"The fitted regression line will always run through the mean of the observed data. In other words, the point (x with bar on top, y with bar on top) will always lie on the estimated (fitted) regression line. Is it true or false?"

Answer:

The function is always increasing

Step-by-step explanation:

To be increasing, the y value needs to be getting bigger as x gets bigger

This is true for all values of x

The function is increasing for all values of x

Answer:

The 90% confidence interval is (0.0131, 0.0845).

Step-by-step explanation:

Before finding the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Old process:

125 out of 580, so:

[tex]p_O = \frac{125}{580} = 0.2155[/tex]

[tex]s_O = \sqrt{\frac{0.2155*0.7845}{580}} = 0.0171[/tex]

New process:

130 out of 780. So

[tex]p_N = \frac{130}{780} = 0.1667[/tex]

[tex]s_N = \sqrt{\frac{0.1667*0.8333}{780}} = 0.0133[/tex]

Distribution of the difference:

[tex]p = p_O - p_N = 0.2155 - 0.1667 = 0.0488[/tex]

[tex]s = \sqrt{s_O^2+s_N^2} = \sqrt{0.0171^2 + 0.0133^2} = 0.0217[/tex]

Confidence interval:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower bound of the interval is:

[tex]p - zs = 0.0488 - 1.645*0.0217 = 0.0131[/tex]

The upper bound of the interval is:

[tex]p + zs = 0.0488 + 1.645*0.0217 = 0.0845[/tex]

The 90% confidence interval is (0.0131, 0.0845).

Answer:

C

Step-by-step explanation:

the fibrin definition tells us that the first term of the sequence a1 = 6

so, B is out.

and for every following term we always add 7 to every previous term to create the next one.

so, when I add 7 to 6, what is my second term in the sequence ? 7+6 = 13

not 42, not -7

therefore, only C is correct.

and 13+7 = 20

and 20+7 = 27

it all fits

Answer:

Your dollar target for food service is $22,680

Step-by-step explanation:

It is given in the question that total sales are = $54,000

your food service is 42% of your total sales = 42% × $54,000

=  × 54,000

= 0.42 × 54,000

= $22,680

Work Shown:

1 pack of white = 2 shirts = A

1 pack of blue = 6 shirts

5 packs of blue = 5*6 = 30 shirts = B

A+B = 2 white shirts + 30 blue shirts = 32 shirts total

Answer:

32 T-shirts in total

Step-by-step explanation:

1 white has 2

1 blue has 6

1*2=2 white T

5*6=30  blue T

30+2=32

Step-by-step explanation:

SO, OT is parallel to the vector a+2b

Answer:

12 cm

Step-by-step explanation:

12+26/2 ×x =228

19x =228

X=12cm

Answer:

1500000

Step-by-step explanation:

1 metre = 100 cm

15000metre =15000*100

=1500000

Answer:

A. x = 1/2

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4x² + 3 = 4x + 2

Step 2: Solve for x

Answer:

-3/2 ±1/2 sqrt(5) = x

Step-by-step explanation:

f(x) = 2x^2 + 6x + 2

Set the function equal to 0

0 = 2x^2 + 6x + 2

Factor out 2

0 = 2(x^2 + 3x + 1)

Divide by 2

0 = (x^2 + 3x + 1)

Subtract 1 from each side

-1 = x^2 +3x

Complete the square by dividing the x coefficient by 2 and then squaring

(3/2)^2 = 9/4

-1 +9/4 = x^2 +3x+9/4

-4/4+9/4 = (x+3/2) ^2

5/4 = (x+3/2) ^2

Taking the square root of each side

± sqrt(5/4) = sqrt( (x+3/2) ^2)

±1/2 sqrt(5) =  (x+3/2)

Subtract 3/2 from each side

-3/2 ±1/2 sqrt(5) = x

Answer:

7 and 10

Step-by-step explanation:

7 * 10 = 70

7 + 10 = 17

Answer:

10 and 7

Step-by-step explanation:

call them a and b, respectively

so a*b=70 -> b=70/a

a+b=17 ->a+70/a=17 ->a=10 b =7

Answer:

Step-by-step explanation:

192

Answer:

Step-by-step explanation:

Answer:

[tex]0.76d[/tex]

Step-by-step explanation:

Given

[tex]Formula = d - (0.24)d[/tex]

Required

Equivalent expression

We have:

[tex]Formula = d - (0.24)d[/tex]

Open bracket

[tex]Formula = d - 0.24d[/tex]

[tex]Formula = 0.76d[/tex]

Answer:

part 1:

a) After 37.72 years, there will be $270,183.29421

b) After 11.9 years, there will be double the amount originally put in the account(60,015.17148)

part 2:

38 years

Step-by-step explanation:

a)

30000(1.06)^t

t=37.72

30000(1.06)^37.73 = 270,183.29421

b)

30000(1.06)^t

t=11.9

30000(1.06)^11.9 = 60,015.17148

part 2)

37.72 rounded to the nearest tenth is 38

... select this as the brainliest please!!...

Answer:

x = 8

Step-by-step explanation:

The question had specified that x is equal to 8.

x=8

please mark this answer as brainlist

Answer:

5а⁶=а⁶+а⁶+а⁶+а⁶+а⁶

~~~~~~~~

Answer: The area is 22 17/64.

Step-by-step explanation:

base = 7 1/8 = 57/8

height = 6 1/4 = 25/4

area = 1/2*b*h

= 1/2*57/8*25/4

= 1425/64

= 22 17/64

There are 365 ways of forming an executive Committee of four in a social club consisting of 15 members

If a particular man must be in the committee, we can choose the remaining 3 members from the remaining 14 members. The number of ways to choose 3 members from 14 is given by the combination:

14Cr3 = [tex]\frac{14!}{3! 11!}[/tex] = [tex]\frac{14x13x12}{3x2x1}[/tex] = 364

Therefore, there are 364 ways of forming an executive committee of four in a social club consisting of 15 members, if a particular man must be in the committee.

Learn more about combination here:

https://brainly.com/question/28065038

#SPJ1

Answer:

Simpler equations and inequalities as such could be typed into an online graphing calculator such as Desmos! Remember this because you'll need it for future harder math classes :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

a1 = 3

d = -3

an = a1 + (n - 1)*d

an = a1 + (n - 1)*-3

Try it

Let n = 5

a5 = 3 + (5 - 1)*-3

a5 = 3 + 4*-3

a5 = 3 - 12

a5 = - 9 which is exactly what it should be.

The interesting one to try is n = 2

a2 = a1 + (2 - 1)*-3

a3 = 3  + 1(-3)

a3 = 3 - 3

a3 =0

Which is exactly what the second term is. It's interesting because you would never guess that 0 is what you get.

Answer:

17ft

Step-by-step explanation:

5*2 + 3.5*2=17

Answer:

click in photo

nejdjjd

nxndjdbbdjf

lấy x=0 ta có y= -2 => A(0;-2)

lấy y=0 ta có x=2 => B(2;0)

nối 2 điểm A và B ta có đồ thị:

hi  

x/6 = 10

In a equation , you can use every math operation you know as long as you do the same thing on both sides.  

Here we have   x/6 = 10  

But what I want is  x .  

Here X is split in 6.  So  I 'm going to multiplicate all by 6 to find the original amount of X  

In bold operation that are often not written but that you must understand to do that kind of exercices.

So  :  x/6 = 10

      (x/6) *6  = 10 *6

        6x/6 =  60

             x = 60

Answer: -2(d) is the answer.

Step-by-step explanation:

x1 = 3

y1 = -5

x2 = -2

y2 = 5

slope (m) = rise/run = (y2 - y1)/(x2-x1)

                                =(5-(-5))/(-2-3)

                                 =   10/-5

                                 = -2

Answer:

Step-by-step explanation:

The one-to-one functions g and h are defined as follows.

g={(-7,-6), (-5,4), (4,-7)(7,6)}

h(x)= 3x-14

Find the following.

g-1(4)=

"g-1(4)" just says "Find the pair of coordinates that has 4 for its

y-coordinate, and the answer is its x-coordinate".  So we look through those

and find (-5,4) is the only one of those up there that has a 4 for it's y-

coordinate, and so its x-coordinate is -5 and we write:

g-1(4)=-5  

The Required value for the function are:

1. g⁻¹(-3) = -1.

2. h⁻¹(x) = (x - 2) / 7.

3. (h o h⁻¹)(0) = -16/49.

1. g⁻¹(-3):

Looking at the pairs in g, we can see that (-1, -3) is the pair where the output is -3.

Therefore, g⁻¹(-3) = -1.

2. h⁻¹(x):

To find h⁻¹(x), we need to solve the equation h(y) = x for y.

The given function h(x) = (x - 2) / 7.

So, let's substitute y for h⁻¹(x):

(x - 2) / 7 = y

x - 2 = 7y

Now, solve for y by dividing both sides by 7:

y = (x - 2) / 7

Therefore, h⁻¹(x) = (x - 2) / 7.

3. (h o h⁻¹)(0):

To find (h o h⁻¹)(0), we need to evaluate the composition of h and h⁻¹ at 0.

First, we find h⁻¹(0):

h⁻¹(0) = (0 - 2) / 7 = -2/7

Now, we substitute h⁻¹(0) into h:

h(h⁻¹(0)) = h(-2/7) = (-2/7 - 2) / 7 = (-2 - 14) / 49 = -16/49

Therefore, (h o h⁻¹)(0) = -16/49.

Learn more about Function here:

https://brainly.com/question/30721594

#SPJ2

Answer:

%17.80

Step-by-step explanation:

17.8% is the probability that more than 4 are wearing their seat belts.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that Police estimate that 25% of drivers drive without their seat belts.

If they stop 6 drivers at random we need to find the probability that more than 4 are wearing their seat belts.

For each driver stopped, there are only two possible outcomes. Either they are wearing their seatbelts, or they are not.

he drivers are chosen at random, which mean that the probability of a driver wearing their seatbelts is independent from other drivers.

Police estimate that​ 25% of drivers drive without their seat belts.

This means that 75% wear their seatbelts, so P=0.75

If they stop 6 drivers at​ random, find the probability that all of them are wearing their seat belts.

[tex]P(X=x)=C_{n,x} p^{x} (1-p)^{n-x}[/tex]

[tex]P(X=6)=C_{6,6} 0.75^{6} (1-0.75)^{0} =0.1780[/tex]

Hence, 17.8% is the probability that more than 4 are wearing their seat belts.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ5

Answer:

1/4

Step-by-step explanation:

12/4= 3

Each paid $3 but as a fraction 3/12=1/4

Answer:

[tex] \frac{1}{4} [/tex]

Step-by-step

12÷4=3

3/12=1/4-each pay this fraction

Answer:

x = -5

Step-by-step explanation:

4-2(x+7) = 3(x+5)

Distribute

4 - 2x-14 = 3x+15

Combine like terms

-2x-10 = 3x+15

Add 2x to each side

-2x-10 +2x =3x+2x+15

-10 = 5x+15

Subtract 15 from each side

-10-15 = 5x+15-15

-25 = 5x

Divide by 5

-25/5 = 5x/5

-5 =x