which of the following is a geometric sequence -3,3,-3,3... 11,16,21,26, ... 6, 13, 19, 24, ... -2,6,14,22, ...

Answer:

35

Step-by-step explanation:

3x7=35

There are 60 students and 13 teachers on a bus .what is the ratio of students to teachers.

Answer:

0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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]

A hotel manager believes that 23% of the hotel rooms are booked.

This means that [tex]p = 0.23[/tex]

Sample of 610 rooms

This means that [tex]n = 610[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.23[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{610}} = 0.017[/tex]

What is the probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%?

p-value of Z when X = 0.23 + 0.03 = 0.26 subtracted by the p-value of Z when X = 0.23 - 0.03 = 0.2. So

X = 0.26

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.26 - 0.23}{0.017}[/tex]

[tex]Z = 1.76[/tex]

[tex]Z = 1.76[/tex] has a p-value of 0.9608

X = 0.2

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.2 - 0.23}{0.017}[/tex]

[tex]Z = -1.76[/tex]

[tex]Z = -1.76[/tex] has a p-value of 0.0392

0.9608 - 0.0392 = 0.9216

0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%

Solution :

a). [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y)$[/tex]

  Now, if X = Y, then :

  [tex]P(X|Y)=\left\{\begin{matrix} 1,& \text{if } x=y \\ 0, & \text{otherwise }\end{matrix}\right.[/tex]

Then, E[X|Y] = x = y

So, [tex]$\text{Var} (X|Y) =E((X-X)^2 |Y)$[/tex]

                      [tex]$=E(0|Y)$[/tex]

                      = 0

Therefore, this statement is TRUE.

b). If X = Y , then Var (X) = Var (Y)

And as Var (X|Y) = 0, so Var (X|Y) ≠ Var (X), except when all the elements of Y are same.

So this statement is FALSE.

c). As defined earlier,

  [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y=y)$[/tex]

  So, this statement is also TRUE.

d). The statement is TRUE because [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y=y)$[/tex].

e). FALSE

   Because, [tex]$\text{Var} (X|Y) =E ((X-E(X|Y=y))^2 |Y=y)$[/tex]

Answer:

Step-by-step explanation:

(x+3)(x+1)=1

x²+3x+x+3=1

x²+4x+2=0

x²+4x+4=-2+4

(x+2)²=2

x+2=±√2

x=2+√2

and x=2-√2

so x≠-3

and x≠-1

Answer:

[tex]{ \bf{c). \: g(x) = {2}^{x} - 2 }}[/tex]

Answer:

the car travels 10km then 15km 60* north of east

Step-by-step explanation:

Answer:

f(-1) = 1

f(0) = 20

f(2) = 38

Step-by-step explanation:

f(-1) = 9×-1 + 10 = -9 + 10 = 1

f(0) = 9×0 + 20 = 0 + 20 = 20

f(2) = 9×2 + 20 = 18 + 20 = 38

we needed to use the second definition for f(0), because that is the same as saying x=0.

and that is in the domain of the second function definition ( x>=0).

Answer:

We know that for a line:

y = a*x + b

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

Any line with a slope equal to -(1/a) will be perpendicular to the one above.

So here we start with the line:

3x + 4y + 5 = 0

let's rewrite this as:

4y = -3x - 5

y = -(3/4)*x - (5/4)

So a line perpendicular to this one, has a slope equal to:

- (-4/3) = (4/3)

So the perpendicular line will be something like:

y = (4/3)*x + c

We know that this line passes through the point (a, 3)

this means that, when x = a, y must be equal to 3.

Replacing these in the above line equation, we get:

3 = (4/3)*a + c

c = 3 - (4/3)*a

Then the equation for our line is:

y = (4/3)*x + 3 - (4/3)*a

We can rewrite this as:

y = (4/3)*(x -a) + 3

now we need to find the point where this line ( y = -(3/4)*x - (5/4)) and the original line intersect.

We can find this by solving:

(4/3)*(x -a) + 3 =  y = -(3/4)*x - (5/4)

(4/3)*(x -a) + 3  = -(3/4)*x - (5/4)

(4/3)*x - (3/4)*x = -(4/3)*a - 3 - (5/4)

(16/12)*x - (9/12)*x = -(4/3)*a - 12/4 - 5/4

(7/12)*x = -(4/13)*a - 17/4

x = (-(4/13)*a - 17/4)*(12/7) = - (48/91)*a - 51/7

And the y-value is given by inputin this in any of the two lines, for example with the first one we get:

y =  -(3/4)*(- (48/91)*a - 51/7) - (5/4)

  = (36/91)*a + (153/28) - 5/4

Then the intersection point is:

( - (48/91)*a - 51/7,  (36/91)*a + (153/28) - 5/4)

And we want that the distance between this point, and our original point (3, a) to be equal to 4.

Remember that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)^2 + (b - d)^2)

So here, the distance between (a, 3) and ( - (48/91)*a - 51/7,  (36/91)*a + (153/28) - 5/4) is 4

4 = √( (a + (48/91)*a + 51/7)^2 + (3 -  (36/91)*a + (153/28) - 5/4 )^2)

If we square both sides, we get:

4^2 = 16 =  (a + (48/91)*a + 51/7)^2 + (3 -  (36/91)*a - (153/28) + 5/4 )^2)

Now we need to solve this for a.

16 = (a*(1 + 48/91)  + 51/7)^2 + ( -(36/91)*a  + 3 - 5/4 + (153/28) )^2

16 = ( a*(139/91) + 51/7)^2 + ( -(36/91)*a  - (43/28) )^2

16 = a^2*(139/91)^2 + 2*a*(139/91)*51/7 + (51/7)^2 +  a^2*(36/91)^2 + 2*(36/91)*a*(43/28) + (43/28)^2

16 = a^2*( (139/91)^2 + (36/91)^2) + a*( 2*(139/91)*51/7 + 2*(36/91)*(43/28)) +  (51/7)^2 + (43/28)^2

At this point we can see that this is really messy, so let's start solving these fractions.

16 = (2.49)*a^2 + a*(23.47) + 55.44

0 = (2.49)*a^2 + a*(23.47) + 55.44 - 16

0 = (2.49)*a^2 + a*(23.47) + 39.44

Now we can use the Bhaskara's formula for quadratic equations, the two solutions will be:

[tex]a = \frac{-23.47 \pm \sqrt{23.47^2 - 4*2.49*39.4} }{2*2.49} \\\\a = \frac{-23.47 \pm 12.57 }{4.98}[/tex]

Then the two possible values of a are:

a = (-23.47 + 12.57)/4.98  = -2.19

a = (-23.47 - 12.57)/4.98 = -7.23

Answer:

The option B, c2=a2+b2−2ab• cos(B) is the right answer.

Answer:

so first we start from the left

425*167=70975

but instead of adding this to 233 we use pemdas so instead we do

233*425=99025

now we add them together

70975+99025=170000

Hope This Helps!!!

Answer:

170,000

Step-by-step explanation:

425 × 167 + 233 × 425

= (425 × 167) + (233 × 425)

= 70,975 + 99,025

= 170,000

Answer:

You have a total of $11.50

Step-by-step explanation:

We first subtract $19.75 by $8.25 and the result will be $11.50

Answer:

11.50

Step-by-step explanation:

19.75-8.35= 11.50

May I have the brainiest?

Answer:

C. <C is congruent to <Y

Step-by-step explanation:

to be AAS the angles need to be next to each other

Answer: the answer is 12/13

You have some data points labeled by [tex]x[/tex]. They form the set {3, 5, 7}.

The mean, [tex]\bar x[/tex], is the average of these values:

[tex]\bar x = \dfrac{3+5+7}3 = \dfrac{15}3 = 5[/tex]

Then in the column labeled [tex]x-\bar x[/tex], what you're doing is computing the difference between each data point [tex]x[/tex] and the mean [tex]\bar x[/tex]:

[tex]x=3 \implies x-\bar x = 3 - 5 = -2[/tex]

[tex]x=5 \implies x-\bar x = 5-5 = 0[/tex]

[tex]x=7 \implies x-\bar x = 7 - 5 = 2[/tex]

These are sometimes called "residuals".

In the next column, you square these values:

[tex]x=3 \implies (x-\bar x)^2 = (-2)^2 = 4[/tex]

[tex]x=5 \implies (x-\bar x)^2 = 0^2 = 0[/tex]

[tex]x=7 \implies (x-\bar x)^2 = 2^2 = 4[/tex]

and the variance of the data is the sum of these so-called "squared residuals".

If X ~ Exponential(µ), then the mean of X is 1/µ. So if the mean of X is twice the mean of Y, then the mean of Y is 1/(2µ), so that Y ~ Exponential(2µ).

We're given that

P(X > 50) = 1 - P(X ≤ 50) = 1 - Fx (50) ≈ 0.7788

==>   Fx (50) = P(X ≤ 50) ≈ 0.2212

where Fx is the CDF of X, which is given for 0 ≤ x < ∞ to be

Fx (x) = 1 - exp(-µx)

Solve for µ :

1 - exp(-50µ) ≈ 0.2212   ==>   µ ≈ -ln(0.7788)/50 ≈ 0.005

Then we have

P (Y > 40) = 1 - P (Y ≤ 40) = 1 - Fy (40)

where Fy is the CDF of Y,

Fy (y) = 1 - exp(-2µy)

so that

P (Y > 40) ≈ 1 - exp(-2 × 0.005 × 40) ≈ 0.3297

Answer:

Let the width of the garden =x meter

Then length=(x+4) meter

Half perimeter =36 m

So perimeter of garden =(2×36)=72 meters

According to the question

⇒2(l+b)=72

⇒2(x+x+4)=72

⇒2x+2x+4=74⇒4x=64⇒x=16 meters

Hence,the width of the garden =16 meters

The length of the garden =(16+4)=20 meters

OPTION C is the correct answer.

The ΔAFE ≅ ΔBHG  by the angle, side and angle theorem are congruent. Option (A) is correct.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

The figure shows models of a roof truss. Based on the markings, there is enough information to prove that

ΔAFE ≅ ΔBHG

∠EFA=∠GHB  (90 degrees )

EF = GH  (equal side)

EAF = GBH (the side opposite to the angle is equal)

ΔAFE ≅ ΔBHG  (ASA )

Thus, ΔAFE ≅ ΔBHG  by the angle, side and angle theorem are congruent.

Learn more about triangles here:

https://brainly.com/question/14366937

#SPJ2

9514 1404 393

Answer:

  P'(-1, -2)

Step-by-step explanation:

The transformation for 270° CCW rotation is ...

  (x, y) ⇒ (y, -x)

Then the image of the given point is ...

  P(2, -1) ⇒ P'(-1, -2)

Answer:

Please find the complete question in the attached file.

Step-by-step explanation:

Total quantities of plant-produced pollutants:

[tex]=(10.88+15.82+0.92) \ L\\\\=27.62\ L[/tex]

We are three medicinal plants here, Pinecrest, Macon, and Ogala. The average number of contaminants produced by plants would be

[tex]\to 27.62\div 3 \\\\\to \frac{27.62}{3} \\\\ \to 9.206 \ L[/tex]

Answer:

It means that there are two answers, a positive one and a negative one.

Step-by-step explanation:

If you get +-5, then you have two answers: +5 and -5

Answer:

A dot product is the product of the magnitude of the vectors and the cos of the angle between them. A cross product is the product of the magnitude of the vectors and the sine of the angle that they subtend on each other.

Step-by-step explanation:

Answer:maybe B?

Step-by-step explanation:

Answer:

50.24 or 50.272

Step-by-step explanation:

Square radius and then times by 3.14 or 3.142

4^2*3.14 = 50.24

4^2*3.142 = 50.272

Hello!

x² + 6x + 1 = 0 <=>

<=> x = -6±√6²-4×1×1/2×1 <=>

<=> x = -6±√36-4/2 <=>

<=> x = -6±√32/2 <=>

<=> x = -6±2²√2/2 <=>

<=> x = -6±4√2/2 <=>

<=> x = -6+4√2/2 <=>

and

<=> x = -6-4√2/2 <=>

<=> x = -3+2√2 <=>

and

<=> x = -3-2√2 <=>

x1 = -3-2√2 and x2 = -3+2√2

Good luck! :)

Answer:

Needed point estimate is $372

Step-by-step explanation:

Given:

Number of houses in resident area = 121

Monthly mean car payment = $372

Find:

Best point estimate for the mean monthly car payment

Explanation:

The "best point estimate" for such average monthly automobile payment for all inhabitants of the nearby apartment complex is used as the "sample mean." In this example, a $372 sample was obtained on 121 residents.

As a result, the needed point estimate is $372.

Answer:

c

Step-by-step explanation:

Answer:

c is the correct answer