A regular polygon has an interior angle of 172º.
Find the number of sides of this polygon.

Answer:

171 > 117

Step-by-step explanation:

171 is greater than 117 meaning the alligator is eating the bigger number, 171.

Answer:

If the vertical line intersects the graph in at most one point, then the given graph represents a function. If the vertical line intersects the graph in more than one point, then the given graph does not represent a function.

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Step-by-step explanation:

Answer:

Step-by-step explanation:

For a graph to be a function, there must not be more than one element in the range for each element of the domain.

If x represents the doman, and y represents the range (as usual, in graphing) then each value on the the x-axis should not have more than one point in the graph on it, directly above it, or directly below it. Like if you had a point (5, 7) and also had point (5, -7), that is not a function. The x, 5, has more than one y-value  paired with it.

Visually, any vertical line through the graph should not intersect the graph at more than one point. If it does, then the graph is not a function.

This is called the vertical line test.

I have attached a graphic.

Answer:

42?

Step-by-step explanation:

Answer:11

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

The boundary lines are drawn by considering the relation as an equation.

The first "equation" describes a line with slope -8/3 through the y-intercept point (0, 6). Another point on that line would be 8 units down and 3 units right of (0, 6), at (3, -2). Both inequalities include the "or equal to" case, so both boundary lines are solid lines.

Since we have y ≥ ( ), the shading is above the line.

__

The second "equation" describes a line with a slope of 5/3 through the y-intercept point (0, -7). Another point would be 5 units up and 3 units right of (0, -7), at (3, -2). Since we have y ≤ ( ), the shading is below the line.

That is, the solution region is in the right-hand quadrant of the X where the lines cross. It includes the lines themselves.

Answer:

452.16 m³

Step-by-step explanation:

Given

Formula

Solving

By fraction method, 55/16 pounds of rice Belle purchased.

In math, what is a fraction?

Part of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.

                                 Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.

  = 2 3/4 * 5/4

   = 5/4 * 2 + 5/4 *  3/4

   = 5/2 + 5/4 * 3/4

  = 5/2 + 15/ 4 * 4

  = 5/2 + 15/16

  common denominator and write the numerators above common denominator   =   5 *8/16 + 15/16

         = 40/16 + 15/16

         = 40 + 15/16

          = 55/16

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Answer:

1. Yes 2. No 3. Yes 4. No

Step-by-step explanation: 1 is a function because none of the x values repeat, 2 isn't a function because in the x coordinates, -2 repeats, 3 is a function because if you were to draw a (vertical) line through each point, none of them have two points on one line, 4 is a function because none of the x coordinates point to more than one y coordinate

The height of the stand is 15 inches

The formula for determining the volume of a right triangular pyramid is expressed as;

V = 1/3 BA × h

Given that the parameters are;

To determine the base area, we have;

Base area = 1/2  × 81

Base area = 40. 5 in²

Substitute the values

202. 5 = 1/3 × 40. 5 × h

Divide  the values

202. 5 = 13. 5h

Make 'h' the subject of the formula, we have;

h = 15 inches

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Answer:

para de ser joto cuhhhhhhhhhhhhh

Step-by-step explanation:

ok ok ok so no sabo

Answer:

Yes

Hehe......

Answer: Yes

Step-by-step explanation:

Answer:156

Step-by-step explanation:

Answer: The formula for the mathematical function that takes as input an RGB color vector ⟨r,g,b⟩ and yields as output the RGB color vector that is the unique shade of gray whose total amount of light (r+g+b) is equal to that of the input is:

(r+g+b)/3, (r+g+b)/3, (r+g+b)/3

Step-by-step explanation: RGB color space is a way to represent colors digitally, where each color is represented by a combination of red, green, and blue values ranging from 0 to 255. To obtain a unique shade of gray whose total amount of light (r+g+b) is equal to that of the input color, we have to set all three color channels to the average value of the red, green and blue values.

To calculate this average value we use the formula: (r+g+b)/3

So the output of the function is ⟨(r+g+b)/3, (r+g+b)/3, (r+g+b)/3⟩ which is the unique shade of gray whose total amount of light is equal to that of the input color.

Note: This is one way to convert color to gray, other methods exist like using luminosity or other weights to RGB channels.

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.

Let's see how to calculate Mean, Median, Mode and Midrange.

Mean = 13 + 15 + 18 + 18 + 21 / 5

Mean = 85 / 5

Mean = 17

Median = 18 (as it is the middle term of the data)

Mode = 18 (as it is most recurring number)

Midrange = 21 + 13 / 2

Midrange = 34 / 2

Midrange = 17

Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

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Answer:

the answer is 135

Step-by-step explanation:

Answer:

2 squared - 7 + -4

Step-by-step explanation:

The better statistics which can be used to compare the given distributions are mean and standard deviation.

A z-core is also referred to as a standard score and it can be defined as a statistical measure of the distance between a data point (raw score) and the mean, especially when standard deviation units are used.

In Mathematics, z-scores can either be negative or positive and it is generally calculated by using this formula:

\(Z=\frac{x\;-\;u}{\delta}\)

Where:

In conclusion, the better statistics which can be used to compare the given distributions are mean and standard deviation.

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Answer:

y = -5/4x -4

Step-by-step explanation:

slope(m)= -5/4

x1=-4,y1=1

using the formula for one point form

y-y1=m(x-x1)

y-1= -5/4(x-(-4))

y-1 = -5/4x + -5/4 × +4

y - 1 = -5/4x -5

y=-5/4x -5 + 1

y = -5/4x -4.

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Answer:

I think the triangle is not a parallelogram because it is three sided. A parallelogram needs 4 sides.

Step-by-step explanation:

The smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.

A figure known as an angle is created by two rays or line segments that meet at a place known as the vertex of the angle. The sides or legs of the angle are other names for the rays or line segments.

To determine the smaller angle made by the two hands of a clock when it is 3 o'clock, we can use the following formula:

angle = |(11/2) * m - 30h|

where:

m is the number of minutes past the hour (in this case, since it is 3 o'clock, m = 0)

h is the hour (in this case, h = 3)

By using this formula, we get:

angle = |(11/2) * 0 - 30(3)| = |0 - 90| = 90

Therefore, the smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.

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From the above, it can be seen that the nature of polynomial functions is dependent on its degree. Higher the degree of any polynomial function, then higher is its growth. A function which grows faster than a polynomial function is y = f(x) = ax, where a>1. Thus, for any of the positive integers n the function f (x) is said to grow faster than that of fn(x).

Thus, the exponential function having base greater than 1, i.e., a > 1 is defined as y = f(x) = ax. The domain of exponential function will be the set of entire real numbers R and the range are said to be the set of all the positive real numbers.

It must be noted that exponential function is increasing and the point (0, 1) always lies on the graph of an exponential function. Also, it is very close to zero if the value of x is mostly negative.

Exponential function having base 10 is known as a common exponential function. Consider the following series:

Derivative of logarithmic and exponential function 5

The value of this series lies between 2 & 3. It is represented by e. Keeping e as base the function, we get y = ex, which is a very important function in mathematics known as a natural exponential function.

For a > 1, the logarithm of b to base a is x if ax = b. Thus, loga b = x if ax = b. This function is known as logarithmic function.

Derivative of logarithmic and exponential function 2

For base a = 10, this function is known as common logarithm and for the base a = e, it is known as natural logarithm denoted by ln x. Following are some of the important observations regarding logarithmic functions which have a base a>1.

   The domain of log function consists of positive real numbers only, as we cannot interpret the meaning of log functions for negative values.

   For the log function, though the domain is only the set of positive real numbers, the range is set of all real values, i.e. R

   When we plot the graph of log functions and move from left to right, the functions show increasing behaviour.

   The graph of log function never cuts x-axis or y-axis, though it seems to tend towards them.

Derivative of logarithmic and exponential function 3

   Logap = α, logbp = β and logba = µ, then aα = p, bβ = p and bµ = a

   Logbpq = Logbp + Logbq

   Logbpy = ylogbp

   Logb (p/q) = logbp – logbq

Exponential Function Derivative

Let us now focus on the derivative of exponential functions.

The derivative of ex with respect to x is ex, i.e. d(ex)/dx = ex

It is noted that the exponential function f(x) =ex  has a special property. It means that the derivative of the function is the function itself.

(i.e) f ‘(x) = ex = f(x)

Exponential Series

Exponential Functions

Exponential Function Properties

The exponential graph of a function represents the exponential function properties.

Let us consider the exponential function, y=2x

The graph of function y=2x is shown below. First, the property of the exponential function graph when the base is greater than 1.

Exponential Functions

Exponential Function Graph for y=2x

The graph passes through the point (0,1).

   The domain is all real numbers

   The range is y>0

   The graph is increasing

   The graph is asymptotic to the x-axis as x approaches negative infinity

   The graph increases without bound as x approaches positive infinity

   The graph is continuous

   The graph is smooth

Exponential Functions

Exponential Function Graph y=2-x

The graph of function y=2-x is shown above. The properties of the exponential function and its graph when the base is between 0 and 1 are given.

   The line passes through the point (0,1)

   The domain includes all real numbers

   The range is of y>0

   It forms a decreasing graph

   The line in the graph above is asymptotic to the x-axis as x approaches positive infinity

   The line increases without bound as x approaches negative infinity

   It is a continuous graph

   It forms a smooth graph

Exponential Function Rules

Some important exponential rules are given below:

If a>0, and  b>0, the following hold true for all the real numbers x and y:

       ax ay = ax+y

       ax/ay = ax-y

       (ax)y = axy

       axbx=(ab)x

       (a/b)x= ax/bx

       a0=1

       a-x= 1/ ax

Exponential Functions Examples

The examples of exponential functions are:

   f(x) = 2x

   f(x) = 1/ 2x = 2-x

   f(x) = 2x+3

   f(x) = 0.5x

Solved problem

Question:

Simplify the exponential equation 2x-2x+1

Solution:

Given exponential equation: 2x-2x+1

By using the property: ax ay = ax+y

Hence, 2x+1 can be written as 2x. 2

Thus the given equation is written as:

2x-2x+1 =2x-2x. 2

Now, factor out the term 2x

2x-2x+1 =2x-2x. 2 = 2x(1-2)

2x-2x+1 = 2x(-1)

2x-2x+1 = – 2x

STEP - BY - STEP EXPLANATION

What to find?

The zeros of the given equatiion.

The graph of the given equation.

Given:

Step 1

Put y=0

Step 2

Solving by factorization method;

Replace the coefficient of x, with two numbers whose product gives -8 and whose sum gives 2.

The numbers are: 4 and -2.

Step 3

Factorize;

Step 4

Determine the x- values.

x = -4 and 2

Step 5

Write the quadratic equation in vertex form.

The vertex is (-1, -9). This implies the graph opens upward with a vertex (-1, -9).

ANSWER

Answer:

a) P(Z > 1.09) = 0.1379

b) P(Z < -0.22) = 0.4129.

c) P(Z < -1.96) = 0.025, P(Z > -1.96) = 0.025

d) Z = 1.4

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

a. P(Z > 1.09)

This is 1 subtracted by the pvalue of Z = 1.09.

Z = 1.09 has a pvalue of 0.8621

1 - 0.8621 = 0.1379, so

P(Z > 1.09) = 0.1379

b. P(Z < -0.22)

This is the pvalue of Z = -0.22.

Z = -0.22 has a pvalue of 0.4129. So

P(Z < -0.22) = 0.4129.

c) P(Z < -1.96) or P(Z > -1.96)

Z = -1.96 has a pvalue of 0.025. So

1 - 0.025 = 0.975

P(Z < -1.96) = 0.025

P(Z > -1.96) = 0.025

d. What is the value of Z if only 8.08% of all possible Z-values are larger?

Z with a pvalue of 100 - 8.08 = 91.92 = 0.9192, so Z = 1.4

Answer:

1: the balance after 8 years is approximately $151.78.

2:  is approximately 7%.

Step-by-step explanation:

1: The balance after t years with continuous compounding can be calculated using the formula:

B = Pe^(rt)

Where:

P = 120 dollars (initial deposit)

r = 2.5% = 0.025 (interest rate in decimal form)

t = 8 years

Substituting these values into the formula, we get:

B = 120e^(0.025*8) ≈ 151.78

Therefore, the balance after 8 years is approximately $151.78.

2: The interest rate can be found using the formula:

A = Pe^(rt)

Taking the natural logarithm of both sides and solving for r, we get:

r = ln(A/P) / t

Where:

A = 4055 dollars (final amount)

P = 1000 dollars (initial investment)

t = 20 years

Substituting these values into the formula, we get:

r = ln(4055/1000) / 20 ≈ 0.0774

Converting to a percentage and rounding to the nearest whole number, we get:

r ≈ 7%

Therefore, the interest rate, if compounded continuously, is approximately 7%.

Answer:

1. $146.57

2. 7%.

Step-by-step explanation:

1.

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

To use this formula, we first need to convert the annual interest rate to a decimal:

r = 2 1/2 = 2.5%

r = 2.5/100 = 0.025

Now we can plug in the values:

A = 120e^(0.025*8)

A ≈ $146.57

Therefore, the balance after 8 years is approximately $146.57

2.

The formula for continuous compounding is: A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

We can rearrange this formula to solve for the interest rate:

r = ln(A/P)/t

Where ln represents the natural logarithm.

Now we can plug in the given values:

r = ln(4055/1000)/20

r ≈ 0.069or 7.1%

Therefore, the interest rate, rounded to the nearest whole number, is 7%.

the final result of the double integral is `(4/3)*a. we have to Integrate the inner integral with respect to z.

what is inner integral ?

An inner integral is a mathematical term that refers to the integral function that is evaluated first in a double integral.

In the given question,

To solve this double integral, we will use the following steps:

Integrate the inner integral with respect to z.

Evaluate the result of the inner integral at  upper and lower limits of z.

Substitute the result of the inner integral into the outer integral and integrate with respect to y.

Evaluate the result of the outer integral at the upper and lower limits of y.

Simplify the expression.

Now, let's apply these steps to solve the given double integral:

Integrate the inner integral with respect to z:

∫(x²*z + y²*z + z³) dz = x²/2*z² + y²/2*z² + z^4/4 + C

where C is the constant of integration.

Evaluate the result of the inner integral at the upper and lower limits of z:

(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)

Substitute the result of the inner integral into the outer integral and integrate with respect to y:

markdown

∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

Evaluate the result of the outer integral at the upper and lower limits of y:

= ∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

from y = -sqrt(a²-x²) to y = sqrt(a²-x²)

= (2/3)*x²*(a²-x²)¹⁵ + (2/3)*(a²-x²)²⁵

- (2/3)*x²*(-a²+x²)¹⁵ + (2/3)*(-a²+x²)²⁵

Simplify the expression:

= (4/3)*a³ - (4/3)*a*x²

Therefore, the final result of the double integral is `(4/3)*a

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Thus, probability that the one drawn penny is from 1977 dated pennies is 6/25.

The probability about an occurrence in an experiment is the likelihood that the event will occur. Any event's probability is a number between (including all) "0" and "1".

If an event's probability is represented by P(E), then we get

Given data:

Total pennies = 50

number of 1977 dated pennies = 12

probability = favourable outcome / total outcome

probability(1977 dated pennies) = number of 1977 dated pennies/ Total pennies

probability(1977 dated pennies) = 12/50

Divide numerator and denominator by 2.

probability(1977 dated pennies) = 6/25

Thus, probability that the one drawn penny is from 1977 dated pennies is 6/25.

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Answer:

4y-x-3  = 0

Step-by-step explanation:

 Slope = 0.500/2.000 = 0.250

 x-intercept = 3/-1 = -3.00000

 y-intercept = 3/4 = 0.75000

The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

Here, we have,

we know that,

The sum of the angles in a triangle add to 180

x+2x+6x = 180

Combine like terms

9x= 180

Divide by 9

9x/9 = 180/9

x = 20.

Hence, The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

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complete question:

The sum of the angle measures in a triangle is 180°. The angles of a certain triangle measure x°, 2x°, and 6x°. Solve for x.