The angle between the lines of sight from a lighthouse to a tugboat and to a cargo ship is 27°. The angle between the lines of sight at the cargo ship is twice the angle between the lines of sight at the tugboat. What are the angles at the tugboat and at the cargo ship?

Answer:

Step-by-step explanation:

Let us first make the denominators equal, so

600 x 700 = 420000

[tex]\frac{480}{600} * \frac{700}{700} \\\\= \frac{336000}{420000}[/tex]

Similarly,

[tex]\frac{560}{700} * \frac{600}{600} = \frac{336000}{420000}[/tex]

By comparison, both of them are equal.

Hope It Helps!

Answer:The coordinates of the resulting point after the reflection across the y - axis will be P'(3, 2).

What do you mean by reflection of coordinates?

A reflection on the coordinate plane is a type of transformation. It takes a geometric figure such as a point, line segment, or shape and transforms it into a congruent geometric figure called the image.

Given is a point (-3, 2) reflected across the y - axis.

Now, when any given coordinate is reflected across the y - axis then, the sign of the x - coordinate is inverted and the y - coordinate remains same.

As given, the coordinates of the point are - P(-3, 2)

Now, after reflection across the y - axis, the new coordinates of the image of this point will be -

x' = - (- 3) = 3

y' = y = 2

P'(3, 2)

Therefore, the coordinates of the resulting point after the reflection across the y - axis will be P'(3, 2)

Answer:

3,2

Step-by-step explanation: Just took the test

The simplest form of the ratio 2m : 8cm : 40mm is

50mm : 2mm : 1mm

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

For we to simplify the ratio , we have to convert the unit to the least form. The least form of the unit is millimeter

2m = 2× 1000mm = 2000mm

8cm = 8 × 10 = 80mm

40mm = 40mm

therefore the ratio will be in form of

2000mm : 80mm ; 40mm

divide through by 10

200mm : 8mm : 4mm

divide through by 4

50mm : 2mm : 1mm

therefore the simplest form of the ratio 2m: 8cm : 40mm is 50mm : 2mm : 1mm

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Answer:153

Step-by-step explanation

we can see height is equal to 9. if we consider height and 10sm as sides of rectangle, we can say top of trapezoid is equal to 10 as well.

Area of trapezoid is A=(a+b)/2*h

h-height=9

a-top=10

b-bottom=10+7+7=24

A=(10+24)/2*h=34/2*9=17*9=153

Answer:

8 degrees

Step-by-step explanation:

Given in the picture, hope it helps.

The discriminant, D of the quadratic equation [tex]3x\² + 3 \frac 13x + \frac 13[/tex] when calculated is 64/9

The quadratic equation is given as

[tex]3x\² + 3 \frac 13x + \frac 13[/tex]

The discriminant of a quadratic equation of the form ax² + bx +c = 0 is given by the expression b² - 4ac

In this case, we have the quadratic equation [tex]3x\² + 3 \frac 13x + \frac 13[/tex], which can be written in the standard form as

[tex]3x\² + \frac {10}3x + \frac 13[/tex]

Comparing with the standard form ax² + bx + c = 0,

we have a = 3, b = 10/3 and c = 1/3

The discriminant of this quadratic equation is therefore:

D = b² - 4ac

[tex]D = (\frac{10}{3})\² - 4 \cdot 3 \cdot \frac{1}{3}[/tex]

D = 64/9

Hence, the discriminant of [tex]3x\² + 3 \frac 13x + \frac 13[/tex] is 64/9

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the shortest distance from the parking lot to the beach is 24 m and the distance between the beach and the refreshment stand is 18 m.

The answer is C: 24 m; 18 m. To find the shortest distance from the parking lot to the beach, one should measure the distance between the two locations. The distance between the parking lot and the beach is 24 m. To find the distance between the beach and the refreshment stand, one should measure the distance between the two locations. The distance between the beach and the refreshment stand is 18 m. Therefore, the shortest distance from the parking lot to the beach is 24 m and the distance between the beach and the refreshment stand is 18 m.

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Answer:

Step-by-step explanation: 55 i think

Answer:

2%?

Step-by-step explanation:

m = 532 - (57 * h) represents the number of miles remaining after h hours of traveling at an average speed of 57 miles per hour.

The equation m = 532 - (57 * h) is used to represent the number of miles remaining, m, after h hours of traveling at an average speed of 57 miles per hour. The equation works by taking the total distance, 532 miles, and subtracting the product of the average speed, 57 miles per hour, and the amount of hours traveled, h. The result of the equation is the number of miles remaining, m. For example, if the family has been traveling for four hours, the equation would be m = 532 - (57 * 4). Solving the equation, m = 344, meaning the family has 344 miles left to travel. This equation allows the family to easily determine how many miles they have left to travel, given the average speed and amount of time traveled.

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Answer: y= 116x

Step-by-step explanation:

Answer:

  f(-3) = 6

Step-by-step explanation:

You want the value of f(-3) given a graph of f(x).

To find the value of f(-3), locate -3 on the x-axis. Follow the vertical grid line to where it intersects the graph of f(x). Follow the horizontal grid line from there to the axis marked f(x), and read the value on the vertical scale.

The attachment shows this process, and that the value of f(-3) is 6.

__

Additional comment

Unless there is information to the contrary, the usual assumption is that each grid line represents one unit. Positive is to the right of the vertical axis, and up from the horizontal axis. Then x=-3 is 3 grid lines left of the vertical axis.

The notation f(x) means the value of function f depends on the value x. The expression f(-3) is the function value when x=-3. Here, it is found by reading the graph. In other situations, it might be found from a table or by evaluating an algebraic expression.

The probability that a customer ordered a hot drink, given that they ordered a small, is approximately 0.045.

A mathematical technique called the Bayes theorem enables us to revise our views or probability regarding an occurrence in light of fresh data or evidence. It has the name of the reverend Thomas Bayes, a statistician and philosopher active in the 18th century. According to the Bayes theorem, the likelihood of an event A given that an event B has already happened is equal to the likelihood of an event B given that an event A has already occurred, multiplied by the prior likelihood of an event A, divided by the previous likelihood of an event B.

The Baye's Theorem is given as:

P(B|A) = P(A|B) × P(B) / P(A)

Here,

P(A) is the probability that a customer ordered a small drink = 0.22.

P(B) is the probability that a customer ordered a hot drink, regardless of whether it was small or medium or large = 0.05.

P(A|B) is the probability that a customer ordered a small drink, given that they ordered a hot drink = 0.2.

Substitute the value we have:

P(B|A) = P(A|B) × P(B) / P(A) = (0.2 × 0.05) / 0.22 ≈ 0.045

Therefore, the probability that a customer ordered a hot drink, given that they ordered a small, is approximately 0.045.

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The measures in the circles are calculated as:

2. FD = 22; 4. US = 58

6. MN = 11; 8. YZ = 34

The Intersecting Chords Theorem states that when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

2. 12(3x - 5) = 15(8) [based on the Intersecting Chords Theorem]

36x - 60 = 120

36x = 120 + 60

36x = 180

x = 5

FD = 3x - 5 + 12 = 3(5) - 5 + 12

FD = 22

4. 30(3x + 1) = 42(x + 11) [based on the Intersecting Chords Theorem]

90x + 30 = 42x + 462

90x - 42x = -30 + 462

48x = 432

x = 9

US = 3x + 1 + 30 = 3(9) + 1 + 30 = 58

6. (2x - 7 + 9)(9) = (8 + 10)(10) [based on the intersecting secants theorem]

18x + 18 = 180

18x = 180 - 18

18x = 162

x = 9

MN = 2x - 7 = 2(9) - 7

MN = 11

8. (2x + 12 + 6)(6) = (x + 3 + 10)(10) [based on the intersecting secants theorem]

12x + 108 = 10x + 130

12x - 10x = -108 + 130

2x = 22

x = 11

YZ = 2x + 12 = 2(11) + 12

YZ = 34

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Answer: The graph is translated to the left 9 units

Step-by-step explanation:

When the thing is negative it will move to the right it will be positive. When it's negative it will move to the left than it will be negative.

Answer: Tazi-D

Bugsy-B: 0.16 per ounce

Tazi-D: 0.14 per ounce

Step-by-step explanation:

divide the $ by the ounce for both.

Answer:

Answer:

Slopem=−49

As a decimal:

m = -0.444444

Step-by-step explanation:

Slope m with two points

Graph of the line for y = mx + b

Point Slope Form y - y1 = m(x - x1)

Slope Intercept Form y = mx + b

Standard Form Ax + By = C

y-intercept, when x = 0

x-intercept, when y = 0

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. For [tex]0 ≤ x ≤ 2, F(1) = (1^3/12) = 0.0833.So, P(X ≤ 1) = 0.0833.[/tex] Hence, the correct option is (a) P(X ≤ 1).

Given that X denotes the amount of time a book on two-hour reserve is actually checked out, and the cdf is the following:

[tex]cdf: 0 , x<0f(x) = ((x^2)/4) , 0 <= x <= 21 , 2<= x[/tex]

To use the cdf to obtain the following.P(X ≤ 1)

So, the probability distribution function is the derivative of the cumulative distribution function.

∴ f(x) = d/dx(F(x))

Also, from the cdf, we know that:

[tex]f(x) = 0 when x < 0.f(x) = ((x^2)/4) when 0 ≤ x ≤ 2.[/tex]

f(x) = 1 when x ≥ 2.

Using the above conditions, we have to calculate the following:

(a) P(X ≤ 1)

Here, P(X ≤ 1) = F(1).

When[tex]0 ≤ x ≤ 2, F(x) = ∫[0,x] f(t)dt=∫[0,x] (t^2/4)dt=[t^3/12]0x=(x^3/12)[/tex]

Thus, for[tex]0 ≤ x ≤ 2, F(x) = (x^3/12).[/tex]

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Mila should receive 44.44% of the profit.

An equation is a statement that asserts the equality of two expressions, typically with one or more variables. Equations are used to represent relationships between different quantities, such as the relationship between the length and width of a rectangle or the relationship between the time and distance traveled by an object.

Profit is the financial gain that is earned by a business or an individual after all expenses and costs have been subtracted from revenue or income. It is the difference between the amount earned from sales or services and the costs incurred to produce or provide those goods or services.

In the given question,

Let's begin by determining the amount of money each person invested in the project.

Let Sydney's investment be x.

Roy's investment is twice Sydney's, so Roy invested 2x.

Mila's investment is twice Roy's, so Mila invested 2(2x) = 4x.

Taniya's investment is half of Mila's, so Taniya invested 0.5(4x) = 2x.

The total amount invested is x + 2x + 4x + 2x = 9x.

Now, we need to find the percentage of profit Mila should receive. Since the profit is shared in proportion to the amount invested, Mila should receive a fraction of the profit equal to her investment divided by the total investment.

Mila's share = (Mila's investment) / (Total investment) x (Total profit)

Mila's share = (4x / 9x) x 27000

Mila's share = 12000

So Mila should receive $12,000 of the profit. To find the percentage of profit Mila should receive, we can divide her share by the total profit and multiply by 100:

Percentage of profit Mila should receive = (Mila's share / Total profit) x 100%

Percentage of profit Mila should receive = (12,000 / 27,000) x 100%

Percentage of profit Mila should receive = 44.44%

Therefore, Mila should receive 44.44% of the profit.

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Answer:

y = 4x + 15

Step-by-step explanation:

Using 'y=mx+c' form,

Since m = 4,

y = 4x + c

Substituting (-5, -5) into the above equation:

-5 = -20 + c

c = 15

Hence,

y = 4x + 15

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The work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.

A particle of mass 0.58 kg is subject to a force that is always pointed towards east or west but whose magnitude changes sinusoidally with time. With the positive x-axis pointed towards the east, the x-component of the force is given as follows: fx(t) = (2.6 N) sin(2.2t)where t is in seconds.

The work done by the force as the particle moves from x = 0 m to x = 2.2 m: For a sinusoidal force that changes with time, the work done is given by W = ∫F dx where F is the force, and dx is the displacement. For this problem, the force is given by fx(t) = (2.6 N) sin(2.2t)dx is the displacement, which is given by dx = x2 – x1 where x2 = 2.2 m, and x1 = 0 m.

Substituting for F and dx, we get W = ∫02.2(2.6 sin(2.2t)) dx= 2.6 ∫02.2 sin(2.2t) dx= 2.6 [(-1/2.2) cos(2.2t)]02.2= 1.18 (cos(4.84) – 1)≈ -0.53 J. So, the work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.

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The slope of the linear function that represents the cost of plan B is $0.17.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Since Plan B has the same monthly base charge as plan A, we can logically deduce that the data points (0, 14.45) and (45, 22.10) lie on the linear function.

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (22.10 - 14.45)/(45 - 0)

Slope (m) = $0.17

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Complete Question:

Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table. Monthly Charge for Plan A Minutes used, x Monthly charge ($), y 0 14.45 3 14.84 6 15.23 9 15.62 12 16.01 Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?

Answer:

Step-by-step explanation:

2/3*6

6*6

12

The time needed to paint 3 rooms together is given as follows:

308.4 minutes.

The time needed is obtained applying the proportions in the context of the problem.

First we use the together rate, which is the sum of each separate rate, for the time needed to paint a single wall, hence:

1/x = 1/45 + 1/60

1/x = 7/180

7x = 180

x = 180/7

x = 25.7 minutes per wall.

The number of walls in 3 rooms is given as follows:

3 x 4 = 12 walls.

Thus the time needed to paint the 3 rooms is given as follows:

25.7 x 12 = 308.4 minutes.

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the height of the firecracker after 4 seconds from launch is 68 feet.

To find the height of the firecracker after 4 seconds from launch, we need to plug in t = 4 into the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This gives us h(4) =[tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. Therefore, the height of the firecracker after 4 seconds from launch is 68 feet.

To find the height of the firecracker after 4 seconds from launch, we need to use the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This equation models the path of the firecracker, with h(t) being the height in feet of the firecracker at any given time, t. When we plug in t = 4, we get h(4) = [tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. So, the height of the firecracker 4 seconds after launch is 68 feet. This equation allows us to calculate the height of the firecracker at any given time, making it a useful tool for predicting the trajectory of the firecracker.

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Answer:

43

Step-by-step explanation:

We can simplify the expression:

[tex]4^2 + 3^3[/tex]

by rewriting exponents as multiplication of their base.

[tex]4^2 + 3^3[/tex]

[tex]= (4\cdot 4) + (3\cdot 3 \cdot 3)[/tex]

Then, we can simplify using the order of operations (PEMDAS).

[tex](4\cdot 4) + (3\cdot 3 \cdot 3)[/tex]

[tex]= 16 + (9 \cdot 3)[/tex]

[tex]= 16 + 27[/tex]

[tex]\boxed{= 43}[/tex]

The prοperty the equatiοn illustrates-4x-1/4=1 is multiplicatiοn inverse.

The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns.

οr,

A mathematical expressiοn cοmpοsed οf twο expressiοns jοined tοgether by the equal sign.

Given equatiοn is (-4)×(-1/4) = 1.

The name οf prοperties are

Distributive Prοperty: a(b+c) = ab + bc

Cοmmutative Prοperty: ab =ba

Assοciative Prοperty :a(bc) = (ab)c

Identity Prοperty a×b=1

Inverse Prοperty: a×b=1

These characteristics hοld true in mathematical and algebraic expressiοns just as they dο in prοpοsitiοnal language.

In the Inverse Prοperty, the prοduct οf a number and its inverse is equal tο 1.

The given equatiοn represents Inverse Prοperty.

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Randy's claim is not correct Therefore, he cannot purchase 3.5 pounds of chicken salad for $23.50

To determine if Randy's claim is correct, we can use the given linear graph and points to find the equation of the line that represents the relationship between the amount of chicken salad purchased and the cost.

We can use the two points (1, 7.5) and (3, 22.5) to find the slope of the line:

slope = (change in y) / (change in x)

slope = (22.5 - 7.5) / (3 - 1)

slope = 15 / 2

slope = 7.5

Now we can use the slope-intercept form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept, to find the equation of the line:

y = 7.5x + b

To find b, we can use one of the points on the line, such as (1, 7.5):

7.5 = 7.5(1) + b

b = 0

So the equation of the line is:

y = 7.5x

Now we can use this equation to check if Randy's claim is correct. If he can purchase 3.5 pounds of chicken salad for $23.50, we can plug in x = 3.5 and see if y = 23.5:

y = 7.5x

y = 7.5(3.5)

y = 26.25

Since y = 26.25 is not equal to $23.50

Therefore, Randy's claim is not correct

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The given question is incomplete, the complete question is:

Randy claims that he can purchase 3. 5 pounds of chicken salad for $23. 50. Is he correct? Explain.

Answer:

3x³- 8x² + 2x +3

Step-by-step explanation:

All you need to do is multiply everything in the second bracket with the first bracket like you would normally do with double brackets.

3x³-3x²-5x²+5x-3x+3=

3x³-8x²+2x+3

The total mass of the apples Alex picked is 25 2/5 kilograms.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants

To find the total mass of the apples Alex picked, we need to add the mass of the red apples and the mass of the green apples.

First, let's convert the mixed numbers to improper fractions to make the addition easier:

15 ⅘ = 15 + 8/10 = 15 + 4/5 = 75/5 + 4/5 = 79/5

9 ⅗ = 9 + 6/10 = 9 + 3/5 = 45/5 + 3/5 = 48/5

Now we can add the fractions:

79/5 + 48/5 = (79 + 48)/5 = 127/5

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case:

127/5 = 25 2/5

Therefore, the total mass of the apples Alex picked is 25 2/5 kilograms.

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