Find the equivalent ratio to the ratio 9 to 27 by simplifying the ratio. 3 to 1 , 1 to 3, 1 to 27 ,9 to 3

To find the largest rectangle with its base on the x-axis that can be inscribed under the graph of y = xcos(x), we need to maximize the area of the rectangle.

The base of the rectangle will lie on the x-axis, so the height of the rectangle will be determined by the function y = xcos(x).

To find the maximum area, we need to locate the critical points of the function xcos(x). We can do this by finding where the derivative of the function equals zero or does not exist.

Taking the derivative of xcos(x) with respect to x, we have:

d/dx (xcos(x)) = cos(x) - xsin(x)

Setting this derivative equal to zero, we get:

cos(x) - xsin(x) = 0

We need to solve this equation to find the critical points.

Unfortunately, there is no exact algebraic solution for this equation. We can use numerical methods or graphing software to approximate the critical points.

Once we have the critical points, we can evaluate the function y = xcos(x) at these points to find the height of the rectangle.

Finally, we can calculate the area of the rectangle by multiplying the base (x-coordinate of the critical points) with the corresponding height (y = xcos(x)).

Answer:

constant temperature is -56.5°C (-69.7°F), and this is also the lowest assumed temperature in respect to ISA.

Answer:

The pizza restaurant put 1/10 of the sauce on each pizza.

Step-by-step explanation:

Take the 3/5, and on a calculator divide the 3 by the 5:

0.6

Then, take the 0.6 and divide it by the 6 pizzas:

0.1, converted into a fraction equals 1/10.

The pizza restaurant put 1/10 of the sauce on each pizza.

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Answer:

x=15/19

Step-by-step explanation:

You have to start by multiplying the denominators by the numerators. I doesn't matter which you do first, as you can see, I chose to multiply the 6 by the 4x first.

Once that is completed, it is a simple matter of rearranging the equation so it begins with x=...

To do this, just subtract 5x and then divide by 19 on both sides to get the final fraction.

I have attached a photograph of my workings.

The expression to get the length is:

L = (x + 3)cm

And when x = 2, the length is 5 cm.

Remember that for a rectangle of length L and width W, the area is:

A = L*W

In this case, we know that W = 6cm and the area equation is:

A = L*6cm = (6*x + 18)cm^2

Solving that for L:

L = (6*x + 18)cm/6

L = (x + 3)cm

That is the expression to get the length.

If x = 2, then we replace the variable x by 2 in the above expression so we get:

L = (2 + 3)cm  =5cm

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The estimated solution to the system of equations is:

Choice C) x = -3/4, y = -3 1/2.

Given that a system of equations y = -2x - 5 and y = 2x - 2

We need to see what the solution of the system is, by graphing,

To estimate the solution to the system of equations y = -2x - 5 and y = 2x - 2, we can analyze the interactive graph.

Based on the equations, we see that the coefficients of x in both equations have opposite signs, which indicates that the lines will intersect.

Let's analyze the graph to determine the approximate intersection point.

Looking at the graph, it appears that the lines intersect at the point (-3/4, -3 1/2). Comparing this point with the given choices, we find that it matches Choice C: x = -3/4 and y = -3 1/2.

Therefore, the estimated solution to the system of equations is:

Choice C) x = -3/4, y = -3 1/2.

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(a) correctly describes the relationship between a parameter and a statistic.

The correct description is:

a) A statistic is calculated from sample data and is generally used to estimate a parameter.

In statistics, a parameter refers to a characteristic or measure that describes a population, while a statistic is a characteristic or measure calculated from sample data. Statistics are often used to estimate or infer the corresponding parameters of the population. Therefore, option (a) correctly describes the relationship between a parameter and a statistic.

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Answer:

3x +8 = -5x

3x + 5x = -8

8x = -8x

x = -8 /8

x = -1

Hope it helps...

Please contact me for further explanation....

A statement best describes the functions represented by the tables is that: A. function p is nonlinear and exponential.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the standard form of the equation of a linear function is given by;

y = mx + c

Based on the data provided in the table, we would determine the slope:

Slope, m = Δp(x)/Δx

Slope, m = (16-4)/(1-0)

Slope, m = 12/1

Slope, m = 12.

Slope, m = (64-16)/(2-0)

Slope, m = 48/2

Slope, m = 24.

For the slope of g(x), we have:

Slope, m = Δg(x)/Δx

Slope, m = (15-3)/(2-0)

Slope, m = 12/2

Slope, m = 6.

Slope, m = (33-15)/(5-2)

Slope, m = 18/3

Slope, m = 6.

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Answer:

a

Step-by-step explanation:

Answer:

46.67$

Step-by-step explanation:

using the is/of method and %/100

60/100 x 28/x  cross mult

2800/60x = 46.666

round to nearest hundreth

Answer:

y = 3x  + b

3x is the slope

y = 3x + 1 because 1 is the y intercept

Step-by-step explanation:

Answer:

y = 3x + 1

Step-by-step explanation:

You know the  y intercept by looking where the line hits the y axis, which is at (0,1), so you know the "b" of the equation is 1. Then, you do rise over run. If you rise 3 and run 1, you get to another point, so I know the slope is 3/1 or 3.

Answer:

A.32.10

Step-by-step explanation:

You have to remember to subtract the $35 then start to figure out how much he paid every month for a year.

The probability that a student chosen randomly from the class plays both basketball and baseball is 2/13.

What are outcomes?

An outcome is a potential outcome of an experiment or trial in probability theory. Each conceivable result of a specific experiment is distinct, and many results are incompatible (only one outcome will occur on each trial of the experiment).

Given that the total number of students in the class is 26. 6 of them play basketball and 15 of them play baseball. There are 9 students who play neither sport.

The number of students who play at least one sport is (26 - 9) = 17.

Assume that n(A) = 6

n(B) = 15.

n(A∪ B) = 17

n(A∪ B) = n(A) + n(B) - n(A∩B)

17 = 15 + 6 - n(A∩B)

n(A∩B) = 21 - 17

n(A∩B) = 4

Therefore 4 students plays both basketball and baseball.

The number of outcomes of favorable event is 4.

The number of total outcomes is 26.

Probability = The number of favorable outcomes/ Total number of outcomes

The probability is 4/26 = 2/13

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The standard deviation of McDonovan, Inc.'s stock returns is approximately 19.54%.

To calculate the standard deviation for McDonovan, Inc.'s stock returns using the provided information, we can use the following steps:

1. Assign weights to each return based on their respective probabilities.

Boom: Probability = 0.20, Return = 0.40

Normal: Probability = 0.60, Return = 0.15

Recession: Probability = 0.20, Return = -0.20

2. Calculate the expected return by taking the weighted average of the returns.

Expected Return = (0.20 × 0.40) + (0.60 × 0.15) + (0.20 × -0.20) = 0.09 or 9%

3. Calculate the squared difference between each return and the expected return.

Boom: (0.40 - 0.09)² = 0.1296

Normal: (0.15 - 0.09)² = 0.0036

Recession: (-0.20 - 0.09)² = 0.0736

4. Calculate the variance by taking the weighted average of the squared differences.

Variance = (0.20 × 0.1296) + (0.60 × 0.0036) + (0.20 × 0.0736) = 0.03808

5. Take the square root of the variance to obtain the standard deviation.

Standard Deviation = √(0.03808) = 0.1954 or 19.54%

Therefore, the standard deviation of McDonovan, Inc.'s stock returns is approximately 19.54%.

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1. The x-intercept of a function is the point where the line crosses the x-axis. At this point, the y-coordinate is equal to zero.

You can identify the point from the graph or calculate the coordinates by replacing the equation of the linear function with y=0 and determine the corresponding value of x.

-Looking at the graph, the red line, that corresponds to the equation y=x-3, crosses the x-axis at point (3,0)

-Replacing the equation of the function by y=0:

The x-intercept has coordinates at (3,0)

2. The y-coordinate is the point where the red line crosses the y-axis. At this point, the x-coordinate is equal to zero.

You can identify this point directly from the graph, or calculate it by replacing the equation of the line with x=0 and calculate the corresponding value of y.

-Looking at the graph, the red line crosses the y-axis at the point (0,-3)

-Replace the equation with x=0

The y-intercept is (0,-3)

3. The equation y=4x+2 is represented in the graph by the blue line

As before, you have to identify the point where the line crosses the x-axis.

-From the graph:

-Replace the equation with y=0 and calculate the corresponding value of x:

The x-intercept is (-1/2,0)

4. The y-intercept is the point where the blue line crosses the y-axis.

-You can identify it from the graph:

-Or replace the equation with x=0 and determine the corresponding value of y

The coordinates of the y-intercept are (0,2)

Equation can use to find the number of water balloons w in the bin before Naomi trips is w - 13 = 15.

As per the given data, Naomi's carries a bin of water balloons outside for the balloon toss, she trips and breaks 13 balloons.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The number of water balloons w in the bin before Naomi trips.

She counts the remaining water balloons, and there are 15 left.

According to the question, the equation is

w - 13 = 15

⇒ w = 15 + 13

⇒ w = 28

Hence, equation which is used to find the number of water balloons w in the bin before Naomi trips is w - 13 = 15.

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Answer:

D. 4√2

Step-by-step explanation:

A triangle with 45°, 45°, and 90° is a special right triangle.

hypotenuse = √2 · leg

1. Set up the equation

8 = √2 · x

2. Divide by √2 and solve

x = \(\frac{8}{\sqrt{2} }\) · \(\frac{\sqrt{2} }{\sqrt{2}}\) = \(\frac{8\sqrt{2} }{2}\) = 4√2

Answer:

84 in.

Step-by-step explanation:

6*6=36/2=18

6*11=66

18+66=84

The value of n, considering the exponential expression for this problem, is given as follows:

n = 4.

The exponential expression for this problem is defined as follows:

\(n^4p^7t^9 = \frac{4n^3p^7}{t^{-9}}\)

To solve for the variable n, we can isolate it, as follows:

\(\frac{n^4}{4n^3} = \frac{p^7}{p^7 \times t^9 \times t^{-9}}\)

When two terms with the same base and different exponents are divided, the base remains constant while the exponents are subtracted, as follows:

When two terms with the same base and different exponents are multiplied, the base remains constant while the exponents are added, as follows:

\(t^9 \times t^{-9} = t^{9 - 9} = t^0 = 1\)

Hence the simplified expression can be written as follows:

\(\frac{n^4}{4n^3} = \frac{p^7}{p^7 \times t^9 \times t^{-9}}\)

\(\frac{n}{4} = 1\)

Applying cross multiplication, the value of n is then given as follows:

n = 4 x 1

n = 4.

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Answer:

$306

Step-by-step explanation:

we know that

Erika earns 9$ per hour

so

By proportion

Find how much she earn during the total hours of two weeks

The total hours of two weeks is equal to

\(14+20=34 hours\)

\(\frac{9}{1} \frac{money}{hour} = \frac{x}{34} \frac{money}{hours}\)

\(x =34\)×\(9\)

x = 306$

therefore

the answer is

$306

Answer: 25, 20, 15, 10, 5.

Step-by-step explanation:

The first five terms of the sequence are:

25, 20, 15, 10, 5.

To find the nth term, we use the formula:

an = an-1 - 5

Starting with a1 = 25:

a2 = a1 - 5 = 25 - 5 = 20

a3 = a2 - 5 = 20 - 5 = 15

a4 = a3 - 5 = 15 - 5 = 10

a5 = a4 - 5 = 10 - 5 = 5

So, the first five terms are 25, 20, 15, 10, 5.

The two quantities to be inversely proportional to each other  when one quantity's value rises relative to another's decline or vice versa

What is Proportionality?

The two sequences of numbers are proportional or directly proportional if the ratio between the corresponding elements of two sequences of numbers, typically experimental data, is constant and is known as the coefficient of proportionality constant.

When one quantity's value increases relative to another's drop or vice versa, they are said to be inversely proportionate. It suggests that the two quantities have different fundamental behaviors. For instance, there is an inverse relationship between time and speed.

As you increase the speed, the time gets shorter. Other names for this type of percentage in this context include reciprocal proportion, inverse proportion, oscillating inversely, and inverse variation. The expression for X and Y, two variables having inverse proportions, is;

x 1/y or x y-1

As a result, when one quantity's value increases in comparison to another's decrease or vice versa, the two values are said to be inversely proportional to one another.

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Domain and Range of the given rational functions are:Given rational function f(x) = 3/(x-1)The denominator of f(x) cannot be zero.x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}

The range of f(x) is all real numbers except zero.Given rational function f(x) = (2x)/(x-4)The denominator of f(x) cannot be zero.x ≠ 4 Therefore the domain of f(x) is {x | x ≠ 4}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x+3)/(5x-5)The denominator of f(x) cannot be zero.5x - 5 ≠ 0x ≠ 1 Therefore the domain of f(x) is {x | x ≠ 1}The range of f(x) is all real numbers except 1/5.Given rational function f(x) = (2+x)/(2x)The denominator of f(x) cannot be zero.x ≠ 0 Therefore the domain of f(x) is {x | x ≠ 0}The range of f(x) is all real numbers except zero.Given rational function f(x) = (x^2+4x+3)/(x^2-9)For the denominator of f(x) to exist,x ≠ 3, -3

Therefore the domain of f(x) is {x | x ≠ 3, x ≠ -3}The range of f(x) is all real numbers except 1, -1. Function Domain Rangef(x) = 3/(x-1) {x | x ≠ 1} All real numbers except zerof(x) = (2x)/(x-4) {x | x ≠ 4} All real numbers except zerof(x) = (x+3)/(5x-5) {x | x ≠ 1} All real numbers except 1/5f(x) = (2+x)/(2x) {x | x ≠ 0} All real numbers except zerof(x) = (x^2+4x+3)/(x^2-9) {x | x ≠ 3, x ≠ -3} All real numbers except 1, -1

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Answer:

D)

Step-by-step explanation:

Answer:

k = (-55) / 8

k = (-3005) / 8

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 510(0.309016^2))) / 2)^2)) / 2)^2)) / 2

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 1469.59)))))^2)) / 2)

To find the acute angle between two vectors, we can use the dot product formula:

angle = arccos((a * b) / (||a|| * ||b||))

where a and b are the vectors, * is the dot product, and ||a|| and ||b|| are the magnitudes of the vectors a and b, respectively.

In this case, the dot product of a and b is (i - kj) * (i + j) = i^2 - kj * i + kj * i + kj^2 = 2i - k^2j

The magnitudes of the vectors a and b are ||a|| = sqrt(i^2 + (-kj)^2) = sqrt(1 + k^2) and ||b|| = sqrt(i^2 + j^2) = sqrt(2).

Substituting these values into the formula above, we get:

angle = arccos((2i - k^2j) / (sqrt(1 + k^2) * sqrt(2)))

Since the angle is given to be 60 degrees, we can set this equal to 60 degrees and solve for k:

60 = arccos((2i - k^2j) / (sqrt(1 + k^2) * sqrt(2)))

We can use the inverse cosine function to solve for k:

k = sqrt(1 / (cos(60)^2 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

Since cos(60) = 0.5, we can substitute this value in and solve for k:

k = sqrt(1 / (0.5^2 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

k = sqrt(1 / (0.25 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

k = sqrt(1 / (0.25 - (4i^2 / (1 + k^2) * 2)^2))

k = sqrt(1 / (0.25 - (16 / (1 + k^2))^2))

k = sqrt(1 / (0.25 - 256 / (1 + k^2)^2))

k = sqrt((1 + k^2)^2 / (256 - (1 + k^2)^2))

k = sqrt((1 + k^4) / (256 - 1 - 2k^2 - k^4))

k = sqrt((k^4 + 1) / (255 - 2k^2))

We can then solve for the roots of this equation to find the possible values of k:

k = sqrt((k^4 + 1) / (255 - 2k^2))

k^4 - (255 - 2k^2)k^2 + 1 = 0

This is a quartic equation and can be solved using the quartic formula:

k = sqrt((-b +- sqrt(b^2 - 4ac)) / 2a)

where a, b, and c are the coefficients of the polynomial. In this case, a = 1, b = -(255 - 2k^2), and c = 1.

Substituting these values into the quartic formula, we get:

k = sqrt((-(-(255 - 2k^2)) +- sqrt((-(255 - 2k^2))^2 - 4 * 1 * 1)) / 2 * 1)

k = sqrt((255 - 2k^2 +- sqrt((255 - 2k^2)^2 - 4)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(255^2 - 510k^2 + 4k^4)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(255^2 - 510k^2)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(65025 - 510k^2)) / 2)

Solving for the roots of this equation gives us the possible values of k:

k = (-255 + sqrt(65025 - 510k^2)) / 2

k = (-255 - sqrt(65025 - 510k^2)) / 2

The first equation gives us one possible value of k:

k = (-255 + sqrt(65025 - 510k^2)) / 2

Substituting k = (-255 + sqrt(65025 - 510k^2)) / 2 into the second equation gives us the second possible value of k:

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2

Simplifying this expression gives us the final possible value of k:

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2)^2)) / 2

Therefore, the possible values of k are:

k = (-255 + sqrt(65025 - 510k^2)) / 2

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2

solve for k in each

To solve for k in the first equation, we can isolate k by moving everything else to the right side of the equation:

k = (-255 + sqrt(65025 - 510k^2)) / 2

2k = -255 + sqrt(65025 - 510k^2)

2k + 255 = sqrt(65025 - 510k^2)

(2k + 255)^2 = 65025 - 510k^2

4k^2 + 1020k + 65025 = 65025 - 510k^2

4k^2 + 1530k + 65025 = 0

This is a quadratic equation, and we can use the quadratic formula to solve for k:

k = (-b +- sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the polynomial. In this case, a = 4, b = 1530, and c = 65025.

Substituting these values into the quadratic formula gives us:

k = (-1530 +- sqrt(1530^2 - 4 * 4 * 65025)) / 2 * 4

k = (-1530 +- sqrt(3080400 - 2601000)) / 8

k = (-1530 +- sqrt(477900)) / 8

k = (-1530 +- sqrt(222725)) / 8

k = (-1530 + 1475) / 8

k = (-55) / 8

k = (-1530 - 1475) / 8

k = (-3005) / 8

Therefore, the solutions to the first equation are:

k = (-55) / 8

k = (-3005) / 8

Answer:

-0.7071.

Step-by-step explanation:

The value of function sin 315 is -1/2.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Sin 315 degrees can be found by using the unit circle.

The unit circle is a circle with the radius of one centered at the origin of a coordinate plane.

Every point on the unit circle is a point that is one unit away from the origin.

The unit circle is used to help find the exact values of the trigonometric functions at specific angles.

The angle 315 degrees is in the fourth quadrant of the unit circle, so the x-coordinate is negative and the y-coordinate is negative.

Using the x-coordinate, we can calculate the sine to be -1/2.

Hence, the value of function sin 315 is -1/2.

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The quotient of the polynomials is 6x^2 - 2x + 5 with a remainder of -50.

To find the quotient of the polynomials  ÷ (2x + 5), you can use polynomial long division as follows:

       6x^2 - 2x + 5

 -----------------------

2x + 5 | 12x^3 + 26x^2 + 25

- (12x^3 + 30x^2)

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

-4x^2 + 25

- (-4x^2 - 10x)

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

35x + 25

- (35x + 75)

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

-50

Therefore, the quotient of the polynomials is 6x^2 - 2x + 5 with a remainder of -50.

-5x+2=-4(7)

-5x+2=-28

28+2=5x

30=5x

6=x