An escalator in a department store carries people a vertical distance of 14 feet between floors. How
long is the escalator if it makes an angle of 30° with the ground?

Feet : ____

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Answer:

y=4x-7

Step-by-step explanation:

first, find b

5=4*3+b

5=12+b

b=-7

The interest of the CD account's of Ethan after 6 year is  $756.

For the given question;

Ethan deposit $7,000 into a certificate of deposit CD for 6 years.

The formula for finding the simple interest is;

SI = PRT/100

where,

Put the values in the formula,

SI = 7,000×1.8×6/100

Simplifying;

SI = 756.

Thus, the simple interest gained after 6 years will be $756.

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Answer:

the correct answer is 1 1/2 cups of sugar

Answer:

1 1/2 cups of sugar

Step-by-step explanation:

you add 1/2 + 1/2 and get 1 and then add 1 + 1/2 and you get

1 1/2. Your Welcome

By using the concept of mean and standard deviation, it can be calculated that the critical values of t has an absolute value of 2.308

What is mean and Standard Deviation?

Suppose there is a data set. Mean is used to find the average of all the values of the data set.

Variance is the sum of the square of the deviation from the mean.

On taking the square root of the variance, Standard deviation is obtained.

Class 1                  Class 2                     d          \(d - \bar{d}\)            \((d - \bar{d})^2\)

87                         87                             0           1.444            2.0851

78                         86                            -8          -6.556          42.9811

87                         92                            -5          -3.556          12.6451

85                         90                            -5          -3.556          12.6451

93                         90                             3           4.444           19.7491

98                         91                              7            8.444           71.3011

83                         89                            -6           -4.556          20.7571

82                         78                              4            5.444          29.6371

73                         76                             -3            -1.556          2.4211

Total                      -                               - 13            -               214.2222

Here number of observations (n) = 9

\(\bar{d} = \frac{-13}{9}\)

\(\bar{d} = -1.444\)

Standard Deviation (SD) = \(\sqrt{\frac{214.2222}{8}}\)

SD = 5.1747

Now,

\(H_0 : \mu_d = 0\ against \ H_a : \mu_d \neq 0\\\)

The test statistic used here is t - test

\(t = \frac{-1.444 - 0}{\frac{5.1747}{\sqrt{9}}}\\\)

t = 0.84

Degree of freedom (Df) = 9-1 = 8

critical value of t at the given level of significance at Df of 8 = 2.308

At 0.05 level of significance, 0.84 falls to the left of 2.308 which is the acceptance region

So the null hypothesis has been accepted.

Absolute value of Critical values of t = 2.308

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To obtain the Maclaurin series for the function f(x) = 8 cos(x^7), we can start by using the Maclaurin series expansion for the cosine function. The Maclaurin series expansion for cos(x) is given by:

cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...

To incorporate the x^7 term in the function f(x) = 8 cos(x^7), we need to substitute x^7 in place of x in the cosine series expansion:

f(x) = 8 cos((x^7)^7)

To simplify this expression, we can rewrite it as:

f(x) = 8 cos(x^(49))

Now, we can substitute the Maclaurin series expansion for cos(x) into this expression:

f(x) = 8 [1 - (x^(49))^2/2! + (x^(49))^4/4! - (x^(49))^6/6! + ...]

Simplifying further, we get:

f(x) = 8 [1 - x^98/2! + x^196/4! - x^294/6! + ...]

This is the Maclaurin series for the function f(x) = 8 cos(x^7), which can be used to approximate the value of the function for small values of x. The more terms we include in the series, the more accurate the approximation will be.

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The union and intersection of n sets that are all subsets of the universal set u can be found using bit strings.

Bit strings are a way of representing sets as strings of binary digits. To represent a set, each element is assigned a digit of 0 or 1. A 1 indicates that the element is in the set, while a 0 indicates that the element is not in the set.

The union of the sets is found by combining the bit strings and setting any digit that is 1 in any of the sets to a 1. The intersection is found by comparing the bit strings and setting any digit that is 1 in all of the sets to a 1.

By using bit strings, we can quickly and accurately find the union and intersection of n sets that are all subsets of the universal set u.

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Using Excel, the probability that at least 35 of the 154 randomly selected vehicles exceed 110 kilometers per hour when 17.7% of vehicles exceed this speed on the expressway is approximately 0.0027, rounded to four decimal places.

To solve this problem in Excel, we can use the binomial distribution function. In this case, the probability of success (a vehicle exceeding 110 kilometers per hour) is p = 0.177, and the number of trials (vehicles selected) is n = 154.

We want to find the probability of at least 35 successes (vehicles exceeding 110 kilometers per hour), which can be calculated using the formula:

=1-BINOM.DIST(34,154,0.177,TRUE)

This formula gives a probability of 0.0027, which is the probability that at least 35 of the selected vehicles exceed 110 kilometers per hour. Therefore, the answer is 0.0027, rounded to four decimal places.

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In the experiment, the independent variable is the amount of sunlight received by the clover plants.

The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.

The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.

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A list that shows the possible outcomes of one day one method of travel:

Monday, bus,

Monday, subway,

Monday, taxi,

Tuesday, bus,

Tuesday, subway,

Tuesday, taxi

The correct answer is an option (B)

Let A represents the set of days.

A = {Monday, Tuesday}

And set B represents the method of transportaion/travel.

B = {bus, subway,  taxi }

To find the list of possible outcomes of one day one method of travel we find the product of set A and set B.

We know that for non-empty sets A and B the Cartesian Product is given by AxB = {(a,b) | a ∈ A and b ∈ B}.

It is a set of all ordered pairs (a, b)

For above sets A and B,

A × B = {(Monday, bus), (Monday, subway), (Monday, taxi), (Tuesday, bus), (Tuesday, subway), (Tuesday, taxi)}

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Find the complete question below.

Answer:

The probability that at most 26 people out of the 300 surveyed say their favorite sport is auto racing is approximately 0.8750 or 87.50%.

Step-by-step explanation:

To solve this problem, we'll use the normal approximation to the binomial distribution.

Step 1: Determine the mean and standard deviation.

Mean (µ) = n * p = 300 * 0.07 = 21

Standard deviation (σ) = √(n * p * (1-p)) = √(300 * 0.07 * 0.93) ≈ 4.34

Step 2: Calculate the z-score. z = (x - µ) / σ = (26 - 21) / 4.34 ≈ 1.151

Step 3: Use a z-table to find the probability corresponding to the z-score. The probability for z = 1.151 is 0.8750.

Step 4: Since we want the probability that the number of people who say their favorite sport is auto racing is at most 26, the result from the z-table is the final answer i.e. Probability = 0.8750

So, the probability that at most 26 people out of the 300 surveyed say their favorite sport is auto racing is approximately 0.8750 or 87.50%.

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Answer:

-9 >= x

Step-by-step explanation:

5x + 1 <= 3x - 17

add 17 to both sides- that will cancel the one on the right side. And on left side it would add to 18

5x + 18 <= 3x

then subtract 5x from both sides- that will cancel the one on left side. And on the right side ur left with negative 2x

18 <= -2x

divide both sides by negative 2... since dividing by -2 u have to slip the inequality sign.

-9 => x

hi

5x+1 ≤ 3x-17

5x-3x≤ -17 -1

2x≤ -18

x≤  -18/2

x≤ -9

solutions :  x ∈ ] -∞; -9]

Answer:

~18.28 ft. / 12 + 2π ft. (Read explanation please!)

Step-by-step explanation:

I) Find the square's perimeter:

Obviously, a square's perimeter is its side length x 4. However, there would be a semicircle on top of it. So, to find it we use:

4 x 3 = 16 ft. (Since 1 of the sides is covered by the semicircle)

II) Find the semicircle's perimeter:

Finding the semicircle's perimeter is a bit more complicated, but no worries! We can use this formula:

πr + 2r (pi x radius + radius x 2)

But WAIT: We need to make sure we remove that one side of the square we mentioned earlier. So we would use:

πr (pi x radius)

In terms of π, the perimeter would be:

2π = 2π ft.

Or, if you used a standard approximation of π, let's say 3.14, it would be:

2(3.14) = ~6.28 ft.

III) Add them up:

If we wanted to state the total perimeter using 3.14 as π, we would say the formula is:

2(3.14) + 4(3) = 18.28 ft.

Or in terms of π:

2π + 4(3) = 12 + 2π ft.

Based on the given information, we need to compute probabilities related to a lognormal distribution with a mean of 83.6 and a variance of 169.70. These probabilities can be calculated using the properties and characteristics of the lognormal distribution.

To compute the desired probabilities, we can utilize the properties of the lognormal distribution. The lognormal distribution is characterized by its mean (µ) and variance (σ²), which in this case are given as 83.6 and 169.70, respectively.

Some common probabilities that can be computed include the probability of Y being less than a certain value (P(Y < a)), the probability of Y being greater than a certain value (P(Y > a)), and the probability of Y falling within a specific interval (P(a < Y < b)).

To calculate these probabilities, we can transform the lognormal distribution to a standard normal distribution using the natural logarithm. By applying the appropriate transformations and utilizing the properties of the standard normal distribution, we can find the corresponding probabilities using a z-table or statistical software.

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Answer:

Step-by-step explanation:The only one you probably can never do is B. It get's you no where. The way A is written, it is not much help to write 18 in base 2. So A and B both won't work. The common logs and the natural logs will both work

Log(4^(x + 3)) = Log(18)

(x + 3) Log(4) = log (18)

(x + 3) * 0.6021 = 1.2553

x + 3 = 1.2553/0.6021

x + 3 = 2.08496

Now all you need do is subtract 3 from both sides. The natural logs will give you the same answer.

You could take base-4 logs of both sides and it is a possible first step, but d and e are much more efficient. You have to change both sides to base 4 before you can proceed. This one is kind of iffy.  It does say possible first steps.

Randomly selected employees, proportional sampling based on department or job role, stratified sampling, geographically diverse employees, represent the opinions of all employees.

These approaches help ensure diversity, account for various characteristics, and provide a comprehensive perspective on the company's workforce. To obtain a representative sample for a survey, it is crucial to consider factors such as demographics, job roles, and geographical distribution. Randomly selecting employees from different departments, levels, and locations ensures a diverse representation of the workforce.

Proportional sampling, where the sample size is determined based on the proportion of employees in each department or job role, helps reflect the overall composition of the company. Stratified sampling involves dividing employees into strata based on specific characteristics and then randomly selecting employees from each stratum, ensuring representation across different segments of the company. Including employees from different offices or locations accounts for regional variations and provides a more comprehensive perspective.

Lastly, including both long-tenured and recently hired employees captures a range of experiences and opinions. By considering these groups, the survey sample can be designed to represent the opinions and preferences of all employees in the company.

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Answer:

(2,4),(−1,1)

Step-by-step explanation:

The theater has a tοtal οf 56 red seats and 32 blue seats, making a tοtal οf 88 seats.

If each sectiοn has 14 red seats, then there are a tοtal οf 4 x 14 = <<4 × 14=56>>56 red seats in the theater.

Tο find οut hοw many blue seats are in each sectiοn, we need tο subtract the number οf red seats frοm the tοtal number οf seats in each sectiοn:

88 tοtal seats / 4 sectiοns = 22 seats per sectiοn

22 seats per sectiοn - 14 red seats per sectiοn = 8 blue seats per sectiοn

Therefοre, each sectiοn has 8 blue seats, and the theater has a tοtal οf 4 x 8 = <<4 × 8=32>>32 blue seats.

Sο, the theater has a tοtal οf 56 red seats and 32 blue seats, making a tοtal οf 88 seats.

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The cartesian equation for the curve given by r = 9 tan(θ) sec(θ) is:

y = x(sec(x))^2, where x = θ - π/2.

The given polar equation can be simplified using the trigonometric identity for tangent and secant:

r = 9 tan(θ) sec(θ)

r = 9 sin(θ) / cos(θ) * 1 / cos(θ)

r = 9 sin(θ) / cos^2(θ)

Converting to cartesian coordinates using r^2 = x^2 + y^2 and x = r cos(θ), y = r sin(θ), we get:

(x^2 + y^2) = 81 y / x^2

Multiplying both sides by x^2, we get:

x^2 + y^2 = 81y / x^2 * x^2

x^2y^2 + x^4 - 81y = 0

Substituting x = θ - π/2, we get:

(y / (θ - π/2))^2 + (y / (θ - π/2))^4 - 81y = 0

Simplifying this expression gives us the cartesian equation for the curve:

y = x(sec(x))^2, where x = θ - π/2.

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Answer:

-56-7k

Step-by-step explanation:

=> -7(8+k)

Expanding brackets using distributive property

=> (-7*8) + (-7*k)

=> -56 + (-7k)

=> -56-7k

Answer:

-56 - 7k

Step-by-step explanation:

Use the distributive property.

-7(8 + k) = -7 * 8 + (-7) * k = -56 - 7k

2.6

Given the expression;

Simplify the expression in the bracket to have:

Simplify the result to have;

Hence the result of the given function on simplification is 2.6

Answer:

X = 12

Step-by-step explanation:

(4x+2) = 50 bc the angles are the same

subtract 2

4x=48

divide by 4

x=12

Answer:

m = 2/3, you were correct

Step-by-step explanation:

plot the point on a graph

calculate the rise by going up alongside the y axis

the rise is 2

calcualte the run it takes to get to the second point

the run is 3

m = rise/run = 2/3

m = 2/3

Plz mark as brainliest if correct! Have a nice day!!!

Step-by-step explanation:

The slope is the coefficient of x, which is 4.

The y-intercept is the constant term after x, which is -5.

The slope of the line is 4, and the y-intercept is -5.

To find the slope and y-intercept of the equation y = 4x - 5, we can compare it to the slope-intercept form of a linear equation, which is y = mx + b.

In the equation y = 4x - 5:

The coefficient of x is 4, which represents the slope of the line.

The constant term -5 represents the y-intercept, which is the value of y when x is 0.

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The rotation rule used in this problem is given as follows:

90º counterclockwise rotation.

The five more known rotation rules are given as follows:

The equivalent vertices for this problem are given as follows:

Hence the rule is given as follows:

(x,y) -> (-y,x).

Which is a 90º counterclockwise rotation.

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A triangular bandana has an area of 86 square inches. The height of the triangle is 5 3/8 inches. An equation to find the length of the base of the triangle is 86 = 1/2 * b * 43/8

The length of the triangle's base is 32 inches.

We know that the formula for calculating the area of a triangle is:

1/2 * base * height = area

We also know that the triangle's height is 5 3/8 inches, which may be expressed as a mixed number:

Height = 5 + 3/8 inch = 43/8 inch

Let b be the base of the triangle.

Substituting these numbers into the area formula yields:

86 = 1/2 * b * 43/8

To find b, multiply both sides of the equation by 2/43:

86 * 2/43 = 2/43 * 1/2 * b * 43/8

4 = b/8

b = 32

As a result, the length of the triangle's base is 32 inches.

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775757874875875345634634563456

Answer:

B

Step-by-step explanation:

a fraction is equal to 0 when the numerator is 0

x - 4 = 0

x = 4

The correct answer is x=4.

Step-by-step explanation:

When the numerator is 0, a fraction is equal to 0.

x - 4 = 0

x = 4

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9) (2x + 3)(4x² - 6x + 9) 10) (4-3b)(4² + 12b + 9b²)

11) (2m -3r)(4m² + 6mr + 9r²) 12) (5a + 2b)(25a² - 10ab + 4b²)

Explanation:

Factoring a Sum of Cubes:

a³ + b³ = (a + b)(a² – ab + b²)

Factoring a Difference of Cubes:

a³ – b³ = (a – b)(a² + ab + b²)

9) 8x³+27

2³x³ + 3³ = (2x)³ + 3³

(2x)³ + 3³ = (2x + 3)((2x)² -(2x)(3) + 3²)

= (2x + 3)(4x² - 6x + 9)

10) 64 - 27b³

4³ - 3³b³ = 4³ - (3b)³

4³ - (3b)³ = (4-3b)(4² + (4)(3b) + (3b)²

= (4-3b)(4² + 12b + 9b²)

11) 8m³ - 27r³

2³m³ - 3³r³ = (2m)³ - (3r)³

(2m)³ - (3r)³ = (2m -3r)((2m)² + (2m)(3r) + (3r)²)

= (2m -3r)(4m² + 6mr + 9r²)

12) 125a³+8b³

5³a³ + 2³b³ = (5a)³ + (2b)³

(5a)³ + (2b)³ = (5a + 2b)((5a)² - (5a)(2b) + (2b)²)

= (5a + 2b)(25a² - 10ab + 4b²)