How far apart is 27 and -54

Write the explicit rule for this arithmetic sequence 9,12,15,18…

MArishka [77]

Answer:

an=9+(n−1)3, an=3n+6

Step-by-step explanation:

Arithmetic Sequence:

d=3

This is the formula of an arithmetic sequence.

an=a1+d(n−1)

Step 1: Substitute in the values of

a1=9 and d=3.

an=9+(3)(n−1)

Step 2: Simplify each term.

an=9+3n−3

Step 3: Subtract 3 from 9.

an=3n+6

4 0

2 years ago

Filing status of "head of house hold" is for married taxpayers who have dependents

Mashutka [201]

True is the answer

Hope this helps!

4 0

3 years ago

Read 2 more answers

4. A small high school holds its graduation ceremony in the gym. Because of seating constraints, students are limited to a maxim

Ad libitum [116K]

Answer:

(a) The mean and standard deviation of X is 2.6 and 1.2 respectively.

(b) The mean and standard deviation of T are 390 and 180 respectively.

(c) The distribution of T is N (390, 180²). The probability that all students’ requests can be accommodated is 0.7291.

Step-by-step explanation:

(a)

The random variable X is defined as the number of tickets requested by a randomly selected graduating student.

The probability distribution of the number of tickets wanted by the students for the graduation ceremony is as follows:

X P (X)

0 0.05

1 0.15

2 0.25

3 0.25

4 0.30

The formula to compute the mean is:

$\mu=\sum x\cdot P(X)$

Compute the mean number of tickets requested by a student as follows:

$\mu=\sum x\cdot P(X)\\=(0\times 0.05)+(1\times 0.15)+(2\times 0.25)+(3\times 0.25)+(4\times 0.30)\\=2.6$

The formula of standard deviation of the number of tickets requested by a student as follows:

$\sigma=\sqrt{E(X^{2})-\mu^{2}}$

Compute the standard deviation as follows:

$\sigma=\sqrt{E(X^{2})-\mu^{2}}\\=\sqrt{[(0^{2}\times 0.05)+(1^{2}\times 0.15)+(2^{2}\times 0.25)+(3^{2}\times 0.25)+(4^{2}\times 0.30)]-(2.6)^{2}}\\=\sqrt{1.44}\\=1.2$

Thus, the mean and standard deviation of X is 2.6 and 1.2 respectively.

(b)

The random variable T is defined as the total number of tickets requested by the 150 students graduating this year.

That is, T = 150 X

Compute the mean of T as follows:

$\mu=E(T)\\=E(150\cdot X)\\=150\times E(X)\\=150\times 2.6\\=390$

Compute the standard deviation of T as follows:

$\sigma=SD(T)\\=SD(150\cdot X)\\=\sqrt{V(150\cdot X)}\\=\sqrt{150^{2}}\times SD(X)\\=150\times 1.2\\=180$

Thus, the mean and standard deviation of T are 390 and 180 respectively.

(c)

The maximum number of seats at the gym is, 500.

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e ∑X, will be approximately normally distributed.

Here T = total number of seats requested.

Then, the mean of the distribution of the sum of values of X is given by,

$\mu_{T}=n\times \mu_{X}=390$

And the standard deviation of the distribution of the sum of values of X is given by,

$\sigma_{T}=n\times \sigma_{X}=180$

So, the distribution of T is N (390, 180²).

Compute the probability that all students’ requests can be accommodated, i.e. less than 500 seats were requested as follows:

$P(T$

Thus, the probability that all students’ requests can be accommodated is 0.7291.

8 0

2 years ago

Suppose y varies directly with x, and y= 10 when x=-2. What direct variation equation relates x and y? What is the value of y wh

Musya8 [376]

The statement " y varies directly as x ," means that when x increases,y increases by the same factor. In other words, y and x always have the same ratio:

= k

where k is the constant of variation.
We can also express the relationship between x and y as:

y = kx

where k is the constant of variation.

Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x , and y = 6 when x = 2 , the constant of variation is k = = 3 . Thus, the equation describing this direct variation is y = 3x .

Example 1: If y varies directly as x , and x = 12 when y = 9 , what is the equation that describes this direct variation?

k = = 
y = x

Example 2: If y varies directly as x , and the constant of variation is k = , what is y when x = 9 ?

y = x = (9) = 15

As previously stated, k is constant for every point; i.e., the ratio between the y -coordinate of a point and the x -coordinate of a point is constant. Thus, given any two points (x 1, y 1) and (x 2, y 2) that satisfy the equation, = k and = k . Consequently, = for any two points that satisfy the equation.

Example 3: If y varies directly as x , and y = 15 when x = 10 , then what is y when x = 6 ?

 = 
 = 
6() = y 
y = 9

3 0

2 years ago

Abcd is a square. given only the choices below, which properties would you use to prove aeb ≅ dec by asa?

Darina [25.2K]

All sides are congruent
Opposite sides are ||

I just took the test so I’m putting all the answers:)
1. A
2. D
3. 6
4. 12
5. C
6. -1/3
7. 4in^2
8. A
9. D
10. It’s diagonals bisect each other and it diagonals are | to each other
11. BC
12. C
13. SAS
14. A
15. Trapezoid
16. C
17. B
18. 9.6
19. (2,-2)
20. 13
21. B
22. 2.1 feet
23. B,D, E
24. |||
25. Squiggly line with point above the 0
26. 144°
27. 2pi/3
28. 20 rad/sec
29. C
30. 1/2
31. B
32. B
33.B
34. D
35. D
36 37 and 38 I couldn’t find on the internet so I didn’t do them. Homely this helps somebody feel free to use these answers to answer other questions about this test. God Bless

7 0

2 years ago