Compute the least-squares regression line for the given data set. Use a TI-84 calculator. Round final answers to four decimal places, as needed.
x 5 7 6 2 1
y 4 3 2 5 1
Regression line equation: ŷ = _______ + _______ x.

Answer:

A. they are parallel because their slopes are equal.

Step-by-step explanation:

edge 2020

Answer:

its A in egde

Step-by-step explanation:

Answer:

5x^3-2

[tex]ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2[/tex]

Explanation:

The two terms are [tex]5x^3[/tex] and [tex]2[/tex]. Terms are separated by either a plus or minus.

We can write it as [tex]5x^3+(-2)[/tex] which is an equivalent form. Here the two terms are [tex]5x^3[/tex] and [tex]-2[/tex]. This is because adding a negative is the same as subtracting.

The coefficient is the number to the left of the variable.

The degree is the largest exponent, which helps form the leading term.

The third degree polynomial written above is considered a cubic binomial. "Cubic"  refers to the third degree, while "binomial" means there are 2 terms.

We can write something like [tex]5x^3[/tex] as 5x^3 when it comes to computer settings.

[tex]_9C_7=\dfrac{9!}{7!2!}=\dfrac{8\cdot9}{2}=36[/tex]

Answer:

7.5 cm²

Step-by-step explanation:

Dimensions of the large ∆:

[tex] base (b) = 3cm, height (h) = 9cm [/tex]

[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]

Dimensions of the small ∆:

[tex] base (b) = 2cm, height (h) = 6cm [/tex]

[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]

Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²

Answer:

36

Step-by-step explanation:

formula of area for square:

A=s^2

s=6

A=6^2

A=36

Answer:

36

Step-by-step explanation:

I got it right

Answer:

Low             Q1                Median              Q3                 High

6                  9                     11                      12.5                14

The interquartile range = 3.5

Step-by-step explanation:

Given that:

Consider the following ordered data. 6 9 9 10 11 11 12 13 14

From the above dataset, the highest value = 14  and the lowest value = 6

The median is the middle number = 11

For Q1, i.e the median  of the lower half

we have the ordered data = 6, 9, 9, 10

here , we have to values as the middle number , n order to determine the median, the mean will be the mean average of the two middle numbers.

i.e

median = [tex]\dfrac{9+9}{2}[/tex]

median = [tex]\dfrac{18}{2}[/tex]

median = 9

Q3, i.e median of the upper half

we have the ordered data = 11 12 13 14

The same use case is applicable here.

Median = [tex]\dfrac{12+13}{2}[/tex]

Median = [tex]\dfrac{25}{2}[/tex]

Median = 12.5

Low             Q1                Median              Q3                 High

6                  9                     11                      12.5                14

The interquartile range = Q3 - Q1

The interquartile range =  12.5 - 9

The interquartile range = 3.5

Answer:

see below

Step-by-step explanation:

Difference is subtract

(8-2)

Then add this to x

(8-2) +x

6+x

Answer:

150,000

Step-by-step explanation:

1 m = 100 cm

260 m = 260 * 100 cm = 26000 cm

15 m = 15 * 100 cm = 1500 cm

area of floor = LW = 26000 cm * 1500 cm = 39,000,000 cm^2

area of 1 tile = 26 cm + 10 cm = 260 cm^2

number of tiles needed = 39,000,000/260 = 150,000

Answer: 150,000 tiles

Answer:

x

Step-by-step explanation:

probability is the branch of mathematics concerning numeral descriptions of how likely an event is to occur or how likely it is that a proposition is true

Answer:

3

Step-by-step explanation:

f(x)=3x-3

g(x)=-x^2+4,

f(2) = 3(2) -3 = 6-3 =3

g(-2) = -(-2)^2+4 = -4+4 = 0

f(2)-g(-2)= = 3-0 = 3

Answer:

B

Step-by-step explanation:

x can not be greater than (1,325-270)/26 because $270 is fixed for the rental

Answer:

50%

Step-by-step explanation:

Girls                                            Boys

total:                 59                     total:                              41

- Chemistry       35                   - Physics                           2

                       = 24                                    =                     39

                                                 - Chemistry ( 30 - 6 )      24

                                                                   =                     15

Total boys and girls for Biology = 35 + 15 = 50

% = 50/100*100

   = 50%

Answer:

See below.

Step-by-step explanation:

First, recall the meanings of the domain and range.

The domain is the span of x-values covered by the graph.

And the range is the span of y-values covered by the graph.

1)

So, we have here an absolute value function.

As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:

[tex]\{x|x\in\textbb{R}\}[/tex]

(You are correct!)

For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:

[tex]\{y|y\leq 7\}[/tex]

2)

We have here an ellipse.

First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:

[tex]-4\leq x\leq 6[/tex]

So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:

[tex]\{x|-4\leq x\leq 6\}[/tex]

For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:

[tex]-5\leq y\leq 1[/tex]

This represents all the y-values between -5 and 1, including -5 and 1.

In set notation, thi is:

[tex]\{y|-5\leq y\leq 1\}[/tex]

Answer:

C. -8, -6, -4, -2, ...

Step-by-step explanation:

An arithmetic sequence increases by the same amount every time through addition or subtraction. There is a common difference.

A: -2, 4, -6, 8, ... If there were a common difference, the numbers would not switch between being positive and back to negative. The numbers would either keep going positive or keep going negative.

B: 2, 4, 8, 16, ... The common difference between 16 and 8 is 16 - 8 = 8. The difference between 8 and 4 is 8 - 4 = 4. Since the difference changes between the numbers, this is not an arithmetic sequence.

C. -8, -6, -4, -2, ... The common difference between -2 and -4 is -2 - (-4) = -2 + 4 = 2. The difference between -4 and -6 is -4 - (-6) = -4 + 6 = 2. The difference between -6 and -8 is -6 - (-8) = -6 + 8 = 2. Since the common difference is always two, this is an arithmetic sequence.

Hope this helps!

Answer:

x = 2 and x = -2

Step-by-step explanation:

To find the vertical asymptotes, set the denominator equal to zero and solve for x:

vertical asymptotes are x = 2 and x = -2

Step-by-step explanation:

Hello, there!!!

It's so simple here,

Here,

we have is 1 angle is 120°and other is 3x°.

now,

3x°=120° {because when two st.line intersects eachother then the opposite angle formed are equal}

so, 3x°=120

or, x=120°/3

=40°

Therefore, the value of x is 40°.

Hope it helps....

Answer:

  17 by 21 inches

Step-by-step explanation:

The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...

  L + W = 38

  LW = 357

__

Solution:

  W(38 -W) = 357 . . . . . substitute for L

  -(W^2 -76W) = 357 . . expand on the left

  -(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square

  (W -19)^2 = 4 . . . . . . . write as a square

  W -19 = ±√4 = ±2 . . . take the square root; next, add 19

  W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other

The dimensions are 17 by 21 inches.

Answer:

Step-by-step explanation:

First we start with 12 pounds

On Monday, she and her friends eat 4 pounds. So we have 8 now.

On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.

On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15

On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.

On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.

On Saturday, her mom gives her one more pound. 2 + 1 = 3.

On Sunday, she finally has 3 pounds.

Answer:

nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Step-by-step explanation:

Answer:

First convert them which will be

-7/5 - (-4/5)

so when you subtract a negative number from negative number they actually subtract ex = -4-(-2) = -2

so its simply 7/5-4/5 then add a negative sign

so

3/5

now add negative sign so

-3/5

Answer:

4/7

Step-by-step explanation:

divide both by two for its simplest form

Answer:4/7

Step-by-step explanation

Divide both the numerator and denominator by 2

The result for the numerator is 8/2=4

that of the denominator is 14/2=7

Therefore the resultant answer is 4/7

Answer:

  subtracting 56 instead of adding (or adding wrong)

Step-by-step explanation:

She wrote ...

  x - 56 = 230

  x - 56 - 56 = 230 -56 . . . . correct application of the addition property*

  x = 230 -56 . . . . . . . . . . . . incorrect simplification

Correctly done, the third line would be ...

  x -112 = 174

This would have made Sherina realize that the error was in subtracting 56 instead of adding it. The correct solution would be ...

  x - 56 + 56 = 230 + 56 . . . using the addition property of equality

  x = 286 . . . . . . . . . . . . . . . . correct simplification on both sides

__

There were two errors:

  1) incorrect strategy --- subtracting 56 instead of adding

  2) incorrect simplification --- simplifying -56 -56 to zero instead of -112

We don't know whether you want to count the error in thinking as the first error, or the error in execution where the mechanics of addition were incorrectly done.

_____

* The addition property of equality requires the same number be added to both sides of the equation. Sherina did that correctly. However, the number chosen to be added was the opposite of the number that would usefully work toward a solution.

Answer:

D: Sherina should have added 56 to both sides of the equation.

Step-by-step explanation:

I got a 100% on my test.

I hope this helps.

Answer:

The  90% confidence interval is  [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  64

     The sample  mean is  [tex]\= x = \$ 32, 000[/tex]

     The  standard deviation is  [tex]\sigma= \$ 8, 200[/tex]

Given that the confidence interval is  90% then the level of significance is mathematically evaluated as

             [tex]\alpha = 100 - 90[/tex]

             [tex]\alpha = 10 \%[/tex]

            [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table , the value is  

       [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

  Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{ \sqrt{n} }[/tex]

  =>   [tex]E = 1.645 * \frac{ 8200 }{ \sqrt{64} }[/tex]

  =>   [tex]E = 1686.13[/tex]

The 90% confidence interval is mathematically represented as

      [tex]\= x - E < \mu < \= x + E[/tex]

 =>    [tex]32000 - 1689.13 < \mu < 32000 + 1689.13[/tex]

=>    [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]

Answer:

[tex]\huge\boxed{a=9 ; b = -8}[/tex]

Step-by-step explanation:

[tex]f(x) = \frac{ax+b}{x}[/tex]

Putting x = 1

=> [tex]f(1) = \frac{a(1)+b}{1}[/tex]

Given that f(1) = 1

=> [tex]1 = a + b[/tex]

=> [tex]a+b = 1[/tex]  -------------------(1)

Now,

Putting x = 2

=> [tex]f(2) = \frac{a(2)+b}{2}[/tex]

Given that f(2) = 5

=> [tex]5 = \frac{2a+b}{2}[/tex]

=> [tex]2a+b = 5*2[/tex]

=> [tex]2a+b = 10[/tex]  ----------------(2)

Subtracting (2) from (1)

[tex]a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9[/tex]

For b , Put a = 9 in equation (1)

[tex]9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8[/tex]

(a)

[tex]\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)[/tex]

[tex]\dfrac{\partial f}{\partial y}=\dfrac{\mathrm dg}{\mathrm dy}=y^2\implies g(y)=\dfrac{y^3}3+C[/tex]

[tex]\implies f(x,y)=\dfrac{x^3+y^3}3+C[/tex]

(b)

[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\mathbf r=f(2,8)-f(-1,2)=\boxed{171}[/tex]

Answer:

D question,somewhat confusing, itsit's like simultaneous equation,but values are different

Answer:

x = 4 + 2y/3

Step-by-step explanation:

Answer:

0.000014

Step-by-step explanation:

The chart is not provided so i will use an example chart to explain the answer. Here is a sample chart:

City X's Population by Age

0-24 years old 33%

25-44 years old 22%

45-64 years old 21%

65 or older 24%

In order to find probability of independent events we find the probability of each event occurring separately and then multiply the calculated probabilities together in the following way:

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

probability that the first 2 are 65 or older

Let A be the event that the first 2 are 65 or older

The probability of 65 or older 24% i.e. 0.24

So the probability that first 2 are 65 or older is:

0.24(select resident 1) * 0.24(select resident 2)

P(A) = 0.24 * 0.24

       = 0.0576

P(A) = 0.0576

probability that the next 3 are 25-44 years old

Let B be the event that the next 3 are 25-44 years old

25-44 years old 22%  i.e. 0.22

So the probability that the next 3 are 25-44 years old is:

0.22 * 0.22* 0.22

P(B) = 0.22 * 0.22 * 0.22

      = 0.010648

P(B) = 0.010648

probability that next 2 are 24 or younger

Let C be the event that the next 2 are 24 or younger

0-24 years old 33% i.e. 0.33

So the probability that the next 2 are 24 or younger is:

0.33 * 0.33

P(C) = 0.33 * 0.33

       = 0.1089

P(C) = 0.1089

probability that last is 45-64 years old

Let D be the event that last is 45-64 years old

45-64 years old 21%  i.e. 0.21

So the probability that last is 45-64 years old is:

0.21

P(D) = 0.21

So probability of these independent events is computed as:

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

                                        = 0.0576 * 0.010648  * 0.1089  * 0.21

                                        = 0.000014

Answer:

60

Step-by-step explanation:

5 is 60 inch

Answer:

Step-by-step explanation:

A probability density function (pdf) is used for continuous random variables. That is why p is between 0 and 1 (the two extremes - 0 and 1 - exclusive).

X = 100pth percentile of W

Y = 100(1-p)th percentile of W

Expressing Y as a function of X;

Y = 100(1-p)th = 100th - 100pth

Recall that 100pth is same as X, so substitute;

Y = 100th - X

where 100th = hundredth percentile of W and X = 100pth percentile of W  

Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

We have a line of best fit:

h = –21.962x + 114.655

As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.

Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

Learn more about the line of best fit here:

brainly.com/question/14279419

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