unit 8 right triangles and trigonomerty homework3 trigonomerty rations and finding missing sides

Worker B appears to be more consistent in performance, while Worker B is more efficient from an overall point of view.

To determine who appears to be more consistent in performance, we need to compare the standard deviations of A and B. Both A and B have a standard deviation of 1.5 hours, which means that they have the same level of consistency in their performance.

To determine who is more efficient from an overall point of view, we need to compare the mean times of A and B. Worker B has a mean time of 4 hours, which is less than the mean time of Worker A (5 hours). This means that Worker B is more efficient than Worker A in completing the job from an overall point of view.

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Answer:

Step-by-step explanation:

Answer:

1.31313123x10^{46}

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

Isosceles triangle has two congruent angles.

∠ + ∠ + 130 = 180

2∠ = 50

∠ = 25

Answer:

25°

Step-by-step explanation:

In an isosceles triangle, 2 angles are equal.

The sum total of all angles in a triangle = 180

Assume unknown angle as x.

As 1 angle is already given, the equation is

130 + x + x = 180

130 + 2x = 180

2x = 50

x = 25°

Answer:

incomplete question, could u provide the whole question please?

Answer:

2468

Step-by-step explanation:

By determining in triangle MPQ,  NR || PQ, if QM= 31, RM= 21 and PM= 4PN , [tex]\frac{PN}{NM} \neq \frac{QR}{RM}[/tex] , So correct option is A.

A triangle is a three-sided polygon that consists of three line segments, or sides, that intersect at three points, or vertices. Triangles are one of the fundamental shapes in geometry and have numerous properties and applications in mathematics, science, and engineering.

Triangles can be classified based on the lengths of their sides and the measures of their angles. Triangles with three equal sides are called equilateral triangles, while triangles with two equal sides are called isosceles triangles. Triangles with no equal sides are called scalene triangles. Triangles can also be classified based on the measures of their angles, with acute triangles having all angles less than 90 degrees, obtuse triangles having one angle greater than 90 degrees, and right triangles having one angle equal to 90 degrees.

The Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, is a fundamental concept in trigonometry and has numerous practical applications.

Overall, triangles are an important shape in mathematics and have many practical applications in fields such as engineering, architecture, and physics.

As shown in the question:

QM= 31, RM= 21, PM= 4PN

So RQ= 31-21= 10

[tex]\frac{PN}{NM} = \frac{1}{3}\\[/tex]

[tex]\frac{QR}{RM}= \frac{10}{21}[/tex]

So, [tex]\frac{PN}{NM} \neq \frac{QR}{RM}[/tex]

NR and PQ are not parallel .

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The complete question is:

Answer:0.08

Step-by-step explanation:If you divide the (1/3)/4 that will get you 0.08

Answer:

v = 10

Step-by-step explanation:

[tex] \dashrightarrow \: { \sf{ {v}^{2} - {u}^{2} = 2as}} \: \: \: \\ \\ \dashrightarrow \: { \sf{ {v}^{2} = {u}^{2} + 2as }} \: \: \: \\ \\ \dashrightarrow \: { \sf{v = \sqrt{ {u}^{2} + 2as} }} \\ \\ \: \: \: \: \: \: \: { \colorbox{lightblue}{substitute \: variables}} \\ \\ \dashrightarrow \: { \sf{v = \sqrt{ {4}^{2} + 2(2 \times 21) } }} \\ \\ \dashrightarrow \: { \sf{v = \sqrt{16 + 84} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\dashrightarrow \: { \sf{v = \sqrt{100} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow \: { \sf{v = 10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

A telephone call center uses two customer service representatives (csrs) during the 8:30 a.m. to 9:00 a.m. time period. the standard service rate is 2.0 minutes per telephone call per csr. assuming a target labor utilization rate of 70 percent, Therefore, these two CSRs can handle approximately 3 calls during this half-hour period.

Given a telephone call center uses two customer service representatives (CSRs)

during the 8:30 a.m. to 9:00 a.m. time period, and the standard service rate is 2.0 minutes per telephone call per CSR. Assuming a target labor utilization rate of 70%,

we have to determine the number of calls these two CSRs can handle during this half-hour period.

The formula to calculate the number of calls that can be handled during this half-hour period is:

Number of calls = (number of servers x utilization rate x service time) / arrival rate

                          = (2 x 0.70 x 2) / 1

                          = 2.8 calls (rounded to the nearest whole number)

Therefore, these two CSRs can handle approximately 3 calls during this half-hour period.

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The length that Sarah should make the box in order to minimize the cost of the materials used, is 18 cm.

We know that each can holds 450 cubic centimeters of soda and is 12 centimeters tall. Let's first find the radius of the soda can.

The volume of a cylinder is given by the formula:

V = πr²h

Plugging in the given values:

r = √(450 / (π x 12))

r ≈ 1.77 cm

Now, we know that the box must hold 15 soda cans, and they fit in the box in rows of 3. This means there are 3 rows along the width and 5 rows along the length of the box.

Width: 3 cans x diameter = 3 x 2 x 1.77 ≈ 10.62 cm (since the diameter is twice the radius)

Length: 5 cans * diameter = 5 x 2 x 1.77 = 18 cm

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The patient value-added percentage is 17%. The doctor and the waiting are the two separate activities that happened one after another in the hospital. The value-added time is the time that creates value for the customers or patients.

Patient value-added percentage refers to the percentage of time that adds value to the patient.

The patient value-added percentage can be calculated using the following formula,

Value-added percentage = Value-added time ÷ Total time

The given values are,Waiting time = 25 minutes

Visit time = 5 minutes

Total time = Waiting time + Visit time= 25 + 5= 30 minutes

The value-added time is the time that creates value for the customers or patients.

The visit time is the value-added time in this case.

Value-added time = Visit time= 5 minutes

Putting the values in the formula,

Value-added percentage = Value-added time ÷ Total time= 5 ÷ 30= 1 ÷ 6= 0.1666...

The value-added percentage is 16.66… which is approximately 17%.Therefore, the patient value-added percentage is 17%.

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According to the question the surface area of the sphere with volume 4/3 mi^3 is: S = 4π^(1/3) square units.

The volume of a cube is measured in terms of the total amount of cube unit that something that fills. Simply put, volume is the entire amount of space that an object occupies. The formula a3, wherein there is the cube's edge, can be used to determine the cube's volume.

The formula given is:

[tex]S = \pi ^(1/3) * (6V)^(2/3)[/tex]

We are given that [tex]V = 4/3 mi^3[/tex]. Substituting this into the formula:

[tex]S = π^(1/3) * (6(4/3))^(2/3)\\S = π^(1/3) * (8)^(2/3)[/tex]

Now we need to evaluate [tex]8^{2/3}[/tex]. This means finding the number that, when raised to the power of 3, gives us 8. This is the cube root of 8, which is 2:

[tex]8^{2/3} = (2^3)^(2/3)= 2^(3*2/3)= 2^2 = 4[/tex]

Substituting this back into the formula:

[tex]S =\pi ^(1/3) * 4[/tex]

So the surface area of the sphere with volume [tex]4/3 mi^3[/tex]is:

[tex]S = 4\pi ^(1/3)[/tex]square units.

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a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled Sprinkles going to a value of 12, the second bar labeled Nuts going to a value of 17, the third bar labeled Hot Fudge going to a value of 44, and the fourth bar labeled Chocolate Chips going to a value of 27 correctly displays the data.

Answer:

292

Step-by-step explanation:

To find the 41st term of the sequence 12, 19, 26, we need to first find the common difference, d, between consecutive terms. We can do this by subtracting the first term from the second term (or the second term from the third term). So the common difference is 7. Now we can use the formula for the nth term of an arithmetic sequence. where an is the nth term, a1 is the first term, d is the common difference, and n is the term we want to find. Substituting the given values, you get the 41st sequence is 292.

There are 16 ways to choose a chairman, vice chairman, and secretary under these conditions

Since, the chairman must be a Democrat and the vice chairman must be a Republican, we have one choice for the chairman (out of the 10 Democrats) and one choice for the vice chairman (out of the 7 Republicans).

For the secretary, we have 16 people left to choose from (since we have already chosen the chairman and vice chairman), and it can be either a Democrat or a Republican.

Therefore, the number of ways to choose a chairman, vice chairman, and secretary is:

¹⁶C₁ = 16

So, there are 16 ways to choose a chairman, vice chairman, and secretary under these conditions

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Answer:

82 square feet

Step-by-step explanation:

The surface area of this pyramid:

[tex]5(4) + 2(\frac{1}{2} (4)(7) + \frac{1}{2} (5)(6.8))[/tex]

[tex]20 + 2(14 + 17)[/tex]

[tex]20 + 2(31) = 20 + 62 = 82[/tex]

Answer:

$105.00

Step-by-step explanation:

To find the total cost of the mirror, we need to first calculate its area. The area of the mirror can be found by multiplying its length by its width.

So, the area of the mirror would be:

Area = Length x Width

Area = 7 feet x 5 feet

Area = 35 square feet

Now that we know the area of the mirror, we can calculate the total cost by multiplying the area by the price per square foot:

Total Cost = Area x Price per square foot

Total Cost = 35 square feet x $3.00 per square foot

Total Cost = $105.00

Therefore, the total cost of the mirror would be $105.00.

Answer:105$

Step-by-step explanation: all you need to do is 5x7=35

35 is the amount of square feet the square has. Then you do 35 x 3.00=

105$

It is likely that Batter A, who swings the bat from a resting position on his shoulder, will hit the ball a greater distance than Batter B, who hits the ball with the bat directly behind it. This is because Batter A is able to generate more power and momentum with his swing, whereas Batter B's swing may be more limited in its range of motion and force.

Answer:

The Place Value of '4' will be 400 if we keep it in the Hundreds place
The Face Value of '4' will remain the same

describe four right that individuals in relationships have when they stay together

Answer:

The mean is 25 and the median is 23

The odds of spinning a 3 on any given turn is 1 out of 7 or 14%. This can be expressed as a decimal by dividing 14 by 100, which yields  probability of 0.14.

To calculate this, we divide the number of favorable outcomes (1) by the total number of possible outcomes (7). This is the same as the probability of spinning a 3 on a given turn, which can be expressed as a decimal, fraction, or percentage.The odds of spinning a 3 on any given turn is 1 out of 7 or 14%. This can be expressed as a decimal by dividing 14 by 100, which yields 0.14. To calculate this, we divide the number of favorable outcomes (1) by the total number of possible outcomes (7). This is the same as the probability of spinning a 3 on a given turn, which can be expressed as a decimal, fraction, or percentage.

P(Spin a 3) = favorable outcomes/ total outcomes

= 1/7

= 0.14

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According to the solving volume of the cylinder where the Brianna has collected approximately 99.1 grams of trace element (rounded to one decimal place).

The cylinder has a circular base and is a three-dimensional shape. A group of circular discs placed on top of one another might be thought of as a cylinder. Consider a situation where we need to figure out how much sugar can fit inside a cylindrical box.

In other words, we want to figure out the volume or capacity of this box. A cylindrical box's capacity is essentially equal to the volume of the cylinder inside. As a result, the volume of a three-dimensional shape is determined by how much space it takes up.

The volume of the cylinder is given by the formula V = πr²h

where r is the radius and h is the height.

Substituting the given values,

we get V = π(9.6 cm)²(11.6 cm) = 3,301.57 cm³ (rounded to two decimal places).

Since the sample contains 0.03 grams of trace element for every cubic centimeter of water,

Brianna has collected approximately 0.03 × 3,301.57 = 99.05 grams of trace element (rounded to two decimal places).

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The amount of grams per serving that are not carbohydrates or protein in the new cereal is 24.05 grams.

In the preceding question, we were told that the amount of carbohydrates in both Cornbits and Tasty Oats is 700% of the amount of protein. The amount of protein is 12 grams. So, we can conclude that the amount of carbohydrates is 700% 0f 12 grams which equal 84 grams. Also, we know that there are 5 grams of protein in 45 grams of Cornbits cereal.

Now 20% less grams of carbohydrates gives us 0.8 × 84 = 67.2

while 75% more grams of protein per serving than Cornbits gives us 175% × 5 = 8.75

The number of grams per serving that are not carbohydrates or protein in the new cereal will be:

100 - 67.2 - 8.75 = 24.05.

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Answer:

Hopes this helps

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be the angle Y has a value of roughly 76.4 degrees.

What precisely is a triangle?

Because a triangle has four or more extra parts, it is a polygon. Its form is a straightforward rectangle. A triangle is a rectangle with the edges A, B, and C. A singular plane but instead cube are produced by Euclidean geometry when the sides aren't truly collinear. A triangular is a shape if it has three sides and three angles. Angles are the points where a quadrilateral three sides meet. A triangle's sides add up to 180 degrees.

Here,

We can determine the images of locations A, B, and C using the following method:

=> A': (-yA, xA)

=> B': (-yB, xB)

=> C": (-yC', xC')

where C' is the rotated version of location C.

We can determine the side lengths of triangular ABC using the Law of Cosines:

Assume that

=>  a = BC = 2R sin(A/2) = 2R sin(45/2) 1.441R,

=> b = AC = 2R sin(B/2) = 2R sin(55/2) 1.663R, and

=> c = AB = 2R sin(C/2) = 2R sin(80/2) 2.219R.

where R represents the triangular ABC's circumradius.

Now, by turning point C 90 degrees anticlockwise with respect to the origin, we can determine the coordinates of point C':

xC' = -yC

yC' = xC

Then, to obtain the picture of point C, we can reflect point C' across the line y = x:

xC"=yC' and yC"=xC'

Again employing the Law of Cosines, we can determine the triangular XYZ's side lengths:

=> x = YZ = 2R sin(A'/2) = 2R sin(35) ≈ 1.189R

=> y = XZ = 2R sin(B'/2) = 2R sin(45) ≈ 1.414R

=> z = XY = 2R sin(C'/2) = 2R sin(55) ≈ 1.630R

where the picture angles of angles A, B, and C are A', B', and C', respectively.

Last but not least, we can apply the Law of Cosines once more to determine the size of angle Y:

cos(Y) i= t (x2 + z2 - y2)/ (2xz)

cos(Y) = 0.224 Y = 76.4 °

As a result, the angle Y has a value of roughly 76.4 degree

To graph the average and standard deviation of a given list of values, you should use a bar graph or a histogram.

1. Calculate the average (mean) of the given list of values.
2. Calculate the standard deviation of the given list of values.
3. Create a bar graph or histogram with two bars.
4. Label the first bar as "Average" and set its height to the calculated average value.
5. Label the second bar as "Standard Deviation" and set its height to the calculated standard deviation value.

This graph will visually represent the average and standard deviation of the given list of values.

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The probability that a student chosen at random will play the bass is 12/43.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or experiments. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. An event with a probability of 0 means it is impossible, while an event with a probability of 1 means it is certain to occur. Probabilities between 0 and 1 indicate the degree of uncertainty of the event occurring.

To find the probability that a student chosen at random will play the bass, we need to find the total number of students who play the bass and divide it by the total number of students in the middle school School of Rock.

The total number of students who play the bass is the sum of the number of seventh-grade students who play bass and the number of eighth-grade students who play bass:

Total number of bass players = 14 + 10 = 24

The total number of students in the middle school School of Rock is the sum of the number of seventh-grade students and the number of eighth-grade students:

Total number of students = 12 + 14 + 9 + 5 + 10 + 36 = 86

Therefore, the probability that a student chosen at random will play the bass is:

P(bass) = Total number of bass players / Total number of students = 24/86

To simplify this fraction, we can divide both the numerator and denominator by 2:

P(bass) = (24/2) / (86/2) = 12/43

Therefore, the probability that a student chosen at random will play the bass is 12/43.

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Answer:

  x = 1, x = 5

Step-by-step explanation:

You want the solutions to the absolute value equation ...

  |x -7| = |2x -8|

Each of the absolute value functions is equivalent to a piecewise-defined function. The boundary for the pieces is the turning point of the absolute value function, where its argument is zero.

The turning points are ...

  x -7 = 0   ⇒   x = 7

  2x -8 = 0   ⇒   x = 8/2 = 4

This means the equivalent piecewise equation will have 3 pieces. We know the absolute value function is defined as ...

  [tex]|x|=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge0\end{cases}[/tex]

If we write the equation in the form |x -7| - |2x -8| = 0, we have ...

  [tex]0=\begin{cases}-(x-7)-(-(2x-8))&\text{for }x < 4\\-(x-7)-(2x-8)&\text{for }4\le x < 7\\(x-7)-(2x-8)&\text{for }7\le x\end{cases}[/tex]

The equation simplifies to ...

  -x +7 +2x -8 = 0

  x -1 = 0 . . . . collect terms

  x = 1 . . . . . . a value in the domain. This is one solution.

The equation simplifies to ...

  -x +7 -2x +8 = 0

  15 = 3x . . . . . . . . . . add 3x

  5 = x . . . . . . . . a value in the domain. This is another solution

The equation simplifies to

  x -7 -2x +8 = 0

  -x +1 = 0

  x = 1 . . . . . . . . . not in the domain 7 ≤ x, so not a solution

The solutions are x = 1 and x = 5.

__

Check

  |1 -7| = |2·1 -8|   ⇒   |-6| = |-6| . . . . true

  |5 -7| = |2·5 -8|   ⇒   |-2| = |2| . . . . true

Both solutions check in the original equation.