Which of the following statements about trapezoids must be true?
Question 15 options:

A)

Opposite angles are equal.

B)

Both pairs of opposite sides are parallel.

C)

One pair of opposite sides is parallel.

D)

Opposite sides are equal.

Given that 15 food booths were rented out for ‘d’ days at $100 plus $5 per day. On the food booths only, the company will earn 15($100+$5d) = $1500 + $75d Given that 20 game booths were rented out for ‘d’ days at $50 plus $7 per day. On the game booths only, the company will earn 20($50 + $7d) = $1000 + $140d

The total amount that the company is paid is therefore, $1500 + $75d + $1000 + $140d = $2500 + $215d

Answer:

36.909m

Step-by-step explanation:

6.339+0.170+30.4

=36.909m

Answer:

0

Step-by-step explanation:

Answer:

ask a Tutor its easier when they tell u the answer

Step-by-step explanation:

Area of the triangle with two sides equal 4 cm and 5 cm and the included angle equal to 30° is

\( = \frac{1}{2} \times 4 \times 5 \times sin30 \\ = \frac{1}{2} \times 4 \times 5 \times \frac{1}{2} \\ = 5 \: cm^{2} \)

Hope it will help :)❤

Answer:

A. A'(3,9); ect

Step-by-step explanation:

correct on edg.

To determine the number of different routes from the FedEx warehouse to the five destinations (Kinko's, City Hall, the insurance office, the lawyer's office, and the bank), we can use the concept of permutations.

Since all the destinations need to be visited, we need to find the number of permutations of the five destinations. This can be calculated as 5 factorial (5!) since the order of the destinations matters.

5! = 5 x 4 x 3 x 2 x 1 = 120

Therefore, there are 120 different routes possible.

To determine the best delivery sequence among Exercises 5, 6, and 7, we would need to examine the specific sequences given in those exercises. Without the specific sequences, it is not possible to determine which exercise generates the best delivery sequence.

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The correct statement is: The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.

The rate of change in a linear function represents how the dependent variable (in this case, height) changes with respect to the independent variable (time). To find the rate of change in this scenario, we can calculate the slope of the line that goes through the given points (2, 3) and (4, 6).

The slope of a line is determined by the change in the y-values divided by the change in the x-values. In this case, the change in y is 6 - 3 = 3 inches, and the change in x is 4 - 2 = 2 years.

Therefore, the rate of change is 3 inches / 2 years = 1.5 inches per year. This means that for every additional year of growth, the plant's height increases by an average of 1.5 inches.

Now, let's analyze the given statements:

1. The rate of change of a linear function is always the same.

  This statement is true. In a linear function, the rate of change (slope) remains constant throughout the entire graph.

2. The rate of change of a linear function always increases as the input increases.

  This statement is not necessarily true. The rate of change can be positive or negative, depending on whether the line slopes upward or downward.

3. The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.

  This statement is true. We calculated the rate of change to be 1.5 inches per year.

4. The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.

  This statement is not necessarily true. The rate of change may vary depending on the specific section of the graph being considered. However, we only calculated the rate of change between 2 and 4 years, so we cannot determine the rate of change over a larger time frame based on this information.

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Answer:

9 + 10 = 19

Step-by-step explanation:

im guessing your bored too LOL

Answer:

19 because you add 10 with 9 to get 19

Answer:no

Step-by-step explanation:

That phrase is saying -1000>1/2 which is NOT true because a negative will always be less than a positive number even if it’s a fraction

Answer:

Terrence made $30 more than Teresa.

Step-by-step explanation:

Giving the following information:

Terrence earns $450 per week.

Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.

First, we need to structure the total income formula for each:

Terrence= 450

Teresa= 300 + 0.06*x

x= sales

Now, for $2,000 sales of books:

Terrence= $450

Teresa= 300 + 0.06*2,000= $420

The most likely to generalize to it's population of interest is a stratified random sample of 120

a stratified random sample 120

Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members’ shared attributes or characteristics, such as income or educational attainment. Stratified random sampling has numerous applications and benefits, such as studying population demographics and life expectancy.

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The equation that can be used to find the number of lessons Fred must teach this month for the amount he brings in to equal the amount he spends is: 60n = 114.5 + 45.5 + 20n. So, Fred must teach 0.8 or approximately 1 lesson this month for the amount he brings in to equal the amount he spends.

The expression for the expenses for Fred in a month would be: $114.50 (online advertisements) + $45.50 (website) + $20n (cost of using the pool facilities) = $160n

In a month, Fred earns $60 per lesson. If n is the number of lessons he teaches, then he earns a total of 60n.To find how many lessons Fred must teach this month for the amount he brings in to equal the amount he spends, we can equate the earnings with the expenses and solve for n: 60n = 160n + 100n + 114.5 + 45.5

60n = 160n + 100n + 160

60n = 260n + 160

-200n = 160

n = 160/-200 n = -0.8

Therefore, Fred must teach 0.8 or approximately 1 lesson this month for the amount he brings in to equal the amount he spends.

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Answer:

the ratio used was 1:19

Step-by-step explanation:

let a be the action figure version

let r be the real iron man

let's list out the important things.

a = 4''

r = 6'4''

one foot has 12 inches

convert r into inches:

6 × 12 = 72           (6 feet in r)

       r = 76''          (72 + 4)

r = 76''

a = 4''

ratio is 4:76

simplify

4:76

2:38

1:19

the ratio they used is 1:19

good luck,

-cheesetoasty

The solution of function is \(\(\iint_R (2xy - 4y) \,dA = \frac{81}{10}\).\)

Given the region \(\mathrm{R}\) in the first quadrant bounded by the curves \(\(x = 3\), \(y = x^2\) and \(y = 0\).\)

Evaluate: \(\(\iint_R (2xy - 4y) \,dA\)\)

The limits of integration are: \(\[\int_{0}^{3} \int_{0}^{x^2} (2xy - 4y) \,dy \,dx\]\)

In the inner integral, we will evaluate with respect to \(y\) keeping \(x\) constant.

                 \(\[\int (2xy - 4y) \,dy = x(y^2 - 2y)\]\)

Now, we can integrate with respect to \(x\) keeping the limits from 0 to 3\

  \(\int_{0}^{3} \int_{0}^{x^2} (2xy - 4y) \,dy \,dx\)

= \(\int_{0}^{3} \left[x\frac{y^2}{2}-2xy\right]_{0}^{x^2}\,dx\]\[\)

= \(\int_{0}^{3} x\left(\frac{x^4}{2}-2x^3\right) \,dx\)

 = \(\int_{0}^{3} \frac{x^5}{2}-2x^4 \,dx\] \\\[\int_{0}^{3} \frac{x^5}{2}-2x^4 \,dx\)

   = \(\left[\frac{x^6}{12}-\frac{2x^5}{5}\right]_{0}^{3}\)

  = \(\frac{81}{10}\]\)

Hence, \(\iint_R (2xy - 4y) \,dA = \frac{81}{10}\)

Given the region \(\mathrm{R}\) in the first quadrant bounded by the curves \(x = 3\), \(y = x^2\) and \(y = 0\).

\(\iint_R (2xy - 4y) \,dA\)\[\begin{aligned}

\iint_R (2xy - 4y) \,dA &

= \int_{0}^{3}

\int_{0}^{x^2} (2xy - 4y) \,dy \,dx \\&

= \int_{0}^{3} \left[x\frac{y^2}{2}-2xy\right]_{0}^{x^2}\,dx \\&

= \int_{0}^{3} x\left(\frac{x^4}{2}-2x^3\right) \,dx \\&

= \int_{0}^{3} \frac{x^5}{2}-2x^4 \,dx \\&

= \left[\frac{x^6}{12}-\frac{2x^5}{5}\right]_{0}^{3} \\&

= \frac{81}{10}\end{aligned}\]

Hence, \(\iint_R (2xy - 4y) \,dA = \frac{81}{10}\).

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Answer:

There is only one perfect number between 20 to 30 which is 28.

The number 28 is a perfect number because its factors are 1, 2, 4, 7, 14 and 28.

Answer:

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Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The slope is 5 which is times to the variable x. Remember, any number times to the variable x which is given in this form, this means that it is the slope.

Hope this helps, thank you !!

We have been given that side length of pyramid the square base is 12 cm and its slant height is 10 cm. We are asked to find the height of the pyramid.

We will use slant height of a pyramid formula to solve our given problem.

\(s=\sqrt{h^2+\frac{1}{4}a^2}\),where,

s = Slant height,

h = Height,

a = Each side of square base.

Upon substituting our given values in above formula, we will get:

\(10=\sqrt{h^2+\frac{1}{4}\cdot 12^2}\)

\(10=\sqrt{h^2+\frac{1}{4}\cdot 144}\)

\(10=\sqrt{h^2+36}\)

Switch sides:

\(\sqrt{h^2+36}=10\)

Let us square both sides:

\((\sqrt{h^2+36})^2=10^2\)

\(h^2+36=100\)

\(h^2+36-36=100-36\)

\(h^2=64\)

Now we will take positive square root of both sides.

\(\sqrt{h^2}=\sqrt{64}\)

\(h=8\)

Therefore, the height of the pyramid is 8 cm and option 'b' is the correct choice.

LU decomposition and Gaussian elimination are both methods used to solve systems of linear equations. However, there are certain scenarios where LU decomposition is preferred over Gaussian elimination.

LU decomposition is useful when you have a system of linear equations that remains unchanged, but you need to solve it for different right-hand sides. Instead of performing the costly and time-consuming Gaussian elimination repeatedly, LU decomposition allows you to factorize the coefficient matrix once and then solve for different right-hand sides efficiently. LU decomposition also helps in solving systems with multiple right-hand sides simultaneously. Once the matrix is factorized into its lower triangular (L) and upper triangular (U) components, you can easily solve for each right-hand side by substituting the values into the lower and upper triangular matrices.

Additionally, LU decomposition can be advantageous when you want to compute the determinant or the inverse of a matrix. The factorized form of the matrix simplifies these computations compared to performing Gaussian elimination. In summary, LU decomposition is preferred over Gaussian elimination when you need to solve a system of linear equations for different right-hand sides, solve systems with multiple right-hand sides simultaneously, or perform computations involving the determinant or inverse of a matrix. It provides computational efficiency and avoids redundant calculations compared to the Gaussian elimination method.

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The length of side u in triangle STU i s approximately 6.34 units.

Triangle STU measures: s=8.4, t=6.9, and m∠S=58 degrees

In order to find the length u, we will use the law of cosines .

u² = s²+ t² -2stcos(m∠s)

where m∠s is the measure of angles in degrees.

u² = s²+ t² -2stcos(m∠s)

u² =8.4² +6.9² -2(8.4*6.9cos 58

u² = 118.17 -77.95

u² = 40.22

Taking the square root both sides, we get.

u = 6.34

Therefore, the length of side u in triangle STU i s approximately 6.34 units.

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Answer:

  u ≈ 9.7 units

Step-by-step explanation:

You want side u in triangle STU with s = 8.4, t = 6.9 and S = 58°.

We are given two sides and the angle opposite the larger of them. This means the triangle can be solved using the law of sines, and there will be one solution.

  s/sin(S) = t/sin(T) = u/sin(U)

With the given values, we can find angle T to be ...

  T = arcsin(t/s·sin(S))

  T = arcsin(6.9/8.4·sin(58°)) ≈ 44.156°

Then angle U will be ...

  180° -58° -44.156° = 77.844°

Using the same law of sines relation, we find side u to be ...

  u = s·sin(U)/sin(S)

  u = 8.4·sin(77.844°)/sin(58°) ≈ 9.683

The length of side u is about 9.7 units.

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Answer:

Shawn.

Step-by-step explanation:

We can solve for apples per hour and pears per hour. For Shawn, to get the apples per hour, we do 4/2 which is 2 bushels of apples per hour. For pears, we do 5/2 which is 2.5 bushels of pears per hour.

When Carla is picking, we can do:4/3 which is 1 and 1/3, which is her apple bushel picking per hour. For her pears, she picks them at 2 bushels of pears per hour.

Since Shawn picks her apples quicker per hour, and her pears quicker per hour, Shawn picks at a faster fruit pace.

The lateral surface area of the cone is 20π square units.

To find the lateral surface area of a right circular cone generated by revolving the region bounded by y = 3x/4, y = 3, and x = 0 about the y-axis, we need to follow these steps,

1. Find the height and slant height of the cone.
2. Use the formula for the lateral surface area of a cone: LSA = πr * l, where r is the radius and l is the slant height.

Find the height and slant height of the cone.
The equation of the line is y = 3x/4. We are given that y = 3, so we can solve for x:
3 = 3x/4
x = 4

Thus, the height (h) of the cone is 3, and the base radius (r) is 4. To find the slant height (l), we can use the Pythagorean theorem:
l² = h² + r²
l² = 3² + 4²
l² = 9 + 16
l² = 25
l = 5

Use the formula for the lateral surface area of a cone.
LSA = πr * l
LSA = π(4) * (5)
LSA = 20π

The lateral surface area of the cone is 20π square units.

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Answer:

Answer and Explanation: Given polynomial expression is: (5x2+3x−5)−(x2 −6x−4) ( 5 x 2 + 3 x − 5) − ( x 2 − 6 x − 4).

Step-by-step explanation:

Answer:

25x^2 -20x +4

Step-by-step explanation:

(5x-2)^2

FOIL

(5x-2)(5x-2)

25x^2 -10x -10x +4

25x^2 -20x +4

Answer:

number 4 and 6

Step-by-step explanation:

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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