Given that cos x = 3/5 and 0

The sequence of steps that translates figure W to figure X are -

Refer to the image attached. It shows figure W and figure X. We can write the sequence of steps for the given translation as -

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The missing statement and the reason in the two-column proof:

EC = BC; property iof isosceles triangles

The corret answer is an option (A)

A two-column proof to show that AB/AD = BC/DC is:

        Statement                                        Reason

       ∠1 ≅ ∠2                                               given

       ∠1 ≅ ∠5                          alternate interior angles theorem

       ∠3 ≅ ∠4                                vertical angles theorem

ΔABD is similar to ΔCED                  AA similarity

  AB/AD = EC/DC                         property of similar triangles

        ∠2 ≅ ∠5                     substitution property of congruency

         EC = BC                          property iof isosceles triangles

        AB/AD = BC/DC               substitution property of equality

Therefore, the correct answer is an option (A)

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Find the complete question below.

The solution is:

(a) A (20, 60), B = (0, 0) and C = (80, 0).

(b) The values of x and y that maximize the objective function are

(20, 60).

(c) From graph  we can see that (20, 60) is the maximum value of the objective function on the feasible region.

We have,

The set of all possible points of an optimization problem that satisfy the problem's constraints—which may include inequalities, equalities, and integer constraints—is referred to in mathematics as a feasible region, feasible set, search space, or solution space.

Given,

x ≥0, y ≥ 0

x + y ≤ 80

y ≤ 3x

Objective function: z = 250x + 300y

(a) For the given constraints the feasible region is attached below.

The feasible region is ABC.

where, A (20, 60), B = (0, 0) and C = (80, 0).

(b) Now to find the values of x and y which maximize the objective function.

z = 250x + 300y

At A = (20, 60)

z = 250(20) + 300(60) = 5000 + 18000 = 23000

At B = (0, 0)

z = 250(0) + 300(0) = 0

At C(80, 0)

z = 250(80) + 300(0) = 2000 + 0 = 2000

Therefore, the values of x and y that maximize the objective function are (20, 60).

(c) From graph  we can see that (20, 60) is the maximum value of the objective function on the feasible region.

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The appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.

The given data set is:

2, 10, 10, 12, 12, 20

To determine the appropriate measure of variability, we need to consider the spread or dispersion of the data. In this case, we can see that the range,

20 - 2 = 18.

A better measure of variability for this data set is the interquartile range (IQR), which is the range of the middle 50% of the data. To find the IQR, we first need to find the median of the data:

2, 10, 10, 12, 12, 20

The median is the middle value when the data set is arranged in order, which is 11. We can then divide the data set into two halves:

2, 10, 10 and 12, 12, 20

The lower half has a median of 10, and the upper half has a median of 12. The IQR is the difference between these medians:

IQR = 12 - 10 = 2

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.

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Answer:

C

Step-by-step explanation:

To find the sum of the rational expressions, we need to add the two expressions and simplify if possible:

(2x-1)/(7x+x+2) + (x-2)/(8x-2)

Simplifying the denominators, we get:

(2x-1)/(8x+2) + (x-2)/(8x-2)

Now, we need to find the LCD, which is (8x+2)(8x-2) = 64x²-4:

[(2x-1)(8x-2) + (x-2)(8x+2)] / (64x²-4)

Simplifying the numerator, we get:

[16x²-4x-16x+4+8x²-2x+16x-4] / (64x²-4)

Combining like terms, we get:

(24x²-2) / (64x²-4)

Factoring out a 2 from the numerator and denominator, we get:

2(12x²-1) / 2(32x²-2)

Simplifying further, we get:

(12x²-1) / (16x²-1)

Therefore, the sum of the rational expressions is:

12x²-1

-----------

16x²-1

So, the answer is option C.

The value of x for the intersecting chords is derived to be 14 which makes option C correct.

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

x × 32 = 16 × 28

32x = 448

32x/32 = 144/32 {divide through by 32}

x = 14

Therefore, the value of x for the intersecting chords is derived to be 14

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Answer:

�

=

1.154701

Step-by-step explanation:

12x sqaured - 2 = 14

so first add 2 to make it 16 in the other side.

12x sqaured =16 then divide the sqaured and get 4 on the other side

so 12x = 4 then the answer is 4/12 or 1/3

Answer:

Step-by-step explanation:

12x²-2=14              add 2 to both sides

12x²=16                  divide both sides by 12

x² = 16/12             reduce by dividing top and bottom by 4

x²=4/3                  take square root of both sides to cancel square

                            when you take sq root you also get ±

x=±[tex]\sqrt{\frac{4}{3} }[/tex]                    you can take square root of 4

= ±  [tex]\frac{2}{\sqrt{3} }[/tex]                        you can never leave root on bottom so multiply by

                              root on top and bottom  to simplify

= ± [tex]\frac{2}{\sqrt{3} } \frac{\sqrt{3} }{\sqrt{3} }[/tex]

= ±  [tex]\frac{2\sqrt{3} }{3}[/tex]

The graph which represents the number of months it will take Talia to save at least $200 is Line B.

Given that,

Talia tutors and wants to save money.

Talia currently has $60 and plans to save an additional $35 per month.

Current amount = $60

Additional amount each month = $35

Let n be the number of months taken to at least save $200.

60 + 35n ≥ 200

35n ≥ 140

n ≥ 4

So the graph will be a number line which has a closed circle on 4 and pointing to the right, because number of months should be either equal to or greater than 4.

Hence the correct option is B.

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The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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Each of the other three clerks have to complete 3 reports each.

The top employee finishes 40% of the reports, or: 0.40 x 15 = 6 reports.

Therefore, the other three clerks must finish the remaining 60% of the reports.

Total reports to be completed by the other clerks = 0.60 x 15 = 9 reports

We may distribute the remaining reports evenly among the other clerks since they all have an equal number of reports to complete:

Number of reports each of the other clerks have to complete = 9 reports ÷ 3 clerks = 3 reports

Therefore, each of the other three clerks have to complete 3 reports each.

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A linear equation that describe how x and y are related include the following: A. y = -8x.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 24/-3 = 16/-2 = 8/-1 = -8/1 = -16/2

Constant of proportionality, k = -8.

Therefore, the required linear equation is given by;

y = kx

y = -8x

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The value of the n is 1

In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.

To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.

(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:

18 = k(2)

k = 18/2

k = 9

Now that we have found the value of k, we can use it to find n when y = 9:

9 = 9n

n = 1

Therefore, the value of n is 1.

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Answer:

7

Step-by-step explanation:

All of the numbers are going up by 4 so what times 4 gives 28

thats 7

Marcus jogged approximately 2 1/2 miles over the weekend.

We need to discover a common denominator to add the miles run on Saturday and Sunday. Because 10 is the least common multiple of 5 and 2,

we may convert the fractions to have a denominator of 10:

1 2/5 = 1 + 4/5 = 5/5 + 4/5 = 9/5

9/10 = 0.9 = 9/10

Now we can add the two distances:

9/5 + 9/10 = 18/10 + 9/10 = 27/10

Rounding 27/10 to the nearest 1/2 gives:

27/10 ≈ 2 1/2

Therefore, Marcus jogged approximately 2 1/2 miles over the weekend.

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It took approximately 151 seconds to decrease 9 ft water in conical tank.

The volume of a conical tank with vertex down and radius 8 ft and height 20 ft is V = (1/3)πr²h

When the water is 9 ft deep

= (1/3) ×3.14×(8)²×(9)

= 602.88 ft³

We know that the rate of change of volume is 4 ft³/sec. So, the rate of change of depth can be calculated as follows:

Rate of change of depth (dh/dt) = Volume of tank/4 ft³ per sec

= 602.88/4

= 150.72 sec

Therefore, it took approximately 151 seconds to decrease 9 ft water in conical tank.

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The amount of dry ingredients used in the cake recipe is approximately 7 cups.

To find the total amount of dry ingredients used in the cake recipe, we need to add up the amounts of flour, sugar, and cocoa.

3 ½ cups of flour is equal to 3 cups plus 0.5 cups, or 3 cups and 8 ounces.

2 ⅔ cups of sugar is equal to 2 cups plus 0.67 cups, or 2 cups and 10.72 ounces.

1 ¾ cups of cocoa is equal to 1 cup plus 0.75 cups, or 1 cup and 12 ounces.

Adding these amounts together, we get:

3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

To the nearest cup, this is equal to 7 cups.

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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The estimate the number of pieces of food collected by mice is 96 and closest estimate to 24 is given by option b. 20.

Number of pieces of food collected by mice every day = 24 pieces

Total number of days mice collects the food = 4 days

To estimate the total number of pieces of food collected,

Now, multiply the number of pieces collected each day by the number of days,

Total number of pieces

= 24 pieces/day × 4 days

= 96 pieces

To estimate the answer closest to 24, we can round 24 to the nearest tens.

The nearest tens to 24 is 20.

Therefore, the estimate of collection of food pieces in 4 days by mice is equal to 96 and the closest estimate to 24 is option b. 20.

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The above question is incomplete , the complete question is:

A family of mice is collecting pieces of food that fall on the floor in a restaurant. If the mice collect 24 pieces of food every day for 4 days, we want to estimate the number of pieces of food they have collected. Which of the following is the closest estimate to 24?

a. 10

b. 20

c. 30

d. 40

Answer:r=3cscθ

Step-by-step explanation:The equation y = 3 represents a horizontal line at a distance of 3 units above the x-axis in the Cartesian coordinate system. To convert this equation into polar form, we can use the fact that x = rcos(theta) and y = rsin(theta) in polar coordinates.

Since y = 3 for all values of x, we can say that r*sin(theta) = 3. Solving for r, we get:

r = 3/sin(theta)

This equation represents a family of circles with center at the origin and radius 3/sin(theta), for all values of theta except for multiples of pi. We can simplify this equation by using the identity sin(theta) = 1/csc(theta), giving us:

r = 3csc(theta)

The number of adult that paid is 234 and the number of seniors that pad is 60.

A movie theatre charges 11$ for adults and 9$ for seniors. On a particular day when 294 people paid an admission, the total receipts were 3114.

Therefore, let's find how many paid for adult and for seniors.

Let

x = number that paid for adult

y = number that paid for senior

Hence, the situation forms the following equation.

x + y = 294

11x + 9y = 3114

multiply equation(i) by 11

11x + 11y = 3234

11x + 9y = 3114

subtract the equation

2y = 120

y = 120 / 2

y = 60

Let's find x

x = 294 - 60

x = 234

Therefore,

number of adults that paid= 234

number of seniors that paid = 60

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Being male and preferring Brand A are independent, as:

P(male|Brand A) = P(male).

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

From the table, we are already given the relative frequencies, hence the probability of being male is given as follows:

0.5 + 0.15 = 0.65.

The conditional probability of being male, given that the person prefers brand A, is given as follows:

P(male|Brand A) = P(male and Brand A)/P(Brand A) = 0.5/0.8 =  0.625.

As the probabilities are equal, the events are independent.

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Ronald will need 128π square feet to paint all the surfaces of the 8 Columns.

The formula for the total surface area of a cylinder is given by:

A = 2πr(r + h)

Where r is the radius and h is the height

In this case, each wooden cylindrical columns is 7 feet tall and have a diameter of 2 feet. Thus:

r = 2/2 = 1 feet and h = 7 feet

Thus, the total surface area of each wooden cylindrical columns will be:

A = 2π * 1 * (1 + 7)

A =  2π * 1 * 8

A = 16π square feet

Then the total surface areas of all the 8 Columns will be:

A = 8 * 16π

A = 128π square feet

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Answer:

3

Step-by-step explanation:

The answer is three because u need to simply the fractions

1)  Total time elapsed = 4 hours 59 minutes.

2)  Total time elapsed =  6 hours 12 minutes

3)  Total time elapsed =   6 hours 2 minutes

1) Time difference from 12:00 noon to 4:00 p.m = 4 hours

Time difference from 4:00 p.m to 4:59 p.m. = 59 minutes

So, the total time elapsed = 4 hours 59 minutes.

2) The time difference from 1:23 a.m. to 2:00 a.m. = 37 minutes

The time difference from 2:00 a.m to 7:00 a.m. = 5 hours

The time difference from 7:00 a.m. to 7:35 a.m. = 35 minutes

Here, the minutes elasped = 37 + 35

                                             = 72 minutes

                                             = 1 hour 12 minutes

So, So, the total hours elapsed = 5 + 1

                                                    = 6 hours

Thus, the total time elapsed = 6 hours 12 minutes

3) Time difference from 11:28 p.m. to 12:00 midnight = 32 minutes

Time difference from 12:00 midnight to 5:30 a.m. = 5 hours 30 minutes

Here, the minutes elasped = 32 + 30

                                             = 62 minutes

                                             = 1 hour 2 minutes

So, the total time elapsed =  6 hours 2 minutes

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Answer:

it's b to to the angles rotation that is giving 180 each side of the square is 90 degrees now you add them up

The x-intercepts for the function y = cos x, where 0≤x≤ 2n are

x = π/2, x = 3π/2, and x = 2π

We have,

The cosine function has an x-intercept whenever it crosses the x-axis, which happens at every multiple of π/2 radians (or 90 degrees).

So the x-intercepts for the graph y = cos x, where 0 ≤ x ≤ 2π are at

x = π/2, x = 3π/2, and x = 2π

(corresponding to 90 degrees, 270 degrees, and 360 degrees).

Now,

If we take 2n to be a multiple of 2π (i.e., 2n = k2π for some integer k), then the x-intercepts for the graph y = cos x,

where 0 ≤ x ≤ 2n, will be at x = kπ/2 for k = 0, 1, 2, ..., 4n-1.

The x-intercepts for the graph y = cos x, where 0≤x≤ 2n are

x = π/2, x = 3π/2, and x = 2π

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Assuming the Social Security contribution rate is 6.2% of the wage, Ted's contribution to Social Security can be calculated as follows:

Ted's total wage for the month = 160 hours * $10/hour = $1600

Social Security contribution = 6.2% * $1600 = $99.20

Therefore, the answer is option C. $99.20.

Jenny earns $36 in interest in one year in her savings account.

To calculate the interest that Jenny earns in one year on her savings account, we can use the formula for simple interest:

I = P x r x t

where I is the interest earned, P is the principal amount (in this case, $1200), r is the interest rate (in decimal form), and t is the time period (in years).

In this case, the interest rate is 3% per year, which can be written as 0.03 in decimal form. The time period is one year. So we have:

I = 1200 x 0.03 x 1

I = $36

Therefore, Jenny earns $36 in interest in one year in her savings account.

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Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)