an agriculturalist working with australian pine trees wanted to investigate the relationship between the age and the height of the australian pine. a random sample of australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the australian pine based on the age, in years, of the tree. Predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?

The number of adults that can get in the considered elevator if there are 10 children already in it is 4 adults.

Suppose that the capacity of the considered elevator is expressed in the third form (neither in terms of children nor in terms of adults), as 'k'.

So, we have: k = 15 children = 15x (say each children covers x capacity)

and k = 11 adults = 11y (say each adult covers y capacity)

(here, we assumed that capacity is linearly covered, ie if one person covers some capacity, then two people cover the sum of their covered capacity).

It is given that there are 10 children in the elevator right now.

That means, k-10x = 15x -10x = 5x capacity is still remaining.

Converting x to y, as shown below:

[tex]15x = 11y[/tex]

[tex]x= \frac{11y}{15}[/tex]

Thus, 5x is equivalent to:

[tex]5x =5( \frac{11y}{15})[/tex] [tex]= \frac{11y}{3}[/tex]

It is smaller than 4y but bigger than 3y. Therefore, 3 more adults can come in it, as 4 will make the elevator get overloaded.

Thus, the number of adults that can get in the considered elevator if there are 10 children already in it is 4 adults.

The human beings-transferring enterprise has come an extended way because 1852 when Elisha Graves Otis invented the elevator safety brake and inspired a method to a customary hassle—a way to competently flow freight from floor to ground without risking lives and destroying the cargo.

If one is at the pinnacle ground of construction, all elevators will come from beneath (none can come from above), and then go away going down, while if one is on the second from the top floor, an elevator going to the pinnacle floor will skip first on the way up, and then rapidly later on at the way down – consequently, whilst a same.

Once the elevator is falling greater than half of as fast as the speed you get via jumping from rest, jumping reduces your energy and could soften the fall. in case you attempted jumping simply as soon because the elevator started to fall, you'll honestly come to be falling from a more height, and hit tougher.

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Six unrelated African American people in the United State are elected at random then the probability that  all three have type O+ blood would be 0.103823

The probability that a person in the United States has type O+ blood is 47%. Three unrelated people in the United States are selected at random. Find the probability that  all three have type O+ blood.

Since the probability of having a O+ blood is an independent event, so to find probability that  all three have type O+ blood we will use multiplication rule of independent events as:

0.47*0.47*0.47= 0.103823

Therefore, the probability that  all three have type O+ blood would be 0.103823

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Answer: 1

Step-by-step explanation: -2 times x the x would just be 1 so -2 times 1 equals -2 then -2 plus 3 is 1

A chart that compares three sets of values in a three-dimension chart is called surface.

A two-dimensional collection of points (flat surface), a three-dimensional collection of points with a curved cross section (curved surface), or the perimeter of any three-dimensional solid are all examples of surfaces in geometry.

A surface is typically a continuous boundary that separates two areas of a three-dimensional space. For instance, a sphere's surface divides its interior from its exterior, and a horizontal plane divides the half-planes above and below it. Despite the fact that regions they contain are three-dimensional and have a volume, surfaces are basically two-dimensional and have an area. Despite this, surfaces are frequently referred to by the names of the regions they surround. Differential geometry studies the characteristics of surfaces, particularly the concept of curvature.

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To carpet the rectangular floor, it will cost $1,137.6. The result if obtained by multiplying the area of the carpet by the cost per square yard.

To calculate the cost of a product, multiply the product price for one item by the quantity.

We have a rectangular floor with a dimension of 27 feet by 24 feet. The carpet cost is $15.8 per square yard. Find the total cost to carpet it!

Let's change the unit of length.

The area of the carpet is

A = 9 yard × 8 yard

A = 72 square yard

The total cost is

C = A × price/square yard

C = 72 × $15.8

C = $1,137.6

Hence, the total cost to carpet the floor is $1,137.6.

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Shortest time taken for a is 0.666hours and for b is 0.866hours.

Take a variable x on the possible road. Evaluate an equation of time in terms of x and find the extrema of the function. To find extrema differentiate the function and equal it to zero. Then find the roots of equation to get the extreme value, which should be the minimum time path.

A is initial point

P is oasis

S is intermediate point

Let us assume he directly reaches  x km from N at S.

then AS=[tex]\sqrt{100+X^2}[/tex] and SP=20-X

Time taken:

[tex]\frac{\sqrt{100+X^2}}{30}[/tex]+[tex]\frac{20-X}{50}[/tex]

Differentiating it and putting this to zero gives extrema value

[tex]\frac{2x}{60(\sqrt{100+X^2})}[/tex]=[tex]\frac{1}{50}[/tex]

⇒[tex]\frac{50x}{30}[/tex]=[tex]\sqrt{100+X^2}[/tex]

⇒By squaring on both sides

⇒100+X^2=[tex]\frac{25x^2}{9}[/tex]

⇒x=7.5km

x is independent of PN as while differentiating PN term became 0

Now time:

a) t= [tex]\frac{\sqrt{100+7.5^2}}{30}[/tex]+[tex]\frac{20-7.5}{50}[/tex]=0.666hours

b) t=[tex]\frac{\sqrt{100+7.5^2}}{30}[/tex]+[tex]\frac{30-7.5}{50}[/tex]=0.866hours

Shortest time taken for a is 0.666hours and for b is 0.866hours.

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Answer:

y = 3x - 3

Step-by-step explanation:

Answer:

y = 3x + 3

Step-by-step explanation:

When two lines are parallel, this means they have the same slope!

So, first, we are going to take the slope from the equation y = 3x - 11 and use it in our new equation

SLOPE = 3

Next, we use the point-slope formula to make a new equation for the coordinate (4,9) ⇒ x = 4 and y = 9

Point-slope equation = y - y1 = m ( x - x1 )

Let's plug in and solve!

y - 9 = 3 ( x - 4 )

Simplify to turn it into INTERCEPT FORM !

y - 9 = 3x - 12

y = 3x + 3

This is the final answer!

I hope I helped! Let me know if you have any questions about my answer! :)

to properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term then it is a true statement

we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.

So, For his purpose, we know that the

A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.

And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.

By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.

So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.

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The solution to the given quadratic equation by completing the square is; x = 3 ± √2

We are given the quadratic equation;

y = x² - 6x + 7

1) Set the value of y to zero to get;

x² - 6x + 7 = 0

2)  Remove the constant term from both sides using the opposite operation to get;

x² - 6x = -7

3) Take half of the x term and square it and add to both sides of the equation to get;
x² - 6x + 9 = -7 + 9

4) Rewrite the perfect square on the left to get;

(x - 3)²  = 2

5) Take the square root of both sides to get;

x - 3 = ±√2

6) The solution will be;

x = 3 ± √2

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Answer: see below

Step-by-step explanation:

They intersect at the point (2,6) which is the solution

Answer:

+$95

Step-by-step explanation:

We want to write a singles number that can represent this change

We know that David received $95

When someone receive something, it is positive

So to represent this, we simply put +$95

David made a profit of 95 dollars as a result of the transaction. As a result, you display this as a positive signed number, which is +95.

Positive numbers are generally used to express positive changes in the world of mathematics, especially when working with signed numbers. In order to describe a change of 95 dollars given to David, you would use a positive signed number, which in this case would be +95. You can tell that this was an increase or gain by putting the plus symbol (plus) before the 95; in this case, David made a profit of 95 dollars.

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Answer:

B

Step-by-step explanation:

they have same slopes,the slopes is 1/2,it mean they can't intersect

Answer:

1 liter

Step-by-step explanation:

A milliliter is 1/1000 of a meter; measuring a pool by millimeters wouldn't make sense.

Answer: 5

Step-by-step explanation:

slope is m in the formula y=mx+b

plug in the numbers for m and that's the slope

Answer:

B

Step-by-step explanation:

Standard Deviation of given set of numbers is 0.71

The two key areas in statistics are variance and standard deviation. It is a metric for statistical data dispersion. The degree to which values in a distribution deviate from the distribution's average is known as dispersion.

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a small variation, and when they are far spaced from the mean, there is a large variation.

Standard Deviation Formula:

σ=[tex]\sqrt{\frac{sigma(xi-m)^2}{n} }[/tex]

Given 6,4,5,5

m=[tex]\frac{6+4+5+5}{4}[/tex]=5;

⇒σ=[tex]\sqrt{\frac{(6-5)^2+(4-5)^2+(5-5)^2+(5-5)^2}{4} }[/tex]=0.707≅0.71

Standard Deviation of given set of numbers is 0.71

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Answer:

-2,838

Step-by-step explanation:

A good way to do this is 2,938-100 which equals 2,838. Then since you know it will be a negative number add the negative sign.

Answer:

15 dimes and 6 pennies

Answer:

The correct answer is (b) SSA.   -- -- Read carefuly for total understanding

Step-by-step explanation:

In geometry, congruence is a relationship between two figures that means they have the same size and shape. In other words, congruent figures can be perfectly superimposed on one another. There are several criteria that can be used to determine whether two triangles are congruent.

However, the SSA (side-side-angle) criterion does not guarantee that two triangles are congruent. In other words, just because two triangles have two sides and the included angle congruent does not necessarily mean that the triangles are congruent. This is why the answer is (b) SSA.

Answer:

True

Step-by-step explanation:

The probabilities of all outcomes add to 1.

Answer:

2.15

Step-by-step explanation:

I will assume that "−1/4(−8.6)" is telling us to multiply (-8.6) times -(1/4):

(-1/4)*(-8.6)

= (8.6/4)

= 2.15

Answer: z=10, y=7

Step-by-step explanation:

z+30=40

y+10=17

solve for z by isolating z, Subtract 30 from both sides

z+30-30=40-30

z=10

solve for y by isolating y, Subtract 10 from both sides

y+10-10=17-10

y=7

If a and b are independent events with p(a) = 0.38 and p(b) = 0.55, then p(a | b) = 0.38

In the given question, a and b are independent events with p(a) = 0.38 and p(b) = 0.55, then we have to find p(a | b).

Events classified as independent do not depend on other events for their occurrence.

The likelihood of both A and B happening is equal to the sum of the probabilities of A and B, which is how mathematics expresses the independence of events A and B.

If A and B are independent events, then

P(A and B) = P(A) * P(B)

Then P(A | B) = P(A and B) / P(B)

P(A | B) = P(A) * P(B) / P(B)

P(A | B) = P(A) = 0.38

Hence, if a and b are independent events with p(a) = 0.38 and p(b) = 0.55, then p(a | b) = 0.38.

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Answer:

Dilation

-by-step explanation:

the figure is dilated (larger than original)

Step-by-step explanation:

since the roller coaster takes always 8 people at a time, this problem is simply to find how often 8 fits into 346 and how many people are remaining (when we cannot fill all 8 places anymore at the end).

that is what division is for.

346 / 8 = 43 and remainder 2

as 8×43 = 344, plus 2 is then 346.

so, the remainder (2 people) will be on the last ride.

To find the number of people on the last ride of the roller coaster, divide the total number of people waiting in line by the number of people the roller coaster can fit at a time.

To find the number of people on the last ride of the roller coaster, we need to divide the total number of people waiting in line by the number of people the roller coaster can fit at a time. In this case, we have 346 people waiting and the roller coaster can fit 8 people at a time. Dividing 346 by 8 gives us 43 with a remainder of 2. This means that there will be 43 full rides, and on the last ride, there will be 2 people left.

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The 5th value of the 60% percentile is 47 when for each test score in the data set is 12, 28, 35, 47, 49, 50.

Given that,

For each test score in the data set, the percentile rank is determined. 12, 28, 35, 42, 47, 49,  

We have to find what number represents the 60% of the population.

We know that,

So,

Percentile rank =[(Number of values below x)+0.5]/ total number of values × 100

For 12,

Percentile rank = [0 +0.5]/7×100

= 7th

For 28,

Percentile rank = [1 +0.5]/7×100

= 21st

For 35,

Percentile rank = [2 +0.5]/7×100

= 36th

For 42,

Percentile rank = [3 +0.5]/7×100

= 50th

For 47,

Percentile rank = [4 +0.5]/7×100

= 64th

For 49,

Percentile rank = [5 +0.5]/7×100

= 79th

For 50,

Percentile rank = [6 +0.5]/7×100

= 93rd

Now,

n = 7

60th percentile = 60% of n

So,

60% of n = 60/100×7

= 0.6×7

= 4.2

Therefore, The 5th value of the 60% percentile is 47 when for each test score in the data set is 12, 28, 35, 47, 49, 50.

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