Problems 17, 20 Please

Answer:

[tex]\frac{3}{4} = \frac{6}{8} = \frac{9}{12} = \frac{18}{24} [/tex]

The required fraction of the number of trees in a full row that is the number of trees in the extra row is 6/10.

Number of full rows = 8450 trees / 125 trees/row = 67.6 rows

Since Emiliano cannot plant a fraction of a row, the number of full rows he plants is 67.

To find the number of trees in the extra row, we need to subtract the number of trees in the full rows from the total number of trees:

Number of trees in the extra row = 8450 trees - (125 trees/row × 67 rows) = 75 trees

Therefore, Emiliano plants 67 full rows and an extra row with 75 trees.

To find the fraction of the number of trees in a full row that is the number of trees in the extra row, we need to divide the number of trees in the extra row by the number of trees in a full row:

Fraction of the number of trees in a full row that is the number of trees in the extra row = 55 trees / 125 trees/row = 0.6 or 60/100 or 6/10

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1 inch is the diameter of the driven pulley.

Let's use D to represent the driven pulley's diameter. The speed decrease needed, according to the issue description, is a 4 to 1 reduction.

This implies that the ratio of the diameters is also 4 to 1, as the speeds are inversely proportional to the diameters:

D/4 = 1/4

Multiplying both sides by 4 gives:

D = 1

Therefore, the diameter of the driven pulley should be 1 inch.

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The factor that one should consider when choosing a career is D. All of the above.

In choosing a career, a student should consider the required education and training involved, the work environment, and their potential earnings.

Other factors to consider include:

Thus, all the listed factors should be considered when choosing a career.

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Answer:

19683

Step-by-step explanation:

3 to the power of 8 is 6561,

so just put 6561 multiplied by itself 3 times.

(6561 X 6561 X 6561).

Answer:

3⁸ × 3 = 19,683

Answer:

Step-by-step explanation:

54 - 18 = 36

so...

18 + 36 = 54

The total amount spent is $9.50.

We have,

2 1/2 yards of fabric cost 7.00.

3 rolls of ribbon cost 2.50.

So, the total amount of money spend

= Cost of fabric + cost of ribbon

= 7 + 2.50

= $9.50

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Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.

Circumcenter : The point of intersection of the three perpendicular bisectors.

Incenter : The point of intersection of the three angle bisectors.

Centroid : The point of intersection of the three medians.

Orthocenter : The point where all the three altitudes of the triangle meet or intersect each other.

In conclusion, based on the information, Point T is the orthocenter of this triangle because it is the point where all the three altitudes of the triangle are intersecting each other.

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The coefficients a, b, and c in the 12th term of the expanded form are 312, 64, and 11, respectively.

The 12th term is 312(64x^3)(y^11) or 19968x^3y^11.

We would use the binomial theorem formula

Σ [n! / (k!(n - k)!) * a^(n - k) * b^k] for k = 0 to n.

For our calculation, we have affirmed that n equals 14 whereas a and b are equivalent to 4x and y respectively.

Our objective parameter is set to the twelfth term where k holds the value of 11 (as k begins counting from zero).

Thus substituting these values in the binomial equation, it follows:

(4x + y)^14 = Σ [14! / (k!(14 - k)!) * (4x)^(14 - k) * y^k] from k= 0 to 14.

From this derivation, the number we had sought becomes calculable by assigning value k equals 11:

Term_12 = 14! / (11!(14 - 11)!) * (4x)^(14 - 11) * y^11.

The above simplifies after that further leading to:

Term_12 = 14!/(11! × 3!) × (4x)^3×y^11\

Term_12=(14 × 13 × 12)/(3 × 2 × 1) × (4x)^3 × y^11

which leads to, after computation:

Term_12= 2 ×13 × 12×64x^3y^11

Immediately from our results, the constant values a, b, and c have become clear:

a = 2 × 13 × 12 which reduces to 312

b = 64

c = 11

Thus note that for term 12: 'a' is equal to 312; 'b' is represented by 64 while 'c' stands for 11.

Simplification of this value would lead to expressing the twelfth term as 19968 x^3 y^11.

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Given the expression (4x + y)^14, find the coefficients a, b, and c in the 12th term of the expanded form

A linear equation is an equation in which each term has at max one degree. The table that represents a linear function is Table 1. Thus, the correct option is A.

We have,

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.

For the table to represent a linear function, the function must have a constant slope between any two points.

For the first table, the slope between the first two points is,

m = (7-3)/(2-1) = 4

The slope between the last two points is,

m = (15-11)/(4-3)

Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.

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The volume of the sphere is 5,575.28 ft³.

The volume of the sphere is calculated by applying the following formula as shown below;

V = ⁴/₃ πr³

where;

The radius of the sphere is calculated as follows;

r = d/2

where;

r = 22 ft / 2

r = 11 ft

The volume of the sphere is calculated as;

V = ⁴/₃ π(11)³

V = 5,575.28 ft³

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In this table, the constant of proportionality is 15.5.

The constant of proportionality is the ratio that one value has compared to another.

In other words, the constant of proportionality is the quotient of the numerator and the denominator.

The constant of proportionality can also be referred to as the slope, gradient, or unit rate.

X            y         Constant of Proportionality

2          31            15.5 (31/5)

5          77.5        15.5 (77.5/5)

7.5      116.25      15.5 (116.25/7.5)

Thus, the constant of proportionality, which can also be computed as the slope or unit rate is 15.5.

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Answer:

1875

Step-by-step explanation:

Yearly income = $90000

Monthly income = 90000÷12 = $7500

Monthly rent = 25%×7500 = $1875

If "∠A" is complementing angle "∠B" and "∠C" is complementing "∠B", then the true statement is (a) ∠A ≅ ∠C, because both the angles have the same measure.

The "Complementary-Angles" are two angles that add up to 90 degrees, which is also known as a right-angle. When two angles are complementary, they are said to complement each other.

Since the angles : ∠A and ∠C are both complementary to ∠B, we can write :

⇒ ∠A + ∠B = 90°,

⇒ ∠B + ∠C = 90°,

Next, We subtract "∠B" from both sides of each equation,
We get;

⇒ ∠A = 90° - ∠B,

⇒ ∠C = 90° - ∠B,

We see that the measure of the angle "A" and angle "C" is same.

Therefore, ∠A and ∠C have the same measure, option (a) is the correct answer.

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The given question is incomplete, the complete question is

If ∠A is a complementary angle of ∠B and ∠C is a complementary angle of ∠B, then which of the following statements is true?

(a) ∠A ≅ ∠C

(b) ∠A ≅ ∠B

(c) ∠A + ∠C ≅ ∠B

(d) ∠B ≅ ∠C

Expressing the trig ratio as a function of 50°, we have sin310° = sin(360 - 50)°

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

sin310°

The above expression is a sine function of 310 degrees

By mathematical expression, we have

360 - 50 = 310 degrees

This means that we can replace 310 degrees with (360 - 50) degrees in sin310°

So; in terms of 50 degrees, we have

sin310° = sin(360 - 50)°

Hence, the expression sin310° in terms of 50 degrees is sin(360 - 50)°

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x < -2 is the solution for the given inequality.

To solve the inequality:

-3(x - 3) > 5 - 5x

We can start by using the distributive property and simplifying both sides of the inequality:

-3x + 9 > 5 - 5x

Next, we can add 5x to both sides of the inequality to get the x terms on one side:

2x + 9 > 5

Then, we can subtract 9 from both sides of the inequality to isolate the variable:

2x > -4

Finally, we divide both sides by 2, remembering to reverse the inequality because we are dividing by a negative number (-3):

x < -2

Therefore, the solution to the inequality is x < -2.

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From greatest to least5.25, 1, 3/4 (or 0.75), -5/2 (or -2.5), -8.345

To sort these numbers from largest to smallest, we must establish a consistent format for swift comparison.

Among the various numbers included are whole figures, fractions and decimals, causing us to mix them uniformly first so that they match— in decimals.

-5/2 = -2.5

5.25 = 5.25 (no alteration required)

1 = 1.0 (to simplify analysis, only adding decimal points)

3/4 = 0.75

-8.345 = -8.345 (essentially unchanged)

At this point, we can effortlessly contrast and compare the numbers.

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This has to do with the solution the quadratic equation given as: y=x² - 5x -14.

To factorize the quadratic equation - y =  x² - 5x -14, we need to find two numbers that multiply to -14 and add up to -5.

We can list out the factors of -14 as follows:

-1 and 14

1 and -14

-2 and 7

2 and -7

Out of these pairs, the numbers that add up to -5 are -2 and 7.

Therefore, we can factorize the equation as:

y = (x - 2)(x + 7)

To find the zeros or x-intercepts, we set each factor equal to 0 and solve for x:

x - 2 = 0, x + 7 = 0

x = 2, x = -7

So the solutions are (2, 0) and (-7, 0).

The axis of symetry is the average of the x-intercepts

This is (2 - 7)/2 = -2.5.

Substituting this  value into   the equation:

y = (-2.5 )² - 5 (-2.5 ) - 14 = -  20.25

So the vertex is (  -2.5, -20.25).

The domain of the function is all real numbers, since there are no restrictions on the input x.

The range of the function is y ≥ -20.25, since the vertex is the lowest point of the parabola and the graph extends upward from there. See the graph attached.

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A bag of daffodil bulbs costs $12 and a bag of windflower bulbs $8.

Let's use the letters "w" for the price of a bag of windflower bulbs and "d" for the price of a bag of daffodil bulbs.

We may construct the following system of equations based on the above information:

Perry's sales:

w + d = 20 (equation 1)

Darryl's sales:

7w + d = 68 (equation 2)

To solve for w and d, we can use the elimination method. Multiplying equation 1 by -1, we get:

-w - d = -20

Adding this to equation 2, we eliminate d and get:

6w = 48

Dividing both sides by 6, we get:

w = 8

Substituting this value of w into equation 1, we can solve for d:

8 + d = 20

d = 12

Therefore, a bag of windflower bulbs costs $8 and a bag of daffodil bulbs costs $12.

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Mathland Bakery sold 23 apple pies and 13 cherry pies on that day.

Since a represents apple and c represents cherry:

We can now go ahead to solve for a and c using a simultaneous equation approach.

From equation (1)

a = 36 - c

Substituting this expression into equation (2), we get:

Therefore, 13 cherry pies were sold. To find the number of apple pies sold, we can substitute this value of c into equation 1:

Therefore, 23 apple pies were sold.

In other words, Mathland Bakery sold 23 apple pies and 13 cherry pies on that day.

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The numeric values of the piecewise function in this problem are given as follows:

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

A piecewise function is a function that has different definitions, based on the input x of the function.

For values of x that are of 1 or less, the function is defined as follows:

f(x) = x.

Hence the numeric values in this interval are given as follows:

For values of x that are greater than 1, the function is defined as follows:

f(x) = -x + 4.

Hence, at x = 3, the numeric value of the function is given as follows:

f(3) = -3 + 4 = 1.

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Answer: red = 9, yellow = 15 green = 24, total = 48 notepads were bought.

Step-by-step explanation:

3 x 3 = 9, so 9 red. 3 x 5 = 15, so 15 yellow. 3 x 8 = 24, so 24 green. In total this is equal to 48 notepads. 9 + 15 + 24 = 48.

The value of the expressions are;

a. 4n - 8

b. 64

c. 18

d. 5(n + 3)

Algebraic expressions are described as expressions that consists of terms, constants, coefficients, factors and variables.

They are also identified to consist of mathematical operations which includes;

Using the distributive property, we have;

a. 4(n - 2)

expand the bracket, we get;

4n - 8

b. . 8(2+6)

8(8)

expand the bracket

64

c. 6•8-6•5

48 - 30

Subtract

18

d. 5n+15

factorize the expression

5(n + 3)

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The resultant force is gotten  as 173.3780

A resultant force is described as  the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition

we determine resultant force by following these steps:

See attached image for full working

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All city residents who support the arts. Therefore, the option C is the correct answer.

As the city official would lie to know that if public support for increased funding of arts programs. By collecting data the officials show the survey after every 25 persons and ask for their opinion.

They also tend to raise a fund that states the population in the scenario of a city resident that supports the arts.

The population in this scenario is the people surveyed by the city official. The city official is conducting a survey outside a concert hall after a show, which means they are targeting people who have just attended a show. Since the city official is asking every 25th person to exit their opinion about raising funds for the arts, these are the people who are included in the population being surveyed.

Therefore, the option C is the correct answer.

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Answer:

,-3

A magic square is a square grid where the numbers in each row, column, and diagonal add up to the same total. In this case, we have 8 numbers to fill in a 3x3 grid, so we'll start with the number in the middle cell, which must be 1 to balance the negative numbers around it:

|- - -|

|- 1 -|

|- - -|

Now let's fill in the other cells one at a time, following the rule that each row, column, and diagonal must add up to the same total (which we'll call S):

|-2 - -|

|- 1 -|

|- - -|

We can't put -3 in the top left corner, since that would leave us with two negative numbers in the top row. Instead, we'll put -3 in the bottom right corner:

|-2 - -|

|- 1 -|

|- -3 -|

Now we need to find a number to put in the top row that will make it add up to S. The sum of the top row so far is -2, and we need it to be S/3, since there are 3 cells in the row. So we need to find a number x that satisfies:

-2 + x = S/3

Multiplying by 3 and adding 2 to both sides, we get:

3x = S + 6

So the number we need to put in the top row is (S+6)/3. We'll call this number y:

|-2 y -|

|- 1 -|

|- -3 -|

Now let's find a number to put in the bottom row. The sum of the bottom row so far is -3, and we need it to be S/3. So we need to find a number z that satisfies:

-3 + z = S/3

Multiplying by 3 and adding 3 to both sides, we get:

3z = S + 9

So the number we need to put in the bottom row is (S+9)/3. We'll call this number w:

|-2 y -|

|- 1 -|

|w -3 z|

Finally, let's find a number to put in the top right corner. The sum of the diagonal from top right to bottom left is -2+1-z, which must be equal to S. So we have:

S = -2 + 1 - z

Simplifying, we get:

S = -1 - z

Since we know that the sum of each row is S, we can add up the numbers in the top row and subtract that from S to get:

S -2 - y = -1 - z

Simplifying, we get:

S = z - y + 1

Now we can substitute in expressions for S, y, and z to get an equation for w:

(z + 6)/3 - 2 - (S+6)/3 = -3(z + 9)/3 + 1

Multiplying by 3 to clear the fractions, we get:

z + 6 - 2(S+6) = -3z - 24 + 3

Simplifying, we get:

2S = 2z - 27

So the value of w must satisfy:

(w + 9)/3 + (S+9)/3 = -3z - 24 + 1

Multiplying by 3 to clear the fractions, we get:

w + 9 + S + 9 = -9z - 69

Substituting in expressions for S and z, we get:

w + 9 + (z - y + 1) + 9 = -9z - 69

Simplifying, we get:

w = -10z - 88

Now we can plug in values for z

The addition of the outlier will affect the distribution in that b) The distribution will become skewed left.

When a score of 12 is added as an outlier, it shifts the distribution of data towards the left-sided direction resulting in skewness. This can be deduced from observing that the median is closer to the lower end of the range of collected data.

Additionally, the introduction of the outlier has substantially decreased the mean value, indicating that the deviation value has pulled the mean downwards and altered the symmetry of the original distribution by making it asymmetrically distributed in a leftward manner.

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The distributive property of multiplication can be used to calculate the sum of the difference between the multiples of the variables expression as follows;

[tex]\sum\limits_{i = 1}^{124} (29\cdot a_i - 13 \cdot b_i)[/tex] = -30

The distributive property states that multiplying the difference between addend by a value produces a result which is equivalent to the multiplication of each addend individually and finding the difference from the resulting values.

The distributive property of multiplication indicates that we get;

Where; [tex]\sum\limits_{i=1}^{124} a_i = -10[/tex], and [tex]\sum\limits_{i=1}^{124} b_i = -20[/tex]

[tex]\sum\limits_{i=1}^{124} (29\cdot a_i - 13\cdot b_i) = 29 \times \sum\limits_{i=1}^{124} a_i - 13 \times \sum\limits_{i=1}^{124} b_i = 29 \times (-20) - 13 \times (-10))[/tex]

29 × (-10) - 13 × (-20) = -30

Therefore;

[tex]\sum\limits_{i=1}^{124} (29\cdot a_i - 13\cdot b_i) =-30[/tex]

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Applying the inscribed angle theorem, the measure of angle STU in the circle is: 29°.

When an inscribed angle intercepts an arc in a circle, the measure of the inscribed angle is always half of the measure of the arc it intercepts, based on the inscribed angle theorem.

Angle STU is an inscribed angle that intercepts arc SU in the given circle, therefore:

(5x - 16) = 1/2(12x - 50)

Solve for x:

2(5x - 16) = 12x - 50

10x - 32 = 12x - 50

10x - 12x = 32 - 50

-2x = -18

x = 9

m∡STU = (5x - 16) = 5(9) - 16

m∡STU = 29°

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