Point P1 located along the proposed centerline of a roadway was observes from an instrument set up at point A. The observed bearing and distance are N 50°34' W; 78.67m Coordinates of A: Northings = 257.78m Eastings = 345.25m Centerline P1 14. Determine the coordinate of P1 (Northing). a) 319.34 b) 298.67 15. Determine the coordinate of P1 (Easting). a) 303.45 b) 245.67 •A Instrument set up c) 312.34 c) 284.49 d) 307,45 d) 310.67

Answer: We can use a proportion to solve the problem:

17 gallons / 355 miles = x gallons / 284 miles

Cross-multiplying, we get:

17 * 284 = 355 * x

4844 = 355x

x = 13.66 (rounded to two decimal places)

Therefore, Mai would need approximately 13.66 gallons of gas to drive 284 miles at the same rate.

Step-by-step explanation:

The b is in the plane spanned by a1 and a2 for h = ±1. For any other value of h, b is not in the plane spanned by a1 and a2.

To determine for what values of h is b in the plane spanned by a1 and a2.

We need to check if b can be written as a linear combination of a1 and a2.

If b can be written as a linear combination of a1 and a2 then it is in the plane spanned by a1 and a2.

Otherwise,

It is not in the plane.

We can write the equation for a plane using a point on the plane and the normal vector to the plane.

Since a1 and a2 are in the plane, we can find the normal vector by taking the cross product of a1 and a2:

n = a1 x a2

n = <0 -h 1> x <1 0 -h>

n = <-h -1 0>

So, the equation for the plane spanned by a1 and a2 is:

-h(x) - y = 0

We can substitute b = (h, -1, 3h) into this equation and see if it satisfies the equation.

-h(h) - (-1) = 0

-\(h^2\) + 1 = 0

\(h^2\) = 1

h = ±1

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Answer:

6 hours.

Step-by-step explanation:

To find out her speed, divide 174 by 3.

She is driving 58mph.

Now, divide 348 by 58 to see how many hours it will take.

348/58=6.

6 hours.

we can use the Pythagorean theorem to find the distance from the port:

Distance from port = √(Horizontal displacement)² + (Vertical displacement)²

Calculating these values will give us the distance of the ship from the port.

To calculate the distance of the ship from the port, we can use the concept of vector addition.

By breaking down the ship's journey into two components, we can find the resultant displacement, which represents the distance from the port.

First, let's calculate the horizontal and vertical components of the ship's displacement for each leg of the journey.

Leg 1:Distance: 21 km

Bearing: 32°

Horizontal component: 21 km * cos(32°)Vertical component: 21 km * sin(32°)

Leg 2:

Distance: 45 kmBearing: 287°

Horizontal component: 45 km * cos(287°)

Vertical component: 45 km * sin(287°)

Next, we can sum up the horizontal and vertical components to find the resultant displacement.

Horizontal displacement: (21 km * cos(32°)) + (45 km * cos(287°))Vertical displacement: (21 km * sin(32°)) + (45 km * sin(287°))

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Answer:

$6.00

Step-by-step explanation:

Volume of the figure = volume of triangular prism + volume of trapezoidal prism = 497 m³.

Volume of any prism = Base area × height of the prism

Thus:

Volume of the figure = volume of triangular prism + volume of trapezoidal prism

Volume of triangular prism = 1/2(b×h)×L = 1/2(8 × 4) × 14

Volume of triangular prism = 224 m³

Volume of trapezoidal prism = 1/2(b1+b2)×h×L = 1/2(8 + 5) × 3 × 14

Volume of trapezoidal prism = 273 m³

Volume of the figure = 224 + 273 = 497 m³.

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Answer:

497

Step-by-step explanation:

Answer:

C; 62 to 68 inches

Step-by-step explanation:

Here, we want to get the population range that is having a probability of 68%

From the empirical rule, a measure of 1 standard deviation above the mean, with 1 standard deviation below the mean will give a total percentage of 68%

From the question;

1 standard deviation above the mean is 65 + 3 = 68

1 standard deviation below the mean is 65-3 = 62

so the range of the height of the population is 62 to 68 inches

The function g is defined by the following rule. g(x) = 2x +1​ can be represented in the method given below-

How does this occur?

The function f with g is written as (fg)(x)=f(g(x)), and is understood as f of g of x. The function g will be used in place of any x in the function f, according to this statement (x)

f(x), where x is the input, is a common way to refer to a function. A function can be conceptualized as y = f in general (x).

This is how by taking various x value we can find the value of g(x) = 2x +1​

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Answer:

2.1

Step-by-step explanation:

The value of x is 311.14, 1527.15 and 1.61%.

Given that x = PV(1+r)^t. Assume PV=190.00, r=9.00%, and t=5.00.

Substitute the given values in the above expression, we get

x = 190(1 + 0.09) ^ 5

Simplify the above expression, we get: x = 190(1.09) ^ 5 = x = 190 × 1.63861881 = x = 311.1371749

Thus, the value of x is 311.14 (rounded to 2 decimal places).

Given that x = FV/(1+r)^t. Assume FV=3,054.00, r=9.00%, and t=8.00.

Substitute the given values in the above expression, we get: x = 3054/(1 + 0.09) ^ 8

Simplify the above expression, we get;: x = 3054/1.999675406`x = 1527.15

Thus, the value of x is 1527.15 (rounded to 2 decimal places).

Given that FV = P(1 + x) ^ t. Assume FV=1,017.00, PV=835.00, and t=6.00.

Substitute the given values in the above expression, we get: 1,017 = 835(1 + x) ^ 6

Divide both sides of the equation by 835.00, we get: 1,017/835 = (1 + x) ^ 6

Take the 6th root of both sides of the equation, we get: (1.215568862)^(1/6) = 1 + x

Simplify the above expression, we get: 1.0160907 = 1 + x = x = 1.0160907 - 1 = x = 0.0160907

Converting decimal into percentage, we get: 0.0160907 × 100 = 1.61%

Thus, the value of x is 1.61% (rounded to 2 decimal places).

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The solution is Option A.

The value of the 13th number from the equation A = ( -2/3 ) ( n - 1 ) is A = -8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( -2/3 ) ( n - 1 )   be equation (1)

On simplifying the equation , we get

The thirteenth number in the list is n = 13

So , when n = 13

A = ( -2/3 ) ( n - 1 )

A = ( -2/3 ) ( 13 - 1 )

On further simplification , we get

A = ( -2/3 ) ( 12 )

A = ( -2 ) x 4

So , the value of A = -8

Hence , the thirteenth number in the list is A = -8

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The probability of selecting two Harry Potter DVDs at random, one after the other, is 1/110.

The probability of selecting a Harry Potter DVD at random is dependent on the total number of DVDs and the number of Harry Potter DVDs in the collection. Let's assume there are a total of 100 DVDs and 10 of them are Harry Potter films.

When selecting the first DVD, the probability of picking a Harry Potter film is 10/100 = 1/10.

After selecting the first DVD, there are 99 DVDs left, with 9 Harry Potter films remaining.

When selecting the second DVD, the probability of picking another Harry Potter film, while keeping the first one in hand, is 9/99 = 1/11.

To find the probability of both DVDs being Harry Potter films, we multiply the probabilities: (1/10) * (1/11) = 1/110.

Therefore, the probability that both DVDs will be Harry Potter films is 1/110.

In conclusion, the probability of selecting two Harry Potter DVDs at random, one after the other, is 1/110.

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Answer:

\( \frac{1}{2} \)

Hope this helps!

Answer:

Step-by-step explanation:

Slope= (y1-y2)\(x1-x2)=(3-4)\(6-8)=0.5

The solution for the inequalities is x > - 1 OR x < -1.

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given  : 5x - 29 > -34 OR 2x + 31 < 29.

to solve the equations,

5x - 29 > -34 OR 2x + 31 < 29.

For 5x - 29 > -34

On adding both sides by 29.

5x > - 34 + 29 .

5x > -5

On dividing both sides by 5.

x > - 1 .

For 2x + 31 < 29.

On subtracting both sides by 31

2x < 29 -31

2x < - 2

On dividing both sides by 2.

x < -1

So , x > - 1 OR x < -1 .

Therefore, option A is correct.

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The total revenue from adult ticket sales (10a) must be greater than or equal to $1200.

Let's represent the number of student tickets sold as 's' and the number of adult tickets sold as 'a'.

The revenue from student ticket sales can be calculated as 7.50s, and the revenue from adult ticket sales can be calculated as 10a.

To satisfy the constraint that the drama club must make no less than $1200, we can write the following inequality:

7.50s + 10a ≥ 1200

This inequality states that the total revenue from student ticket sales (7.50s) plus the total revenue from adult ticket sales (10a) must be greater than or equal to $1200.

This inequality ensures that the ticket sales generate enough revenue to cover the show's costs. The drama club needs to sell enough tickets, both student and adult, to meet or exceed the minimum revenue requirement of $1200.

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Divide the numerator by the denominator to create a mixed number from an incorrect fraction. The mixed number is created after the division in such a way that the achieved quotient becomes the whole number, the leftover becomes the new numerator, and the denominator stays the same.

A mixed number is one that combines both a proper fraction and a full number. Mixed fractions are another name for mixed numbers.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. "Top-heavy" fractions are sometimes used to describe improper fractions.

Follow these procedures to convert a mixed number to an incorrect fraction:

1. Divide the entire number by the numerator.

2. Increase the numerator by that sum.

3. Add that total to the denominator from the previous step.

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_____________________________________________________

\(4+2\times (-4)+8\times (-1)\)

_____________________________________________________

\(4-2\times 4+8\times (-1)\)

\(4-2\times 4-8\)

______________________________________________________

\(4-8-8\)

______________________________________________________

\(-4-8\)

\(-12\)

I hope this helps you

:)

The dimensions of the poster with the smallest area are 48 cm by 16 cm.

Let the width of the printed material be x cm and the height be y cm. Then the total width of the poster including the margins is (x + 16) cm, and the total height is (y + 24) cm.

The total area of the poster is the area of the printed material plus the area of the margins:

(x + 16)(y + 24) = 1536

Expanding the left side, we get:

xy + 16y + 24x + 384 = 1536

Rearranging terms, we get:

xy = 1152 - 16y - 24x

To find the dimensions of the poster with the smallest area, we want to minimize the product xy subject to the constraint given by the equation above.

One way to do this is to use the method of Lagrange multipliers. Let L = xy + λ[(x + 16)(y + 24) - 1536] be the Lagrangian, where λ is a Lagrange multiplier. Setting the partial derivatives of L with respect to x, y, and λ equal to zero, we get:

y + 16λ = 0

x + 24λ = 0

(x + 16)(y + 24) = 1536

From the first two equations, we get:

x = -24λ

y = -16λ

Substituting these into the third equation, we get:

(-24λ + 16)(-16λ + 24) = 1536

Simplifying, we get:

-6λ + 4 = 0

Therefore, λ = 2/3. Substituting this into the expressions for x and y, we get:

x = -16

y = -32

These values give the dimensions of the printed material. To find the dimensions of the poster, we add the margins:

width = x + 16 + 16 = 48 cm

height = y + 24 + 24 = 16 cm

Therefore, the dimensions of the poster with the smallest area are 48 cm by 16 cm.

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Answer:

it's b

Step-by-step explanation:

the reason it's b is because conduction happens when something hot comes in contact with something cold which heats the cold thing up and cooling the hot thing eventually they will both be room temperature

Option D is correct, no because  (2√3, 2) is less than 4 units away from the origin

To determine if a point lies on a circle centered at the origin, we can use the distance formula.

The distance between the origin (0, 0) and the point (2√3, 2) is:

√[(2√3 - 0)² + (2 - 0)²] = √[12 + 4] = √16 = 4

Since the distance between the origin and the point (2√3, 2) is exactly 4 units, the point lies on the circle centered at the origin with a radius of 4 units.

Hence,  no because  (2√3, 2) is less than 4 units away from the origin, option D is correct

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Answer:

50, 90, 65, 25

Step-by-step explanation:

I dont know how to get to it that is why I searched it up :/

The mean of the function f(x) = (1/10)e^(-x/10) for x ≥ 0 is 0. Thus, the correct answer is A) 0.10.

To find the mean of the function f(x) = (1/10)e^(-x/10) for x ≥ 0, we need to calculate the definite integral of xf(x) over the range of x ≥ 0 and divide it by the integral of f(x) over the same range.

The integral of xf(x) is given by ∫(x/10)e^(-x/10) dx, and the integral of f(x) is ∫(1/10)e^(-x/10) dx.

To evaluate these integrals, we can use integration by parts. Let's use the formula ∫u dv = uv - ∫v du, where u = x/10 and dv = e^(-x/10) dx.

Differentiating u with respect to x, we have du = (1/10) dx.

Integrating dv, we have v = -e^(-x/10).

Applying the integration by parts formula, we get:

∫(x/10)e^(-x/10) dx = -(x/10)e^(-x/10) + ∫(1/10)e^(-x/10) dx.

Simplifying further, we have:

∫(x/10)e^(-x/10) dx = -(x/10)e^(-x/10) - e^(-x/10) + C,

where C is the constant of integration.

Now, to find the mean, we need to evaluate the definite integral of xf(x) and divide it by the definite integral of f(x). The range is x ≥ 0.

Let's evaluate the definite integrals:

∫[0, ∞] (x/10)e^(-x/10) dx = lim(b→∞) [-(x/10)e^(-x/10) - e^(-x/10)] [0, b]

= -[b/10)e^(-b/10) - e^(-b/10)] + (0/10)e^(-0/10) - e^(-0/10)

= 0.

∫[0, ∞] (1/10)e^(-x/10) dx = lim(b→∞) [-e^(-x/10)] [0, b]

= -e^(-b/10) + e^(-0/10)

= 1.

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Answer:

5/12

Step-by-step explanation:

A light rail system can be described as a smaller rail-based transportation system that is powered by electricity, providing efficient and sustainable urban transit options for passengers.

A light rail system refers to a smaller rail-based transportation system that operates within urban or suburban areas. It typically consists of light rail vehicles (LRVs) that run on tracks, similar to a traditional railway system. However, light rail systems are designed to serve shorter distances and provide more frequent stops compared to heavy rail systems.

One distinguishing characteristic of a light rail system is that it is powered by electricity. The LRVs usually run on overhead electrical wires or through an electrified third rail system. This electric power source allows for a more sustainable and environmentally-friendly mode of transportation.

Light rail systems are often integrated into the existing urban infrastructure and provide convenient and efficient transportation options for commuters. They offer a balance between the capacity of traditional heavy rail systems and the flexibility of buses. Light rail vehicles can accommodate a significant number of passengers and operate on fixed routes, offering a reliable and comfortable mode of public transportation.

Overall, a light rail system can be described as a smaller rail-based transportation system that is powered by electricity, providing efficient and sustainable urban transit options for passengers.

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Answer:

\(3k = 36\)

\(k = 12\)

Answer:

12

Step-by-step explanation:

If y = 36 and X = 3 then K would = (y divided by x) so it would be 36 divide 3

that being 12 so, therefore, the answer is 12.

K= 12

Answer:

The distance is 816 km

Step-by-step explanation:

We can define average velocity as the quotient between the total distance traveled and the time it takes to travel that distance.

Here we will get the average velocity of 1,000 km/h.

----------------------------

To get the average velocity of the rocket, we need to know the distance that it travels and the time it needs to travel that distance.

We know that:

Then the average velocity is given by:

AV = (2,200 km)/(2.2 h) = 1,000 km/h.

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Answer:

c=0

Step-by-step explanation:

0 + 12=12

c+12=12

Cancel out the 12 by subtracting it on both sides

c+12=12

 -12 -12

c=0

---

hope it helps

sorry if it doesn't

Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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Answer:

-5

-3 + -5 = -8