One of the same side interior angles of two parallel lines is 20* less than the other same side interior angle. Find the measures of the two angles

Answer:

= 0.38 m/s

Step-by-step explanation:

▪Total distance = 800 m

5 min = 100 m

▪Remaining distance = 800 - 100 = 700 m

20 min = 700 m

▪Total time taken = 20 + 10 + 5 = 35 min

If 1 min = 60 sec

What about 35 min = ?

= 35 x 60

= 2100 sec

▪Average speed = TD ÷ TT

= 800 ÷ 2100

= 0.38 m/s

Answer: not exactly sure what you meant but I don’t see a table so I’m guessing you should go for 90

Step-by-step explanation:

The efficiency of the power screw in raising the load is approximately 6976%.

The efficiency of a power screw can be calculated using the formula: Efficiency = (Ideal Mechanical Advantage / Actual Mechanical Advantage) x 100% To find the Ideal Mechanical Advantage (IMA) of the screw, we can use the formula:

IMA = (π / tan(α)) x (π / 2) x (D / P)

Where: π is the mathematical constant pi (approximately 3.14159) tan(α) is the coefficient of friction (given as 0.20) D is the major diameter of the screw (given as 19 mm) P is the pitch of the screw, which can be calculated as (25.4 mm / number of threads per inch) First, let's calculate the pitch: Number of threads per inch = 6

Pitch = 25.4 mm / 6 = 4.23 mm (approximately)

Now, we can substitute the values into the formula to find IMA:

IMA = (π / tan(α)) x (π / 2) x (19 mm / 4.23 mm)

Using the given coefficient of friction, we have:

IMA = (π / 0.20) x (π / 2) x (19 mm / 4.23 mm)

Simplifying the equation, we get:

IMA = 9.87 x 1.57 x 4.49

Calculating IMA, we find:

IMA ≈ 69.76

Now, we need to find the Actual Mechanical Advantage (AMA), which can be calculated using the formula:

AMA = Load / Effort

Where:

Load is the weight being lifted (given as 17.80 kN)

Effort is the force applied to turn the screw

Since the screw is being used to lift the load, the Effort is equal to the load.

AMA = 17.80 kin / 17.80 kin

AMA = 1

Now, we can calculate the efficiency using the formula:

Efficiency = (IMA / AMA) x 100%

Efficiency = (69.76 / 1) x 100%

Efficiency ≈ 6976%

The efficiency of the power screw in raising the load is approximately 6976%.

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The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

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To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.

Given matrix D:

D = | k 0 0 |

| 3 k² k³ |

| 0 kª k³ kº |

| k k k |

| 0 0 0 |

| k¹⁰ |

The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

- 0(det | 3 k² k³ |

| 0 kª k³ |

| k k k |)

+ 0(det | 3 k² k³ |

| k k k |

| k k k |)

Simplifying further, we have:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

Now, we can calculate the determinant of the 3x3 submatrix:

det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |

This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:

det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº

Now, we can set det(D) equal to 1024 and solve for k:

k⁴+kº = 1024

Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.

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Answer:

d. All of the above are true

Step-by-step explanation:

All of the following statements,

a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.

b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative.

C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant.

are true

The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer:

"Nothing but net" won the game

Step-by-step explanation:

Answer:

they won

61 to 43

Step-by-step explanation:

Answer:

Step-by-step explanation: The parallel sides of a trapezium are called the bases and the distance between them is the height. Therefore if 6cm and 15cm are the bases and 9cm is the height, then the area is A= ½(b1+b2)×h, where b1 is 6cm and b2 is 15cm and h is 9cm. Therefore the Area= ½(6+15)×9=94,5cm.

Answer:

shush its hard like my

Step-by-step explanation:

Answer:

-6x +2

Step-by-step explanation:

( x + 3 ) + ( − 7 x − 1 )

Combine like terms

x -7x   +3 -1

-6x +2

Answer:

-6x + 2.

Step-by-step explanation:

Remove brackets.

Rewrite as like terms.

Calculate .

Hello there mate ☺️,

\(8 {x}^{11} \)is the correct answer.

For explanation, please check the attached image of answer.

✍️ By Benjemin ☺️

The equation of the line through \((1,2)\) which make equal intercepts on the axis \(x+y=3\)

The equation of the line through (1,2) makes an equal intercept on the axis

The formula of the intercept form is

\(\frac{x}{a} +\frac{y}{b} =1\)

If they make an equal intercept

\(a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a\)

Put the value of the point in the axis, and we get.

\(1+2=a\\a=3\)

Put the value in the equation, and we get.

\(x+y=3\)

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Answer:

Step-by-step explanation:

I'm sorry, but you have not provided any image about the quadrilateral in your question, so I cannot give you its most specific name. Quadrilaterals are a broad class of polygons with four sides, and they can have various specific names depending on their properties and characteristics, such as square, rectangle, parallelogram, trapezoid, kite, rhombus, etc. Please provide more information about the quadrilateral you are referring to.

The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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The required probability is 0.852

Here, n=15

P(X ≤5) = P(X = 1)+...+ P(X = 5)

            = [(¹⁵₀)(0.25)⁰ (1-025)¹⁵⁻⁰ +...(¹⁵₅)(0.25)⁵ (1-0.25)¹⁵⁻⁵]

            = 0.01336+...+0.16515

            = 0.85163

            = 0.852  (Round to 3 decimal place)

Hence, the required probability is 0.852

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Answer:

40.3°

Step-by-step explanation:

sin x/ (5.3) = sin 90/ (8.2)

sin x = (5.3 sin 90) / 8.2

= 5.3/8.2

x = arcsin (5.3/8.2)

= 40.3° to 1 dp

The measure of angle x using Trigonometry is 40.263215° or 40.3.

Trigonometry is a branch of mathematics that deals with the study of relationships involving the angles and sides of triangles. It is especially useful in understanding the properties and behavior of right-angled triangles.

Sine ratio is defined as the ratio of the length of the side opposite an angle to the length of the triangle's hypotenuse.

From the figure,

Perpendicular = 5.3 m

Hypotenuse = 8.2 m

Using Trigonometry

sin x = P / H

sin x = 5.3/ 8.2

sin x = 0.6463

Using Inverse Trigonometry

x = \(sin^{-1}\)(0.6463)

x= 40.263215°

Thus, the measure of angle x is 40.3.

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Answer:

1/2

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

The unadjusted trial balance of The Lexington Group as of May 31, 20Y6, contains errors resulting in an unequal debit and credit balance of $27,875.

The unadjusted trial balance is a statement that lists all the accounts and their balances before any adjustments are made. It is used as a starting point to prepare the financial statements. In this case, the unadjusted trial balance of The Lexington Group shows a debit total of $608,125 and a credit total of $636,000, resulting in a difference of $27,875.

The errors mentioned in the question are the reasons for the imbalance. Let's go through each error:

1. The cash entered on the trial balance was overstated by $7,000. This means that the cash balance is higher than it should be by $7,000, resulting in an inflated debit balance.

2. A cash receipt of $8,200 was posted as a debit to cash of $2,800. This error resulted in an understatement of the cash balance by $5,400.

3. A debit of $16,500 to accounts receivable was not posted. As a result, the accounts receivable balance is understated by $16,500.

4. A return of $125 of defective supplies was erroneously posted as a $1,250 credit to supplies. This error caused an overstatement of the supplies balance by $1,125.

5. An insurance policy acquired at a cost of $3,600 was posted as a credit to prepaid insurance. This mistake resulted in an understatement of the prepaid insurance balance by $3,600.

6. The balance of notes payable was understated by $9,000. This means that the liability for notes payable is lower by $9,000 than it should be.

7. A credit of $10,000 in accounts payable was overlooked when determining the balance of the account. This error led to an understatement of the accounts payable balance by $10,000.

8. A debit of $5,000 for dividends was posted as a credit to retained earnings. This mistake caused an understatement of the dividends and an overstatement of the retained earnings by $5,000.

9. The balance of $60,300 in rent expense was entered as $63,000 in the trial balance. This error resulted in an overstatement of the rent expense by $2,700.

10. Gas, electricity, and water expense, with a balance of $16,350, was omitted from the trial balance. This omission caused an understatement of the total expenses by $16,350.

When we analyze the errors, we find that some accounts have been overstated, some have been understated, and some transactions have been completely omitted. These errors have led to an imbalance between the debit and credit sides of the trial balance.

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The correct answer is A. line. A line is a straight path that extends infinitely in both directions. It has no endpoints and continues indefinitely.

A line is a basic geometric object that is defined by two points or can be represented by a single equation. It is characterized by its straightness and infinite length, extending in both directions without any boundaries or endpoints. A line can be represented by a straight line segment with two distinct points or by an equation such as y = mx + b in a coordinate system.

On the other hand, a plane refers to a two-dimensional flat surface that extends infinitely in all directions. It is not a straight path but rather a flat, continuous surface. A ray, is a part of a line that has one endpoint and extends infinitely in one direction. It is not a straight path that continues indefinitely in both directions like a line.

A triangle is a closed geometric shape with three sides and three angles. It is not a straight path but rather a closed figure formed by connecting three non-collinear points.Therefore ,the correct answer is A.

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Answer: P = 4/52 = 0.077 or 7.7%

Step-by-step explanation:

I will answer in English.

We have a deck of 52 cards, and we want to find the probability of drawing, at random, a 1.

We have 4 1's in the deck, one for spades, one for hearts, one for diamonds and one for clovers.

So the probability can be calculated as the quotient between the total number of 1's in the deck and the total number of cards in the deck, this is:

P = 4/52 = 0.077

The linear equation that can be used to find the number of calories (y) Ray burns when he walks for x minutes is y = 4x.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

The equation can be written in the form y = mx + c.

Now,

Take two coordinates fr om the graph.

(1, 4) and (2, 8)

So,

m = (8 - 4) / (2 - 1)

m = 4/1

m = 4

And,

(1, 4) = (x, y)

4 = 4 x 1 + c

4 = 4 + c

c = 0

Now,

y = mx + c

y = 4x + 0

y = 4x

Thus,

The linear equation is y = 4x.

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In quadrant IV, \(\cos(A)\) is positive. So

\(\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258\)

Then by the definition of tangent,

\(\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}\)

Answer:

The amount of deposit required is R37,999  for both

The percentage of purchase price for the required deposit is 20%

Therefore, deposit required=20%*R189,995

                                              =R37,999

The balance owed is the outstanding balance after payment of deposit plus the interest, bearing in mind that interest is computed using the simple interest approach

I=PRT

balance after payment of deposit=R189,995-R37,999

                                                       =R151,996

R=13.5% per year

T=48 months and 54 months

Interest on 48 month option=151,996*13.5%*48/12

                                              = R82,077.84

Interest on 54 month option=151,996*13.5%*54/12

                                              = R 92,337.57

The total payment without the initial deposit is the outstanding balance after payment of deposit plus the interest

Total payment for 48 month option=R151,996+R 92,337.57

                                                          =R  244,333.57

Total payment for 54 month option=R151,996+R82,077.84

                                                          =R 234,073.84

                                              Hope it helped!

This statement 'During the early days of analytics, data was often obtained from the domain experts using manual processes to build mathematical or knowledge-based models' is true and not false.

During the early days of analytics, data was often obtained from domain experts using manual processes to build mathematical or knowledge-based models. Before the advent of computers and digital data storage, data was typically collected and processed manually. This often involved subject matter experts manually collecting data and performing calculations by hand to develop models and draw insights. Over time, as computing technology and data storage capabilities improved, analytics has evolved to rely increasingly on automated processes and sophisticated algorithms.

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The perimeter and area of the given composite figure are:

Area = 50 cm²

Perimeter = 42 cm

To find the total surface area of the composite figure, we will find the area of each individual surfaces and then add them together.

Formula for area of a triangle is:

Area = ¹/₂ * base * height

Formula for area of a rectangle is:

Area = Length * Width

Thus:

T.S.A = 2(¹/₂ * 4 * 5) + (10 * 3)

T.S.A = 20 + 30

T.S.A = 50 cm²

The perimeter will be the sum of the entire boundary length. Thus:

Perimeter = 3 + 10 + 10 + 3 + 3 + 3 + 5 + 5

Perimeter = 42 cm

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Answer:

Step-by-step explanation:

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