(02.07)Two similar triangles are shown below:

Two triangles are shown. The sides of the triangle on the left are marked 4, 5, 6. The sides of the triangle on the right are marked as 3, 2, and 2.5. For the triangle on the left, the angle between sides marked 6 and 5 is labeled as p, marked by a double arc, and the angle between the sides marked 6 and 4 is labeled as q, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 2 and 3 is labeled as r and the angle between the sides marked 2.5 and 3 is labeled as s, marked by a double arc. The angle between the sides 2 and 2.5 is labeled as t, marked by a triple arc and it is also the angle on the top vertex of this triangle.

Which two sets of angles are corresponding angles?

∠p and ∠r; ∠q and ∠s
∠p and ∠s; ∠q and ∠r
∠p and ∠t; ∠q and ∠s
∠p and ∠t; ∠q and ∠r
Question 4(Multiple Choice Worth 4 points)
plsssssssss help

It has been proved that the number e is irrational.

(a) To show that eˣ is strictly increasing on R, we can find its derivative with respect to x.

The derivative of eˣ is also eˣ, which is always positive for all x in R.

Since the derivative is positive, eˣ is strictly increasing on R.

(b) We will use Lagrange's Remainder Theorem to show that for all n ∈ N, the error term satisfies the inequality:

\(R_n(x) = |\frac{(e^x - P_n(x))}{n!}| < \frac{1}{n!}\)

Here, Pₙ(x) is the nth-degree Taylor polynomial of eˣ at a = 0.

Given the estimate e < 3, we can deduce that the maximum of the error term is max{1, 3}.

Therefore, for all n ∈ N:
\(|\frac{(e^x - P_n(x))}{n!}| < \frac{1}{n!} < max\{1, 3\}\)

Now, we will multiply the inequality by n!:
\(|\frac{(e^x - P_n(x))}{n! }\times n!| < \frac{1}{n!} \times n!\)

We get:
|(eˣ - Pₙ(x))| < 1

This inequality suggests the existence of an integer between 0 and 1, which is a contradiction because there is no integer between 0 and 1. Therefore, e must be irrational.

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The given rule of the translation is

(x,y) → ( x - 7 , y + 3)

so, the point A (1 , 1) after translation, it will be ( 1 - 7 , 1 + 3 ) = (-6 , 4)

Point B (8 , 3) after translation, it will be ( 8 - 7 , 3 + 3 ) = ( 1 , 6 )

Point C ( 6 , 5) after translation, it will be ( 6 -7 , 5 + 3) = ( -1 , 8)

The value of the unknown should be set at 5 so that 98 of 6- oz. mugs won't overflow is A)5.18.

Given data

A soft- drink machine can be regulated so that it discharges an normal of? oz. per mug. The ounces of filler are typically distributed with a standard divagation of0.4 oz.

What value should be set at so that 98 of 6- oz. mugs won't overflow?

Let μ be the mean ounces of filler per mug.

μ can be attained by using the formula

μ = 6 oz. = 6/8 = 0.75 mugs.

Now, given σ = 0.4 oz.

The Z- score for a 6- oz mug can be calculated as follows

z = ( x- μ)/ σ

Then, x = 6 oz = 6/8 = 0.75 mugs.

μ = 0.75 mugs

σ = 0.4 oz.

z = (0.75-0.75)/0.4 = 0

For 98 of 6- oz mugs to not overflow, we need to find the value of μ similar that P( z Since the Normal distribution is symmetric about the mean, we have

P( 0< z We can look up the value of

z_score for P( 0< z

standard normal distribution table or use the inverse function on a calculator similar as Excel.

Using a table, we get the value ofz_score = 2.33.

Now, z = ( x- μ)/ σ2.33 = (0.75- μ)/0.4

μ = 0.75-0.4 ×2.33

μ = 0.75-0.932

μ = -0.182 oz.6 oz in terms of ounces = 6 *0.125 = 0.75 oz.

oz per mug in terms of ounces = ? *0.125 oz.

Using the values from above

μ = -0.1820.75 = 0.568 oz. ≈0.57 oz.

= 0.57/0.125 = 4.56 or 5

So, the value of the unknown should be set at 5 so that 98 of 6- oz. mugs won't overflow is A)5.18.

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Answer:

1. 150mi

2. 2&1/2

3. He needs to know how many miles is each city.

Step-by-step explanation:

Answer:

3.14 would be answer !

Step-by-step explanation:

Answer:

option D

\( {10x}^{2} + 3x - 8\)

Answer:I would say A I found out 2X^2+-1 first

Step-by-step explanation:2x

2

+−1

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax

n

is nax

n−1

.

2×2x

2−1

Multiply 2 times 2.

4x

2−1

Subtract 1 from 2.

4x

1

For any term t, t

1

=t.

4x

Then I saw that 6-2 making 4 so I chose the first one

The difference between groups and the sample size makes the results of a study statistically significant.

Statistical significance is a measure of the likelihood that the results of a study are not due to chance. In order for a result to be statistically significant, it must meet two criteria:

The difference between groups must be large enough to be unlikely to occur by chance. This is typically assessed using a statistical test such as a t-test or an ANOVA.

The result of the test is expressed as a p-value, which represents the probability of obtaining the observed results if there were no true difference between groups. A p-value of less than 0.05 (or 5%) is generally considered to be statistically significant.

The sample size must be large enough to reduce the possibility of sampling error. A larger sample size generally increases the power of a study, making it more likely to detect a true effect.

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Answer:

A and D

Step-by-step explanation:

-Reflection only

-rotation, then translation

Reflection  and rotation, then translation is the transformation(s) can be used to map one triangle onto the other.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The triangles are congruent by SSS

JKL and MKL are the two triangles which sharing same segment KL.

A reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points this set is called the axis or plane of reflection.

Rotation, then translation is also used in the given triangle.

Hence, reflection  and rotation, then translation is the transformation(s) can be used to map one triangle onto the other.

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Answer:

C.

Step-by-step explanation:

The two solution are y = 0 and y = \(x^{4}\)

y' = 4y3/4, y(0) = 0

The initial condition y(0) =0 implies that the graph of the solution curves will pass through the origin.

Consider the curve y = 0, passing through the origin.

Substitute y =0 in y' = 4y3/4

y' =0

Therefore, y=0 is a solution curve of the given differential equation.

Consider the curve y = x, passing through the origin.

Substitute y =x  in y' = 4y3/4

x' = 4x3/4

1 = 4x3/4 not balanced equation.

Therefore, y =x is not a solution curve of the differential equation.

Now, consider y = \(x^{3}\) passing through the origin.

Substitute y = \(x^{3}\) in y' = 4y3/4

\(x^{3}=4(x^{3} )^3/4\)

3\(x^{2} =4x^9/^{4}\) not balanced equation.

Therefore, y = x^3 is not a solution curve of the given differential equation.

Now, consider y = x\(x^{4}\) passing through the origin

Substitute y = \(x^{4}\) in y' = 4y3/4

\(x^{4}=4(x^4)^{3/4}\)

\(4x^3=4(x^4)^{12/4}\\ 4x^3=4x^3\)

Therefore, y = \(x^{3}\) is a solution curve of the given differential equation.

So, the two solution are y = 0 and y = \(x^{4}\)

Therefore, the two solutions are y = 0 and y =\(x^{4}\)

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Answer:

The perimeter is 24 feet :]

hope this helps! <33

Answer:

12 feet

Step-by-step explanation:

The perimeter of a rectangle is just the sum of all the sides. There are four sides, two that represent the width, and two that are the length. Basically, the easiest way for us to find the perimeter of this shape is to add together the length and the width 2 times.

4 + 2 + 4 + 2 = 12

So, the perimeter of the mirror is 12 feet! I hope this helps! Have a lovely day!! :)

Answer:

largest is F smallest is L

Step-by-step explanation:

F= 84 which is a higher number that L=44 or X=52 and X=52 is bigger that L=44 and Smaller that F=84

(a) There is no extreme value of A subject to the given constraint,

(b) For x = 0, y + z² ≤ 16.

y is between -4 and 4. In this case, f(y,z) = y² and the maximum value is 16.

For x = ±y, z = 4 - y².

y is between -2 and 2. In this case, f(y,z) = 2y² - y⁴ and the maximum value is 2.

When dividing by a variable, one should always keep in mind that the variable cannot be equal to zero. In other words, if the value of the variable is zero, the function or expression will not be defined or will give an undefined result. The reason is that division by zero is not defined in the set of real numbers.

Therefore, one should exclude the value of zero from the domain of the function or expression.

In part (a) of the given question, we are asked to find the global maximum and minimum of A(x,y,z) = 12 + 3x + y² - 2y subject to the constraint x + y + z = 2.

Let's find the partial derivatives of A with respect to x, y, and z.

∂A/∂x = 3

∂A/∂y = 2y - 2 = 2(y - 1)

∂A/∂z = 0

Now, we have to solve the system of equations consisting of the partial derivatives and the constraint equation.

\(3 = \lambda_1 + \lambda_2,\\2y - 2 = \lambda_1 + \lambda_2,\\\lambda_1x + \lambda_2x = 0,\\\lambda_1y + \lambda_2y - 1 = 0,\\\lambda_1z + \lambda_2z = 1.\)

Substituting the values of the partial derivatives, we get:

\(\lambda_1 + \lambda_2 = 3,\\\lambda_1 + \lambda_2 = -2,\\\lambda_1(3) + \lambda_2(0) = 0,\\\lambda_1(y - 1) + \lambda_2(y - 1) = 0,\\\lambda_1(0) + \lambda_2(1) = 1.\)

The second and third equations are contradictory. So, under the given constraint, A has no extreme value.

In part (b), we are asked to find the global maximum and minimum of A(x,y,z) = x² + y² on the closed bounded domain x² + y + z² ≤ 16.

Let's use the method of Lagrange multipliers to solve the problem. We have to find the critical points of the function f(x,y,z) = x² + y² subject to the constraint x² + y + z² = 16.

We have to solve the system of equations consisting of the partial derivatives of f, the partial derivatives of the constraint function, and the equation of the constraint function.

2x = λ(2x),

2y = λ(1),

2z = λ(2z).

Substituting the value of λ from the second equation into the first equation, we get: x = 0 or x = ±y.

Substituting the values of x and λ from the first and second equations into the third equation, we get:

z = 4 - y² or z = 0.

Since the constraint is x² + y + z² ≤ 16, we have to consider the following cases:

Case 1: x = 0, y + z² ≤ 16.

So, y is between -4 and 4. The maximum value of f(y,z)=y² is 16 in this case.

Case 2: x = ±y, z = 4 - y².

So, y is between -2 and 2. The maximum value of f(y,z) = 2y² - y⁴ is 2 in this case.

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Answer:

answer below

Step-by-step explanation:

x=4

y=8

AE line equals 16

sf line equals 20

st line equals 10

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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There are 9438 different committees possible without Tarzan and Jane together.

a) To find the total number of possible committees, we need to choose 7 people out of 16 people, regardless of their gender. We can do this using the combination formula:

\(${{16}\choose{7}} = \frac{16!}{7!(16-7)!} = 11440$\)

Therefore, there are 11440 different 7-person committees possible.

b) If the committee must be made up of women only, we need to choose 7 women out of the 10 women available. We can do this using the combination formula again:

\(${{10}\choose{7}} = \frac{10!}{7!(10-7)!} = 120$\)

Therefore, there are 120 different 7-woman committees possible.

c) If the committee must be made up of 5 men and 2 women, we need to choose 5 men out of 6 men available, and 2 women out of 10 women available. We can do this using the combination formula:

\(${{6}\choose{5}} \times {{10}\choose{2}} = \frac{6!}{5!(6-5)!} \times \frac{10!}{2!(10-2)!} = 6 \times 45 \times 9 = 2430$\)

Therefore, there are 2430 different committees possible with 5 men and 2 women.

d)

i) If Tarzan and Jane must be together on the committee, we can treat them as a single entity and then choose 6 more people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{6}} = \frac{14!}{6!(14-6)!} = 3003$\)

Therefore, there are 3003 different committees possible with Tarzan and Jane together.

ii) If Tarzan and Jane refuse to serve on the committee, we need to choose 7 people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{7}} = \frac{14!}{7!(14-7)!} = 3432$\)

Therefore, there are 3432 different committees possible without Tarzan and Jane.

iii) If Tarzan and Jane are not on the committee together, we can count the number of committees that include both of them and subtract it from the total number of committees. The number of committees that include both Tarzan and Jane can be found by treating them as a single entity and choosing 5 more people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{5}} = \frac{14!}{5!(14-5)!} = 2002$\)

Therefore, the number of committees that do not include both Tarzan and Jane is:

\($11440 - 2002 = 9438$\)

Therefore, there are 9438 different committees possible without Tarzan and Jane together.

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To increase usability in a spreadsheet, you can use comments, descriptive labels, and data validation.

To increase usability in a spreadsheet, you can utilize the following techniques:

1. Comments: Comments allow you to add explanatory notes or instructions within cells. They can provide additional context or clarify the purpose of certain data or formulas. Users can view comments by hovering over the respective cell, making it helpful for collaboration and documentation.

2. Descriptive Labels: Instead of relying solely on cell references or generic labels, use descriptive labels that clearly indicate the purpose of each column, row, or range of cells. This approach enhances readability and makes it easier for users to understand the data and navigate through the spreadsheet.

3. Data Validation: Implement data validation rules to ensure the accuracy and integrity of the data entered into the spreadsheet. Data validation allows you to define constraints or conditions for input, such as numeric ranges, predefined lists, or specific text formats. It helps prevent errors and assists users in entering valid data.

4. Formatting: Properly formatting the cells, columns, and rows can greatly enhance usability. Use consistent formatting for similar types of data, apply color schemes or conditional formatting to highlight important information or trends, and adjust the column widths and row heights to optimize readability.

5. Sheet Organization: Organize the spreadsheet by using multiple sheets if needed. Group related information on separate sheets, and provide clear sheet names that reflect the content or purpose of each sheet. This helps users locate and navigate to specific sections or data within the spreadsheet.

6. Clear Instructions or Documentation: Provide clear instructions or documentation either within the spreadsheet or as separate documentation. Explain the purpose of the spreadsheet, any specific procedures or workflows, and how to interpret the data or use any embedded formulas or macros. This helps users understand the spreadsheet's functionality and ensures consistent usage.

7. Error Handling: Implement error handling mechanisms to provide informative error messages or alerts when users input incorrect or incompatible data. Clear error messages guide users in correcting their input and reduce frustration when dealing with potential errors.

By incorporating comments, descriptive labels, data validation, formatting, sheet organization, clear instructions/documentation, and error handling, you can significantly enhance the usability of your spreadsheet and make it more user-friendly for both yourself and others who interact with it.

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Answer:

The width of a rectangle is 6x + 8, and the length of the rectangle is 12x + 16. Determine the ratio of the width to the perimeter. Supply the following: a. Perimeter = 2l + 2w = _______________ b. Ratio = wP _______________________ c. Final answer in simplest form:

Answer:

Hermana

Step-by-step explanation:

Answer:

3:30

Step-by-step explanation:

Answer: we cant answer it here we need an app that we can draw on

Step-by-step explanation:

(a) Yes, the air in the house would exceed the long-term health standard if the groundwater is in equilibrium with the air in the house.

(b) The budget equation for TCE is dct/dt = k(c+ - CT) - Q(ca - CT).

(c) The characteristic time t for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation is given by t = Ahk/Q. For the given values, t = 1.4 years. A large value of t indicates a significant TCE problem.

(d) The minimum value of Q to keep CT below 20 ppm is 160 cfm. This is more than the residential requirement of 40 cfm.

(a) The Henry's Law constant for TCE is 0.4, which means that the concentration of TCE in air at equilibrium with water is 40% of the concentration in water. The groundwater concentration is 110 ppm, so the equilibrium air concentration would be 44 ppm. This exceeds the long-term health standard of 25 ppm.

(b) The flux of TCE through the floor is given by FT = k(c+ - CT), where k is a measured constant, c+ is the concentration of TCE in the groundwater, and CT is the concentration of TCE in the air in the house. The normal strategy for remediating vapor intrusion is to install fans in the house that ventilate the house with outside air. The outside ambient air has a concentration of ca. The budget equation for TCE is dct/dt = k(c+ - CT) - Q(ca - CT), where dct/dt is the rate of change of the concentration of TCE in the house, k is the flux constant, c+ is the concentration of TCE in the groundwater, CT is the concentration of TCE in the air in the house, Q is the ventilation rate, and ca is the concentration of TCE in the outside air.

(c) The characteristic time t for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation is given by t = Ahk/Q, where Ah is the area of the house, k is the flux constant, and Q is the ventilation rate. For the given values, t = 1.4 years. A large value of t indicates a significant TCE problem.

(d) The minimum value of Q to keep CT below 20 ppm is 160 cfm. This is more than the residential requirement of 40 cfm. The difference is due to the fact that the groundwater concentration is much higher than the ambient air concentration.

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The area to the right of 0.75 (i.e., the probability that z is greater than 0.75) is: 1 - 0.7734 = 0.2266 This means that the probability of getting a value greater than 4.5 in this non-standard normal distribution is approximately 0.2266.

To answer this question, we need to use the normal distribution table. However, since the distribution is non-standard, we need to standardize the value of 4.5 using the formula: z = (x - μ) / σ where μ is the mean and σ is the standard deviation.

Substituting the given values, we get: z = (4.5 - 3) / 2 z = 0.75 Now, we need to find the probability that z is greater than 0.75. Looking at the normal distribution table, we find that the area to the left of 0.75 is 0.7734.

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Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

Answer:

B)6^-2

Because

6^-2

1/6²

1/36

Step-by-step explanation:

Answer:

b , c , f

Step-by-step explanation:

1/36 = 0.028

a) 3^-6 = 0.0014

b)6^-2 = 0.028

c) 6^3/6^5 = 0.028

d)6^2/ 6^-1 = 216

e) 6×6^-2 = 0.1667

f) 6^-9×6^7​ = 0.028

Answer:

acute

hope this helps

have a good day :)

Step-by-step explanation:

Answer: 90°

Step-by-step explanation:

Angle b is vertical to the angle that has a measure of 90°

Answer:

m=1= slope

Step-by-step explanation:

here u do rise/ run

and the dots there are helping you to make it

you need to join them by doing rise over run

you go 3 to the right from the dot at the bottom and 3 up

which is 3/3 that equals to 1

if this is not right, please tell me

if it right then your welcome