Area of Composite Shapes (Trapezoids and Triangles)

WILL GIVE BRAINLIEST The sequence 7 21 63 189......shows the number of jumping jacks justin did each week, starting with the fir

vovangra [49]

A

this is a geometric sequence since there exists a common ratio r between the terms

r = $\frac{21}{7}$ = $\frac{63}{21}$ = $\frac{189}{63}$ = 3

B

to obtain the next term in the sequence multiply the previous term by 3

$a_{n+1}$ = 3 $a_{n}$ ← recursive rule

C

the n th term of a geometric sequence is

$a_{n}$ = $a_{1}$ $r^{n-1}$

where $a_{1}$ is the first term in the sequence

$a_{n}$ = 7 × $3^{n-1}$ ← explicit rule

3 0

3 years ago

42:15 =<br> What is the ratio

vfiekz [6]

The ratio is 14:5, as 42 divided by 3 is 14 and 15 divided by 3 is 5.

8 0

2 years ago

(10 pts) (a) (2 pts) What is the difference between an ordinary differential equation and an initial value problem? (b) (2 pts)

laiz [17]

Answer:

Step-by-step explanation:

(A) The difference between an ordinary differential equation and an initial value problem is that an initial value problem is a differential equation which has condition(s) for optimization, such as a given value of the function at some point in the domain.

(B) The difference between a particular solution and a general solution to an equation is that a particular solution is any specific figure that can satisfy the equation while a general solution is a statement that comprises all particular solutions of the equation.

(C) Example of a second order linear ODE:

M(t)Y"(t) + N(t)Y'(t) + O(t)Y(t) = K(t)

The equation will be homogeneous if K(t)=0 and heterogeneous if $K(t)\neq 0$

Example of a second order nonlinear ODE:

$Y=-3K(Y){2}$

(D) Example of a nonlinear fourth order ODE:

$K^4(x) - \beta f [x, k(x)] = 0$

4 0

3 years ago

The length of time that an auditor spends reviewing an invoice is approximately normally distributed with a mean of 600 seconds

Bumek [7]

Answer: 11.5%

Explanation:

Since 1 minute = 60 seconds, we multiply 12 minutes by 60 so that 12 minutes = 720 seconds. Thus, we're looking for a probability that the auditor will spend more than 720 seconds.

Now, we get the z-score for 720 seconds by the following formula:

$\text{z-score} = \frac{x - \mu}{\sigma}$

where

$t = \text{time for the auditor to finish his work } = 720 \text{ seconds}
\\ \mu = \text{average time for the auditor to finish his work } = 600 \text{ seconds}
\\ \sigma = \text{standard deviation } = 100 \text{ seconds}$

So, the z-score of 720 seconds is given by:

$\text{z-score} = \frac{x - \mu}{\sigma}
\\
\\ \text{z-score} = \frac{720 - 600}{100}
\\
\\ \boxed{\text{z-score} = 1.2}$

Let

t = time for the auditor to finish his work
z = z-score of time t

Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:

$P(t \ \textgreater \ 720) 
\\ = P(z \ \textgreater \ 1.2)
\\ = 1 - P(z \leq 1.2)
\\ = 1 - 0.885
\\ \boxed{P(t \ \textgreater \ 720) = 0.115}$

Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice.

8 0

3 years ago

Find the slope from the table.

Schach [20]

Answer:

slope = 4/1 or 4

Step-by-step explanation:

(2, 14)

(1, 10)

Formula = $\frac{y^2-y^1}{x^2-x^1}$

14-10 over 2 -1

4/ 1 = 4

5 0

2 years ago