in the given figure AB || CD PROVE THAT p+q+r = 180

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%.

To learn more about Mechanical Advantage visit:

brainly.com/question/24056098

#SPJ11

Answer:

4000 millilitres

Step-by-step explanation:

She brought 32 L of water to the football game and divided the water equally between 8 coolers.

Therefore, cooler will have:

32 / 8 = 4 L

1 litre = 1000 millilitres

4 litres = 4 * 1000 = 4000 millilitres

Each cooler will have 4000 millilitres.

The statement that best interprets the value 29,864 in the quadratic regression equation (y = -0.004·x² + 34.637·x - 29,864) for the data in the table forecasting the company's profit based on the number of units sold is the option;

A regression equation is an equation that aims at discovering the relationship between a dependent or output variable and the input or independent variable.

The possible data in the question, obtained from a similar question, posted online, is presented as follows;

Number of Units\({}\) Profits ($)

500 \({}\)                  -10,000

1200  \({}\)                3000

2500 \({}\)                27000

3200 \({}\)                40000

3600 \({}\)                45000

4300 \({}\)                47000

5000 \({}\)                45000

6750 \({}\)                20000

Based on the above data, using the Polynomial trendline option of Order 2, in MS Excel, the quadratic regression equation, obtained using the Display Equation on chart option is; y = -0.004·x² + 34.637·x -29,864

The function, f(x) = -0.004·x² + 34.637·x -29,864, indicates that at x = 0, which is the point where 0 units have produced, we get;

Initial Profits = f(0) = -0.004 × 0² + 34.637 × 0 -29,864 = -29,864

The value, -29,864 indicates a loss of $29,864, therefore;

Learn more on regression equations here: https://brainly.com/question/17101427

#SPJ1

Answer:

Step-by-step explanation:

The company has an initial loss of about $29,864

Given the following quadratic expression:

Let's check if the given equation can be solved by factoring.

a.) Let's determine the original equation.

From the original equation, we observed that the constant 155/9 is not a perfect square. For the original quadratic equation to be factorable, we must apply the method of completing the square.

Therefore, we can say that the original quadratic equation can't be solved by factoring.

The paint cans and the spaces serve as examples of equivalent ratios. 5.5 cans of paint will be required to cover 2200 sq. unit.

Two ratios that have the same values are said to be equivalent. The same number can be used to multiply or divide both sums to get an equivalent ratio. The method is the same as determining equivalent fractions. When two or more ratios are reduced to their most basic form, they have the same value. Examples of equivalent ratios are 1:2, 2:4, and 4:8. In their most basic form, all three ratios have the same value, which is 1:2. They are in proportion if two ratios are equal. Equations in algebra are said to be equivalent if their solutions or roots are equal. When the same amount or expression is added to or removed from both sides of an equation, the result is the same.

To paint a 2200 square unit space, 5.5 cans are required.

The given parameter is:

Cans: Area\(=1:400\)

Express as fraction

Cans/Area\(=1/400\)

Multiply both sides by Area

Cans\(=\frac{1}{400}*Area\)

When the area is 2200, we have:

Cans\(=\frac{1}{400}*2200\)

Cans\(=5.5\)

5.5 cans are therefore required to paint a 2200 units square space.

To know more about equivalent ratios here

https://brainly.com/question/1706633

#SPJ4

follow me...

(•‿•)

Success

Answer:

quoitent will be 0.086368

hope it help u dear

Since the circle is divided into 9 equal parts, this will serve as our denominator. Each slice is 1/9 of the circle.

Since Vincent marked two parts of the circle, that measures 2/9 of the circle.

We know that one whole circle is one revolution and that is 360 degrees.

Hence, to measure the marked angle, we can use the expression:

Answer:

Step-by-step explanation:

A surface analysis chart is a type of weather map that displays information about the current pressure and wind patterns over a particular region. The chart provides a snapshot of the weather conditions at a specific point in time and helps meteorologists to identify and track the location, movement, and development of high- and low-pressure systems, fronts, and other weather features.

The surface analysis chart typically shows a map of the Earth's surface with various meteorological symbols and information, including isobars (lines of equal pressure), fronts (boundaries between different air masses), and wind direction and speed. The chart may also include information about temperature, precipitation, and cloud cover.

Surface analysis charts are used in weather forecasting, air traffic control, and other applications where an understanding of current weather conditions is important. They provide important information for short-term weather forecasting, such as predicting the location of fronts and the development of thunderstorms, and for long-term weather planning, such as determining the most suitable routes for shipping or aviation.

Answer:

i sho need it thx babe

Step-by-step explanation:

Answer:

6.875

Step-by-step explanation:

(i know old but answer)

The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

for similar questions on distance.

https://brainly.com/question/26046491

#SPJ8

Constructing a confidence interval for the mean of a distribution based on one sample is Confidence level = 1 - significance level.

The definition of the confidence level is (1-α). Zα is the number of standard deviations from the mean at which X with a certain probability lies. If Z = 1.96 is selected, the likelihood that the real mean falls inside the range is set at 0.95, hence we are asking for the 95% confidence interval.

Let us consider,

Confidence level = c

significance level \(= \alpha\)

\(c = 1 - \alpha\)

Fore more such question on confidence level.

https://brainly.com/question/29634773

#SPJ4

Answer:

C.Tammy’s estimate is right, but the actual product should be 24.78.

Step-by-step explanation:

i took the assessment! thank you for your attention and i hope i helped!!

Answer:

the answer is C which is Tammy’s estimate is right, but the actual product should be 24.78.

Step-by-step explanation:

Option (D) Has minimal data storage requirements

To determine the vertices of image U′V′W′ after a 180° counterclockwise rotation, we can apply the following transformation rules:

Using these rules, we can find the vertices of image U′V′W′ as follows:

Therefore, the vertices of image U′V′W′ after a 180° counterclockwise rotation are U′(0, -2), V′(1, -3), and W′(3, -3).

So, the answer is option (b) U′(0, −2), V′(1, −3), W′(3, −3).

The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

To know more about direct labor:

https://brainly.com/question/13126873

#SPJ4

Answer:

Step-by-step explanation:

The standard form equation for a circle is

\((x-h)^2+(y-k)^2=r^2\)

where h and k are the coordinates of the center. Our center is given as (-6,7)  and the radius is given as 9, so that information fits into our standard form like this:

\((x-(-6))^2+(y-7)^2=9^2\) and simplified, it looks like this:

\((x+6)^2+(y-7)^2=81\)

That's choice C

Boxplots are not recommended for use with bimodal or any multimodal distributions.

Boxplots, also known as box-and-whisker plots, are graphical representations of the distribution of a dataset. They provide information about the median, quartiles, and potential outliers. Boxplots are particularly useful for summarizing unimodal, skewed, or symmetric distributions.

However, boxplots are not ideal for representing bimodal or multimodal distributions. Bimodal distributions have two distinct peaks or modes, while multimodal distributions have more than two peaks. In these cases, a boxplot may not effectively capture the complexity and characteristics of the distribution.

Boxplots are primarily designed to show the central tendency and spread of unimodal distributions or distributions that exhibit skewness or symmetry. They work well in these cases because they summarize key statistical measures and provide a clear visual representation of the spread.

For bimodal or multimodal distributions, other types of visualizations, such as histograms or kernel density plots, are often more suitable. These visualizations can better depict the multiple modes and capture the intricacies of the distribution.

In summary, boxplots are not recommended for use with bimodal or multimodal distributions, as they may not effectively represent the complexity and characteristics of these types of distributions.

Learn more about boxplots here:

https://brainly.com/question/30469695

#SPJ11

Answer:

Step-by-step explanation:as we know that arc length is

s=r*∅

as given angle in degree so  convert it in radian we get

angle=2.09 rad

r=3.5 cm

hence we get

s=3.5*2.09 =7.315 cm

perimeter of sector = s +d  where d=2*r=2*3.5=7 cm

perimeter of sector=7.315+7=14.315 cm

if you like it then hit the stars and tag it a brain-list

Answer:

4/9

Step-by-step explanation:

2/3 × 2/3 is 4/9

2×2 is 4 and 3×3 is 9

To calculate the probability of selecting a boy or a red-haired person as a homeroom representative to student council, we need to find the probability of each event and then use the formula P(A or B) = P(A) + P(B) - P(A and B).

There are 31 students in total (16 girls + 15 boys). The probability of selecting a boy is 15/31.

There are 5 red-haired students (3 girls + 2 boys). The probability of selecting a red-haired person is 5/31.

However, we need to account for the overlap between boys and red-haired students. There are 2 red-haired boys, so the probability of selecting a red-haired boy is 2/31.

Now we can use the formula: P(boy or red-haired) = P(boy) + P(red-haired) - P(boy and red-haired) = (15/31) + (5/31) - (2/31) = 18/31.

So, the probability of selecting a boy or a red-haired person as a homeroom representative to student council is 18/31.

Learn more about probability:

https://brainly.com/question/24756209

#SPJ11

The error interval for x when rounded to one decimal place as 8.7 is (8.65, 8.74).

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

Here,

The rounded value of 8.7 is the midpoint of the error interval and any number between 8.65 and 8.74 would round to 8.7 when rounded to one decimal place.

Thus, the error interval for x when rounded to one decimal place is (8.65, 8.74).

Learn more about round the decimal here;

brainly.com/question/867784

#SPJ1

In the triangle , the value οf x is 42.4.

What is law of sine?

Law οf sines establishes the ratiο οf a triangle's sides and establishes that each side's sine angle is equal tο the οther. Other names fοr sines include sine Iaw, sine ruIe, and sine frmuIa.

Tο determine the unknοwn angle οr the side οf a unique triangle, the sine wave is used. Any triangle that is nοt a right triangle is cοnsidered a unique triangle. At least twο angles and their assοciated side measurements shοuld be used when using the Iaw οf sine.

The trigonometric functiοn, the law of sine is,

\(\frac{sin(A)}{a}=\frac{sin(B)}{b}\)

In the given triangle  using law οf sine then,

=> \(\frac{sinM}{NL}=\frac{sinN}{ML}\)

=> \(\frac{sin88\textdegree}{x}=\frac{sin38\textdegree}{26}\)

=> x = \(\frac{sin88\textdegree\times26}{sin38\textdegree}\)

=> x = 42.2

Hence the value οf x is 42.2.

To learn more about law of sine refer the below link

https://brainly.com/question/27174058

#SPJ1

Therefore, 31.8 ounces of the 17% alloy and (110 - 31.8) = 78.2 ounces of the 19% alloy should be mixed to form 110 ounces of the desired alloy.

Let's assume the number of ounces of the 17% alloy to be mixed is x, and the number of ounces of the 19% alloy to be mixed is 110 - x (since the total desired alloy is 110 ounces). To find the amount of copper in the resulting alloy, we can set up the equation:

0.17x + 0.19(110 - x) = 0.184(110)

Simplifying the equation:

0.17x + 20.9 - 0.19x = 20.264

Combine like terms:

-0.02x = -0.636

Divide both sides by -0.02:

x = 31.8

To know more about ounces,

https://brainly.com/question/17387252

#SPJ11

Answer:

$16.80

Step-by-step explanation:

20/100 = 0.20

14 x 0.20 = 2.8

14 + 2.8 = 16.8

Answer:

28.00

Step-by-step explanation:

14.00. x 20 = 28.00

28 divided by 14= 2

Finding f(g(x)), g (f(x)), f(f(x)), g (g(x)) is g(g(x))=2g²(x)-4=2(2x²-4)²-4=16x⁴-64x²+28. The inverses of the functions: f(x) = -2x¹-2; g(x) = x-3 X+2 is  x+2/x-6.

a)Given that: f(x) = 3x + 2; g(x) = 2x²-4;

Now, to find: f(g(x))

We substitute g(x) in the place of x in f(x) to get: f(g(x))=3g(x)+2=3(2x²-4)+2=6x²-10g(f(x))

Substituting f(x) in the place of x in g(x) to get: g(f(x))=2f²(x)-4=2(3x+2)²-4=18x²+24x+4f(f(x))

Substituting f(x) in the place of x in f(x) to get: f(f(x))=3f(x)+2=3(3x+2)+2=9x+8g(g(x))

Substituting g(x) in the place of x in g(x) to get: g(g(x))=2g²(x)-4=2(2x²-4)²-4=16x⁴-64x²+28

b)To find the inverse of f(x) = -2x¹-2

Substituting y in the place of f(x) to get: y=-2x-2

Making x the subject of the formula: y+2=-2x

Dividing the whole equation by -2 and changing the places of y and x: f⁻¹(x) = -(x+2)

To find the inverse of g(x) = x-3 X+2

Substituting y in the place of g(x) to get: y=x-3 x+2

Making x the subject of the formula: y(x+2)=x+6x=y+2y-6

Substituting x in the place of y: f⁻¹(x) = x+2/x-6

More on inverses: https://brainly.com/question/30339780

#SPJ11

The arrow's motion can be described by parametric equations: x = V₀cosθt and y = -4.9t² + V₀sinθt + h, where V₀ is the initial velocity, θ is the launch angle, t is the time, and h is the initial height. To determine the time the arrow is in the air before touching the ground and the maximum height reached, we need to solve for the corresponding values in the equations.

(a) To find the time the arrow is in the air before touching the ground for the final time, we need to determine the value of t when y equals zero (the ground level). We can set the equation -4.9t² + V₀sinθt + h = 0 and solve for t. This equation represents the vertical motion of the arrow. Once we find the value of t, we can round it to the nearest tenth.

(b) To determine the maximum height reached by the arrow, we need to find the vertex of the parabolic equation -4.9t² + V₀sinθt + h. The maximum height occurs at the vertex of the parabola, which corresponds to the highest point of the arrow's trajectory. We can use the formula t = -b/2a, where a = -4.9 and b = V₀sinθ, to find the time at which the maximum height is reached. Once we find the value of t, we can substitute it into the equation y = -4.9t² + V₀sinθt + h to calculate the maximum height, rounding it to the nearest whole number.

By solving for the time when the arrow touches the ground and finding the maximum height, we can better understand the arrow's motion and trajectory.

Learn more about parabola here:

https://brainly.com/question/29267743

#SPJ11

Answer:

6/5

Step-by-step explanation:

1/5 + (2/5 + 3/5)

solve for the bracket first

1/5 +(2+3/5)

1/5 + (5/5)

1/5 + 1

1+1*5/5

6/5

another method

1/5 + (2/5 +3/5)

open brackets)

1/5 + 2/5 + 3/5

since their denominator are same u can add their numerator

1+2+3/5

6/5

Answer:

the last one

Step-by-step explanation:

Both are used then the sencond is used as well