What value is equivalent to 32 · 43?

Answer:

33%

Step-by-step explanation:

- The area of the inner white circle is π4² = 16π

- The area of the blue "band" is π7² - π4² = 33π

- The total area is π10² = 100π

The ratio of the blue band and the total area is 33π/100π ×100% = 33%

Answer:

                      x=20

Step-by-step explanation:  your welcome      

                             2 x + 140 = 180

                                    -140 l -140

                                    2 x   l 40

                                    2x    l 2x

                                     x = 20

9514 1404 393

Answer:

Step-by-step explanation:

The speed is the ratio of the change in distance to the corresponding change in time.

Vehicle A moves from a position of 12 m to one of 28 m in 50 seconds, so its speed is ...

  A = (28 -12)/50 m/s = 16/50 m/s = 0.32 m/s

Vehicle B moves from 0 to 28 m in 50 seconds, so its speed is ...

  B = (28 m)/(50 s) = 0.56 m/s

The first one is r=5

The second one is m=175

Answer:

1. r=5  2.m=175

HOPE THIS HELPS :)

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

7r+10=45

Step 2: Subtract 10 from both sides.

7r+10−10=45−10

7r=35

Step 3: Divide both sides by 7.

7r /7 = 35 /7

r=5

Step 1: Simplify both sides of the equation.

m /5 −9=26

1 /5 m+−9=26

1 /5 m−9=26

Step 2: Add 9 to both sides.

1 /5 m−9+9=26+9

1 /5 m=35

Step 3: Multiply both sides by 5.

5*( 1 /5 m)=(5)*(35)

m=175

To find the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives the probability that a standard normal random variable is less than or equal to a given value. In this case, we need to find the probability that z is less than or equal to 2.67 and subtract the probability that z is less than or equal to -0.15.

Using a standard normal distribution table or a statistical calculator, we can find the corresponding probabilities:

P(z < 2.67) ≈ 0.9960

P(z < -0.15) ≈ 0.4404

To find the probability of the interval (-0.15 < z < 2.67), we subtract the probability of z < -0.15 from the probability of z < 2.67:

P(-0.15 < z < 2.67) ≈ P(z < 2.67) - P(z < -0.15)

≈ 0.9960 - 0.4404

≈ 0.5556

Therefore, the probability of the interval (-0.15 < z < 2.67) in a standard normal distribution is approximately 0.5556.

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Answer:

Hey! I hope this helps. I used ratio, I divided $28.50 by 2 to find out how much she worked for in an hour then I multiplied by 15.

The critical point of the function f(x, y) = x^2 - 5xy + 6y^2 + 8x - 8y + 8 is (4/3, 2/3).

To find the critical points of the function f(x, y) = x^2 - 5xy + 6y^2 + 8x - 8y + 8, we need to find the points where the partial derivatives with respect to x and y are both equal to zero.

Taking the partial derivative with respect to x, we get:

∂f/∂x = 2x - 5y + 8

Setting ∂f/∂x = 0 and solving for x, we have:

2x - 5y + 8 = 0

Taking the partial derivative with respect to y, we get:

∂f/∂y = -5x + 12y - 8

Setting ∂f/∂y = 0 and solving for y, we have:

-5x + 12y - 8 = 0

Now we have a system of two equations:

2x - 5y + 8 = 0

-5x + 12y - 8 = 0

Solvig this system of equations, we find that there is a unique solution:

x = 4/3

y = 2/3

Therefore, the critical point is (4/3, 2/3).

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Answer:

Step-by-step explanation:

si...  yono  em usho de cmopu preo sloo estoy usand una jjssjsjsj jsjsj  c

Answer + Explanation:

Since you just flip the fraction if you have a negative power, you get

1.) 6 to the power of -1 = 1/6

2.) 6 to the power of -2 = 1/36

3.) 6 to the power of -3 = 1/216

4.) 6 to the power of -4 = 1/1296

Answer: P=2300 (1- 0.05)^x

Step-by-step explanation:

Answer:

Graph the function.

Step-by-step explanation:

The volume of the cylinder after the prism is cut out is 593 cm^3.

To calculate the volume of the cylinder after the prism is cut out, we need to first determine the volume of the prism that will be removed. This can be found by multiplying the length, width, and height of the prism. Once we have this value, we can subtract it from the original volume of the cylinder.

For example, if the cylinder has a radius of 5 cm and a height of 10 cm, and the prism to be removed has a length of 6 cm, a width of 4 cm, and a height of 8 cm, we can calculate the volume of the prism as follows:

Volume of prism = length x width x height
Volume of prism = 6 cm x 4 cm x 8 cm
Volume of prism = 192 cm^3

To find the volume of the cylinder after the prism is cut out, we simply subtract the volume of the prism from the original volume of the cylinder:

Volume of cylinder = pi x radius^2 x height
Volume of cylinder = 3.14 x 5^2 x 10
Volume of cylinder = 785 cm^3

Volume of cylinder after prism is cut out = 785 cm^3 - 192 cm^3
Volume of cylinder after prism is cut out = 593 cm^3

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Numerical integration is a numerical analysis technique for calculating the approximate numerical value of a definite integral.

In general, integrals can be either indefinite integrals or definite integrals. A definite integral is an integral with limits of integration, while an indefinite integral is an integral without limits of integration.A numerical integration formula is an algorithm that calculates the approximate numerical value of a definite integral. Numerical integration is based on the approximation of the integrand using a numerical quadrature formula.

The numerical quadrature formula is used to approximate the value of the integral by breaking it up into small parts and summing the parts together.Equations for the calculation of integration by trapezoidal rule (1/2)h[f(x0)+2(f(x1)+...+f(xn-1))+f(xn)] where h= Δx [the space between the values], and x0, x1, x2...xn are the coordinates of the abscissas of the nodes. The basic principle is to replace the integral by a simple sum that can be calculated numerically. This is done by partitioning the interval of integration into subintervals, approximating the integrand on each subinterval by an interpolating polynomial, and then evaluating the integral of each polynomial.

Based on the given table of unequally spaced data, we are to calculate the approximate numerical value of the definite integral. To do this, we will use the integration formula as given by the trapezoidal rule which is 1/2 h[f(x0)+2(f(x1)+...+f(xn-1))+f(xn)] where h = Δx [the space between the values], and x0, x1, x2...xn are the coordinates of the abscissas of the nodes.  The table can be represented as follows:x            0.1 0.3 0.5 0.7 0.95 1.2f(x)      1 0.9048 0.7408 0.6065 0.4966 0.3867 0.3012Let Δx = 0.1 + 0.2 + 0.2 + 0.25 + 0.25 = 1, and n = 5Substituting into the integration formula, we have; 1/2[1(1)+2(0.9048+0.7408+0.6065+0.4966)+0.3867]1/2[1 + 2.3037+ 1.5136+ 1.1932 + 0.3867]1/2[6.3972]= 3.1986 (to 4 decimal places)

Therefore, the approximate numerical value of the definite integral is 3.1986.

The approximate numerical value of a definite integral can be calculated using numerical integration formulas such as the trapezoidal rule. The trapezoidal rule can be used to calculate the approximate numerical value of a definite integral of an unequally spaced table of data.

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The correct answer is (a) \(y^2 - x^2 = x + 7y\) for the polar equation.

Polar coordinates are a two-dimensional coordinate system that uses an angle and a radius to designate a point in the plane. A polar equation is a mathematical equation that expresses a curve in terms of these coordinates. Circles, ellipses, and spirals are examples of forms with radial symmetry that are frequently described using polar equations. They are frequently employed to simulate physical events that have rotational or circular symmetry in engineering, physics, and other disciplines. Computer programmes and graphing calculators both use polar equations to represent two-dimensional curves.

To convert the polar equation\(r = sinθ\) into a cartesian equation, we use the following identities:

\(x = r cosθy = r sinθ\)

Substituting these into the given polar equation, we get:

\(x = sinθ cosθy = sinθ sinθ = sin^2θ\)
Now we eliminate θ by using the identity:

\(sin^2θ + cos^2θ = 1\)

Rearranging and substituting, we get:

\(x^2 + y^2 = x(sinθ cosθ) + y(sin^2θ)\\x^2 + y^2 = x(2sinθ cosθ) + y(sin^2θ + cos^2θ)\\x^2 + y^2 = 2xy + y\)

Therefore, the correct answer is (a)\(y^2 - x^2 = x + 7y\).

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If the class collected $660 from ticket sales, the drama class sold a total of 90 student tickets. Let's assume that the number of adult tickets sold is x.

Since the drama class sold 25 more student tickets than adult tickets, the number of student tickets sold can be expressed as (x + 25).

The total revenue from ticket sales is given as $660. Adult tickets cost $6 each and student tickets cost $3 each. Therefore, the total revenue can be expressed as 6x + 3(x + 25).

Setting up the equation: 6x + 3(x + 25) = 660.

Simplifying the equation: 6x + 3x + 75 = 660.

Combining like terms: 9x + 75 = 660.

Subtracting 75 from both sides: 9x = 585.

Dividing both sides by 9: x = 65.

Therefore, the drama class sold 65 adult tickets.

To find the number of student tickets sold, we substitute the value of x into the expression (x + 25): (65 + 25) = 90.

Thus, the drama class sold 90 student tickets.

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The quadratic equation x² - 9 has two real roots.

The quadratic equation x² + 3 · x - 10 has two real roots.

The cubic equation x³ - 5 · x² + 10 · x - 8 has two complex conjugate roots and a real root.

According to complex conjugate root theorem, if a quadratic equation has a root of the form a + i b, where a, b are real numbers, then the other root is  a - i b. In addition, roots of quadratic equations of the form a · x² + b · x + c, where a, b, c are real coefficients. By quadratic formula, the equation has complex conjugate roots if:

b² + 4 · a · c < 0

Now we proceed to check each quadratic equations:

Case 1: (a = 1, b = 0, c = - 9)

D = 0² - 4 · 1 · (- 9)

D = 36

The equation has no complex conjugate roots.

Case 2: (a = 1, b = 3, c = - 10)

D = 3² - 4 · 1 · (- 10)

D = 9 + 40

D = 49

The equation has no complex conjugate roots.

The latter case is represented by a cubic equation, whose standard form is a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients. The equation has a real root and two complex conjugate roots if the following condition is met:

18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² < 0

Now we proceed to find the nature of the roots of the polynomial: (a = 1, b = - 5, c = 10, d = - 8)

D = 18 · 1 · (- 5) · 10 · (- 8) - 4 · (- 5)³ · (- 8) + (- 5)² · 10² - 4 · 1 · 10³ - 27 · 1² · (- 8)²

D = - 28

The equation has a real root and two complex conjugate roots.

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ANSWER

3 rotten apples

EXPLANATION

We know that Amber and Jacob have the same fraction of rotten apples in their bags.

Jacob's bag has 4 apples in total, of which 1 is rotten. Thus, the fraction of rotten apples he has is,

Amber has the same fraction in her bag, but she has a total of 4 apples. If n is the number of rotten apples in Amber's bag,

We have to find n so that n/12 equals 1/4.

Multiply both sides by 12,

So, Amber's bag has exactly 3 rotten apples

Yes , rotating is  a congruence transformation.

What is a congruence transformation?

A transformation that changes the position of the figure while not dynamical its size or form is termed a congruity transformation.

Main body:

A congruity transformation is that the movement or locating of a form specified it produces a form that is congruent to the initial.

Translations, reflections, and rotations are the three types of congruence transformations. That is, the pre-image and the image are always congruent.

Hence ,rotating is  a congruence transformation.

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An equation for the translation of y = 6/x that has the asymptotes x =4 and y = 5 is y = 6/(x - 4) + 5.

Given,

Vertical asymptotes x = 4

Horizontal asymptotes y = 5

The graph of y = 6/x has vertical asymptote x = 0 (the y-axis) and horizontal asymptote y = 0 (the x-axis).

An asymptote is a line to which the curve converges.

When the resulting independent variable is zero, the vertical asymptote occurs.

The values of the dependent variable coincide with the horizontal asymptote when the independent variable diverges to plus or minus infinity.

The translation formula is y = 6/(x - 4) + 5

Therefore, the equation is y = 6/(x - 4) + 5.

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Answer:

x = 8

Step-by-step explanation:

x + 5 = 2x - 3

-x      = -x        subtract x from both sides.

   5 = 1x - 3

   +3 =      +3        add 3 to both sides.

8 = 1x

x = 8

Answer:

Maude

Step-by-step explanation:

Maude's collection has 5 heavy metal out of a total of 8 albums

Claude's collection has 7 heavy metal out of a total of 12 albums

if you divide 5 by 8 you get .625, which is the same as 62.5%

if you divide 7 by 12 you get .583, which is the same as 58.3%

62.5% is greater than 58.3%

Answer: Grandma

Step-by-step explanation:

His grandmother because the chance a heavy metal album comes on is 5 times out of 8 while his grandfather is 7 times out of 12. For a better representation grandma is 15/24 while grandpa is 14/24.

Answer:

x ≥ 2

Step-by-step explanation:

Given expression:

         –4x + 7 ≤ –1

Now let us solve this problem;

           –4x + 7 ≤ –1

  Add (-7) to both sides of the expression;

           –4x + 7 + (-7) ≤ –1 + (-7)

              -4x  ≤ - 8

Now multiply both sides by \(-\frac{1}{4}\) this will change the inequality sign

             \(-\frac{1}{4}\) x  -4x  ≤ - 8 x  \(-\frac{1}{4}\)

                   x ≥ 2

For all values of x greater than or equal to 2, the inequality is true.

The solution to the inverse equation is  = -7

from the question, we have the following parameters that can be used in our computation:

f(x) = 6(x + 7) − 7

So, we have

f(x) = 6x + 35

For the inverse function, we have

x = 6y + 35

So, we have

y = (x - 35)/6

When the function and the inverse are equal, we have

6(x + 7) − 7 = (x - 35)/6

When solved for x, we have

x = -7

Hence, the value of x is -7

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Question

Solve f(x) = f^-1}(x). enter all the solutions, separated by commas.

f(x) = 6(x + 7) − 7

Answer:

The 3rd answer

Step-by-step explanation:

Step 1: Rewrite the square root

(8^1/3)^x

Step 2: Multiply exponents

8^(x/3)

Remember when exponenting an exponent, you multiply the 2 exponents together.

Answer: The third choice, 8^(x/3)

Step-by-step explanation:

If you were to right the cube root of 8 in fractional exponent form, it would be 8^(1/3).

Now, we have (8)^1/3*x

Then we multiply 1/3 with x to get:

8^(x/3)

Hope this helps

To determine the number of sewing machines needed if operations ran two 8-hour shifts per day, we can follow the steps mentioned below.

To calculate-
1. Calculate the total number of hours worked per week:
  2 shifts per day * 8 hours per shift * 5 days per week = 80 hours per week.

2. Determine the number of sewing machines needed per hour:
  This depends on the production capacity of each sewing machine. Let's say each machine can produce 10 units per hour.

3. Divide the total number of hours worked per week by the production capacity per hour:
  80 hours per week / 10 units per hour = 8 sewing machines needed.

Therefore, if operations ran two 8-hour shifts per day, 5 days per week, approximately 8 sewing machines would be needed. Remember to round the answer to the nearest whole number, as indicated in the question.

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Answer:

at 6 minutes and 8.25 minutes

Step-by-step explanation:

When the time reaches 6 minutes, the line touches 35mph. Same goes for 8.25 minutes.

Answer:

3/13 which is 0.23 as a decimal

Step-by-step explanation:

Given

Solving, step-by-step

Answer:

\(1\)

Step-by-step explanation:

The coefficient of a polynomial expression is the coefficient of the term with the highest exponent. We can see that the term with the highest exponent is \(x^3\). So, the leading coefficient is its coefficient which is \(1\).

Note that any number can be written as the product of that number and \(1\) as multiplying by \(1\) does not fundamentally change that number. In our given example, \(x^3\) is equivalent to \(1x^3\).

Answer:

6 or -6

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

Step 2: Take square root of both sides.

Therefore, the answer is 6 or -6.