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The value of x and y are 25 and 25√3 respectively.

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Given a right angled triangle and an angle 30°.

Length of hypotenuse = 50 units

Sine of an angle in a right angled triangle is the ratio of opposite side to hypotenuse.

sin (30°) = x / 50

x = sin (30°) × 50

x = (1/2) × 50

x = 25 units

Cosine of an angle in a right angled triangle is the ratio of adjacent side to hypotenuse.

cos (30°) = y / 50

y = cos (30°) × 50

y = (√3 / 2) × 50

y = 25√3 units

Hence the value of x is 25 units and the value of y is 25√3 units.

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The required pressure for the given information is 55.6 N/m².

Pressure is defined as the force exerted per unit area. It can be calculated by dividing the force by the area over which it is spread. In this case, the force is 506 N and the area is 9.1 m², so the pressure can be calculated as follows:

pressure = force / area

= 506 N / 9.1 m²

= 55.6 N/m².

The unit of pressure is N/m² or Pascal (Pa). Therefore, the pressure in this case is 55.6 Pa. This means that for every square meter of area, there is a force of 55.6 N acting on it. The pressure can be used to determine the force required to cause deformation of an object, the amount of gas in a container, and many other physical phenomena.

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Answer:

Step-by-step explanation:

A positive correlation indicates that: the value of one variable increases, the value of the other increases.

There are many instances in daily life where we employ related variables, such as height and weight. Ice cream sales rise in tandem with rising temperatures. Therefore, we refer to two variables as being correlated when they are connected. There are 4 different kinds. i.e., a perfect correlation, a perfect correlation, a negative correlation, and no correlation.

The supplied two variables move in the same direction when there is a positive correlation (i.e increasing together o decreasing together). So, in this case, the correlation coefficient is positive. We may claim that as one variable rises, the other variable likewise increases since they are going in the same direction.

The necessary response is,

As the values of one variable increase, the values of the other variable also tend to increase.

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Complete question: Two variables have a positive association when

a. the values of one variable tend to increase as the values of the other variable increase.

b. the values of one variable tend to decrease as the values of the other variable increase.

c. the values of one variable tend to increase regardless of how the values of the other variable change.

d. the values of both variables are always positive

The probability 7C3 = 35 possible ways to place 7 identical balls into 3 identical boxes.

The number of ways to place 7 identical balls into 3 identical boxes can be calculated by using the combination formula. The formula for combinations is nCr = n! / (r! (n-r)!), where n represents the total number of items and r represents the number of items being chosen. In this case, n = 7 and r = 3, so the formula becomes 7C3 = 7! / (3! (7-3)!). This simplifies to 7C3 = 7! / (3!4!) = 35. Therefore, there are 35 possible ways to place 7 identical balls into 3 identical boxes.

In each case, the balls can be placed into one box, two boxes, or three boxes, depending on how many balls are placed in each box. If one ball is placed in each box, then the remaining four balls can be placed in any of the boxes, giving four possibilities. If two balls are placed in each box, then the remaining one ball can be placed in any of the boxes, giving three possibilities. Finally, if all seven balls are placed in one box, then there is only one possibility. When the combinations of each scenario are added together, the total number of possible ways to place 7 identical balls into 3 identical boxes is 35.

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Answer:

75 degrees

Step-by-step explanation:

on the long line that goes out to 132 is a supplementary line so that means the angle next to 132 will make the line equal 180

180 - 132 = 48

so now we know the inside angles are 48 and 57

A triangle has 180 degrees in it so

x + 48 + 57 = 180

x + 105 = 180

x = 75

The value of x is 20 degrees.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two two angles are two pairs of supplementary angles. Meaning that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

a ║ b, m∠3 = 5x + 10, and m∠5 = 3x + 10.

Thus interior angles are supplementary;

m∠3+ m∠5 = 180°

5x+ 10 + 3x + 10 = 180°

8x + 20 = 180

8x = 160

x= 160/8

x= 20°

Hence, the value of x is 20 degrees.

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Answer:

command+shift+3

Step-by-step explanation:

hope this helped :)

A polynomial in standard form that represents the area of paper that can be painted is equals to the x² - 48x + 540.

We have, a painter wants to painting on a paper. He starts with a blank piece of rice paper with dimensions 30 inch by 18 inch .

The total length of paper, l = 30 inch

Total width of paper , w = 18 inch

Area of paper = l× w = 18× 30

= 540 inch²

Now, painter wants to leave a uniform border.

The width of border = x inches

length of border = x inches

and paint the remaining paper. So, the length of paper which is painted = l - x

= (30 - x) inches

Width of paper which is painted = w - x = ( 18 - x) inches

Now, the painted area of paper, A = painted length × painted width

= (30 - x)( 18- x)

= 540 - 18 x - 30x + x²

= x² - 48 x + 540

which is a standard polynomial form of painted area.

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Answer: 0.4

Step-by-step explanation:

1/25 = 0.04 which is also 4% (.04 * 100)

The expression that represents the amount of money after t years when $10,000 is compounded quarterly at 12% interest is C. $10,000 (1 + 0.12)^4t.

The compound interest formula or equation for finding the final amount after some years of the principal compounded at an interest rate is given as follows:

Formula for the Final Amount:

A = P(1 + r/n)^{nt}

Where:

A = The Final amount

P = The initial principal

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Thus, the correct expression for finding the final amount after t years under the compound interest system is given by Option C.

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Work Shown:

y+47 = 90

y = 90-47

y = 43

Given :-

To find:-

Answer:-

Firstly as we know that the measure of a straight line is 180° . The given line is made up of 3 angles , which are 47° , y° and one right angle i.e. 90°.

So the sum of all these angles will be 180° as these are the angles of a straight line.

So that,

[tex]\implies 47^o + y^o + 90^o = 180^o\\[/tex]

[tex]\implies 137^o + y^o = 180^o \\[/tex]

[tex]\implies y^o = 180^o-137^o\\[/tex]

[tex]\implies \underline{\underline{ y = 43}} \\[/tex]

Hence the value of y is 43 .

and we are done!

The value of the given ratio for triangle ACE and BCD include the following:

1.)25/16

2.)10/7

3.) 1

4.) 14/19

5.) 4/5

6.) 4/1

7.) 16/5

8.) 29/45

In order to calculate the ratio, the value of the missing parts of the triangle should be calculated such as line BD, and CE, by the use of Pythagorean formula.

The Pythagorean formula = c² = a² + b²

For first triangle:

BC = a = 20

CD = b = 14

BD = c = ?

C² = 20²+14²

c² = 400+196

c² = 596

C = √596

C = 24 = BC

The ratio of the given sides of the triangle include the following:

1.) = AC = 20+5 = 25; CE = 25/16

2.) BC:CD = 20/14 = 10/7

3.) BD:AE = 24/24 = 1

4.) CD:CE = 14/19

5.) BC:AC = 20/25 = 4/5

6.) BC:AB = 20/5 = 4/1

7.) CD:DE = 16/5

8.) perimeter of BCD = 20+14+24 = 58; perimeter of ACE =25+24+21 = 70

The ratio of perimeter of BCD:ACE = 58/70 = 29/45

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Answer:

below

Step-by-step explanation:

The upper and lower horizontal lines are parallel

 so y = 71°      alternate angles with transverse line

then z = 180 - 71 - 65 = 44°     ( interior angles of a triangle sum to 180 °)

Answer:

2

Explanation:

you need to find the common denominators. Looking at the problem, there are 3 different denominators. 8, 16, and 4. To tell the difference, here they are bolder and italicized to see the difference.

1 3/8+13/16-3/16+2/8-1/4

We can combine the common denominators, leaving us with this:

1 5/8+10/16-1/4

Then you need to make the denominators the same, and since 4 times 2 is 8, you can multiply the numerator and denominator by 2 so the denominator is 8. Then since you can divide 16 by 2 and it equals 8, and the numerator is even, you can divide the numerator and denomorator by 2 so the denominator is also 8. This ends up looking like this:

1 5/8+5/8-2/8

Then you need to combine the common denominators again, leaving you with this:

1 8/8

You can simplify that to simply “2”

(From the start you can also take the 1 and make the original operation into 11/8+13/16 etc., but for this equation it was possible to leave it out until the end and only write it as a placeholder and reminder until the very end. Then at the end I added back in.)

Answer:

It has no solution.

Step-by-step explanation:

5(x - 2) = 8 + 5x

5x - 10 = 8 + 5x

5x = 18 + 5x

0 = 18

The variable cancels out, so there is no solution to substitute it for.

On solving the provided question, we can say that angle a = 113

;angle b = 57;

angle c = 57  

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that converge at a center point known as the angle's vertex.

Two rays can create an angle in the plane where they are arranged. Additionally, when two planes collide, an angle is created. Dihedral angles are what they are called. An angle is a possible shape for two rays or lines with a common termination in planar geometry. The English term "angle" derives from the Latin word "angulus," which meaning "horn." The vertex is the common endpoint of the two rays, also known as the sides of the angle.

from the 3rd figure, we have -

angle a = 113 ( vertical opposite angle)

angle b = 180 - a    (Corresponding angles)

180 - 113 = 57

b = 57

angle c = 57  ( vertical opposite angle)

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The ratio of the area of the two similar figures is 9 : 16.

Based on the question above, by comparing side shape 1 with side shape 2.

6 : (6+2)

6 : 8

3 : 4

For the ratio of area between the two figures, you can square each one.

3 : 4 = 3² : 4² = 9 : 16

Similar polygons have the same angles and proportional sides. "Proportional" means that the lengths occur in equal proportions (e.g., if the base of triangle 1 is twice the length of the shortest side of triangle 1, then the base of triangle 2 is the length of triangle 2). twice the length of the shortest side).

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The blanks are filled as follows

coordinate   key feature    does the coordinate        justification

                                                   make sense  

(-7.565, 0)   it is a key feature          yes                      This is a zero

(0, 37)          it is a key feature          yes                      it is the y - intercept

(6, 46)          it is a key feature          yes                      it is the vertex

The constraint is that the range will always be

{y | y ∈ R ≤ 46}

The vertex of a quadratic function is the highest or lowest point of the parabolic graph of the function, which is also the turning point of the graph.

The vertex of a quadratic function in the form of y = ax^2 + bx + c is given by the coordinates

(x, y) = (-b/(2a), -(b^2 - 4ac)/(4a)).

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A reasonable number of pages Carlos can write in 5 hours is between 20 and 25 pages.

Therefore the answer is C.

First, we need to find the average number of pages Carlos can write in one hour by dividing the number of pages he can write in 3/4 hour by 3/4:

(3 to 4 pages) / (3/4 hour) = 4 to 5.33 pages per hour

So, we can see that Carlos can write between 4 to 5.33 pages in an hour.

Next, we'll multiply that number by 5 to find the number of pages he can write in 5 hours:

(4 to 5.33 pages/hour ) * 5 hours = 20 to 26.65 pages

Since we can say that, he reads between 20 and 26 pages.

Therefore, the reasonable number of pages Carlos can write in 5 hours is between 20 and 25, which corresponds to option C.

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The CPA selected the probability-proportional-to-size (PPS) sampling technique because it enables the selection of items in a population in proportion to the items' sizes. This technique yields a more accurate audit by precisely measuring the population of accounts receivable balances.

CPAs frequently employ the probability-proportional-to-size (PPS) sampling technique, also known as dollar-unit sampling, when examining the receivables balances of their clients. With this approach, it is possible to choose population members based on how big they are. The CPA can precisely gauge the population of accounts receivable amounts as a result, which is advantageous. A more accurate audit is made possible by the fact that the larger items in the population are more likely to be chosen than the smaller ones. Additionally, when the sample size grows, the audit's accuracy rises as well, which is another reason CPAs like to employ PPS sampling in their audits. This approach is advantageous because it ensures that the CPA is assessing the population of accounts receivable balances precisely and that the audit is carried out in a precise and trustworthy manner.

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Answer:

156.8

Step-by-step explanation:

1.6 * 98

The measure of 2D is five-halves the measure of ZY, the measure of each angle of the deck.

D and R are opposite sides & G and Y are also opposite sides.

So, we have:

∠D = ∠R = 5/2 ∠Y

and

∠G = ∠Y

The sum of angles is given as:

∠D + ∠G + ∠Y + ∠R = 360

Substitute values for ∠D, ∠G, ∠R

5/2 ∠Y + 5/2 ∠Y + ∠Y + ∠Y = 360

Multiply both sides by 2/14,

∠Y = 51.43

So:

∠G , ∠Y = 51.43

∠D = 5/2 ∠Y

∠D = 128.57

Therefore, measure of angle m∠D = 128.57°, m∠G = 51.43°, m∠R = 128.57°, m∠Y = 51.43°.

A parallelogram is a two-dimensional flat shape with four angles. The internal angles on either side are equal. The transversal's angles on the same side are supplementary, which means they sum to 180 degrees. As a result, a parallelogram's internal angles add up to 360 degrees.

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Total 4 dummy variables would be needed to include this categorical variable in a regression model.

A regression analysis serves as the foundation for many types of forecasting and determining the effects on target variables. When you hear about studies in the news about fuel efficiency, pollution causes, or the effects of screen time on learning, a regression model is frequently used to back up their claims.

A dummy variable (also known as an indicator variable or simply dummy) in regression analysis is one that takes the values 0 or 1 to indicate the absence or presence of some classification impact that may be predicted to shift the result.

Total 4 dummy variables would be needed to include this categorical variable in a regression model.

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The number of sides in the regular polygon would be -

n{sides} = 360/K.

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

The segments of a polygonal circuit are called its edges or sides.

Given is that exterior angle of a regular polygon measures {K°}.

In a regular polygon, the size of each exterior angle =

m∠E = 360° ÷ n{Sides}

m∠E = 360°/n{Sides}

n{sides} = 360°/m∠E

n{sides} = 360/K

Therefore, the number of sides in the regular polygon would be -

n{sides} = 360/K.

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The degrees in radian measures of the angle is 240 degrees or 4.188 radians.

The central angle of a circle is the angle formed by two of its radii. the two places on either side of the circle where the radii meet.

The angle measure between two consecutive numbers on a clock is 360/12 = 30 degrees.

At 2 the clock hand is at 2, the angle is:

30(2) = 60 degrees.

At 10, the angle is:

30(10) = 300 degrees

The angle between 2 and 10 is:

300 - 60 = 240 degrees.

Hence, the degrees in radian measures of the angle is 240 degrees or 4.188 radians.

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Answer:

200 seconds

Step-by-step explanation:

1 km = 1000m

3 km = 3000m

How long would it take to travel 3 km at a speed of 15 m/s?

The equation to solve this is:

Time = Distance / Rate

D = 3km or 3000m

R = 15 m/s

3000 divided by 15 = 200 seconds

So, it would take 200 seconds to travel 3 km at a speed of 15 m/s

Answer:

Below

Step-by-step explanation:

You need to have consistent units

  3 km = 3000 m

Distance / rate = time

 3000 m / 15 m/s = 200 seconds