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Answer:  7x²  - 14x

Steps: 7(-2x + x²)

Apply the distributive law [ a(b + c) = ab + ac ]:   7(-2x) + 7x²

Apply negative/positive rules:  -7 × 2x + 7x²

Simplify: 7x²  - 14x

Answer:

-2

Step-by-step explanation:

4 + (-6) = -2

Step-by-step explanation:

1 -5/8

lcm=8

8-5=3

3/8

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Step-by-step explanation:

the distance as Hypotenuse, and the x and y coordinate differences as legs create a right-angled triangle.

and Pythagoras helps us

c² = a² + b²

with c being the Hypotenuse, and a and b are the legs.

the differences of coordinates are calculated by subtracting one from the other. it is important that for both x and y differences the same sequence of what point gets subtracted from what is kept.

distance² = (1 - -4)² + (-9 - -1)² = (1+4)² + (-9+1)² =

= 5² + (-8)² = 25 + 64 = 89

distance = sqrt(89)

Therefore, the components of vector E⃗ are Ex = 1 and Ey = -11. Thus, E⃗ = (1, -11).

To solve this equation, let's break it down component-wise. Given:

E⃗ = 2A⃗ + 3B⃗

We can write the equation in terms of its components:

Ex = 2Ax + 3Bx

Ey = 2Ay + 3By

We are also given the components of vectors A⃗ and B⃗:

Ax = 5

Ay = 2

Bx = -3

By = -5

Substituting these values into the equation, we have:

Ex = 2(5) + 3(-3)

Ey = 2(2) + 3(-5)

Simplifying:

Ex = 10 - 9

Ey = 4 - 15

Ex = 1

Ey = -11

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The sample is baised.

Since all the students who attended the football game will most likely want a football stadium to be built and those that do no want a stadium to be built are not proportionately represented in this sample

Hence, the minimum number of at-the-door tickets she needs to sell to make her goal is (B) 334.

Given information: Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets $25. The venue has the capacity to hold 400 people.

The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise at least $5,000 for her school.

The minimum number of at-the-door tickets she needs to sell to make her goal can be calculated as follows;

Let's suppose that x represents the number of pre-sale tickets, and y represents the number of at-the-door tickets Anna needs to sell.

Then the following equation represents the total amount of money Anna will earn after selling the given number of tickets;

10x + 25y ≥ 5,000

If she sells all the tickets, she will have sold a total of x + y tickets. But, we know that the venue has a capacity of 400 people.

So, we also know that;

x + y ≤ 400

Solving the two equations for y gives;

10x + 25y ≥ 5,00025y ≥ 5,000 - 10x y ≥ (5,000 - 10x)/25y ≥ 200 - 0.4xy ≤ 333.3 - 0.4x

Answer: B.334.

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The Balmer series, the second line would have ni = 4, indicating that the electron transitions from the fourth energy level to the second energy level.

The Balmer series is a series of spectral lines in the emission spectrum of hydrogen. It corresponds to transitions of electrons in hydrogen atoms from higher energy levels (initial states) to the second energy level (final state) with nf = 2.

In the Balmer series, the first line is associated with an initial energy level ni = 3. This means that the electron starts in the third energy level and transitions to the second energy level (nf = 2). Each line in the series corresponds to a different transition between energy levels.

Based on this information, the second line in the Balmer series would correspond to a transition where the electron starts from the fourth energy level (ni = 4) and ends up in the second energy level (nf = 2). This transition represents a higher energy change compared to the first line in the series.

Therefore, for the Balmer series, the second line would have ni = 4, indicating that the electron transitions from the fourth energy level to the second energy level.

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Answer:

x = -3 ± 2√2

Step-by-step explanation:

x² + 6x + 1 = 0

Let's solve by completing the square.

Add -1 and 9 on both sides.

x² + 6x + 9 = 8

Factor left side.

(x + 3)² = 8

Take square root on both sides.

x + 3 = ±√8

Add -3 to both sides.

x = -3 ± 2√2

Answer:

1. Find the prime factorization of each number.

2. Write each number as a product of primes, matching primes vertically when possible.

3. Bring down the same numbers in each column and the remaining numbers in each column.

4. Multiply the factors to get the LCM.

for example the lcm of 24 and 36

= 24 = (2 × 2 × 2 × 3) = 2^3 × 3^1

 and 36 = (2 × 2 × 3 × 3) = 2^2 × 3^2

LCM(24, 36) = 2^2 × 3 × 2 × = 72

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we can use integer 0 as a sea level.

To construct an interval, estimate for mu with 95% confidence for the first question, we use the formula:
Interval estimate = x ± (zα/2 * σ/√n)

where x is the sample mean, σ is the known population standard deviation, n is the sample size, zα/2 is the z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence). Plugging in the values, we get:

Interval estimate = 850 ± (1.96 * 50/√100) = 850 ± 9.8
So the 95% confidence interval is from 840.2 to 859.8.

For the second question, where sigma is assumed to be 100, we use the same formula but with σ = 100:

Interval estimate = 850 ± (1.96 * 100/√100) = 850 ± 19.6
So the 95% confidence interval is from 830.4 to 869.6.

For the third question, where sigma is assumed to be 200, we again use the same formula but with σ = 200:

Interval estimate = 850 ± (1.96 * 200/√100) = 850 ± 39.2
So the 95% confidence interval is from 810.8 to 889.2.

As we can see, the confidence interval gets wider as sigma increases. This is because a larger standard deviation indicates greater variability in the population, which means there is more uncertainty in the sample mean as an estimate of the true population mean. Therefore, a wider interval is needed to account for this increased uncertainty.

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The number of chicken wing orders is 90 and the number of sliders is 45.

According to the question,

We have the following information:

Each order of chicken wings sells for $7.25-while each order of hamburger sliders sells for $3. On Friday, Tyler made a total of $595 in revenue from all sliders and wings-sales. There were twice as many chicken wing orders sold than there were sliders sold.

Now, let's take the number of sliders to be x and the number of chicken wing orders to be y.

y = 2x

Now, we have the following expression:

7.25x+3(2x) = 595

7.25x+6x = 595

13.25x = 595

x = 45 (This value is rounded off to a whole number)

Now, the number of wing sales:

y = 2*45

y = 90

Hence, the number of chicken wing orders is 90 and the number of sliders is 45.

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The probability of 00 occurring on a spin of the wheel is approximately equal to 0.0276.

The probability that 00 will occur on a spin of the wheel can be calculated by dividing the number of favorable outcomes (i.e., the number of times 00 can occur) by the total number of possible outcomes.

In this case, there are 38 containers on the roulette wheel, and 00 is 5% larger than any of the others. This means that the size of the container for 00 is 105% of the size of the other containers.

Since the probability is directly proportional to the size of the container, the probability of 00 occurring is 105% of the probability of any other value occurring.

So, the probability of 00 occurring on a spin of the wheel is 105% divided by the sum of 105% and 37 times 100% (which represents the probability of any other value occurring).

Mathematically, this can be expressed as: (105% / (105% + 37 * 100%)).

Calculating this expression will give you the probability of 00 occurring on a spin of the wheel which is approximately equal to 0.0276.

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Answer:

k = 4

Step-by-step explanation:

Rearrange so that like terms are on either side of the equation

4k - 2k - 2k + 2k = 5 + 3

Simplify

2k = 8

Divide both sides by two to make k on its own

k = 4

You are correct, well done!

Answer:

4k−3−2k=2k+5−2k Answer

2k−3=5 Answer

2k−3+3=5+3 Answer

2k=8 Answer

2k2=82 Answer

k=4 Answer

Step-by-step explanation:

The volume of the  is right triangular prism is   600 cubic feet.

In a right triangular prism, the area of the triangular base is 50 square feet, and the height of the prism is 12 feet. To find the volume of the prism, we can use the formula:

Volume = Base Area × Height

Step 1: Identify the base area, which is given as 50 square feet.
Step 2: Identify the height of the prism, which is given as 12 feet.
Step 3: Multiply the base area by the height to find the volume.

Volume = 50 square feet × 12 feet = 600 cubic feet

So, the volume of the right triangular prism is 600 cubic feet.

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To find the volume of a rectangular prism, we can use the following formula:

\(V=lwh\)

1000 mL = 1 L

We're given:

To solve this question, we could follow these steps:

Find the volume of the tank

\(V=lwh\)

⇒ Plug in the measurements: 75 cm by 45 cm by 35 cm
\(V=75*45*35\\V=118125\)

Divide the volume of the tank by the capacity of the jug

There is a relationship between cm³ and mL, not cm³ and L. Convert the 1.75 L for the jug capacity to mL:

1.75 × 1000

= 1750

118125 ÷ 1750

= 67.5

It takes 68 full jugs of water to fill the tank.

Answer:

A. 6 units

Step-by-step explanation:

took the test

The correct option is OA. y+4= -3(x-3). L 4.6.3 Test (CST): Linear Equations Solution: We are given that a line passes through (3,-4) and has a slope of -3.

We will use point slope form of line to obtain the equation of liney - y1 = m(x - x1).

Plugging in the values, we get,y - (-4) = -3(x - 3).

Simplifying the above expression, we get y + 4 = -3x + 9y = -3x + 9 - 4y = -3x + 5y = -3x + 5.

This equation is in slope intercept form of line where slope is -3 and y-intercept is 5.The above equation is not matching with any of the options given.

Let's try to put the equation in standard form of line,ax + by = c=> 3x + y = 5

Multiplying all the terms by -1,-3x - y = -5

We observe that option (A) satisfies the above equation of line, therefore correct option is OA. y+4= -3(x-3).

Thus, the correct option is OA. y+4= -3(x-3).

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Therefore, the equation of the tangent line to the curve xe^y + ye^x = 2 at the point (0, 2) is y = -x + 2.

To find an equation of the tangent line to the curve xe^y + ye^x = 2 at the point (0, 2), we need to use the concept of differentiation.

First, we differentiate both sides of the equation with respect to x using the product rule and the chain rule:

(d/dx)[xe^y] + (d/dx)[ye^x] = (d/dx)[2]

e^y + xe^y(dy/dx) + e^x(dy/dx) + ye^x = 0

Simplifying this expression and evaluating it at the point (0, 2), where x = 0 and y = 1, we get:

e^1 + 0 + e^0(dy/dx) + 2e^0 = 0

dy/dx = -1

Therefore, the slope of the tangent line at the point (0, 2) is -1.

Next, we can use the point-slope form of a line to find the equation of the tangent line. We know the slope is -1 and the point (0, 2) lies on the line, so we can write:

y - 2 = -1(x - 0)

Simplifying this expression, we get:

y = -x + 2

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The trigonometric ratio values for the mentioned angles are:

To find the trigonometric ratio values, we use the unit circle which represents the values of sine, cosine, and tangent of all angles in the first quadrant (0 to 90 degrees). From there, we can use reference angles and the periodicity of trigonometric functions to find the values for other angles.

For example, to find Sin 120 degrees, we can use the reference angle of 60 degrees (180 - 120) and the fact that the sine function is negative in the second quadrant, so:

Sin 120 degrees = - Sin 60 degrees = \($-\frac{\sqrt{3}}{2}$\)

Similarly, to find Cos 150 degrees, we can use the reference angle of 30 degrees (180 - 150) and the fact that the cosine function is negative in the third quadrant, so:

Cos 150 degrees = - Cos 30 degrees =\($-\frac{\sqrt{3}}{2}\)

And to find Tan 225 degrees, we can use the reference angle of 45 degrees (225 - 180) and the fact that the tangent function is positive in the second and fourth quadrants, so:

Tan 225 degrees = Tan 45 degrees = 1.

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Answer:

\(\frac{-x^{2}+5x-1}{2x^{2} -x-1}\)

Step-by-step explanation:

Answer:

False they would be equal

Step-by-step explanation:

Answer:

20 and 28

Step-by-step explanation:

Let x represent the current age of Hari and y represent the current age of Harry

Since the current ratio is 5:7:

5/7 = x/y  

→ 5y = 7x  (1)

Hari's age will be x+4 and Harry's age will be y+4 four years later. Since the ration of their ages will be 3:4 four years later:

3/4 = (x+4)/(y+4)  (2)

→ 3(y+4) = 4(x+4)

→ 3y + 12 = 4x + 16

→ 3y = 4x + 4 (Substitute the y as 7x/5 from the equation 1)

→ 3(7x/5) = 4x + 4

→  21x = 20x + 20

→ x = 20

y = 7x/5 = 7(20)/5 = 28

These lines will be parallel to the initial line and will intersect the final velocity line at the corresponding values (122 for the lower estimate and 298 for the upper estimate)

To sketch the velocity against time, you can take the following steps:

First, calculate the acceleration using the given data by using the formula;

acceleration = (final velocity - initial velocity)/time

Where; Initial velocity is the velocity before applying the brakes

Final velocity is the velocity at which the car comes to stop

Time is the time it takes to stop the car (6 seconds in this case)

Now, calculate the lower and upper estimates using the formula;

Lower estimate = initial velocity + (acceleration x time)

Upper estimate = initial velocity + (2 x acceleration x time)

Sketch the graph using the following steps;

On the vertical axis, plot the velocity of the car

On the horizontal axis, plot the time

Start from the initial velocity and draw a straight line with the calculated acceleration until the end of the time (6 seconds)This straight line will give you the final velocity (0 in this case)

Now, draw two more lines, one with the lower estimate and the other with the upper estimate

Finally, label the axes and the lines with their corresponding values.'

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The z-score for X = 48, given a population with a standard deviation of 8 and a mean of 40, is 1.

A bell-shaped curve, also known as a normal distribution, is a symmetric curve with a single peak resembling a bell. It is commonly used to represent data that follows a normal distribution pattern.

In the provided graph, the location of the mean (μ) is marked on the bell-shaped curve. Additionally, the numbers corresponding to each standard deviation, which are -1, -2, +1, and +2, are also indicated. These values represent the distance from the mean in terms of standard deviations.

To calculate the z-score for X = 48, we can use the z-score formula: $z = \frac{X - \mu}{\sigma}$, where X is the raw score, μ is the population mean, and σ is the population standard deviation.

Applying the formula to the given values, we have:

$z = \frac{48 - 40}{8} = 1$

Therefore, the z-score for X = 48 is 1.

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Using Green's theorem, we can evaluate the line integral ∮c [y^3 dx - x^3 dy] around the closed curve C given by the equation x^2 + y^2 = 1, parameterized by x = cos(θ) and y = sin(θ) with 0 ≤ θ ≤ 2π.

Green's theorem states that the line integral around a closed curve C of a vector field F can be computed as the double integral of the curl of F over the region R enclosed by C.

First, we need to find the curl of the vector field F = (y^3, -x^3). Taking the partial derivatives of the components with respect to x and y, we obtain:

∂F/∂x = 0 - 3x^2 = -3x^2

∂F/∂y = 3y^2 - 0 = 3y^2

Now, we calculate the double integral of the curl of F over the region R enclosed by the curve C. Since C is a unit circle centered at the origin, the region R is the entire interior of the circle.

Using polar coordinates, we substitute x = cos(θ) and y = sin(θ) into the curl components and multiply by the appropriate Jacobian factor. The integral becomes:

∫∫R (3y^2 - (-3x^2)) dA

∫∫R (3sin^2(θ) + 3cos^2(θ)) dA

∫∫R 3 dA

3 * Area(R)

Since R is the unit circle, its area is π, so the line integral evaluates to:

3 * π

Therefore, the line integral ∮c [y^3 dx - x^3 dy] around the closed curve C is equal to 3π.

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