If Isabelle went on a slide that was 100 feet long with a ladder to the
top measuring 35 feet, how far is the bottom of the slide to the bottom
of the ladder? Round to the nearest foot.

Answers

Answer 1
The bottom of the slide is 65 feet, rounding to the nearest foot is 70 feet
Answer 2

93.7 feet is the distance from the bottom of the slide to the bottom of the ladder.

Let us consider the distance from the bottom of the ladder to the bottom of the slide "x" (the unknown we want to find).

The ladder's length is 35 feet, and the slide's length is 100 feet.

According to the Pythagorean theorem:

c² = a² + b²

where c is the hypotenuse (the ladder's length), and a and b are the two other sides of the right-angled triangle (the distances we want to find).

In this case, the equation becomes:

35²= x² + 100²

Solving for x:

1225 = x² + 10000

x² = 10000 - 1225

x² = 8775

Taking the square root of both sides to find "x":

x = √8775

x = 93.7 feet

So, the distance from the bottom of the slide to the bottom of the ladder is 93.7 feet.

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Related Questions

Find and interpret the mean absolute deviation of the data.

24, 26, 28, 28, 30, 30, 32, 32, 34,36

Answers

Answer:

hi will u follow me?

in roblox username gameitrexplayzYT

Step-by-step explanation:

in how many ways can 3 students be seated in a row of 3 chairs if jack insists on sitting in the first chair?

Answers

There are 2 ways that 3 students be seated in a row of 3 chairs with jack in the first chair

What is permutation?

It is the ordered arrangement of members belonging to a set with no repeats.

To solve this problem the formula and the permutation procedure we must use is:

nPr = n! / (n-r)!

Where:

nPr = permutationn = total number of objectsr = number of selected objects! = factorial of the number

Information about the problem:

n = 2r = 2

Applying the permutation formula we have:

nPr = n! / (n-r)!

3P3 = 2! / (2-2)!

3P3 = 2! / 0!

3P3 = 2*1 / 1

3P3 = 2

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please can someone help my assignment​

please can someone help my assignment

Answers

Answer:

Step-by-step explanation:

In ΔJOY and ΔLAF,

If ∠O ≅ ∠J

And \(\frac{JO}{AL}=\frac{YO}{FA}\)

Then ΔJOY ~ ΔLAF

By SAS property of similarity of two triangles.

(If two corresponding sides of the triangles are proportional and angles between these sides are equal)

Compare the budgets of Hong Kong, United States of America, and
Korea based on your definition of a budget, in terms of contents,
formats, advantages, and disadvantages, etc.

Answers

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

Hong Kong Budget:
Contents: The Hong Kong budget comprises revenue and expenditure. It provides a detailed analysis of expected sources of income and the allocation of funds.Format: The Hong Kong budget is presented in a clear and concise format, including charts and graphs to aid understanding.Advantages: The budget is easy to understand, and it promotes transparency and accountability.Disadvantages: It does not provide detailed information on tax expenditures and lacks public participation in the budget process.

United States Budget:

Contents: The US budget comprises revenue, expenditures, and deficit or surplus. It includes an analysis of taxes, social security, and Medicare.Format: The US budget is presented in a complex and lengthy format, including tables, graphs, and other financial documents.Advantages: The budget provides detailed information on tax expenditures and encourages public participation in the budget process.Disadvantages: The budget can be challenging to understand due to its complexity, and it may not provide an accurate depiction of federal spending.

Korean Budget:

Contents: The Korean budget comprises revenue, expenditures, and surplus or deficit. It includes detailed information on taxes, social security, and public welfare.Format: The Korean budget is presented in a clear and concise format, including tables and charts to aid understanding.Advantages: The budget is easy to understand, and it promotes transparency and accountability. It also provides detailed information on social welfare expenditures.Disadvantages: The budget may not provide an accurate depiction of government spending, and it may not include information on hidden expenditures.

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Guys can you please help. I dont understand. Thank you. :))))

Lines AB and CD intersect at E. If the measure of angle AEC=5x-20 and the measure of angle BED=x+50, find, in degrees, the measure of angle CEB.

Answers

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

i need some help doing this

i need some help doing this

Answers

are there certain numbers you have to use in the table?

What are a couple of examples of a situation where you feel that statistical guidance should perform well. Further, please tell me why you believe the statistical guidance should do well in this situation

Answers

Statistical guidance should perform well in situations such as clinical trials and market research where rigorous data analysis and inference are necessary. Statistical methods provide a systematic approach to control biases, handle variability, and draw reliable conclusions, ensuring accurate decision-making and predictions based on the data.

Statistical methods are crucial in determining sample sizes, designing the study, and analyzing the data to draw valid conclusions about the effectiveness and safety of the treatment.

In this situation, statistical guidance should do well because it provides a systematic framework to control for biases, random variability, and confounding factors, ensuring robust and reliable results that can be generalized to a larger population.

One example where statistical guidance should perform well is in clinical trials for new drugs or treatments.

Another example is in market research and opinion polling. Statistical techniques can be used to collect and analyze data from a representative sample of the target population, allowing for accurate estimation and prediction of consumer preferences, market trends, or election outcomes.

Statistical guidance should do well in this situation because it provides methods for random sampling, hypothesis testing, and confidence interval estimation, which help minimize sampling errors and increase the reliability of the findings.

Additionally, statistical models can capture complex relationships and make accurate predictions based on the observed data.

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Help! The two triangles are similar. WHAT IS THE VALUE OF YX?

Help! The two triangles are similar. WHAT IS THE VALUE OF YX?

Answers

Answer:

I'm sorry I don't know how to put in words of how to solve but the answer would be

ZY = 3 ft

XY= 7.42 ft

Can’t figure this one out

Cant figure this one out

Answers

B……………. Thank me laterrr.

in the process of a statistical investigation, we often take information from a sample from the population because:

Answers

We often take information from a sample from the population in the process of a statistical investigation because it is often impractical or impossible to collect data from the entire population.

In statistical investigation, a sample is a subset of a population that is selected for study. Collecting data from an entire population can be impractical or impossible due to cost, time, or other constraints. By studying a representative sample, statistical inferences can be made about the entire population with a certain degree of confidence.

The size and selection of the sample are important factors that affect the accuracy of the statistical inference. Generally, larger samples are more representative of the population and lead to more accurate estimates of population parameters.

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. a) When you see multiplication in an equation, how does that help you come up with a context?​

Answers

The presence of multiplication in an equation shows a context of repeated addition of values of that equation.

What is multiplication?

Multiplication is defined as one of the major arithmetic operation that shows the repeated addition of values of which a final figure is gotten. The other arithmetic operations include the following:

Division,Addition andSubtraction.

When there is multiplication sign in a mathematical expression it shows the context that repeated addition is needed to arrive at the desired value.

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The length of a rectangle is 2 inches less than 7 times the width. The perimeter is 76 inches. Find the length and width.​

Answers

Answer:

10

Step-by-step explanation:

2inch>[7width<76

S^<10

Asappppp , pls help me :((

Asappppp , pls help me :((

Answers

Answer:

Not a function

Step-by-step explanation:

This is not a function because every x value has more than one y value. Think about it this way. If you have a person and you are telling them to go to three different places at once, they can't. That means this isn't a function. Hope this helps!

Answer: That is not a function

Hope it helped

Step-by-step explanation:

Out of the total respondents, the percentage of respondents from the 46–55 age group who rated the film excellent is %. write your answer up to two decimal places.

Answers

Missing data:

Viewer's Age Group  Excellent Good Average Poor Marginal Total

16–25                          52                 42       12       7           113

26–35                          33                50         5       9          97

36–45                          58                 12       28      34         132

46–55                          25                17       22       12            76

56 +                               12                 5          3         8             28

Marginal Total             180               126      70      70           446

A rating of good or excellent indicates the audience liked the movie, while a rating of poor indicates the audience disliked the movie.

How to determine the rating of the film from the 46–55 age group?

A movie producer accomplished a survey behind a preview screening of her latest movie to estimate how the film would be accepted by viewers from various age groups. The table displays the numbers of viewers in various age groups who ranked the film excellent, good, average, and poor.

25/446 = 0.05605

0.05605 \(*\) 100% = 5.605%

Out of the entire respondents, the percentage of respondents from the 46–55 age group who ranked the film excellent exists at 5.605%.

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Which system models this situation? y = 26x and y = 8,400(x-500)2 15,900 y = 26x and y = -0.030(x-500)2 15,900 y = x/26 and y = -0.030(x-500)2 15,900 y = x/26 and y =8,400(x-500)2 15,900

Answers

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

According to the statement

we have given that Vertex

(h,k) = (500, 15900)

And One of the points on the graph

(x,y) = (0,8400)

FIRST PART: we have to find the quadratic function

We can find the quadratic function by parabola's equation formula

y = a (x - h)² + k  -(1)

Input the numbers to the formula, to find the value of a

y = a (x - h)² + k

8400 = a(0 - 500)² + 15900

8400 = a (500)² + 15900

8400 = 250000a + 15900

-250000a = 15900 - 8400

-250000a = 7500

a = 7500/-250000

a = 0.03

Now,

Submit a to the formula (1)

y = a (x - h)² + k

y = 0.03 (x - 500)² + 15900

this is the quadratic equation.

SECOND PART: Find the linear function

the total cost = cost each helmet × the number of helmet

y = 26x

So,

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

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Disclaimer: This question was incomplete. Please find the full content below.

Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)

x= number of helmets

y = amount in dollars

Which system models this situation?

a) y = 26x and y = 8,400(x-500)2+15,900

b) y = 26x and y = -0.030(x-500)2+15,900

c) y = x/26 and y = -0.030(x-500)2+15,900

d) y = x/26 and y =8,400(x-500)2+15,900

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Answer:

B. y = 26x and y = -0.030(x-500)2+15,900

Step-by-step explanation:

Which system models this situation? y = 26x and y = 8,400(x-500)2 15,900 y = 26x and y = -0.030(x-500)2

Find the value of x. Please if you can solve two questions sorry foe that I just don’t have time in 20 minutes it must be returned

Find the value of x. Please if you can solve two questions sorry foe that I just dont have time in 20

Answers

Answer:

x = 116

Explanation:

We can name the angles as follows:

So, taking into account the figure, the sum of angle A and the angle with measure 26 is equal to 90. Then, the value of angle A is:

A + 26 = 90

A + 26 - 26 = 90 - 26

A = 64

Then, angles A and B are part of an isosceles triangle. So, the measure of them is the same:

B = A

B = 64

Finally, the sum of angles B and x is 180 degrees because they form a straight line. So, the value of x is:

B + x = 180

64 + x = 180

64 + x - 64 = 180 - 64

x = 116

Therefore, the answer is x = 116

Find the value of x. Please if you can solve two questions sorry foe that I just dont have time in 20

A tennis ballisstruck and departs from the racket horizontally with a speed of 28.8 m/s. The ball hits the court at a horizontal distance of 20.3 m from the racket. How far above the court is the tennis ball when it leaves the racket? (a) Number Units Attempts:unlimited

Answers

To determine how far above the court the tennis ball is when it leaves the racket, we can use the equation of motion for projectile motion in the vertical direction. Since the ball is struck horizontally, its initial vertical velocity is 0 m/s.

The equation for vertical displacement (Δy) in projectile motion is given by:

Δy = v₀y * t + (1/2) * g * t²

where:

Δy is the vertical displacement

v₀y is the initial vertical velocity

t is the time of flight

g is the acceleration due to gravity (approximately 9.8 m/s²)

Since the initial vertical velocity is 0 m/s, the first term on the right side of the equation becomes 0.

We can rearrange the equation to solve for Δy:

Δy = (1/2) * g * t²

Now, we need to find the time of flight (t). We can use the horizontal distance traveled by the ball to calculate the time of flight:

horizontal distance = v₀x * t

where v₀x is the initial horizontal velocity. Since the ball is struck horizontally, v₀x remains constant throughout its motion.

In this case, the horizontal distance traveled by the ball is 20.3 m and the initial horizontal velocity is 28.8 m/s.

20.3 m = 28.8 m/s * t

Solving for t:

t = 20.3 m / 28.8 m/s ≈ 0.705 s

Now, substitute the value of t into the equation for Δy:

Δy = (1/2) * 9.8 m/s² * (0.705 s)²

Δy ≈ 2.07 m

Therefore, the tennis ball is approximately 2.07 meters above the court when it leaves the racket.

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Can someone please help

Can someone please help

Answers

1/4 is your answerrrrrrrr

Answer:

1/4

Step-by-step explanation:

5/6=10/12

(10/12)-(7/12)= (10-7)/12= 3/12 = 1/4

which of the following are a problem with a parallel conversion: (select all that apply) :a) there is a higher riskb) the old hardware might failc) there is a lower riskd) the users have to enter data into both systemse) there is an abrupt conversion

Answers

A parallel conversion is a method of implementing a new system in which the old and new systems run simultaneously for a period of time. While this approach can have its benefits, there are also potential problems that may arise.

One of the problems with a parallel conversion is that there is a higher risk, as there are two systems running at the same time, which can be costly and require additional resources. Another problem is that the old hardware might fail, which can cause data loss or delays in the conversion process. On the other hand, a lower risk may not be applicable in a parallel conversion because the risk factor is already high. Also, the users have to enter data into both systems, which can be time-consuming and prone to errors. Finally, an abrupt conversion is not applicable in a parallel conversion because both systems are running together. Overall, the parallel conversion method requires careful planning and execution to minimize the potential problems and ensure a smooth transition.

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NEED HELP ASAP!!! PLSSSSSSSSSSSSSSSSSSSS

NEED HELP ASAP!!! PLSSSSSSSSSSSSSSSSSSSS

Answers

Answer:

p(x) = 6x - 15

Step-by-step explanation:

So, first you subtract the cost of the necklace from the revenue, equating to 6x. Then, you take your constant, 15, and plug it into the equation for profit, giving you the finished equation of p(x) = 6x - 15. Hope this helps! (:

Answer: p(x) = 6x - 15          Answer is B

Step-by-step explanation:

They are wanting to know p(x)

Given:

r(x) = 10x

c(x) = 4x +15

p(x) = r(x) - c(x)                 >substitute r(x) and c(x)

p(x) = 10x - (4x + 15)         >Distribute -

p(x) = 10x - 4x - 15            >combine like terms

p(x) = 6x - 15          Answer is B

motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. assume a production process produces items with a mean weight of 11 ounces. a. the process standard deviation is , and the process control is set at plus or minus standard deviations. units with weights less than or greater than ounces will be classified as defects. what is the probability of a defect (to 4 decimals)? 0.3173 in a production run of parts, how many defects would be found (to the nearest whole number)? 16 b. through process design improvements, the process standard deviation can be reduced to . assume the process control remains the same, with weights less than or greater than ounces being classified as defects. what is the probability of a defect (to 4 decimals)? in a production run of parts, how many defects would be found (to the nearest whole number)? c. what is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard deviations from the mean?

Answers

(a) (i) 0.3174 = 31.74% probability of a defect

(ii) The expected number of defects for a 1,000-unit production run is 317.

(b) (i) 0.0026 = 0.26% probability of a defect

(ii) The expected number of defects for a 1,000-unit production run is 3.

(C) Reduces the process standard deviation and causes no change in the number of defects.

When the distribution is normal, we use the z-score formula.

In a set with mean  and standard deviation, the score of a measure X is given by:

         Z = X-μ /σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question a:

We have that: μ = 10 and σ = 0.12

(i). Calculate the probability of a defect.

Less than 9.88 or greater than 10.12. These probabilities are equal, so we find one and multiply by 2.

Probability of less than 9.88:

This is the p-value of Z when X = 9.88. Thus,

  Z = X-μ /σ

⇒ Z = 9.88 - 10/0.12

⇒ Z = -1, has a p-value of 0.1587

⇒ 2× 0.1587 = 0.3174

This means 0.3174 = 31.74% probability of a defect

(ii)  Calculate the expected number of defects for a 1,000-unit production run.

The expected number of defects is 31.74% of 1000. So

0.3174*1000 = 317.4

Rounding to the nearest integer

The expected number of defects for a 1,000-unit production run is 317.

Question (b):

The mean remains the same, but the standard deviation is now

(i) Calculate the probability of a defect.

Less than 9.88 or greater than 10.12. These probabilities are equal, so we find one and multiply by 2.

Probability of less than 9.88:

This is the p-value of Z when X = 9.88. Thus,

   Z = X-μ /σ

⇒ Z = 9.88 -10/0.04

⇒ Z = -3

⇒ Z = -3, has a p-value of 0.0013

which means 2× 0.0013 = 0.0026

from which 0.0026 = 0.26% probability of a defect

(ii) Calculate the expected number of defects for a 1,000-unit production run. The expected number of defects is 31.74% of 1000. Thus,

⇒ 0.0026*1000 = 2.6

Rounding to the nearest integer

The expected number of defects for a 1,000-unit production run is 3.

(C) The advantage of reducing process variation, thereby causing problem limits to be at a greater number of standard deviations from the mean Reduces the process standard deviation and causes no change in the number of defects.

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the equilibrium price is the price at which the quantity

Answers

The equilibrium price is the price at the equilibrium price is the price that brings supply and demand into balance, ensuring that the market clears and there is neither a shortage nor a surplus of goods.

The equilibrium price is the price at which the quantity demanded by consumers equals the quantity supplied by producers in a market. It is the point of balance between supply and demand.

At the equilibrium price, there is no shortage or surplus of goods in the market. The quantity demanded by consumers at that price matches the quantity supplied by producers, resulting in a state of market equilibrium.

If the price is set above the equilibrium price, there will be a surplus of goods because the quantity supplied exceeds the quantity demanded. Producers will be left with excess inventory, and they may need to lower the price to sell their goods.

On the other hand, if the price is set below the equilibrium price, there will be a shortage of goods because the quantity demanded exceeds the quantity supplied. Consumers will be willing to buy more goods at the lower price, and producers may need to raise the price to meet the increased demand.

Therefore, the equilibrium price is the price that brings supply and demand into balance, ensuring that the market clears and there is neither a shortage nor a surplus of goods.

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The ratio of areas of two triangles with common base is 4:5. The height of smaller triangle is 6cm. Find height of greater triangle.​

Answers

Answer:

Height of the greater triangle is 7.5 cm (Approximately).

Step-by-step explanation:

Given that

The ratio of two triangles with common base = 4:5

Let they be 4x cm² and 5x cm²

The area of the bigger triangle = 5x cm²

The area of the smaller triangle = 4x cm²

also,

Given that

The base of two triangles are same

Let the base of the two triangles be b cm

Height of the smaller triangle = 6 cm

Now,

Area of the triangle = (1/2)×base×height sq.units

⇛Area of the smaller triangle

⇛(1/2)×b×6 = 4

⇛6b/2 = 4

⇛3×b = 4

⇛b= 4/3 cm

.°. b = 4/3 cm

Now,

The length of the base = 4/3 cm

Area of the greater triangle = 5 cm²

⇛(1/2)×(4/3)×h = 5

⇛(4/6)×h = 5

⇛(2/3)×h = 5

⇛h = 5/(2/3)

= 5×3/2

= 15/2

⇛h = 7.5 cm (Approximately)

Answer: Therefore, Height of the greater triangle is 7.5 cm.

Please let me know if you have any other questions.

What is the term in mathematics for the operation or number that leaves others unchanged when combined with them? In multiplication, it is one, while in addition, it is zero?

Answers

The term is called an identity element. In multiplication, the identity element is one because any number multiplied by one results in the same number. In addition, the identity element is zero because any number added to zero results in the same number.


The term in mathematics for the operation or number that leaves others unchanged when combined with them is called the identity element.

It is also known by the name of neutral element.

In multiplication, the identity element is one (1) because when you multiply a number by one the result remains the same as the original number. For any number a,

a1=1a=a.

While in addition, the identity element is zero (0) because when you add zero to a number, the result remains the same as the original number. For any number a,

a+0=0+a=a.

There is no identity element for subtraction, and division only has an identity element for certain sets.

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why couldn't Pythagoras use the pythagorean theorem as we know it?

Answers

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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Does anyone know how to solve this?


(2x^2)-6x+9 can be written in the form (a(x-b)^2)+c where a b c can be written as integers or fractions in their simplest form.


a) work out the values of a b c
b) using your answer to part a), solve (2x^2)-6x+9=12.5. give any fractions or surds in your answers in their simplest forms.

Answers

Answer:

it needs to be written step by step

PLEASE ANSWER I NEED IT ASAP WILL AWARD BRAINLIEST AND GIVE POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

PLEASE ANSWER I NEED IT ASAP WILL AWARD BRAINLIEST AND GIVE POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

For 9:

1. Angle T and angle M are congruent because they are given

2. The line AH bisects angle THM because it is given

3. Angle 1 and angle 2 are congruent because of properties of angle bisection

4. The line AH is congruent to the line HA because of the reflexive property

5. Triangle TAH is congruent to triangle MHA because of AAS

6. The line TA is congruent to MA because of congruent triangles

For 10:

1. Angle H and angle J are congruent because it is given

2. G is the midpoint of FI because it is given

3. Angle 1 and angle 2 are congruent because they are vertical angles

4. Line HG is equal to line JG because of properties of midpoints

5. The triangles HIG and JFG are congruent because of AAS

6. The lines HI and JF are congruent because of congruent triangles

Samantha plays a trivia game. She earns 3 points for each
correct answer and loses 0.75 points for each incorrect
answer. She gets 11 correct answers and 4 incorrect
answers.
What is her score for the game?

Answers

Answer:

33/36

Step-by-step explanation:

take 0.75 x 4 = 3

then take

11 x 3 = 33

total score = 36

36 - 3 = 33

so the answer is 33/36

Answer:

Samantha would score 30 points

Step-by-step explanation:

If we multiply 11 x 3 we would get 33, the 11 represents the correct awnsers and the 3 represents the points

If we multiply 0.75 and 4 we get 3, this represents the incorrect

Next I subtracted 33 and 3 to get the answer of 30.

If she considers 10 m to be the height of the triangle, what should she use as the triangle’s base?

Answers

Area of a triangle = 1/2 (base x height) Here, we are given the height of the triangle as 10 m; hence, we can use the above formula to determine the base of the triangle.

Area of a triangle = 1/2 (b x 10) Given that we want the base of the triangle, we can rearrange the above equation to obtain the following:

b = (2 x Area of a triangle)/10

Since we do not have the value of the area of the triangle, we will use the Pythagorean theorem to find the third side, which will assist us in determining the area of the triangle.

Pythagorean Theorem states that:

Hence, we can use this theorem to calculate the third side of the triangle. The triangle's hypotenuse is equal to 10m, which is the given height of the triangle.

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1. (From the textbook, 5.1(a)). Does the following production function exhibit constant returns to scale? Y
t

=A[αK
t
v
v−1



+(1−α)N
t
v
v−1



]
v−1
v

Answers

The production function Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v does not exhibit constant returns to scale.

What is constant returns to scale?

The concept of constant returns to scale is a property of production functions. It refers to a situation in which an increase in inputs such as labor, capital, or both results in a proportionate rise in output.

How to determine whether a production function has constant returns to scale?

The production function Y = f(K, N) exhibits constant returns to scale if, for all values of K and N, there is a scalar λ such that Y(λK, λN) = λY(K, N)

If this condition holds, then we can say that the production function exhibits constant returns to scale.

Does the production function Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v exhibit constant returns to scale?

Let us determine whether the production function

Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v

exhibits constant returns to scale using the definition above.

Y(λK, λN) = A[α(λK) v (v−1) + (1−α)(λN) v (v−1)] v−1vY(λK, λN)

Y(λK, λN) = A[λvαK v (v−1) + λv(1−α)N v (v−1)] v−1vY(λK, λN)

Y(λK, λN) = A[λvαK v (v−1)v−1v + λv(1−α)N v (v−1)v−1v]Y(λK, λN)

Y(λK, λN) = λvA[αK v−1 + (1−α)N v−1] v

Since λ appears outside the bracket, the production function does not satisfy the condition of constant returns to scale because λ is not eliminated on both sides of the equation.

Therefore, we can conclude that the production function Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v does not exhibit constant returns to scale.

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