Find the exact value of cos() if tan x can x = in in quadrant III.

The conditional probability that the outcome of the coin toss was heads can be calculated using Bayes' theorem. The conditional probability that the outcome of the toss was heads given that a white ball was selected is 26/63.

Let's denote H as the event that the outcome of the coin toss was heads, and W as the event that a white ball was selected. We want to find P(H|W), the probability of the coin toss being heads given that a white ball was selected.

According to Bayes' theorem, we have:

P(H|W) = P(W|H) * P(H) / P(W)

P(W|H) is the probability of selecting a white ball given that the outcome of the coin toss was headed. Since the first mug is chosen in this case, which contains two white balls out of a total of nine balls, P(W|H) = 2/9.

P(H) is the probability of the coin toss being heads, which is 1/2 since the coin is fair.

P(W) is the probability of selecting a white ball, regardless of the outcome of the coin toss. There are a total of seven white balls out of thirteen balls (two from the first mug and five from the second mug), so P(W) = 7/13.

Therefore, substituting these values into Bayes' theorem:

P(H|W) = (2/9) * (1/2) / (7/13)

Simplifying this expression:

P(H|W) = 26/63

Therefore, the conditional probability that the outcome of the toss was heads given that a white ball was selected is 26/63.

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Answer: A solution to an equation is a number that can be plugged in for the variable to make a true number statement. Example 1: Substituting 2 for x in.

Step-by-step explanation:

,11

Step-by-step explanation:

let's face it.

100-45=55. 55/5=11

therefore,The maxium number is 11

It will take 2 hours for Molly and her little brother to mow the lawn while working together.

Molly can mow a lawn in 3 hours and her little brother can mow the lawn in 6 hours.

The task is to calculate how long it will take to mow the lawn while working together.

When two people work together, their work rates add up, so the total work rate is given by the sum of their individual work rates.

Let M represent the work rate of Molly and B represent the work rate of her little brother.

Then: M = 1/3 (Molly can mow a lawn in 3 hours)B = 1/6 (Little brother can mow a lawn in 6 hours)

When working together, their combined work rate is the sum of their individual work rates.

Hence, their combined work rate is given by: M + B = 1/3 + 1/6 (Adding the work rates of both)

M + B = 1/2 (Adding both fractions, the LCD of the two fractions is 6)

So, the combined work rate of Molly and her brother is 1/2.

This means that they can complete one lawn in 2 hours.

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Answer:

5q + 9

Step-by-step explanation:

The Concept in that Question is adding Like-Terms

6q + 4 - q + 5 = ( 6q - q ) + ( 4 + 5 ) = 5q + 9

The correct option is (F) y = 3^x

The exponential function equivalent to y = log₃x is y = 3^x.

To understand why this is the correct answer, let's break it down step-by-step:

1. The equation y = log₃x represents a logarithmic function with a base of 3. This means that the logarithm is asking the question "What exponent do we need to raise 3 to in order to get x?"

2. To find the equivalent exponential function, we need to rewrite the logarithmic equation in exponential form. In exponential form, the base (3) is raised to the power of the exponent (x) to give us the value of x.

3. Therefore, the exponential function equivalent to y = log₃x is y = 3^x. This means that for any given x value, we raise 3 to the power of x to get the corresponding y value.

Let's consider an example to further illustrate this concept:

If we have the equation y = log₃9, we can rewrite it in exponential form as 9 = 3^y. This means that 3 raised to the power of y equals 9.

To find the value of y, we need to determine the exponent that we need to raise 3 to in order to get 9. In this case, y would be 2, because 3^2 is equal to 9.

In summary, the exponential function equivalent to y = log₃x is y = 3^x. This means that the base (3) is raised to the power of the exponent (x) to give us the corresponding y value.

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One beautiful mathematical idea is the concept of the Golden Ratio. The Golden Ratio is a mathematical ratio that is approximately equal to 1.618. It can be found in various natural and artistic phenomena, such as the proportions of the human body and the dimensions of famous artworks like the Parthenon. The beauty of the Golden Ratio lies in its aesthetic appeal and harmonious proportions, which can be appreciated by individuals from different backgrounds.

The Golden Ratio is a mathematical concept that can be understood by considering the relationship between two quantities. It is the ratio of the larger quantity to the smaller quantity, and this ratio is approximately equal to 1.618. This ratio has been observed in various natural and artistic contexts, which adds to its beauty. For example, the proportions of the human body, such as the ratio of the height to the navel compared to the navel to the floor, are often close to the Golden Ratio. Similarly, famous artworks, such as the Parthenon in Athens, exhibit dimensions that are related to the Golden Ratio.
The beauty of the Golden Ratio is similar to other kinds of beauty that humans encounter in the sense that it evokes a sense of harmony, balance, and aesthetic appeal. It demonstrates the presence of underlying mathematical principles that govern patterns and proportions in the natural and artistic world. This beauty can be appreciated by individuals regardless of their mathematical background, as it appeals to our innate sense of visual harmony and proportion. The elegance of the Golden Ratio lies in its ability to bridge mathematics and aesthetics, showcasing the interconnectedness between these domains of human experience.

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Your mum and your dad should help you with this

Answer:

5,200rs

Step-by-step explanation:

Answer:

0.37

Step-by-step explanation:

please mark me as brainlest

The present value is approximately $624,732.39. To determine which method would give Ms. Lucy Brier the highest winnings, we need to calculate the present value of each option .

Using the appropriate opportunity cost of 8% p.a. compounded quarterly. The method with the highest present value will result in the highest winnings. a) For $30,000 each quarter for 6 years with the first payment received immediately, we can calculate the present value using the formula for the present value of an ordinary annuity: Present Value = C * (1 - (1 + r/n)^(-n*t)) / (r/n). Where: C = Cash flow per period = $30,000; r = Annual interest rate = 8% = 0.08; n = Number of compounding periods per year = 4 (quarterly compounding); t = Number of years = 6. Using the formula, the present value is approximately $151,297.11. b) For $500,000 received immediately, the present value is simply the same amount, $500,000. c) For $120,000 each year for 5 years with the first payment in 1 year's time, we can calculate the present value of an ordinary annuity starting in 1 year: Present Value = C * (1 - (1 + r/n)^(-n*t)) / (r/n). Where: C = Cash flow per period = $120,000; r = Annual interest rate = 8% = 0.08; n = Number of compounding periods per year = 4 (quarterly compounding); t = Number of years = 5.

Using the formula, the present value is approximately $472,347.55. d) For $37,000 each quarter for 4 years with the first payment in 3 months' time, we can calculate the present value of an ordinary annuity starting in 3 months: Present Value = C * (1 - (1 + r/n)^(-n*t)) / (r/n). Where: C = Cash flow per period = $37,000. r = Annual interest rate = 8% = 0.08. n = Number of compounding periods per year = 4 (quarterly compounding). t = Number of years = 4.Using the formula, the present value is approximately $142,934.37. e) For $75,000 each year for 11 years with the first payment in 1 year's time, we can calculate the present value of an ordinary annuity starting in 1 year: Present Value = C * (1 - (1 + r/n)^(-n*t)) / (r/n). Where: C = Cash flow per period = $75,000; r = Annual interest rate = 8% = 0.08; n = Number of compounding periods per year = 4 (quarterly compounding); t = Number of years = 11. Using the formula, the present value is approximately $624,732.39. Comparing the present values, we can see that option e) with $75,000 each year for 11 years starting in 1 year's time has the highest present value and, therefore, would give Ms. Lucy Brier the highest winnings.

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Answer:

28 g. ................

Answer:

Circumference - 2 * pi * r

Step-by-step explanation:

multiply radius by 2.

multiply by pi

Answer:

Step-by-step explanation:

If the sum of two angles is one right angle or 90°, then one angle is said to be complementary of the other. Thus, 25° and 65°; θ° and (90 - θ)° are complementary to each other.

Suppose a rotating line rotates about O in the anti-clockwise sense and starting from its initial position

The missing angles are

A. = 130 degrees

B. = 55 degrees

C. = 145 degrees

D. = 73 degrees

E. = 43 degrees

F. = 23 degrees

G. = 61 degrees

H. = 90 degrees

I. = 50 degrees

J. = 27 degrees

K. = 25 degrees

Assuming the missing angle in each case is x

A. Angle on a straight line = 180 degree

x + 50 = 180

x = 130 degrees

B. Angle at a point = 360 degrees

209 + 96 + x = 360

x = 360 - 96 - 209

= 55 degrees

C. Angle on a straight line = 180 degree

= 145 degrees

D. Vertical angles are equal, using vertical angle theorem

= 73 degrees

E.  vertical angle theorem

= 43 degrees

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You should deposit approximately $340.84 monthly to reach $293,000 in 28 years at a 4.4% annual interest rate compounded monthly.

To calculate the monthly deposit required for an investment plan paying 4.4% interest compounded monthly to reach $293,000 in 28 years, we use the future value of an annuity formula:

FV = P * (((1 + r)^n - 1) / r)

Here, FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of payments. First, convert the annual interest rate (4.4%) to a monthly rate by dividing by 12, which gives 0.0367 (4.4%/12) or 0.00367 as a decimal. The number of payments (n) is 28 years * 12 months/year = 336.

We want to find P, so rearrange the formula:

P = FV / (((1 + r)^n - 1) / r)

Substitute the values:

P = $293,000 / (((1 + 0.00367)^336 - 1) / 0.00367)

P ≈ $340.84

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The coordinates of the endpoint B is (-2,-5).

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Midpoint M( -5,0 )

Endpoint A ( -8,5 )

Endpoint B

Plug the given values into the above formula and solve for x₂ and y₂.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

(x,y) = ( (x₁+x₂)/2, (y₁+y₂)/2 )

x = (x₁+x₂)/2

2x = x₁ + x₂

2( -5 ) = -8 + x₂

-10 = -8 + x₂

-10 + 8 = x₂

-2 = x₂

x₂ = -2.

y = (y₁+y₂)/2

2y = (y₁+y₂)

2y = y₁ + y₂

2( 0 ) = 5 +  y₂

0 = 5 +  y₂

-5 =  y₂

y₂ = -5

Therefore, the endpoint B is (-2,-5).

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Answer:

2y+6x=180

Step-by-step explanation:

Because we know that side lengths BD, DC, and AD are all congruent, we can conclude that triangles BDA and CDA are congruent because they have at least two congruent sides. Since these triangles are both 45-45-90 triangles, angle C is equal to 45 degrees, or 3x. 45/3 is 15, so x=15. Angle B is equal to 45 degrees, or y, so y=45.

From there, we plug these numbers into the equation with 2(45) + 6(15), or 90+90 = 180.

Hello,

I hope you and your family are doing well!

To find the amount of simple interest earned by Min Kurata's money, we can use the formula:

I = P * r * t

Where I is the amount of interest earned, P is the principal (the initial amount deposited), r is the annual interest rate, and t is the time in years.

In this case, the principal is $875, the annual interest rate is 4%, and the time is 3 months. Since the time is given in months, we need to convert it to years by dividing it by the number of months in a year (12):

t = 3 months / 12 months/year = 0.25 years

Plugging these values into the formula gives:

I = $875 * 0.04 * 0.25 = $35

So Min Kurata's money earned $35 in simple interest.

To find the total amount in the account, we can add the amount of interest to the principal:

total amount = $875 + $35 = $910

So the total amount in the account after 3 months is $910.

Please consider leaving 5 stars and brainliest if you find this answer helpful since it does help me continue helping others.

Happy Holidays!

Answer:

20

Step-by-step explanation:

(4-1 + 8 ÷ 8 )= 4

4 x 5 = 20

Answer:

  22°

Step-by-step explanation:

Two legs of a right triangle are given, so the tangent relation is the one that is relevant to finding the angle.

  Tan = Opposite/Adjacent

  tan(α) = 0.7/1.7

  α = arctan(7/17) ≈ 22.4°

The angle of the door stop is about 22°.

Option C  "Each shirt cost $15.75" could be correct as it represents the cost per shirt before adding the sales tax.

The expression given is 1.065(15.75x-10), where x represents the number of shirts. The expression has two parts: 15.75x, which represents the cost of x number of shirts before sales tax, and -10, which represents a discount of $10 applied to the total cost. Multiplying this expression by 1.065 adds the 6.5% sales tax to the cost.

Option A is not correct as the expression has a discount of $10 applied to the total cost, not per shirt. Option B is partially correct as it represents the percentage of the sales tax, but not the cost per shirt. Option D and E are not relevant as they are not related to the given expression.

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Complete Question

The expression below represents the cost, in dollars, for Shaim to purchase shirts.

1.065(15.75x-10)

If represents the number of shirts, which of the following statement(s) could be correct? Select all that apply. Juqtuo Sygn

A. Each shirt costs $10.

B. The sales tax is 6.5%.

C. Each shirt cost $15.75.

D. The cost of 2 portraits with tax is $33.55

E. The cost of 2 portraits is $22.90 with the discount.

The expression 1.065(15.75x - 10) represents the cost, in dollars, for Shaim to purchase shirts.

We can use this information to determine which of the following statement(s) could be correct:

A. Each shirt costs $10.

This statement is incorrect because $10 is subtracted from 15.75x, so the cost per shirt is actually greater than $10.

B. The sales tax is 6.5%.

This statement is correct because the expression includes a 6.5% sales tax, which is represented by the factor of 1.065.

C. Each shirt cost $15.75.

This statement is incorrect because the expression includes a discount of $10, so the actual cost per shirt is less than $15.75.

D. The cost of 2 portraits with tax is $33.55.

This statement is incorrect because the expression represents the cost of shirts, not portraits.

E. The cost of 2 portraits is $22.90 with the discount.

This statement is incorrect because the expression represents the cost of shirts, not portraits.

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Mike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology.

He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. Mike has 4 children; the 2 oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son Mike Sullivan, III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than 10 books. He owns a travel agency and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where he enjoys gardening.

Michael Sullivan, III has training in mathematics, statistics and economics, with a varied teaching background that includes 27 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series which he writes with his father, Michael Sullivan.

Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series. When not in the classroom or writing, Michael enjoys spending time with his 3 children, Michael, Kevin and Marissa, and playing golf. Now that his 2 sons are getting older, he has the opportunity to do both at the same time!

Product details

Publisher ‏ : ‎ Pearson; 4th edition (8 January 2018)

Language ‏ : ‎ English

Hardcover ‏ : ‎ 1224 pages

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Answer: [b + 4 = -10]

Step-by-step explanation: We are given the equation b = -14 and told to, given this information, evaluate b + 4 = ? and find ?. Given b = -14 we can plug in -14 for b in b + 4 = ?. This gives us -14 + 4 = ?. Adding this up gives us the answer of -10. Hope that this makes sense and helps, and good afternoon to you!

-Show work-

\(b=-14\\(b)+4=?\)

\((-14)+4=?\)

\(10 = ?\\?=10\)

a. In a random sample of 1,000 births, the expected number of births that take place by Caesarian section is:

E(X) = n*p = 1,000 * 0.32 = 320 births

Therefore, on average, 320 births out of 1,000 will take place by Caesarian section.

b. The variance of the number of Caesarian section births in a sample of 1,000 births is:

Var(X) = np(1-p) = 1,000 * 0.32 * (1-0.32) = 217.60

The standard deviation is the square root of the variance:

SD(X) = sqrt(Var(X)) = sqrt(217.60) = 14.76

Therefore, the standard deviation of the number of Caesarian section births in a sample of 1,000 births is 14.76.

c. To form an interval that is likely to contain the number of Caesarian section births in a sample of 1,000 births, we can use the normal distribution and the central limit theorem. Since n*p = 320 is greater than 10, we can assume that the distribution of the number of Caesarian section births in a sample of 1,000 births is approximately normal.

The 95% confidence interval for the number of Caesarian section births is:

320 ± 1.96*(14.76) = (291.16, 348.84)

Therefore, we can be 95% confident that the number of Caesarian section births in a sample of 1,000 births will be between 291 and 349.

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The probability density function (PDF) for the minimum of a set of random variables can be found by taking the derivative of the cumulative distribution function (CDF) of the minimum.

If X1, X2, ..., Xn are the random variables, the PDF of the minimum Y = min(X1, X2, ..., Xn) is given by:

fY(y) = n * fX(y) * [F(X1(y))^(n-1)],

where fX(y) is the PDF of the individual random variable X and F(X1(y)) is the CDF of X evaluated at y.

The probability density function (PDF) of the sum of two independent, continuous random variables can be obtained by convolving their individual PDFs. If X and Y are independent random variables with PDFs fX(x) and fY(y) respectively, then the PDF of their sum Z = X + Y is given by:

fZ(z) = ∫[fX(z-y) * fY(y)] dy,

where the integral is taken over the range of possible values for y.

The probability density function (PDF) of the ratio of two independent, continuous random variables can be found using the transformation method. If X and Y are independent random variables with PDFs fX(x) and fY(y) respectively, and Z = X / Y, then the PDF of Z is given by:

fZ(z) = ∫[fX(zy) * |y| * fY(y)] dy,

where the integral is taken over the range of possible values for y. The absolute value |y| is included to account for both positive and negative values of y.

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Circular equations are often organized in the following form:

\((x-h)^2+(y-k)^2=r^2\)

To find the equation of a circle given its center and a point:

We're given:

Plug the center into the general equation:

\((x-(-7))^2+(y-7)^2=r^2\\(x+7)^2+(y-7)^2=r^2\)

Plug in the given point (-2,-5) and find r²:

\(((-2)+7)^2+((-5)-7)^2=r^2\\(5)^2+(-12)^2=r^2\\25+144=r^2\\r^2=169\)

Plug the center and radius back into the original equation:

\((x-h)^2+(y-k)^2=169\\(x+7)^2+(y-7)^2=169\)

\((x+7)^2+(y-7)^2=169\)

The solution of the linear equation 2.8y+6+0.2y=5y-14 is y=10.

Given linear equation 2.8y+6+0.2y=5y-14 and we have to find the solution of the equation.

An equation is relationship between two or more variables which is expressed in equal to form. It is solved in order to find the values of variables. Equation of two variables look like ax+ by=x.

The given linear equation is 2.8y+6+0.2y=5y-14 which can be solved as under:

2.8y+6+0.2y=5y-14

We have to add the coefficients of same variables. Coefficients are the numbers which are present with the variable.

3y+6=5y-14

We have to take same variables at one side.

3y-5y=-14-6

-2y=-20

y=-20/-2

y=10

Hence the solution of the linear equation 2.8y+6+0.2y=5y-14  is y=10.

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