Evaluate the coefficient of x^5 and x^4 in the binomial expansion of (x/3-3)^7. Hence find the coefficient of x^5 in (x/3-3)^7(x-6)

Answer:

Step-by-step explanation:

The probability of spinning a white and an A on the first spinner is 1/4. This means that the probability of spinning a white and an A on the first spinner is 1 out of 4 or 25%.

The probability of spinning a striped and an A on the second spinner is 3/4. This means that the probability of spinning a striped and an A on the second spinner is 3 out of 4 or 75%.The probability of spinning a striped and an A on both spinners is the product of the probabilities of spinning a striped and an A on both spinners. This means the probability of spinning a striped and an A on both spinners is 3/16 or 18.75%.The probability of spinning a white and a ~A on the second spinner is 1/4. This means that the probability of spinning a white and a ~A on the second spinner is 1 out of 4 or 25%.In conclusion, the probability of spinning a white and an A on the first spinner is 25%, the probability of spinning a striped and an A on the second spinner is 75%, the probability of spinning a striped and an A on both spinners is 18.75%, and the probability of spinning a white and a ~A on the second spinner is 25%.

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

hi! i’m pretty sure it’s -18 and -20

Step-by-step explanation:

Answer:

160/81

Step-by-step explanation:

Convert all the mixed fractions into improper fractions

Use the Area formula A=L x W

A = 16/9 x 10/9

A= 160/81 or 1 79/81

Answer:

The answer is f^-1(x)=0^3\(\sqrt{x}\)+2

Step-by-step explanation: Now we just change y back to f(x) and add a 0−1 to write it in inverse notation We begin with f(x)= x 3−2 . To find the inverse of any equation, just switch x and y No, before we do that, I'm going to change the equation. I'm going to rename f(x) to y , just so that I don't have to deal with the parentheses or anything. Now, all I have to do is change what f (x) is called, not it's actual value. Anyways, we have y = x 3 − 2 Now we switch x and y and then solve for y Now we've got x = y 3−2 If we add 2 on both sides we have x + 2 = y 3 Now we just need to get y as simple as possible, which we'll do by cube rooting both sides of the equation. That leaves us with y=0 3√x+2 Now we just change y back to f(x) and add a 0−1 to write it in inverse notation

Answer: A

Step-by-step explanation:

The equation option 3rd is correct option.

An expression or a statement that comprises two algebraic expressions with the same value and are separated by an equal symbol in between them.

Given that, four equation,

5 = 3x/2 - 8

Adding 8 to both sides,

5 + 8 = 3x/2 - 8 + 8

13 = 3x/2

Multiplying by 2 to both sides,

13*2 = 3x/2*2

26 = 3x

x = 26/3

Hence, equation 3rd is the correct answer.

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Complete question:

When the pallet was placed on the scale, the reading came back as 325 total pounds. Note that this was including the pallet itself, which weighed 35 pounds.

How many cartons of each product were on the pallet? Create two equations to represent the situation and then solve the system. Show all work. Express your final answer using a complete sentence and appropriate units

Answer:

we have 25 and 55 cartons of each product

Step-by-step explanation:

we have number of carton = 10 x 8 = 80

each level has 10, and leves are 8 high

two types of product packages,

we call them w and x

w + x = 80 ------ equation 1

w has 3 pounds weight

x has 5 pounds weight

3*w +5*x

3w + 5x

total weight = 325

we subtract weight of pallet 35

= 325 - 35 = 290

3w + 5x = 290-------- equation 2

we have two equations

w + x = 80------(1)

3w + 5x = 290-------(2)

from equation 1,

w = 80 - x

put this value above in equation 2

3(80-x) + 5x = 290

240-3x+5x = 290

240+2x = 290

2x = 290-240

2x = 50

divide through by 2

x = 25

put value of x in equation 1

w + 25 = 80

w = 80-25

w = 55

so we have 55 cartons of w and 25 cartons of product x

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

A graph that represent the system of quadratic equations is shown in the image attached below.

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

By expanding the bracket, we have:

f(x) = (x - 4)(x + 4)

f(x) = x² - 4x + 4x - 16

f(x) = x² - 16

Since the leading coefficient (value of a) in the given quadratic function y = x² - 8x + 12 is positive 1, we can logically deduce that the parabola would open upward and the y-intercept is given by the ordered pair (0, 12).

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The width of the dog run is 20 feet.

In the given problem, the length of the dog run is given as 30 feet.

The area of the dog run is also given as 240 square feet.

Using the formula for the area of a rectangle (A = lw), we can solve for the width (w).

Rearranging the formula, we have w = A / l.

Plugging in the values, we get w = 240 / 30 = 8 feet.

Since the width is given as (30 minus x) feet, we can set up an equation:

30 - x = 8. Solving for x, we find x = 22.

Therefore, the width of the dog run is 20 feet (30 - 22 = 8).

In this problem, the length and width of the dog run are defined by the dimensions of the fence being built around it.

The area of the dog run is given as 240 square feet.

By using the formula for the area of a rectangle, we can solve for the width. We are also given that the length is 30 feet.

Setting up an equation with the given width (30 minus x) and solving for x, we find that x is equal to 22.

This means that the width of the dog run is 8 feet. The main answer to the problem is that the width of the dog run is 20 feet (30 - 22 = 8).

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Answer:

m<20

Step-by-step explanation:

m must be less than 20

m < 20

or

20 > m

The equation that represents a quadratic function written in vertex with a vertex of (3,5) and passes through the point (1, 13) is y = 2(x - 3)^2 + 5

The given parameters are:

A quadratic equation is represented as:

y = a(x - h)^2 + k

So, we have:

y = a(x - 3)^2 + 5

Substitute (x,y) = (1,13) in the equation

13 = a(1 - 3)^2 + 5

Evaluate the exponent

13 = 4a + 5

Subtract 5 from both sides

4a = 8

Divide both sides by 4

a = 2

Substitute a = 2 in y = a(x - 3)^2 + 5

y = 2(x - 3)^2 + 5

Hence, the equation of the quadratic function is y = 2(x - 3)^2 + 5

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Answer:

The Population is 865000

Step-by-step explanation:

0.7 Million is equal to 700,000

700,000 + 165,000=865000

Answer: f(-3)=g(-3)

Step-by-step explanation:

The graphs intersect at x = -3.

The correct option is f(-3) = g(-3).

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given that two lines are intersecting at point (-3, -4)

Therefore the system of equations of these two have a solution at (-3, -4)

So, if taking the lines as function,

We have f(x) and g(x),

so both of them are intersecting at (-3, -4) so the range when the domain is -3 will be equal.

Hence the correct option is f(-3) = g(-3).

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Answer:

610023626728387383838

Answer:

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

Let the cost of the meal be x.

Adding a tip of 19%:

Answer:

Wyatt should multiply with 1.19.

Step-by-step explanation:

Forming the expression,

→ 1 + (19% of 1)

Now the required number is,

→ 1 + (19% of 1)

→ 1 + ((19/100) × 1)

→ 1 + (19/100)

→ 1 + 0.19 = 1.19

Hence, required number is 1.19.

Answer:

The guitarist makes 70$ a performance

Step-by-step explanation:

To find how much he makes per performance we need to make an equation where how much he makes per performance is x

The equation would be:

6×x=420

Then we would divide both sides by 6

6÷6×x=420÷6

which would make the equation

x=70

meaning that the guitarist makes 70$ per performance

Let performances be x

\(\\ \sf{:}\dashrightarrow 6x(2)=420\)

\(\\ \sf{:}\dashrightarrow 12x=420\)

\(\\ \sf{:}\dashrightarrow x=420/12\)

\(\\ \sf{:}\dashrightarrow x=35\)

Answer:

60

Step-by-step explanation:

We are using sigma notation to solve for a sum of arithmetic sequences:

The 5 stands for stop at i = 5 (inclusive)

The i = 1 stands for start at i = 1

The 12 stands for expression of each term in the sum

In response to the given question, we can state that Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.

Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.

Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.

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The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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Answer:

I'm 80% sure its greater than, because $10 per week for 30 weeks Is 300 I think

The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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The expression equivalent to -2log₂x + 4log₂y + 4log₂z is log₂(yz)⁴/x².

To answer the question, we need to know the laws of logarithm

Since we want to find the expression equivalent to -2log₂x + 4log₂y + 4log₂z, we simplify using these laws, we have

-2log₂x + 4log₂y + 4log₂z = log₂x⁻² + log₂y⁴ + log₂z⁴ (appying the power law)

= log₂x⁻²y⁴z⁴ (applying the multiplication law)

= log₂y⁴z⁴/x²

= log₂(yz)⁴/x²

So, the expression equivalent to -2log₂x + 4log₂y + 4log₂z is log₂(yz)⁴/x².

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Answer:

C.log_2(yz^4/x^2)

Step-by-step explanation:

I took the Algebra exam

Answer:

x < x and -3x < -3x

Step-by-step explanation:

x cannot be less than itself so there would be no solution.

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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