True or False: This table describes a linear function. XY 1 5 2 8 3 10

An investment of P dollars increased to A dollars in t years. If interest was compounded continuously, find the interest rate. (

Gemiola [76]

Answer: the interest rate is 6%

Step-by-step explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

A = $4482

P = 1000

t = 25 years

Therefore,

4482 = 1000 x 2.7183^(r x 25)

4482/1000 = 2.7183^25r

4.482 = 2.7183^25r

Taking ln of both sides, it becomes

Ln 4.482 = 25rLn2.7183

1.5 = 25r

r = 1.5/25 = 0.06

r = 0.06 × 100 = 6%

5 0

3 years ago

Help Pls :) I cannot find the answer

yuradex [85]

Answer:

1815 pi cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the diameter =22

so the radius is d/2 = 22/2 =11

V = pi (11)^2 (15)

V = pi1815

V = 1815 pi cm^3

8 0

3 years ago

An art teacher has a jar containing b buttons to distribute to her class for a project. In order to give each in the class 6 but

Nastasia [14]

Answer:

22

Step-by-step explanation:

Given:

An art teacher has the total number of buttons = $b$

1. In order to give each in the class 6 buttons, she will need 18 more buttons.

2. If she gives each child 5 buttons, she will have 4 left over.

Question asked:

How many children are in the class ?

Solution:

Let total number of children in the class = $x$

As given that, 18 more buttons will be needed to give 6 buttons to each.

The equation will be:-

$b+18=6x\\b-6x=-18\ (equation\ 1)$

Also given that, If she gives 5 buttons to each, she will have 4 left over.

The equation will be:-

$b-5x=4\ (equation\ 2)$

Subtraction equation 2 from 1

$b-6x-(b-5x)=-18-4\\b-6x-b+5x=-22\\-6x+5x=-22\\-x=-22\\Minus\ canceled\ by\ minus\\x=22$

Hence, total number of children are 22.

4 0

3 years ago

What is the length of the dotted line in the diagram below? Leave your answer in simplest radical form.

Pachacha [2.7K]

Answer:

$\sqrt{93}$

Step-by-step explanation:

8^2+5^2=c^2

64+25=c^2

89=c^2

c= $\sqrt{89}$ <-- this is the length of the rectangle at the bottom

2^2+( $\sqrt{89}$ )^2=c^2

4+89=c^2

c= $\sqrt{93}$ <-- length of dotted line (diagonal)

6 0

2 years ago

Read 2 more answers

Assume the random variable x has a binomial distribution with the given probability of obtaining a success. Find the following.

borishaifa [10]

Answer:

P(x > 10) = 0.6981.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this question:

$n = 14, p = 0.8$

P(x>10)

$P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 11) = C_{14,11}.(0.8)^{11}.(0.2)^{3} = 0.2501$

$P(X = 12) = C_{14,12}.(0.8)^{12}.(0.2)^{2} = 0.2501$

$P(X = 13) = C_{14,13}.(0.8)^{13}.(0.2)^{1} = 0.1539$

$P(X = 14) = C_{14,14}.(0.8)^{14}.(0.2)^{0} = 0.0440$

$P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.2501 + 0.2501 + 0.1539 + 0.0440 = 0.6981$

So P(x > 10) = 0.6981.

8 0

3 years ago