If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?​

\(-1 + i\sqrt3\) lies in the second quadrant of the complex plane, so its argument is

\(\arg(-1 + i\sqrt3) = \pi - \tan^{-1}\left(-\sqrt3\right) = \dfrac{2\pi}3 = 120^\circ\)

Then any sixth root of \(-1+i\sqrt3\) will have an argument of

\(\dfrac{120^\circ + 360^\circ n}6\)

where \(n\in\{0,1,2,3,4,5\}\).

When \(n=0\), we have

\(\dfrac{120^\circ}6 = 20^\circ\)

so D is a sixth root.

The other sixth roots are separated by arguments of 60 degrees (80, 140, 200, 260, and 320).

Using the slope-point formula for the equation of a line we get:

Answer:

The dimensions of the box if it is to use the minimum possible amount of metal are,

⇒ 2.714 m, 2.714 m, 1.358 m

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A container with an open top is to have 10 m³ capacity.

Now,

Let the dimensions are x, y and z.

Since, Volume of box = 10 m³

Hence, We get;

⇒ xyz = 10

⇒ z = 10/xy

Since, A container is open in top.

Hence, The surface area = 2xz + 2yz + xy

Substitute z = 10/xy;

⇒ S.A = 2x (10/xy) + 2y (10/xy) + xy

          = 20/y + 20/x + xy

For minimum metal;

⇒ d (S.A)/ dx = 0

⇒ - 20/x² + y = 0

⇒ y = 20/x²  ..(i)

And, d (S.A) / dy = 0

⇒ - 20/y² + x = 0

⇒ x = 20/y²   ..(ii)

Divide equation (i) and ((ii);

⇒ x = y

Hence, We get;

⇒ xyz = 10

⇒ x³ = 10

⇒ x = 2.714

And, y = 2.714

So, The value of z is,

⇒ z = 10/xy

⇒ z = 10 / 2.714×2.714

⇒ z = 1.358 m

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Answer:

-5.875

Step-by-step explanation:

Answer:

\(y1 = 4 \\ x1 = 3\)

\(y - y1 = m(x - x1)\)

\(y - 4 = 0(x - 3)\)

\(y - 4 = 0\)

\(y = 4\)

Step-by-step explanation:

plsssssssssssssssssssssssssssssssssssssssssssssssssssssssdssssssssssssssssssssssssssssssssssssssssss do it don't be lazy.

The coordinates of the equation are (-2, -7), (-1, -5), (0, -3), (1, -1) and (2, 1)

The value of x and y in the given equation or in the graph is together represented by (x, y) and called coordinates.

Given is an equation, y = 2x-3

And we have x values = -2, -1, 0, 1 and 2, To find the corresponding value of y, we will use one by one the values of x in the equations,

When, x = -2,

y = -2(2) - 3

y = -7

(-2, -7)

When x = -1

y = 2(-1) - 3

y = -5

(-1, -5)

When x = 0

y = 2(0) - 3

y = -3

(0, -3)

When x = 1

y = 2(1)-3

y = -1

(1, -1)

When x = 2

y = 2(2) - 3

y = 1

(2, 1)

Hence, the value of y are -7, -5, -3, -1 and 1

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After 13 hours, there will be 1145 bacteria, with their number doubling every 28 hours.

The exponential growth formula is y = y0.e (kt).

The formula for exponential decay is y = y₀.e^(-kt).

We may apply the formula, to double the rate of bacterial growth.

\(y_f=y_0*2^\frac{t_r}{t}\), where   \(y_f\) represents the final population, \(y_0\)  is the initial population, \(t_r\)  is the period of time we must estimate, and  \(t\)  represents the time rate growth.

Thus, based on the information provided, the quantity of bacteria after 13 hours will be,

\(y_f=830*2\frac{13}{28} \\\\y_f=830*1.38\\\\y_f=1144.86\)

or 1145 bacterias.

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Answer: The height of Nasim's kite above the ground is 51.79 feet

Step-by-step explanation

Let h represent the height from Nasim hand to the kite, hence:

sin(28) = h / 105

h = 49.29

Kite height above the ground = 2.5 + 49.29 = 51.79 feet

The height of Nasim's kite above the ground is 51.79 feet

Answer:

The height of Nasim kite above the ground is 51.79 feet

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height from Nasim hand to the kite, hence:

sin(28) = h / 105

h = 49.29

Kite height above the ground = 2.5 + 49.29 = 51.79 feet

The height of Nasim kite above the ground is 51.79 feet

Answer:

The parameter comes from the population, and the population is set. The statistic comes from the sample, and multiple samples can be taken from a population, therefore it can vary.

Step-by-step explanation:

Answer:

x=5    y=3      z=5

Step-by-step explanation:

The coefficient is the number in front of the variable

Answer:

Step-by-step explanation:

The coefficient in an expression is the multiplier of a designated part of a term of the expression.

__

The given expression is

  5z -2 +6x +3y

It consists of four (4) terms, added together. One term is a constant, -2. The others each have a single variable that is multiplied by a constant. When we ask for the coefficient of the variable, we are asking for the value of that constant multiplier.

The term containing x is 6x. The multiplier of x in that term is 6, so we say ...

  the coefficient of x is 6.

The term containing y is 3y. The multiplier of y in that term is 3, so we say ...

  the coefficient of y is 3.

The term containing z is 5z. The multiplier of z in that term is 5, so we say ...

  the coefficient of z is 5.

__

In an expression such as πr²h, different parts of the expression will have different coefficients. If we ask for the coefficient of the expression, we are generally asking for the constant: π. (The Greek letter pi is the symbol used to represent the irrational constant ratio between the circumference and diameter of a circle. Is is about 3.1415926535....)

If we ask for the coefficient of h, we are asking for the product (πr²) that multiplies h in this expression. Similarly, the coefficient of r² is (πh). Note that we have specified a "designated part" of the expression for which we want the coefficient. This is important when we are solving equations.

__

The commutative property of multiplication means that parts of a product can be written in any order. That is, 5·z is the same product as z·5. When the constant and variable parts of the expression can be unambiguously identified, the order does not matter. In some cases, a constant coefficient may come in several parts: 3z·5·2 has a z-coefficient of 30, for example.

See below for a case where there may be some ambiguity.

__

In the expression r², the constant 2 that comes after the variable, written as a superscript, is called an "exponent," not a coefficient. Often on Brainly, and sometimes in curriculum materials, you will see this written as r2, because superscripts do not get properly rendered. If you're writing this in plain text, the form r^2 is preferred.

Based on the description provided, the section of the chart that represents the point where a bill is first debated in subcommittees is: C and D

In the given chart, the parallel lines represent the progression of a bill through various stages in the legislative process. The boxes on the top line represent one set of actions or steps, while the boxes on the bottom line represent another set of actions or steps.

Moving from left to right on the chart, the boxes A and B are paired, representing a particular stage in the process. Similarly, the boxes C and D are paired, indicating another stage in the process.

In the context of the question, the stage where a bill is first debated in subcommittees is represented by the boxes C and D.

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A multiplication equation to show an equivalent fraction of 15 using fifteenths would gives 10/75

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We have to write an equivalent fraction of 15 using fifteenths.

2/15

So let multiply by 5 .

2 / 15 x  5/ 5 = 10/75

Thus, 10/75 is equivalent expression.

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The value for the Inequality 13x ≤ 200 is x ≤ 15.384.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

13 times a number x is less than or equal to 200.

Now, Writing the Inequality Mathematically

13x ≤ 200

x ≤ 200 / 13

x ≤ 15.384

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Answer:

5: 40.6

6: 26.57

7: 22.21

8: 66.35

Step-by-step explanation:

I am going to assume that you know

SOH CAH TOA (if you don't just ask)

For 5: we have the adjacent and opposite side, we need the angle

I think here it's easiest to use TOA

so we have

tanx=60/70

take the arctan or tan^-1 and get

arctan(60/70)=x x= 40.6

For number 6 it's just the same deal

tanx=10/20

arctan(10/20) =x =26.57

For number 7 we have the adjacent side and we need to find the oppsoite side

for this I will once again use TOA

tan(48)=x/20

20tan(48)=x=22.21

For number 8 it's the same deal as 7

tan53=x/50

50tan53=x=66.35

Answer:

It is True 200% legit!

Step-by-step explanation:

The 90.1 percent can be written as a fraction in the simplest form is 901/1000.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have a percentage 90.1%

To convert it into the fraction in the simplest form we can do as follows:

= 90.1%

\(= \dfrac{90.1}{100}\)

= 0.901

\(= \dfrac{901}{1000}\)

Thus, the 90.1 percent can be written as a fraction in the simplest form is 901/1000.

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The expression is written as;

Part A : Length, L = 4x - 5

Part B:  (4x-5)(3x)

The formula for the area of a rectangle is expressed as;

A = lw

Given that;

substitute the expressions, we get;

12x² - 15x = 3x(l)

divide both sides by 3x, we get;

Length, l = 12x²/3x - 15x/3x

Divide the values, we get;

Length, L = 4x - 5

Area = (4x-5)(3x)

multiply the values

Area = 12x² - 15x

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Answer:

-5/3

Step-by-step explanation:

10-15=-5

6-3=3

Answer:

-5/3

Step-by-step explanation:

m=y2-y1/x2-x1

10-15-(-5)

6-3=3

-5/3

hope this helped :3

sorry if it is wrong

Answer:

DF is 3 and angle B is 28

Step-by-step explanation:

If both are congruent, the measurements are the same.

Answer:

DF = 3, Angle B = 28

Step-by-step explanation:

Look how the congruence statement is written. Ac goes with Df and angle E goes with angle B, so they are congruent.

The algebraic values of x include:

Using the same reasoning as in the previous problem:

24² + 45² = x²

576 + 2025 = x²

2601 = x²

x = ±51

Since x represents a length, discard the negative solution. Therefore, the value of x is 51.

Using the Pythagorean Theorem:

30² + 40² = x²

900 + 1600 = x²

2500 = x²

x = ±50

Since x represents a length, discard the negative solution. Therefore, the value of x is 50.

Using the Pythagorean Theorem:

18² + 80² = x²

324 + 6400 = x²

6724 = x²

x = ±82

Since x represents a length, discard the negative solution. Therefore, the value of x is 82.

Using the Pythagorean Theorem:

18² + 4² = x²

324 + 16 = x²

340 = x²

x = √340 = 2√85

Therefore, the value of x is 2√85 in simplest radical form.

Using the Pythagorean Theorem:

8² + 5² = x²

64 + 25 = x²

89 = x²

x = √89

Therefore, the value of x is √89 in simplest radical form.

Using the Pythagorean Theorem:

20² + 18² = x²

400 + 324 = x²

724 = x²

x = √724 = 2√181

Therefore, the value of x is 2√181 in simplest radical form.

Using the Pythagorean Theorem:

25² + 3² = x²

625 + 9 = x²

634 = x²

x = √634

Therefore, the value of x is √634 in simplest radical form.

Using the Pythagorean Theorem:

3² + 6² = x²

9 + 36 = x²

45 = x²

x = √45 = 3√5

Therefore, the value of x is 3√5 in simplest radical form.

Using the Pythagorean Theorem:

22² + 4² = x²

484 + 16 = x²

500 = x²

x = √500 = 10√5

Therefore, the value of x is 10√5 in simplest radical form.

To determine if a triangle is a right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore:

a² + b² = c²

Substituting a = 8, b = 15, and c = 17:

8² + 15² = 17²

64 + 225 = 289

289 = 289

Since the equation is true, the triangle satisfies the Pythagorean Theorem and is therefore a right triangle.

Using the same method:

27² + 36² = 45²

729 + 1296 = 2025

2025 ≠ 2025

Since the equation is false, the triangle does not satisfy the Pythagorean Theorem and is therefore not a right triangle.

Using the same method:

9² + 11² = 4²

81 + 121 = 16

202 ≠ 16

Since the equation is false, the triangle does not satisfy the Pythagorean Theorem and is therefore not a right triangle.

To determine the classification of this triangle, compare the lengths of its sides. If all sides are less than the sum of the other two, then the triangle is acute; if one side is greater than or equal to the sum of the other two, then the triangle is obtuse; and if one side is equal to the sum of the other two, then the triangle is degenerate (a straight line).

Substituting a = 3, b = 4, and c = 6:

a + b = 3 + 4 = 7 < c

b + c = 4 + 6 = 10 > a

a + c = 3 + 6 = 9 > b

Since none of the sides are equal to or greater than the sum of the other two, the triangle is acute.

Substituting a = 9, b = 11, and c = 16:

a + b = 9 + 11 = 20 < c

b + c = 11 + 16 = 27 > a

a + c = 9 + 16 = 25 > b

Since none of the sides are equal to or greater than the sum of the other two, the triangle is acute.

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Image transcribed:

Algebra Find the value of x.

1. 12, 9, x

To start, use the Pythagorean Theorem. Then substitute 9 for a, 12 for b, and x for c.

2. 45 24 x

3. 30, 40, x

4. 80, 18, x

Algebra Find the value of x. Express your answer in simplest radical form.

8. 18, 4, x

9. 8, 5, x

10. 20, 18, x

11. 25, 3, x

12. 3, 6, x

13. 22, 4, x

Is each triangle a right triangle? Explain.

16. 15, 17, 8

17. 27, 45, 36

18. 9, 11, 4

The lengths of the sides of a triangle are given. Classify each triangle as acute, right, or obtuse.

19. 3,4,6

To start, compare to a+b. Substitute the greatest length for c.

20. 9, 11, 16

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

The question is not complete, below is the complete question:

What is meant by the term 90% confident? when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.

b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.

c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.

d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.

Answer:

The correct answer is:

If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.  (c)

Step-by-step explanation:

a 90% confidence level means that if repeated samples were taken, 9 out of 10 times, the confidence intervals of the sample chosen will be close to the mean (true value), which is a true representation of the population parameter. when using confidence intervals, there are always margins of allowable accuracy, and this is suggested by using standard diviations snd variances.

I attached a simple document to this answer that will give you more insight into confidence intervals used in statistics.

Answer:

Length = 14 m, Width = 7 m

Step-by-step explanation:

Let the length is l and width is b.

Width, b = l-7

Area of the rectangle, A = 98 m²

We know that, the area of a rectangle is as follow :

\(A=lb\)

So,

\(98=l(l-7)\\\\98=l^2-7l\\\\l^2-7l-98=0\\\\l^2+7l-14l-98=0\\\\l(l+7)-14(l+7)=0\\\\l=14,-7\)

Length can't be negative. So,

Width, b = 14-7 = 7 m

So, the dimensions of the rectangle are 14 m and 7 m respectively.

Answer:

\(the \: time \: will \: be \: \boxed{1.8 \: hrs} \to \: \\ this \: is \: true \: since \: the \: car \: traveled \: with \: lower \: speed : \\ it \: will \: then \: cover \: the \: same \: distance \\ \: with \: mor e\: time. \: this \: is \: true \:s ince \to \boxed{1.8 \: hrs \: > 1.6 \: hrs}\)

Explanation:

\(since \: velocity \: is \: given \: as \to \\ v = \frac{d}{t} \\ then \: the \: time \: is \to \\ t = \frac{d}{v} \: since \: (d) \: is \: constant \: in \: this \: case \to \\ when \: (v\: is \: 100 \: km {(h)}^{ - 1} ) \: then \: the \: time \: is \to \\ t = \frac{160}{100} = 1.6 \: hrs \\ \\ when \: (v\: \: is \: 90 \: {km(h)}^{ - 1}) \: then \: the \: time \: is \to \\ t = \frac{160}{90} = 1.7777777778 \\ hence \: the \: time \: will \: be \: \boxed{1.778 \: hrs}\)

♨Rage♨

There are 4 cups of brown sugar are required for every 12 cups of white sugar.

A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:

2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar

To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:

2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar

24 cups brown sugar = 6x cups brown sugar

x = 24/6

x = 4

So, 4 cups of brown sugar are required for every 12 cups of white sugar.

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To transform a function 1 unit up, we add 1 outside of the function

h(x) = |x| +1

shifting it 4 units to the left, we will add 4 units from x inside

h(x) = |x+4| +1

The transformed function is

h(x) = |x+4| +1

Answer:

1. Differentiated Instruction: This intervention involves tailoring lessons and activities to meet the individual learning needs and preferences of students. For example, a teacher can design various instructional materials for students with different skill levels to ensure they engage in the lesson and learn effectively.

2. Explicit Instruction: This intervention involves breaking down a complex process or concept into smaller, more manageable parts, and explaining each part clearly and explicitly. The teacher provides ample opportunities for students to practice and apply what they have learned.

3. Formative Assessment: This intervention involves using ongoing, informal assessments to monitor students' progress and provide feedback to both students and teachers to make necessary adjustments. Teachers can use formative assessments to identify areas of difficulty and intervene early.

4. Collaborative Learning: This intervention involves encouraging students to work together in pairs or small groups to complete tasks or solve problems. Within these groups, students share ideas, clarify misunderstandings, and learn from each other.

Differentiated Instruction, Small Group Instruction, Formative Assessment, Peer Tutoring, Real-World Connections and Positive Feedback are the strategies to assist the child.

Teaching can be defined as engagement with learners to enable their understanding and application of knowledge, concepts and processes

Differentiated Instruction, Small Group Instruction, Formative Assessment, Peer Tutoring, Real-World Connections and Positive Feedback:

These strategies are effective because they are research-based and have been shown to support students' learning in mathematics.

By catering to the specific needs of students, providing individualized support, and making connections to the real world, students are more likely to engage in mathematics, understand mathematical concepts, and develop positive attitudes towards mathematics.

Hence, Differentiated Instruction, Small Group Instruction, Formative Assessment, Peer Tutoring, Real-World Connections and Positive Feedback are the strategies to assist the child.

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Answer:

rthrthrt

Step-by-step explanation:

Answer:

16.3333 (and so on)

Step-by-step explanation:

This is easy to figure out by using the inverse operation of multiplication, which is division. We divide 49/3, which equals 16.3 (with the 3 repeating), so that is the answer!

Hope this helps and have a nice day (～*▽*)～

The slope of the graph is equal to 1 for all x between x= 0 and x=3.

Starting at x=3 the function value y increases as x increases.

The slope of the graph is equal to 3 for x between x=3 and x=5

For x between x=0 and x=4, the function value of y is ≤ 0.

For x between x=4 and x=8 the function of value y is ≥ 0.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (0 - 3)/(3 - 0)

Slope (m) = -3/3

Slope (m) = -1.

For x between x=3 and x=5, the slope is given by;

Slope (m) = (3 + 3)/(5 - 3)

Slope (m) = 6/2

Slope (m) = 3.

By critically observing the graph of this function, we can logically deduce that the function value of y is less than or equal to 0 for x between x=0 and x=4 and greater than or equal to 0 for x between x=4 and x=8.

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