Which equation illustrates the commutative property of addition?.

The length of a standard basketball court is 94 feet (28.65 meters), and the width is 50 feet (15.24 meters).

A standard basketball court is rectangular in shape and follows certain dimensions specified by the International Basketball Federation (FIBA) and the National Basketball Association (NBA). The length and width of a basketball court may vary slightly depending on the governing body and the level of play, but the most commonly used dimensions are as follows:

The length of a basketball court is typically 94 feet (28.65 meters) in professional settings. This length is measured from baseline to baseline, parallel to the sidelines.

The width of a basketball court is usually 50 feet (15.24 meters). This width is measured from sideline to sideline, perpendicular to the baselines.

These dimensions provide a standardized playing area for basketball games, ensuring consistency across different courts and facilitating fair play. It's important to note that while these measurements represent the standard dimensions, there can be slight variations in court size depending on factors such as the venue, league, or specific regulations in different countries.

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Answer:

{0, 1, 2, 3, 4, 5}

Step-by-step explanation:

The universal set has to have at least the same elements as has the set you are dealing with.

Answer: {0, 1, 2, 3, 4, 5}

Two possible ways to write 9/10 as a sum of fractions are 1/2 + 4/5 and 3/5 + 3/10.

To write9/10 as a sum of  fragments, we need to find two  fragments with a common denominator that add up to9/10. One way to do this is to express9/10 as the sum of two  fragments with denominators that are multiples of 10.   One possible way to do this is   = 1/24/5   Both  fragments on the right- hand side have denominators that are multiples of 10, and when we add them together, we get9/10.

9 = 2x + y

We can then solve for x and y by trying different values until we find a solution that works. One possible solution is x=3 and y=3:

9/10 = 3/5 + 3/10

3/5 + 3/10 = 6/10 + 3/10 = 9/10

Since 9/10 is equal to 9/10, we have shown that 9/10 can be written as a sum of fractions.

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Answer:

optional A is the correct answer

Answer: y is 12  

step - by - step: 8+8=16 and 6+6=12

so it is       6            12

                 _     =      _      so its (B)

                 8            16

Answer:

sorry just need points

Step-by-step explanation:

32 and 30

It determines statistic.

Since the researcher is studying a sample of 50 women who have lost weight of  pounds so since it is a sample and of a definite size so it means it is a sample so they determines statistic.

A statistic (singular) or sample statistic is any quantity calculated from values ​​in a sample that is considered for statistical purposes. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The mean (or average) of the sample values ​​is a statistic. The term statistic is used both for a function and for the value of the function on a given sample. When a statistic is used for a specific purpose, it may be labeled with a name indicating its purpose.

When a statistic is used to estimate a population parameter, the statistic is called an estimator. A population parameter is any characteristic of the population under study, but when it is not possible to directly measure the value of the population parameter, statistical methods are used to derive the probable value of the parameter based on statistics calculated from the sample. drawn from the population. For example, the sample mean is an unbiased estimate of the population mean. This means that the expected value of the sample mean is equal to the true population mean

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The values of csc W and cos W of the angle are:

csc W =  (√85)/2

cos W = 9/√85

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

since acute angle W has sin W = 2/√85 and sec W = (√85)/9.

Recall that: csc W = 1/sinW and sec W = 1/cos W.

Therefore, if sin W = 2/√85, csc W = (√85)/2

Also, if sec W = (√85)/9, cos W = 9/√85

Therefore, the values of csc W and cos W are (√85)/2 and 9/√85 respectively

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Answer:

Step-by-step explanation:

volume of sphere = 4πr³/3

= 4π×512/3

≈ 2143.6 cm³

The probability of selecting three balls of the same color without replacement is 0.0545, and with replacement is 0.0393. The probability of selecting three balls of different colors without replacement is 0.4591, and with replacement is 0.4968.

(a) To select a set of 3 balls that are all of the same color, we need to choose one of the three colors (red, blue, or green), and then select 3 balls of that color from the urn. There are three ways to choose the color of the balls. For each color, the number of ways to select 3 balls of that color is given by the number of combinations of 3 balls from the set of balls of that color. Thus, the total number of ways to select a set of 3 balls that are all of the same color is:

Number of ways to select 3 red balls + number of ways to select 3 blue balls + number of ways to select 3 green balls

= (5 choose 3) + (6 choose 3) + (8 choose 3)

= 10 + 20 + 56

= 86

The total number of ways to select any set of 3 balls from the urn is given by the number of combinations of 3 balls from the set of 19 balls in the urn:

Total number of ways to select any set of 3 balls = (19 choose 3) = 969

Therefore, the probability that each of the balls will be of the same color is:

P(each ball of the same color) = (number of ways to select 3 balls of the same color) / (total number of ways to select any set of 3 balls)

= 86 / 969

= 0.089

So the probability that each of the balls will be of the same color is approximately 0.089 or 8.9%.

(b) To select a set of 3 balls that are of different colors, we need to choose one ball of each color from the urn. The number of ways to select one ball of each color is given by the product of the number of balls of each color:

Number of ways to select 1 ball of each color = 5 x 6 x 8 = 240

The total number of ways to select any set of 3 balls from the urn is still 969.

Therefore, the probability that each of the balls will be of different colors is:

P(each ball of different color) = (number of ways to select 1 ball of each color) / (total number of ways to select any set of 3 balls)

= 240 / 969

= 0.248

So the probability that each of the balls will be of different colors is approximately 0.248 or 24.8%.

When the balls are selected with replacement, the probabilities remain the same because the probabilities of selecting each ball are unchanged on each draw.

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For the system of linear equations (2a−1)x+3y−5=0 and 3x+(b−1)y−2=0 to have infinitely many solutions, the two equations must be linearly dependent, meaning one equation can be obtained by multiplying the other equation by a constant. This can be achieved when the ratios of the coefficients of x, y, and constants in the two equations are equal, except for a scalar multiple. Therefore, setting (2a-1)/3 = -2/(b-1) = -5/2, we get a = -1/2 and b = 9.

To find the values of a and b such that the system of linear equations (2a−1)x+3y−5=0 and 3x+(b−1)y−2=0 has infinitely many solutions, we need to find the condition under which the two equations are linearly dependent.

If the two equations are linearly dependent, it means that one equation can be obtained by multiplying the other equation by a constant. Mathematically, this can be represented as:

k(2a−1)x + k(3y) − k(5) = 0 where k is a non-zero constant

and 3x + (b−1)y − 2 = 0

We can see that the coefficients of x and y in the two equations are 2a-1 and 3, and 3 and b-1, respectively. For the equations to be linearly dependent, the ratios of these coefficients must be equal, except for a scalar multiple. In other words:

(2a-1)/3 = (b-1)/(-2) = k where k is a non-zero constant

We can solve for k by setting any two ratios equal to each other. Let's set the first ratio equal to the second ratio:

(2a-1)/3 = (b-1)/(-2)

Cross-multiplying, we get:

-4a + 2 = 3b - 3

Simplifying, we get:

-4a + 3b = 5

Next, let's set the first ratio equal to the third ratio:

(2a-1)/3 = -5/2

Cross-multiplying, we get:

4a - 2 = -15

Simplifying, we get:

4a = -13

Solving for a, we get:

a = -13/4

Substituting this value of a into the equation -4a + 3b = 5, we get:

-4(-13/4) + 3b = 5

Simplifying, we get:

13 + 3b = 5

Solving for b, we get:

b = 9

Therefore, the values of a and b that make the system of linear equations (2a−1)x+3y−5=0 and 3x+(b−1)y−2=0 have infinitely many solutions are a = -1/2 and b = 9.

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Let m = slope

m = (6 - 4)/(3 - 2)

m = 2/1

m = 2

The slope is 2.

Answer:

-2/1 is the slope for the question

The sample variance is the most accurate point estimate of the population variance sigmasquared.

The best point estimate of the population variance is the sample variance. This is because the sample variance is an unbiased estimator of the population variance, meaning that it is the most accurate estimate of the population variance. The sample variance is calculated by taking each individual data point, subtracting the sample mean, squaring the result, and then summing the results. The sample variance then is the sum of these squared differences divided by the number of data points minus one. This is a consistent estimator, meaning that it will always produce the same result even if the sample size is different. This is why the sample variance is the best point estimate for the population variance.

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The expression \([2(cosθ + i sinθ)]^18\), where θ = 31°, can be simplified and written in rectangular form as \([2^18 cos(18θ) + i 2^18 sin(18θ)].\)

To find the power of the complex number [2(cosθ + i sinθ)]^18, we can utilize De Moivre's theorem. According to De Moivre's theorem, for any complex number z = r(cosθ + i sinθ) and a positive integer n, the expression z^n can be written as [r^n cos(nθ) + i r^n sin(nθ)].

In this case, we have [2(cosθ + i sinθ)]^18, where θ = 31°. Substituting the values into De Moivre's theorem, we get:

\([2(cosθ + i sinθ)]^18 = [2^18 cos(18θ) + i 2^18 sin(18θ)]\)

Hence, the expression [2(cosθ + i sinθ)]^18 simplifies to \([2^18 cos(18θ) + i 2^18 sin(18θ)\)]. This is the exact value of the expression in rectangular form, where the real part is \(2^18 cos(18θ)\) and the imaginary part is 2^18 sin(18θ).

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Answer:

18.7

Step-by-step explanation:

First find the degree of J which is 6 (found this by doing 180=160+14=6

so then you make the fraction J/sin14=8.1/sin6

cross multiply so its Jsin6=8.1sin14

to get J by itself you divide by sin 6 so

J=8.1sin14 divided by sin6 which equals 18.7

The length of \(l\) is approximately 18.8 inches.

In this question we know the value of two angles, in sexagesimal degrees, and a length of the triangle, in inches, we must determine the length \(l\) by the law of sine:

\(\frac{l}{\sin \angle L} = \frac{j}{\sin \angle J}\) (1)

\(\angle J = 180^{\circ} - \angle K - \angle L\) (2)

If we know that \(j = 8.1\,in\), \(\angle K = 160^{\circ}\) and \(\angle L = 14^{\circ}\), then the length of \(l\) is:

\(\angle J = 180^{\circ}-160^{\circ}-14^{\circ}\)

\(\angle J = 6^{\circ}\)

\(l = j\cdot \left( \frac{\sin \angle L}{\sin \angle J} \right)\)

\(l = (8.1\,in)\cdot \left(\frac{\sin 14^{\circ}}{\sin 6^{\circ}} \right)\)

\(l \approx 18.8\,in\)

The length of \(l\) is approximately 18.8 inches.

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Answer:

\(\displaystyle m=\frac{-2}{3}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph

Point (-3, 1)

Point (3, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Greetings from Brasil....

From Pythagoras we have

AB² = AC² + BC²

13² = 12² + X²

Answer:

5 cm

Step-by-step explanation:

Pythagoras theorem gives us:

\(hypotenuse^{2} = side^{2} + side^{2}\)

We know the hypotenuse is 13 cm.

We know one side is 12 cm.

\(13^{2} = 12^{2} + side^{2}\)

\(169= 144 + side^{2}\)

Subtracting 144 from both sides:

\(25 = side^{2}\)

Reversing the sides:

\(side^{2}=25\)

\(\sqrt{side^{2}}= \±\sqrt{25}\)

\(side = \±\sqrt{25}\)

\(side = \±5\)

Since a distance can't be negative:

\(side=5\)

The third side is 5 cm.

Answer:

-6

Step-by-step explanation:

Step 1: Simplify the Equation

Step 2: Solve the equation

Step 3: Find the answer and check the answer

Step-by-step explanation:

Remove the parentheses

3h+6+4=8

Collect the like terms

3h=8-6-4

3h= -2

Divide both sides by 3

h= -2/3

Part a

we have the function

R=-0.1x^3+11x62-100x

using a graphing tool

Part b

we have that

The value of x cannot be a negative number

The value of R can be a negative number

therefore

part c

the answer part c is the option A and C

The coordinates along the directed line segment is (-4, 5/3)

This involves dividing a line into proportional ratios

The points are given as:

A  = (-7, 2)

B = (2, 1)

The ratio on the segment can be represented as;

m : n = 1 : 2

So, we have the coordinates of the point that lies along the directed line segment to be

Point = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

So, we have:

Point  = 1/(1 + 2) * (1 * 2 + 2 * -7, 1 * 1 + 2 * 2)

Evaluate

Point  = 1/3 * (-12, 5)

Evaluate the products

Point  = (-4, 5/3)

Hence, the coordinates of the point is (-4, 5/3)

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Answer:

Exactly 1 triangle is possible

Step-by-step explanation:

For any given 3 side lengths, (in our case 4 cm, 6 cm, 9 cm) exactly one triangle is possible

Answer:

False.

Step-by-step explanation:

The RMS (Root Mean Square) value of a sine wave represents the equivalent DC voltage that would produce the same amount of power in a resistive load. However, the heat produced in a resistor is directly proportional to the square of the current passing through it (according to Joule's Law). In the case of an AC waveform, the current continuously changes direction, resulting in a time-varying power dissipation. Therefore, comparing the RMS value of an AC waveform to a DC voltage is not directly applicable in terms of heat produced in a resistor.

Given that

The point is (-2, 4) and the slope is 3.

And we have to find the point-slope equation for this data.

Explanation -

First, we will write the formula to find the point-slope equation and then we will substitute the values to find the required equation.

The general point-slope equation is given as

We have slope, m = 3 and point (x1, y1) = (-2, 4)

Hence the required equation is

So the correct option is B.

Final answer -

Answer:

12x+16-4y

Step-by-step explanation:

Answer:

lets start with x = 5x+7x=12x

now y = 2y-6y= -4y

now reg numbers = 8+8=16

now add all of them not litteraly add by add as in make them into a expression

so

12x-4y+16

The test statistic for this sample and the p-value for this sample is  t = 0.467.

Given:

sample of size n=305

M=83.6

SD=14.9.

Significance level of α = 0.001 . H o : μ = 82.4 H a : μ ≠ 82.4

To find the Test statistic

\(test=\frac{\bar x-\mu}{\frac{s.t}{\sqrt{n} } }\)

    \(=\frac{82.4.6-83.6}{\frac{14.9}{\sqrt{305} } }\)

     \(0.467\)

P-value:

With t = 0.467.

p-value = (1 - 0.467)

0.533 > 0.001

So, fail to reject H₀

Therefore, the failing to reject the Null Hypothesis.

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Answer:

y = 17/4 - 3/4x

Step-by-step explanation:

\(3x + 4y = 17\)

Subtract 3x from both sides.

\(4y = 17 - 3x\)

Divide by 4 from both sides to isolate y.

\(y = \frac{17 - 3x}{4} \)

Answer:

When the imposter is sus da da da da da da dada ding

Step-by-step explanation:

Answer:

220 squared units

Step-by-step explanation:

first, find the area of the rectangle by multiplying 8 by 20. Then, fin the area of the triangle by multiplying 6 by 20 and then dividing the result by 2.

8*20=160

6*20=120

120/2=60

Finally, add them together and you get 220 units squared.

Answer:

1 1/8

Step-by-step explanation:

3/4 = 6/8 ( 3x2= 6 numerator ) ( 4x2= 8 denominator )

6/8 + 3/8 = 9/8 = 1 1/8

Answer:

1 1/8

Step-by-step explanation:

3/4 = 6/8 ( 3x2= 6 numerator ) ( 4x2= 8 denominator )

6/8 + 3/8 = 9/8 = 1 1/8

Answer:

72

Step-by-step explanation:

24 x 3 = 72

20 x 3 = 60

4 x 3 = 12

60+12= 72