The following is an outline of a proof that e is irrational. Note that 0! = 1. (a) Show that e" is strictly increasing on R. (b) Use Larange’s Remainder Theorem at a = () and the estimate e < 3 to show that, for all n E N, 1 1 0 max{q, 3}. Substitute e = p/q in the inequalities in part (b) and multiply the inequality by n!. Show that this leads to the existence of an integer between 0 and which is a contradiction.

Answer:

n+1/4n

Step-by-step explanation:

\( \fbox{(2,5)}\)

Hello, substitute all the given coordinates & see if RHS match with LHS

given equation,

y = 4x-3

First coordinate,

(x,y) = (2,5)

5= 4×2-3

5=5

Hence, first solution satisfies the given equation,

let's solve for rest other cordinates,

second coordinate,

(x,y) = (5,5)

5= 4×5-3

5 ≠ 17

does not satisfy,

third coordinate,

(x,y) = (4,5)

5= 4×4-3

5 ≠ 13

does not satisfy,

fourth coordinate,

(x,y) = (4,5)

5 = 4×3-3

5 ≠ 9

does not satisfy.

Hence the correct answer is (2,5)

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A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.

You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).

Given,

A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.

Let s represent the truck's speed and (s+20) represent the car's speed.

to determine each vehicle's time

Time = Speed / Distance

truck time = 350/s

Time in an automobile is 350/(s+20)

Truck time - car time = 2 hours

So,

(350/s) - [350/(s+20)] = 2

LCM is s(s+20)

[350(s+20) - 350s]/s(s+20) = 2

Cross multiplying,

350(s+20) - 350s = 2s(s+20)

Simplifying the equation,

350s + 7000 - 350s = 2s² + 40s

Now, we have quadratic equation to simplify,

2s² + 40s - 7000 = 0

Dividing the equation by 2

s² + 20s - 3500 = 0

Factorizing,

s= 50

s= -70 (impossible because of the sign)

Hence the truck's speed is s = 50 km/h.

The speed of the car is s + 20 = 70 km/h.

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Answer:

The answer is "4.8 and 463.011"

Step-by-step explanation:

Please find the complete question in the attached file.

Given:

side\(= 9.6 \ in\\\\\)

let the radius of the ball

\(2r=9.6 \ in\\\\r=\frac{9.6}{2}\\\\r= 4.8 \ in\\\\\)  

The radius of the basketball \(= 4.8 \ in\\\\\)

The volume of the basketball\(=\frac{4}{3}\pi r^3=\frac{4}{3}\times 3.14 \times 4.8^3= 463.011 \ in^3\)

Answer:

see below

Step-by-step explanation:

A: Some points could be (1, 7.5), (2, 7), (3, 6.5), (4, 6), (5, 5.5) and (6, 5) because the y-coordinates all represent the heights of the candle after the x hours.

B: This is a function because no input has multiple outputs.

C: It would still be a function because no input would have multiple outputs.

Answer:

Have a great day!!

Step-by-step explanation:

Part A: my rate of change was first y= - 5x + 8 the reason i put a negative sign beforehand is that when the candle melts its height it's decreasing 

(0,8),(1,7.5)(2,7)(3,6.5)(4,6)(5, 5.5)

Part B: This is a function because there is one different output for each different input

Part C: yes, it still would be a function because the numbers haven't changed and are exactly the same and it still has one input for each output.

(0,8), (1,75), (2,7), (3,6.5), (4,6), (5,5.5)

In summary, the Total Diet Study conducted by the FDA typically tests around 280 different food samples each year. This study helps monitor the levels of contaminants and nutrients in the average American diet and informs the FDA's regulations and recommendations regarding food safety and nutrition.

The Total Diet Study (TDS) is conducted by the U.S. Food and Drug Administration (FDA) to monitor the levels of various contaminants and nutrients in the average American diet. The study aims to assess potential health risks associated with these substances.
Each year, the TDS collects and analyzes a wide range of food samples from different locations throughout the United States. These samples include fruits, vegetables, grains, dairy products, meat, and seafood, among others.
The number of food samples tested during each TDS cycle may vary, but the study typically analyzes around 280 different food items. These items are selected based on their significance in the American diet and their potential for contamination or nutrient analysis.
By analyzing these food samples, the FDA can identify any potential risks associated with contaminants or nutrient deficiencies. This information helps the FDA in setting regulations and recommendations to ensure the safety and nutritional quality of the food supply.

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The average speed of the car is 40 km/hr.

It would take a car 3 hours to cover 120 km at a speed of 40 km/h.

The car moves for a time period of 3 hours.

The car has to travel a total distance of 120 km.

As we know the formula of speed is distance/time,

Hence, s = d/t km/hr

Let speed, distance and time be s, d, t respectively.

So by putting the values,

speed s = d/t = 120/3 = 40 km/hr.

Hence it can be said that the car would cover 120 km at the speed of 40 km/hr in 3 hours.

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Hello there!

I hope you and your family are staying safe and healthy!

P.S. I did my best drawing the problem :)

\(Tan 32 = \frac{800}{x}\)

\(x = \frac{800}{tan32}\)

\(Tan 27 = \frac{800}{y}\)

\(y=\frac{800}{tan27}\)

Answer: ~289.8 ft

I hope this makes sense! See picture for additional info.

As always, it is my pleasure to help students like you!

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For the values of x , the corresponding values of y are :

Answer:a scientific law is the description of an observed phenomenon. It doesn't explain why the phenomenon exists or what causes it. The explanation of a phenomenon is called a scientific theory. It is a misconception that theories turn into laws with enough research.

Step-by-step explanation:

The Relationship between the points D(6, 9) and A(8, 12) can be described as a dilation with a factor of 1.5. Point A is located 1.5 times farther from the origin compared to point D, in both the horizontal and vertical directions. Additionally, A is an enlargement of D.

The relationship between the points D(6, 9) and A(8, 12) can be described in terms of dilations. In mathematics, a dilation is a transformation that changes the size of an object while keeping its shape intact. It involves scaling the object by a certain factor, either enlarging or reducing it.

To understand the relationship between D and A, we can calculate the dilation factor. The dilation factor, denoted by 'k', is the ratio of the corresponding side lengths or distances between the pre-image (original object) and the image (transformed object).

The dilation factor between D(6, 9) and A(8, 12):

First, we need to find the change in x-coordinates and y-coordinates:

Δx = 8 - 6 = 2

Δy = 12 - 9 = 3

Next, we calculate the dilation factor:

k = Δy / Δx = 3 / 2 = 1.5

The dilation factor of 1.5 indicates that the image point A is 1.5 times as far from the origin (point D) compared to the pre-image. This means that A is located at a greater distance from the origin than D, both horizontally and vertically.

Moreover, since the dilation factor is positive, the dilation is an enlargement. This means that A is enlarged with respect to D. The ratio of the corresponding side lengths will also be 1.5.

the relationship between the points D(6, 9) and A(8, 12) can be described as a dilation with a factor of 1.5. Point A is located 1.5 times farther from the origin compared to point D, in both the horizontal and vertical directions. Additionally, A is an enlargement of D.

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Given:

Let's solve for the value of x.

Hence the value of x is 5

Answer:

48

Step-by-step explanation:

P would equal 30 but you would have to multiply it by 5/8 so you would get 48.

a

jfjoydx9tdzrzfzixitxxytxixutx

The future value of the ordinary annuity with a payment of $850, an interest rate of 1.50% compounded semiannually for 3 years, is approximately $5,139.80.

To calculate the future value of an ordinary annuity, we can use the formula:

FV = PMT * ((1 + r)^n - 1) / r

Where:

FV represents the future value

PMT is the payment amount

r is the interest rate per compounding period

n is the number of compounding periods

In this case, the payment amount (PMT) is $850, the interest rate (r) is 1.50% (or 0.015 as a decimal), and the compounding is done semiannually for 3 years.

First, we need to calculate the number of compounding periods (n). Since the compounding is done semiannually, and there are 3 years, the number of compounding periods will be:

n = 2 * 3 = 6

Now, we can plug the values into the formula:

FV = 850 * ((1 + 0.015)^6 - 1) / 0.015

Calculating this expression, we find:

FV ≈ $5,139.80

Therefore, the future value of the ordinary annuity with a payment of $850, an interest rate of 1.50% compounded semiannually for 3 years, is approximately $5,139.80.

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Answer:

r = 152/55

Step-by-step explanation:

122 - 44r = - 30 + 11r

122 - 44r - 11r = - 30

- 44r - 11r = - 30 - 122

- 55r = - 30 - 122

- 55r = - 152

Using the distributive property, the expression 4(2.9x - 7.8y) - 6 expands to

The distributive property states that when you have a number or term multiplied by a sum or difference in parentheses, you distribute the multiplication to each term inside the parentheses.

In the given expression, we have:

4(2.9x - 7.8y) - 6

multiply 4 by each term inside the parentheses:

4 * 2.9x = 11.6x

4 * (-7.8y) = -31.2y

rewrite the expression:

11.6x - 31.2y - 6

using the distributive property, the expression 4(2.9x - 7.8y) - 6 expands to 11.6x - 31.2y - 6.

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Answer:

54

Step-by-step explanation:

Both Triangles: 12

Square: 10.5

Back rectangle: 14

Front Rectangle: 17.5

And just add all of them together

Answer:

A,C,D

Step-by-step explanation:

When b=0, there is a proportional relationship.

The slope in y=mx+b is the value next to x.

Using RISE/RUN when there is a change of 3 units in x, there is a change of 2 units in y.

Answer:

2 11 33 41 44 49

Step-by-step explanation:

33+41=74 74÷2=37

Answer: The medians the middle, so you put in order to 2, 11, 33, 41, 44, and 49. Then, you just pick the number in the middle and since it's 33 and 41, you add them together then divide by 2 and you answer is 37. I hope this helps you!

Answer:

Step-by-step explanation:

6

Answer:

6 girls

Step-by-step explanation:

ratio is 2:1 meaning for every 2 girls there's 1 boy

since there's 3 boys, just double the amount (3x2) and you get 6

i. The wage would increase by 0.12 units.

ii. The wage would increase by 0.6 units.

iii. The relationship between wage and age is not linear but instead has a quadratic shape.

(i) The coefficient of edu does give the slope of the relationship between the wage and education. In the given equation, the coefficient of edu is 0.12.

This means that for every one unit increase in education (in years), the wage increases by 0.12 units.

For example, if a worker's education increases by 5 years, the wage would increase by 0.12 * 5 = 0.6 units.

(ii) The coefficient of age does represent the slope of the relationship between the wage and age. In the given equation, the coefficient of age is 0.06.

This means that for every one unit increase in age, the wage increases by 0.06 units.

For example, if a worker's age increases by 10 years, the wage would increase by 0.06 * 10 = 0.6 units.

(iii) The coefficient of age² does not represent the slope of the relationship between the wage and age. Instead, it represents the curvature of the relationship.

In the given equation, the coefficient of age² is -0.007.  As age increases, the wage initially increases at a decreasing rate, and then starts to decrease.

The coefficient of age² captures this pattern of the relationship.

In the second part of the question, if an inexperienced researcher specifies the PRF for economic growth incorrectly, it can lead to biased and inconsistent estimates of the coefficients. In terms of the estimation of β2 (the coefficient of inf), it would be difficult to determine the true relationship between domestic inflation and economic growth.

The estimated coefficient may be distorted and may not accurately capture the effect of domestic inflation on GDP growth.

In terms of the unbiasedness property of the coefficient of the variable of interest, if the regression model is misspecified, the coefficient estimates may not be unbiased. This means that the estimated coefficients may not provide an accurate representation of the true relationship between the variables. The graphical illustration of this would show a biased slope, where the estimated relationship deviates from the true relationship.

In summary, it is crucial to specify the correct regression model and ensure that it captures the true relationship between the variables of interest to obtain accurate and unbiased estimates.

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Answer:

I think it's 70%.

Answer:

AHAHAHAHA

Step-by-step explanation:

nope LOL

Answer:

gftrtrtgfrtrftgtrgty

Step-by-step explanation:

fgrtfgtrfggtrfgtrfgtrfgtrfgytrfgtrfgtr

Answer:

Your number is 3

Step-by-step explanation:

3*3 is 9 and there are no other numbers multiplied by itself to get 9

Answer:

The range is 12, 0, -6

Explanation:

Given the function:

f(x) = 4 - 2x

We want to find the range of this function, given that the domain is:

-4, 0, 5

This can be done by replacing x by each element ot the domain in the given function, find f(x).

For element -4

f(-4) = 4 - 2(-4)

= 4 + 8

= 12

For element 0

f(0) = 4 - 2(0)

= 4 - 0

= 0

For element 5

f(5) = 4 - 2(5)

= 4 - 10

= -6

The range is 12, 0, -6

A direct relationship between two variables is reflected in a "POSITIVE" correlation coefficient.

Correlation is a statistical technique for measuring and describing the relationship between two variables.

The variables move in the same direction when they have a positive correlation. In other words, as one variable increases, so does the other, and conversely, as one variable decreases, so does the other.

Typically, the two variables are simply observed rather than manipulated. Two scores from the same individuals are required for the correlation.

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Answer:EF to AD

Step-by-step explanation: