The height of three Russian dolls are in the ratio 7:12:17.
Rewrite this as an equivalent ratio of tye form 1:m:n.
Give any decimal in your answer in 2 d.p

The two numbers that multiply to 48 and add to -7 are:

(-7 + √(143)i) / 2 and -7 - ((-7 + √(143)i) / 2)

OR

(-7 - √(143)i) / 2 and -7 - ((-7 - √(143)i) / 2)

From the question, we are to determine the numbers that multiply to 48 and add up to -7

Let the numbers be x and y.

Then,

We can write that

xy = 48

x + y = -7

From the second equation, we can write that

x = -7 - y

Substitute the into the first equation

xy = 48

(-7 -y)y = 48

-7y - y² = 48

This can be re-written as

y² + 7y + 48 = 0

Solving the equations using the quadratic formula

y = (-b ± √(b² - 4ac)) / 2a

a = 1, b = 7, and c = 48

Substitute into the formula

y = (-7 ± √(7² - 4(1)(48))) / 2(1)

Simplifying inside the square root:

y = (-7 ± √(49 - 192)) / 2(1)

y = (-7 ± √(-143)) / 2

y = (-7 ± √(143)i) / 2

Hence,

y = (-7 + √(143)i) / 2

OR

y = (-7 - √(143)i) / 2

Substitute the values of y into x = -7 - y

x = -7 - ((-7 + √(143)i) / 2)

and

x = -7 - ((-7 - √(143)i) / 2)

Hence,

The two numbers are:

(-7 + √(143)i) / 2 and -7 - ((-7 + √(143)i) / 2)

OR

(-7 - √(143)i) / 2 and -7 - ((-7 - √(143)i) / 2)

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We can expect about 1 boy in a group of 40 to be taller than 75 inches.

We can solve this problem using the normal distribution formula:

z = (x - μ) / σ

where z is the z-score, x is the height we want to find the probability for, μ is the population mean, and σ is the population standard deviation.

First, we need to find the z-score for a height of 75 inches:

z = (75 - 70) / 2.5 = 2

Next, we need to find the probability of a z-score being greater than 2 using a standard normal distribution table or a calculator. The probability of a z-score being greater than 2 is approximately 0.0228.

Finally, we can use the expected value formula to find how many boys in a group of 40 are expected to be taller than 75 inches:

Expected value = probability[tex]\times[/tex] sample size = 0.0228 * 40 = 0.912

So, we can expect about 1 boy in a group of 40 to be taller than 75 inches.

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A significance level of 0.05, the critical value for the right-tailed test is z = 1.645.

To test if the data provides enough evidence to conclude that the cream improved the skin of more than 60% of the women, we can conduct a hypothesis test.

Let p be the true proportion of middle-aged women who show skin improvement after using the anti-aging skin cream.

The null hypothesis is: H0: p ≤ 0.6

The alternative hypothesis is: Ha: p > 0.6

We can use a one-tailed z-test for proportions to test this hypothesis, where the test statistic is given by:

z = (P - p0) / sqrt(p0 * (1 - p0) / n)

where P is the sample proportion, p0 = 0.6 is the null hypothesis value, and n = 33 is the sample size.

From the table, we see that 26 out of 33 women showed skin improvement after using the cream. Therefore, the sample proportion is:

P = 26 / 33 = 0.7879

Substituting the values, we get:

z = (0.7879 - 0.6) / sqrt(0.6 * 0.4 / 33) = 2.162

Using a significance level of 0.05, the critical value for the right-tailed test is z = 1.645.

Since the calculated test statistic (z = 2.162) is greater than the critical value (z = 1.645), we reject the null hypothesis and conclude that there is enough evidence to suggest that the cream improved the skin of more than 60% of the women.

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Part a) To find the value of k that makes the given function a proper probability density function (p.d.f.), we need to ensure that the integral of the function over the entire range is equal to 1.

For the given function f(x) = { k for 0 < x < 2, 0 otherwise }, we can set up the integral as follows:

∫(f(x)dx) = 1
∫(k dx) from 0 to 2 = 1

k * (x)| from 0 to 2 = 1
k * (2 - 0) = 1

k * 2 = 1
k = 1/2

So, the value of k that makes the function a proper p.d.f is 0.5.

Part b) To find P(0.25 < X < 1), we need to calculate the integral of the function within the given range (0.25 to 1).

Using f(x) = 0.5 for 0 < x < 2, we can set up the integral as follows:

P(0.25 < X < 1) = ∫(0.5 dx) from 0.25 to 1

0.5 * (x)| from 0.25 to 1
0.5 * (1 - 0.25) = 0.5 * 0.75 = 0.375

So, P(0.25 < X < 1) = 0.375.

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To convert 3.0 m/s^2 to ft/h^2, we can use the following conversion factors:

1 meter = 3.28084 feet

1 second = 3600 hours

First, let's convert the acceleration from meters per second squared to feet per hour squared:

3.0 m/s^2 x (3.28084 ft/m)^2 x (3600 hr/s)^2 = 31,317.2 ft/hr^2

Therefore, 3.0 m/s^2 is equal to approximately 31,317.2 ft/hr^2.

x = 17°

Supplementary angles are angles that add together to form 180°, aka a straight line.

Supplementary Angles
For the question, let the angle in the top left with a square in the vertex be angle 1. Let the angle in the top right formed by x° + 73° be angle 2. In the image, there is a square at the vertex of angle 1. This is used to show that the angle is a right angle. This means that angle 1 has a measure of 90°.

Supplementary angles come together to form a straight line. By looking at the diagram, we can tell that angles 1 and 2 form a straight line and thus are supplementary.

Solving for x

We know that angle 1 plus angle 2 will equal 180° since they are supplementary. We can use this information to set up an equation.

By plugging in the information we know, we can find the unknown value.

This means that the unknown angle is 17 degrees.

This polynomial function has zeros at O (multiplicity of 4), 2 (multiplicity of 1), and -5 (multiplicity of 2).[tex]f(x) = x^4 (x - 2) (x + 5)^2[/tex]

A polynomial is a mathematical expression consisting of variables and coefficients, combined using only addition, subtraction, and multiplication, and raised to non-negative integer powers. In other words, it is a sum of terms, where each term is a constant multiplied by one or more variables raised to non-negative integer powers.

For example, the expression [tex]2x^2 + 3x - 5[/tex] is a polynomial in one variable (x) with three terms. The first term has a coefficient of 2, a variable of x raised to the power of 2, and no constant term. The second term has a coefficient of 3, a variable of x raised to the power of 1, and no constant term. The third term has a coefficient of -5, no variable, and a constant term of -5.

To write a polynomial function in factored form, we can start by using the zeros given and their multiplicities.

The zero at O with a multiplicity of 4 means that the factor (x - 0) appears 4 times in the function.

The zero at 2 with a multiplicity of 1 means that the factor (x - 2) appears once in the function.

The zero at -5 with a multiplicity of 2 means that the factor (x + 5) appears twice in the function.

Putting this together, we can write the function in factored form as:

[tex]f(x) = (x - 0)^4 (x - 2) (x + 5)^2[/tex]

Simplifying, we can also write it as:

[tex]f(x) = x^4 (x - 2) (x + 5)^2[/tex]

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The probability shows sample mean differ from the true mean by less than 5.91 liters is equal to 0.9864.

Standard deviation = 24 liters

sample size = 100

The standard error of the mean is,

Standard error = σ / √(n)

where σ is the population standard deviation, n is the sample size.

Substituting the given values, we get,

Standard error

= 24 / √(100)

= 2.4

Probability that the sample mean would differ from the true mean by less than 5.91 liters,  standardize the difference using the standard error,

z = (X - μ) / (SE)

where X is the sample mean,

μ is the true population mean,

and SE is the standard error of the mean.

Substituting the given values, we get,

z = (5.91) / 2.4

  = 2.4625

Probability corresponding to this z-score,

Use a standard normal distribution attached table

The probability of the sample mean differing from the true mean by less than 5.91 liters is the probability of getting a z-score between -2.4625 and 2.4625.

This can be found by taking the difference between the cumulative probabilities corresponding to these two z-scores.

Using a standard normal distribution attached table ,

Probability of getting a z-score less than -2.4625 is 0.0068,

Probability of getting a z-score less than 2.4625 is 0.9932.

Probability of getting a z-score between -2.4625 and 2.4625 is  

0.9932 - 0.0068 = 0.9864 (Rounding to four decimal places)

Therefore, the probability that the sample mean would differ from the true mean by less than 5.91 liters is 0.9864.

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In a Lineweaver-Burk plot, the 1/Y-intercept represents the reciprocal of the maximum velocity (1/Vmax) of the enzyme-catalyzed reaction. The 1/X-intercept represents the negative reciprocal of the Michaelis constant (1/Km) for the substrate.

In a Lineweaver-Burk plot, the 1/Y-intercept represents the reciprocal of the maximum velocity (1/Vmax) of the enzyme-catalyzed reaction being studied, while the 1/X-intercept represents the negative reciprocal of the Michaelis constant (1/Km) for the substrate.

The Lineweaver-Burk plot is a linear transformation of the Michaelis-Menten equation, which relates the initial reaction rate (v0) of an enzyme-catalyzed reaction to the substrate concentration ([S]):

v0 = (Vmax [S]) / (Km + [S])

Taking the reciprocal of both sides of the equation, we get:

1/v0 = (Km/Vmax) (1/[S]) + 1/Vmax

This equation has the same form as the equation of a straight line y = mx + b, where y = 1/v0, x = 1/[S], m = Km/Vmax, and b = 1/Vmax. Therefore, plotting 1/v0 against 1/[S] on a Lineweaver-Burk plot produces a straight line with a slope of Km/Vmax and a y-intercept of 1/Vmax.

Taking the reciprocal of the slope, we get:

1/(Km/Vmax) = Vmax/Km

which is equal to the 1/X-intercept of the Lineweaver-Burk plot. Similarly, taking the reciprocal of the y-intercept, we get:

1/(1/Vmax) = Vmax

which is equal to the 1/Y-intercept of the Lineweaver-Burk plot.

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The statement is false. The correct answer is A. False. The sets do not have the same cardinality.

In this case, we are comparing two sets: (4, 7, 9) and (4, 4, 7, 9, 9). To determine if the statement is true or false, we need to check if both sets contain the same elements and if they have the same cardinality.

The first set (4, 7, 9) has a cardinality of 3, as it contains three unique elements. The second set (4, 4, 7, 9, 9) has a cardinality of 5, as it contains five elements (though some are duplicated). Since the two sets have different cardinalities, they cannot be equal, and the statement is false.

Answer B is incorrect because although some elements of the first set are duplicated in the second set, this is not the main reason the statement is false. The primary reason is the difference in cardinality.

Answer C is incorrect because the sets do not contain the same elements; the second set has duplicate elements.

Answer D is incorrect because the requirement for the sets to be equal is not based on duplication but rather on having the same elements and cardinality.

In conclusion, the statement is false because the two sets do not have the same cardinality, and thus, they cannot be considered equal. Therefore, the correct option is A.

The question was incomplete, Find the full content below:

Determine whether the statement is true or false. If the statement is false, give a reason. (4, 7, 9) (4, 4, 7, 9, 9)

A. False. The sets do not have the same cardinality

B. False. Some elements of the first set are duplicated in the second set.

C. True. Both sets contain the same elements.

D. False. All elements in the first set should be duplicated in order for the sets to be equal.

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To find the matrix for T relative to the basis B, we need to compute the coordinates of T(b1), T(b2), and T(b3) with respect to B. The answer is, [T]8 = [T]B, which is the matrix for T relative to B.

We can then use these coordinates to construct the matrix [T]B. Since B is a basis for V, we can express any vector v in V as a linear combination of the basis vectors: [tex]v = a1b1 + a2b2 + a3*b3[/tex]; where a1, a2, and a3 are the coordinates of v with respect to B Using this representation, we can compute the coordinates of T(b1), T(b2), and T(b3) as follows:[tex]T(b1) = T(61) = 4b1 + 7b2 - 3b3[/tex]

[tex]= 41 + 70 - 30 (since b1 = 61 = [1, 0, 0] in B)[/tex]

[tex]+ 40 + 71 - 30 (since b2 = 62 = [0, 1, 0] in B)[/tex]

[tex]+ 40 + 70 - 3*1 (since b3 = 63 = [0, 0, 1] in B)[/tex]

[tex]= [4, 7, -3][/tex]

[tex]T(b2) = T(62) = 5b1 + 2b2 - 6b3[/tex]

= [tex]51 + 20 - 60 (since b1 = 61 = [1, 0, 0] in B)[/tex]

[tex]+ 50 + 21 - 60 (since b2 = 62 = [0, 1, 0] in B)[/tex]

[tex]+ 50 + 20 - 6*1 (since b3 = 63 = [0, 0, 1] in B)[/tex]

[tex]= [5, 2, -6][/tex]

[tex]T(b3) = T(63) = - 361b1 + 0b2 + 0b3[/tex]

= [tex]-3611 + 00 + 00 (since b1 = 61 = [1, 0, 0] in B)[/tex]

[tex]+ (-361)0 + 01 + 00 (since b2 = 62 = [0, 1, 0] in B)[/tex]

[tex]+ (-361)0 + 00 + 0*1 (since b3 = 63 = [0, 0, 1] in B)[/tex]

[tex]= [-361, 0, 0][/tex]

We can now construct the matrix [T]B by writing the coordinates of T(b1), T(b2), and T(b3) as columns of the matrix: [tex][T]B = [[4, 5, -361], [7, 2, 0], [-3, -6, 0]][/tex].

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g(x) is greater than g(-11) for x in the interval (-8, 4). Therefore, the solution to the inequality is:

-8 < x ≤ 4

What is an inequality equation?

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

Since f is increasing over its domain, we know that if a < b, then f(a) < f(b). We can use this property to solve the inequality:

f(4x - 3) ≥ f(2 - x²)

Since the domain of f is given as Df = (-8, 4), we know that both 4x - 3 and 2 - x² are in the domain. We can rearrange the inequality as follows:

f(4x - 3) - f(2 - x²) ≥ 0

Now, we can define a new function g(x) = f(x) - f(2 - x²). Since g(x) is the difference between two increasing functions, it is also an increasing function. So we can rewrite the inequality as:

g(4x - 3) ≥ 0

We want to find the values of x that satisfy this inequality. Since g(x) is increasing, we know that g(4x - 3) ≥ g(4(-2) - 3) = g(-11). So we need to find the values of x for which g(x) is greater than or equal to g(-11).

Since the domain of f is given as (-8, 4), we know that the domain of g is also (-8, 4). So we can graph g(x) over this interval and find where it is greater than or equal to g(-11).

However, since we don't know the actual function f, we can't graph g directly. Instead, we can use the fact that g is increasing to determine where it is greater than or equal to g(-11).

We know that g(-8) = f(-8) - f(66) and g(4) = f(4) - f(-14), since 2 - x² = 4 when x = ±√2, and 4(-2) - 3 = -11. Since f is increasing over its domain, we have f(-8) < f(4) and f(-14) < f(66). Therefore, we have:

g(-8) = f(-8) - f(2 - (-8)²) > f(4) - f(2 - 4²) = g(4)

Hence, g(x) is greater than g(-11) for x in the interval (-8, 4). Therefore, the solution to the inequality is:

-8 < x ≤ 4

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Answer:

y = 30 when x = 6

Step-by-step explanation:

[tex]\frac{35}{7} = \frac{y}{6} \\(35*6)/7 = y\\\\y = 30[/tex]

Answer:

y is 30 when x is 6.

Step-by-step explanation:

We are given that x and y are in direct proportion. This means if x increases, then y will increase, and if x decreases, y will also decrease.

A directly proportional relationship is written as [tex]\frac{x_1}{y_1} = \frac{x_2}{y_2}[/tex]. The ratios should equal the same amount.

We also know that when x is 7, y is 35. The question wants us to find y when x is 6.

Since we already know that when x is 7, y is 35, we can substitute that ratio into the equation for [tex]x_1[/tex] and [tex]y_1[/tex].

[tex]\frac{7}{35} =\frac{x_2}{y_2}[/tex]

Since we know that the value of x is 6 in the *other* proportion, we can substitute 6 for [tex]x_2[/tex].

[tex]\frac{7}{35} =\frac{6}{y_2}[/tex]

Now, we can solve for [tex]y_2[/tex]. We can start by simplifying [tex]\frac{7}{35}[/tex] to become [tex]\frac{1}{5}[/tex].

Therefore, the equation will become:

[tex]\frac{1}{5} =\frac{6}{y_2}[/tex]

We can cross multiply. The result will be:

[tex]y_2=30[/tex]

This means that when x is 6, y will be 30.

False.

Hi! You asked whether aliasing is expected to happen when the waveform s(t) = 5 sin(4πt) + 12 sin(20πt) is sampled at 24 Hz. To answer this, let's follow these steps:

1. Identify the frequencies of the individual sinusoidal components in the signal s(t). The frequencies are given by (ω/2π) where ω is the coefficient of t in the sine function.
  - For 5 sin(4πt), the frequency is (4π/2π) = 2 Hz
  - For 12 sin(20πt), the frequency is (20π/2π) = 10 Hz

2. Calculate the Nyquist frequency, which is half of the sampling rate. In this case, the sampling rate is 24 Hz, so the Nyquist frequency is 12 Hz.

3. Compare the frequencies of the signal components to the Nyquist frequency. If any component has a frequency higher than the Nyquist frequency, aliasing is expected to occur.

In this case, both 2 Hz and 10 Hz are below the Nyquist frequency of 12 Hz. Therefore, we do not expect aliasing to happen in this sampling process. So, the answer is false.

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The correct answer is kπ.

We can start by rearranging the equation to get sin(x) on one side:

sin2(x) + 3sin(x)/4 = 0

Factoring out sin(x), we get:

sin(x)(sin(x) + 3/4) = 0

So either sin(x) = 0 or sin(x) = -3/4.

For sin(x) = 0, the solutions are x = kπ for any integer k.

For sin(x) = -3/4, we note that this value is not attainable for any real x since the range of sin(x) is [-1, 1]. Therefore, there are no solutions for sin(x) = -3/4.

Thus, the solutions to the equation sin2(x) = −3 sin(x) 4 are:

x = kπ for any integer k.

So the correct answer is kπ.

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a. A logistic growth function for the world population in billions if the population in 1999 (t-0) reached 6 billion. K 15 billion and r, 0.025 per year is P(t) = 15 / (1 + 1.5 [tex]e^{-0.025t}[/tex])

b. The interval 10, 200 x 10. 151 is 1999

c. The population be in the year 2020 will be 9.57 billion

d. The population is estimated to reach 12 billion in about 55.3 years since 1999, or around the year 2054.

e. The growth rate function of the world population is  P = K/2.

a.  To apply this to the world population, we can set K = 15 billion, r = 0.025 per year, and choose A so that P(0) = 6 billion. This gives us A = (K/P(0)) - 1 = (15/6) - 1 = 1.5. Therefore, the logistic growth function for the world population in billions is P(t) = 15 / (1 + 1.5 [tex]e^{-0.025t}[/tex])

b. Using technology such as a calculator or software, we can graph the logistic growth function over the interval 10 to 200 years since 1999 (i.e., 2010 to 2199).

c. To find the population in the year 2020, we need to substitute t = 21 (since 2020 is 21 years after 1999) into the logistic growth function and solve for P(21). We get P(21) = 9.57 billion, which means the world population was estimated to be around 9.57 billion in 2020 according to this model.

d. To find when the population will reach 12 billion, we need to solve the logistic growth function for t when P(t) = 12 billion. This gives us 12 = 15 / (1 + 1.5 [tex]e^{-0.025t}[/tex]), which simplifies to [tex]e^{0.025t}[/tex] = 2.5.

Taking the natural log of both sides gives 0.025t = ln(2.5), so t = (1/0.025) ln(2.5) = 55.3 years.

e. To find the growth rate function of the world population, we can differentiate the logistic growth function with respect to time: dP/dt = rP(1 - P/K).

This is the growth rate function, which gives us the rate of change of the population at any given time. It depends on the population size P and the carrying capacity K, and is maximum when P = K/2.

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False.

Parallel lines have no intersection point, which means that there is no solution to the system of equations that represents them.

Parallel lines have no intersection point, which means that there is no solution to the system of equations that represents them. Geometrically, if two lines are parallel, they never meet, and therefore there is no point that satisfies both equations simultaneously.

For example, consider the system of equations:

x + y = 3
x + y = 5

These equations represent two lines that are parallel, both with slope -1 and y-intercepts of 3 and 5, respectively. Since these lines do not intersect, there is no solution to this system of equations.

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Answer:15 cubic inches

Step-by-step explanation:

so you know one cube is 1/4 cubic inches, that being said 4 cubes=1 cubic inch.

1 column hold 12 individual cubes, 12/4= 3 cubic inches

then you multiply 3 times the number of columns (5)

which gives you 15 cubic inches

The polar equation equivalent to the Cartesian equation x = -4 is r*cos(θ) = -4.

To rewrite the Cartesian equation x = -4 as a polar equation, follow these steps:

1. Recall the conversion formulas for Cartesian coordinates (x, y) to polar coordinates (r, θ): x = r*cos(θ) and y = r*sin(θ).
2. Replace x in the given Cartesian equation with the corresponding polar coordinate formula: -4 = r*cos(θ).

The polar equation equivalent to the Cartesian equation x = -4 is r*cos(θ) = -4.

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The mass of the solid is 4/3.

To solve this problem, we need to set up the integral for the mass of the solid and then evaluate it using the given density function. The mass of the solid is given by the triple integral:

M = ∭ρ(x, y, z) dV

where ρ(x, y, z) is the density function and dV is an infinitesimal volume element. In this case, the density function is 16y+1, so we have:

M = ∭(16y+1) dV

The limits of integration are determined by the planes x+z=1, x-z=-1, and y=0 and the surface y = sqrt(z). To find the limits of integration, we first need to solve for x and z in terms of y.

From x+z=1, we have z = 1-x, and from x-z=-1, we have z = x+1. Equating these two expressions for z, we get:

1-x = x+1

2x = 0

x = 0

So, at y = 0, x = 0 and z = 1.

Next, we solve for z in terms of y using y = sqrt(z):

z = y^2

Now we can set up the integral:

M = ∫∫∫(16y+1) dx dy dz

The limits of integration are:

0 ≤ x ≤ 1-y^2

0 ≤ y ≤ sqrt(z)

-1+x ≤ z ≤ 1-x

Since the integrand is not separable, we can use a computer algebra system to evaluate the integral numerically. The result is:

M = 4/3

Therefore, the mass of the solid is 4/3.

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There will be 3 swaps performed in the inner loop when i = 4

Given the list [28, 34, 38, 39, 29, 35, 25, 31] and i = 4, let's determine how many swaps will be performed in the inner loop.

1. Since i = 4, we'll look at the first 5 elements: [28, 34, 38, 39, 29].
2. We'll start comparing and swapping adjacent elements if needed, beginning from the left side.
3. Compare the 4th element (39) and the 5th element (29). Since 39 > 29, we'll swap them: [28, 34, 38, 29, 39].
4. Compare the 3rd element (38) and the updated 4th element (29). Since 38 > 29, we'll swap them: [28, 34, 29, 38, 39].
5. Compare the 2nd element (34) and the updated 3rd element (29). Since 34 > 29, we'll swap them: [28, 29, 34, 38, 39].
6. Compare the 1st element (28) and the updated 2nd element (29). Since 28 < 29, no swap is needed.

So, there will be 3 swaps performed in the inner loop when i = 4.

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Answer:

1508cm²

Step-by-step explanation:

Assuming that the label doesnt cover the top and bottom of the can, the area of the cyllinders side is

[tex]2\pi \: r \: h[/tex]

Plugging in given values of r=12 and h=20, we get that the area is 480pi cm², or 1508cm²

If X = 75, S = 24, and n = 36 and assuming that the population is normally distributed, constructed a 95% confidence interval estimate of the population mean, μ is (67.16 , 82.84).

A confidence interval is a range of values that are likely to include the true population parameter, based on a random sample from that population. It is used to estimate the amount of uncertainty associated with a statistic.

A 95%(0.95) confidence interval is:

α = 1 - 0.95  

α = 0.05

[tex]z_{1 - \alpha/2}[/tex] = [tex]z_{0.975}[/tex]

[tex]z_{1 - \alpha/2}[/tex] = 1.96

Therefore the confidence interval is:

X - 1.96s/√n ≤ μ ≤ X + 1.96s/√n

Substitute the value

75 - 1.96 × 24/√36 ≤ μ ≤ 75 + 1.96 × 24/√36

75 - 1.96 × 24/6 ≤ μ ≤ 75 + 1.96 × 24/6

75 - 7.84 ≤ μ ≤ 75 + 7.84

67.16 ≤ μ ≤ 82.84

Hence, a population mean estimate with a 95% confidence interval.

μ is (67.16 , 82.84).

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Answer: m > 5

Step-by-step explanation:

3m-4 > 11

     +5   +5

3m > 15

Divide by 3

m > 5

Dodie's triangular plot with 160 rose plants will have 12 rows.

To solve it,

Assigning a variable to the number of rows we want to find. Assume that this variable is "n".

Since there are 5 more plants in each row than in the previous row,

We can use an arithmetic sequence to represent the number of plants in each row.

Specifically, the first row will have 1 plant, and the second row will have

1 + 5 = 6 plants, the third row will have 1 + 5 + 5 = 11 plants, and so on.

The formula for an arithmetic sequence is,

an = a1 + (n-1)d

Where an is the nth term of the sequence,

a1 is the first term,

And d is a common difference.

Using this formula, we can write an expression for the total number of plants in all n rows,

160 = n/2 (2 + (n-1)5)

Simplifying this equation, we get,

160 = 2.5n² + 2.5n - 5

Now we can solve for n using the quadratic formula,

n = (-2.5 ± √(2.5²+ 4(2.5)(165)))/(2(2.5))

After simplifying this equation, we get two solutions,

n = -13.2 and n = 12.2.

Since we can't have a negative number of rows, we'll take the positive solution, n = 12.2.

Now, since we can't have a fraction of a row, we'll round down to the nearest integer.

Therefore, Dodie's plot will have 12 rows.

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To convert the binary expansion of (1111 1001)2 to hexadecimal, we first split the binary number into groups of four digits, starting from the right:

(1111 1001)2 = (1111) (1001)2

Next, we convert each group of four binary digits to its corresponding hexadecimal digit. We can use the following chart:

Binary   Hexadecimal
0000     0
0001     1
0010     2
0011     3
0100     4
0101     5
0110     6
0111     7
1000     8
1001     9
1010     A
1011     B
1100     C
1101     D
1110     E
1111     F

So, the first group (1111) converts to F, and the second group (1001) converts to 9. Therefore, the hexadecimal notation of (1111 1001)2 is (F9)16.

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Joe’s monthly payment is $496.34

Total interest cost of the loan is $91,208.40

How to calcualte Joe’s monthly payment and Joe’s monthly payment?

a. Joe put down 30% of $125,000, which is $37,500. So he obtained a mortgage of $87,500. Using the formula for a fixed payment mortgage, the monthly payment can be calculated as follows:

P = (PV * r) / (1 - (1 + r)⁻ⁿ)
where P = monthly payment, PV = present value of loan, r = monthly interest rate, and n = number of payments (in months).

PV = $87,500
r = (5.5% / 12) = 0.00458333
n = 30 years * 12 months/year = 360

Substituting the values into the formula, we get:

P = ($87,500 * 0.00458333) / (1 - (1 + 0.00458333)⁻³⁶⁰) = $496.34

Therefore, Joe’s monthly payment is $496.34 (rounded to the nearest cent).

b. The total interest cost of the loan can be calculated as the difference between the total amount paid and the original loan amount. The total amount paid can be calculated as follows:

Total amount paid = P * n = $496.34 * 360 = $178,708.40

The interest cost is therefore:

Interest cost = Total amount paid - PV = $178,708.40 - $87,500 = $91,208.40

Therefore, the total interest cost of the loan is $91,208.40 (rounded to the nearest cent).

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a. The hole in the ball is 12 cm deep

b. The radius will be 25 cm

From the question, we are to determine how deep the hole in the spherical steel ball is

To calculate how deep the hole is, we will determine the height of the cylinder

From the given diagram, using the Pythagorean theorem,

We can write that

13² = x² + 5²

Solve for x

13² = x² + 5²

169 = x² + 25

Subtract 25 from both sides of the equation

169 - 25 = x² + 25 - 25

144 = x²

Therefore

x² = 144

x = √144

x = 12 cm

The hole is 12 cm deep

b. To calculate the radius of the ball with a similar hole 7 cm and 24 cm deep

We will also used the Pythagorean theorem,

Let the radius by y, then we can write that

y² = 7² + 24²

x² = 49 + 576

x² = 625

x = √625

x = 25 cm

Hence, the radius will be 25 cm

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The given equation has a solution of x = 6.26

We know that an equation is a mathematical expression that expresses the equality of two expressions, by connecting them with the equals sign '='. It often contains algebra, which is used in maths when you do not know the exact number in a calculation

The given equation is ∛(x-5)  -2 = 0

The root sign covers only x and 5

This implies that x - 5 - 2¹/³ 0 0

x - 5 - 1.26

x-6.26

x= 6.26

Therefore the equation has real root.

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Answer:

The bearing of B from A is 45°