A cruise line ship left Port A and traveled 90 miles due west and then 400 miles due north. At this point, the ship docked at Port B What is the shortest distance between Port A and Port B?

Applying the trigonometry ratios, the correct option is: B. none of these are correct.

The trigonometry ratios are SOH CAH TOA, which are used for solving a right triangle.

Use the trigonometry ratio to find out which option is correct.

Cos Z = adj/hyp = 61/CZ, so option A is incorrect.

Sin Z = opp/hyp = 73/CZ,  so option C is incorrect.

Tan Z = opp/adj = 73/61,  so option D is incorrect.

Thus, the answer is: B. none of these are correct.

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It looks like the boundaries of [tex]R[/tex] are the lines [tex]y=\dfrac23x [/tex] and [tex]y=3x[/tex], as well as the hyperbolas [tex]xy=\frac23[/tex] and [tex]xy=3[/tex]. Naturally, the domain of integration is the set

[tex]R = \left\{(x,y) ~:~ \dfrac{2x}3 \le y \le 3x \text{ and } \dfrac23 \le xy \le 3 \right\}[/tex]

By substituting [tex]x=\frac uv[/tex] and [tex]y=v[/tex], so [tex]xy=u[/tex], we have

[tex]\dfrac23 \le xy \le 3 \implies \dfrac23 \le u \le 3[/tex]

and

[tex]\dfrac{2x}3 \le y \le 3x \implies \dfrac{2u}{3v} \le v \le \dfrac{3u}v \implies \dfrac{2u}3 \le v^2 \le 3u \implies \sqrt{\dfrac{2u}3} \le v \le \sqrt{3u}[/tex]

so that

[tex]R = \left\{(u,v) ~:~ \dfrac23 \le u \le 3 \text{ and } \sqrt{\dfrac{2u}3 \le v \le \sqrt{3u}\right\}[/tex]

Compute the Jacobian for this transformation and its determinant.

[tex]J = \begin{bmatrix}x_u & x_v \\ y_u & y_v\end{bmatrix} = \begin{bmatrix}\dfrac1v & -\dfrac u{v^2} \\\\ 0 & 1 \end{bmatrix} \implies \det(J) = \dfrac1v[/tex]

Then the area element under this change of variables is

[tex]dA = dx\,dy = \dfrac{du\,dv}v[/tex]

and the integral transforms to

[tex]\displaystyle \iint_R 9xy \, dA = \int_{2/3}^3 \int_{\sqrt{2u/3}}^{\sqrt{3u}} \frac{dv\,du}v[/tex]

Now compute it.

[tex]\displaystyle \iint_R 9xy \, dA = \int_{2/3}^3 \ln|v|\bigg|_{v=\sqrt{2u/3}}^{v=\sqrt{3u}} \,du \\\\ ~~~~~~~~ = \int_{2/3}^3 \ln\left(\sqrt{3u}\right) - \ln\left(\sqrt{\frac{2u}3}\right) \, du \\\\ ~~~~~~~~ = \frac12 \int_{2/3}^3 \ln(3u) - \ln\left(\frac{2u}3\right) \, du \\\\ ~~~~~~~~ = \frac12 \int_{2/3}^3 \ln\left(\frac{3u}{\frac{2u}3}\right) \, du \\\\ ~~~~~~~~ = \frac12 \ln\left(\frac92\right) \int_{2/3}^3 du \\\\ ~~~~~~~~ = \frac12 \ln\left(\frac92\right) \left(3-\frac23\right) = \boxed{\frac76 \ln\left(\frac92\right)}[/tex]

The value of 'x' from the expression is 1/3

Given the expression;

[tex]x + \frac{x}{3} = \frac{4}{9}[/tex]

Find the LCM of the left side, we have

[tex]\frac{3x + x}{3} = \frac{4}{9}[/tex]

Cross multiply

[tex]9(4x) = 4 *3[/tex]

[tex]36x = 12[/tex]

Make 'x' the subject

[tex]x = \frac{12}{36}[/tex]

x = [tex]\frac{1}{3}[/tex]

Thus, the value of 'x' from the expression is 1/3

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Hello !

Answer:

[tex]\boxed{\sf x=\dfrac{1}{3} }[/tex]

Step-by-step explanation:

Our aim is to find the value of x that verifies the following equation :

[tex]\sf x+\frac{x}{3} =\frac{4}{9}[/tex]

Let's isolate x :

Multiply both sides by 3 :

[tex]\sf 3(x+\frac{x}{3} )=\frac{4}{9}\times 3\\ \sf 3x+x=\frac{4}{3}[/tex]

Now we can combine like terms :

[tex]\sf 4x=\frac{4}{3}[/tex]

Finally, let's divide both sides by 4 :

[tex]\sf \frac{4x}{4} =\frac{4}{3} \times \frac{1}{4} \\\boxed{\sf x=\dfrac{1}{3} }[/tex]

Have a nice day ;)

Answer:

150 minutes

Step-by-step explanation:

If Anna read 75% of her 300-page book, then she has already read:

300 × 75%

= 300×0.75

= 225

225 pages.

If Anna has already read 225 pages, then she has:

300 - 225 = 75

75 pages left still to read.

If Anna reads 2 minutes per page, then she has

75 × 2 = 150 minutes.

She has 150 minutes of reading left to finish her book.

By the way, it's weird to say you have 150 minutes of something to do. In real life 150 minutes = 2 1/2 hours. jfyi. Have a great day!

The value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06

The expression is given as:

[tex]x \sim B (10, 0.75)[/tex]

This means that:

n = 10

p = 0.75

The probability is then calculated as

[tex]P(x)= ^nC_x * p^x *(1 - p)^{n-x[/tex]

This gives

[tex]P(5)= ^{10}C_5 * 0.75^5 *(1 - 0.75)^5[/tex]

Evaluate the combination expression

[tex]P(5)= 252 * 0.75^5 *0.25^5[/tex]

Evaluate

P(5)= 0.06

Hence, the value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06

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If P(a)=0.5 and P(b) =0.45, then P(a ∩ b) is 0.225.

Independent events are events such that the occurrence of one event won't affect the other.

Therefore,

P(a) × P(b) = P(a ∩ b)

Hence,

P(a) = 0.5

P(b) = 0.45

Therefore,

P(a ∩ b) = 0.5 × 0.45

P(a ∩ b) = 0.225

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Answer:

See below.

Step-by-step explanation:

Here is an example:-

Solve by elimination:

2x - 3y  =   0

3x + 2y =  13

To eliminate the y terms Multiply the first equation by 2 and the second by 3. This gives:

4x  - 6y = 0

9x + 6y = 39      Adding the 2 equations:

13x + 0 = 39

13x = 39

x = 39/13 = 3

Finally we find y by plugging x = 3 into the first equation:

2(3) - 3y = 0

3y = 2(3) = 6

y = 2.

Answer:

1/xyz^3

Step-by-step explanation:

exponents are subtracted when divided

x^0 is 1

negative exponents are positive in the denominator

(4x^0y^-2z^-3) / (4xy-1)

(4xy^-2z^-3) / (4xy^-1)

x-1y^-1z^-3

1/xyz^3

The information to fill one the box regarding the proof include:

It should be noted that when two triangles of each corresponding sides are equal, then it's said that they are similar.

Here AB = CD, and AD = CB as they illustrate the fact that they are parallel.

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Probability of someone over age 30 winning the tickets is; 38.46%

We are given;

Number of People over 30 years of age = 15

Number of people between 20 and 30 years old = 14

Number of People under 20 years old = 10

Total number of people in the group = 15 + 14 + 10 = 39

Thus;

Probability of someone over age 30 winning the tickets = 15/39 = 38.46%

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The cost of 2 chairs is = $30

The cost of 1 table = $60

Step-by-step explanation:

Let a table represent x

A chair represents y

4x + 3y = 225.......eq 1

3x + 4y = 195........eq 2

Use elimination method

x - y = 30

x= 30 + y...... Eq 3

Substitute the value of x into equation 1

4(30+ y) + 3y= 225

120 + 4y + 3y= 225

7y + 120= 225

7y= 225-120

7y= 105

y= 15

Substitute the value of y in eq 2

3x + 15 = 195

3x= 195-15

3x= 180

x= 60

Therefore, the cost of 2 chairs is 15 * 2= $30

The cost of 1 table = $60

Answer:

65

Step-by-step explanation:

Answer:

3x²y (2x²-3y²+ 4y)

Step-by-step explanation:

Factor the expression 6x^4y-9x²y³+12x²y².

First, check if there is a GCF. The GCF is 3x²y.

3x²y (2x²-3y²+ 4y).

This equation cannot be factored further. Therefore, the answer is
3x²y (2x²-3y²+ 4y).

Hope this helps!

Answer:

3x²y(-3y²+4y+2)

Step-by-step explanation:

6x⁴y-9x²y³+12x²y²

solution:

first common

3x²y(2x²-3y²+4y)

3x²y(-3y²+4y+2)

The correct option is (c) h = 10sin(π15t)+35.

The equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds is  h = 10sin(π15t)+35.

The blades of a turbine, which resemble propellers and function much like an airplane wing, capture the wind's energy.

A pocket of low-pressure air develops on one side of the blade when the wind blows. The blade is subsequently drawn toward the low-pressure air pocket, which turns the rotor.

Calculation for the equation of the model height-

Let's now review each choice individually and select the best one.

The blade is horizontal at time t = 0. As a result, h = 35 at t = 0 is valid for all of the possibilities in this situation.

They accomplish two spins in a minute. The blades will so complete one rotation in 30 seconds. and they will complete a quarter rotation in 15/2 seconds. Because of this, the blade will be vertically up from time t = 0 to t = 15/2. Its height in this instance should be 35 + 10 = 45 ft. Let's now examine the available possibilities.

If we put t=15/2 in the options

Option (a) gives h = 25

Option (b) gives h = -10sin(15/2) + 35

Option (c) gives h = 45

Option (d) gives h = 10sin(15/2) + 35

Therefore, the correct equation is given in option c.

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The complete question is -

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

a) h = −10sin(π15t)+35  

b) h = −10sin(πt)+35

c) h = 10sin(π15t)+35

d) h = 10sin(πt)+35

Answer:

c) 700

Step-by-step explanation:

Add 800 and 600, and then divide by the number of number, or in this case, two. This should give you 700.

[tex]\textbf{ Heya !}[/tex]

Your Answer Is:-

[tex]\sf{9x\div6}[/tex]

because,

               it has a coefficient of 9 (a number that comes before a variable)

`hope that was helpful to u ~

We can to convert the expression  [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression   [tex]\sqrt[5]{9}[/tex].  by using the laws of indices.

A radical expression is an expression of the form ⁿ√x where it is called the nth root of x.

Now, to write [tex](3^{\frac{1}{5} } )^{2}[/tex] as  the radical expression [tex]\sqrt[5]{9}[/tex], we use following laws of indices

So,  [tex](3^{\frac{1}{5} } )^{2} = (3^{2} )^{\frac{1}{5} }[/tex]

  [tex](3^{2} )^{\frac{1}{5} } = 9^{\frac{1}{5} } = \sqrt[5]{9}[/tex]

Thus, we can to convert the expression  [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression   [tex]\sqrt[5]{9}[/tex].  by using the laws of indices.

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Answer:

D.

Step-by-step explanation:

Standard deviation tells us the dispersion of data/scores around the mean.

We can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.

A standard deviation (or σ) is a measure of how widely distributed the data is about the mean (μ). A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out. A standard deviation around 0 suggests that data points are close to the mean, whereas a high or low standard deviation indicates that data points are above or below the mean, respectively.

We use the following formula to compute the standard deviation:

[tex]\sigma = \sqrt\frac{{\sum_{i=1}^{N}\left | x_i - \mu \right | }^2}{N}[/tex]

In this formula, σ is the standard deviation, [tex]x_i[/tex] is the data point in the set we are solving for, μ is the mean, and N is the total number of data points.

In the question, we are asked to tell what standard deviations tell us from the given options.

From the above discussion, we can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.

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The results of dividing 1 into pieces that are each 1/9 of a whole is 9

1 ÷ 1/9

1 ÷ 1/9

= 1 × 9/1

= (1 × 9) / (1 × 1)

= 9/1

= 9

Complete question:

If 1 is divided into pieces that are each 1/9 of a whole, how many pieces are there

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Based on the calculations, the correct value of the test statistic is equal to 3.2.

For samples A and B, the hypothesis is given by:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

Since both samples have a normal distribution, we would use a pooled z-test to determine the value of the test statistic:

[tex]z = \frac{\bar{x_1} - \bar{x_2} -(\mu_1 - \mu_2) }{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_1^2}{n_1}} }[/tex]

Substituting the given parameters into the formula, we have;

[tex]z = \frac{33 - 25 -(0) }{\sqrt{\frac{3^2}{4} + \frac{4^2}{4}} }\\\\z = \frac{8 }{\sqrt{\frac{9}{4} + \frac{16}{4}} }\\\\z = \frac{8 }{\sqrt{\frac{25}{4} } }\\\\z = \frac{8 }{\frac{5}{2} }}\\\\z = 8 \times \frac{2}{5}[/tex]

z = 3.2.

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An analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a parameter.

Therefore, an analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a parameter.

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The statement, "the lateral surface area of cone A is exactly half of that of cylinder B" is: A. True.

Lateral surface area of cone = πrl

Lateral surface area of cylinder = 2πrh

Lateral surface area of cone A = πrl = πrh

Lateral surface area of cylinder B = 2πrh

This means the lateral surface area of cylinder B is twice that of cone A. Thus, lateral surface area of cone A is exactly half of that of cylinder B.

The answer is: A. True.

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Hello,

[tex]34 = p + 19[/tex]

[tex]34 - 19 = p + 19 - 19[/tex]

[tex]15 = p[/tex]

[tex]p = 15[/tex]

The area of the parallelogram is 135 square meters.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal).

Properties of parallelogram are-

The area of parallelogram = Base×Height

A = B×H

Calculation for the area of the given parallelogram.

The base is 15 meters.

The height is 9 meters

Area = 15×9

        = 135

Therefore, the area of the parallelogram is 135 square meter.

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The price that must be charged for a 1-hour tutoring session to produce this amount of revenue is 24.5 dollars

The first thing to do with word problem is to understand the question. After that, make analysis of the question.

It is given that a A private tutoring company charges $20 for a 1-hour session. Currently, 300 students are each tutored for an hour each week. Since the company is losing money, the owner has decided to increase the price. For each 50¢ increase, That is $20.5 for each students.

If she estimates that 5 fewer students will participate, that is, 295 students, and the company needs to bring in $6,210 per week to stay in business.

Let us assume that 1 hour per day. And there are 7 days in a week.

Divide the money by 7 to know the value per day

6210/7 = 887.14

Now, divide the amount per day by 250 students to know the amount per student per hour

887.14/295 = 3.007

The price that must be charged for a 1-hour tutoring session to produce this amount of revenue should be 20.5 + 4 = 24.5 dollars

Therefore, each student will pay $24.5 per hour

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Basado en la información, el valor de abc + bca + cab debe ser de 60.

El valor de la combinación de estás tres letras es de 20.

Según la propiedad conmutativa el orden de los factores sumados no debe afectar su resultado, por lo que:

20+20+20 = 60

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a. The probability that exactly one is defective is 0.2025

b. The probability that none will be defective is 0.0769

c. The probability rate that should be used is 2%

d. The modified production process is better.

The question has to do with binomial probability.

Binomial probability is probability in which the event can only have two values or is binary.

Given the binomial probability formula,

P(X = x) = ⁿCₓpˣ(1 - p)ⁿ ⁻ ˣ

where

For the probability that exactly one is defective, x = 1

So, P(x = 1) = ⁵⁰C₁p¹(1 - p)⁵⁰ ⁻ ¹

= ⁵⁰C₁p(1 - p)⁴⁹

= ⁵⁰C₁(0.05)(1 - 0.05)⁴⁹

= ⁵⁰C₁(0.05)(0.95)⁴⁹

= 50(0.05)(0.95)⁴⁹

= 50(0.05)(0.081)

= 0.2025

So, the probability that exactly one is defective is 0.2025

For the probability that exactly one is defective, x = 0

So, P(x = 0) = ⁵⁰C₀p⁰(1 - p)⁵⁰ ⁻ ⁰

= ⁵⁰C₀(1 - p)⁵⁰

= ⁵⁰C₀(1 - 0.05)⁵⁰

= ⁵⁰C₀(0.95)⁵⁰

= 1 × (0.95)⁵⁰

= 0.0769

So, the probability that none will be defective is 0.0769

Since the modified result results in a defective rate of one out of 50 pens.

The probability rate that should be used is p = number of defective pens/total number of pens = 1/50

= 1/50 × 100 %

= 2%

The probability rate that should be used is 2%

Since the defective rate of the modified production process is 2% which is less than that of the previous production process which is 5%, the modified production process is better.

So, the modified production process is better.

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The number of three-digit number you can make is 8

The usable digits are given as:

4 and 9

Since the two digits can be repeated, then we have

First = 2

Second = 2

Third = 2

So, we have:

Total = 2 * 2 * 2

Evaluate

Total = 8

Hence, the number of three-digit number you can make is 8

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