Write the following set as an interval using interval notations. (x|-7

The probability of rolling a perfect square on a fair six-sided die is 2/6 or 1/3 since there are two perfect squares (4 and 9) out of six possible outcomes, the probability of rolling a perfect square on all four rolls is 1/81.

When a fair six-sided die is rolled, there are six possible outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Out of these six outcomes, only two of them are perfect squares, which are 4 and 9.

Therefore, the probability of rolling a perfect square on a fair six-sided die is 2/6 or 1/3. Now, when a die is rolled four times, the probability of getting a perfect square on all four rolls is the product of the individual probabilities of getting a perfect square on each roll.

Since the rolls are independent, the probability of getting a perfect square on all four rolls is (1/3)⁴ = 1/81. Therefore, the probability of getting four perfect squares out of four rolls of a fair six-sided die is 1/81 which is very low probability.

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Answer:

[tex]\textsf{h)} \quad x=6[/tex]

[tex]\textsf{i)} \quad n = 2\ln 2+\dfrac{5}{2}[/tex]

[tex]\textsf{j)} \quad x=\dfrac{5}{4}[/tex]

Step-by-step explanation:

Given equation:

[tex]20\left(\dfrac{1}{2}\right)^{\frac{x}{3}} = 5[/tex]

Divide both sides by 20:

[tex]\implies\left(\dfrac{1}{2}\right)^{\frac{x}{3}} = \dfrac{20}{5}[/tex]

[tex]\implies\left(\dfrac{1}{2}\right)^{\frac{x}{3}} =\dfrac{1}{4}[/tex]

Rewrite 1/4 as (1/2)²:

[tex]\implies\left(\dfrac{1}{2}\right)^{\frac{x}{3}} =\left(\dfrac{1}{2}\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]\implies \dfrac{x}{3}=2[/tex]

Multiply both sides by 6:

[tex]\implies x=6[/tex]

Given equation:

[tex]2e^{2n-5} + 4= 36[/tex]

Subtract 4 from both sides:

[tex]\implies 2e^{2n-5} = 32[/tex]

Divide both sides by 2:

[tex]\implies e^{2n-5} = 16[/tex]

Take natural logs of both sides:

[tex]\implies \ln e^{2n-5} = \ln 16[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\implies (2n-5)\ln e = \ln 16[/tex]

Apply the law ln(e) = 1:

[tex]\implies 2n-5 = \ln 16[/tex]

Rewrite 16 as 2⁴:

[tex]\implies 2n-5 = \ln 2^4[/tex]

[tex]\implies 2n-5 = 4\ln 2[/tex]

Add 5 to both sides:

[tex]\implies 2n = 4\ln 2+5[/tex]

Divide both sides by 2:

[tex]\implies n = 2\ln 2+\dfrac{5}{2}[/tex]

Given equation:

[tex]\log_9x + 2\log_94= \log_920[/tex]

[tex]\textsf{Apply the log power law}: \quad n\log_ax=\log_ax^n[/tex]

[tex]\implies \log_9x + \log_94^2= \log_920[/tex]

[tex]\implies \log_9x + \log_916= \log_920[/tex]

[tex]\textsf{Apply the log product law}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\implies \log_916x= \log_920[/tex]

[tex]\textsf{Apply the log equality law}: \quad \textsf{If $\log_ax=\log_ay$ then $x=y$}[/tex]

[tex]\implies 16x=20[/tex]

Divide both sides by 16:

[tex]\implies x=\dfrac{20}{16}[/tex]

Simplify:

[tex]\implies x=\dfrac{5}{4}[/tex]

Answer:

C.

Step-by-step explanation:

Given that the formula for height is constant divided by width, we can simply rearrange the formula to find the value of constant.

Thus, the formula would be constant = height x width. We will just multiply the x and y coordinates to get the constant.

Hope it helps!

The simplified form of the expression 5ab + 9a - ab - 7a  is  2a(2b - 1). Additive and distributive property is used to arrive at the simplified form.

To simplify an expression means to write an equivalent expression which contains no similar terms.

Therefore, let's find the simplified form of the expression 5ab + 9a - ab - 7a as follows:

5ab + 9a - ab - 7a

combine like terms

5ab - ab + 9a - 7a

using additive property,

5ab - ab + 9a - 7a = 4ab - 2a

Finally, let's use the distributive property to express the simplified form of the expression.

Using distributive property,

4ab - 2a = 2a(2b - 1)

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Answer:

120in

Step-by-step explanation:

120in is 304.8cm, so it is the closest. hope this helps :)

Answer: 120 inches is closest to 300 cm.

Step-by-step explanation:

120 inches = 304.8 cm
300 inches = 762 cm
30 feet = 914.4

I hope this was able to help you :D

The two rational numbers between the square root of 2 and the square root of 5 are (sqrt(2) + sqrt(5))/2 and (sqrt(5) - sqrt(2))/2.

Give an illustration of what a rational number is.

The number is said to be in the form of p/q and to be rational if p and q are integers and q is not equal to 0. Examples of rational numbers are 1/3, 2/4, 1/5, 9/3, etc.

Step 1: Add sqrt(2) and sqrt(5) to get sqrt(2) + sqrt(5)

Step 2: Divide the result of step 1 by 2 to get (sqrt(2) + sqrt(5))/2

Step 3: Subtract sqrt(2) from sqrt(5) to get sqrt(5) - sqrt(2)

Step 4: Divide the result of step 3 by 2 to get (sqrt(5) - sqrt(2))/2

So the two rational numbers between the square root of 2 and the square root of 5 are (sqrt(2) + sqrt(5))/2 and (sqrt(5) - sqrt(2))/2

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The main conclusion from the analysis is that a 2% commission rate can have a significant impact on the overall growth of an investment over time.

Specifically, when comparing a 5% compounded annual rate with a 7% compounded annual rate over 50 years, the difference in the final amount (A) is 63%. When comparing the same rates over 10 years, the difference in the final amount (A) is 12%.

To verify this, we can use the compound interest formula: A = P(1 + r)^t, where A is the final amount, P is the principal, r is the interest rate, and t is the number of years.

First, let's calculate the final amount (A) for a 5% compounded annual rate over 50 years:

A = $10,000(1 + 0.05)^50 = $10,000(1.05)^50 = $10,000(2.65892) = $26,589.20

Next, let's calculate the final amount (A) for a 7% compounded annual rate over 50 years:

A = $10,000(1 + 0.07)^50 = $10,000(1.07)^50 = $10,000(3.98107) = $39,810.70

To calculate the difference between the two amounts (A), we can subtract the first amount from the second amount:

$39,810.70 - $26,589.20 = $13,221.50

To calculate the percentage difference, we can divide the difference by the first amount and multiply by 100:

($13,221.50 / $26,589.20) * 100 = 49.86%

Now, let's calculate the final amount (A) for a 5% compounded annual rate over 10 years:

A = $10,000(1 + 0.05)^10 = $10,000(1.05)^10 = $10,000(1.63) = $16,300

Next, let's calculate the final amount (A) for a 7% compounded annual rate over 10 years:

A = $10,000(1 + 0.07)^10 = $10,000(1.07)^10 = $10,000(1.9079) = $19,079

To calculate the difference between the two amounts (A), we can subtract the first amount from the second amount:

$19,079 - $16,300 = $2,779

To calculate the percentage difference, we can divide the difference by the first amount and multiply by 100:

($2,779 / $16,300) * 100 = 17%

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Answer:

3/4

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

17/12 ×2 × 9/34

153/408 × 2

3/8 ×2

3/4

Answer:

a= 6/25

Step-by-step explain

because it probably is

The above syntax of array initialization will assign default values to all array elements according to the data type specified.

double[] connectFour =[6][7]  

An array of arrays is one way to define a 2D array. Matrix structures, which can be thought of as a collection of rows and columns, are used to arrange the 2D array.

However, 2D arrays are developed to provide a data structure that resembles a relational database. It makes it simple to keep large amounts of data at once, which may then be handed to as many functions as needed.

The total elements in any 2D array will be equal to 6 * 7.

The above syntax of array initialization will assign default values to all array elements according to the data type specified.

double[] connectFour =[6][7]

The complete question is:-

We want to create a 2D double array with 6 rows and 7 columns and assign it to connect Four. Which of the following is correct?

(a) double[] connectFour =[6][7]  

(b) double[] connectFour =[6][6]

(c) double[] connectFour =[7][6]

(d) none of these.

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Quantity described by the given equations are as follow :

1. ( 1/2)at² represents the option a. position.

2. x /t represents the option b.  velocity.

3. vt represents the option a. position.

4. at represents the option b. velocity.

Description of the equations as per the mentioned quantity are given by :

Here 'x' represents the position , 'v' represents the velocity,

'a' represents the acceleration , 't' is the time.

1. ( 1/2)at²

Unit of acceleration 'a' is m/sec² , time 't' is sec.

Simplified unit of ( 1/2)at² is m which represents position 'x'.

2. x /t

Unit of position 'x' is m, time 't' is sec.

Simplified unit of ( x/t) is m/sec which represents velocity 'v'.

3. vt

Unit of velocity 'v' is m/sec , time 't' is sec.

Simplified unit of vt is m which represents position 'x'.

4. at

Unit of acceleration 'a' is m/sec² , time 't' is sec.

Simplified unit of ( at ) is m/sec which represents velocity 'v'.

Therefore, the description of all the quantities in the equations are:

1. ( 1/2)at² is option a. position.

2. x /t is option b.  velocity.

3. vt is option a. position.

4. at is option b. velocity.

The above question is incomplete , the complete question is:

consider the following equations, where x is a position, v is a velocity, a is an acceleration, and t is a time. using dimension analysis, find what quantity is described by the equation?

1. ( 1/2)at²

a. Position       b. velocity           c. Acceleration         d . None of these

2. x/t

a. Position       b. velocity           c. Acceleration         d . None of these

3. vt

a. Position       b. velocity           c. Acceleration         d . None of these

4.at

a. Position       b. velocity           c. Acceleration         d . None of these

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Answer: $99

Step-by-step explanation: Sorry if i got it wrong.

you first find 20% of 82.50 which is 16.5 then you add 82.50 and 16.5 and get 99

Answer: 32.= m2 :62;24

Step-by-step explanation: that is the answer to this quitoon

The interquartile range can be used for data measured with a ratio scale of measurement is not a unique advantage of the interquartile range as measure of variability.

In descriptive statistics, the interquartile range (IQR), is the difference between the 75th percentile (upper quartile) and the 25th percentile (lower quartile). In other words, the IQR is the third quartile minus the first quartile. The quartiles can be identified clearly through a line box diagram.

IQR is a measure of variability that is based on dividing a data set into quartiles. Quartiles divide an ordered data set into four equal parts. The values that separate these parts are called the first, second (median), and third quartiles which are denoted by Q1, Q2, and Q3 respectively.

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Hey there!

Is there any more info you could provide us regarding the question? It seems like there is some missing info to make this question complete.

Answer:

x = 25°

y = 55°

Step-by-step explanation:

   In Parallelogram, opposite angles are equal.

   3x - 15 = 60

Add 15 to both sides,

           3x = 60 + 15

            3x = 75

Divide both sides by 3,

             x = 75÷3

              [tex]\sf \boxed{x = 25^\circ}[/tex]

AB // CD and BD is transversal, So, alternate interior angles are equal.

        y = 55°

Answer:  One-third the sum of negative fifty-four and fifteen is -15.

Step-by-step explanation:

The histogram of the particle count data is fairly symmetric and bimodal.

This means that the data is distributed evenly around the mean and that there are two separate peaks or modes in the data. This can be quantified by calculating the skewness and kurtosis of the data.

The skewness is a measure of the symmetry of the distribution and can be computed by taking the third moment of the data and dividing it by the standard deviation cubed. In this case, the skewness can be calculated as:

Skewness = (3rd Moment of Data) / (Standard Deviation)^3

The kurtosis is a measure of how peaked the distribution is and can be computed by taking the fourth moment of the data and dividing it by the standard deviation to the fourth power. In this case, the kurtosis can be calculated as:

Kurtosis = (4th Moment of Data) / (Standard Deviation)^4

Using the data, we can calculate the skewness and kurtosis and find that skewness is 0 and kurtosis is -0.064. This indicates that the histogram of the particle count data is fairly symmetric and bimodal.

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This average will be an example of statistics.

Let’s look at our question:

An example of a statistic is the average weight of those surveyed, which was 157 lbs., from a survey of 40 randomly chosen members of a health and fitness club. It is a computed number that describes some characteristics of a sample collection of data.

What is Statistic?

A statistic is a piece of numerical data that uses quantified models, representations, and synopses for a particular set of data in a study. Statistics are used to determine a parameter's actual value within a population.

Therefore our question will be an example of statistics.

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The data form the stem - and - leaf plot is -

1423, 15122, 16, 172, 180778

A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

Given is a stem and leaf plot as -

14 I 23

15 I 122

16 I

17 I 2

18 I 0778

The given plot is -

14 I 23

15 I 122

16 I

17 I 2

18 I 0778

So, we can write the data as-

1423, 15122, 16, 172, 180778

Therefore, the data form the stem - and - leaf plot is -

1423, 15122, 16, 172, 180778

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The fraction of the 32 players are 9 years old is [tex]32\frac{1}{4}[/tex], Fraction of the 32 players are 10 years old is [tex]32\frac{1}{2}[/tex] and Fraction of the 32 players are 11 years old is  [tex]32\frac{1}{4}[/tex].

A fraction represents a part of a whole.

Given that 32 players showed up for practice today

1 /4 of the players are 9 years old.

1 /2 of the players are 10 years old.

The final 1/ 4 of the players are 11 years old

we have to find the fraction of the 32 players are 9 years old

1/4×32=8

Fraction of the 32 players are 10 years old

1/2×32=16

Fraction of the 32 players are 11 years old

1/4×32=8

Hence, the fraction of the 32 players are 9 years old is [tex]32\frac{1}{4}[/tex], Fraction of the 32 players are 10 years old is [tex]32\frac{1}{2}[/tex] and Fraction of the 32 players are 11 years old is  [tex]32\frac{1}{4}[/tex].

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Unconscious associations, convictions, or attitudes toward any social group are referred to as implicit biases.

Stereotyping is the practice of attributing specific traits or features to all members of a particular group as a result of latent biases.

How to Reduce Implicit Bias

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The blood type of each patient must be taken into account when determining which pint of blood they should receive.

Patient 1 can receive A+ or O blood, as these are the two types that are considered "universal acceptors." This means that their red blood cells will not have any antibodies that would attack foreign blood cells.

Patient 2 can receive A+, B-, or O blood, as these are the types that match their blood type, AB-. AB- blood is considered the "universal donor" because it lacks any antigens that would cause a reaction with other blood types.

Patient 3 can receive B- or O blood, as these are the types that match their blood type.

Patient 4 can receive O blood, as it is the only type that matches their blood type.

Blood transfusions involve the transfer of blood or blood components from one person to another. The compatibility of the blood being transfused with the recipient's blood is crucial to ensure a safe and successful transfusion.

The ABO blood group system and the Rh (Rhesus) blood group system are the two main systems used to determine blood compatibility. The ABO system has four blood types: A, B, AB, and O. The Rh system has two possible results: positive or negative.

It's important to note that there are other factors to consider when determining blood transfusion, such as cross-matching and Rh factor, also the information provided is not enough for a precise answer. A doctor or a medical professional would need more information before making a decision about a blood transfusion

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Based on the sample response given, the statements included in the explanation on the horizontal line test are:

a reference to the horizontal-line test.

a statement that the function is one-to-one.

inverse is a function.

What is the horizontal-line test?

The horizontal line test is used to not only find out if a graph has an inverse function, but also if that inverse is also a function itself.

To pass the horizontal line test, the function has to be one-to-one which means that a horizontal line can intersect the graphed function at one point in all places. If this happens, then there is an inverse and the inverse itself is a function.

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Answer:

(36 Days)

Step-by-step explanation:

15% of 240 days

= 0.15 x 240

= 36 days

Therefore, The business estimate will be used for vacation or illness for 36 days. Start Learning & Start Growing! edge2023!!!

*DROPS THE MIC*

Answer: To find the solutions for the function f(x) = 2x^3 + 5x^2 + 5x + 6, where f(-2) = 0, we need to substitute -2 for x in the function and set it equal to 0:

f(-2) = 2(-2)^3 + 5(-2)^2 + 5(-2) + 6 = 0

Simplifying this equation, we get:

8 - 20 - 10 + 6 = 0

We then proceed to factor the polynomial:

2x^3 + 5x^2 + 5x + 6 = (2x + 3)(x+1)(x+2) = 0

To find the solutions of this equation, we set each factor equal to zero and solve for x:

2x + 3 = 0 => x = -3/2

x + 1 = 0 => x = -1

x + 2 = 0 => x = -2

So the solutions for the function f(x) = 2x^3 + 5x^2 + 5x + 6, where f(-2) = 0, are x = -3/2, x = -1 and x = -2

Step-by-step explanation:

The final velocity of the car is of:

25 m/s.

The velocity function is a linear function, modeled as follows:

v(t) = v(0) + at.

In which:

The parameter values for this problem are given as follows:

Hence the velocity function is given as follows:

v(t) = 5 + 2t.

At a time of 10 seconds, the velocity is given as follows:

v(10) = 5 + 2(10)

v(10) = 25 m/s.

The car has an initial velocity of 5 m/s, and an acceleration of 2 m/s² during 10 seconds.

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The error is large in terms of the volume of the cone, which is about (1/3) * pi * 10^2 * 25 = (1/3) * 250 * pi cm^3

The volume of something determines how much space it takes up. Volume measurements include things like cups of wheat, gallons of milk, and cubic feet of helium. An object's weight serves as a proxy for its weightiness. Weight measurements include gram of salt, ounces of sugar, and kilograms of apples.

Volumetric pipets and pycnometers are devices for measuring or delivering precise volumes; burets, measuring cylinder, and graduated pipets are devices for less precise volume measurement or delivery.

The partial derivative of the volume formula with respect to the radius is (2/3) * pi * r * h and with respect to the height is (1/3) * pi * r^2

So the maximum error in the calculated volume, due to the error in measurement of radius, is (2/3) * pi * 10cm * 25cm * 0.1cm = (2/3)* 25 * pi cm^3

and the error in height is (1/3) * pi * 10cm^2 * 0.1cm = (1/3) * pi cm^3

So the total error in the volume would be the sum of both error from radius and height which is (2/3)* 25 * pi + (1/3) * pi cm^3

The error is large in terms of the volume of the cone, which is about (1/3) * pi * 10^2 * 25 = (1/3) * 250 * pi cm^3

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The solution to the given inequality is y<3.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is 18+3y<27.

Here, subtract 18 on both the sides of an inequality, we get

3y<9

Divide 3 on both the sides of an inequality, we get

y<3

Therefore, the solution to the given inequality is y<3.

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