What is the measure of arc WYZ?

A)231

B)200

C)255

D)168

Answer:

40

Step-by-step explanation:

The clock loses 2 minutes every 1/5 hour. A whole hour, or 5/5 would be 10 minutes lost. For four hours, multiply that by 4, so 10x4=20.

The number of real solutions for each of the given equations is as follows:
Equation Number of Solutions
y = -3x2 + x + 12 2
y = 2x2 - 6x + 5 1
y = x2 + 7x - 11 2
y = -x2 - 8x - 16 2

An equation is a statement that expresses a mathematical relationship between two or more terms or variables. An equation is read as “equals” when two expressions are connected by an equal sign. Equations can be used to solve a variety of problems, from the most basic to the most complex. They are essential tools for understanding the world around us, from the motion of planets to the behavior of atoms.

For the equation y = -3x2 + x + 12, there are two real solutions. This can be determined by using the quadratic formula, which states that the number of real solutions for an equation of the form ax2 + bx + c = 0 is equal to the number of roots of the equation, and is given by:

Number of Real Solutions = (-b ±√(b2-4ac))/2a

In this case, a = -3, b = 1, and c = 12. Plugging these values into the equation, we get:

Number of Real Solutions = (-1 ±√(12-(-48)))/2(-3)

Number of Real Solutions = (-1 ±√(60))/(-6)

Number of Real Solutions = (-1 ±√60)/(-6)

Number of Real Solutions = (1 ±√60)/3

Number of Real Solutions = 2

For the equation y = 2x2 - 6x + 5, there is one real solution. This can be determined by the same method as above, with the values a = 2, b = -6, and c = 5. Plugging these values into the equation, we get:

Number of Real Solutions = (-(-6) ±√((-6)2-4(2)(5)))/2(2)

Number of Real Solutions = (6 ±√(36-40))/4

Number of Real Solutions = (6 ±√(-4))/4

Number of Real Solutions = (6 ±(2i))/4

Number of Real Solutions = 1

For the equation y = x2 + 7x - 11, there are two real solutions. This can be determined by the same method as above, with the values a = 1, b = 7, and c = -11. Plugging these values into the equation, we get:

Number of Real Solutions = (-7 ±√((7)2-4(1)(-11)))/2(1)

Number of Real Solutions = (-7 ±√(49+44))/2

Number of Real Solutions = (-7 ±√93)/2

Number of Real Solutions = (1 ±√93)/2

Number of Real Solutions = 2

For the equation y = -x2 - 8x - 16, there are two real solutions. This can be determined by the same method as above, with the values a = -1, b = -8, and c = -16. Plugging these values into the equation, we get:

Number of Real Solutions = (8 ±√((-8)2-4(-1)(-16)))/2(-1)

Number of Real Solutions = (8 ±√(64+64))/-2

Number of Real Solutions = (8 ±√128)/-2

Number of Real Solutions = (1 ±√128)/-2

Number of Real Solutions = 2

In conclusion, the number of real solutions for each of the given equations is as follows:

Equation Number of Solutions
y = -3x2 + x + 12 2
y = 2x2 - 6x + 5 1
y = x2 + 7x - 11 2
y = -x2 - 8x - 16 2
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Complete questions as follows-
Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16

For each of the preceding equations, the number of real solutions is as follows: Number of Solutions for Equation

y = \(-3x^2\) + x + 12 2

y = \(2x^2\) - 6x + 5 1

y = \(x^2\) + 7x - 11 2

y = -\(x^2\) - 8x - 16 2

A statement expressing a mathematical relationship among two or more terms or variables is called an equation. When two expressions are joined by an equal sign, the equation is read as "equals." The simplest to the most complicated problems can all be resolved using equations. They are crucial tools for comprehending everything around us, from planetary motion to atomic behaviour.

For the equation \(y=-3x^2+x+12\), there are two real solutions.

The number of real solutions for an equation of the type \(ax^2+bx+c=0\) is equal to the number of roots of the equation, according to the quadratic formula, which is given by:

Number of Real Solutions = (-b ±√(b2-4ac))/2a

In this case, a = -3, b = 1, and c = 12.

Number of Real Solutions = (-1 ±√(12-(-48)))/2(-3)

Number of Real Solutions = (-1 ±√(60))/(-6)

Number of Real Solutions = (-1 ±√60)/(-6)

Number of Real Solutions = (1 ±√60)/3

Number of Real Solutions = 2

For the equation \(y=2x^2-6x+5\), there is one real solution.

The same procedure as before can be used to determine this with the variables a = 2, b = -6, and c = 5.

Number of Real Solutions = (-(-6) ±√((-6)2-4(2)(5)))/2(2)

Number of Real Solutions = (6 ±√(36-40))/4

Number of Real Solutions = (6 ±√(-4))/4

Number of Real Solutions = (6 ±(2i))/4

Number of Real Solutions = 1

For the equation \(y=x^2+7x-11\), there are two real solutions.

The same procedure as before can be used to find this with the numbers a = 1, b = 7, and c = -11.

Number of Real Solutions = (-7 ±√((7)2-4(1)(-11)))/2(1)

Number of Real Solutions = (-7 ±√(49+44))/2

Number of Real Solutions = (-7 ±√93)/2

Number of Real Solutions = (1 ±√93)/2

Number of Real Solutions = 2

For the equation \(y=-x^2-8x-16\), there are two real solutions.

The same procedure as before can be used to find this with the numbers a = -1, b = -8, and c = -16.

Number of Real Solutions = (8 ±√((-8)2-4(-1)(-16)))/2(-1)

Number of Real Solutions = (8 ±√(64+64))/-2

Number of Real Solutions = (8 ±√128)/-2

Number of Real Solutions = (1 ±√128)/-2

Number of Real Solutions = 2

In conclusion, there are exactly as many genuine solutions to each of the following equations:

Equation Number of Solutions

y = \(-3x^2\) + x + 12 2

y = \(2x^2\) - 6x + 5 1

y = \(x^2\) + 7x - 11 2

y = -\(x^2\) - 8x - 16 2

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Complete questions as follows-

Determine the number of real solutions for each of the given equations. Equation Number of Solutions \(y = -3x^2 + x + 12 y = 2x^2 - 6x + 5 y = x^2 + 7x - 11 y = -x^2 - 8x - 16\)

Answer:

72/7

Step-by-step explanation:

Answer

{3,1}

Explaination

3 +4=7[1]    x = -4y + 7

// Plug this in for variable  x  in equation [2]

  [2]    4•(-4y+7) - 3y = 9

  [2]     - 19y = -19

// Solve equation [2] for the variable  y

  [2]    19y = 19

  [2]    y = 1

// By now we know this much :

   x = -4y+7

   y = 1

// Use the  y  value to solve for  x

   x = -4(1)+7 = 3

Solution :

{x,y} = {3,1}

Step-by-step explanation:

the value is -5 hope that is good

Answer:

-2.46

Step-by-step explanation:

151/24=6.29

6.29-8.75=-2.46

Answer:

-2.45833333333

Step-by-step explanation:

151 divided by 24= 6.29166666667

6.29166666667-8.75=-2.45833333333

2dp=2.46

Answer:

C. y<5/3x-3

Step-by-step explanation:

First, treat this problem as if you were graphing a normal slope intercept form equation, y=mx+b, where m=slope and b=the y-intercept. To find the slope of the line, find two points on the graph and count the number of units up/down over the number of units right/left. You could also use the slope formula, (y2-y1)/(x2-x1).

Once you have the slope, which, in this equation, is 5/3, find b, the y-intercept. You can find it by seeing where the line intersects with the y-axis (the vertical axis). In this case, b=(-3).

If this was a normal line, the equation would be y=5/3x-3. However, it's an inequality, and we're not quite done yet. We can eliminate answer B.

Look closely at the line. If it's dotted, the symbol is either a less-than/greater-than symbol (< or >). That means the answer can be any number up to that OR any number above that, but not that exact number. If it's a solid line, that means it's either a less-than or equal-to/greater-than or equal-to symbol, which looks like < and >. That means the answer can be that number and any number up to it OR that number and any number above it. This graph shows a dotted line, so we can eliminate answer A.

Now, one of the hardest parts, though it's really quite easy. If an equation is less-than or less-than or equal-to, the shaded region (all the possibilities) would be below the line. This is easy to tell with a horizontal line, easy enough to tell with a diagonal line, and a little difficult with a vertical line. With a vertical line, think of a number line with a single point on it. Anything to the left of the point is less than the point, so you would shade to the left of the line. If an equation is greater-than or greater-than or equal-to, the shaded region would be above the line, because it's the opposite of less-than or less-than or equal-to. Because the shaded region is below the line, the symbol to use in this equation is < because the answer is unknown but definitely below that line, but not on the line, because it's not a solid line, which means the answer is included.

The inequality of this line is y<5/3x-3, which is listed as answer C. Hope that helped! Comment if it didn't make sense.

a) The rate of change of temperature at the point is -1600/√14 °C/m.

b) The direction does the temperature increase fastest at P is by the gradient of T.

c) The maximum rate of increase of temperature at point P is 4200e⁻¹⁴ °C/m.

(a) The rate of change of temperature at point P in the direction towards the point (5, -3, 4) can be found using the directional derivative. The directional derivative is a measure of the rate of change of a function in the direction of a given vector.

To find the directional derivative of T at point P in the direction of the vector v = <5-2, -3-(-1), 4-3> = <3, -2, 1>, we need to take the dot product of the gradient of T at point P with the unit vector in the direction of v:

Evaluating the gradient at P, we get:

∇T(P) = <-1200e⁻¹⁴ , 3600e⁻¹⁴ , -12600e⁻¹⁴ >

The unit vector in the direction of v is:

v/|v| = <3/√14, -2/√14, 1/√14>

So, the directional derivative of T at point P in the direction of v is:

D_v T(P) = ∇T(P) · (v/|v|) = <-1200e⁻¹⁴ , 3600e⁻¹⁴ , -12600e⁻¹⁴ > · <3/√14, -2/√14, 1/√14>

= -1600/√14 °C/m

Therefore, the rate of change of temperature at point P in the direction towards the point (5, -3, 4) is -1600/√14 °C/m.

(b) The temperature increases fastest at point P in the direction of the gradient of T at P. The gradient of T at P gives the direction of steepest ascent of the temperature function at point P.

So, the direction in which the temperature increases fastest at P is given by the gradient of T at P, which is:

∇T(P) = <-1200e⁻¹⁴ , 3600e⁻¹⁴ , -12600e⁻¹⁴

(c) The maximum rate of increase of temperature at point P is given by the magnitude of the gradient of T at P.

So, the maximum rate of increase of temperature at point P is:

|∇T(P)| = √((-1200e⁻¹⁴ )² + (3600e⁻¹⁴ )² + (-12600e⁻¹⁴ )²)

= 4200e^(-14) °C/m

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Answer:

degree of 8

Step-by-step explanation:

Given that f(x) is a polynomial of degree 3. The cubic function (3rd degree) can be expressed as:

\(\displaystyle{f(x) = ax^3 + bx^2 + cx + d}\)

While the g(x) is a polynomial of degree 5. It can be expressed as:

\(\displaystyle{g(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f}\)

And the problem gives us to find "\(\displaystyle{2f(x)4g(x)}\)". First, evaluate each terms:

2f(x)

2f(x) can be evaluated by multiplying 2 in every terms of function f(x):

\(\displaystyle{2f(x) = 2(ax^3+bx^2+cx+d)}\\\\\displaystyle{2f(x) = 2ax^3+2bx^2+2cx+2d}\)

4g(x)

Similar to above one except we change to multiply from f(x) to g(x) by 4:

\(\displaystyle{4g(x) = 4(ax^5 + bx^4 + cx^3 + dx^2 + ex + f)}\\\\\displaystyle{4g(x) = 4ax^5 + 4bx^4 + 4cx^3 + 4dx^2 + 4ex + 4f}\)

Since we are looking for the degree of polynomial, it's not necessary to bring all terms to multiply 2f(x) with 4g(x). We'll be multiplying both functions with the highest degree of individual polynomial.

The highest degree of 2f(x) is 3 which is term of \(\displaystyle{2ax^3}\)

The highest degree of 4g(x) is 5 which is term of \(\displaystyle{4ax^5}\)

Since we are looking for the degree, we only have to evaluate the x-term with exponent:

\(\displaystyle{x^3 \cdot x^5}\)

Apply the law of exponent - add both exponents together:

\(\displaystyle{x^8}\)

Therefore, we can conclude that the degree of polynomial is 7.

=========

In short explanation, it's not necessary to do everything. Since we are looking for degree, we only take \(\displaystyle{x^3}\) which polynomial of degree 3 and \(\displaystyle{x^5}\) which is degree of 5 then multiply both terms together which result in \(\displaystyle{x^8}\) via law of exponent.

Evaluating 2f(x)4g(x) will result with same degree anyways so it's not necessary to evaluate but in case if you want to see what is 2f(x)4g(x) then I've calculated it above.

Answer:

gsuhsuhsjsuueue

Step-by-step explanation:

hsuuehe heg

Answer:

\(tan \: x = \frac{24}{7} \)

Based on the information given, it should be noted that the equivalent equation will be 0.5R.

From the information given, it was stated that we should calculate 20% of R added to 30% of R.

This will be:

= (20% × R) + (30% × R)

= 0.2R + 0.3R

= 0.5R

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The second derivative of the parametrically defined curve represented by the equations \(x(t) = -e^{(-6t)\) and \(y(t) = e^{(2t)\) is:

\(d^2x/dt^2 = -36e^{(-6t)\\d^2y/dt^2 = 4e^{(2t)\)

To find the second derivative of the parametrically defined curve represented by the equations \(x(t) = -e^{(-6t)\) and \(y(t) = e^{(2t)\), we need to differentiate each component twice with respect to t.

First, let's find the first derivative of x(t):

dx/dt = d/dt \((-e^{(-6t)})\)

To differentiate \(-e^{(-6t)\), we use the chain rule:

dx/dt = (-1)(d/dt)(\(e^{(-6t)\)) = -(-6\(e^{(-6t)\)) = 6\(e^{(-6t)\)

Now, let's find the second derivative of x(t):

d²x/dt² = d/dt(dx/dt) = d/dt(6\(e^{(-6t)\))

Using the chain rule again:

d²x/dt² = 6(d/dt)(\(e^{(-6t)\)) = 6(-6\(e^{(-6t)\)) = -36\(e^{(-6t)\)

Next, let's find the first derivative of y(t):

dy/dt = d/dt(\(e^{(2t)\)) = 2\(e^{(2t)\)

Now, let's find the second derivative of y(t):

d²y/dt² = d/dt(dy/dt) = d/dt(2\(e^{(2t)\)) = 4\(e^{(2t)\)

Therefore, the second derivative of the parametrically defined curve represented by the equations x(t) = \(-e^{(-6t)\) and y(t) = \(e^{(2t)\) is:

\(d^2x/dt^2 = -36e^{(-6t)\\d^2y/dt^2 = 4e^{(2t)\)

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Complete Question:

Determine The Second Derivative Of The Parametrically Defined Curve Represented By The Equations \(X(T)= -e^{-6t\) And \(Y(T)=e^{2t.\)

The simplest form of a fraction is when the numerator (top number) and denominator (bottom number) have no common factors.

A fraction is a mathematical expression that represents a part of a whole, where a numerator is divided by a denominator. To simplify a fraction, we must divide both the numerator and the denominator by the same number until we cannot divide any further. To simplify a fraction, you must divide both the numerator and denominator by their greatest common factor (GCF).

For example, let's simplify the fraction 24/36. The GCF of 24 and 36 is 12. So, dividing both numbers by 12 will give us the simplified fraction 2/3.

24 ÷ 12 = 2

36 ÷ 12 = 3

Therefore, the simplified fraction of 24/36 is 2/3.

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Results of the expressions in the integer subtraction is 9

Let's review each expression step by step:

4 - 5: This is a simple subtraction problem that yields a result of -1.

4 + (-5): We can add the opposite of 5 to 4 by changing the sign of 5 to -5 and then adding normally. This yields a result of -1.

(-4) - (-5): We can subtract a negative number by adding its opposite. Therefore, we can add 5 to -4 to get a result of 1.

(-4) + 5: We can add these two numbers normally to get a result of 1.

(-4) - 5: We can add the opposite of 5 to -4 by changing the sign of 5 to -5 and then adding normally. This yields a result of -9.

(-4) + (-5): We can add these two numbers normally by adding their absolute values and then giving the result a negative sign. This yields a result of -9.

4 - (-5): We can subtract a negative number by adding its opposite. Therefore, we can add 5 to 4 to get a result of 9.

4 + 5: We can add these two numbers normally to get a result of 9.

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The normal curve, also known as the Gaussian distribution or the bell curve, is a continuous probability distribution that is symmetrical around its mean.

The normal curve has several properties that make it particularly useful in modeling real-world phenomena. Firstly, it is unimodal, meaning it has a single peak. Secondly, it is symmetric, meaning that the curve is identical on both sides of the mean. Thirdly, it is defined by two parameters, the mean and standard deviation, which determine the location and spread of the curve.

Finally, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations, making it a useful tool for understanding and analyzing large datasets.

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The sum of cubes identity states that a^3 + b^3 = (a+b)(a^2 - ab + b^2). To find the factors of 8x^6 + 27y^3, we can apply this identity to the expression by identifying a and b:

What is the identity of the sum of cubes?

What Does the Algebraic Sum of Cubes Formula Mean? One of the key algebraic identities is the sum of cubes formula. Its symbol is written as a3 + b3 and is interpreted as a cube plus a cube. A3 + b3 = (a + b) (a2 - ab + b2) is how the sum of cubes formula (a3 + b3) is written.

8x^6 + 27y^3 = (2x^2)^3 + (3y)^3

We can then apply the identity to get:

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

This gives us the factors of 8x^6 + 27y^3 as (2x^2 + 3y)(4x^4 - 6x^2y^2 + 9y^2).

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Answer:

6.43% change

Step-by-step explanation:

Have a good one

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

The percent change from week 1 to week 3 rounded to the nearest tenth of a percent is 6.4%.

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

First week:

Time taken to run 100 yards = 14 seconds

Third week:

Time taken to run 100 yards = 13.1 seconds

The percentage change in the time from the first week to the third week:

= [(Time taken at the first week - Time taken at the third week) / Time taken at the first week ] x 100

= [(14 - 13.1) / 14] x 100

= 0.9/14 x 100

= 6.4%

This means that there is 6.4% from the first week to the third week.

Thus,

The percent change from week 1 to week 3 rounded to the nearest tenth of a percent is 6.4%.

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The monthly payments for the same loan would be approximately $694.12.

To calculate the annual payment required to pay off a four-year, $27,000 loan at an interest rate of 9 percent EAR, we can use the formula for the present value of an ordinary annuity:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where:

PV = Loan amount = $27,000

PMT = Annual payment

r = Interest rate per period = 9% = 0.09

n = Number of periods = 4

Plugging in these values into the formula, we can solve for PMT:

$27,000 = PMT * (1 - (1 + 0.09)^(-4)) / 0.09

Simplifying the equation, we have:

$27,000 = PMT * (1 - 0.708222) / 0.09

$27,000 = PMT * 0.291778 / 0.09

PMT = $27,000 * 0.09 / 0.291778

PMT ≈ $8,329.40 (annual payment)

To calculate the monthly payments for the same loan, we can divide the annual payment by 12:

Monthly payment = $8,329.40 / 12

Monthly payment ≈ $694.12

Therefore, the monthly payments for the same loan would be approximately $694.12.

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Answer:

width is 33

Step-by-step explanation:

width (b) =?

length(l)=3

perimeter (p)=?

now,

perimeter = 2(l+b)

or,72= 2(3+ b)

or,72/2= 3+b

or,36= 3+b

or,36-3= b

or,33= b

therefore width is 33

Answer: C is the right answer , which matches the graph

Answer:

The desired point is thus (-1/2, -5).

Step-by-step explanation:

The x-component of this directed line segment is 2 - (-8), or 10, and the y-component is -7 - (1), or -8.  This segment is in Quadrant II, since the x-component is positive and the y-component is negative.

The point of interest is (3/4) of the way in the positive x-direction from x = -8.  We can express this symbolically as -8 + (3/4)(10), or -8 + 7.5, or -1/2.

The point of interest is 3/4 of the way in the negative y direction from 1, or:

1 + (3/4)(-8), or 1 - 6, or -5.

The desired point is thus (-1/2, -5).

Answer:

2:5

Step-by-step explanation:

B: 4

F: 10

Ratio:

4:10

Simplify:

2:5

Hope this helps!

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Ratio of basketballs to footballs is 2:5

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that There are 4 basketballs and there are 10 footballs.

we need to find the ratio of basketballs to footballs

As we know ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Ratio can also be written as fraction form.

Basketballs = 4

Footballs = 10

Ratio of basket balls to footballs is 4/10

As 4 and 10 are multiples of 2 we divide numerator and denominator by 2.

The ratio of basketballs to footballs is 2/5

Hence, ratio of basketballs to footballs is 2:5

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Answer:

B=45

Step-by-step explanation:

let the supplamentary angle of <A is <d

180-A=d

180-135=d

45=d

90+d+B=180

90+45+B=180

135+B=180

B=180-135

B=45

Answer:

The random process described is a symmetrical random walk.

A symmetrical random walk is a mathematical model that represents a series of steps taken in either a forward (+1) or backward (-1) direction, each with equal probability. Starting from point zero, the process involves taking a certain number of steps. The outcome at each step is independent of previous steps, making it a stochastic process. The key characteristic of a symmetrical random walk is that, on average, the process remains centered around its starting point. This means that over a large number of steps, the expected displacement from the starting point approaches zero.

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Answer:

216, 343

Step-by-step explanation:

1, 8, 27, 64, 125 ← are perfect cubes , that is

1³ = 1 × 1 × 1 = 1

2³ = 2 × 2 × 2 = 8

3³ = 3 × 3 × 3 = 27

4³ = 4 × 4 × 4 = 64

5³ = 5 × 5 × 5 = 125

continuing the pattern for 6 and 7

6³ = 6 × 6 × 6 = 216

7³ = 7 × 7 × 7 = 343

thus the next 2 terms in the sequence are 216, 343

Answer: height = 1.91 m

Step-by-step explanation: Using the formula

V=πr2h

Solving for h

h=V

πr2=37.5

π·2.52≈1.90986m

Answer:

10

Step-by-step explanation:

nCr = 5!/(3! × (5 - 3)!)

= 10

123/ 124/ 125/ 134/ 135/ 145/ 234/ 235/ 245/ 345

The formula for combinations is generally n! / (r! (n -- r)!), where n is the total number of possibilities to start and r is the number of selections made. In our example, we have 52 cards; therefore, n = 52.

Answer: get 2 more frames

Step-by-step explanation:

Answer:

quince

Step-by-step explanation:

si el cartón de huevos es la unidad, y son 30 huevos,

responde:

¿cuántos huevos hay en un medio cartón? ​

translation:

if the egg carton is the unit, and it is 30 eggs,

answer:

how many eggs are in a half carton?

30 divided by 2

30

-----   = 15

 2

The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

To learn more about : radians

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