Which is equivalent to 4√9^1/2?

If the average height of two boys is 145 cm and one of the boys has a height of 140 cm, then the height of the other boy is 150 cm.

Let's denote the height of the other boy as x cm. We are given that the average height of the two boys is 145 cm.

According to the concept of average, the sum of the heights of the two boys divided by 2 should equal the average height.

So we can write the equation:

(140 cm + x cm) / 2 = 145 cm

Now, let's solve for x by multiplying both sides of the equation by 2:

140 cm + x cm = 290 cm

Subtracting 140 cm from both sides, we get:

x cm = 150 cm

Therefore, the height of the other boy is 150 cm.

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The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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From the question;

we are given the function

where

p(x) = profit

x = cost of advertising

we are to find the smallest of the two advertising amounts that produce a profit of $800,000.

this implies

p(x) = $800, 000

Therefore we have

by simplifying the equation we get

solving the equation using a calculator

we get the values of x to be

Since cost cannot be negative,

then the real solutions are

Therefore,

The smaller of the two advertising amounts that produce a profit of $800,000 is

x = 32

Answer: -19, -17, -15

Step-by-step explanation:

Suppose the smallest integer is x. The next odd integer would be x+2. The next odd integer after that would be x+4.

Ex. 1, 1+2, 1+4

Now the sum of these three integers equal -51, so x+x+2+x+4=-51

3x+6=-51

3x=-57, x = -19

Now add 2 and 4 to get the next two numbers. -17 and -15

Answer:

\(10^{4} * 10^{3}=(10*10*10*10)(10*10*10) = 10^{7}\\\\10^{4}*10^{4}=(10*10*10*10)(10*10*10*10) = 10^8\\\\(10*10*10)(10*10*10*10*10)=10^3*10^5=10^8\\\)

\(10^{18}*10^{23}=\) (10 x 10 18 times)(10 x 10 23 times) \(=10^{41}\)

just as a note: when you multiply numbers with exponents and they both have the same base, all you have to do is add the exponents.

Ex: \(10^{5}*10^{4}=10^{5+4}=10^{9}\)

To build a box with a square base, no top, and a volume of 100 m³ that uses the minimum amount of material, we need to minimize the surface area while maintaining the volume.

Let x represent the side length of the square base, and h represent the height of the box.

Volume (V) = x²h = 100 m³
Surface Area (SA) = x² + 4xh

First, solve the volume equation for h:

h = 100/x²

Now, substitute this expression for h into the surface area equation:

SA = x² + 4x(100/x²) = x² + 400/x

To minimize the surface area, we'll find the derivative of the surface area equation with respect to x and set it equal to zero:

d(SA)/dx = 2x - 400/x²

Setting the derivative equal to zero and solving for x:

2x - 400/x² = 0
2x³ - 400 = 0
x³ = 200
x = (200)^(1/3) ≈ 5.85 m

Now, plug the value of x back into the equation for h:

h = 100/(5.85²) ≈ 2.93 m

So, the dimensions of the box that minimize the amount of material used are approximately 5.85 m × 5.85 m × 2.93 m.

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Answer:

1.......c

2.....a

3.....b

4......e

5.....d

Because of the size of the black section,

The solution of the given inequality 4(x² - 5) - (x² - 5)² > -12 is x ≥ √3 or x ≤ -√3.

The given inequality is 4(x² - 5) - (x² - 5)² > -12. In order to solve the given inequality, first, we will multiply (x² - 5)² by -1 to get rid of the squared term. Next, we will simplify the terms by using the distributive property. Then, we will collect the like terms and solve the inequality.

Multiply (x² - 5)² by -1. => -(x² - 5)² = -x⁴ + 10x² - 25

Now, the given inequality is:

4(x² - 5) - (x² - 5)² > -12

4(x² - 5) + x⁴ - 10x² + 25 > -12

Simplify the terms by using the distributive property:

4x² - 20 + x⁴ - 10x² + 25 > -12

Simplifying further:

x⁴ - 6x² + 13 > 0

Collect like terms and solve the inequality:

(x² - 3)² + 4 > 0

As the square of any number is always greater than or equal to 0, so

(x² - 3)² ≥ 0 ⇒ (x² - 3)² + 4 ≥ 4

Hence, x² - 3 ≥ 0 ⇒ x² ≥ 3 ⇒ x ≥ ±√3

Therefore, the solution of the given inequality is x ≥ √3 or x ≤ -√3.

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If the medical procedure costs $4500 and the insurance covers 7/8 of the cost, then the amount of the procedure that the insurance covers can be calculated as:

Amount covered by insurance = (7/8) x ($4500)

We can simplify this expression by first finding the value of 7/8 as a decimal:

7/8 = 0.875

Substituting this value back into the expression, we get:

Amount covered by insurance = (0.875) x ($4500)

Simplifying this expression, we get:

Amount covered by insurance = $3,937.50

Therefore, the insurance covers $3,937.50 of the procedure cost.

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d) Use the rejection rule to solve for the value of the sample mean corresponding to the critical value of the test statistic is NOT a step in hypothesis testing(d).

The steps in hypothesis testing are as follows:

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Option d is not one of the steps in hypothesis testing.

Which of the following is NOT a step in hypothesis testing? Select one: a. Find the confidence interval. b. Use the level of significance and the critical value approach to determine the critical value of the test statistic c. Formulate the null and alternative hypotheses d. Use the rejection rule to solve for the value of the sample mean corresponding to the critical value of the test statistic.

Distance between city , D = 782 km.

Number of trips in a week , n = 5.

Total distance covered in a week , d = D × n = 782 × 5 = 3910 km.

Now, distance covered in six weeks is :

\(D'=d\times 6\\\\D'=3910\times 6\ km\\\\D'=23460\ km\)

Therefore, her assumption of travelling 40,000 km in six week is wrong.

Hence, this is the required solution.

Answer:

1mil

Step-by-step explanation:

We are asked to determine the p-values for a proportion that is greater than 0.51. Since we are asked about the hypothesis being greater then the p-value is given by:

This is a right-tailed test. To determine this probability we need to use the fact that:

replacing we get:

Now, from the tables for z-scores in the normal distribution we get:

Therefore, the p-value is 0.0011

The equilateral triangular prism has a surface area of 1997.321 square inches

From the question, the given parameters are

The total surface area of an equilateral triangular prism is calculated using the following formula

Surface area = a(√3/2) + 3(a × h);

Substitute the known values in the above equation

So, we have the following equation

Surface area = 20 * (√3/2) + 3(20 × 33);

Evaluate the product

So, we have the following equation

Surface area = 1997.321

Hence, the surface area of the equilateral triangular prism is 1997.321 square inches

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Since sn = 1/2 - 1/(n + 2), as n → ∞, sn → 1/2. Therefore, the given series converges to 1/2.

The given series is Σn=3∞ 2/(n² - 1)n. We need to express sn as a telescoping sum. Let's start by finding a general formula for the nth term of the series, tn.

tn = 2/(n² - 1)n = 2/[(n - 1)(n + 1)]n.

The given expression can be written as:

Σn=3∞ 2/(n² - 1)n

= Σn=3∞ [1/ (n - 1) - 1/(n + 1)]

Multiplying numerator and denominator of the first term by (n + 1) and the second term by (n - 1), we get

Σn=3∞ [1/ (n - 1) - 1/(n + 1)]

= [1/2 - 1/4] + [1/3 - 1/5] + [1/4 - 1/6] + .......+ [1/n - 1/(n + 2)] + .......

Now, let's find a formula for the nth partial sum, sn.

s1 = [1/2 - 1/4]

s2 = [1/2 - 1/4] + [1/3 - 1/5]

s3 = [1/2 - 1/4] + [1/3 - 1/5] + [1/4 - 1/6]......

s2 = [1/2 - 1/4] + [1/3 - 1/5]

s3 = [1/2 - 1/4] + [1/3 - 1/5] + [1/4 - 1/6]....+ [1/n - 1/(n + 2)]

s3 - s2 = [1/4 - 1/6] + [1/5 - 1/7] + [1/6 - 1/8].....- [1/3 - 1/5]

s4 - s3 = [1/5 - 1/7] + [1/6 - 1/8] + [1/7 - 1/9].....- [1/4 - 1/6]

s4 - s1 = [1/3 - 1/5] + [1/4 - 1/6] + [1/5 - 1/7].....- [1/n - 1/(n + 2)]

It can be observed that, on simplifying sn, the terms get cancelled, leaving only the first and last terms. Hence, sn can be written as:sn = [1/2 - 1/(n + 2)]

Therefore, the given series is a telescoping series, which means that each term after a certain point cancels out with a previous term, leaving only the first and last terms.

Since sn = 1/2 - 1/(n + 2), as n → ∞, sn → 1/2. Therefore, the given series converges to 1/2.

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The number of sides the polygon have 9.

A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.

Given:

We have a polygon can be divided into 5 triangles when the diagonals are drawn from one of its vertices.

As, we know  the number of triangles in a polygon is  = n−2

where n is the number of sides (or vertices)

So, the number of sides the polygon have

n= 5+ 2

n = 7 sides

Thus, the polygon is Heptagon.

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Answer:

No, 0.5m is 50cm, and so 17 is less than 50 and not half a meter.

Answer:

yes

Step-by-step explanation:

0.5 m is 50 cm

Answer:

320.25 centimeters

Step-by-step explanation:

you multiply 10.5 * 30.5

As a result, the horse on the outside has a higher linear speed of about 0.84 meters per second, whereas the horse in the center has a linear speed of 0 metres per second.

To determine which horse has the faster linear speed, we must first compute the linear speed of each horse. The distance travelled per unit of time is referred to as linear speed.

The outside horse completes one revolution in 30 seconds and is 4 metres away from the centre. We divide the distance travelled by the time taken to calculate the linear speed:

Linear Speed = Distance / Time

For the outside horse:

Linear Speed = 2πr / t

where r is the distance from the center (4 meters) and t is the time taken (30 seconds).

Linear Speed = (2π × 4) / 30

Linear Speed ≈ 0.84 meters per second

Now consider the horse in the center. Because the merry-go-round rotates as a whole, the horse towards the center will likewise complete one revolution in 30 seconds. The distance between the center horse and the center point, on the other hand, is zero.

Linear Speed = 2πr / t

For the horse near the center:

Linear Speed = (2π × 0) / 30

Linear Speed = 0 meters per second

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The position number for term 47 is 269.

This is an arithmetic sequence since each term has a common difference. Let us test it.

The difference between 1st and 2nd terms is

-7 + d = -1

d = -1 + 7

  = 6

Now we check the difference for term

The difference between 3rd and 4th terms is

5 + d = 11

d = 11 – 5

  = 6

So the difference is the same so we can apply a common equation for arithmetic sequence

\(a_{n}\) = \(a_{1}\) + d ( n - 1 )

Where :

\(a_{n}\) = number at term n

\(a_{1}\) = first number of sequence

d = difference for each number sequence

n = term

From the question, we need to find the number at position term 47

\(a_{n}\) = \(a_{1}\) + d ( n - 1 )

\(a_{47}\) = -7 + 6 ( 47 - 1 )

    = -7 + 6 ( 46 )

    = -7 + 276

    = 269

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The name of the segment inside the large triangle is called the: 3. angle bisector.

The word "bisect" means to divide into two equal halves. Therefore, an angle bisector can be defined as a line segment that divides the an angle in a triangle into two parts that are of the same angle measure.

The image shows a triangle which has a segment that divides a vertex angle into equal parts. Thus, the segment can be named as an angle bisector.

A perpendicular bisector divides a segment into two equal halves at right angle, while a midsegment joins the middle points of two sides of a triangle. The median also, is a segment that joins a vertex of a triangle to the midpoint of the side that is opposite the angle.

Therefore, we can state that the name of the segment is: 3. angle bisector.

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The unit price that is going to be needed for the 31 minute ride would be 21.4 dollars.

We have the fare for 81 minutes to be $56. 70

Then we are to find the amount that would be needed for 31 minutes.

In order to get this value we would have to cross multiply

such that we would have

81 minutes = $56.70

31 minutes = ?

then 56 * 31 = 1736

1736 / 81

= 21.4 dollars.

Hence we would conclude that the unit price that is going to be needed for the 31 minute ride would be 21.4 dollars.

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Answer:

n = 3/25

Step-by-step explanation:

5(n-1/10)=1/2

5n = 6/10

n = 3/25

Answer:

Step-by-step explanation:

lets remove the parenthesis

5n- 5/10=1/2

5n=1/2+1/2

5n=1

n=1/5

Answer:

£1430

Step-by-step explanation:

Given data

Principal =£1100

Rate= 5%

time = 6 years

The simple interest formula is

A=P(1+rt)

substitute

A=1100(1+0.05*6)

A=1100(1+0.3)

A=1100(1.3)

A=1100*1.3

A=£1430

Hence the balance is £1430

Yes, the mysteries equal 0.06 of the total books.

Marcella said that the mysteries equal 0.06 of the total books.

To check the mysteries equal 0.06 of the total books is correct or not.

We can follow these steps:

1. Identify the total number of books and the number of mysteries: Marcella read 100 books, and 60 of them were mysteries.

2. Calculate the fraction of mysteries: Divide the number of mysteries (60) by the total number of books (100) to find the fraction of mysteries.

3. Compare the fraction with Marcella's claim: If the calculated fraction equals 0.06, then she is correct.

Now let's perform the calculations:

60 mysteries ÷ 100 total books = 0.6

Since 0.6 ≠ 0.06, Marcella's claim that the mysteries equal 0.06 of the total books is incorrect. In reality, mysteries make up 0.6 or 60% of the total books she read.

A model to support this answer could be a pie chart, where the circle represents the 100 books, and the mysteries portion is shaded in. By dividing the circle into 10 equal sections, the mysteries would fill 6 of those sections, which represents 60% of the total books.

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Alaska's population is expected to be (a) 742.671 thousand people at the end of 2022 and it will take approximately (b)11.845 years after the end of 2000 for the population of Alaska to exceed 850,000 people. This will occur in (c)2011.845, or around the middle of the year 2011.

(a) Alaska's population is expected to be 742.671 thousand people at the end of 2022, calculated by setting x = 22 in the equation A(x) = 0.638x^2 + 6.671x + 627.619.

(b) To find when Alaska's population is expected to reach 850,000 people, we need to solve the equation 0.638x^2 + 6.671x + 627.619 = 850. This can be simplified to 0.638x^2 + 6.671x - 222.381 = 0. Using the quadratic formula, we get x = 11.845 and x = -31.117.

Since we are looking for a positive value of x, we can conclude that it will take approximately 11.845 years after the end of 2000 for the population of Alaska to exceed 850,000 people. This will occur in 2011.845, or around the middle of the year 2011.

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