find the measurement of angle E

(a) Draw a scatter diagram of the coefficient of thermal expansion (a) against temperature (T). Comment on the plot and suggest an equation that seems appropriate in relating a to T.

(b) Using linear regression to determine the relation between thermal expansion and the temperature.

(c) Using the regression equation from (b) to calculate the regression residuals for each experimental point and construct a run chart plot for these residuals. Discuss the residual plot commenting on relevant features.

(a) Scatter Diagram The scatter plot of the data in the table, shown below, indicates a strong negative correlation between a and T.

The coefficient of thermal expansion decreases as the temperature decreases.

Equation The equation y = mx + b is often used to describe the linear relationship between two variables,

where m is the slope and b is the y-intercept.

Here, the equation is a linear regression equation. The regression equation is y = -0.0873x + 12.012.

The equation, in this case, is an appropriate description of the data since there appears to be a linear relationship between a and T.

(b) Linear Regression Using the data in the table, the coefficient of thermal expansion (a) was plotted against temperature (T) and a regression equation was calculated.

The regression equation is given by:

y = -0.0873x + 12.012(a)

= -0.0873T + 12.012(c) Regression

Residuals To calculate the residuals, we simply subtract each data point's predicted value from its actual value.

These residuals can be plotted in a run chart. The residuals plot shows that the majority of the residuals are within ± 1 standard deviation.

Thus, it can be said that the residuals are well distributed and evenly scattered around zero.

The vertical spread of the residuals across the entire range of the predictor variable (T) is constant, which indicates that the regression is a good fit for the data.

Therefore, the regression model is appropriate for the given data.

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CM is the perpendicular bisector of AB at M, it means that CM is perpendicular to AB, and AM=BM. Therefore, we have two right triangles, triangle AMC and triangle BMC, with a shared side CM, and AM=BM.

By the Pythagorean theorem, we know that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Applying this to triangles AMC and BMC, we have:

AC² = AM² + CM²

BC² = BM² + CM²

Since AM=BM, we can substitute AM for BM in the second equation, giving:

BC² = AM² + CM²

Since the left-hand sides of these two equations are equal (by the given that CM is the perpendicular bisector of AB), we can set their right-hand sides equal to each other and simplify:

AC² = BC²

Taking the square root of both sides gives us:

AC = BC

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For a sample of 72 batteries, the probability that the average battery life of the sample exceeds 1173.8 minutes is 0.9918.

It states a battery life variance of 8100 minutes and a median battery life of 1192 minutes.

In a sample of 72 batteries, find the probability that the average battery life (x) of the sample exceeds 1173.8 minutes.

Due to the large sample size (n = 72), we can use the central limit theorem to assume that the sample mean follows a normal distribution with mean μ = 1192 and standard deviation σ = sqrt(8100/72) = 30.

So the z-score for x= 1173.8 is

z = (x - μ) / (σ / sqrt(n))

= (1173.8 - 1192) / (30 / square(72))

= -2.4

You can use a standard normal distribution table or calculator to find the probability that a  standard normal random variable is greater than -2.4. This is 0.9918 (rounded to four decimal places).

Therefore, for a sample of 72 batteries, the probability that the average battery life of the sample exceeds 1173.8 minutes is 0.9918 (rounded to four decimal places) if the claim is correct. 

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Answer:

use the slope intercept form of the equation

y = Mx +b

Step-by-step explanation:

6x+5y = -60

5y = -6x - 60

y = (-6/5)x -12

now just plug in zero for x in that above equation ... that will be the y intercept -12

and plug in zero for y and solve for x

0 = (-6/5)x -12

12= -6/5x

(-5/6)(12) = x

-10 = x  

Answer:

12

Step-by-step explanation:

u will need 12 rooms because 15 hikers per room so 178 divided by 15 equals 11.87 so just round that up to 12

Answer:

4 degrees Fahrenheit

Step-by-step explanation:

Answer:

negative four

Step-by-step explanation:

Answer: we can try 0.5x4 OR we can try 0.5+0.5+0.5+0.5=2

Step-by-step explanation:

basic math.

Answer:

Step-by-step explanation

sadly i dont understand

A bijection between two sets is constructed below and also proved that it is both one-one and onto.

The phrase "one-to-one function" should not be mistaken with "one-to-one correspondence," which is used to describe bijective functions, in which each element in the codomain is a precise mirror image of a single element in the domain.

Any function that can work with the operations of two algebraic structures is said to be a homomorphism between them. An injective homomorphism is also referred to as a monomorphism for any commonly occurring algebraic structures, particularly vector spaces.

Let t∈T

Then,

t=2k+1, for some k∈Z

Let s=3k

Then,

s∈S and f(s)=2(s/3)+1

=2k+1

=t

Therefore, for every t∈T there exists s∈S such that f(s)=t

Thus, f is onto.

Hence,

f:S  ----> T is a bijective mapping

⇒|S|=|T|

Now, we have to define a mapping f:S ---?T

By f(x)=2(x/3)+1, ∀x∈S

Given,

S={3k|k∈Z} and T={2k+1:k∈Z}

We have to prove:

|S|=|T|

Let x, y∈ S with f(x)=f(y)

Then,

2(x/3)+1=2(y/3)+1

2(x/3)=2(y/3)

(x/3)=(y/3)

x=y

So, f is one-one

Now, we have proved that f is both one-one and onto.

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Answer:

The value of w is 7.

Step-by-step explanation:

According to Pythagoras theorem,

Hypotenuse²=Perpendicular²+Base²

H²=P²+B²

Here,

Hypotenuse given=7√2

w=y

Perpendicular=Base=x

(7√2)²=x²+x²

49*2=2x²

(49*2)/2=x²

49=x²

√49=x

7=x

Perpendicular=x=7

Answer: 16 − 9 = 7 24 − 16 = 8 33 − 24 = 9

Answer:

mean: 28.73

median: 30

Mode: 42

Range: 36

Step-by-step explanation:

Took the test on edge2020

Answer:

Students from Grover Middle School are recycling aluminum cans. The table shows the total number of cans brought in each school day for a period of six weeks. They collected a total of 862 cans. Use the drop-down menus to define the terms.

Mean:  

✔ 28.73

Median:  

✔ 30

Mode:  

✔ 42

Range:  

✔ 36

Step-by-step explanation:

Correct answers

On the first day, Joe eats a portion of the cake. On the second day, he eats a portion of the remaining cake. To determine the fraction of the whole cake left on the third day, we need to calculate the remaining portion after the second day.

Let's assume that Joe starts with a whole cake, which is equal to 1. On the first day, he eats a fraction of the cake, let's say x. So, the amount of cake left after the first day is (1 - x). On the second day, Joe eats a fraction of the remaining cake, which is (1 - x). Let's call this fraction y. Therefore, the amount of cake left after the second day is (1 - x) * (1 - y). To find the fraction of the whole cake left on the third day, we need to subtract the amount of cake Joe ate on the third day from the amount left after the second day. Since we don't have information about how much Joe ate on the third day, we cannot determine the exact fraction of cake left on the third day.

In conclusion, without knowing the fraction of cake Joe eats on the third day, we cannot calculate the fraction of a whole cake left for Joe to eat on the third day.

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The function in f(t) form that describes the amount of fuel in the plane at time t will be;

⇒ f (t) = 112.25t + 31.425.75

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.

Now,

Since, After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.

Hence, The equation of line passes through the points (13, 32882) and (31, 34902.5)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (32882 - 34902.5) / ((31 - 13)

m = 2020.5 / 18

m = 112.25

Thus, The equation of line with slope 112.25 is,

⇒ y - 32885 = 112.25 (x - 13)

⇒ y - 32885 = 112.25x - 1459.25

⇒ y = 112.25x - 1459.25 + 32885

⇒ y = 112.25x + 31.425.75

Therefore, The function in f(t) form that describes the amount of fuel in the plane at time t will be;

⇒ f (t) = 112.25t + 31.425.75

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If the coin is tossed four times , then the probability of getting exactly two heads and two tails is 3/8   .

the  number of outcomes in tossing a coin is = 2 =  {H , T} ;

the number of outcomes in tossing the coin four times is = 2⁴ = 16 ;

we have to find the probability of getting exactly 2 heads and 2 tails :

So , the required outcomes will be = {HHTT, HTHT, HTTH, THHT, THTH , TTHH}  ;

the number of favorable outcomes is = 6 ;

the probability is = 6/16 = 3/8 .

Therefore , the required probability is 3/8 .

The given question is incomplete , the complete question is

If a coin is tossed 4 times, what is the probability of getting exactly two heads and two tails ?

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The maximum value of y(t) on the interval [0, 4] is y(1) = 1/3 and the minimum value is y(4) = 16/3.

To discover the most extreme and least values ​​of y(t) over the interim [0, 4], we must begin with discovering the basic points of y(t) and after that calculate y(t) at the basic points. 

To find the critical point, we need to find where the derivative of y(t) is zero or undefined. So we start by finding the derivative of y(t).

\(y'(t) = 2t^2 - 10t + 8\)

Setting y'(t) = 0 to find the location equal to zero gives:

\(2t^2 - 10t + 8 = 0\)

Simplified, it looks like this:

\(t^2 - 5t + 4 = 0\)

There is factoring:

(t - 1)(t - 4) = 0

So the critical points are t = 1 and t = 4.

Then evaluate y(t) at the critical points and the endpoints of the interval [0, 4].

y(0) = 0

y(1) = 1/3

y(4) = 16/3

A second derivative test can be used to determine if a value is the maximum or minimum. The second derivative of y(t) is

y''(t) = 4t - 10

At t = 0, y''(t) = -10, which is negative. This means that y(t) has a local maximum at t = 0.

At t = 1, y''(t) = -6, which is also negative. This means that y(t) has a local maximum at t = 1.

At t = 4, y''(t) = 6, which is positive. This means that y(t) has a local minimum at t = 4. Therefore, the maximum value of y(t) on the interval [0, 4] is y(1) = 1/3 and the minimum value is y(4) = 16/3.  

The correct question is

A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=2/3t^3−5t^2+8t. Over the time interval 0<t<5, for what values of t is the speed of the particle increasing?

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Answer:

6, 0, 2, 1

Step-by-step explanation:

Answer:

First multiply 0.579*10=5.79

Now multiply it with 3=17.37

Answer:

the total time spent on backstroke is 64minutes

Step-by-step explanation:

get the ratio of backstroke then divide it by the total ratio then multiply by 120

(8/8+7)×120

=8×8

=64

The linear equation for both Uber and Lyft  will be Y = 0.75x + 3 and

Y = 0.5x + 5 .

A linear equation is an algebraic equation of the form y = mx+b. Involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Here we have,

Uber charge $3 fix on every trip and additional charges on per mile $0.75

So, linear equation be

Y = 0.75x + 3 where, x = no. of mile covered

Similarly, lyft charge $5 fix and $0.5 as an additional

So, linear equation be

Y = 0.5x + 5 where, x = no. of mile covered

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A LOD score is the ratio of probabilities that two genes are linked to the probability that they are not linked, expressed as a log10. This measure is commonly used in linkage analysis, a statistical method used to determine whether genes are located on the same chromosome and thus tend to be inherited together.

In linkage analysis, the LOD score is used to determine the likelihood that two genes are linked, based on the observation of familial inheritance patterns. A LOD score of 3 or higher is generally considered to be strong evidence for linkage, indicating that the likelihood of observing the observed inheritance pattern by chance is less than 1 in 1000.

The LOD score is also used to estimate the distance between two linked genes, with higher LOD scores indicating that the two genes are closer together on the chromosome. In general, the LOD score is a useful tool for identifying genetic loci that contribute to complex diseases or traits.

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Answer:

1.105°

2.35°

3.35,°

4.50°

Step-by-step explanation:

ito po yung answer ko sa assignment you sa Maka tulong

Answer:

a = 7

b = 3 1/2

Step-by-step explanation:

if you add the equations together then the 'b' will zero out

6a = 42

a = 7

substitute 7 for 'a' to solve for 'b'

3(7) - 2b = 14

21 - 2b = 14

-2b = -7

b = 7/2 or 3 1/2

A perfect square is a number obtaining by squaring a whole number

A perfect square can be defined as a number that is being expressed as the product of an integer by itself.

It is also seen as the second exponent of an integer.

In determining the perfect of a number, when you multiply an integer which could be a “whole” number, positive, zero or negative) by itself, the product of the multiplication is termed a square number, or a perfect square.

Perfect square is also described as a number made by squaring a whole number.

Some perfect squares in mathematics are;

Number 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 139, 144, etc

Hence, a perfect square is described as a number that is the product of an integer with itself.

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