A sprinkler sends the water out in a circular pattern.How many feet away from the sprinkler can it spread water if the area forked by the watering pattern is 706.50 square feet? Use 3.14 for pie

(a) P(X < 1470) = 0.8849, P(X >= 950) = 0.7487, (b) the probability that the size of a single droplet is between 950 and 1470 μm is 0.6336, (c) the smallest 2% of all droplets are those smaller than 827 μm in size, and (d) the probability that at least one exceeds 1470 μm is 0.3995.

(a) To find the probability that the size of a single droplet is less than 1470 μm or at least 950 μm, we need to use the standard normal distribution table. To do this, we first need to convert the droplet size to a standard normal variable.

Let X be the droplet size. Then we have:

Z = (X - 1050)/150

The probability that the size of a single droplet is less than 1470 μm is equal to the cumulative distribution function of Z evaluated at Z = (1470 - 1050)/150 = 1.2:

P(X < 1470) = P(Z < 1.2) = 0.8849 (rounded to four decimal places)

The probability that the size of a single droplet is at least 950 μm is equal to 1 minus the cumulative distribution function of Z evaluated at Z = (950 - 1050)/150 = -0.6:

P(X >= 950) = 1 - P(Z < -0.6) = 0.7487 (rounded to four decimal places)

(b) To find the probability that the size of a single droplet is between 950 and 1470 μm, we subtract the cumulative distribution function of Z evaluated at Z = (950 - 1050)/150 = -0.6 from the cumulative distribution function of Z evaluated at Z = (1470 - 1050)/150 = 1.2:

P(950 <= X <= 1470) = P(Z <= 1.2) - P(Z <= -0.6) = 0.8849 - 0.2513 = 0.6336 (rounded to four decimal places)

(c) To find the smallest 2% of all droplets, we find the value of Z such that P(Z <= Z) = 0.02. Using the standard normal distribution table, we find that Z = -2.33. Then, we convert Z back to the original variable X:

X = Z * 150 + 1050 = -2.33 * 150 + 1050 = 827 (rounded to two decimal places)

So, the smallest 2% of all droplets are those smaller than 827 μm in size.

(d) To find the probability that at least one of five independently selected droplets exceeds 1470 μm, we use the cumulative distribution function of a binomial distribution with n = 5 and p = P(X > 1470). The cumulative distribution function of a binomial distribution with parameters n and p is given by:

1 - (1 - p)^n

Using the standard normal distribution table, we find that P(X > 1470) = 1 - P(Z < (1470 - 1050)/150) = 1 - 0.8849 = 0.1151. Then, we plug in n = 5 and p = 0.1151 into the cumulative distribution function formula:

P(at least one exceeds 1470 μm) = 1 - (1 - 0.1151)^5 = 0.3995 (rounded to four decimal places).

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Answer:

m<4 = 100

Step-by-step explanation:

Because 1 is opposite to 4 they equal the same degree

Answer:

Step-by-step explanation:

(1) Yes, the table is proportional

4.5/25  = 5.4/30 = 6.3/35 = 7.2/40  

= 0.18

For a $50 bill the donation will be

50 X 0.18 = $9

Hence, 0.18 times of the dinner bill is donated to charity

(2) Yes, this is also proportional

a1 = 0.47

a2 = 0.68

a3 = 0.89

a4 = 1.10

d = a2 -a1 = a3 -a2 = a4 - a3

= 0.21

For a 6 ounce letter the A.P will be a6 so

a6 = a + 5d

= 0.47 + 5(0.21)

= 0.47 + 1.05

= 1.52

Hence , For every ounce of weight the cost gets increased by 0.21 the weight

The relation between mode, mean and median is:

mode=3median-2mean

Now, to find mean:

2mean=3median-mode

mean=7/2 = 3.5

Let we wish to evaluate the mean  μ of a population. In real practice we would typically take just one sample. Imagine still that we take sample after sample, all of the same size n, and compute the sample mean x¯ every time.

The sample mean x is a random variable: it differs from sample to sample in a way that cannot be predicted with sureness. We will write X¯ when the sample mean is idea of as a random variable and write x for the values that it takes.

The random variable X¯ has a mean, denoted  μX¯, and a standard deviation, denoted  σX¯. Here is an example with such a small population and small sample size that we can indeed write down every single sample.

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The function's multiplicative rate of change will be 0.5. Then, C is the right answer.

Suppose we're trying to determine the multiplication.

To determine the multiplicative power of an item, we just need to divide it by the item immediately preceding it.

Suppose one act is modified

Assume that b is the base, x is the exponent function's power, and an is the leading coefficient.

Exponent is provided as

y = a(b)ˣ

Examples :

Y = 0.125 when x = 2

0.125 = ab² ...1

Y = 0.0625 when x = 3

0.0625 = ab³ ...2

Equation 2 divided by equation 1 yields

b = 0.0625 / 0.125

b = 0.5.

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The complete question is: What is the multiplicative rate of change of the given functions?

a. 1/3

b. 2/3

c. 2

d. 9

Answer:

he can buy total snack with $20

four hot dogs and four peanuts

four hot dogs = $12

four peanuts= $6

6 + 12 = 20

Step-by-step explanation:

The polygons are similar. The  correct similarity statement is JKML ~ PQRS.

Similar polygons are two polygons with the same shape, but different sizes.  If two polygons are similar, then the ratio of the lengths of any two corresponding sides is called the scale factor.

Therefore, the corresponding sides have the same proportion. The corresponding angles of similar polygons are also the same.

Therefore, let's check if the polygons are similar as follows:

Hence,

2.5 / 1.5 = 8  /4.8

Hence, the polygon are similar as follows:

JKML ~ PQRS

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The point that is [tex]\sqrt{2}[/tex] units away from the point (-1, 5) is (-1 + [tex]\sqrt{2}[/tex], 5 + [tex]\sqrt{2}[/tex]).

The Pythagorean theorem is a fundamental mathematical principle that relates the lengths of the sides of a right triangle. The theorem states that the square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the lengths of the other two sides. The Pythagorean theorem states that a^2 + b^2 = c^2.

This theorem has many practical applications in mathematics and science, including the calculation of distances, heights, and angles in a variety of geometric and engineering problems. It is also widely used in trigonometry, where the relationship between the sides and angles of a right triangle is studied.

The Pythagorean theorem was named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. However, the theorem was known and used by the Babylonians and Indians well before Pythagoras was born. In fact, the theorem is so important that it is sometimes called the "Pythagorean theorem" despite the fact that it predates Pythagoras by several centuries.

This can be found by using the Pythagorean theorem to find the distance between the two points and then adding or subtracting that distance from the x and y coordinates of the original point.

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Subtract 1 from each value in the confusion matrix to change it from 1 to 10 to 0 to 9.

To change a confusion matrix from 1 to 10 to 0 to 9, you need to subtract 1 from each value in the matrix. For example, if your original confusion matrix looks like this:

1     2      3

4    5     6

7    8     9

10   11   12

To convert it to a 0 to 9 range, you need to subtract 1 from each value:

0 1 2

3 4 5

6 7 8

9 10 11

This can be easily done using a loop or by using the -1 operator on the entire matrix. The specific method would depend on the programming language and data structure used to represent the matrix.

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The fourth-order Taylor series expansion is

f(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4! ) )f⁽⁴⁾(x) + ... where a = pi/4

The taylor polynomial with 4 nonzero terms of The function f(x)=sin(4x)f(x)=sin⁡(4x) has a series. find the first 4 nonzero terms in the series is f(x) = 4x - (4x)³ + (4x)⁵ - (4x)⁷ + ...

                                       3!        5!      7!

The taylor polynomial can be calculate as follows:

f(x) = sin(4x)

f' = 4cos(4x)

f'' = -16 sin(4x)

f''' = -64 cos(4x)

f⁽⁴⁾ = 256 sin(4x)

f⁽⁵⁾ = 1024 cos(4x)

The fourth-order Taylor series expansion is

f(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4! ) )f⁽⁴⁾(x) + ...

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The fairness of a passenger survey could be improved by oversampling data from the group of passengers who travel during peak ridership hours between 7:00 am and 5:00 pm.

This will ensure that the survey adequately represents the population of interest and provides accurate results.

Oversampling is the method of selecting respondents so that some groups make up a larger share of the survey sample than they do in the population. Oversampling small groups can be difficult and costly, but it lets polls to shed light on groups that would otherwise be too small to report on.

Oversampling and undersampling are methods used in data mining and data analytics to change unequal data classes to create balanced data sets. Oversampling and undersampling are also known as resampling.

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If Mirka is 5 years old, her parents start to give her pocket money of 50p per week , then the amount of pocket money does Mirka get in the first year is £26 .

the amount that Mirka gets per week is = 50p ;

Age of Mirka is = 5 years ;

When Mirka is 5 years old, she starts to receive 50p per week in pocket money. On her birthday, her parents increase her pocket money by 50p.

that means ;

So, for the first year, the pocket money will be 50p per week for 52 weeks (1 year),

Pocket money in the first year = 50p × 52 weeks = £26 .

Therefore , Mirka will get £26 in the first year of her birthday .

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Answer:

the answer would be 75% of the journey

Jon bought 10.5 boxes of cards and Felipe bought 11 boxes of cards, and Jon and Felipe each spent $215 on business cards.

What is the system of equations?

A system of linear equations is a set of two or more equations that includes common variables. To solve a system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

Let x be the number of boxes of cards that Jon bought and y be the number of boxes of cards that Felipe bought.

The equation for Jon's cost is: 10 + 20x = y * (21 + 9)

The equation for Felipe's cost is: 21y + 9 = 10 + 20x

We will solve the system of equations using substitution.

Starting with the second equation, we can simplify: 21y + 9 = 10 + 20x

21y + 9 - 10 = 20x

21y - 1 = 20x

Dividing both sides by 21: y = (20/21)x + 1

We can now substitute this expression for y into the first equation:

10 + 20x = (20/21)x + 10 + 9

10 + 20x = (20/21)x + 19

10 = 19 - (20/21)x

Multiplying both sides by 21:

210 = 19 * 21 - 20x

Subtracting 19 * 21 from both sides:

210 - 19 * 21 = -20x

Divide both sides by -20:

x = 10.5

So, Jon bought 10.5 boxes of cards and Felipe bought (20/21) * 10.5 + 1 = 11 boxes of cards.

To find out how much each spent, we can plug these values back into either equation:

Jon's cost: 10 + 20 * 10.5 = 215

Felipe's cost: 21 * 11 + 9 = 250

So, Jon and Felipe each spent $215 on business cards, buying 10.5 boxes.

Hence, Jon bought 10.5 boxes of cards and Felipe bought 11 boxes of cards, and Jon and Felipe each spent $215 on business cards.

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Yes, the sampling distribution of the difference in sample mean ages is approximately normal.

This is because the Central Limit Theorem states that the sampling distribution of the mean of any sample of size n will be approximately normal, provided that the samples are drawn from a population with a finite variance. Furthermore, the sample sizes in this case (32 and 41) are both greater than 30, which is the minimum sample size needed for the CLT to be valid.

The Central Limit Theorem is a fundamental theorem of statistics that states that the sampling distribution of the means of any sample of size n drawn from a population with a finite variance will be approximately normal, regardless of the shape of the population’s probability distribution.

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The area of the semicircle is 3.14 square feet.

The formula for  area of a semicircle is A = ([tex]\pi[/tex]* r^2) / 2

Here A = Area

         r = Radius

Given:

Given that the radius of the semicircle is 2 feet.

We need to Find out the area of the semicircle.

The value of [tex]\pi[/tex] is 3.14

A = ([tex]\pi[/tex] * 2^2) / 2

Substituting π = 3.14 and r = 2, we get;

A = (3.14 * 4) / 2

A = 6.28 / 2

A = 3.14 square feet

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The equation of a plane in 3-space with equation c1x + c2y + c3z + c4 = 0 can be determined by passing through three non-collinear points (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). This is given by the determinant equation:

Copy code

| x  y  z  1 |

| x1 y1 z1 1 | = 0.

| x2 y2 z2 1 |

| x3 y3 z3 1 |

However, if the three distinct points are collinear, meaning they lie on the same line, then the determinant equation becomes undefined as the determinant of a 3x3 or smaller matrix with linearly dependent rows or columns is equal to zero. This means that there is no plane that passes through three collinear points as a plane requires at least three non-collinear points to be defined.

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The two inequalities that represent the constraints in this situation are

r + c >= 80 and 1.45r + 0.65c <= 200

Let r be the number of roses and c be the number of carnations Victor buys.

So, we have

Total number of flowers: r + c >= 80

Victor has $200 to spend on flowers for the school celebration.

Roses cost $1.45 each and carnations cost $0.65 each.

So, we have

Total spending: 1.45r + 0.65c <= 200

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The tight asymptotic bound for the function f(n) = 4f(n/2) + c is T(n) = O(n²).

A recursion tree is a graphical representation of a recursive function that shows the repeated calls of the function. The tree is constructed by expanding each call of the function into a separate node.

For the given function f(n) = 4f(n/2) + c, the recursion tree is attaced below:

f(n/4) f(n/4) f(n/4) f(n/4)

The height of the tree is log2(n), and at each level, there are 4 calls of the function. Hence, the total number of nodes in the tree would be [tex]4^{log2(n)} = n^2[/tex].

The tight asymptotic bound for the function can be found using the Master Theorem, which states that for a recurrence relation of the form T(n) = aT(n/b) + f(n), if f(n) = O([tex]n^c[/tex]) for some constant c, then T(n) = O([tex]n^d[/tex]), where d = max(c, log b(a)).

For this function, a = 4, b = 2, and c = 1. Hence, d = max(1, log2(4)) = max(1, 2) = 2. Thus, the tight asymptotic bound for the function is T(n) = O([tex]n^2[/tex]).

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Answer:

24 = 31.4n + (–8.4)

Step-by-step explanation:

Answer:

Why not and what??

Step-by-step explanation:

wait why is that and also that not even a question

The number of solutions of the system y = 3x + 5 is one because it is a linear equation.

An equation in which is  the highest power of to the  variables 1 is knowns as the  linear equation. Mathematically: it is an  algebraic equations that can be also  written in the form of  ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.

Linear equations are equations in which the variables are raised to the power of 1, and the graph of the equation is a straight line. As a result, there is only one solution to the equation, which is when the line intersects the x-axis. This means that the equation has only one set of x- and y-coordinates, where x is the independent variable and y is the dependent variable, that satisfy the equation. The x-coordinate of the solution is the same as the value of x that makes the equation true and the y-coordinate is the value of y for this same x-value.

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The nine and seven hundredths can be written as 9.07. The solution has been obtained by using decimals.

What are decimals?

Decimals are a form of number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number.

We are required to write the decimal number of the given words by considering the integral part and the decimal part

So, here the integral part is nine i.e. 9 and the decimal part is seven hundredths i.e. 7/100 = 0.07

Now, after adding both the parts, we get

9 + 0.07 = 9.07

Hence, the nine and seven hundredths can be written as 9.07.

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Answer:

The answer would be 70.4

Answer: 630 rabbits

Step-by-step explanation: it shows that the population of rabbits grows by 70 each 4 years so we will have to add 70 to 560 which is 630 rabbits.

The population of rabbits in the year 2014 will be growing exponentially.

So, we can write a function

P = A · [tex]\alpha ^{x}[/tex]

where,

A is the original rabbits

[tex]\alpha[/tex] is the ratio of the increase

[tex]x[/tex] is the time (the unit is year)

In 2004, the population of the rabbits was 490

∴ P = 490 · [tex]\alpha ^{x}[/tex]

In 2008, the population increases to 560

∴ 560 = 490 · [tex]\alpha ^{2008-2004}[/tex]

   560 = 490 · [tex]\alpha ^{4}[/tex]

  [tex]\alpha ^{4\\[/tex] = [tex]\frac{560}{490}[/tex] = [tex]\frac{8}{7}[/tex]

  [tex]\alpha[/tex]   = [tex]\sqrt{\frac{2\sqrt{14} }{7} }[/tex]

In 2014, x = 2014- 2004 = 10

P = 490 · [tex]\sqrt{\frac{2\sqrt{14}}{7} } ^{10}[/tex]

  ≅ 684

Hence, the population of rabbits in the year 2014 will be approximately 684.

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Answer:

The type of number -5.41 is a rational number.

Step-by-step explanation:

What type of number is -5.41?

A rational number is a number that can be expressed as a fraction of two integers. 5.41 can be expressed as -5.41 / 1000.

An integer and whole number is a number that does not have any fraction or decimal. -5.41 is a decimal number, thus it is not an integer and a whole number.

The contrapositive of the statement "if x is irrational, then so is 1/x" is proven.

Proof by contrapositive: Suppose that x is not irrational, meaning that x can be written as a fraction of two integers, x = a/b, where a and b are integers and b ≠ 0.

If x can be written as a fraction of two integers, then 1/x can be written as a fraction as well: 1/x = b/a.

Since 1/x can be written as a fraction of two integers, it follows that 1/x is rational.

Therefore, if x is not irrational (i.e. it is rational), then 1/x is also rational.

Thus, the contrapositive of the statement "if x is irrational, then so is 1/x" is proven.

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llllllllylylylltyllylltlylltl ok bye

Answer:

Below

Step-by-step explanation:

Since you are working with a number line with decimals. You'll have to convert all of these to decimals.

✓14 and ✓15 would be calculator problems with the following solutions:

✓14 = 3.74

✓15 = 3.87

24/7 is pretty much 24 divided by 7

24/7 = 3.43

Now that you have the 3 in decimal form

✓14 can go between 3.7 and 3.8

✓15 can go between 3.8 and 3.9

24/7 can go between 3.4 and 3.5

The resultant image of point A(-12,3) , after a scale factor 1/3 and a rotation of 270 degrees is (1, 4).

In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object with respect to a specific scale factor, but not its shape.

Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/3 centered at the origin as follows:

Ordered pair A (-12, 3) → Ordered pair A' (-12 × 1/3, 3 × 1/3) = Ordered pair A' (-4, 1).

By applying a rotation of 270° about the origin to the given figure, the location of A" is given by:

(x, y)                                   →         (y, -x)

Ordered pair A' (-12, 3) → Ordered pair A'' = (1, -(-4) = (1, 4).

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