In which quadrant is the point (4, -5)?

The expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).

As per the question, we can write the expression as:

(t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9)

Using product notation, we can write this as:

Π⁷k =1 \((t^k - 9)\)

where Π represents the product of terms, k is the index of the product, and the subscript 7 indicates that the product runs from k = 1 to k = 7.

Therefore, the expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).

Learn more about Expressions here:

brainly.com/question/21751419

#SPJ4

None of the listed methods are used for enumerating sample points in a multiple-step experiment. So, option D is the correct answer.

Graphical methods are important mathematical tools that are very helpful when it comes to managing a vast amount of data. These also help when we need to visually represent data. These methods help quite a lot since they make it easier to keep track of data and understand it as well.

A bar chart and a histogram are similar tools that are used to represent data by plotting them as rectangular bars. These can be either vertical or horizontal. A pie chart is also a tool that uses a shape for data visualization. In its case, it represents data in the shape of a circle and all categories/data sets have their slices. So, this means that these three are not methods that can be used for enumerating sample points in a multiple-step experiment. Hence, option D is the correct option.

Learn more about piecharts on

https://brainly.com/question/16819077?referrer=searchResults

#SPJ4

Answer:

1. <4=115 degrees

2. 180 degrees

4. 5 degrees

6. 110 degrees

7. 180 degrees

8.65 degrees

Step-by-step explanation:

Answer:

216

Step-by-step explanation:

108/2 = 54 per tire

54 x 4 = 216

Answer:

Step-by-step explanation:

108 times 2 is 216

so it costs 216

also if u needed the individual cost of each tire divide 108 by 2

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

Know more about revenue:

https://brainly.com/question/27325673

#SPJ11

Answer:

(a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1) b^1 + C(n, 2)a^(n-2) b^2 + ... + C(n, n-1)a^1 b^(n-1) + C(n, n)a^0 b^n

The binomial expansion of (2x - 3y)^5 is:

32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5

The binomial expansion of the given expression is 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵.

The given expression is (2x-3y)⁵.

In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial.

(2x)⁵+⁵c₁(2x)⁴(3y)¹+⁵C₂(2x)³(3y)²+⁵C₃(2x)²(3y)³+⁵C₄(2x)(3y)⁴+⁵C₅(3y)⁵

= 32x⁵+5(16x⁴)(3y)+10.(8x³)(9y²)+10(4x²)(27y³)+5(2x)(81y⁴)+243y⁵

= 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵

Therefore, the binomial expansion of the given expression is 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵.

To learn more about the binomial expansion visit:

https://brainly.com/question/31363254.

#SPJ2

Answer:

The graph of the function starts high ends low

Step-by-step explanation:

I put the equation into Desmos

Part A

Given f(x) defined below:

The y-intercept is the value of y when x=0.

Vertex

Since the axis of symmetry is given as x=2:

Minimum/Maximum Value

Since the coefficient of x² is negative, there is a maximum value.

• Maximum Value = 9

• The graph opens downwards.

Part B

Given g(x) defined below:

The axis of symmetry is derived using the formula below:

• Axis of Symmetry: x=-1

• Vertex: (-1,-7)

The expression for tan(t) in terms of sin(t) in Quadrant IV is:

tan(t) = √(1 - sin² (t))/sin(t).

In the fourth quadrant, we know that the x-coordinate is positive and the y-coordinate is negative.

If we think of a right angle triangle in  the fourth quadrant with an angle t, where the opposite side is represented by y and the adjacent side is represented by x.

We know that:

sin x = opposite/hypotenuse

Thus:

sin(t) = y/h.

Using the Pythagorean theorem, we can express the hypotenuse in terms of x and y as:

h² = x² + y²

Making y the subject gives:

y = √(h² - x²)

Now, let's consider the tangent function:

tan(t) = y/x.

Substituting √(h² - x²) for y gives us:

tan(t) = (√(h² - x²))/x.

Therefore, in terms of sin(t), the expression for tan(t) in Quadrant IV is:

tan(t) = √(1 - sin² (t))/sin(t).

This expression allows us to calculate the tangent of an angle in terms of its sine when the terminal point is in Quadrant IV.

Read more about Trigonometric ratio in quadrant at: https://brainly.com/question/12172664

#SPJ4

`tantcott+csct = (3sqrt(2) - 4)/3sqrt(2)` when `cost = -5/3` and the terminal point determined by `t` is in Quadrant III.

Given that `cost = -5/3` and the terminal point determined by `t` is in Quadrant III.

In Quadrant III, `x` is negative and `y` is negative. So, `sin(t)` is negative. Hence, we take the negative value of `sqrt(1-cos^2(t))` and represent it as `-sqrt(1-cos^2(t))`.

Since `cost = x/r`, we can take `x = -5` and `r = 3`. Then, `y = sqrt(r^2 - x^2) = sqrt(9 - 25) = -2sqrt(2)`.

So, `sin(t) = -2sqrt(2)/3`.Therefore, `tan(t) = sin(t)/cos(t) = (-2sqrt(2)/3)/(-5/3) = 2sqrt(2)/5`.

Hence, `tan(t) = 2sqrt(2)/5` when the terminal point determined by `t` is in Quadrant III.

-------------------Given that `cost = -5/3` and the terminal point determined by `t` is in Quadrant III.

`tant = sin(t)/cos(t)` and `cot(t) = cos(t)/sin(t)`.

`tantcot(t) + csct = sin(t)/cos(t) × cos(t)/sin(t) + 1/sin(t)`    `= 1 + 1/sin(t)`We know that `sin(t)` is negative in Quadrant III. Hence, we take the negative value of `sqrt(1-cos^2(t))` and represent it as `-sqrt(1-cos^2(t))`.

Since `cost = x/r`, we can take `x = -5` and `r = 3`. Then, `y = sqrt(r^2 - x^2) = sqrt(9 - 25) = -2sqrt(2)`.So, `sin(t) = -2sqrt(2)/3`.

Therefore, `csct = 1/sin(t) = -3sqrt(2)/4`.

Hence, `tantcott+csct = 1 + 1/sin(t) = 1 - 4/3sqrt(2) = (3sqrt(2) - 4)/3sqrt(2)`.

Therefore, `tantcott+csct = (3sqrt(2) - 4)/3sqrt(2)` when `cost = -5/3` and the terminal point determined by `t` is in Quadrant III.

learn more about Quadrant III on:

https://brainly.com/question/29390181

#SPJ11

ANSWER:

y=2x-3

HOPE IT HELPS

Step-by-step explanation:

Add the system of equations each one by one.

I added them all downwards until i found the 4th one to be correct

y = 2x - 3

y = 2x - 3

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

2y = 4x - 6

y = 2x - 3.

To find the value of y in each coordinates given above, substitute their respective x values.

1......y = 2(5) - 3

= 10 - 3

= 7.

2......y = 2(8) - 3

= 16 - 3

= 13.

then write the value you substituted in x on the left side of each bracket & the value you got when you substituted them on the right.

(5 , 7) (8 , 13)

Answer: A

Step-by-step explanation:

Answer:

{x | x is a real number}, {y | y>0}

Explanation:

Given f(x) where:

We want to determine the domain and range of f(x).

Domain

The domain of a function is the set of all the possible values of x for which the function is defined.

In f(x), x can take on any value, therefore, the domain is:

Range

The range of a function is the set of all the possible values of f(x) for which the function is defined.

The value of f(x) will always be greater than 0. Therefore, the range of the function is:

The first option is correct.

We find that the proportion of her laps that fall between 127 and 130 seconds is about 0.139. Any lap time under 135.25 seconds would be considered one of the fastest 2% of her laps. The middle 70% of her laps are between 119 and 131 seconds.

To answer your questions, we first need to have some context on what we're dealing with. You mentioned "her laps," so I assume we're talking about a person who is running or swimming laps. We also need to know the distribution of her lap times (i.e., are they normally distributed, skewed, etc.) in order to answer these questions accurately. For now, let's assume that her lap times are normally distributed.
To find the proportion of her laps that are completed between 127 and 130 seconds, we need to calculate the area under the normal distribution curve between those two values. We can do this using a calculator or a statistical software program, but we need to know the mean and standard deviation of her lap times first.

Let's say the mean is 125 seconds and the standard deviation is 5 seconds. Using a standard normal distribution table or calculator, we find that the proportion of her laps that fall between 127 and 130 seconds is about 0.139.
To find the fastest 2% of laps, we need to look at the upper tail of the distribution. Again, we need to know the mean and standard deviation of her lap times to do this accurately. Let's say the mean is still 125 seconds and the standard deviation is 5 seconds. Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 98th percentile (i.e., the fastest 2% of laps) is about 2.05. We can then use the formula z = (x - mu) / sigma to find that x = z * sigma + mu, where x is the lap time we're looking for. Plugging in the numbers, we get x = 2.05 * 5 + 125 = 135.25 seconds.

Therefore, any lap time under 135.25 seconds would be considered one of the fastest 2% of her laps.
Finally, to find the middle 70% of her laps, we need to look at the area under the normal distribution curve between two values, just like in part However, we need to find the values that correspond to the 15th and 85th percentiles, since those are the cutoffs for the middle 70%. Using the same mean and standard deviation as before, we can use a standard normal distribution table or calculator to find that the z-scores corresponding to the 15th and 85th percentiles are -1.04 and 1.04, respectively.

We can find that the lap times corresponding to those z-scores are 119 seconds and 131 seconds, respectively. Therefore, the middle 70% of her laps are between 119 and 131 seconds.

for more questions on proportion

https://brainly.com/question/870035

#SPJ11

Answer:

AB PARALLEL TO DC AND AD WITH BC

Answer:

8 and 4

Step-by-step explanation:

Answer:

uiuiuiui86767

Step-by-step explanation:

your answer is e330408384

Answer:

3d² + 2d + 3 remainder -2

Step-by-step explanation:

The derivative of `y = ln(cos x/sqrt(4-3x^2))` is given by `(dy)/(dx) = [(-sqrt(4 - 3x^2) * tan x)/cos x] + [(3x * ln(cos x))/ (2 * (4 - 3x^2))]`.

The derivative of the given function `y = ln(cos x/sqrt(4-3x^2))` is given below. By using the quotient rule, we can find the derivative of the given function.The quotient rule: If `y = f(x)/g(x)`, then the derivative of y is given by `(dy)/(dx) = [g(x) * f'(x) - f(x) * g'(x)] / [g(x)]^2`.Now, let's find dy/dx by using the above formula. We have`y = ln(cos x/sqrt(4-3x^2))`We have to differentiate the above function. The function is of the form f(x)/g(x) where f(x) = ln(cos x) and g(x) = sqrt(4 - 3x^2).Here, `f'(x) = -tan x/cos x` and `g'(x) = (-3x) / (2 * sqrt(4 - 3x^2))`.We know that`(dy)/(dx) = [g(x) * f'(x) - f(x) * g'(x)] / [g(x)]^2`Now, substituting the values in the formula, we get`(dy)/(dx) = [sqrt(4 - 3x^2) * (-tan x/cos x) - ln(cos x) * (-3x) / (2 * sqrt(4 - 3x^2))] / [sqrt(4 - 3x^2)]^2`Simplifying, we get`(dy)/(dx) = [(-sqrt(4 - 3x^2) * tan x)/cos x] + [(3x * ln(cos x))/ (2 * (4 - 3x^2))]`Therefore, the derivative of `y = ln(cos x/sqrt(4-3x^2))` is given by `(dy)/(dx) = [(-sqrt(4 - 3x^2) * tan x)/cos x] + [(3x * ln(cos x))/ (2 * (4 - 3x^2))]`.

Learn more about Derivative

brainly.com/question/30365299

#SPJ11

there you goo :)) on the chain up on the left from 3 to 48 they keep multiplying by 2, and the other one, they keep subtracting by 7

The data type of the return value for the method declaration public static double hypotenuse(int a, int b) is option (C) double.

In Java, every method must have a return type that specifies the data type of the value that the method will return after it has executed. In this case, the method hypotenuse has a return type of double, which means that it will return a floating-point value of type double.

The method hypotenuse takes two integer parameters a and b and calculates the length of the hypotenuse of a right triangle using the Pythagorean theorem. The result of this calculation is a floating-point value, which is why the method has a return type of double.

When the method is called, it will execute the calculation and return the result as a double value to the caller. The caller can then use this value in further calculations or assignments.

Therefore, the correct option is (C) double

Learn more about data type here

brainly.com/question/13040910

#SPJ4

Answer:

-12-2y

Step-by-step explanation:

-2[6±5y]±8y

negative × positive=negative

-12-10y±8y=-12-2y

Answer:

∠A≅∠Y        AB≅YZ

∠B≅∠Z          AC≅YX

∠C≅∠X         BC≅ZX

ΔABC ≅ ΔYZX

Step-by-step explanation:

congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle

Answer:

53/5

Step-by-step explanation:

I hope this helps u.

Mark me as brainliest.

Refer to the diagram below for examples of what I mean.

Answer:544

Step-by-step explanation:43 + 25 = 68

68 × 8 = 544

Answer:7.65

Step-by-step explanation:

4.5/10 is 0.45 which is the unit rate then you multiply it with 17 and get 7.65

The equation will be changed into = f(x)= 32

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.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Hence, The equation will be changed into = f(x)= 32

learn more about equations click here:

brainly.com/question/2972832

#SPJ1



The simplification of the given inequalities gives;

1) m > -1/80

2) x < -1/3

1) The multiplicative property of inequality states that both sides of an inequality can be multiplied or divided by the same number and an equivalent inequality can be formed.

Thus, applying that to 8m > -1/10, gives;

Multiply both sides by 1/8 to get;

8m * 1/8 > -1/10 * 1/8

m > -1/80

2) The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.

Thus, applying that to -9/2x > 3/2 gives;

Divide both sides by -9/2 to get;

x < -1/3

Read more about Algebraic Properties of Equality at; https://brainly.com/question/16253595

#SPJ1

Answer: (c) 0

Step-by-step explanation:There is no variable x involved, so we can say that this polynomial is of degree 0.

Polynomial as having a constant term of 5 and no other terms involving x.

If p(x)=x^5 then degree of polynomial is 5

degree of polynomial = highest degree of x

Answer:

5

Step-by-step explanation:

it 5 because its 5 so so so so so so