Find the exact value of the real number y. y = arcsin ( square root 3/2)​

Answer:

Option A) m^9.

Step-by-step explanation:

To simplify the given expression, we can use the rules of exponents which state that when we multiply powers with the same base, we can add their exponents.

So, m² ∙ m⁶ ∙ m can be simplified as:

m² × m⁶ × m = m^(2+6+1) = m^9

Therefore, the simplified form of m² ∙ m⁶ ∙ m is m^9.

the area of the region of points satisfying the inequalities x ≤ 0, y ≤ 0, and y ≥ |x + 4| − 5 is 12.5 square units.

The statement is not true, since 13 is not less than 6. Therefore, the point (3, 2) is not a solution of the linear inequality 3x + 2y < 6.

To determine if the point (3, 2) is a solution of the linear inequality 3x + 2y < 6, we substitute the values of x and y in the inequality and check if it is a true statement or not.

A linear inequality is an inequality in which the variables have a degree of one, and the inequality can be expressed as a linear equation with an inequality symbol. A linear inequality can be represented graphically as a line with a shaded region that either includes or excludes certain points in the coordinate plane.

For example, the inequality 2x + 3y > 6 is a linear inequality. To graph this inequality, we can first plot the line 2x + 3y = 6 by finding its x and y intercepts, which are (3, 0) and (0, 2), respectively. Then, we can choose a test point not on the line, such as (0, 0), and substitute its coordinates into the inequality to see if it is a solution.

3(3) + 2(2) < 6

9 + 4 < 6

13 < 6

The statement is not true, since 13 is not less than 6. Therefore, the point (3, 2) is not a solution of the linear inequality 3x + 2y < 6.

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The histogram below shows the distribution of wild unicorns across the six enchanted forests on Mystical Island. To create a histogram, we first need to determine the range and interval for our bins. We can set the range from 0 to 20 and choose an interval of 5.

The x-axis represents the range of unicorn counts, and the y-axis shows the number of forests that fall into each range of 0 5 10 15 20

As we can see from the histogram, the majority of the enchanted forests have between 10 and 15 wild unicorns. Only one forest has fewer than 5 wild unicorns, while another has more than 15. This visualization allows us to easily compare the unicorn populations across the different forests and identify any outliers.

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The solution to the equation 123x + 360y = 99 is x = 22 and y = -11.

What is Linear Diophantine Equation?

An equation with two or more integer unknowns that are all to a maximum degree of one is known as a linear diophantine equation (LDE).

To solve the equation 123x + 360y = 99, we can use the extended Euclidean algorithm, which is a method for finding the greatest common divisor (GCD) of two integers and expressing it as a linear combination of those integers. We can use the same algorithm to find a solution to the given equation.

First, we need to find the GCD of 123 and 360. We can use the Euclidean algorithm for this:

gcd(123, 360) = gcd(123, 360 - 123*2) = gcd(123, 114)

gcd(123, 114) = gcd(123 - 114, 114) = gcd(9, 114)

gcd(9, 114) = gcd(9, 114 - 9*12) = gcd(9, 6)

gcd(9, 6) = gcd(9 - 6*1, 6) = gcd(3, 6)

gcd(3, 6) = gcd(3, 6 - 3*2) = gcd(3, 0)

gcd(3, 0) = 3

Therefore, the GCD of 123 and 360 is 3.

Now we can use the extended Euclidean algorithm to find integers s and t such that 123s + 360t = 3. This is done by working backwards through the Euclidean algorithm and expressing each remainder as a linear combination of the previous two integers:

gcd(123, 360) = 3

3 = 123s + 360t

3 = 9 - 114

 = 9 - (360 - 123*2)

 = 123*2 - 360*1

s = 2, t = -1

Now we can multiply both sides of the equation by 33 to get a solution to the original equation:

123x + 360y = 99

123*2*33 + 360*(-1)*33 = 3*33

123*66 + 360*(-33) = 99

Finally, we can divide both sides by 3 to get a solution in integers:

123*22 + 360*(-11) = 33

Therefore, x = 22 and y = -11 is a solution to the equation 123x + 360y = 99.

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Based on the data given, the box plot that represents the data is B.

The minimum value is the smallest value in a given set of data. In other words, it is the lowest number in the set. The minimum value is an important measure of central tendency in statistics and is often used in data analysis to understand the range and distribution of the data.

Based on the data given, the box plot that represents the data is B.

This is because the minimum value of the data set is 22, which is shown by the bottom whisker of the box plot. The first quartile is 23, the median is 25, and the third quartile is 27, which are shown by the box. The maximum value is 28, which is shown by the top whisker. The outlier is not shown in this box plot, but it would be indicated by a small circle or asterisk outside of the whiskers.

Box plot A does not include the maximum value of 28, while box plot C does not include the minimum value of 22. Box plot D shows the minimum and maximum values correctly, but the quartile values and whiskers are incorrect. Box plot Y does not have any boxes or whiskers, and box plot X and Z do not show all of the values correctly.

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Answer:

  B

Step-by-step explanation:

You want the difference of the rational expressions (6/x) and (5x/(x+2)).

The difference of rational expressions is found the same way any difference of fractions is found. The fractions are written using a common denominator, and the difference is taken of the numerators.

  [tex]\dfrac{6}{x}-\dfrac{5x}{x+2}=\dfrac{6(x+2)}{x(x+2)}-\dfrac{x(5x)}{x(x+2)}\\\\\\=\dfrac{6x+12-5x^2}{x(x+2)}=\boxed{\dfrac{-5x^2+6x+12}{x^2+2x}}[/tex]

__

Additional comment

Once you realize the common denominator is x(x+2) = x²+2x, you have eliminated all but the correct answer choice.

Answer:

To calculate the infusion rate, we need to use the formula:

Infusion rate (ml/hour) = (dose ordered * patient weight * 60) / (drug concentration * 1000)

where:

Dose ordered is the prescribed dose of the drug per unit of time (0.1 mg/kg/hr in this case).

Patient weight is the weight of the client (78 kg in this case).

Drug concentration is the concentration of the drug in the solution (25 mg/250 ml or 0.1 mg/ml in this case).

Substituting the values we have:

Infusion rate = (0.1 mg/kg/hr) * (78 kg) * 60 / (0.1 mg/ml * 1000)

Simplifying:

Infusion rate = 4.68 ml/hour

Therefore, the practical nurse should program the infusion pump to deliver 4.68 ml/hour (rounded to the nearest tenth).

Answer:

To calculate the infusion rate, we need to use the following formula:

Infusion rate (mL/hour) = Total volume (mL) x Infusion rate (mL/hour) / Time (hour)

First, let's calculate the client's infusion rate in mg/hour:

Infusion rate (mg/hour) = 0.1 mg/kg/hour x 78 kg = 7.8 mg/hour

Now, let's convert the pancuronium dose to mg/mL:

25 mg/250 mL = 0.1 mg/mL

To calculate the total volume of the infusion, we need to assume a time frame. Let's assume that the client needs the infusion for 1 hour. Then:

Total volume (mL) = Infusion rate (mg/hour) / Dose (mg/mL) = 7.8 mg/hour / 0.1 mg/mL = 78 mL/hour

Therefore, the practical nurse should program the infusion pump to deliver 78 ml/hour.

52.4744174417441… is a rational number because it can be expressed as the ratio of two integers: 524691.7 and 9999.

A rational number is one that can be represented as the product of two numbers with a non-zero denominator. Integers, fractions, terminating decimals, and repeating decimals are all examples of rational numbers. A rational number can either have its decimal representation end, as in the instance of 1/2 = 0.5, or it can repeat a pattern of digits, as in the case of 1/3 = 0.3333. Irrational numbers, on the other hand, have decimal representations that do not end or recur and cannot be stated as the ratio of two integers. The square root of 2, pi, and e are a few examples of irrational numbers.

The given rational number is x = 52.4744174417441….

Now, x as a ratio of two integers is shown as:

10000x = 524744.1744174417…

Subtract x from both sides:

9999x = 524691.7

x = 524691.7/9999

Hence, 52.4744174417441… is a rational number because it can be expressed as the ratio of two integers: 524691.7 and 9999.

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Answer:

The Burnets spent .22 × $5,825 = $1,281.50 on taxes and insurance.

The length of the base with area 25/18 square meters is 5/3 meters. This answer is in its simplest form.

The height of a triangle is the length of the line segment that is drawn from the vertex of the triangle perpendicular to the base.

The area of a triangle is given by the equation

A = 1/2 * base * height.

Therefore, we can substitute the value of the area and the height of the triangle into the equation to solve for the base.

A = 1/2 * b * (5/3)

25/18 = 1/2 * b * (5/3)

We will divide left side of the equation by 5/3.

(25/18) / (5/3) = (1/2)*b

(25/18) * 3/5 = (1/2)*b

Now, we can solve for b by dividing the left side of the equation by 1/2

(5/6) / (1/2) = b

b = 5/6 * (2/1)

b = 5/3

Therefore, the length of the base is 5/3 meters. This answer is in its simplest form.

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To distribute -3√3 to (2 + √6), we can use the distributive property:

-3√3 (2 + √6) = (-3√3 * 2) + (-3√3 * √6)

Next, we can simplify each term using the product rule of radicals:

(-3√3 * 2) = -6√3

(-3√3 * √6) = -3√(3

Therefore, when we distribute -3√3 to (2 + √6), we get:

-3√3 (2 + √6) = -6√3 - 9√2.

Answer:

To calculate Darrius' monthly take-home pay, we first need to calculate his annual state income tax. We do this by multiplying his yearly salary by the state income tax rate:

$42,350 x 3.07% = $1,292.94

Next, we subtract the state income tax from his annual salary to get his annual net income:

$42,350 - $1,292.94 = $41,057.06

Finally, we divide his annual net income by 12 to get his monthly take-home pay:

$41,057.06 / 12 = $3,421.42

Therefore, Darrius' monthly take-home pay is $3,421.42.

Step-by-step explanation:

Answer: x= -20

Step-by-step explanation:

The central angle of the given arc, subtending a circle with a radius of 7 cm and a length of 14 cm, is approximately 103.13 degrees.

An arc is a section of a circle's or curve's border in mathematics. It is additionally known as an open shape. The circumference, also referred to as the perimeter, is the measurement around a circular that defines its edge. Consequently, the arc is defined as the separation between any two locations along its circumference.

The angle that an arc of a circle subtends at the center is called the central angle. The central angle is measured in degrees and is formed by the radii that make up the arc.

Given:

Radius of the circle (r) = 7 cm

Length of the arc (s) = 14 cm

To find the central angle (θ) of the arc, we can use the formula:

θ = (s / r) * (180 / π)

where:

s = length of the arc

r = radius of the circle

π = pi (approximately 3.14159...)

Plugging in the given values:

θ = (14 / 7) * (180 / π)

θ = 2 * (180 / π)

θ ≈ 103.13 degrees (rounded to two decimal places)

So, the central angle of the given arc, subtending a circle with a radius of 7 cm and a length of 14 cm, is approximately 103.13 degrees.

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We need a sample size of 98 to estimate the mean with 90% confidence and an error of ±0.25 mpg, using the given range of fuel economy for the 2016 Toyota 4Runner.

Standard deviation is a measure of the amount of variation or dispersion in a set of data. It is a statistical measure that is used to quantify the amount of variation or spread of a set of data values relative to the mean or average value of the data.

(a) Using Method 3, the Empirical Rule for a normal distribution, we know that for a normal distribution, approximately 68% of the values fall within 1 standard deviation from the mean, 95% fall within 2 standard deviations from the mean, and 99.7% fall within 3 standard deviations from the mean.

Therefore, to find the standard deviation for the given range of 17 to 22 mpg, we can use the Empirical Rule as follows:

The range between the mean and the upper limit (22 mpg) is 3 standard deviations, so the standard deviation can be estimated as (22-17)/3 = 1.6667 mpg.

Thus, the estimated standard deviation using Method 3 is 1.6667 mpg, rounded to 4 decimal places.

(b) To find the sample size required to estimate the mean with 90% confidence and an error of ±0.25 mpg, we can use the following formula:

[tex]n = (z*(E))^2[/tex]

where n is the sample size, z is the z-score corresponding to the desired confidence level (90% = 1.645), σ is the estimated standard deviation from part (a), and E is the desired margin of error (±0.25 mpg).

Substituting the values, we get:

[tex]n = (1.645*(1.6667/0.25))^2[/tex]

n ≈ 97.15

Rounding up to the nearest whole number, we get the sample size of 98.

Therefore, we need a sample size of 98 to estimate the mean with 90% confidence and an error of ±0.25 mpg, using the given range of fuel economy for the 2016 Toyota 4Runner.

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Answer: 49

Step-by-step explanation:

6^2=36

26/2=13

36+13=49

HOPEFULLY I HELPED :)

The length of the missing side is approximately 4.73 units.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Here, we have

Given:

∠A = 33.7°

∠C = 26.4°

We have to find the value of b.

Let's label the missing side as b, and use sin(A) = opposite/hypotenuse to find the length of the side opposite angle A:

sin(A) = opposite/hypotenuse

sin(33.7°) = b/8

b = 8 × sin(33.7°)

b ≈ 4.726

Hence, the length of the missing side is approximately 4.73 units.

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Answer

2268 ft²

Step-by-step explanation

1 yard is equivalent to 3 feet. Using this conversion factor, the equivalence of 21 yd is:

 [tex]21 \ \text{yd}=21 \ \text{yd}\times\dfrac{3 \ \text{ft}}{1 \ \text{yd}}[/tex]

[tex]\text{Simplifying the units:}[/tex]

     [tex]21 \ \text{yd}=\dfrac{21\times3}{1 \ \text{}} \ \text{ft}[/tex]

      [tex]21 \ \text{yd}=63 \ \text{ft}[/tex]

Similarly, the equivalence of 12 yards is:

[tex]12 \ \text{yd}=12 \ \text{yd}\times\dfrac{3 \ \text{ft}}{1 \ \text{yd}}[/tex]

     [tex]12 \ \text{yd}=12\times3 \ \text{ft}[/tex]

        [tex]12 \ \text{yd}=36 \ \text{ft}[/tex]

Therefore, the length of the bed is 63 ft and the width is 36 ft.

Finally, the area of the bed (a rectangle) is calculated as follows:

[tex]\text{A}=\text{length}\times\text{width}[/tex]

       [tex]\text{A}=63\times36[/tex]

       [tex]\text{A}=2268 \ \text{ft}^2[/tex]

Answer: 1/6 of a pie

Step-by-step explanation: each friend receives 1/6 of a pie because there are 2 pies being distributed to 12 friends. 2/12 = 1/6

Answer:

1/6 of the pie.

Step-by-step explanation:

We Know

Two pies are shared among 12 friends.

How much did each friend receive?

We take

2 / 12 = 1/6 of the pie

So, each friend receives 1/6 of the pie.

Answer:

The volume is 60cm³

Step-by-step explanation:

(bxhxl)/2 = answer

(5x4x6)/2

5x4 = 20

20x6=120

120/2 = 60

Thus, number of more people who prefer mystery books over historical

fiction books are 48.

A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarise a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments. A certain category is represented by each segment.

Given data:

Number of mystery books = 18% of 600

= 18*600 / 100

= 108

Number of historical fiction books = 10% of 600

= 10*600 / 100

= 60

Difference = Number of mystery books - Number of historical fiction books

Difference = 108 - 60

Difference = 48

Thus, number of more people who prefer mystery books over historical

fiction books are 48.

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Complete question:

The circle graph shows the results of a survey about favorite kinds of books. If 600 people were surveyed, how many more people prefer mystery books than historical fiction books?

The picture is attached.

The maximum head breadth that the helmets will fit is apprοximately 7.96 inches, which rοunds tο 8.0 inches (οptiοn A).

We can use the Z-scοre fοrmula tο find the Z-scοre cοrrespοnding tο the cutοff pοint:

Z = (X - μ) / σ

where X is the head breadth we want tο find, μ is the mean head breadth, σ is the standard deviatiοn, and Z is the Z-scοre cοrrespοnding tο the cutοff pοint.

We want tο find the Z-scοre such that the area tο the right οf it under the standard nοrmal distributiοn curve is 0.025. We can use a standard nοrmal distributiοn table οr calculatοr tο find this Z-scοre, which turns οut tο be apprοximately 1.96.

Tο find the maximum head breadth that the helmets will fit, we need tο find the cutοff pοint beyοnd which the head breadths are in the largest 2.5%.

Nοw we can sοlve fοr X:

1.96 = (X - 6.0) / 1.0

X - 6.0 = 1.96

X = 7.96

Therefοre, the maximum head breadth that the helmets will fit is apprοximately 7.96 inches, which rοunds tο 8.0 inches (οptiοn A).

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Hence, the expressions 8 x + 1 and 5/x are equal. F) 8x+(66) and J) 5x + (101) are the two equivalent expressions.

A mathematical sentence without an equal sign that comprises numbers, quantities, and operations is known as an expression. By changing variables with constants and using the order of actions, it can be evaluated or made simpler. For instance, the phrases "3x + 7" and "4y - 2" are equations, whereas "3x + 7 = 16" is an expression.

given

F and J are the two expressions that are equivalent.

F: 8 ÷ x + (6/6)

6/6 reduced to 1: 8 x + 1

J: 5 x x 1 Converting 5 x to 5x-1, 5x-1 x 1 equals 5/x

Hence, the expressions 8 x + 1 and 5/x are equal. F) 8x+(66) and J) 5x + (101) are the two equivalent expressions.

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The complete question is:-  

Which two expressions are equivalent?

(6.7D | Lesson 6)

F 8÷x+(6'6) and 8÷x. 1

G 6-2 (x - x) and 6 ÷ 2

H 14 ÷ 7. (xx) and 14 ÷ 7

J 5÷x(101)10+and 5 x 1•

Answer:

3 ÷ 2/5 = 3 × 5/2 = 15/2 = 7 1/2

Mohal is 5 years old, and Kiran is 7 years old.

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Let's assume that Mohal's age is x. Then, Kiran's age is x + 2, since their ages are consecutive odd integers and Kiran is older than Mohal.

We are given that the sum of the square of Kiran's age and 3 times Mohal's age is 64:

(x + 2)² + 3x = 64

Expanding the left-hand side and simplifying, we get:

x² + 7x - 56 = 0

This is a quadratic equation in standard form. We can solve for x by using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 7, and c = -56.

Plugging these values into the formula, we get:

x = (-7 ± √(7² - 4(1)(-56))) / 2(1)

x = (-7 ± √(289)) / 2

We take the positive root because x represents Mohal's age, which is a positive integer. Therefore:

x = (-7 + 17) / 2 = 5

So, Mohal is 5 years old, and Kiran is 7 years old.

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To solve the equation:

1/(x+1) + 9/(x+9) = 1

First, we can simplify the equation by finding a common denominator:

((x+9)+9(x+1))/(x+1)(x+9) = 1

Simplifying the numerator, we get:

(10x+18)/(x+1)(x+9) = 1

Cross-multiplying gives:

10x+18 = (x+1)(x+9)

Expanding the right side of the equation, we get:

10x+18 = x^2+10x+9

Simplifying and rearranging gives:

x^2-9 = 0

Using the quadratic formula, we solve for x:

x = (±sqrt(81))/1

x = ±9

Therefore, the solutions to the equation are x = -9 and x = 9.

Answer:

24 boys

Step-by-step explanation:

If 60% of the students in a class are boys, 40% of the students are girls.

Then 16/0.4 = 40 students total

40 - 16 = 24 boys

or you can use 40 x 0.6 = 24 boys