How do you simplify an equation?

Answer:

63 degrees

Step-by-step explanation:

similar triangles have the same angles.

XYZ is similar to EDF. Therefore the measure of angle Z is the same as angle F. The measure of angle Z is 63, so the measure of angle F is also 63.

The measurement of angles are given as  20.92°, 40.83°,  57.76°, 71.17°, 26.21° and 44.7°respectively.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

The given problem can be solved by applying the trigonometric ratios to all of the triangle as follows,

(11) In the given triangle,

Sinθ = 5/14

=> θ = Sin⁻¹(5/14) = 20.92°

(12) In the given triangle,

Tanθ = 7/8.1

=> θ = Tan⁻¹(7/8.1) = 40.83°

(13)  In the given triangle,

Cosθ = 8/15

=> θ = Cos⁻¹(8/15) = 57.76°

(14) In the given triangle,

Tanθ = 8.8/3

=> θ = Tan⁻¹(8.8/3) = 71.17°

(15) In the given triangle,

Tanθ = 6.4/13

=> θ = Tan⁻¹( 6.4/13) = 26.21°

(16) In the given triangle,

Tanθ =9.4/9.5

=> θ = Tan⁻¹( 9.4/9.5) = 44.7°

Hence, the measures of the angles indicated in the triangles are obtained as 20.92°, 40.83°,  57.76°, 71.17°, 26.21° and 44.7°respectively.

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Answer:

1848

Step-by-step explanation:

Step-by-step explanation:

obtuse-larger than 90 degrees

acute-smaller that 90 degrees

right-exactly 90 degrees

The mean of the given data set is 29.5.

The term "mean" refers to the arithmetic average of the data set and is derived by dividing the total number of data points in the data set by the total number of data points. It is a data point that represents the average of all the data points in the collection.

Example :

Find the mean of the following data set.

10, 20, 36, 12, 35, 40, 36, 30, 36, 40

Given,

xi = 10, 20, 36, 12, 35, 40, 36, 30, 36, 40

n = 10

Mean = ∑xi/n

= (10 + 20 + 36 + 12 + 35 + 40 + 36 + 30 + 36 + 40)/10

= 295/10

= 29.5

Therefore, the mean of the given data set is 29.5.

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Find the mean of the following data set.

10, 20, 36, 12, 35, 40, 36, 30, 36, 40

Given,

xi = 10, 20, 36, 12, 35, 40, 36, 30, 36, 40

n = 10

Mean = ∑xi/n

= (10 + 20 + 36 + 12 + 35 + 40 + 36 + 30 + 36 + 40)/10

= 295/10

= 29.5

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

Given that,

We have to find why i squared is equal to negative 1.

We know that,

The imaginary numbers are denoted as i.

We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

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The segment e g contains the points e and g, and it bisects the triangle d e f into two congruent parts.

The points that segment e g contains are the points e and g.

Segment e g bisects triangle d e f, which means that it cuts the triangle into two equal parts. This means that the two sides d e and e f are congruent, and that the vertex angle d e f is divided into two equal angles, d e g with measure 3 y plus 4, and f e g with measure 5 y minus 10.

This can be expressed using the following formula:

Let d e = x

Then d e g = 3x + 4

f e g = 5x - 10

and d e + e f + f e g = 180°

Substituting the values for d e g and f e g, we get:

3x + 4 + x + 5x - 10 = 180°

9x = 196

x = 21.77

Therefore, the length of the sides d e and e f is 21.77.

Since segment e g bisects the base d f, it divides the base into two equal parts, each of length 10.88. The segment e g also divides the vertex angle d e f into two angles, d e g with measure 3 x + 4 = 67.33, and f e g with measure 5 x - 10 = 108.67.

Therefore, segment e g contains the points e and g, and it bisects the triangle d e f into two congruent parts. The segment also divides the vertex angle d e f into two angles, d e g with measure 67.33, and f e g with measure 108.67.

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The answer is x = 4

y = -1

z = -3

3x+2y+z=7

5x+5y+4z=3

3x+2y+3z=1

________

Let's take the first and the third equation, multiply the first one by (-1) and sum them up:

3x+2y+z=7

3x+2y+3z=1

____

-3x-2y-z=-7

3x+2y+3z=1

____

2z = -6

z = -6/2

z = -3

Substitute z in all equations:

3x+2y+z=7

5x+5y+4z=3

3x+2y+3z=1

______

3x + 2y - 3 = 7

5x + 5y - 12 = 3

3x + 2y - 9 = 1

______

3x + 2y = 10

5x + 5y = 15

3x + 2y = 10

The first and the third equations are the same, so one can be excluded:

3x + 2y = 10

5x + 5y = 15

Multiply the first equation by -5 and the second equation by 2 and sum them up:

-15x - 10y = -50

10x + 10y = 30

_________

-5x = -20

x = -20/-5

x = 4

Substitute x:

3x + 2y = 10

12 + 2y = 10

2y = 10 - 12

2y = -2

y = -2/2

y = -1

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Answer:

19 and 13/30

Step-by-step explanation:

First make 2/3 have a common denominator with 23/30

You can do this by multiplying the numerator and denominator of 2/3 to get 20/30

Now add

20/30 + 23/30  = 43/ 30

Simplify this fraction

1 and 13/30

add this to 18

18 + 1 and 13/30 = 19 and 13/30

Therefore, we lack adequate data to draw the conclusion that population means differ.

A result of a statistical test of a hypothesis is a number known as the test statistic. It displays how closely the distribution predicted by your observed data fit the null hypothesis of that statistical test.

Here,

First hypothesis : [tex]H_{0}[/tex] :  u1 - u2 =  0

Alternate hypothesis  : [tex]H_{A}[/tex]:  u1 - u2 ≠ 0

for 0.1 level with two tail test , critical z = 1.645

Rule of Decision: [tex]H_{0}[/tex]  Reject  if the test statistic's absolute value is |z|>1.645

California   , New York

x1            = 64510.00 x2            = 62900.00

n1           = 45                 n2            =                 45

σ1           = 8200.00 σ2           = 7800.00

std error σx1-x2=√(σ21/n1+σ22/n2)=[tex]\sqrt{(8200^2/45+7800^2/45) }[/tex]= 1687.0750

test stat z =(x1-x2-Δo)/σx1-x2    =(64510-62900)/1687.0750 = 0.95

We cannot reject the null hypothesis because the test statistic does not fall into the rejection zone.

Therefore, we lack adequate data to draw the conclusion that population means differ.

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Probability of getting the sum as 4 when a pair of dice is rolled is 1/12.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

No, probability is aways between 0 to 1.

Find total number of possible outcomes

Here it is given that a pair of dice is rolled

So the event points are

= { (1,1), (1,2), (1,3), (1,4),(1,5),(1,6),(2,1), (2,2), (2,3), (2,4),(2,5),(2,6),(3,1), (3,2), (3,3), (3,4),(3,5),(3,6),(4,1), (4,2), (4,3), (4,4),(4,5),(4,6),(5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2), (6,3), (6,4),(6,5),(6,6)}

So the total number of possible outcomes = 36

Let A be the event that of getting a sum of 4

So the event points are (1,3) , (2,2) , (3,1)

So total number of possible outcomes for the event A is 3

Hence the required probability= P(A)= no. of favorable cases to event A/total no of outcomes

=3/36

=1/12

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Answer: 270

Step-by-step explanation:

20 percent = 2/5

Times 54 or 54/1 with 2/5

You should get 270. So Aiden missed 270 free throws.

The two given rectangles are proportional to each other since they have a width-to-length ratio of 2 and the area ratio between them is equal to 9.

Two rectangles are proportional to each other when both have the same length-to-width ratio. The area ratio is defined by the following formula:

r' = (l' · h')/(l · h)      (1)

Where:

l' - Length of the enlarged rectangle.

l - Length of the original rectangle.

h' - Length of the enlarged rectangle.

h - Length of the original rectangle.

Now we determine the length-to-width ratio of each rectangle:

Original rectangle

s = 4/2

s = 2

Enlarge rectangle

s' = 12/6

s' = 2

The two rectangles have the same length-to-width ratio.

The area ratio is:

r' = (12 · 6)/(4 · 2)

r' = 72/8

r' = 9

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Two rectangles are proportional to each other when both have the same length-to-width ratio. The area ratio is defined by the following formula:

r' = (l' · h')/(l · h)      (1)

Now we determine the length-to-width ratio of each rectangle:

Original rectangle

s = 4/2

s = 2

Enlarge rectangle

s' = 12/6

s' = 2

The two rectangles have the same length-to-width ratio.

The area ratio is:

r' = (12 · 6)/(4 · 2)

r' = 72/8

r' = 9

Answer:

m = 12

Step-by-step explanation:

The equation is y=mx +b

Where m is the slope

So, in this case slope is 12

12 is an integer, so my answer is correct!

Answer: (a+b)2 = a2 + b2 + 2ab., (a-b)2 = a2 + b2 – 2ab.,a2 – b2 = (a+b) (a-b)

Step-by-step explanation:

Answer:

2x - 7y > 10

8 + x > 5

3 < 5

Step-by-step explanation:

The equations are

Ax + By + C < 0 or Ax + By + C > 0

There is no equal in a linear inequality

The first option 2x + 8 = 10y is an equation, so it is wrong. The other 3 are correct!

Hypotheses for the test are Null hypothesis and Alternative hypothesis

What is Hypothesis?

A hypothesis is an educated guess while using reasonable thinking, about the answer to a scientific question. Although it is not proof in an experiment, it is the predicted outcome of the experimentation. It can either be supported or not supported at all, but it depends on the data gathered.

The hypotheses for the test in this case are:

Null hypothesis (H0): The mean number of credit hours taken by all UCF students is not significantly different from 11 hours.

Alternative hypothesis (H1): The mean number of credit hours taken by all UCF students is significantly greater than 11 hours.

The null hypothesis represents the assumption that there is no difference between the mean number of credit hours taken by all UCF students and the value being tested (in this case, 11 hours). The alternative hypothesis is the opposite of the null hypothesis, and represents the claim that the mean number of credit hours taken by all UCF students is significantly different from 11 hours.

In this case, the instructor is specifically interested in testing whether the mean number of credit hours taken by all UCF students is significantly greater than 11 hours. Therefore, the alternative hypothesis is that the mean number of credit hours taken by all UCF students is significantly greater than 11 hours.

Hypotheses for the test are Null hypothesis and Alternative hypothesis

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She can only move a certain distance in three seconds, with a lower distance of 33.45 feet and a upper distance of 43.45 feet.

The first three seconds of a race saw a runner's speed rapidly grow.

The time is therefore 3 seconds.

The table provides her speed at half-second intervals.

We are aware,

Speed = Distance / Time

Similarly

Distance = Speed × Time

t equals 0.5 seconds

Then, the lower distance traveled overall is equal to 0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).

Terms are multiplied and added.

= 0.5 × 66.9

= 33.45 feet

The upper distance traveled is equal to 0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)

= 0.5 × 86.9

= 43.45 feet

As a result, Her lower distance in three seconds is therefore 33.45 feet, and her upper distance in three seconds is 43.45 feet.

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The sum of the x and y coordinates of D" is 6

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

D = (-1, -3)

The transformation rule is given as

T(-2,0) R180° about the origin.

Mathematically, this can be represented as

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

So, we have the following representation

D" = (1 + 2, 3)

Evaluate the like terms

D" = (3, 3)

When the coordinates are added, we have

Sum = 3 + 3

Evaluate

Sum = 6

Hence, the sum is 6

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Complete question

A"B"C"D" is the image of ABCD after the composition of transformations

T(-2,0) R180° about the origin.

What is the sum of the x and y coordinates of D" if the coordinate of point D is (-1, -3)?

As per the binomial distribution, the probability that the student gets 7 out of the 10 questions right is 0.1171875

The term binomial distribution refers  a probability distribution used in statistics that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.

Here we have given that the student randomly guesses on 10 true or false questions

And we have to use the binomial model to find the probability that the student gets 7 out of the 10 questions right.

While we looking into the given question, the thing we have identified are listed as follows:

Number of questions = 10

Number of right answer = 7

The probability of getting right answer = 1/2

The probability of getting wrong answer = 1/2

Now, as per the binomial distribution formula it can be written as,

=> P(r) = [10!/7!(10-7)!] x [1/2]⁷ x [1/2]¹⁰⁻⁷

When we simplify this one, then we get,

=> P(r) = 0.1171875

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A set of all rational and irrational numbers is called the real numbers. All real numbers can be plotted on the number line. It is not imaginary number which cannot be quantified. It is denoted by capital Latin letter R.

Rational numbers are number that can be expressed as p/q where p and q are integers and value of q not equal to 0.

For example, -3/4, 5/3, 6/1.

Irrational numbers are not rational numbers but they can be plotted on the number line. It cannot be expressed as a simple ratio.

For example π, √2, -√7.

But √(-7) is an imaginary number.

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Answer:

⭐2 corresponding, congruent angles

⭐1 corresponding, congruent side length that is included between the 2 angles

Example (figures not drawn to scale);

Answer:

m = -3/5

Step-by-step explanation:

We have to get to the equation y = mx + b

3x 5y = -15

We subtract 3x from both sides

5y = -3x - 15

Then we divided by 5 into both sides

y = -3/5x - 3

We know our equation is y = mx + b

m = the slope

b = y-intercept

The slope is -3/5

Answer:

F

Step-by-step explanation:

F. False. The graph of [tex]g[/tex] involved performing a horizontal compression on the graph of [tex]f[/tex].

G. True. Setting [tex]x=0[/tex] yields [tex]g(0)=f(0)[/tex].

H. True. Set [tex]x=-1[/tex].

J. True. The horizontal compression does not change the number of their roots, just the location.

The given expression x² is an algebraic expression where x is the base and 2 is the exponent.

Therefore, the answer is x.

In an expression aᵇ, a is the base and b is the exponent. Here the expression aᵇ implies the base a is multiplied b times. For example x² implies x multiplied twice, that is

x² = x × x

Base number is the number which is multiplied to itself and the exponent denotes the number of times it is multiplied to itself. For example

x⁰ = 1

x¹ = x

x² = x×x

x³ = x×x×x

x⁴ = x×x×x×x

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Tori earns more money.

Given data :

Tori : $24/h; 150% OT

Calculate Tori's overtime (OT) pay

Convert OT rate to decimals --> 150% = 1.

Tori's OT wage is 1.5*$24 = $36

Tori worked for 20h OT. (60h-40h = 20h)

(Regular pay X regular hours worked) + (OT wage X OT hours worked)

= ($24 X 40h) + ($36 X 20h)

= $1680

Matias : 5% commission

Convert 5% to decimals --> 0.05

(Jewelry sold) X (commission rate)

= $21000 X 0.05

= $1050

Since $1680 > $1080, Tori earns more.

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Answer:

1/5 apparently

The average time spent in the system which consists three fax machines is 0.026470 hour. So, option (e) none of the above is right here.

The M/M/1 queuing system is a single-server, infinite-capacity system in which the arrival interval is exponentially distributed with the parameter lambda and the service time is also exponentially distributed with the parameter. If the number of servers is maximum and all are equal, this model is considered an M/M/C queue.

We have, total number of fax machine in a business school is equals to three.

The toner of each machine needs to be changed in 5 hours of use . Time taken by secretary to replace toner cartridge = 15 minutes

We have to calculate average time spent in the system. fax machines , k = 3

Service person , R = 1

Arrival rate, λ = 3/5per hour = 0.6/hour

Service rate, μ =( 60/15) per hour

= 4/hour

Now, using the equation of finite population model M/M/1, the average time spent to maintain the fax machines in system is ,

L = λ² /μ (μ - λ )

plugging the value of μ and λ in above formula we get, L = (0.6)²/4(4-0.6)

= 0.36/13.6 = 0.026470

So, required answer is 0.026470 hour .

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The current value of "i" in the complex numbers is √(-1)

The value of I as current is expressed as Amperes

In order to know what "i" is and what its value is, we must first know what kind of number it is.

The current is the flow of electric charge, it is denoted with the letter "I" and its unit of measure is Amperes, it can take any value even complex numbers.

Complex numbers are known as imaginary numbers and can be defined as an extension of the set of real numbers, since in its structure it has a real number followed by an imaginary number denoted with the letter "i".

In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:

√(-1) = i

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