A right triangle is shown below.
4√2 m
45°
Find the lengths of the missing sides
vertical leg
m
horizontal leg
45°
m

The mean expenses of the XYZ Corporation is 9,811.22.

To compute for the mean expenses of the XYZ Corporation, we need to add up all the total expenses of each city and divide it by the total number of cities.

Total Expenses = 4,933.50 + 6,035.70 + 12,276.00 + 6,237.00 + 14,850.00 + 7,590.00 + 7,260.00 + 6,930.00 + 21,780.00 + 11,220.00
Total Expenses = 98,112.20

Number of Cities = 10

Mean Expenses = Total Expenses / Number of Cities
Mean Expenses = 98,112.20 / 10
Mean Expenses = 9,811.22

The mean expenses of the XYZ Corporation is 9,811.22. Since the answer does not require decimals, we do not need to express it in two decimal places. However, we need to follow the reminder that if the answer is more than three digits, we should not include the comma.

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Answer:

46°

Step-by-step explanation:

180-136= 44

x = 180 -90-44

x = 46

Calculating this expression, we find that the probability of the service time being one minute or less is approximately 0.6321.

Calculating this expression, we find the probability of the service time being between three and seven minutes is approximately 0.1849.

To answer the questions, we will use the exponential probability distribution formula:

f(x) = λ * e^(-λx)

Where λ is the rate parameter (mean service rate) and x is the service time.

a. To find the probability that the service time is one minute or less, we substitute x = 1 and λ = 100/60 (since there are 60 minutes in an hour and the mean service rate is given per hour):

P(X ≤ 1) = λ * e^(-λx)

P(X ≤ 1) = (100/60) * e^(-(100/60) * 1)

b. To find the probability that the service time is two minutes or less, we substitute x = 2 and λ = 100/60:

P(X ≤ 2) = λ * e^(-λx)

P(X ≤ 2) = (100/60) * e^(-(100/60) * 2)

Calculating this expression, we find that the probability of the service time being two minutes or less is approximately 0.8647.

c. To find the probability that the service time is more than two minutes, we subtract the probability of the service time being two minutes or less from 1:

P(X > 2) = 1 - P(X ≤ 2)

Calculating this expression, we find that the probability of the service time being more than two minutes is approximately 0.1353.

d. To find the probability that the service time is between three and seven minutes, we subtract the probability of the service time being less than three minutes from the probability of the service time being less than seven minutes:

P(3 ≤ X ≤ 7) = P(X ≤ 7) - P(X < 3)

P(3 ≤ X ≤ 7) = (100/60) * e^(-(100/60) * 7) - (100/60) * e^(-(100/60) * 3)

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The values of x, y and z in the parallelogram 1 are x = 80, y = 100 and z = 80

Parallelogram 1

Adjacent angles of a parallelogram add up to 180

So, we have

x = 180 - 100

x = 80

Opposite angles are equal

So, we have

y = 100

z = 80

Using the above theorem, we have the values of x, y and z in the other parallelograms to be

Parallelogram 2

x = 180 - 50

x = 130

y = 130

z = 130 --- by corresponding angle theorem

Parallelogram 3

x = 90 --- by vertical angle theorem

Then, we have

y = 60 --- sum of angles in a triangle

z = 60 --- by corresponding angle theorem

Parallelogram 4

x = 100

y = 80

z = 80 --- by corresponding angle theorem

Parallelogram 5

y = 112

x = 180 - 112 - 40 --- sum of angles in a triangle

x = 28

z = 28  --- by corresponding angle theorem

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The length of AC by the given data is about 11.0 cm.

We are given that;

ABCD is a trapezium AB=16cm, AD=11cm, BC=4cm

Now,

We can use these values to find DC. Since ABCD is a trapezium, we know that AB and DC are parallel. Therefore, the distance between them is constant. We can write:

AB−BC=AD−DC

Plugging in the given values, we get:

16−4=11−DC

Solving for DC, we get:

DC=11−12=−1

We can ignore the negative sign since we are only interested in the length of DC. So, DC = 1 cm.

Now we can plug in AD = 11 cm and DC = 1 cm into the Pythagorean theorem and get:

AC2=112+12

AC2=122

Taking the square root of both sides, we get:

AC=122​≈11.045

Rounding to one decimal place, we get:

AC≈11.0 cm

Therefore, by algebra the answer will be 11.0 cm.

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To find the equation in slope-intercept form, y = mx + b, we need to first find the slope using
    [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

In this case we have the two points (1,2) and (4,4), so our calculation looks like:

    [tex]m=\dfrac{4-2}{4-1} = \dfrac{2}{3}[/tex]
Notice this is the same "rise over run" that we can count out on the graph.  If we start at (1,2) and go "up 2 units, right 3 units", then we end up at the point (4,4).

Now we need to find b.  We have [tex]y = \frac{2}{3}x+b[/tex], so we need to substitute in one of the points to find b.  Let's use (1,2):

           [tex]2 = \frac{2}{3}\cdot 1+b[/tex]

           [tex]2 = \frac{2}{3}+b[/tex]

    [tex]2 - \frac{2}{3} =b[/tex]

           [tex]\frac{4}{3} =b[/tex]

This gives us our equation: [tex]y = \frac{2}{3}x+\frac{4}{3}[/tex]

By definition of volume of sphere, The volume of the basketball is,

V = 3052.08 inches³

We have to given that;

The radius of a basketball is 9 inches.

Since, We know that;

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

And,  We know that;

Volume of sphere = 4/3πr³

Where, r is radius of sphere.

And, pi is stand for 3.14.

Hence, We get;

The volume of the basketball is,

⇒ V = = 4/3πr³

Substitute radius (r) = 9 inches, pi = 3.14 in above equation, we get;

⇒ V = 4/3 × 3.14 × 9³ inches³

⇒ V = 4/3 × 3.14 × 243 inches³

⇒ V = 3052.08 inches³

Therefore, The volume of the basketball is,

⇒ V = 3052.08 inches³

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If a person owns 2/3 of a land and sells 1/4 of it, the fraction of the whole land sold can be expressed as 1/4 divided by 2/3.

To divide fractions, we invert the second fraction and multiply. Therefore, we have:

1/4 ÷ 2/3 = 1/4 × 3/2 = 3/8

So, the fraction of the whole land sold is 3/8. This means that the person has 2/3 - 3/8 = 5/24 of the original land remaining after selling 1/4 of it.

To see why this is the case, we can visualize the original land as a pie chart. If the person owns 2/3 of the land, then 1/3 of the land belongs to someone else. If the person sells 1/4 of their share, they are effectively selling 1/4 of 2/3 of the land, or 2/12 of the land. This represents a portion of the pie chart that is 2/12 of the total pie, or 1/6. Therefore, the person now owns 5/6 of the pie chart, or 5/24 of the original land.

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The stopping distance of D40 is 2.56 times the stopping distance of D25.

Given that are two initial velocities: 40 mph and 25 mph, with which the car's stopping distance is D40 and D25.

The final velocity for both is 0 mph (as the car to a stops).

We need to compare the stopping distance D40 to the stopping distance D25.

Use the third equation of motion for both cases to get the comparison.

The equation is given by:

[tex]v^2 - u^2 = 2as.[/tex]

Case 1)

[tex]0 - 40^2 = 2a(D40)[/tex]

Case 2)

[tex]0 - 25^2 = 2a(D25)[/tex]

Comparing the obtained expressions.

[tex]\frac{40^2}{25^2} = \frac{2a(D40)}{2a(D25)}[/tex]

[tex]2.56 = \frac{D40}{D25}[/tex]

[tex]2.565 \times D25 = D40[/tex]

Hence the stopping distance of D40 is 2.56 times the stopping distance of D25.

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The number of servings of the stew the club can make is 24

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

The dot plot

From the dot plot, we have

Total = 4/8 * 2 + 6/8 + 1 * 3 + 1 2/8 * 1

Evaluate

Total = 6

Each serving can take 1/4 pounds

So, we have

Total = 6/(1/4)

Evaluate

Total = 24

Hence, the servings of the stew the club can make is 24

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The required equation is y = 200 - (0.025)t

Hence option C is correct.

According to the given information:

The soil's water content is dropping by 2.5% weekly.

And here, Begin with the 200 gram of water that were initially present in the soil sample on July 1.

Then deduct the weekly water loss,

Which is determined by multiplying the original water amount by 25%  and the number of weeks (t).

Now forming the equation,

⇒ y = 200 - (2.5/100)t

⇒ y = 200 - (0.025)t

Hence, the expression be,

y = 200 - (0.025)t

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Answer:

-6

Step-by-step explanation:

4k-6=2k-16-2

-16-2= -18

4k-6=2k-18

+6= +6 from both sides

4k=2k-12

-2k = -2k from both sides

2k = -12

/2 /2

k= -6

Answer:

buying price = $11764.70

Step-by-step explanation:

selling price = $10000

loss = 15%

85% = 10000

100% = 10000/85 × 100

= $ 11764.70

Answer:

For 1 is it 1 hour and 15 mins?

Step-by-step explanation:

6 by 32 = 30 mins

12 by 32 = 1 hr

13 by 32 = 15

1hr + 15 mins = 1hr 15 mins

Sorry if incorrect

Therefore, the probability that Smith wins 8 dollars before losing all of his money is approximately 0.0479.

To solve this problem, we can use a probability tree diagram to visualize the different possible outcomes.

At each stage, Smith either wins a dollars or loses a dollars, until he either reaches 8 dollars (and wins) or 0 dollars (and loses). We can calculate the probability of each outcome by multiplying the probabilities of the branches leading to that outcome.

Starting with 3 dollars, there are two possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 4 dollars.

Smith loses a dollar with probability 0.6, leaving him with 2 dollars.

From 4 dollars, there are three possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 5 dollars.

Smith loses a dollar with probability 0.6, leaving him with 3 dollars.

Smith wins 4 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 7 dollars.

From 5 dollars, there are two possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 6 dollars.

Smith wins 3 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 8 dollars.

From 6 dollars, there are two possible outcomes:

Smith wins 2 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 8 dollars.

Smith loses a dollar with probability 0.6, leaving him with 5 dollars.

From 7 dollars, there is one possible outcome:

Smith wins 1 dollar with probability 0.4, leaving him with 8 dollars.

Therefore, the probability that Smith wins 8 dollars before losing all of his money is the sum of the probabilities of the outcomes that lead to winning 8 dollars, which is:

0.4 * 0.6 * 0.4 * 0.4 + 0.4 * 0.6 * 0.4 * 0.6 * 0.4 + 0.4 * 0.6 * 0.4 * 0.4 * 0.6 * 0.16 + 0.4 * 0.6 * 0.4 * 0.4 * 0.4 * 0.4 * 0.16 = 0.047872

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The value of $\#(\&4)$ is 81. We first evaluated $\&4$ using the definition given, which gave us the value 9. Then, we substituted this value into the definition of $\#x$ to find the final answer of 81.

To find the value of $\#(\&4)$, we first need to evaluate $\&4$. Using the given definition of $\&x$, we have:

$$\&4 = 4 + 5 = 9$$

Now, we can substitute this value into the definition of $\#x$:

$$\#(\&4) = \#9 = 9^2 = 81$$

Therefore, the value of $\#(\&4)$ is 81. We first evaluated $\&4$ using the definition given, which gave us the value 9. Then, we substituted this value into the definition of $\#x$ to find the final answer of 81.
To find the value of #(&4), let's first compute &4.

According to the definition, &x = x + 5. So, &4 = 4 + 5 = 9.

Now we need to find the value of #9. The definition of #x is x², which means #9 = 9² = 81.

Therefore, the value of #(&4) is 81.

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Answer:

1.1. 3(2a-7)

1.2. 3x(2x+3)

Step-by-step explanation:

Put the common factor on the outside of the parentheses.

1.1. 6a-21

The lowest common factor for 6a and -21 is 3.

     3(2a-7)

1.2. [tex]6x^{2} +9x[/tex]

The lowest common factor for [tex]6x^{2}[/tex] and 9x is 3x.

      3x(2x+3)

The temperature of the water after 4.5 minutes is approximately 153°F.

Using Newton's Law of Cooling to find the value of the decay constant k: T = [tex]Ta + (T0 - Ta) * e^-k*t[/tex]

Substituting the given values, we get:

185 = [tex]69 + (203 - 69) * e^-k*1.5[/tex]

Simplifying, we get:

[tex]116 = 134 * e^ \\^{-1.5k}[/tex]

Dividing both sides by 134, we get:

[tex]0.8657 = e^{-1.5k}[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.8657) = -1.5k

Solving for k, we get:

k ≈ 0.232

Therefore, the value of the decay constant is approximately 0.232.

To find the temperature of the water after 4.5 minutes, we can use Newton's Law of Cooling again, with t = 4.5:

[tex]T = Ta + (T0 - Ta) * e^-k*t[/tex]

[tex]T = 69 + (203 - 69) * e^-0.232*4.5[/tex]

T ≈ 153°F

Therefore, the temperature of the water after 4.5 minutes is approximately 153°F.

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Jan created a pattern using the rule "add 3," and Bill created a pattern using the rule "add 6." In arithmetic sequences, the nth term is given by the formula a + (n-1)d, where a is the first term and d is the common difference between any two consecutive terms.

The common difference is the difference between each pair of consecutive terms in a sequence. Because Jan's pattern has a common difference of 3, the nth term in her sequence is given by a + (n-1)3, and because Bill's pattern has a common difference of 6, the nth term in his sequence is given by a + (n-1)6.The nth term in both Jan and Bill's sequence is a linear function of n. The slope of a line is the common difference between any two consecutive terms in a sequence.

As a result, the slopes of Jan and Bill's patterns are 3 and 6, respectively. In general, two patterns are in a linear relationship if their slopes are constant multiples of one another. In this case, Bill's pattern is the result of multiplying Jan's pattern by a factor of 2. As a result, their patterns have a linear relationship. Answer: The patterns have a linear relationship because Bill's pattern is the result of multiplying Jan's pattern by a factor of 2.

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The value of the excretion is equal to 15 / 16 inches of precipitation per hour.

In this question we find that a precipitation of 5 / 8 inches of rain is registered in a time of 2 / 3 hour and we are asked to find how many precipitation is registered in a time of an hour, that is, the value of the excretion. The excretion can be found by cross multiplication:

r = (5 / 8 in) / (2 / 3 h)

r = 15 / 16 in / h

A precipitation of 15 / 16 inches in a time of an hour is the value of the excretion.

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The construction being demonstrated is constructing a perpendicular bisector.

In this construction, a line is drawn to bisect a given line segment and is perpendicular to that line segment. The perpendicular bisector divides the line segment into two equal parts and creates a right angle at the point of intersection. It is useful in various geometric constructions and applications, such as finding the midpoint of a line segment or constructing equilateral triangles. By constructing a perpendicular bisector, we ensure that the distances from any point on the line to the endpoints of the line segment are equal.

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To find the first term of an arithmetic sequence, use the formula: first term = last term - (number of terms - 1) * common difference.

To find the first term of an arithmetic sequence given the number of terms, the last term, and the common difference, you can use the following formula

First term = Last term - (Number of terms - 1) * Common difference

Here's how to use this formula

Identify the number of terms, the last term, and the common difference of the arithmetic sequence.

Plug these values into the formula.

Simplify the formula using order of operations (PEMDAS) to find the first term.

For example, let's say we have an arithmetic sequence with 10 terms, a last term of 50, and a common difference of 5. Using the formula above, we get

First term = 50 - (10 - 1) * 5

First term = 50 - 9 * 5

First term = 50 - 45

First term = 5

Therefore, the first term of the arithmetic sequence is 5.

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It's important to note that without the actual data, I cannot provide a definitive assessment of the model's appropriateness. I recommend conducting the analysis with the provided dataset to draw accurate conclusions about the suitability of the linear regression model.

To develop an estimated regression equation and assess the appropriateness of a simple linear regression model, we need the specific data from the "productioncost" dataset. Since the data is not provided, I cannot perform the analysis or construct the standardized residual plot.

However, I can provide you with a general approach to determine the appropriateness of a simple linear regression model based on a standardized residual plot. After fitting the regression model, you can calculate the standardized residuals by dividing the residuals by their estimated standard deviation. Plotting these standardized residuals against the predicted values can help assess the model's appropriateness.

In a standardized residual plot, if the residuals exhibit random scatter around the horizontal line at zero, with no discernible patterns or trends, it suggests that the linear regression model is appropriate. On the other hand, if there are systematic patterns or trends in the residuals, such as a curved shape or unequal spread, it indicates that the linear regression model may not adequately capture the relationship between the variables.

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The function operation g(f(8) in the given functions f(x) = 3x+2 and g(x) = √(x-1) is 5.

A function is simply a relationship that maps one input to one output.

Given that:

First, set up the composite result function:

Evaluate g( 3x + 2 ) by substituting in the value of f into g.

g( 3x + 2 ) = √( ( 3x + 2 ) - 1 )

Simplify

g( 3x + 2 ) = √( 3x + 2 - 1 )

g( 3x + 2 ) = √( 3x + 1 )

Evaluate the result function by replacing the x with 8.

g( f(x) ) = √( 3(8) + 1 )

g( f(x) ) = √( 24 + 1 )

g( f(x) ) = √( 25 )

g( f(x) ) = 5

Therefore, the composite result function g( f(x) ) is 5.

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According to the survey, 40% of customers visit late on weekdays and 60% visit late on weekends. Therefore, out of 9,000 customers, we can expect 60% of them to visit late on weekends.

To find out the exact number, we can use the following calculation:

60% of 9,000 = (60/100) x 9,000 = 5,400

Therefore, the manager can expect around 5,400 customers to visit late on weekends out of a total of 9,000 customers.

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To find the volume of the solid with equilateral triangular cross-sections, we need to integrate the area of each equilateral triangle over the interval [0,π]. The area of an equilateral triangle with side length s is given by (s^2√3)/4. Since the triangles have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x. Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2√3/4 dx

Simplifying, we get:

V = √3∫[0,π] sin x dx

Using the substitution u = cos x, we get:

V = √3∫[-1,1] √(1 - u^2) du

Using the formula for the integral of the half-circle, we get:

V = (√3/2)π

Therefore, the volume of the solid is (√3/2)π.

To find the volume of the solid with square cross-sections, we need to integrate the area of each square over the interval [0,π]. Since the squares have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x.

Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2 dx

Simplifying, we get:

V = 4∫[0,π] sin x dx

Using the identity ∫sin x dx = -cos x + C, we get:

V = -4cos x ∣[0,π]

Since cos π = -1 and cos 0 = 1, we get:

V = -4(-1 - 1) = 8

Therefore, the volume of the solid is 8.

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The equation to find the number of minutes m is 12000 - 100m = 4000

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

Initial volume  = 12000 gallons

Rate of draining = 100 gallons per minute

Final volume of water = 4000 gallons

The equation to find the number of minutes m is represented as

f(m) = Initial volume - Rate of draining * m

So, we have

f(m) = 12000 - 100m

When the volume is at 4000 gallons, we have

12000 - 100m = 4000

Hence, the equation to find the number of minutes m is 12000 - 100m = 4000

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The perimeter of the regular nonagon is approximately 29.7 feet.

The apothem of a regular nonagon divides each of its interior angles into two congruent angles.

Therefore, each of the interior angles of the nonagon measures:

(180 - 360/9)/2 = 140 degrees

The sum of the interior angles of a nonagon is (9-2) * 180 = 1260 degrees. Therefore, the measure of each exterior angle of the nonagon is:

360/9 = 40 degrees

In a regular nonagon, all the sides and angles are congruent, so we can divide it into 9 congruent isosceles triangles. Each of these triangles has base s and height a, and its legs are given by:

l =√s² - (a/2)²

The perimeter P of the nonagon is given by:

P = 9s

Substituting the values of s and a, we get:

l = √3.3²- (1.65/2)²

= 3.018 ft (rounded to 3 decimal places)

P = 9(3.3) = 29.7 ft

Therefore, the perimeter of the regular nonagon is approximately 29.7 feet.

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