Equivalent fraction of 12/126

The exact values of the unit circle is cos θ = 9/25 and sin θ = ( √544/25 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

The terminal side of angle θ intersects the unit circle in the first quadrant at ( 9/25 , y )

So , the equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r²   be equation (1)

Substituting the values of x and y in the equation , we get

( 9/25 )² + y² = 1²

On simplifying the equation , we get

( 81/625 ) + y² = 1

Subtracting ( 81/625 ) on both sides of the equation , we get

y² = 544/625

Taking square roots on both sides of the equation , we get

y = √544/25

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

So , the value of cos θ = 9/25 and sin θ = ( √544/25 )

Hence , the equations are solved

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Answer:

sqrt(15² + 3²) = sqrt(15² + 3²)

Step-by-step explanation:

Using Pythagoras:

15 blocks North = 15 blocks south (direction opposite to each other)

3 blocks west = 3 blocks east (directions opposite to each other)

Hence distance traveled (d) :

JARON

D = sqrt(15² + 3²)

MARISOL:

D = sqrt(15² + 3²)

Hence ;

sqrt(15² + 3²) = sqrt(15² + 3²)

Answer:

\(\cot(\theta)\)

Step-by-step explanation:

Trig identities:

\(\csc(\theta)=\dfrac{1}{\sin(\theta)}\)

\(sin^2(\theta)+cos^2(\theta)=1\)

\(\cos(2\theta)=cos^2(\theta)-sin^2(\theta)\)

\(\implies \cos(2\theta)=2cos^2(\theta)-1\)

\(\implies2cos^2(\theta)= \cos(2\theta)+1\)

\(\sin(2\theta)=2\sin(\theta)\cos(\theta)\)

Therefore,

\(\dfrac{\cos(2\theta)+\sin(\theta) \times \csc(\theta)}{\sin(2\theta)}\)

\(=\dfrac{\cos(2\theta)+\dfrac{\sin(\theta)}{\sin(\theta)}}{\sin(2\theta)}\)

\(=\dfrac{\cos(2\theta)+1}{\sin(2\theta)}\)

\(=\dfrac{2cos^2(\theta)}{\sin(2\theta)}\)

\(=\dfrac{2cos^2(\theta)}{2\sin(\theta)\cos(\theta)}\)

\(=\dfrac{cos(\theta)}{\sin(\theta)}\)

\(=\cot(\theta)\)

Answer:

The mode are: 7, 8

Step-by-step explanation:

Given

\(7, 11, 8, 7, 8, 7, 8, 11, 8, 10, 7\)

Required

Determine the mode

We start by arranging the given data in ascending order

The ordered data are:

\(7,7,7,7, 8,8,8,8, 10, 11, 11\)

From the above data.

7 has a frequency of 4

8 has a frequency of 4

10 has a frequency of 1

11 has a frequency of 2

The data with the highest frequency is the mode.

We can see that 7 and 8 both have frequencies of 4

Hence, the mode are: 7, 8

Answer:

The mode are: 7, 8

Step-by-step explanation:

Given System of equation has multiple solution.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation:

-1 = 2x - y and  8x - 4y = -4​

From equation 1

-1 = 2x - y

y = 2x + 1

Substitute this value on equation 2

8x - 4y = -4​

8x - 4(2x + 1) = -4

-4 = -4

An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

Thus, Given System of equation has multiple solution.

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The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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Answer:

400 gumballs are in the gumball machine

Step-by-step explanation:

75% = 300 gumballs

Find 1%:

1% = 300 ÷ 75 = 4 gumballs

Find 100%:

100% = 4 x 100 = 400 gumballs.

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Z-score is 1.27 for x = 72.

According to this z-score, x = 72 is 1.27 standard deviations away from the mean.

What is Standard Deviation?

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given,

On a typing test, John averages 58 words per minute with a standard deviation of 11 words per minute

µ =  58 words per minute.

σ = 11 per minute in words

On a typing test, X represents the maximum words per minute.

On a typing test, John's words per minute are distributed normally.

As X- N, the normal distribution can be described (µ  ,σ)

This indicates that X is normally distributed, with X - N for the mean and SD (58, 11)

Consider John taking a typing test on Sunday and typing 72 words per minute, i.e. x = 72

For John's score, we must determine the Z-score, which may be done as

Z = X-µ/σ

Put known values in the Z-score calculation.

Z = 72 - 58/11

Z-score, thus, is 1.27 when x = 72.

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Answer:

c. x/7

Step-by-step explanation:

seven is dividing something, and X is the placeholder in this equation.

So, since x is being divided by seven, that rules out B., because that's backwards.

A. and D. don't involve division, so they're both incorrect as well.

Thus we are left with C. x/7

Answer:You can use a negative space \! to remove (or reduce) this to your liking. It would be best to define a command for this, for the sake of consistency

Step-by-step explanation:

Answer: 2

Step-by-step explanation: Buying price per Apple=34/8=17/4 Rs

Selling price per Apple=57/12=19/4Rs

Profit per apple=Selling price-Buying price

Profit=  

4

19

​

−  

4

17

​

Profit=  

4

2

​

Profit=  

2

1

​

apples should be sold to earn a net profit of Rs 45

45=x× -  

2

1

​

=2  

Answer (A) 2

Answer:

70 ways

Step-by-step explanation:

We can solve our answer by using factorials, we know that the parade organizer recieved 8 entries in total, but the question asks how many ways he can arrange 4 out of the 8. Our equation will be:

8! / 4!

(8 * 7 * 6 * 5) / (4 * 3 * 2)

1680 / 24

70

There are 70 ways the parade organizer can arrange 4 floats out of the 8 entries.

To find the number of ways the parade organizer can arrange 4 floats out of the 8 entries, we can use the concept of combinations, specifically the combination formula.

The number of ways to choose r objects from a set of n objects is given by the combination formula:

C(n, r) = n! / (r!(n-r)!)

Where n is the total number of objects (8 entries in this case), r is the number of objects to be chosen (4 floats in this case), and ! represents the factorial function (the product of all positive integers up to that number).

Now, let's plug in the values:

C(8, 4) = 8! / (4!(8-4)!)

C(8, 4) = 8! / (4! * 4!)

Now, calculate the factorials:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, which is 40,320.

4! = 4 x 3 x 2 x 1, which is 24.

Now, substitute the values back into the combination formula:

C(8, 4) = 40,320 / (24 x 24)

C(8, 4) = 40,320 / 576

C(8, 4) = 70

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24 crayons can be divided into 324 crayons exactly 13.5 times.

We have,

To find out how many times 24 crayons can be divided into 324 crayons, simply perform the division:

So,

324 crayons ÷ 24 crayons

= 324/24

= 13.5

Therefore,

24 crayons can be divided into 324 crayons exactly 13.5 times.

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Answer:29 degrees

151 degrees

Step-by-step explanation:

Answer:

The graph of the parent function y = 2^x can be transformed to create the graph of y = 2^(3x) by horizontally compressing by a factor of 3. Therefore, the correct answer is C.

Answer:

20 lawyers

Step-by-step explanation:

48 ÷ 12 = 4

which means every year 4 lawyers are hired

5 × 4 = 20

so this means the law firm has hired 20 lawyers in the last 5 years

Answer:

The answer is The function g because the graphs of ƒ and g are symmetrical about the line y = x

Step-by-step explanation:

A function and its inverse function become symmetrical across the line y = x.  

Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

The answer is NO

Reason

x= 2 y= 1

Now input in the first inequality

y≤ -x + 4

1 ≤ -2 +4

1≤ 2 i.e 1 is less than two

Next inequality

y≤ x +1

1 ≤ 2 + 1

1≤ 3 i.e 1 is less than 3

But 1 is not equal to 3 and also not equal to 2

Hence our answer is NO

Answer:

$84.80

Step-by-step explanation:

find the difference between accurate price and written price: 74 - 47 = 27

find written total (before Mrs. Taylor found mistake) by undoing the mean calculation: 82.55 x 12 = $990.60

the total expenses is $27 more than what they thought: 990.60 + 27 = 1017.60

divide accurate total by 12 to find mean: 1017.60 / 12 = $84.80

hope this helps :)

Answer: C

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!

Answer: 2.0431

Step-by-step explanation:

\(\log_{8} 70=\frac{\log 70}{\log 8} \approx 2.0431\)

Answer:

35 marbles were green.

Step-by-step explanation:

70 percent = 7/10

7/10 of 50 (of can be translated to multiplied)

7/10 · 50 = 35.

According to the information, the perimeter of the triangle is ≈ 31.18

To find the distance between two points, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's label the coordinates as follows:

Point 1: (-2, 3)

Point 2: (3, -2)

Now we can substitute these values into the distance formula:

distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)

distance = sqrt((5)^2 + (-5)^2)

distance = sqrt(25 + 25)

distance = sqrt(50)

distance ≈ 7.07

Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.

To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.

Using the distance formula, we can find the length of the sides:

Side 1: (-2,3) to (3,-2)

d = √[(3 - (-2))^2 + (-2 - 3)^2]

= √[5^2 + (-5)^2]

= √50

= 5√2

Side 2: (3,-2) to (-7,-2)

d = √[(-7 - 3)^2 + (-2 - (-2))^2]

= √[(-10)^2 + 0^2]

= 10

Side 3: (-7,-2) to (-2,3)

d = √[(-2 - (-7))^2 + (3 - (-2))^2]

= √[5^2 + 5^2]

= 5√2

Therefore, the perimeter of the triangle is:

5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)

An two of the three sides are equal, so it is an isosceles triangle.

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Answer:

y = 36

Step-by-step explanation:

Given logarithmic equation:

\(\log_4(y-9)+\log_43=\log_481\)

\(\textsf{Apply the \textbf{log product law}}: \quad \log_ax + \log_ay=\log_axy\)

\(\implies \log_4\left(3(y-9)\right)=\log_481\)

\(\textsf{Apply the \textbf{log equality law}}: \quad \textsf{If $\log_ax=\log_ay$ then $x=y$}\)

\(\implies 3(y-9)=81\)

Divide both sides of the equation by 3:

\(\implies \dfrac{3(y-9)}{3}=\dfrac{81}{3}\)

\(\implies y-9=27\)

Add 9 to both sides of the equation:

\(\implies y-9+9=27+9\)

\(\implies y=36\)

Therefore, the solution to the given logarithmic equation is y = 36.

Answer:

y = 1/4x - 7/2

Step-by-step explanation:

To answer this question, we have to use point-slope form:

y - y1 = m(x - x1)

Substitute the numbers into the variables:

y - (-4) = 1/4(x - (-2))

y + 4 = 1/4(x + 2)

y + 4 = 1/4x + 1/2

y = 1/4x - 7/2

To verify your answer, simply substitute the values into your equation:

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

-4 = -1/2 - 7/2

-4 = -8/2

-4 = -4

The total number of students who graduated from the Cincinnati universities and colleges are 15382.

We are given that 6.76 % of Cincinnati college and university graduates majored in Registered Nursing.

The number of the Cincinnati college and university graduates who majored in Registered Nursing = 1026.

We need to find the total number of students that graduated from the Cincinnati universities and colleges altogether in 2016.

Let the total number of students be x.

ATQ:

6.67 % x = 1026

6.67 x = 102600

667 x = 10260000

x = 10260000 / 667

x = 15382.309

Rounding off to the nearest whole number is:

x = 15382.

Therefore, we get that the total number of students who graduated from the Cincinnati universities and colleges are 15382.

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