a 6 ft board is cut into two pieces, on twice as long as the other. How long are the pieces?

Answer:

72 degrees for each exterior angle and 360 degrees for all of them summed.

Step-by-step explanation:

An exterior angle of a polygon is the angle between the line extending one of its sides and the next side.  As you go around a regular n sided polygon doing this, you will rotate through a complete circle of 360 degrees.  All these angles are equal, so each one is 360/n.

For the pentagon, n=5, so the sum of all its exterior angles is 360 degrees and each exterior angle is 360/5=72 degrees.

The number of different orders in which the songs can be played is given as follows:

720 different orders.

The formula for the arrangements of n elements is obtained considering the factorial of the number n, as follows:

A(n) = n!.

In this problem, we are going to order 6 music files, which is also an arrangement of six elements, hence the number of different orders in which the songs can be played is obtained as follows:

A(6) = 6! = 720 different orders.

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Answer:

84° and 48°

Step-by-step explanation:

1st of all, the inner angle of rhombus would total up into 360° and the opposite for each angle is equal to each other.

As ∆WXY = 84°, so

∆WZY = 84°

Any diagonal line in the rhombus would make the angle get divided equally i.e ∆XWZ

So find ∆XWZ first.

∆XWZ = (360° - 84° - 84°) ÷ 2

= 192° ÷ 2

= 96°

∆XWY = 96° ÷ 2

= 48°

The given limit represents the derivative f′(a). The function f(x) can be determined by finding the antiderivative of the derivative function f′(x), and the value of a can be calculated by evaluating the given limit expression.

To find the function f(x), we need to find the antiderivative of f′(x). In this case, f′(x) is represented by cos((π/2)+h)/h. Integrating this function will give us f(x) up to an arbitrary constant. However, since the question asks us to find f(x) in terms of x, we can write f(x) as the definite integral from a constant c to x of f′(t) dt, where f′(t) is the given derivative function.

To calculate the value of a, we evaluate the given limit expression as h approaches 0. Plugging in h = 0 into the expression cos((π/2)+h)/h will result in an indeterminate form of 0/0. This suggests the application of L'Hôpital's rule, which states that for indeterminate forms, taking the derivative of the numerator and denominator and then evaluating the limit can often yield a determinate form. By applying L'Hôpital's rule, we differentiate the numerator and denominator separately and re-evaluate the limit.

In conclusion, finding f(x) requires integrating the given derivative function, and calculating the value of a involves using L'Hôpital's rule to evaluate the given limit expression.

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Answer:

4x^2 + 9x + 23

Step-by-step explanation:

just factor the last equation and combine them all.

Step-by-step explanation:

you get the units making the triangle then use a²+b²=c²

\( \bold \implies{ \bold{The \: correct \: option \: is \: c) \: sin \: 141° < 0}}\)

\( \bf \longrightarrow \tan141\degree = - \frac{b}{a} < 0 \\ \\ \bf \longrightarrow \sin141\degree = \frac{b}{c} > 0 \\ \\ \bf \longrightarrow \cos141 \degree = - \frac{a}{c} < 0\)

The sampling method in which the size of the sample portions is quota sampling, the correct option is A.

We are given that;

The statement= the researcher's belief about the relative size of each class of respondent in the population

Now,

Convenience sampling is a type of non-probability sampling method that involves selecting respondents who are easily accessible or convenient to reach, without considering their representativeness of the population.

Purposive sampling is a type of non-probability sampling method that involves selecting respondents who have specific characteristics or knowledge that are relevant to the research topic, based on the researcher’s purpose or criteria.

Chain referral sampling is a type of non-probability sampling method that involves selecting respondents who are referred by previous respondents, forming a chain of connections. This method is also known as snowball sampling or network sampling.

Therefore, by sampling the answer will be Quota sampling.

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Answer:

Volume = 1/3 ft^3

Step-by-step explanation:

volume of prism is multiplying the dimensions

Volume = (1/3 ft)x(2/3ft)x(1 1/2ft)  

Volume = (1/3 ft)x(2/3ft)x( 3/2ft)

Volume = (1x2x3)/(3x3x2) ft^3 = 6/18 ft^3 = 1/3 ft^3

Option B is correct, the volume of the  right rectangular prism is 1/3 cubic feet.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The given figure is a right rectangular prism.

The length is \(1\frac{1}{2}\) feet

The width is 2/3 feet

The height is 1/3 feet.

Volume=Length×width×Height

= \(1\frac{1}{2}\) ×2/3×1/3

=3/2×2/3×1/3

=1/3 cubic feet

Hence, Option B is correct, the volume of the  right rectangular prism is 1/3 cubic feet.

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The estimated population in 2025 is 356.9

What is estimation ?

In math, estimating can be used to roughly calculate an answer (getting a "rough response") or to verify its accuracy (getting the "proper answer"). Even when estimating large numbers or decimal numbers, you shouldn't need to utilize a calculator or other documented techniques.

Estimation is frequently performed by sampling, which involves counting a small sample of a given thing and extrapolating that number to a wider population. Calculating the number of sweets of a particular size that are contained in a glass jar serves as an illustration of estimation.

There are 125 years from after 1900 to 2025

P = 0.00892t^2 + 1.1149t + 78.4491

P= (0.0089x125x125)+(1.1149x125)+78.4491

 =139.0625+139.3625+78.4491

 =356.87

 =356.9

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Answer:

Answer:

\(k=-8\)

Step-by-step explanation:

We have the two points: (2, -3) and (k, 7).

And we want to find the value of k such that the slope between these two points is -1.

So, we can use the slope formula:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Let (2, -3) be (x₁, y₁) and let (k, 7) be (x₂, y₂). Let's also substitute the slope m for -1. This gives us:

\(-1=\frac{7-(-3)}{k-2}\)

So, let's solve for k. Add in the numerator:

\(-1=\frac{10}{k-2}\)

Notice that we can rewrite the left side as:

\(\frac{-1}{1}=\frac{10}{k-2}\)

Now, we can cross-multiply:

\(-(k-2)=10\)

Divide both sides by -1. This removes the negative on the left:

\(k-2=-10\)

Finally, add 2 to both sides. So, the value of k is:

\(k=-8\)

And we're done!

The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

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Answer:

Step-by-step explanation:

4m = 6m - 2/5

-2m = -2/5

m = 2/5 : 2

The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.

The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.

As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1

As x approaches negative infinity, the value of the function approaches 1.

As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞

As x approaches positive infinity, the value of the function approaches infinity.

As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.

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The probability of not rolling a 2 or 3 is 2/3

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes

Since Paris is not interested in rolling a 2 or 3, the number of favorable outcomes will be ?

Number of favorable outcomes = 6 - 2 = 4

Total number of outcomes = 6

The probability of not rolling 2 or 3 = 4 / 6 = 2/3

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 Using Ratio Test to determine the convergence or divergence of the series. Ratio Test is inconclusive.

The Ratio Test is a method used to determine the convergence or divergence of a series. It works by evaluating the limit of the ratio of successive terms of a series.

If the limit is equal to 0, then the series converges; if the limit is equal to 1, then the series diverges; if the limit is neither 0 nor 1, then the Ratio Test is inconclusive.

To use the Ratio Test to determine the convergence or divergence of the series, we calculate the limit of the ratio of successive terms of the series. If the limit is equal to 0, then the series converges.

if the limit is equal to 1, then the series diverges; if the limit is neither 0 nor 1, then the Ratio Test is inconclusive.

If the Ratio Test is inconclusive, then we can use other methods such as the Root Test, Comparison Test, Integral Test, or Alternating Series Test to determine the convergence or divergence of the series.

I hope this helps!

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The maximum value of the function is approximately 67,179.6 at x ≈ 29.5, and the minimum value of the function is approximately -27,512.5 and occurs at x ≈ -6.5.

We are given the quadratic equation as;

\(y = \dfrac{2}{3} x^{2} + \dfrac{5}{4} x- \dfrac{1}{3}\)

Solving the equation ;

\(y = \dfrac{2}{3} x^{2} + \dfrac{5}{4} x- \dfrac{1}{3} \\\\\\y = \dfrac{8x^{2} + 15x - 4}{12}\)

Using the second formula, we see that the roots of the equation

x = (-(-100) ± √((-100)² - 4(3)(-200))) / (2(3))

x = (-(-100) ± √(10000 2400)) / 6

x = (-(-100) ± √(12400)) / 6

x = (100 ± 20 √(31)) / 3

To determine whether these are maximum or minimum points,

y''(x1) = -6((100 √(31)) / 3) = -200 - 40√(31) < 0  is a local minimum

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Area between each score and the mean in the z score table and then subtract the smaller area from the larger area.

The correct option is b.

The area between each score and the mean in the z score table and then subtract the smaller area from the larger area.

What is Z score: The z-score (aka, standard score) is a dimensionless metric that represents the deviation of a score from the mean in units of the standard deviation.

The formula for computing z-scores is as follows:

Z = (X - μ) / σ

where X is the score,

μ is the mean,

and σ is the standard deviation.

Z-scores can be used to assess the relative position of a score in relation to the distribution's mean and standard deviation.

In this particular question, the Z score of two test scores is 1.2 and 1.5.

To obtain the area between these scores, we have to find the area between each score and the mean in the z-score table, and then subtract the smaller area from the larger area.

First, we need to find the area between 1.2 and 1.5.

We can see the area from the z-score table as P(z < 1.5) - P(z < 1.2).

The following z-score table can be used to find these probabilities:

z-score table

From the table, P(z < 1.5) is equal to 0.9332, and P(z < 1.2) is equal to 0.8849.

Thus, P(1.2 < z < 1.5) = 0.9332 - 0.8849 = 0.0483.

To find the answer to the question, we have to calculate the area between the scores, which is 0.0483 in this case, by finding the area between each score and the mean in the z-score table and then subtracting the smaller area from the larger area.

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Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

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

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Hope this helps! :)

Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

Rectangle and Quadrilateral

Step-by-step explanation:

Hi,

It can't be a rhombus because, in a rhombus, all the sides are equal. The same goes for a square so those two aren't correct. It is a rectangle and in a Quadrilateral, the sides are straight. So your two answers are a rectangle and a Quadrilateral.

I hope this helps :D

The theoretical probability =\(\dfrac{5}{9}\),  The experimental probability  = \(\dfrac{5}{12}\)

The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted.

The sample will be ={1,2,3,4,5,6,7,8,9}=9

favourable outcomes={1,3,5,7,9,}=5

The theoretical probability of spinning and odd number = \(\dfrac{5}{9}\)

As she spends the spinner 12 times

The experimental probability = \(\dfrac{5}{12}\)

Hence the theoretical probability =\(\dfrac{5}{9}\),  The experimental probability  = \(\dfrac{5}{12}\)

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Answer:

The theoretical probability of spinning an odd number is equal to 5/9 The experimental probability of spinning an odd number is equal to 2/3. Therefore, the theoretical probability of spinning an odd number is less. than the experimental probability of spinning an odd number.

if you could give me brainliest i would greatly appreciate it.

The statement that is not true about a rational function of the form f(x) where g and h are polynomial functions is D. A rational function may have many horizontal asymptotes.

A rational function is defined as the ratio of two polynomial functions, where g and h are polynomials and h is not the zero polynomial. The graph of a rational function can have vertical asymptotes, which occur when the denominator of the function is equal to zero. However, a rational function can intersect a vertical asymptote if the numerator is also equal to zero at that point.

Regarding vertical asymptotes, statement A is true. The graph of a rational function will never intersect a vertical asymptote, as long as the function is defined at that point.

Statement B is also true. A rational function may have multiple vertical asymptotes if the denominator has multiple factors that result in the function being undefined at different points.

Statement C is also true. If the degrees of g and h are m and n, respectively, and m is less than or equal to n, then the rational function will have a horizontal asymptote with an equation of y = (a/b).

However, statement D is not true. A rational function can have at most one horizontal asymptote, and this occurs when the degree of g is equal to the degree of h. The equation of the horizontal asymptote is y = (a/b), where a is the leading coefficient of g and b is the leading coefficient of h.

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Answer:

h = 32

Step-by-step explanation:

In the given figure, for the first parallelogram, base is 36 and height is 24 while for the other parallelogram, base is 27 and height is h.

The area of a parallelogram is given by :

A = base × height

So,

The both parallelograms,

\(36\times 24=27h\\\\h=\dfrac{36\times 24}{27}\\\\h=32\)

So, the value of h is 32.

Answer: x=11

Step-by-step explanation:

\(1.5x+3=3(1.5x-10)\\Distribute\\1.5x+3=4.5x-30\)

Subtract 3 from both sides

\(1.5x=4.5x-33\)

Now subtract 4.5x from each side

\(-3x=-33\\Divide\\x=11\)

Answer:

11

Step-by-step explanation:

1.5x+3=3(1.5x-10)

1.5x+3=4.5x-30

4.5x-1.5x-30=3

3x-30=3

3x=3+30

3x=33

x=33/3

x=11

The z-statistic is a valuable tool in statistical analysis to evaluate the significance of a sample statistic in relation to its null distribution.

A z-statistic, also known as a standardized statistic, is a measurement used in hypothesis testing to determine how many standard deviations an observed statistic is from the mean of the null distribution.

This value helps in understanding how likely an observed result is under the null hypothesis.

By comparing the z-statistic to a critical value, one can determine if the observed statistic is significantly different from the null hypothesis expectation.

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A can of soda can be modeled as a right cylinder. Brianna measures its height as 12. 5 cm and its radius as 2. 6 cm. The volume of the can in cubic centimeters is 1030.9 cm³ (rounded to the nearest tenth).

The volume of the can in cubic centimeters is 1030.9.

A cylinder is a 3D geometric shape with 2 bases that are congruent and parallel to each other.

A right circular cylinder is a cylinder in which the bases are circles and are at right angles to the height of the cylinder.

How to find the volume of a cylinder?

The formula to find the volume of a cylinder is given by:

V = πr²h

Where, r is the radius of the cylinder, h is the height of the cylinder, and π is a constant equal to 3.14

Given data: Height = 12.5 cm

Radius = 2.6 cm

We need to find the volume of the can.

The can is modeled as a cylinder.

The height and radius of the can is given.

We can use the formula of the volume of the cylinder to find the volume of the can.

V = πr²hV

= π × (2.6)² × 12.5V

= 3.14 × 6.76 × 12.5V

= 267.1 cm³

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if the correlation between x and y is equal to -1.0, then we know that the prediction of y by x is perfect

The correlation coefficient is a unitless number and must always lie between –1.0 and +1.0, inclusive.

The correlation coefficient, r , gives us information about the strength and direction of a linear relationship between any two variables. (r > 0 is a positive correlation, r < 0 is negative, and |r| closer to 1 means a stronger correlation.

The larger r is in absolute value, the stronger the relationship is between the two variables.

If r is the correlation between two variables x and y then -r is the correlation between y and x

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