What is the probability of having at least 1 of the 3 randomly selected Americans say that they are afraid of heights

By using a graphing calculator and a system of equations, we can determine the value of x and then calculate the lengths of the sides. Substituting the value of x into the dimensions, we can identify the longest side among the three.

Using a graphing calculator, enter the equation 2x^3 + 14x^2 + 12x - 400 = 0 and graph it. Find the x-values where the graph intersects the x-axis, which represent the solutions. Using the calculator's "zero" or "intersect" function, determine the numerical values of x. Substitute these values into the dimensions (x, 2x, and x/6) to find the lengths of the sides. Compare the lengths and identify the longest side. This process allows us to find the length of the longest side using a graphing calculator and a system of equations.

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The sum of the roots of the equation 9x² + 162x + m = 0 can be found using Vieta's formulas. The sum of the roots is equal to -b/a, where b is the coefficient of x and a is the coefficient of x² in the quadratic equation.here the final answer is-18.

For a quadratic equation in the form of ax² + bx + c = 0, Vieta's formulas provide a relationship between the coefficients of the equation and the roots. According to Vieta's formulas, the sum of the roots of a quadratic equation is given by -b/a, where b is the coefficient of x and a is the coefficient of x² in the equation.
In the given equation 9x² + 162x + m = 0, the coefficient of x² is 9 (a) and the coefficient of x is 162 (b). To find the sum of the roots, we use the formula -b/a. Plugging in the values, we have -162/9, which simplifies to -18.
Therefore, the sum of the roots of the equation 9x² + 162x + m = 0 is -18.

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One sample t-test, as it compares the mean birthweight of the mothers in the program to a known population mean.

We have,

The most appropriate hypothesis test for this study would be a

one-sample t-test.

A one-sample t-test is suitable when we want to compare the mean of a single sample to a known population mean or hypothesized value.

In this case, the study aims to test the effectiveness of a new prenatal care program in increasing the birth weight of babies born into poverty.

The researchers would compare the mean birthweight of the 30 mothers who participated in the program to the known population mean birthweight for babies born to mothers living in poverty, which is approximately 2800 grams.

Since the population standard deviation is not given, the t-test is preferred over the z-test, which requires knowledge of the population standard deviation.

The t-test allows for estimating the population standard deviation based on the sample data.

Additionally, the study involves comparing a single sample (30 mothers) to a known population mean, rather than comparing two related samples, making the paired-sample t-test inappropriate for this scenario.

Thus,

The most appropriate hypothesis test for this study would be a

one-sample t-test.

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The national average for height in women is below Megan's height of 5 feet, 6 inches, indicating that Megan is taller than the average woman.

The given information states that Megan is 5 feet, 6 inches tall at the age of 24. It further states that the national average for height in women is 5 feet, 4 inches. By comparing Megan's height with the national average, we can determine that Megan is taller than the average woman.

Since Megan's height of 5 feet, 6 inches exceeds the national average of 5 feet, 4 inches, it is clear that she stands taller than the average woman in the country. This suggests that Megan's height falls above the mean height of women, indicating that she is relatively taller compared to the general female population.

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The equation of the central street PQ is B. -1.5x − 3.5y = -31.5. The slope of the lane is 7/3.

The equation of the given lane passing through points A and B is -7x + 3y = -21.5. To find the equation of the central street PQ, we need to determine a line that is perpendicular to the given lane and passes through the midpoint of AB.

First, let's find the midpoint of AB. The coordinates of point A and B are not provided in the question, so we will assume their coordinates as (x₁, y₁) and (x₂, y₂), respectively. The midpoint (xₘ, yₘ) is given by the formula:

xₘ = (x₁ + x₂) / 2

yₘ = (y₁ + y₂) / 2

Now, let's find the slope of the given lane. The slope of a line can be determined by rearranging the equation into the slope-intercept form (y = mx + b), where m is the slope. Rearranging the equation -7x + 3y = -21.5, we get:

3y = 7x - 21.5

y = (7/3)x - 7.17

The slope of the given lane is 7/3. Since the central street PQ is perpendicular to the given lane, its slope will be the negative reciprocal of 7/3, which is -3/7.

Now, let's use the midpoint and the slope of the central street PQ to determine its equation. Using the point-slope form of a line (y - y₁ = m(x - x₁)), where (x₁, y₁) is the midpoint and m is the slope, we have:

y - yₘ = (-3/7)(x - xₘ)

y - (y₁ + y₂) / 2 = (-3/7)(x - (x₁ + x₂) / 2)

7(y - (y₁ + y₂) / 2) = -3(x - (x₁ + x₂) / 2)

7y - 7(y₁ + y₂) / 2 = -3x + 3(x₁ + x₂) / 2

7y - 7(y₁ + y₂) = -6x + 3(x₁ + x₂)

7y - 7y₁ - 7y₂ = -6x + 3x₁ + 3x₂

-6x + 3x₁ + 3x₂ + 7y - 7y₁ - 7y₂ = 0

-6x + 3(x₁ + x₂) + 7(y - y₁ - y₂) = 0

-6x + 3(x₁ + x₂) + 7(y - y₁ - y₂) = 0

Simplifying the equation, we get:

-6x + 3(x₁ + x₂) + 7(y - y₁ - y₂) = 0

-6x + 3x₁ + 3x₂ + 7y - 7y₁ - 7y₂ = 0

Comparing this equation with the given options, we find that the equation of the central street PQ is B. -1.5x − 3.5y = -31.5.

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The surface area of the prism is 96 cm², with dimensions of 88 cm by 88 cm.

To calculate the surface area of a prism, we need to find the sum of the areas of all its faces. In this case, the prism has a rectangular base with dimensions of 88 cm by 88 cm and four identical rectangular faces.

First, we calculate the area of the base by multiplying the length and width: 88 cm × 88 cm = 7744 cm². Since the base has two identical faces, we add this area twice: 7744 cm² × 2 = 15488 cm².

Next, we calculate the area of the other four faces, which are all identical. Each face is a rectangle with a length of 88 cm (the same as the base) and a height equal to the height of the prism. However, the height is not given in the question, so we cannot determine the area of these faces.

Therefore, with the given information, we can only calculate the surface area of the prism based on the known dimensions of the base, which is 15488 cm². It is important to note that without the height of the prism, we cannot determine the total surface area accurately.

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To determine the z-score for the number of sandwiches delivered in less than 23 minutes at Sammy's Sandwich Shop, we need to calculate the deviation from the mean in terms of standard deviations. The z-score is -1.5.

The z-score measures the number of standard deviations a data point is from the mean. In this case, we have a mean delivery time of 25 minutes and a standard deviation of 2 minutes.

To find the z-score for the number of sandwiches delivered in less than 23 minutes, we calculate the deviation from the mean in terms of standard deviations. The formula for calculating the z-score is: z = (x - μ) / σ, where x is the data point, μ is the mean, and σ is the standard deviation.

Plugging in the given values, we have: z = (23 - 25) / 2 = -2 / 2 = -1.

Therefore, the z-score for the number of sandwiches delivered in less than 23 minutes is -1. This indicates that the delivery time of 23 minutes is 1 standard deviation below the mean.

In summary, the z-score for the number of sandwiches delivered in less than 23 minutes at Sammy's Sandwich Shop is -1.5.

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The expression (a+b+c)(d+e+f) consists of six terms, and each term contains three factors.

To understand the number of terms and factors in this expression, we need to expand it using the distributive property. The distributive property states that each term in the first expression is multiplied by each term in the second expression.

(a+b+c)(d+e+f): ad + ae + a f + bd + be + bf + cd + ce + cf

From the above, we can see that there are six terms, which are ad, ae, a f, bd, be, and bf.

Each term contains three factors: a factor from the first parentheses (a, b, or c), a factor from the second parentheses (d, e, or f), and a multiplication sign connecting them.

Therefore, the expression (a+b+c)(d+e+f) consists of six terms and each term contains three factors.

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Approximately 54.46% of women have weights that are within the specified limits of 138.5 lb to 204 lb.

To calculate the percentage of women with weights within the given limits, we first need to convert the weight limits into z-scores using the mean and standard deviation of the distribution. The z-score for the lower limit (138.5 lb) is approximately -0.5334, and the z-score for the upper limit (204 lb) is approximately 1.0009.

Using a standard normal distribution table or calculator, we find that the area to the left of the z-score -0.5334 is approximately 0.2967, and the area to the left of the z-score 1.0009 is approximately 0.8413.

To find the percentage of women within the specified limits, we subtract the lower probability from the upper probability:

0.8413 - 0.2967 = 0.5446

Converting this probability to a percentage, we get approximately 54.46%.

Therefore, approximately 54.46% of women have weights that fall within the specified limits. Since this percentage is less than 100%, it indicates that some women would be excluded with those specifications.

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Therefore, assuming a consistent annual increment rate of 5%, the salary of the employee in 2007 would be $73,830.27.

To determine the salary of the employee in 2007, we need to consider the annual increment rate.

However, since the annual increment rate is not provided in the question, we will assume a consistent annual increment rate of a certain percentage.

Let's assume the annual increment rate is 5%. This means that the employee's salary increases by 5% each year.

To calculate the salary in 2007, we need to calculate the cumulative increment for 8 years (from 1999 to 2007) and add it to the starting salary of $50,000.

Increment for each year:

Year 2000: $50,000 * 0.05 = $2,500

Year 2001: $52,500 * 0.05 = $2,625

Year 2002: $55,125 * 0.05 = $2,756.25

Year 2003: $57,881.25 * 0.05 = $2,894.06

Year 2004: $60,775.31 * 0.05 = $3,038.77

Year 2005: $63,814.08 * 0.05 = $3,190.70

Year 2006: $66,004.78 * 0.05 = $3,300.24

Year 2007: $69,305.02 * 0.05 = $3,465.25

Cumulative increment:

$2,500 + $2,625 + $2,756.25 + $2,894.06 + $3,038.77 + $3,190.70 + $3,300.24 + $3,465.25 = $23,830.27

Final salary in 2007:

$50,000 + $23,830.27 = $73,830.27

Therefore, assuming a consistent annual increment rate of 5%, the salary of the employee in 2007 would be $73,830.27.

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The overall probability can be calculated as P(exactly three spins) = (1 - P(blue)) × (1 - P(blue)) × P(blue).

To determine the probability of spinning the wheel exactly three times until the pointer stops on blue, we need to understand the given conditions and calculate the likelihood of this specific outcome.

Assuming the wheel has multiple colors and the pointer stops on one color each time, we'll focus on the probability of stopping on blue after spinning the wheel three times.

Let's consider the possible outcomes for each spin. Assuming each spin is independent and the probability of stopping on blue is constant, the probability of stopping on blue for a single spin is denoted as P(blue).

To calculate the probability of spinning the wheel exactly three times until stopping on blue, we multiply the probabilities of not stopping on blue for the first two spins and then stopping on blue on the third spin. Since the spins are independent, we multiply the probabilities together.

The probability of not stopping on blue for the first two spins is given by (1 - P(blue)) × (1 - P(blue)). The probability of stopping on blue on the third spin is simply P(blue).

Thus, the overall probability can be calculated as:

P(exactly three spins) = (1 - P(blue)) × (1 - P(blue)) × P(blue).

Without knowing the specific alue of P(blue), we cannot provide an exact numerical probability. However, if the probability of stopping on blue for a single spin is known, it can be substituted into the formula above to calculate the probability of spinning the wheel exactly three times until stopping on blue.

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The equation that can be used to find the area of the rectangle is the product of its length and width. The formula for the area of a rectangle is:A = l × w where A = area, l = length, and w = width.

The area of a rectangle is the product of its length and width. In the given equations: 3 x 7 = 21, 7 x 4 = 28, 8 x 3 = 24, 6 x 5 = 30, and 6 x 4 = 24, only one equation is multiplying the length and the width.

Hence, option D (7 x 4 = 28) can be used to find the area of the rectangle. The area of a rectangle is the product of its length and width. In the given equations: 3 x 7 = 21, 7 x 4 = 28, 8 x 3 = 24, 6 x 5 = 30, and 6 x 4 = 24, only one equation is multiplying the length and the width.

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The wavelength of yellow light, approximately 0.00002 inches, can be best approximated as a power of 10. Among the given options, the number that represents this length most accurately is 2 x 10^-5.

The given wavelength of yellow light is 0.00002 inches. To express this length as a power of 10, we need to move the decimal point to obtain a number between 1 and 10.
In this case, we move the decimal point five places to the left, resulting in 0.00002 becoming 2 x 10^-5. The exponent of -5 indicates that the decimal point is shifted five places to the left, aligning with the original decimal value of 0.00002 inches.
Option C, 2 x 10^-5, is the closest approximation to the given wavelength. None of the other options match the given value. Option A, 2 x 10^5, is too large, option B, 2 x 10^-4, is too small, and option D, -2 x 10^5, has a negative sign which is not applicable in this context.
Therefore, the best approximation of the wavelength of yellow light, 0.00002 inches, as a power of 10 is represented by option C, 2 x 10^-5.

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The angle x, at which the diagonal beam meets the 10-foot beam at the top of the frame is 16.7°.

Given a right-angled triangle which is given below.

The lengths of the legs are given as 10 feet and 3 feet.

It is required to find the angle x.

The trigonometric function which relates the given angles and sides of the triangle is:

tan x = 3/10

So,

tan x = 0.3

So, x = tan⁻¹(0.3)

         = 0.291 radians

         = 16.699°

         ≈ 16.7°

Hence the correct option for the angle x is 16.7°.

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The derivative of the operations with the functions are: g(x) + h(x) + j(x) = 6x + 2, h(x) + j(x) - g(x) = 6x + 1, j(x)⋅g(x) = 4x + 1, h(x)/g(x) = 3 and j(h(x)) = 36x³ + 6x.

To find the derivatives of the given operations with the functions f(x) = 5, g(x) = x, h(x) = 3x², and j(x) = 2x + 1, we will apply the rules of differentiation.

Gg(x) + h(x) + j(x):

The derivative of a sum of functions is equal to the sum of their derivatives. Therefore, we find:

d/dx[g(x) + h(x) + j(x)] = d/dx g(x) + d/dx h(x) + d/dx j(x)

d/dx[g(x) + h(x) + j(x)] = 0 + 6x + 2

d/dx[g(x) + h(x) + j(x)] = 6x + 2

So, the derivative of g(x) + h(x) + j(x) is 6x + 2.

h(x) + j(x) - g(x):

Similarly, the derivative of a difference of functions is equal to the difference of their derivatives. We have:

d/dx[h(x) + j(x) - g(x)] = d/dx h(x) + d/dx j(x) - d/dx g(x)

d/dx[h(x) + j(x) - g(x)] = 6x + 2 - 1

So, the derivative of h(x) + j(x) - g(x) is 6x + 1.

j(x) ⋅ g(x):

To differentiate the product of two functions, we use the product rule. Applying the rule, we get:

d/dx [j(x) ⋅ g(x)] = g(x) ⋅ d/dx j(x) + j(x) ⋅ d/dx g(x)

d/dx [j(x) ⋅ g(x)] = x ⋅ 2 + (2x + 1) ⋅ 1

Simplifying, we have:

d/dx [j(x) ⋅ g(x)] = 2x + 2x + 1

d/dx [j(x) ⋅ g(x)] = 4x + 1

Therefore, the derivative of j(x) ⋅ g(x) is 4x + 1.

h(x) / g(x):

To differentiate the division of two functions, we use the quotient rule. The rule states:

d/dx [h(x) / g(x)] = (g(x) ⋅ d/dx h(x) - h(x) ⋅ d/dx g(x))/g(x)²

Applying the rule, we find:

d/dx [h(x) / g(x)] = (x ⋅ 6x - 3x² ⋅ 1)/x²

Simplifying, we get:

d/dx [h(x) / g(x)] = (6x² - 3x²) / x²

d/dx [h(x) / g(x)] = 3

Therefore, the derivative of h(x) / g(x) is 3.

j(h(x)):

To find the derivative of a composite function, we use the chain rule. The chain rule states:

d/dx [f(g(x))] = f'(g(x)) ⋅ g'(x)

Applying the chain rule, we have:

d/dx [j(h(x))] = d/dx [j(u)] (where u = h(x))

d/dx [j(h(x))] = d/du [j(u)] ⋅ du/dx

d/dx [j(h(x))] = (2u + 1) ⋅ (d/dx [h(x)])

d/dx [j(h(x))] = (2(3x²) + 1) ⋅ (6x)

Simplifying, we get:

d/dx [j(h(x))] = (6x² + 1) ⋅ (6x)

d/dx [j(h(x))] = 36x³ + 6x

Therefore, the derivative of j(h(x)) is 36x³ + 6x.

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The complete question is:

Next, the following functions are defined: f(x) = 5; g(x) = x h(x) = 3x² j(x) = 2x+1 Find the derivative of the following operations with the functions given above.

g(x)+h(x)+j(x)=

h(x)+j(x)-g(x)=

j(x)⋅g(x)=

h(x)/g(x) =

j(h(x))=

The equation f(x) = 3(x - 8)(x + 2) satisfies the given conditions of having x-intercepts at (8, 0) and (-2, 0), and a y-intercept at (0, -48).

To further explain the equation f(x) = 3(x - 8)(x + 2), let's break it down step by step:

The equation is in factored form, where (x - 8) and (x + 2) represent the linear factors. The x-intercepts occur when f(x) = 0, which means the equation equals zero. By setting the equation equal to zero, we can find the values of x that make the equation true.

So, when we set f(x) = 0, we have: 3(x - 8)(x + 2) = 0

To satisfy this equation, either (x - 8) must equal zero or (x + 2) must equal zero, because multiplying anything by zero results in zero.

Setting (x - 8) = 0, we find x = 8, which gives us the x-intercept (8, 0).

Setting (x + 2) = 0, we find x = -2, which gives us the x-intercept (-2, 0).

Therefore, the equation f(x) = 3(x - 8)(x + 2) satisfies the condition of having x-intercepts at (8, 0) and (-2, 0). Additionally, the y-intercept occurs when x = 0. Substituting x = 0 into the equation, we have: f(0) = 3(0 - 8)(0 + 2) = 3(-8)(2) = -48

This means that when x is zero, the y-value of the equation is -48, giving us the y-intercept (0, -48). Hence, the equation f(x) = 3(x - 8)(x + 2) satisfies the given conditions of having x-intercepts at (8, 0) and (-2, 0), and a y-intercept at (0, -48).

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None of the given options (1, 2, 3, or 4) is the correct value of a for the given function to be linear. The given function

y = xa − 31 is not a linear function because the power of the variable x is greater than 1. Thus its degree is greater than 1. Linear functions have a degree of 1. So, the correct option is none of the above.

For a function to be linear, it must have a degree of 1, i.e., the highest power of the variable is 1, and the graph of a linear function is a straight line. However, the given function y = xa − 31 has a degree of a because the variable x's power is greater than 1. Hence, the given function is not linear. Instead, the given function is a power function of y = an.

When graphed, a power function can have several shapes depending on the values of a and n. In general, if n is an even number and a > 0, the graph of the function has a shape similar to that of a quadratic function with its vertex at the origin. However, if n is an odd number and a > 0, the function graph increases or decreases without bounds depending on whether a is positive or negative.

The given function y = xa − 31 is not linear because its degree is greater than 1. Therefore, none of the given options

(1, 2, 3, or 4) is the correct value of a for the given function to be linear.

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Marco's solution method of graphing the equation  y = 2sin(3x) and y = -0.55 to locate the intervals where 2sin(3x) is less than or equal to -0.55 is valid. By graphing the functions, Marco can visually determine the intervals where the inequality is satisfied.

However, to obtain a precise and accurate solution, he should also consider other methods, such as algebraic manipulation or solving the equation analytically.

Graphing the functions y = 2sin(3x) and y = -0.55 allows Marco to visualize the behavior of the two functions and identify the intervals where 2sin(3x) is less than or equal to -0.55. By comparing the graphs of the two functions, he can determine the values of x for which the inequality is satisfied.

While graphing provides a visual understanding of the solution, it is important to note that it might not yield an exact solution. Graphs can provide an approximate solution, but for precise results, algebraic manipulation or analytical methods should be employed. These methods can provide a more accurate and rigorous solution to the equation.

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La velocidad del recorrido es de 1.67 m/s. Para encontrar la velocidad de un recorrido de 125 m realizado en un tiempo de 75 segundos.

Utilizaremos la fórmula de velocidad promedio, que es la distancia dividida por el tiempo.

Para encontrar la velocidad, sigue estos pasos:

Identifica la distancia recorrida, que es de 125 m.

Identifica el tiempo transcurrido, que es de 75 segundos.

Aplica la fórmula de velocidad promedio: velocidad = distancia / tiempo.

Sustituye los valores conocidos en la fórmula: velocidad = 125 m / 75 s.

Realiza la división: velocidad = 1.67 m/s.

Por lo tanto, la velocidad del recorrido es de 1.67 m/s.

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triangle ABC with angle A and AC missing, we need to solve for the missing parts of the triangle.

Step-by-step explanation:We are given triangle ABC, with angle A and side AC missing. To solve for the missing parts of the triangle, we can use the properties of triangles and trigonometry.Let's start by finding angle A. We know that the sum of angles in a triangle is 180°.

Therefore, we can write:∠A + ∠B + ∠C = 180°

Substituting the values we know, we get:∠A + 60° + 45° = 180°

Simplifying the equation, we get:∠A = 180° - 60° - 45°∠A = 75°

Therefore, angle A measures 75°.Now, we can use trigonometry to find the length of side AC. Since we know the length of sides AB and BC, we can use the Law of Cosines to find the length of AC.

The Law of Cosines states that: c² = a² + b² - 2ab cos(C)

where a, b, and c are the lengths of sides of a triangle, and C is the angle opposite to side c.

Substituting the values we know, we get:AC² = AB² + BC² - 2(AB)(BC) cos(A

)AC² = 6² + 8² - 2(6)(8) cos(75°)

AC² = 36 + 64 - 96 cos(75°)

AC² = 100 - 96 cos(75°)

Using a calculator, we can find that cos(75°) = 0.2588. Substituting this value, we get:AC² = 100 - 96(0.2588)AC² = 100 - 24.8448AC² = 75.1552

Taking the square root of both sides, we get:AC ≈ 8.67

Therefore, side AC has a length of approximately 8.67 units.

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a) Sabrina can type 2 ⅖ pages per hour. To find out how many pages she can type in 8 hours and 20 minutes, we need to convert the time to hours.

b) To convert 8 hours and 20 minutes to hours, we divide the minutes by 60 and add the result to the number of hours. Then, we multiply the total number of hours by Sabrina's typing rate of 2 ⅖ pages per hour to find the total number of pages she can type.

a) Sabrina's typing rate is given as 2 ⅖ pages per hour. This means she can type 2 and two-fifths of a page in one hour.

b) To calculate the total number of pages Sabrina can type in 8 hours and 20 minutes, we convert the time to hours. Since there are 60 minutes in an hour, we divide the minutes by 60 to convert them to hours. In this case, 20 minutes divided by 60 equals 1/3 hours. Adding this to the 8 hours gives us a total of 8 and 1/3 hours.

Next, we multiply the total number of hours (8 1/3) by Sabrina's typing rate (2 ⅖ pages per hour). To multiply fractions, we multiply the numerators and denominators separately. The result is (25/3) * (12/5) = 300/15 = 20 pages.

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With an 80% improvement in typing speed from an initial rate of 50 words per minute, you will be able to type 90 words per minute.

Increasing your typing speed by 80% means you will be able to type 80% more words in the same amount of time. Therefore, if your initial typing speed is 50 words per minute, an 80% improvement would result in a typing speed of 90 words per minute.

To calculate the new typing speed, we first find 80% of the initial typing speed.

80% of 50 is (80/100) * 50 = 0.8 * 50 = 40.

This means that your typing speed will increase by 40 words per minute.

To determine the new typing speed, we add the increase to the initial typing speed:

50 + 40 = 90.

Thus, after the 80% improvement, you will be able to type 90 words per minute.

In summary, with an 80% improvement in typing speed from an initial rate of 50 words per minute, you will be able to type 90 words per minute.


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Given table, b is the output and a is the input. If we take a look at the table, we can see that b increases by 1 when a increases by 1. So, a linear pattern exists in this table.

The answer is Yes.

The other equations do not have a constant rate of change. For instance, the equation b = a - 5 decreases by 5 when a increases by 1, but in the table, b increases by 1 when a increases by 1. Similarly, the equations a = b - 5 and b = a + 1234 have no correlation to the table. Given, Commission earned on sales up to $5,000 = 5% Commission earned on sales greater than $5,000 = 7.5% Amount of commission earned last month = $1,375 Calculation Using the given information, the amount of sales the salesperson had last month is calculated as follows: Let x be the sales amount the salesperson had last month.

So, the commission earned on the first $5,000 of sales is:$5,000 × 5% = $250 Commission earned on sales greater than $5,000 is: $1,375 − $250 = $1,125 So, we can write that: $1,125 = 7.5% × (x − $5,000)

⇒ x − $5,000

= $15,000 ⇒

x = $20,000 Therefore, the salesperson had $20,000 in sales last month. Given table, b is the output and a is the input. If we take a look at the table, we can see that b increases by 1 when a increases by 1. So, a linear pattern exists in this table. That means the correct equation would have a constant rate of change.

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One possible set of measures for the sides of a right triangle with an irrational hypotenuse between 6 and 8 is (3, 4, 5).

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we are looking for a right triangle with a hypotenuse between 6 and 8, and whole number lengths for the other two sides.

One well-known example of a right triangle with whole number side lengths is the (3, 4, 5) triangle. According to the Pythagorean theorem, 3^2 + 4^2 = 5^2, which is true. The length of the hypotenuse in this case is 5, which falls between 6 and 8 as given in the problem.

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The exercise 6.28 gives you the mean and the standard deviation of foot length. It can be used to find the percentage of women who can find shoes that fit. Exercise 6.28 gives us the mean length of a woman's foot is 23.6 cm, with a standard deviation of 1.5 cm.

Women's feet that are 21.6 cm to 25 cm long can wear shoes ranging in size from 5 to 9. Convert the sizes into cm, using the conversion: 1 inch = 2.54 cm. Therefore, sizes 5 to 9 are 22.1 cm to 25.4 cm long.To compute the percentage of women who can find shoes that fit, we need to calculate the area under the curve between 21.6 and 25 cm. This can be done by standardizing the distribution. Standardizing the distribution requires calculating the z-score. The formula for z-score is z = (x - µ) / σ, where x is the value you are interested in, µ is the mean, and σ is the standard deviation. For this problem, the values are x = 21.6, µ = 23.6, and σ = 1.5. Thus, the z-score is:z = (21.6 - 23.6) / 1.5 = -1.33Similarly, the z-score for x = 25 is:z = (25 - 23.6) / 1.5 = 0.93The area under the curve between -1.33 and 0.93 gives the percentage of women whose foot length is between 21.6 cm and 25 cm.

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a) A relative frequency interpretation of the probability of a double-yolk egg being 0.1 is that, in the long run or over a large number of eggs, approximately 10% of eggs will have double yolks.

b) If 5,000 eggs were randomly selected, we can estimate the number of double-yolk eggs we would expect to find by multiplying the probability of a double-yolk egg (0.1) by the total number of eggs (5,000).

Expected number of double-yolk eggs = 0.1 * 5,000 = 500 eggs.

a) The probability of a double-yolk egg being 0.1 can be interpreted as the relative frequency of finding double-yolk eggs over a large number of eggs. It means that if we were to select a significant number of eggs, approximately 10% of them would have double yolks. This interpretation is based on the assumption that the eggs are randomly selected and the probability remains constant.

b) To estimate the number of double-yolk eggs in a sample of 5,000 eggs, we can use the probability given in the article. By multiplying the probability of a double-yolk egg (0.1) by the total number of eggs (5,000), we can calculate the expected number of double-yolk eggs. In this case, the expected number would be 500 eggs. This means that, on average, we would expect to find 500 double-yolk eggs out of the 5,000 eggs randomly selected. It is important to note that this is an expected value based on probability, and the actual number of double-yolk eggs found may vary in any given sample.

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We can conclude that the perimeter of DEF is 20.25.

Given that DEF~CBF, DF = 6, and FC = 8.

We are supposed to find the perimeter of DEF.

To solve this question, we need to know that when two triangles are similar, the ratio of their corresponding sides are in proportion.

Using this information, we can say that the ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides.

Therefore, we can use the following proportion to find the perimeter of DEF and CBF:

Perimeter of DEF/Perimeter of

CBF=DF/FC

= 6/8

= 3/4

Let P be the perimeter of DEF.

Using the above proportion, we can write:

Perimeter of DEF = (DF/FC) × Perimeter of CBF

= (3/4) × 27

= 20.25

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The three integers are 10, 12 and 14.

To find three integers that satisfy the given conditions, we can use the properties of range and mean.

Let's assume the three integers are x, y, and z.

Range is the difference between the largest and smallest values. In this case, the range is given as 7. Therefore, we can set up the equation:

max(x, y, z) - min(x, y, z) = 7.

Mean is the average of the values. The mean is given as 12. Therefore, we can set up the equation:

(x + y + z) / 3 = 12.

We also know that all three integers are less than 20.

Let's solve these equations simultaneously:

From the equation for the mean, we can rewrite it as:

x + y + z = 36.

Now, let's list all the possible combinations of three integers that satisfy the given conditions:

x = 9, y = 12, z = 15

x = 10, y = 12, z = 14

x = 11, y = 12, z = 13

Out of these combinations, only the second one satisfies the condition that all three integers are less than 20.

Therefore, the three integers that meet the given conditions are:

x = 10, y = 12, z = 14.

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The tree's growth rate is 6 inches per month over the course of 6 months.

To find the tree's growth in inches per month over 6 months, divide the total growth of the tree by the number of months it took for the tree to grow.

In this case, the tree grew from a height of 10 inches to a height of 46 inches over 6 months.

Therefore, the tree's growth in inches per month over 6 months is calculated as follows:

=[tex]\frac{\text{Total growth}}{\text{Number of months}}[/tex]

=[tex]\frac{46-10}{6}[/tex]

=[tex]\frac{36}{6}[/tex]

= [tex]6$$[/tex]

Hence, the tree's growth in inches per month over 6 months is 6 inches.

To determine the tree's growth in inches per month over the span of 6 months, we need to calculate the average monthly growth.

The initial height of the tree is 10 inches, and after 6 months, it grew to a height of 46 inches.

To find the growth per month, we can subtract the initial height from the final height and divide it by the number of months:

Growth per month = (Final height - Initial height) / Number of months

In this case, the growth per month would be:

(46 inches - 10 inches) / 6 months

= 36 inches / 6 months

= 6 inches per month

Therefore, the tree's growth rate is 6 inches per month over the course of 6 months.

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The property that justifies Emily's first step include the following: C. division property of equality.

In Mathematics and Geometry, the Commutative Property of Addition states that when two (2) or three (3) numerical values (numbers) are added together, the output (end result) would always remain the same, irrespective of the way in which the numerical values are arranged.

Generally speaking, the Commutative Property of Addition allows the addends to be re-ordered without causing a change in the result, output, or outcome.

By applying the division property of equality to Emily's equation, we have the following;

2(-3x² + 2) + 4 = 18x² - 20

2(-3x² + 2) + 2(2) = 2(9x² - 10)

(-3x² + 2) + 2 = (9x² - 10) ⇒ (division property of equality)

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