You are sent to the local tea shop to pick up 12 drinks. You purchase 8 sweet teas and 4 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.

a) All of the 3 drinks picked are sweet teas.



b) Exactly one drink is sweetened.

The missing dimensions of the triangular plot of land are:

i. b = 2.45

ii. A = 69.5

iii. C = 75.5^o

A cosine rule is a trigonometric function that can be used to determine the length of side, or measure of the internal angles of a none right angled triangle.

Cosine rule states that;

[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2acCos B

To determine the missing values of the triangle in the attached diagram, we have;

[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2acCos B

  = 4^2 + 7^2 - 2(4*7)Cos35^o

  = 16 + 49 -2(36*0.8192)

  = 65 - 58.9824

  = 6.0176

b = (6.0176)^1/2

  = 2.4531

b = 2.45

From sine rule,

a/ Sin A = b/Sin B = c/ Sin C

a/ Sin A = b/Sin B

4/Sin A = 2.45/ Sin 35

Sin A = 4* Sin 35/ 2.45

        = 0.9365

A = Sin^-1 0.9365

  = 69.47

A = 69.5

So to determine the value of C, we have;

A + B + C = 180^o

69.5 + 35 + C = 180

104.5 + C = 180

C = 180 - 104.5

   = 75.5

C = 75.5^o

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The function is transformed by horizontal translation to the right is applied first, followed by the vertical translation downward

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

y = 3ˣ

Let the transformed function be f' ( x )

y' = 3⁽ˣ⁻²⁾ - 4

Horizontal Translation: When compared to the basic function, y = 3x, the function's "(x-2)" inside the exponent of 3 causes a horizontal translation to the right of 2 units.

This results in a 2 unit shift along the x-axis of the function's graph.

Vertical Translation: In comparison to the base function y = 3x, the "-4" at the end of the function causes a vertical translation downward of 4 units.

This results in a 4 unit downward shift of the function's y-axis graph.

Hence , the function is transformed

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The simplified expression is given as follows:

7/x³.

Where the coefficients are:

The expression in this problem is defined as follows:

x³(1/4 x³)(28x^-9).

To obtain the coefficient c, we must multiply the coefficients of each expression, as follows:

c = 1 x 1/4 x 28

c = 7.

When two terms with the same base and different exponents are multiplied, we keep the bases and add the exponents, hence:

3 + 3 - 9 = -3.

The negative exponents goes in the denominator, hence the simplified expression is given as follows:

7/x³.

Meaning that the exponent is of e = 3.

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Answer:

? = 13.7

Step-by-step explanation:

Right triangle equation A^2 + B^2 = C^2

7.6^2 + 11.4^2 =

57.76 + 129.96 = 187.72

find the square root of 187.72 by putting it in the calculator

187.72 = 13.70109485^2

Estimate = 13.7^2

Answer:

B- 24cm^2

Step-by-step explanation:

for the square part of the shape the length is 7-2=5, 5*4=20

For the triangle, the base is 2, the height is 4, 2*4 is 8, since it’s a triangle the area is divided by 2 so 8/2 is 4.
Adding the areas of the shapes together you get 20+4=24cm^2

Answer:

the second one is x= -1

*this stuff is genuinely easy. I'm in 10th grade and all you have to do is put it in the calculator. If you have a tinspire like me you could make the x into a 1 in the calculator, put the whole thing in graph and it'll trace the answer for you. If your teacher wants to see work then maybe don't do that but let me know and I'll send the work for you.

Answer:

Step-by-step explanation:

1

If the daily prices are $ 1.50 for children and $ 2.25 for adults, a total of 284 children and 255 adults swam at the public pool that day.

Let's assume that the number of children who swam in the pool is x, and the number of adults who swam in the pool is y.

From the problem statement, we know that the total number of people who swam in the pool is 539. Therefore, we can write:

x + y = 539

We also know that the total receipts for admission are $1017.00. The price for a child is $1.50 and the price for an adult is $2.25. Therefore, the total revenue can be expressed as:

1.5x + 2.25y = 1017

Now we have two equations with two variables. We can solve for x and y by using any method of solving linear equations. For example, we can use the substitution method to solve for x and y:

x + y = 539 → x = 539 - y

Substituting this value of x into the second equation, we get:

1.5(539 - y) + 2.25y = 1017

Simplifying and solving for y, we get:

y = 255

Substituting this value of y into the equation x + y = 539, we get:

x = 539 - 255 = 284

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the total cost for the company including commission is $15,917

The commission is a sum of money that an employer pays as a fee or a percentage to an employee for completing a certain task or for generating new business by promoting the company's products or services. Incentives or sales commissions are other names for it. In general, anyone can earn a commission; it's not just for salespeople. The commission comes on top of the wage.

The company's policy, which ensures basic compensation and commission over a specific number of deal closures, determines the proportion of commission.

Equity ownership in a corporation is represented by shares. Shares are a type of financial asset that some businesses use to guarantee an equitable dividend distribution of any declared residual profits.

according to question,

total cost of 100 shares = 100*44.41 = $4441

total cost of 600 shares = 600*19.08 = $11448

broker charges for all 700 shares = 700*0.04 = $28

total cost acquired by the company is = $4441+$11448+$28

                                                               = $15917

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Answer: x=-5,y=3

Step-by-step explanation: Add the 2 equations together, 3x+x=4x, y+(-y)=0, and -12-8=-20. This leaves us with 4x=-20, so x=-5. Plug x back into the equation, so -5-y=-8, add 5 to both sides  so -y=-3, and y=3.

Answer:

Step-by-step explanation:

To solve this problem, we need to use the distance formula to find the length of each side of the triangle, and then apply the Pythagorean theorem to determine whether the triangle is a right triangle.

Let's label the three vertices of the triangle as A, B, and C, and their coordinates as follows:

A = (-2, 5)

B = (3, -1)

C = (1, 3)

The length of AB is:

AB = sqrt((3 - (-2))^2 + (-1 - 5)^2) = sqrt(25 + 36) = sqrt(61)

The length of AC is:

AC = sqrt((1 - (-2))^2 + (3 - 5)^2) = sqrt(9 + 4) = sqrt(13)

The length of BC is:

BC = sqrt((1 - 3)^2 + (3 - (-1))^2) = sqrt(4 + 16) = sqrt(20) = 2sqrt(5)

Now, we need to check whether the triangle is a right triangle. We can do this by checking whether the sum of the squares of the two shorter sides (AB and AC) is equal to the square of the longest side (BC). If it is, then the triangle is a right triangle.

AB^2 + AC^2 = 61 + 13 = 74

BC^2 = (2sqrt(5))^2 = 20

Since AB^2 + AC^2 is not equal to BC^2, the triangle is not a right triangle.

Therefore, the answer is: "The triangle is not a right triangle."

The balance A for $1900 invested at a rate of 8% for 8 years and compounded n times per year is approximately

$3,538.62, when compounded annually.

$3,601.77 when compounded semi-annually

$3,663.13 when compounded quarterly

$3,710.58 when compounded monthly

$3,748.26 when compounded daily

$3,754.04 when compounded continuously.

We have,

The balance A for $1900 was invested at a rate of 8% for 8 years and compounded n times per year.

A = P(1 + r/n)^(n*t)

where P is the principal amount ($1900 in this case), r is the annual interest rate (8%), t is the number of years (8), and n is the number of times compounded per year.

When compounded annually (n = 1):

A = $1900(1 + 0.08/1)^(1*8) = $1900(1.08)^8 ≈ $3,538.62

When compounded semi-annually (n = 2):

A = $1900(1 + 0.08/2)^(2*8) = $1900(1.04)^16 ≈ $3,601.77

When compounded quarterly (n = 4):

A = $1900(1 + 0.08/4)^(4*8) = $1900(1.02)^32 ≈ $3,663.13

When compounded monthly (n = 12):

A = $1900(1 + 0.08/12)^(12*8) = $1900(1.00666667)^96 ≈ $3,710.58

When compounded daily (n = 365):

A = $1900(1 + 0.08/365)^(365*8) = $1900(1.00021918)^2920 ≈ $3,748.26

When compounded continuously:

A = Pe^(rt) = $1900e^(0.08*8) ≈ $3,754.04

Now,

n     1                2             4           12                365        continuous

A    $3,538.6    $3,601.77  $3,663.13   $3,710.55     $3,748.26   $3,754.04

Therefore,

The balance A for $1900 invested at a rate of 8% for 8 years and compounded n times per year is approximately $3,538.62.

When compounded annually, $3,601.77 when compounded semi-annually, $3,663.13 when compounded quarterly, $3,710.58 when compounded monthly, $3,748.26 when compounded daily, and $3,754.04 when compounded continuously.

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Let's use the variable "x" to represent the number of 3-inch bolts that James bought.

We know that he bought a total of 16 bolts, so the number of 4-inch bolts he bought would be 16 - x.

The cost of the 3-inch bolts is 36 cents each, so the total cost of the 3-inch bolts would be 0.36x dollars.

Similarly, the cost of the 4-inch bolts is 42 cents each, so the total cost of the 4-inch bolts would be 0.42(16 - x) dollars.

We know that the total cost of all the bolts was $6.00, so we can set up the following equation:

0.36x + 0.42(16 - x) = 6.00

Simplifying and solving for x, we get:

0.36x + 6.72 - 0.42x = 6.00

-0.06x = -0.72

x = 12

Therefore, James bought 12 of the 3-inch bolts.

If the normally distributed heights have mean as 69, then the probability that he can fit through the doorway without bending is 0.9938.

In "Normal-Distribution", probability refers to the likelihood of a continuous random variable falling within a certain range of values

We first convert the height of the doorway and the height of the male passenger to z-scores by using z = (x - μ) / σ,

where:

x = height (doorway height or male passenger height)

μ = mean of the male height,

σ = standard deviation of male height,

For the doorway height:

⇒ [tex]Z_{doorway}[/tex] = (76 - 69.0)/2.8 = 2.50,

For a male passenger:

⇒ [tex]Z_{male}[/tex] = (x - 69.0)/2.8,

To find the probability that a randomly selected male passenger can fit through the doorway without bending, we need to find the proportion of the "male-population" that has a height less than or equal to the height of the doorway;

⇒ P([tex]Z_{male}[/tex]  ≤  [tex]Z_{doorway}[/tex] ) = P([tex]Z_{male}[/tex]  ≤ 2.50) and

We know that the value of P(z ≤ 2.50) is 0.9938,

Therefore, the required probability is approximately 0.9938.

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The given question is incomplete, the complete question is

An airliner carries 350 passengers and has doors with a height of 76 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in,

If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending.

Assuming no withdrawals, the investment will grow to $5960 in approximately 2.63 years.

To answer this problem, use the compound interest formula:

A = (1 + r/n)(n*t).

We're looking for t so we can rearrange the formula to find it:

n = (log(A/P) / log(1 + r/n))

When we substitute the provided values, we get:

12.63 t = (log(5960/5000) / log(1 + 0.048/12))

Hence, assuming no withdrawals, the investment will grow to $5960 in approximately 2.63 years.

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Answer:

  √(205)/13

Step-by-step explanation:

You want sec(θ) when cot(θ) = 13/6.

Some calculators can figure this directly as ...

  [tex]\sec{(\cot^{-1}\dfrac{13}{6})}=\boxed{\dfrac{\sqrt{205}}{13}}[/tex]

Others need to make use of the trig relations ...

  tan(θ) = 1/cot(θ)

  sec(θ) = √(tan²(θ) +1)

or

  sec(θ) = 1/cos(θ)

The tangent of the angle is

  tan(θ) = 1/cot(θ) = 1/(13/6) = 6/13.

Then the secant is ...

  sec(θ) = √((6/13)² +1) = √(6² +13²)/13

  sec(θ) = √205/13

A calculator can get there from ...

  sec(θ) = 1/cos(arctan(6/13)) = √205/13

This polynomial cannot be factored any further using integer coefficients, so our final factored form is: 40w²11 + 16w²6 = 8w²6(5w²5 + 2)

How to solve?

To factor the polynomial 40w²11 + 16w²6, we need to look for common factors in the two terms. We notice that both terms have a factor of 8w²6, so we can factor that out:

40w²11 + 16w²6 = 8w²6(5w²5 + 2)

Now, we have factored out the greatest common factor of the two terms, leaving us with the remaining factor of 5w²5 + 2. This polynomial cannot be factored any further using integer coefficients, so our final factored form is:

40w²11 + 16w²6 = 8w²6(5w²5 + 2)

This form of the polynomial is useful for simplifying expressions, finding roots, and solving equations.

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Answer:

Alex's gross pay for the month is $18/hour x 140 hours = $2520.

The total deductions from his paycheck are:

$180.00 (FICA) + $215.00 (Federal income tax) + $62.00 (State income tax) + $72.89 (Health insurance) + $50.00 (Retirement savings) = $579.89

So Alex's net pay (take-home pay) is:

$2520 (gross pay) - $579.89 (deductions) = $1940.11

To find the percentage of his gross pay that he took home, we can divide his net pay by his gross pay and multiply by 100:

($1940.11 / $2520) x 100 = 77.06%

Therefore, Alex took home 77.06% of his gross pay after deductions.

Answer:

Step-by-step explanation:

Dilation by 3 means that you increase the length of each of the sides by 3. Since ED was 2 units long, the plotted dilation of ED is 6 units long. By multiplying each of the lengths of the sides by 3 units, you will be able to draw the whole image.

Answer:

see the attached image

Step-by-step explanation:

For a dilation of scale factor 3, we can multiply each side length by 3.

1. What is 18%? 1500 * .18 = 270
2. Write the equation. 1500 - 270(x) = 50
3. Single out your X by subtracting 1500 from both sides. -250x = -1450
4. X still isn't singled out. Divide by -250. x = 1450/270 (two negatives produce a positive).
5. Simplify. x = 145/27 (fraction), 5.370370 (decimal)

Assuming 18% each year is constant through the months (say, 1.5% decrease each month), your computer will be worth $50 around 5.4 (rounded) years.

Answer:

1) 35%

2) 73%

3) 23%

4) 57%

5) 13%

6) 37%

Step-by-step explanation:

The general solution is to grab the total, which is 100%, and subtract the percentage of the given problems to find the solution. In some problems you have to add some percentages togheder to finish the problem.

So, in the first problem you subtract the percentage of girls to the whole class percentage: 100%-65%=35%.

In the second, whole package minus the red ones: 100%-27%= 73%

In the third, group of children minus swimmers: 100%-78%=22%

In the fourth, 100%-43%= 57%.

In the fifth, there is won percentage, loss percentage, and the remaining percentage you need to add to make 100% is the tie percentage.

So if we do the reverse (subtracting both win and loss percentage to have the tie percentage): 100%-45%-42%=13%.

In the sixth, it's the same thing as the fifth problem: subtracting the basketball and hockey from the whole children percentage that chose the sport: 100%-35%-28%=37%.

I hope this helped

Angle or arc HGJ is measured at 275 for given figure.

Arcs may be created from the circumference of a circle. It is referred to as the curved line that connects two locations on a circle's perimeter and splits it into segments. The length of an arc is inversely proportional to the angle it makes at the centre of the circle.

When the central angle rises, so does the arc's length, and vice versa. Arcs are commonly used to depict and compute measurements of circles and circular objects in geometry, trigonometry, and physics.

For given problem,

mHGJ= 360° - mJH = 360°-( mJl + mlH ) =  360°-(30°+55°)

         = 360°-85° = 275°

Hence, arc or angle HGJ= 275 degrees

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i) The after-tax operating cash flows that will be remitted to the parent company each year are USD 73.53, 110.30 and USD 146.34.

ii) The Net Present Value of the project are USD 66.85, USD 91.90 and USD 107.50.

iii) The MNC may want to consider other investment opportunities or reassess the assumptions used in this analysis.

iv) As per the subsidiary, the firm may be better off remitting earnings on a regular basis to minimize exchange rate risk and invest in a diversified portfolio of assets to mitigate other types of risks.

i) To calculate the after-tax operating cash flows that will be remitted to the parent company each year, we need to first calculate the operating cash flows in CAD and then convert them to USD while taking into account the tax on remitted funds. Let's assume the operating cash flows for each year are CAD 100, CAD 150, and CAD 200, respectively.

In year 1, the CAD 100 operating cash flow is remitted to the parent company in USD. Using the exchange rate of C$1.02 per US$, this is equal to USD 98.04. However, the MNC must pay a 25% tax on this amount, so the after-tax cash flow is USD 73.53.

In year 2, the CAD 150 operating cash flow is remitted to the parent company in USD. Using the same exchange rate of C$1.02 per US$, this is equal to USD 147.06. After the 25% tax on remitted funds, the after-tax cash flow is USD 110.30.

In year 3, the CAD 200 operating cash flow is remitted to the parent company in USD. However, the exchange rate has changed to C$1.025 per US$, so the CAD 200 is now equal to USD 195.12. After the 25% tax on remitted funds, the after-tax cash flow is USD 146.34.

Therefore, the after-tax operating cash flows that will be remitted to the parent company each year are USD 73.53, USD 110.30, and USD 146.34, respectively.

ii) To calculate the Net Present Value (NPV) of the project, we need to discount the after-tax operating cash flows back to their present value using a discount rate that reflects the riskiness of the project. Let's assume a discount rate of 10%. Using this rate, we can calculate the present value of each year's after-tax cash flow as follows:

Year 1: USD 73.53 / (1 + 0.10)¹ = USD 66.85

Year 2: USD 110.30 / (1 + 0.10)² = USD 91.90

Year 3: USD 146.34 / (1 + 0.10)³ = USD 107.50

iii) Based on the calculated NPV, the MNC should not accept the project. The negative NPV indicates that the project is not expected to create value for the MNC's investors. Additionally, the after-tax operating cash flows that will be remitted to the parent company each year are not sufficient to compensate for the investment's costs and the 25% tax on remitted funds.

iv) The drawback of Flagstaff Corp.'s approach of reinvesting earnings in Mexican government securities for 10 years before remitting accumulated earnings to the United States is that it exposes the firm to exchange rate risk. Over the course of 10 years, exchange rates between the Mexican peso and the U.S. dollar could fluctuate significantly, potentially eroding the value of the accumulated earnings when they are finally remitted. Additionally, there is no guarantee that the Mexican government securities will continue to provide a high interest rate over the entire 10-year period.

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Step-by-step explanation:

a it be 3/21 to get red which is 0.143

b to get not red if u don't replace red would be 12/18 so it be 0.6666 but if u replace it then it would be 0.517

The statement that describes the behavior of the function f(x) is: The graph approaches 0 as x approaches infinity.

The correct answer is an option (b)

Consider the function [tex]f(x) = \frac{2x}{1-x^2}[/tex]

Consider the limit of function f(x) as x approaches infinity (x → ∞)

[tex]\lim_{n \to \infty} f(x)\\\\= \lim_{n \to \infty} \frac{2x}{1-x^2} \\\\= \lim_{n \to \infty} \frac{2x/x}{(1-x^2)/x}\\\\ = \lim_{n \to \infty} \frac{-2}{x}[/tex]

= 0

This means that when x approaches infinity the term x² grows rapidly

So, 1 - x², which is in the denominator will decrease, become a large negative more rapid than the x in the numerator.

We can say that the function approaches zero.

Thus the correct statement is: The graph approaches 0 as x approaches infinity.

The correct answer is an option (b)

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The complete question is:

Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction?

a) The graph approaches –2 as x approaches infinity.

b) The graph approaches 0 as x approaches infinity.

c) The graph approaches 1 as x approaches infinity.

d) The graph approaches 2 as x approaches infinity.