which equation is equivalent to -19+6x-5=3x

Answer:

The person's total salary over the first 6 years is $231,750.

To determine the person's total salary over the first 6 years, we need to calculate the sum of the salary for each year.

Given information:

- Initial salary: $34,000

- Annual raise: $1,850

- Number of years: 6

To calculate the total salary, we can use the arithmetic progression formula:

[ S = frac{n}{2} left(2a + (n - 1)dright) ]

Where:

- ( S ) is the sum of the salaries

- ( n ) is the number of terms (years)

- ( a ) is the first term (initial salary)

- ( d ) is the common difference (annual raise)

Substituting the given values, we have:

[ S = frac{6}{2} left(2(34000) + (6 - 1)(1850)right) ]

Simplifying the expression:

[ S = 3 left( 68000 + 5 times 1850 right) ]

[ S = 3 left( 68000 + 9250 right) ]

[ S = 3 times 77250 ]

[ S = 231750 ]

Therefore, the person's total salary over the first 6 years is $231,750.

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Answer:

Standard form:

x^5+9x³-4x²+16

Leading coefficient:

1

(coefficient of x^5=1)

Answer:

(x+4)(x+12)

Step-by-step explanation:

Answer:

(x +4) (x+12)

Step-by-step explanation:

product 48

Sum 16 ( 12 and 4)

(x2 +12x) +(4x +48)

=(x+4) (x+12)

The value of the given triple integral is 16π/3 (5/4)^(5/2).

We are given the region E bounded by the paraboloid x = 5y^2 - 5z^2 and the plane x = 5. We need to evaluate the triple integral 8x dV over this region.

Converting to cylindrical coordinates, we have x = 5y^2 - 5z^2 = 5r^2 cos^2 θ - 5z^2. The region E can be expressed as 0 ≤ z ≤ √(y^2/5 - y^4/25) and 0 ≤ y ≤ √(x-5)/5.

Substituting for x in terms of y and z, we get 0 ≤ z ≤ √(y^2/5 - y^4/25), 0 ≤ y ≤ √(5y^2 - 25)/5, and 0 ≤ θ ≤ 2π. Also, we have r ≥ 0.

Therefore, the integral becomes:

∫∫∫E 8x dV = ∫₀^√(5/4) ∫₀^√(5y^2 - 25)/5 ∫₀^{2π} 8(5r^2 cos^2 θ) r dz dy dθ

Simplifying and evaluating the integrals, we get:

∫∫∫E 8x dV = 16π/3 (5/4)^(5/2).

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The value of the triple integral is 320/7.

We can set up the triple integral as follows:

∫∫∫ 8x dV

Where the limits of integration are determined by the bounds of the region E, which is bounded by the paraboloid x = 5y^2 + 5z^2 and the plane x = 5.

Since x is bounded by the plane x = 5, we can set up the limits of integration for x as follows:

5y^2 + 5z^2 ≤ x ≤ 5

The region E is symmetric with respect to the yz-plane, so we can set up the limits of integration for y and z as follows:

-√(x/5 - z^2/5) ≤ y ≤ √(x/5 - z^2/5)

-√(x/5) ≤ z ≤ √(x/5)

Putting it all together, we get:

∫ from 0 to 5 ∫ from -√(x/5) to √(x/5) ∫ from -√(x/5 - z^2/5) to √(x/5 - z^2/5) 8x dy dz dx

We can simplify the limits of integration by switching the order of integration. Since the integrand does not depend on y or z, we can integrate y and z first:

∫ from 0 to 5 ∫ from -√(x/5) to √(x/5) ∫ from -√(x/5 - z^2/5) to √(x/5 - z^2/5) 8x dy dz dx

= ∫ from 0 to 5 ∫ from -√(x/5) to √(x/5) 8x ∫ from -√(x/5 - z^2/5) to √(x/5 - z^2/5) dy dz dx

The limits of integration for y and z depend on x and z, so we can integrate z first:

∫ from 0 to 5 ∫ from -√(x/5) to √(x/5) 8x ∫ from -√(x/5) to √(x/5) √(x/5 - z^2/5) + √(x/5 - z^2/5) dz dx

= ∫ from 0 to 5 ∫ from -√(x/5) to √(x/5) 16x√(x/5 - z^2/5) dz dx

Finally, we can integrate y:

∫ from 0 to 5 32/3 x^(5/2) dx

= 320/7

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Answer:

12.56%

Step-by-step explanation:

Total Area = bh = 10*10 = 100 square units.

Area of the red circle = \(\pi r^2=3.14\cdot 2^2=12.56\:\) square units.

\(\frac{12.56}{100}\cdot 100\%=12.56\%\)

The 8th term of the sequence is 4374. A geometric sequence is a sequence in which each term after the first is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio.

To find the 8th term of the geometric sequence, we can use the formula for the nth term of a geometric sequence:

an = a1 x r^(n-1)

where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

Given that the first term is 2 and the common ratio is 3, we have:

a1 = 2
r = 3

Plugging in n = 8, we get:

a8 = 2 x 3^(8-1)
a8 = 2 x 3^7
a8 = 2 x 2187
a8 = 4374


In summary, a geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a constant called the common ratio. In this case, the first term is 2 and the common ratio is 3. We can use the formula an = a1 x r^(n-1) to find the nth term of the sequence. By plugging in n = 8, we get the 8th term of the sequence as 4374.

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Answer:

idk

Step-by-step explanation:

Answer (#2):

125 (degrees)

Step-by-step explanation:

<ATH= 180 - x

the sum of the degrees in a triangle is 180, so <ATH=180-43-82=55 (degrees)

x=180-55=43+82=125 (degrees)

Answer (#3):

x=11, <C=12 (degrees)

Step-by-step explanation:

(3x+28)+(5x+52)+(2x-10)=10x+70=180

x=110/10=11

Answer:

sidekick egocentric Jayco

Answer:

Step-by-step explanation:

AX=9x+21, CX=14x+1, because AX=CX we can say

14x+1=9x+21, subtract 9x from both sides

5x+1=21, subtract 1 from both sides

5x=20. divide both sides by 5

x=4

Since CX is half of AC we can say

AC=2(14x+1)

AC=28x+2, and since x=4

AC=28(4)+2

AC=114

It's difficult to say whether the conditions for constructing a t-confidence interval are met based on the information provided. To construct a t-confidence interval, three conditions must be met:

The sampling method must be random. It's not specified in the problem whether the method of selecting the vehicles was random or not, so it's impossible to say whether this condition is met.

The sample size must be large enough. A sample size of 100 vehicles is considered to be large enough for the normal/large sample condition to be met.

The population must be approximately normally distributed or the sample size must be large. Since the problem does not specify anything about the distribution of the population, it is not clear if this condition is met.

Given that the information provided does not give enough details to state whether the conditions for constructing a t-confidence interval are met or not.

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Answer:

200020ft

Step-by-step explanation:

Based on the provided information of speed, A) Beth gets to San Francisco first. B) The first to arrive has to wait for 20 minutes for the second to arrive.

A) To find out who gets to San Francisco first, we need to calculate the time it takes for each of them to travel the distance of 400 miles.

For Brian, we use the formula time = distance / speed:

time = 400 miles / 50 mph = 8 hours

So Brian will arrive in San Francisco at 4:00 p.m. (8:00 a.m. + 8 hours).

For Beth, we use the same formula:

time = 400 miles / 60 mph = 6.67 hours

So Beth will arrive in San Francisco at 3:40 p.m. (9:00 a.m. + 6.67 hours).

Therefore, Beth gets to San Francisco first.

B) To find out how long the first to arrive has to wait for the second, we subtract the arrival time of the first from the arrival time of the second:

wait time = 4:00 p.m. - 3:40 p.m. = 0.33 hours = 20 minutes

So the first to arrive has to wait for 20 minutes for the second to arrive.

Note: The question is incomplete. The complete question probably is: Brian leaves Los Angeles at 8:00 a.m. to drive to San Francisco, 400 miles away. He travels at a steady speed of 50 mph. Beth leaves Los Angeles at 9:00 a.m. and drives at a steady speed of 60 mph. A) Who gets to San Francisco first? B) How long does the first to arrive have to wait for the second?

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Answer:

The linear equation represents a proportional relationship and its constant of proportionality is \(k = \frac{2}{5}\).

Step-by-step explanation:

A proportional relationship exists when the following relationship is observed:

\(u = k\cdot v\)

Where:

\(u\) - Dependent variable.

\(v\) - Independent variable.

\(k\) - Proportionality constant.

If \(y =\frac{2}{5}\cdot x - 4\) and \(v = x\) and \(u = y+4\), the following expresion is found:

\(y = \frac{2}{5}\cdot x -4\)

\(y + 4 = \frac{2}{5}\cdot x\)

\(u = \frac{2}{5}\cdot v\)

The linear equation represents a proportional relationship and its constant of proportionality is \(k = \frac{2}{5}\).

In this case, y1 = 15 and x1 = -4. Substituting these values into the point-slope form, we get: y - 15 = 2(x - (-4)) , Simplifying, we get: y = 2x + 21

y = 2x + 21

To find the equation of the line that passes through the point (-4, 15) and is perpendicular to y = -2x - 9, we can use the slope formula.

The slope of the line y = -2x - 9 is m = -2. The slope of a perpendicular line is the negative reciprocal of m, or m = 2.

We can use the point-slope form of a line to find the equation of the line. The point-slope form of a line is y - y1 = m(x - x1).

In this case, y1 = 15 and x1 = -4. Substituting these values into the point-slope form, we get:

y - 15 = 2(x - (-4))

Simplifying, we get:

y = 2x + 21

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The one-third of the job will take md/3n days. The result is obtained by using the concept of inverse proportion.

Inverse proportion is a proportionality relationship when one value increases and the other decreases.

Assuming that the workers are working at the same rate, the more workers will complete the job more quickly. It means the more workers that do the job, the less time needed. We use inverse proportion to solve this problem.

We have workers and time to complete a job. Let's say e is the time for n workers to complete the job.

By the inverse proportion concept, we get

m/n = e/d

e = md/n days

To complete one-third of the job, they need

⅓e = ⅓ (md/n)

⅓e = md/3n

Hence, it will take md/3n days to complete the one-third of the job.

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The first one is 2

the second one is 6

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

5 words per minute

Step-by-step explanation:

To find her rate in words per minute simply divide the number of words she can type in 8 minutes (40) by 8.

40 / 8 = 5

Her rate is 5 words per minute

Graph of the given function is as follows:Graph of y = sin(3x + θ) which passes through the points (−3π/2, −1), (−π/2, 0), (π/2, 0), and (3π/2, 1) with period T = 2π / 3.

Given function is y]

= sin(3x + θ)

Step 1: Period of the given trigonometric function is given by T

= 2π / ω Here, ω

= 3∴ T

= 2π / 3

Step 2: The interval of the given trigonometric function is (-∞, ∞)Step 3: Dividing the interval into four equal parts, we setInterval

= (-3π/2, -π/2) U (-π/2, π/2) U (π/2, 3π/2) U (3π/2, 5π/2)

Now, we will complete the table using the given interval as follows:

xy(-3π/2)

= sin[3(-3π/2) + θ]

= sin[-9π/2 + θ](-π/2)

= sin[3(-π/2) + θ]

= sin[-3π/2 + θ](π/2)

= sin[3(π/2) + θ]

= sin[3π/2 + θ](3π/2)

= sin[3(3π/2) + θ]

= sin[9π/2 + θ].

Graph of the given function is as follows:Graph of y

= sin(3x + θ) which passes through the points (−3π/2, −1), (−π/2, 0), (π/2, 0), and (3π/2, 1) with period T

= 2π / 3.

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Answer:

the answer is c. ........

Answer:

C.

Step-by-step explanation:

enlarging the capacity of the dock to handle two boats at a time can help in achieving the goal of minimizing customer waiting time and approaching an average time in the system close to 10 minutes.

Enlarging the capacity of the dock to handle two boats at a time can be a good way of achieving the goal of having the customer's average time in the system as close to 10 minutes as possible, but not exceeding 10 minutes. Let's analyze the statements provided:

Both channels will be empty approximately ______% of the time.
Enlarging the capacity to handle two boats at a time means that both channels can be utilized simultaneously.

If we assume that boat arrivals follow a random and evenly distributed pattern, the probability of both channels being empty at the same time is the product of the probabilities of each channel being empty.

If the arrival rate of boats is within the capacity of the dock, it is likely that both channels will be empty a significant portion of the time. The specific percentage will depend on the arrival rate and other factors.

When customers do show up, they ______ likely to have to wait for 10 minutes.
By enlarging the capacity and having two boats being served simultaneously, the waiting time for customers is expected to be reduced compared to when only one boat can be served at a time.

This means that customers are less likely to have to wait for the full 10 minutes.

On the whole, the expansion _______ be the best way of achieving their goal.
Based on the information provided, enlarging the capacity of the dock to handle two boats at a time seems like a reasonable approach to achieve the goal of having the customer's average time in the system as close to 10 minutes as possible.

However, without specific data on boat arrival rates, service times, and other factors, it is not possible to determine definitively if it is the best way.

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An equation to model the price based on the size of the pack. Let t be the number of tomatoes. Let p be the price per pack is p=0.25*t.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units. What can units and values be?

Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this case, the apples are the units, and the cost of the apples is the value. While solving a problem using the unitary method, it is important to recognize the units and values.

Cherry tomatoes are old at the store. A 12-pack cost $3, a 16-pack cost $4, and a 24-pack cost $6.

let

Where t represents the number of tomatoes, and p represents the price per pack. The terms in the equation represent the cost per tomato for each pack size.

we know that.

pack 12 costs ⇒ $3

1 pack ⇒ x

x=\(\frac{3}{12}\)

x=$0.25 (cost of one tomatoes)

An equation for the function

p=0.25*t

Therefore, the answer is p=0.25*t.

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Answer:

It's B

Step-by-step explanation:

Given that we have the graph of f(x), we want to see which one is the graph of its inverse. i just had that question and i got a 100 on it

I hope that helped.............

-

Differentiation is a mathematical operation that calculates the rate at which a function changes with respect to its independent variable. The derivative of the given function using chain rule is:

\(\dfrac{dy}{dx}= \dfrac{6x^5 + 12x^3}{x^6 + 3x^4 + 1}\)

To differentiate the given function, \(y = \ln\left( x^6 + 3x^4 + 1 \right)\), with respect to x, we must use the chain method.

Let \(u = {x^6 + 3x^4 + 1}_{\text}\), then y = ln u Differentiating both sides of y = ln u with respect to x:

\(\dfrac{dy}{dx} = \dfrac{du}{dx} \cdot \dfrac{1}{u}\) We need to find du/dx, where \(u = {x^6 + 3x^4 + 1}_{\text}\).

Applying the power method and sum method of differentiation:\(\dfrac{du}{dx} = 6x^5 + 12x^3 = 6x^5 + 12x^3\)

Finally, we can substitute these values into the formula:

\(\dfrac{dy}{dx} = \dfrac{du}{dx} \cdot \dfrac{1}{u} = \dfrac{6x^5 + 12x^3}{x^6 + 3x^4 + 1}\)

Therefore, the differentiation of \(y &= \ln(x^6 + 3x^4 + 1) \\\\\dfrac{dy}{dx} &= \dfrac{d}{dx} \ln(x^6 + 3x^4 + 1) \\\\&= \dfrac{6x^5 + 12x^3}{x^6 + 3x^4 + 1}\)

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