what distance does the tip of the minute hand on a clock travel in 11 minutes if the minute hand is 23 cm long?

The missing side is [tex]5\sqrt{3}[/tex].

What are basic Trigonometric functions?

The angles of sine,  cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.

In a Right-angled triangle, the tangent of an angle is equal to the opposite side/adjacent side.

from the given figure,

tan 60° = x/5

[tex]\sqrt{3}=\frac{x}{5}\\ x=5\sqrt{3}[/tex]

Therefore, The missing side is [tex]5\sqrt{3}[/tex].

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The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.

Regression analysis is a powerful statistical tool used to estimate the relationship between two or more variables. The ordinary least squares (OLS) method is the most commonly used regression method. However, the OLS method is sensitive to outliers in the data.

LAD regression is a robust alternative to OLS regression because it minimizes the sum of the absolute vertical differences between the regression line and the data points. This method is also known as L1 regression.

Let's consider an example of a simple linear regression model with n observations, where Y is the dependent variable and X is the independent variable.

The OLS method estimates the parameters of the regression line by minimizing the sum of the squared vertical differences between the observed data points and the predicted values of the regression line.

In mathematical terms, the OLS method can be represented as follows:

minimize the sum of squared vertical differences,

min(β₀, β₁) ∑ (yₐ - β₀ - β₁ xₐ)²

However, if the data contains outliers, the OLS method may produce biased estimates of the parameters of the regression line, leading to incorrect predictions. On the other hand, LAD regression minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line.

In conclusion, the LAD regression is an alternative to OLS that reduces the sensitivity to outliers. The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.

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The amount of money that the items will cost you to send through United States Postal Service would be = $13.3

The dimensions of the first envelope = 20 L, 10°H and 4"W

The weight of the first envelope = 10 ounce.

The first envelope is a parcel because the dimensions are larger than 11.5 L, 6.125" H, 0.25"W.

The price per ounce = $1.22

10 ounce = 1.22×10 = $12.2

The dimensions of the second envelope = 8 L, 5" H and 0.20 W.

The weight of the second envelope = 2.5 ounce.

The second letter is of normal letter size because of the dimensions (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W, max. weight 3.5 oz)

The price per ounce = $0.44

2.5 ounce = 2.5× 0.44 = $1.1

The total price = 12.2+1.1 = $13.3

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Answer:

the answer is x=23.84 which is A

Step-by-step explanation:

using SOH CAH TOA

tan0 =opp/adj

where 0=40,opposite =20,adjacent =x

tan 40=20/x

0.8391=20/x

0.8391x=2

divide both sides by 0.8391

x=23.84

The smallest sample size that will result in a margin of error of no more than 5% for a 95% confidence interval is given as follows:

385.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error is modeled as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

We have no estimate, hence we consider that:

[tex]\pi = 0.5[/tex]

The minimum sample size is obtained as n when M = 0.05, hence:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96 \times 0.5[/tex]

[tex]\sqrt{n} = 1.96 \times 10[/tex] (0.5/0.05 = 10).

[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]

n = 384.16

Hence rounded to 385, as a sample size of 384 would have a margin of error slightly above 0.05.

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The equation of the graph is y = (5x + 10)/(x²-1).

The correct option is c.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

The graph of the equation is given in the image.

From the graph:

When x = 0, then y = -10.

And when y = 0, then x = -2.

y = (5x + 10)/(x²-1)

Substituting the values,

we get,

when x = 0, then y = -10.

And when y = 0, then x = -2.

From the given choices:

The equation,

y = (5x + 10)/(x²-1) satisfies the points.

Hence, the equation is y = (5x + 10)/(x²-1).

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The missing number in the sequence is 64

From the question, we have the following parameters that can be used in our computation:

1, 4, 16, ____, 256, 1024, ...​

Using the above as a guide, we have the following:

To obtain the next term, we can multiply the previous term by 4:

So, we have

Next term = 16 * 4

Next term = 64

Therefore, the next term in the sequence is 64.

The completed sequence is: 1, 4, 16, 64, 256, 1024, ...

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A reflection over the x-axis.

A vertical stretch by 11 units.

A translation left by 5 units.

A translation up 4 units.

The reflection of a function across the x- or y-axis is another transformation that may be used. In contrast to a horizontal reflection, which reflects a graph horizontally across the y-axis, a vertical reflection reflects a graph vertically across the x-axis.

An illustration of a transformation is a reflection, which flips a shape (referred to as the pre image) over a line (referred to as the line of reflection) to produce a new shape (called the image). Imagine what would happen if you flipped the form over the line in order to graph a reflection.

Here, f(x) = 1/x²

Now, reflect the graph over the x-axis to obtain the graph of:

f(x) = -1/x²

Now, stretch the graph vertically by 11 units to get the graph of:

f(x) = -11/x²

Again, translate the graph left by 5 units to obtain the graph of:

f(x) = - 11 / (x + 5)²

Now, translate the graph up by 4 units to obtain the graph of:

f(x) = 4 - {11 / (x + 5)²}

Hence,

A reflection over the x-axis. A vertical stretch by 11 units. A translation left by 5 units. A translation up 4 units.

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The expression when completed is 0.9 [<] 0.95

From the question, we have the following parameters that can be used in our computation:

9 10 19 20​

Rewrite the expression properly

So, we have the following representation

9/10 [ ] 19/20​

Next, we evaluate the expressions

This gives

0.9 [ ] 0.95

0.9 is less than 0.95

So, we have

0.9 [<] 0.95

The above represents the complete statement

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The length of points IJ given the total length of HJ and length HI is 8

The line HJ is measured as 20

If HI = 12

Then, subtract to find IJ

IJ = HJ - HI

= 20 - 12

IJ = 8

Therefore, length of points IJ is 8

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Answer:

Step-by-step explanation:

The binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

Given that binomial  (x+5) is a factor of x² + 8x + 15.

We need to find the other factor.

Let us solve x² + 8x + 15=0

x² + 5x +3x+ 15=0

x(x+5)+3(x+5)=0

(x+3)(x+5)

So the other binomial factor is x+3.

Hence, the binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.

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Answer:

1. $1900

2. $9

Step-by-step explanation:

Part a:

‘If she doesn’t sell any copies of History is Fun’ means x = 0:

[tex]y = 1900 + 9(0)[/tex]

∴ y = Melissa’s total pay = $1900

Part b:
Rearranging the equation:

[tex]y = 9x + 1900[/tex]

∴m = slope of equation = positive 9

  c = y-intercept = 1900

The shape of the graph would be increasing or ascending. And since the Number of copies (x) can never be negative, this means that the amount of pay CANNOT be less than $1900. The amount of $1900 is her minimum pay

The value of m for this equation indicates the change in Melissa’s total pay for every copy she sells.

∴Change in Melissa’s total pay = 9 dollars

After adding and subtracting the rational expressions , the simplified rational expression is 4x - 4/x² - 5/x³ + 9  .

We first simplify each expression inside the parentheses :

that means :

⇒ (2x + 5/x² -3x) = (2x - 3x + 5/x²) = (-x + 5/x²) ;

⇒ (3x + 5/x³ - 9x) = (-6x + 5/x³)  ;

⇒ (x + 1/x² - 9) = (-9 + x + 1/x²)  ;

Now we substitute these expressions into original equation/expression :

we get ; (-x + 5/x²) - (-6x + 5/x³) - (-9 + x + 1/x²)

Simplifying further ,

we get ;

⇒ -x + 5/x² + 6x - 5/x³ + 9 - x - 1/x²  ;

On Combining the like terms, we get ;

⇒ 4x - 4/x² - 5/x³ + 9

Therefore, the simplified rational expression is 4x - 4/x² - 5/x³ + 9.

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The given question is incomplete , the complete question is

Adding and subtracting rational expressions, Simplify the rational expression  (2x + 5/x² -3x) - (3x + 5/x³ - 9x) - (x + 1/x² - 9)  .

Answer:

s^2 + n^2 = 116

Step-by-step explanation:

s^2 + n^2 = ?

s^2 = 80

n = 6

n^2 = 36

s^2 +n^2 = 80 + 36

s^2 +n^2 = 116

The expression is a summation formula, representing the sum of a series of values. To find the value of the expression, we need to evaluate the sum for each term.

The general formula for each term is:

900(1.04)^n

where n is the term number and 1.04 is the common ratio.

For the first term (n = 1), the formula is:

900(1.04)^1 = 900 * 1.04 = 937.6

For the second term (n = 2), the formula is:

900(1.04)^2 = 900 * 1.04^2 = 976.9792

And so on, for each term. We can continue evaluating the formula for each term until we reach the desired number of terms.

Let's evaluate the expression for n = 10 terms.

The sum of the first 10 terms is:

937.6 + 976.9792 + 1018.057312 + ... + 1412.14803883

The value of the expression is approximately 1412.15.

Rounding to the nearest integer, the answer is 1412.

Answer:

12 ways

Step-by-step explanation:

the mother and father can either stand at the front/back or back/front respectively (2 ways)

that leaves 3 children in the middle -- there are 3 choices for the first child to go, 2 for the second, and 1 for the third = 3! = 6

6 ways for the children * 2 ways for the parents = 12 ways

Answer:

9°

Step-by-step explanation:

x + 4x + 5x + 6x + 7x + 8x + 9x = 360

40x = 360

x = 9

The smallest angle measures x, and x = 9, so its measure is 9°.

Answer: 9°

Based on the information, Wendy will need to purchase 48 quarts of paint

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house.

The amount of paint needed will be:

= 4/1 × 12

= 48 quarts

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Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house. a. Write equivalent ratios to determine the amount of green and white paint she will need to purchase. b. If there are 4 quarts in 1 gallon, how many quarts of paint does she need to purchase

Answer:

x + y = -9

Step-by-step explanation:

let x = -8, y = -1

the equation that passes through the point (-8,-1) is x + y = -9

Answer:

24.67

Step-by-step explanation:

6 x 3 = 18

18 plus 6 = 24

X-M=0.60

P-3=7

24.67

Step-by-step explanation:

173 bagels left after the first hour.

Answer:  TRUE  Flóki reportedly released three ravens, and then sailed in the general direction that they flew, eventually discovering Iceland.

Step-by-step explanation:

A histogram would be the most appropriate graphical display to present data by grouping the results into groups of 25 cm.

A histogram is a graphical representation of data that shows the distribution of a set of continuous data by dividing the data into bins (or intervals) and showing the frequency of observations within each bin. The histogram provides a visual representation of the distribution of data, showing the shape, central tendency, and spread of the data.

In this case, the farmer has measured the height of every tree in a large orchard in centimeters and wants to present the data in groups of 25 cm. To create a histogram for this data, the first step would be to divide the data into bins, or intervals, of 25 cm.

Once the bins are created, the next step is to count the number of observations (tree heights) that fall within each bin. This information can be represented as a bar graph, where the height of each bar represents the frequency of observations within the corresponding bin.

By presenting the data in this way, the farmer can easily see the distribution of tree heights in the orchard. The shape of the histogram can indicate whether the data is symmetrical, skewed, multimodal, or uniform.

The central tendency of the data can be determined by looking at the peak of the histogram, which represents the most frequent range of tree heights. The spread of the data can be determined by looking at the width of the histogram and the range of tree heights represented.

In conclusion, a histogram is the most appropriate graphical display to present the results of the tree heights in groups of 25 cm because it provides a visual representation of the distribution of the data and allows the farmer to see the shape, central tendency, and spread of the tree heights in the orchard.

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The correct statement regarding the probabilities is given as follows:

c. The experimental probability is 4% higher than the theoretical probability.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For the theoretical probability, we have that the coin is equally as likely to fall heads or tails, hence:

p = 1/2

p = 0.5 = 50%.

For the experimental probability, we have that on 100 trials, 54 resulted in heads, hence:

p = 54/100

p = 0.54 = 54%.

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Answer:

85.71% chance of randomly selecting a student who owns at least one laptop or one desktop

Step-by-step explanation:

Out of a total of 70 students, only 10 own neither a laptop nor a desktop. This means that the probability of selecting a student with at least one of the two is [tex]\frac{60}{70}[/tex] or [tex]\frac{6}{7}[/tex].

If we convert this fraction into a percentage and round to the nearest hundredth, it equals:

85.71%

The cost of spending the fencing around will be $1312.5.

The perimeter of any two-dimensional figure is defined as the sum of all the sides of the figure. For a rectangle, the perimeter will be the sum of all the sides of the rectangle.

Given that the graph of rectangle ABCD depicts Kenny's intentions for erecting a safety fence to surround a construction site. The units on the graph each correspond to 25 ft.

Kenny decides to construct a fence that encloses a wider region after carefully reviewing the drawings. Given that fencing costs $5.25 per foot and Kenny enlarges rectangle ABCD by a scale factor of 2.5

Perimeter = 4 x side x scale factor

Perimeter = 4 x 25 x 2.5

Perimeter = 250 feet.

The cost of fencing will be,

Cost = 250 x $5.25

Cost = $1312.5

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Answer:

1.  2^n + 1.

2. (n +1)/(n + 4)

Step-by-step explanation:

1. 3 5 9 17....

3 = 2^1 + 1

5 = 2^2 + 1

9 = 2^3 + 1

17 = 2^4 + 1

Therefore the nth term is

2^n+ 1 .

2. Looking at the fractions we see that:

Numerators are 2, 3, 4 ,5..

and denominators are  5, 6, 7, 8

So the nth term is

(n + 1) / (n + 4)

The non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.

The simplified expression that represents the total number of members after the third year is 4.5(53 + x).

Let's call the number of members from the other club "x".

After the first year, the total number of members is 20 + x, and it doubles to 2(20 + x) = 40 + 2x.

After the second year, half of the members from the other club leave, so there are 0.5x members left from the other club. And another 40 members join, so the total number of members is (40 + 2x - 0.5x) + 40 = 80 + 1.5x.

After the third year, the total number of members triples, so we have 3(80 + 1.5x) = 240 + 4.5x.

Therefore, the non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.

To simplify, we can factor out 4.5 from the expression to get 4.5(53 + x). So the simplified expression that represents the total number of members after the third year is 4.5(53 + x).

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