

-12 I   2

  5

the dividende = 17

the divider = 6

the quotient = 2

the rest = 5

17 = 2 x 6 + 5

Answer:

your answer is B

Step-by-step explanation:

because if you look at the c coordinator plane 1 is on y=1 and x=1 so if you just decrease but yet add you'll get y=2 and x+2 and you'll get B

Yes, Both diagonal are equal in length with √ 80 units.

We have to given that;

The coordinates of rectangle PQRS are P(1, 6), Q(1, 2), R(9, 2), and S(9, 6).

Hence, The length of diagonal are PR and QS.

Since, We know that;

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, Length of PR is,

PR = √ (x₂ - x₁)² + (y₂ - y₁)²

PR = √ (9 - 1)² + (2 - 6)²

PR = √ 64 + 16

PR = √ 80

And, Lenght of QS is,

QS = √ (x₂ - x₁)² + (y₂ - y₁)²

QS = √ (9 - 1)² + (2 - 6)²

QS = √ 64 + 16

QS = √ 80

Thus, Both diagonal are equal in length with √ 80 units.

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Answer:

x+116

Step-by-step explanation:

add the expressions.

have a great day and thx for your inquiry :)

Answer:

a. Since blue occurs a fraction z of the time and the red and green portions have equal area, the probability of landing on green is (1 - z)/2.

b. The area diagram for spinning the spinner twice would have three sections: blue, green, and red. Each section would be divided into three smaller sections: BB, BG, BR, GB, GG, GR, RB, RG, and RR. The diagram would show all 9 possible outcomes of spinning the spinner twice.

c. The region on the area diagram corresponding to getting the same color on the spinner twice would be the diagonal line from the upper left to the lower right, going through the GG, BB, and RR sections.

d. The probability that both spins give the same color can be calculated as follows:

- The probability of getting blue on the first spin is z.

- The probability of getting green on the first spin is (1 - z)/2.

- The probability of getting red on the first spin is (1 - z)/2.

- If the first spin is blue, the probability of getting blue again on the second spin is z. The same applies to green and red.

- Therefore, the probability of getting the same color on both spins is z^2 + ((1 - z)/2)^2 + ((1 - z)/2)^2 = z^2 + (1 - z)^2/4.

e. If you know that you got the same color twice, the probability that the color was blue can be calculated using Bayes' theorem:

- Let A be the event that you got blue twice, and let B be the event that you got the same color twice.

- Then P(A|B) = P(B|A) * P(A) / P(B), where P(A) = z^2, P(B|A) = 1, and P(B) = z^2 + ((1 - z)/2)^2 + ((1 - z)/2)^2 = z^2 + (1 - z)^2/4.

- Therefore, P(A|B) = z^2 / (z^2 + (1 - z)^2/4).

Step-by-step explanation:

Hope this helps

Answer:

1.91

Step-by-step explanation:

12+4.67+1.42=18.09

20-18.09=1.91

The correct solution to the system of equations is (2, 0).

Looking at the data, we can observe the following coordinate pairs: (-4, -3), (0, -1), (2, 0), and (6, 2). We can calculate the slope using any two of these points. Let's take the points (0, -1) and (2, 0):

slope = (y2 - y1) / (x2 - x1)

= (0 - (-1)) / (2 - 0)

= 1 / 2

= 0.5

Therefore, the slope of the second line is 0.5, not -3/4 as previously mentioned.

Using the correct slope, we can find the equation of the second line using the point-slope form:

y - y1 = m(x - x1) (where m is the slope and (x1, y1) is a point on the line)

Using the point (2, 0):

y - 0 = 0.5(x - 2)

y = 0.5x - 1

Now, when we solve the system of equations:

y = -2x + 4 (equation 1)

y = 0.5x - 1 (equation 2)

Setting equation 1 equal to equation 2:

-2x + 4 = 0.5x - 1

Simplifying the equation:

-2.5x = -5

Dividing both sides by -2.5:

x = 2

Substituting x = 2 into equation 2:

y = 0.5(2) - 1

y = 1 - 1

y = 0

Therefore, the correct solution to the system of equations is (2, 0).

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In order to convert the base of the logarithm from base 10 to any other base and calculate intensities, we need the change of base formula.

To solve this problem, we need to use the logarithmic property known as the "change of base formula" which states that:

log_a (b) = log_c (b) / log_c (a)

This formula allows us to change the base of a logarithm from one value to another.

In this case, we want to find the ratio of the intensity of the first speaker to that of the second speaker, which is given by:

ratio = intensity of the first speaker/intensity of the second speaker

To calculate this ratio, we need to first convert the decibel values to intensities using the formula:

intensity = 10^(dB/10)

where dB is the decibel value.

For the first speaker, the intensity is:

intensity of the first speaker = [tex]10^{(85/10)} = 7.94 *10^8[/tex]

For the second speaker, the intensity is:

the intensity of the second speaker [tex]= 10^{(75/10)} = 1.78 * 10^7[/tex]

Now we can calculate the ratio of intensities:

[tex]ratio = (7.94 * 10^8) / (1.78 * 10^7) = 44.66[/tex]

This means that the sound from the first speaker is 44.66 times more intense than the sound from the second speaker.

Therefore, we need the change of base formula to change the base of the logarithm from 10 to any other base to calculate the intensities.

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Answer:

332.88

Step-by-step explanation:

To find the median of this data set, we first need to determine the total number of observations. This is given by the last cumulative frequency, which is 189.

Since the total number of observations is an odd number, we can find the median by identifying the middle value. The middle value is the observation that has half the data below it and half the data above it.

To find this value, we can divide the total number of observations by 2:

189 ÷ 2 = 94.5

This means that the median observation falls in the 330-339 range, since the cumulative frequency at the end of this range is 38, which is the smallest cumulative frequency greater than 94.5.

To find the exact median value, we can use the following formula:

Median = L + ((N/2 - CF) / f)

where:

L = lower limit of the median class (in this case, 330)

N = total number of observations (in this case, 189)

CF = cumulative frequency of the class preceding the median class (in this case, 20)

f = frequency of the median class (in this case, 24)

Plugging in the values, we get:

Median = 330 + ((94.5 - 20) / 24)

= 330 + (74.5 / 24)

≈ 332.88

Therefore, the median of the given scores is approximately 332.88.

The probability that 12 or more bikes will be returned out of 335 stolen bikes is approximately 0.1747 (17.47%).

Let X be the random variable representing the number of bikes returned out of 335 stolen bikes.

We are given that the probability of a single bike being returned which is:

p = 0.03 (3% written as a decimal).

We can use the binomial distribution to calculate the probability of X bikes being returned:

P(X = k) = [tex]335C_{k} * p^{k} * (1-p)^{335-k}[/tex]

where [tex]335C_{k}[/tex] reads 335 combination k.

To find the probability that fewer than 12 bikes will be returned, we can calculate the cumulative probability:

P(X < 12) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 11)

Using a calculator, we find that:

P(X < 12) = 0.8253.

The probability of 12 or more bikes being returned can be calculated as the complement of the probability of fewer than 12 bikes being returned:

P(X ≥ 12) = 1 - P(X < 12) = 1 - 0.8253 = 0.1747

Therefore, the probability that 12 or more bikes will be returned out of 335 stolen bikes is approximately 0.1747 or 17.47%.

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If two variables are directly proportional, this means that the ratio of the two variables is constant. In other words, if x and y are directly proportional, then there exists some constant k such that:

y = kx

To find the missing value in the table, we can first calculate the value of k using any set of corresponding values for x and y. For example, we can use the first row of the table:

y = kx 9 = k(-3) k = -3

Now that we know k, we can use it to find the missing value for the second row:

y = kx y = (-3)(-5) y = 15

Therefore, the missing value in the table is 15.

Answer:

x= 0•5

Step-by-step explanation:

x÷2/3=3/4

3/2x=3/4

x= 3/4 ÷2/3

The spread of the data is not relevant to determining which class used the most paper overall.

Mrs. Potter's class used the most paper overall based on the data displayed because it has a larger median value of 16 pieces of paper. The median value of Mr. Howard's class is 11 pieces of paper.

The spread of the data is not relevant to determining which class used the most paper overall.

Therefore, the correct answer is Mrs. Potter's class; it has a larger median value of 16 pieces of paper.

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Using simplex method to maximize the given function is (x, y, z) = (17.33, 1.33, 0) and f = 35.67.

To solve the given linear programming problem using the simplex method, follow these steps:

Step 1: Convert the problem into standard form.

Step 2: Set up the initial simplex tableau.

Step 3: Perform iterations of the simplex method.

Step 4: Determine the solution and the maximum value of the objective function.

Step 1: Convert the problem into standard form:

Introduce slack variables to convert the inequality constraints into equations:

Maximize f = 7x + 11y + 4z

Subject to:

3x + 5y + 4z + s1 = 30

3x + 2y + s2 = 4

x + 2y + s3 = 8

All variables are nonnegative: x ≥ 0, y ≥ 0, z ≥ 0, s1 ≥ 0, s2 ≥ 0, s3 ≥ 0.

Step 2: Set up the initial simplex tableau:

Construct the initial simplex tableau using the coefficients of the variables and the right-hand side values of the equations is attached (tableau 1).

Step 3: Perform iterations of the simplex method:

Apply the simplex method by selecting the most negative value in the bottom row (the objective row) as the pivot column and the minimum ratio test to determine the pivot row.

Iteration 1:

Pivot column: y (since it has the most negative coefficient in the bottom row)

Pivot row: s2 (minimum ratio: 4/2 = 2)

Perform row operations to make the pivot element 1 and other elements in the pivot column zero:

Divide the pivot row by the pivot element (2/2 = 1/1 = 1).

Subtract appropriate multiples of the pivot row from other rows to make the elements in the pivot column zero.

Updated tableau after iteration 1 attached (tableau 2).

Iteration 2:

Perform row operations to make the pivot element 1 and other elements in the pivot column zero:

Divide the pivot row by the pivot element (3/2).

Subtract appropriate multiples of the pivot row from other rows to make the elements in the pivot column zero.

Updated tableau after iteration 2 also attached (tableau 3).

Iteration 3:

Since all coefficients in the bottom row are non-negative, the optimal solution has been reached. We can read the values of variables x, y, z, and the objective function f directly from the tableau.

The optimal solution is:

x = 17.33

y = 1.33

z = 0

f = 35.67

Therefore, (x, y, z) = (17.33, 1.33, 0) and f = 35.67.

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Using MACRS rates, the book value of the $2,500 computer after 3 years is $720.

MACRS (Modified Accelerated Cost Recovery System) rates are prearranged percentages used for the purposes of tax.

They compute how much an asset depreciates each year based on its class and expected lifespan.

Using MACRS rates, we shall calculate the book value of a $2,500 computer after 3 years in this way.

First, we shall apply the respective depreciation rates to the initial cost and subtract the accumulated depreciation each year.

Year 1:

Depreciation = Year 1 MACRS Rate x Initial Cost

Depreciation = 20.0% × $2,500 = $500

Year 2:

Depreciation = Year 2 MACRS Rate x Initial Cost

Depreciation = 32.0% × $2,500 = $800

Year 3:

Depreciation = Year 3 MACRS Rate x Initial Cost

Depreciation = 19.2% × $2,500 = $480

Next, subtract the accumulated depreciation from the initial cost to have the book value for each year:

Year 1:

Book Value = Initial Cost - Depreciation

Book Value = $2,500 - $500 = $2,000

Year 2:

Book Value = Year 1 Book Value - Year 2 Depreciation

Book Value = $2,000 - $800 = $1,200

Year 3:

Book Value = Year 2 Book Value  - Year 3 Depreciation

Book Value = $1,200 - $480 = $720

Therefore, the book value of the $2,500 computer after 3 years is $720.

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From the first equation, we can rearrange to get x = 12 + y.

Substituting that into the second equation, we get y^2 = 5(12 + y - 2) = 50 + 5y.

This simplifies to y^2 - 5y - 50 = 0.

Using the quadratic formula, we can solve for y to get y = 10 or y = -5.

Therefore, two possible values of y are 10 and -5.

The temperature difference between the optimum temperatures of bacteria X and Y is 25°C.

To find the temperature difference between the optimum temperatures of bacteria X and Y, we subtract the temperature of bacteria Y from the temperature of bacteria X.

Temperature difference = Optimum temperature of bacteria X - Optimum temperature of bacteria Y

Temperature difference = -31°C - (-56°C)

When we subtract a negative number, it is equivalent to adding its positive value. Therefore, -(-56°C) is the same as +56°C.

Temperature difference = -31°C + 56°C

To add these temperatures, we need to consider the sign of the result. In this case, we have a negative temperature (-31°C) and a positive temperature (+56°C). When adding numbers with different signs, we subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.

Absolute value of -31°C = 31°C

Absolute value of +56°C = 56°C

Since 56°C > 31°C, the result will have a positive sign.

Temperature difference = 56°C - 31°C = 25°C

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Part 1a) An exponential function is a better model to represent the data because the rate of change is not constant instead of using a linear function, whose rate of change (slope) is constant.

Part 1b) The slope between each points are different.  So, the data is best represented by an exponential function.

Part 2a) The estimated number of college degrees earned in the United States in 2050 is about 2 million.

Part 2b) The estimated number is more likely to be an under-estimation.

Exponential equations increase by a constant exponent or power, written in the form of $$f(x) = ab{x}$$.

Linear equations or functions increase by a constant slope, written in the form of y = mx + b, where m is the slope.

Year    College degrees

            (  thousands)

1910                37

1930             122

1950            432

1970            792

1990          1,051

2010          1,650

Using exponential smoothing in Excel, the result of the prediction shows that 2,237,000 college degrees will be earned in 2050.

The number of college degrees earned in the United States in 2050 = 2,237,000 ≈ 2 million.

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We can match the numbers in Column I with their square roots in Column II as follows:

1. √844 = C. 29.1

2. √900 = H. 30

3. √650 = G. 25.5

4. √784 = E. 28

5. √699 = B. 26.4

6. √805 = D. 28.4

7. √729 = A. 27

To find the square roots of the numbers, we can simply punch the sign into the calculator and insert the figures in it. For instance, to find the square root of 900, we can simply insert the figure into the calculator while inputting the square root sign before it.

To determine if your answer is correct, try squaring the numbers. The output should be the original numbers provided.

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Answer:

259.8

Step-by-step explanation:

The apothem of a regular polygon is a segment whose endpoints are the center of the polygon and the midpoint of one side.

Look at the bottom of the drawing. The dimension 17.32 is the distance between two opposite parallel sides of the regular hexagon base. If you draw a segment that is parallel to two opposite sides of the hexagon and passes through the center of the hexagon, it is twice the length of the apothem.

Here,

apothem = 17.32/2 = 8.66

If you divide the hexagon into 6 congruent triangles, each triangle is an equilateral triangle. Then the side of the hexagon measures 10.

A = 1/2 pa

p = perimeter = 6 × side length = 6 × 10

a = apothem = 8.66

A = 1/2 × (6 × 10) × 8.66

A = 259.8

Answer:

[tex] \frac{3( {5}^{8} - 1) }{5 - 1} = 292968[/tex]