what is the area of ABC

The arc length of the sector is 7.85 meters whose circumference is 20π meters.

In geometry, a sector is a part of a circle enclosed by two radii and an arc. The arc of a sector is a portion of the circumference of the circle. Sectors are often used in geometry and trigonometry to calculate areas, angles, and other measurements.

The equation for a circle's circumference is:

C = 2πr

Since we know the circumference of the circle, we can solve for the radius:

20π = 2πr

Dividing both sides by 2π, we get:

r = 10

Arc length = (central angle / 360°) x 2πr

where r is the radius and the central angle is in degrees.

Plugging in the given values, we get:

Arc length = (45° / 360°) x 2 x 3.14 x 10

Arc length = (1/8) x 62.8

Arc length = 7.85 meters

Therefore, the arc length of the sector is 7.85 meters.

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The another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.

The process of generating random variates from a binomial distribution using the inverse transform method for discrete distribution is done as follows:Step 1: Determine the probability mass function (pmf) of the binomial distribution with parameters n and p. For example, for a binomial distribution with n = 6 and p = 0.4, the pmf is given by:P(X=k) = (6 choose k)(0.4)^k(1-0.4)^(6-k), where k=0,1,2,3,4,5,6Step 2: Calculate the cumulative distribution function (CDF) of the binomial distribution by summing the pmf up to each value of k. The CDF is given by:F(k) = P(X ≤ k) = ΣP(X=i) for i=0 to k, where k=0,1,2,3,4,5,6Step 3: Generate a uniform random variate, U, between 0 and 1. For example, U=0.23456.Step 4: Find the smallest value of k such that F(k) ≥ U. This value of k is the random variate X. For example, if U=0.23456, then F(0)=0.10737, F(1)=0.38223, and F(2)=0.74304. Since F(1) is the smallest value of F(k) that is greater than or equal to U, X=1. Therefore, a random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=1.To find another random variate from the same distribution, repeat steps 3 and 4. For example, U=0.987654, F(0)=0.10737, F(1)=0.38223, F(2)=0.74304, F(3)=0.91892, F(4)=0.98544, and F(5)=0.99856. Since F(3) is the smallest value of F(k) that is greater than or equal to U, X=3. Therefore, another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.

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Answer:

Step-by-step explanation:

Rewrite

3

a

2

10

b

6

as

(

a

b

3

)

2

3

10

.

√

(

a

b

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)

2

3

10

Pull terms out from under the radical.

a

b

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10

Rewrite

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as

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10

.

a

b

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⋅

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10

Combine.

a

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Multiply

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by

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a

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3

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Combine and simplify the denominator.

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Simplify the numerator.

Tap for more steps...

a

√

30

b

3

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10

Move

10

to the left of

b

3

.

a

√

30

10

b

3

Step-by-step explanation:

[tex]{ \tt{ \sqrt{ \frac{3 {a}^{2} }{10 {b}^{6} } } }} = { \tt{ \frac{ {(3a {}^{2}) }^{ \frac{1}{2} } }{ {(10b {}^{6} )}^{ \frac{1}{2} } } }} \\ \\ = { \tt{ \frac{a \sqrt{3} }{ {b}^{3} \sqrt{10} } }} \\ \\ = { \tt{ \frac{a \sqrt{3} }{ {b}^{3} \sqrt{10} } }}[/tex]

Answer:

Rs 750

Step-by-step explanation:

Given, No. of kurtas: 18, Each with CP = Rs 1000.

So, SP of 18 kurtas: 18*1000 = Rs. 18000

Also, 3 sets of kurtas were damaged.

Therefore, Remaining kurtas: 18-3 = 15. SP of each: Rs 1250.

SP of 15 kurtas: 15*1250 = Rs. 18750

So, Clearly SP>CP, Profit.

We know Profit= SP-CP

= 18750-18000 = Rs 750

Answer: 7 dollars 18 cents.

Step-by-step explanation:

Step-by-step explanation:

This graph shows a quadratic curve with roots 0 and -4

The polynomial is therefore

x² -x(α+β) + αβ

x² -x(0-4) + 0(-4)

x² +4x +0

x² + 4x

But it's an n-shaped curve, meaning a is negative

Multiply through by -1

-x² - 4x

y = -x² - 4x

So when the input value y = 3, we have

3 = -x² - 4x

Rearrange

x² + 4x + 3 = 0

Factorize

x² + 3x + x + 3 = 0

x(x + 3) +1(x + 3) = 0

(x + 1) (x + 3) = 0

x + 1 = 0 and x + 3 = 0

x = 0-1 and x = 0-3

Therefore,

x = -1 and -3

Check the graph to confirm

By answering the presented question, we may conclude that As a result, expressions Ivanna's average speed is approximately 2.311 miles per hour.

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

We can use the formula:

rate = distance / time

Let's calculate Ivanna's rate for the first part of her journey:

rate = distance divided by time = 12 miles divided by 5 hours = 2.4 miles per hour

Let us now compute Ivanna's rate for the second leg of her journey:

rate = distance divided by time = 20 miles divided by 9 hours = 2.222... miles per hour

As a result, Ivanna's overall rate is the average of these two rates:

rate = (2.4 miles per hour + 2.222... miles per hour) / 2 = 2.311... miles per hour

As a result, Ivanna's average speed is approximately 2.311 miles per hour.

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Step-by-step explanation:

1. sqrt(x + 6)/5 = 2

sqrt(x + 6) = 10

x + 6 = 100

x = 94

sqrt(94 + 6)/5 = 2

sqrt(100)/5 = 2

10/5 = 2

2 = 2

confirmed.

2.

sqrt(9x + 2) = sqrt(11x - 12)

9x + 2 = 11x - 12

14 = 2x

x = 7

sqrt(9×7 + 2) = sqrt(11×7 - 12)

sqrt(63 + 2) = sqrt(77 - 12)

sqrt(65) = sqrt(65)

confirmed.

3.

cubic root(6x + 3) + 10 = 13

cubic root(6x + 3) = 3

6x + 3 = 27

6x = 24

x = 4

cubic root(6×4 + 3) + 10 = 13

cubic root(24 + 3) + 10 = 13

cubic root(27) + 10 = 13

3 + 10 = 13

13 = 13

confirmed.

4.

2×sqrt(5x - 4) - 24 = -6

sqrt(5x - 4) - 12 = -3

sqrt(5x - 4) = 9

5x - 4 = 81

5x = 85

x = 17

2×sqrt(5×17 - 4) - 24 = -6

2×sqrt(85 - 4) - 24 = -6

2×sqrt(81) - 24 = -6

2×9 - 24 = -6

18 - 24 = -6

-6 = -6

confirmed.

For the given ratio of ingredients 3/14 of Alex's drink is made from blackcurrants.

Comparing two numbers or values using ratios, which are often stated as fractions or colons. In mathematics, ratios are used to represent connections between various objects or numbers, such as the ratio of a rectangle's length to breadth or the proportion of boys to girls in a class. Ratios can be sped up or stated in a variety of ways, such decimals or percentages.

The given ratio for blackcurrants to raspberries is 2:5.

The total ratio is:

2 + 5 = 7

Hence, the fraction of the puree made from blackcurrants is = 2/7.

Now, ratio of fruit puree to milk is 3:1 = 3 + 1 = 4.

Hence, the fraction of the milkshake made from fruit puree is = 3/4.

For blackcurrants we have:

(2/7) * (3/4) = 6/28 = 3/14

Hence, for the given ratio of ingredients 3/14 of Alex's drink is made from blackcurrants.

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Answer:

mn(4m - 7n)

Step-by-step explanation:

➠ 4m^2n-7mn^2

➠ 2^2 x m^2n - 7mn^2

➠ mn([tex](\frac{2^2*m^2n}{mn} -\frac{7mn^2}{mn} )[/tex]

➠ mn([tex]2^2*m^{2-1}-(7n^{2-1}))[/tex]

➠ mn(4m - 7n)

The compound interest on ₹4000 at a rate of 5% p.a. for 3 years is ₹631.03.

The formula to calculate compound interest is:

[tex]A= P(1+\frac{R}{N} )^{nt}[/tex]

Where:

A = Final amount (including interest)

P = Principal amount

r = Annual interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

In this case, P = ₹4000, N = 3 years, R = 5% per annum (p.a.), which means r = 0.05 and n = 1 (compounded annually).

So, plugging in the values in the formula:

[tex]A= 4000(1+\frac{0.05}{1} )^{1*3}[/tex]

[tex]A= 4000(1.05)^{3}[/tex]

[tex]A = 4631.03[/tex] (rounded to 2 decimal places)

Compound interest is a type of interest that is calculated not only on the initial amount of money borrowed or invested but also on the accumulated interest from previous periods. In other words, the interest earned in each period is added to the principal amount, and the new total becomes the basis for calculating interest in the next period.

This compounding effect can result in significant growth in the value of an investment or debt over time, especially if the interest rate is high and the period of investment or debt repayment is long. For example, if you invest $1,000 at an annual interest rate of 5% compounded annually, you will earn $50 in interest at the end of the first year, and your new total will be $1,050.

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Answer:

slope is 1/3

y-intercept is -4

Step-by-step explanation:

x - 3y = 12

3y = x - 12

y = 1/3x - 4

according to y = mx + b, m is slope and b is y-intercept

slope is 1/3

y-intercept is -4

Answer:

83°

Step-by-step explanation:

the total angle of a triangle is 180° degree so 180°-(44°+53°)=83°

The cost of a pair is D) $15 for shorts.

To solve this problem, we need to set up a system of equations based on the information given for both Stephanie and Ashley's purchases. Let T be the cost of a t-shirt and S be the cost of a pair of shorts.

For Stephanie's purchases, we have:

[tex]2T + 3S = 105[/tex]

For Ashley's purchases, we have:

[tex]3T + 2S = 95[/tex]

Using matrices, we can solve this system of equations by setting up the augmented matrix and using row operations:

[2 3 | 105]

[3 2 | 95]

After row operations, we get:

[1 0 | 15]

[0 1 | 25]

Therefore, the cost of a pair of shorts is $15.

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The total distance travelled by Lisa in a day is found to be 10.24 miles.

Pythagoras (born 570 BC) developed a theorem known as the Pythagorean Theorem, which is exclusively applicable to right triangles.

According to the Pythagorean Theorem, a right triangle's hypotenuse square is equal to the sum of its other two sides. The side opposite the right angle is known as the hypotenuse.

Pythagoras theorem:

a² + b² = c²

Given case:

Here,

a = b = 3 units

Put the values;

3² + 3² = c²

2*9 = c²

c = 3√2

c = 4.24

Total distance = 4.24+ 3 + 3

Total distance = 10.24 miles

Thus, the total distance travelled by Lisa in a day is found to be 10.24 miles.

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Answer: $27,306

Step-by-step explanation: Forensic Scientist's take home pay is around $58,894

You do 86,200-58,894=27,306

The Chi-square test of variance is appropriate to use.

The correct model from the list to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units by sampling the GPAs of 40 SJSU students is the "One sample, Chi-square test of variance. "The Chi-square test of variance is used to determine whether the variance of a population is equal to a specific value. In the Chi-square test of variance, the null hypothesis is that the variance of the population is equal to the specific value or the variance is not greater than the specific value. The Chi-square test of variance is used when the sample is random, the sample is normally distributed, and the variable is measured on a continuous scale. In the given problem, the researcher wants to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units.

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In tests of significance about an unknown parameter of some population, "We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true" is considered strong evidence against the null hypothesis. The correct answer is Option (D).

We apply the principle of hypothesis testing to test a population's claims in inferential statistics. The null hypothesis (H₀) is always a statement about the population parameter that we believe to be true. However, we use the sample data to decide whether the null hypothesis is true or not. When we perform the hypothesis testing, we must consider the level of significance, the sample size, and the nature of the test.

The value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true is considered strong evidence against the null hypothesis. In other words, if the value of the test statistic is greater than the critical value, we can reject the null hypothesis. Consequently, we will have sufficient evidence to support the alternative hypothesis.

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Answer:(a + 1) (3a + x)

Step-by-step explanation:

Factor a+1 out of  3a ( a + 1 ) + x (a + 1 )

Hope this helps

Therefore, the area of the rectangle is 6 7/8 square inches.

Area is a measurement of the amount of space inside a 2-dimensional shape, such as a rectangle, triangle, circle, or any other polygon. It is usually measured in square units, such as square inches, square feet, square meters, etc. The formula for finding the area of a shape depends on the type of shape. For example, the area of a rectangle is calculated by multiplying its length by its width, while the area of a circle is calculated by multiplying the square of its radius by pi (3.14).

Here,

Here's how to draw a shape with fractional side lengths and find its area:

Draw a rectangle with side lengths of 2 1/2 inches and 3 3/4 inches.

Divide the rectangle into smaller squares or rectangles to make it easier to calculate the area.

For example, you can divide the rectangle into two smaller rectangles with side lengths of 2 1/2 inches and 1 3/4 inches, and 2 1/2 inches and 2 inches respectively.

Calculate the area of each smaller rectangle by multiplying the length by the width.

The total area of the rectangle is the sum of the areas of the smaller rectangles.

So the area of the rectangle would be:

Area = (2 1/2 inches x 1 3/4 inches) + (2 1/2 inches x 2 inches)

Area = (5/2 inches x 7/4 inches) + (5/2 inches x 2 inches)

Area = (35/8 square inches) + (10/4 square inches)

Area = (35/8 square inches) + (20/8 square inches)

Area = (55/8 square inches)

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The side length x of the right angle triangle is 25 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The sides of a right triangle can be found using Pythagoras's theorem. Let's use Pythagoras's theorem to find the side x.

Hence,

c² = a² + b²

where

Therefore,

a = 24 units

b = 7 units

Hence,

24² + 7² = x²

576 + 49 = x²

625 = x²

square root both sides of the equation

x = √625

x = 25 units

Therefore,

x = 25 units

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the initial speed with which the particle was projected is approximately 29.7 m/s.

How to solve?

We can solve this problem using the equations of motion for a particle moving under constant acceleration due to gravity.

Let v be the initial velocity with which the particle was projected, and let θ be the angle of projection with respect to the horizontal. Since the particle is launched from a height of 15m, its initial vertical velocity is v sin(θ), and its initial horizontal velocity is v cos(θ).

The time taken for the particle to hit the ground can be found by using the equation:

y = y0 + v0t + 1/2at²

where y is the vertical displacement, y0 is the initial vertical position, v0 is the initial vertical velocity, a is the acceleration due to gravity (-9.8 m/s²), and t is the time taken.

Since the particle starts and ends at the same vertical position (15m), we have:

y - y0 = 0

Substituting the values, we get:

0 = 15 + v sin(θ)t - 1/2(9.8)t²

Simplifying and rearranging, we get:

4.9t² - vt - 30 = 0

Using the quadratic formula, we get:

t = (v ±√(v² + 4(4.9)(30))) / (2(4.9))

Since we want the time taken for the particle to hit the ground, we take the positive root:

t = (v + √(v² + 588)) / 9.8

Now, we can use the horizontal displacement to find the initial speed v. Since the particle travels a horizontal distance of 30m in time t, we have:

x = v cos(θ) t

Substituting the values, we get:

30 = v cos(θ) [(v +√(v² + 588)) / 9.8]

Simplifying and rearranging, we get:

v² - 882 = 0

Using the quadratic formula again, we get:

v = ±√(882)

Since the initial velocity must be positive, we take the positive root:

v ≈ 29.7 m/s

Therefore, the initial speed with which the particle was projected is approximately 29.7 m/s.

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A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Therefore

a) Probability that exactly 14 fish survive, Let x be the number of fish that survive. Using Binomial distribution, we have:[tex]P(X = x) = C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n is the total number of fish, p is the probability of survival and C(n,x) is the binomial coefficient. We have n = 20, p = 0.8 (since 20% die) and x = 14. [tex]C(20,14) * (0.8)^14 * (0.2)^6 = 38760 * 0.000016777216 * 0.0264241152 = 0.263[/tex] Therefore, the probability that exactly 14 fish survive is 0.263

b) Probability that at least 10 fish survive To find this probability, we can find the probability that 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 fish die, and subtract this probability from 1. Using the same formula as in (a), we have: [tex]P(X <= 9) = \sum  C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n = 20, p = 0.8 and x varies from 0 to 9. Using a calculator or software, we find:P(X <= 9) = 0.0169Therefore,P(X >= 10) = 1 - P(X <= 9) = 1 - 0.0169 = 0.983 Therefore, the probability that at least 10 fish survive is 0.983.

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All the experimental probabilities of the coin lands heads up 42 times and tails up 28 times as discuss below 5 points.

Experimental probability is the ratio of the number of times an event occurs to the total number of trials or experiments conducted. It is calculated by performing an experiment or observation and recording the outcomes, and then finding the ratio of the number of times the desired outcome occurred to the total number of trials.

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As discussed in the next five paragraphs, the coin lands heads up 42 times and tails up 28 times in all experimental probability.

The ratio of the frequency of an occurrence to the total number of trials or experiments is known as the experimental probability. It is determined by carrying out an experiment or making an observation, noting the results, and then calculating the ratio of the number of times the desired result appeared to the total number of trials.

42/70, or 0.6, is the experimental likelihood that the coin will land facing up.

The experimental likelihood that the coin will fall tails up is 28/70, or 0.4.

Theoretically, there is a 0.5 percent chance that the coin will land with its head up.

Theoretically, there is a 0.5 percent chance that the coin will fall tails up.

According to the experimental probability, Liz is more likely to flip heads than tails.

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The conclusion in the argument is "the good, according to Plato, is that which furthers a person's real interests." which it is the correct answer.

In a well-structured argument, the conclusion is what the argument aims to prove.

The conclusion can be located at the beginning or end of the argument, and it should always be precise, clear, and understandable.

The conclusion in the argument above is that "the good, according to Plato, is that which furthers a person's real interests."

The argument tries to explain that the good in Plato's philosophical teachings is a thing that advances a person's genuine interests.

The statement "it follows that" is the premise that links the argument with the conclusion.

The premise and the conclusion have a relationship of cause and effect, and this implies that the argument's conclusion is "the good, according to Plato, is that which furthers a person's real interests."

Therefore, the right option is: the good, according to Plato, is that which furthers a person's real interests.

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Answer:

x = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the lower right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} } }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]  ( cross- multiply )

x = 4[tex]\sqrt{2}[/tex]

The maximum possible number of handshakes that can happen at the party with 23 people with at most 22 other people is 253. This is calculated by combination.

Twenty-three people attend a party. each person shakes hands with at most 22 other people.

To find the maximum possible number of handshakes, assuming that any two people can shake hands at most once, we need to use Combination by finding the number of unique pairs of people in the party.

nCr (combination) to find the number of unique pairs of people.

Therefore,[tex]^nC_r = \frac{n!}{(n-r)!  r!}[/tex]

where n is the total number of people and r is the number of people in a handshake at a time.

Therefore, the number of unique pairs of people that can shake hands at most once is:

[tex]^{23}C_2 = \frac{23!}{(23-2)!  (2!)}[/tex] [tex]=\frac{23 X22}{2} = 253[/tex]

Hence, the maximum possible number of handshakes that can happen at the party is 253.

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In a system of two equations, the graph of one line has a positive slope and the graph of the other line has a negative slope. This statement is indicative of a system of linear equations which will have no solution.

A system of linear equations is a collection of two or more linear equations with the same variables. A system of linear equations is a collection of two or more linear equations with the same variables. A solution of a system of linear equations is a set of values that make all of the equations true.

Let's look at the general form of two linear equations that are given:

y = mx + by = nx + c

where m and n are the slopes of each line. If m and n have different signs, one is positive and one is negative, then they will never meet and therefore will have no solution. We can thus conclude that the system of two equations has no solution.

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Answer:

-21

Step-by-step explanation:

y^2 + 8y - 9                       y = -6

(-6)² + 8(-6) - 9

36 - 48 - 9

-21

So, the answer is -21

Answer:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}

Step-by-step explanation:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}