Geometry: write formal proofs, ASAP!!!!!

Answer:

$490

Step-by-step explanation:

Answer:

Dimensions: 11 meters by 27 meters

2. \(76=2w+2(2w+5)\)

Step-by-step explanation:

Finding Dimensions:

The perimeter of a rectangle can be written as \(2l+2w\) where \(l\) is the length and \(w\) is the width. It is given that the length is 5 more than twice the length of width and the perimeter of the rectangle is 76 meters.

With this information we can write:

Length = \(2w+5\)

\(2(2w+5)+2w = 76\) (perimeter of the rectangle)

\(4w+10+2w=76\)

\(6w=66\)

\(w=11\)

Length = \(2(11)+5\)

Length = \(27\)

∴ The dimensions of the rectangle is 11 meters by 27 meters.

Perimeter

Since the length can be written as \(2w+5\), the equation that represents the perimeter of the rectangle is \(76=2w+2(2w+5)\)

Answer:

C. 1/2(18 x 6)

Step-by-step explanation:

1/2 base x height is the equation used, so plug in the numbers and you get 1/2(18 x 6)

Answer:

C

Step-by-step explanation:

We see that the shaded area of the rectangle is a right triangle. This is great for us.

The formula for finding the area of a triangle is (base*height)/2=area. Over here, the base is 18 and the height is 6, so we plug in those numbers and get (18*6)/2=108/2=54. I just went ahead and looked at all the answers knowing the answer but you can tell it isn't A or B because there is addition and you can tell it isn't A or C because it doesn't half it.

Please tell me if you have any questions.

In all cases, we use hypothesis testing to determine if the sample mean is significantly different from the hypothesized population mean of 40. The results of the test will help us make conclusions about the population mean based on the information gathered from the sample.

(a) State the null hypothesis:
The null hypothesis (H0) is the claim that there is no significant difference between the population mean and the value specified. In this case:
H0: µ = 40

(b) State the alternate hypothesis if you have no information regarding how the population means might differ from 40:
The alternate hypothesis (H1) is the claim that the population mean is different from the value specified. In this case:
H1: µ ≠ 40

(c) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may exceed 40:
If you believe that the population mean may be greater than 40, the alternate hypothesis would be:
H1: µ > 40

(d) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may be less than 40:
If you believe that the population mean may be less than 40, the alternate hypothesis would be:
H1: µ < 40

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Answer:

3. x=8, y=4, (8,4)

x=12,y=6, (12,6)

Step-by-step explanation:

Ratio is 2:1

3. x=8, y= 4 (8,4)

x=12, y=8 (12,8)

4.

Step-by-step explanation:

4.Rule for cookies?

It goes up by 4's.

5.Rule for fruit bars?

It goes up by 2's.

Answer:

Sarah and Lisa would spend an equal amount $15 per month and download 5 movies

If the expected frequencies are not all equal, we can determine them by using the equation enp for each individual category, where n is the total number of observations and p is the probability for the category. This equation helps us calculate the expected frequency for each category based on their probabilities and the total number of observations.

On the other hand, if the expected frequencies are equal, we can determine them by using the equation n/k, where n is the total number of observations and k is the number of categories. This equation helps us distribute the total number of observations equally among the categories when the expected frequencies are equal.

Expected frequencies do not necessarily have to be whole numbers. They can be decimals or fractions depending on the context and calculations involved.

Goodness-of-fit hypothesis tests can be left-tailed, right-tailed, or two-tailed. These different types of tests allow us to assess whether the observed data significantly deviates from the expected frequencies. The choice of the tail depends on the specific research question and the alternative hypothesis being tested.

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Answer:

n=5

Step-by-step explanation:

All of the bases are 9 so you can set the exponents equal to each other.

Exponents in a fraction mean subtraction so 7-n = 2

-n=-5

n=5

Answer:

He is about 6 years old (5 years 11 months)

Step-by-step explanation:

13 - 7 and 3 - 2

The extra amount that Adam will have to pay in comparison to Melissa is $300.

Adams and Melissa have taken out a $15,000 loan for a new car. They have to repay the loan in four years.

Melissa has to pay an interest rate of 3% per year while Adam has to pay an interest rate of 3.5% per year.

Melissa's monthly payments are $321 while Adam's monthly payments are $325.

We have to find the extra amount that Adam will have to pay in comparison to Melissa.

Let's calculate the amount Melissa will pay in 4 years

Interest = P × R × T

Interest = 15000 × 3/100 × 4

Interest = $1800

Total amount Melissa will have to pay in 4 years = Principal + Interest

Total amount Melissa will have to pay = $15,000 + $1,800

                                                                = $16,800

Let's calculate the amount Adam will pay in 4 years

Interest =  P × R × T

Interest = 15000 × 3.5/100 *× 4

Interest = $2100

Total amount Adam will have to pay in 4 years = Principal + Interest

Total amount Adam will have to pay = $15,000 + $2,100

                                                             = $17,100

Difference in the amount that Adam and Melissa will pay = Amount Adam will pay - Amount Melissa will pay

Difference = $17,100 - $16,800

Difference = $300

Therefore, the extra amount that Adam will have to pay in comparison to Melissa is $300.

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Answer:

138

Step-by-step explanation:

Divide the shaded area to a rectangle and a triangle

Shaded rectangle area = 10 * 12 = 120

Shaded triangle area = (6 * 12)/2 = 72/2 = 36

Area of unshaded rectangle

Shaded area= 120 + 36 - 18 = 156 - 18 = 138

Hope this helps :)

Have a great day!

Answer:

the answer is approximately normal

Step-by-step explanation:

Therefore, In the figure, a∥b  angle m∠7 = 34° .

An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. Angles of two rays lie in the plane containing the rays. Angles can also result from the intersection of two planes. Dihedral angles are the name given to them.

Here,

Given that a and b are parallel lines,

∠3 and ∠7  are corresponding angles and congruent

m∠3 = 34°

thus ,m∠7 =m∠3 = 34°

so, m∠7 = 34°

Therefore, In the figure, a∥b  m∠7 = 34° .

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The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level.

not significantly more than 3 minutes.

The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.

1. The null hypothesis is that the population mean is equal to 3 minutes.

2. A sample of 100 customers was taken, with an average length of calling time of 3.1 minutes and a sample standard deviation of 0.5 minutes.

3. The p-value from the sample data is 0.28, which is higher than the 0.05 significance level.

4. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.

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Maximize Z = -2x1 + x2 - 4x3 + 3x4 subject to the following constraints:

x1 + x2 + x3 + 2x4 + s1 = 4,

-x1 + x3 + x4 - s2 = -1,

2x1 + x2 + s3 = 2,

and x1 + 2x2 + x3 + 2x4 = 2, where x1, x2, x3, x4, s1, s2, s3 ≥ 0.

To reformulate the given problem in the standard form of a linear programming model, we need to convert all the inequalities into equations and express all variables as non-negative.

The standard form of a linear programming problem is as follows:

Maximize (Z) = c1x1 + c2x2 + c3x3 + c4x4

Subject to:

a11x1 + a12x2 + a13x3 + a14x4 = b1

a21x1 + a22x2 + a23x3 + a24x4 = b2

a31x1 + a32x2 + a33x3 + a34x4 = b3

an1x1 + an2x2 + an3x3 + an4x4 = bn

x1, x2, x3, x4 >= 0

Now let's reformulate the given problem:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 <= 4

-x1 + 0x2 + x3 + x4 >= -1

2x1 + x2 + 0x3 + 0x4 <= 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4 >= 0

The reformulated linear programming problem in standard form is as follows:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 + s1 = 4

-x1 + x3 + x4 - s2 = -1

2x1 + x2 + s3 = 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4, s1, s2, s3 >= 0

Note: The reformulated problem includes slack variables s1, s2, and s3 to convert the inequalities into equations, and all variables are non-negative.

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Answer:

24hrs

Step-by-step explanation:

100 devide by 25 x 6

Answer:

(3√5)/2

Step-by-step explanation:

\(Hypotenuse = c =21\\Adjacent=a =6\\\alpha=angle\\Using SOHCAHTOA ,\\Cos \alpha =\frac{adj}{hyp} \\Cos \alpha =\frac{6}{21} \\\alpha = cos^{-1} \frac{6}{21}\\\alpha =73.398\\\\Tan \alpha =\\Tan 73.4\\= 3.354\\=\frac{3\sqrt{5} }{2}\)

The labor cost percentage for next Friday at Fawlty Towers would be approximately 0.63%, which is closest to the option a. 0.05%.

To calculate the labor cost percentage for next Friday at the Fawlty Towers, we need to consider the number of rooms, the time required to clean each room, the number of working hours, the labor rate, and the occupancy rate. Here are the steps to determine the labor cost percentage:

Calculate the number of rooms to be cleaned. If the hotel has 1000 rooms and the occupancy rate for next Friday is 80%, then the number of occupied rooms would be 1000 * 0.8 = 800 rooms.

Calculate the total time required to clean the rooms. Since each room attendant is allocated 30 minutes per room, the total time required would be 800 rooms * 30 minutes = 24,000 minutes.

Convert the total cleaning time to hours. Since there are 60 minutes in an hour, the total cleaning time would be 24,000 minutes / 60 = 400 hours.

Calculate the total labor cost. Each room attendant works 8 hours per day, so for 400 hours, the hotel would require 400 hours / 8 hours = 50 room attendants. Considering their hourly rate of $15, the total labor cost would be 50 room attendants * $15/hour = $750.

Calculate the total revenue. The Average Daily Rate (ADR) is expected to be $150, and with an occupancy rate of 80%, the total revenue would be 800 rooms * $150/room = $120,000.

Calculate the labor cost percentage. Divide the total labor cost ($750) by the total revenue ($120,000) and multiply by 100 to get the percentage: ($750 / $120,000) * 100 = 0.625%.

Therefore, the labor cost percentage for next Friday at Fawlty Towers would be approximately 0.63%, which is closest to the option 0.05%.

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The Fawlty Towers is a Nuxury 1000 room hotel catering to business executives. The occupancy for nad Friday is expected to be 80% Room attendants are allocated 30 minutes to clean each room Room attendants work 8 hours per day at a rate of $15/hour. ADR is expected to be $150 What would the labour cost percentage be for next Friday assuming everything stays the same?

a. 0.05%

b. 5.00%

c. 20.00%

d. 0.20%

The functions y = 2 (1/5)^x - 5 and y = 4^x are compared as follows

                                  y = 2 (1/5)^x - 5             y = 4^x

Initial value:               2                                    1

base function:        1/5 = decay function       4 = growth function

Translation:             5 units down                    no transformation

A decay function is a mathematical function used in various fields such as physics, engineering, economics, and machine learning, to model the reduction or decline of a value over time.

It is a type of function that decreases at a rate proportional to its current value, so that it approaches zero as time progresses.

Decay function are exponential functions with the base function as

This is the opposite of growth function which has values greater than 1

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To determine which payment plan the real estate investor would prefer, we need to compare the present value of each payment option. Assuming a discount rate of 0%, meaning no time value of money is considered, we can directly compare the payment amounts.

1. Payment of $2,000 at the first of each month: This results in a total payment of $24,000 over the 12-month lease.

2. Upfront payment of $24,000: This option requires paying the full amount at the beginning of the lease.

3. Payment of $2,000 at the end of each month: Similar to option 1, this results in a total payment of $24,000 over the 12-month lease.

4. Upfront payment of $12,000 and $12,000 half-way through the lease: This option requires paying $12,000 at the beginning of the lease and another $12,000 halfway through the lease.

Since all the payment options have a total cost of $24,000, the real estate investor would likely prefer the payment plan that offers more flexibility or matches their cash flow preferences. Options 1 and 3 provide the investor with the option to pay monthly, while options 2 and 4 require a larger upfront payment. The choice would depend on the investor's financial situation and preferences.

1/2 an hour =30 minutes

1/6 of an hour=10 minutes

30÷10=3

3×1= 3 miles

If the value of a is negative in the equation ý = ax, the line will go down and to the left.

The correct option is B.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

In general, the sign of "a" in the slope-intercept equation y = ax + b determines the direction of the line.

Where a is the slope of the line and b is the y-intercept.

If "a" is positive, the line goes up and to the right,

and if "a" is negative, the line goes down and to the right.

Therefore, the correct answer is option B: "goes down and to the left."

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Answer:

180g of eggs

Step-by-step explanation:

divide 120 by 2 = 60

then times 60 by 3 = 180g

Answer:

D

Step-by-step explanation:

you would see this as correct because it has a larger numerator than its denominator.

Answer:  The sum of the numbers is 3x + 12

Step-by-step explanation: A brief explanation of an arithmetic progression would be useful for a start.

An arithmetic progression (also known as arithmetic sequence) is series of consecutive numbers in which every term in the entire series is determined by adding a common difference to the previous term. In other words, if x and y are two successive numbers in an arithmetic term, y can be determined by adding the common difference to x. Similarly, the term that comes after y is determined by adding the same common difference to y.

As stated in the question, the numbers x, y and z are successive terms of an arithmetic progression, and the common difference is given as 4. This simply means;

y = x + 4

z = y + 4

z = (x + 4) + 4

z = x + 8

The terms x, y and z can now be re-written as follows,

x, x + 4, and x + 8

The sum of these numbers therefore is derived as,

Sum = x + x + 4 + x + 8

Sum = 3x + 12

The solution of the inequality is:

s ≥ -0.86

And the graph can be seen on the image at the end.

Here we want to find and graph the solution set of the inequality below:

(2/5)*s + 7 ≥ 3 - 4.2*s

To do so, first we need to isolate s in one of the sides, then let's do that:

(2/5)*s + 7 ≥ 3 - 4.2*s

(2/5)*s + 4.2*s ≥ 3 - 7

(2/5 + 4.2)*s  ≥ -4

And we know that 4.2 = 21/5

Then:

(2/5 + 21/5)*s  ≥ -4

(23/5)*s ≥ -4

s ≥ -4*5/23

s ≥ -20/23

s ≥ -0.86

The graph of this will something like the one below:

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Based on the original image, if this figure is reflected across the x-axis the orientation of the new or reflected figure should be the one shown in A or the first image.

In geometry and related fields, a reflection is equivalent to a mirror image. Due to this, the reflection of an image is the same size as the original image, it has the same sides and also the same dimensions. However, the orientation is going to be inverted, this means the right side is going to show on the left side and vice versa.

Based on this, the image that correctly shows the reflection of the figure is the first image or A.

Note: This question is incomplete; below I attach the missing images:

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