Linear regression describes the extent to which _______ predicts ________.

Please see attached document for the graphs:

The functions with the given graphs can't be solutions of the differential equation dy dt = et(y − 1)2.

(a) won’t work, since it has negative slope on portions of its solutions. The slope, e t (y − 1)2 , is a nonnegative function.

(b) won’t work, since it has positive slope at y = 1, where the slope must be flat.

Functions with given graphs cannot be solutions to the differential equation dy / dt = e^t(y-1)^2 because their graphs don't satisfy the conditions imposed by the equation, such as non-oscillatory behavior and non-linear variation with time.

The question pertains to why certain functions represented by their graphs cannot be solutions to the differential equation dy / dt = et(y-1)2. The explanation lies in the structure of the given differential equation and the properties of function graphs.

Equation dy / dt = et(y-1)2 is a non-linear first order differential equation. To be a solution to this equation, a function's graph must satisfy certain conditions imposed by the equation. However, if certain function graphs represent an undefined curve or if their graphs demonstrate oscillatory behavior, they do not satisfy these criteria.

For instance, the differential equation demands non-oscillatory behavior as seen in the general solution provided in the reference: Yn(x) = Ce-Bx +De+Bx. This form describes a gradual attenuation of y(x), i.e., it does not oscillate. Similarly, if a graph represents a function that varies non-linearly with time (like In[A] vs. Time), it does not represent a solution to the differential equation as well.

Thus, the inability of certain function graphs to satisfy the conditions required by the given differential equation is the reason they cannot be its solutions.

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Answer: The second statement is true. It is a reduction because 0 < n < 1.

Step-by-step explanation:

Given: A triangle is dilated by a scale factor of n = 1/3 .

as n is less than 1 but greater than 0.

A dilation is a rigid transformation that forms an image that is the same shape as of the original figure, but with a different size.  A dilation transform a figure by scalar factor 'n' about the center of dilation is a fixed point in the plane which never change.

A dilation that forms a larger image is known as enlargement.  A dilation that forms a smaller image is known as reduction.

• If n is greater than 1, then the image is an enlargement.

• If n is between 0 and 1, then the image is a reduction .

• If n is 1, the figure and then the image are exactly same.

Answer:

2nd statement

Step-by-step explanation:

Answer: Weight of the oil is 672.74 grams.

Step-by-step explanation:

Since we have given that

Radius of cylinder = 5 cm

Height of cylinder = 10 cm

Volume of cylinder would be

[tex]\pi r^2h\\\\=3.14\times 5\times 5\times 10\\\\=785\ cm^3[/tex]

Weight of 10W-40 oil = 0.857 grams per cubic cm

So, Weight of the oil in the can would be

Volume × Weight per cm³

[tex]=785.71\times 0.857\\\\=672.74\ grams[/tex]

Hence, Weight of the oil is 672.74 grams.

7/10-1/5 = 7/10-2/10 = 5/10 = 1/2

 so 280 pennies fills 1/2 of her piggy bank

 so 280*2 = 560

her piggy bank can hold 560 pennies

1 gallon = 231 cubic inches

7cm = 2.75591 inches ( round to 2.76 )

10 x 10 x 2.76 = 276 cubic inches

there will be more than enough room for the gallon of paint

276-231 = 45 cubic inches of space left over

Answer:

B) 6,700,000,000 people.

Step-by-step explanation:

We have been given that in 2008, there were [tex]6.7\times 10^9[/tex] people living on earth. We are asked to convert our given population in standard notation.

While changing scientific notation to standard notation we just move the decimal as many times as the exponent indicates. We can see that our exponent is 9, so we will move the decimal to 9 places right.

[tex]6.7\times 10^9=6.7\times 1000000000[/tex]

[tex]6.7\times 10^9=6700000000[/tex]

Therefore, there were 6,700,000,000 people living on earth and option B is the correct choice.

Answer:

B.)6,700,000,000

Step-by-step explanation:

SO when you have to transform from the scientific notation into standar notation, you just have to move the decimal point to the right the number of positions that the scientific notation has as the exponent, in this case it is 9, so you move one position the decimal point to the right to make the number 67, and then add 8 zero´s to the right:

6,700,000,000

As you can see you moved the decimal point 9 positions to the right.

So that´s how you can convert scientific notation to standard notation.

The coordinates of the points of intersections of [tex]l[/tex] and the curve are [tex](x_{1}, y_{1}) = (4,3)[/tex] and [tex](x_{2}, y_{2}) = (1.5, 8)[/tex].

According to the statement, we get the following nonlinear system of equations:

[tex]x\cdot y = 12[/tex] (1)

[tex]2\cdot x + y = 11[/tex] (2)

Now we proceed to solve for each variable by algebraic means. By (1):

[tex]y = \frac{12}{x}[/tex]

Then we apply the formula in (2):

[tex]2\cdot x + \frac{12}{x} = 11[/tex]

[tex]2\cdot x^{2}+12 = 11\cdot x[/tex]

[tex]2\cdot x^{2}-11\cdot x +12 = 0[/tex]

Roots are found by the quadratic formula and (1):

[tex]x_{1} = 4[/tex], [tex]y_{1} = 3[/tex]

[tex]x_{2} = 1.5[/tex], [tex]y_{2} = 8[/tex]

The coordinates of the points of intersections of [tex]l[/tex] and the curve are [tex](x_{1}, y_{1}) = (4,3)[/tex] and [tex](x_{2}, y_{2}) = (1.5, 8)[/tex].

We kindly invite to check this question on systems of equations: https://brainly.com/question/9351049

13 hearts

 a 13/52 probability.

that reduces to a 1/4 probability of getting a heart

Answer: 40 inches squared

Step-by-step explanation:

1. first, you multiply, do 5*16 what does that give you? (80)

2. then, divide your answer by 2 what do you get? (40)

3. lastly, it should look like this: 5*16=(answer)/2=(answer)

hope this helps

I think it's 2(x+3).

Answer: 2(x+3)

paralyzed;live

Final answer:

The probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%, calculated using the Central Limit Theorem to find the standard error and z-scores.

Explanation:

To calculate the probability that the sample mean diameter of the tennis balls is between 2.62 and 2.64 inches, we can use the Central Limit Theorem since we are dealing with a sample of tennis balls rather than just one. The Central Limit Theorem tells us that the sampling distribution of the sample mean will be normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is called the standard error (SE).

Given that the population mean (μ) is 2.63 inches, the population standard deviation (σ) is 0.03 inch, and the sample size (n) is 9, we first calculate the standard error (SE) as follows:

SE = σ / √n = 0.03 / √9 = 0.03 / 3 = 0.01 inch.

Next, we convert the sample mean range (2.62, 2.64) to z-scores, which are measures of how many standard deviations an element is from the mean.

Z for 2.62 = (2.62 - μ) / SE = (2.62 - 2.63) / 0.01 = -0.01 / 0.01 = -1
Z for 2.64 = (2.64 - μ) / SE = (2.64 - 2.63) / 0.01 = 0.01 / 0.01 = 1

Using a standard normal distribution table or calculator, we find the probabilities corresponding to these z-scores. The probability of a z-score being between -1 and 1 is approximately 0.6827 (68.27%).

Therefore, the probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%.