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3 years ago

If a =1 + r + 7r and b = 1 -r ,find an expression that equals A+ 3B in standard form. Answer:

Mathematics

1 answer:

Trava [24]3 years ago

7 0

Answer:

A+3B=4+5r

Step-by-step explanation:

Given that,

A = 1+r+7r

B = 1-r

We need to find an expression that is equal to A+3B.

Putting the values of A and B in A+3B, we get :

A+3B = 1+r+7r + 3(1-r)

=1+8r+3-3r

=(1+3) +(8r-3r)

=4+5r

Hence, the values of A+3B equals 4+5r.

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A set of final examination grades in a calculus course wasfound to be normally distributed with a mean of 69 and a standarddevia

Aleksandr [31]

Answer:

a) P ( X < 91 ) = 0.9927

b) P ( 65 < X < 91 ) = 0.6585

c) P(81 < X < 89 ) =0.0781

d) X = 83.8

Step-by-step explanation:

Given:

- Mean of the distribution u = 69

- standard deviation sigma = 9

Find:

a. what is the probability of getting a grade of 91 or less on this exam?

b. What percentage of students scored between 65 and 89?

c. What percentage of students scored between 81 and 89?

d. Only 5% of the students taking the test scored higher than what grade?

Solution:

- We will declare a random variable X denoting the score that a student gets on a final exam. So,

X ~ N ( 69 , 9 )

- After defining our variable X follows a normal distribution. We can compute the probabilities as follows:

a) P ( X < 91 ) ?

- Compute the Z-score value as follows:

Z = (91 - 69) / 9 = 2.4444

- Now use the Z-score tables and look for z = 2.444:

P( X < 91 ) = P ( Z < 2.4444) = 0.9927

b) P ( 65 < X < 89 ) ?

- Compute the Z-score values as follows:

Z = (89 - 69) / 9 = 2.2.222

Z = (65 - 69) / 9 = -0.4444

- Now use the Z-score tables and look for z = 2.222 and Z = -0.4444:

P(65 < X < 89 ) = P ( -0.444< Z < 2.2222) = 0.6585

b) P ( 81 < X < 89 ) ?

- Compute the Z-score values as follows:

Z = (89 - 69) / 9 = 2.2.222

Z = (81 - 69) / 9 = 1.3333

- Now use the Z-score tables and look for z = 2.222 and Z = 1.333:

P(81 < X < 89 ) = P ( 1.333< Z < 2.2222) = 0.0781

c) P ( X > a ) = 0.05 , a?

- Compute the Z-score values as follows:

Z = (a - 69) / 9 = q

- Now use the Z-score tables and look for z value that corresponds to:

P( X > a ) = P ( Z > q ) = 0.05

- The corresponding Z-value is: q = 1.6444

Hence,

Z = (a - 69) / 9 = 1.644

a = 83.8

4 0

3 years ago

What is the answer to 2(17+3)=?

Effectus [21]

The answer is 40 easy

4 0

3 years ago

Read 2 more answers

Answer plzzzz asappp !!

Scorpion4ik [409]

N + 7 > (or equal to) 53 is the answer

4 0

4 years ago

A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the chemical is given by the equatio

GaryK [48]

Answer:

a) $N=N_0e^{-0.069t}$

b) $N=696.9$ grams

c) $t=10$ days

Step-by-step explanation:

We are going to use separation of variables to solve.

Get all your t's to one side and your N's to opposing side.

$\frac{dN}{dt}=-0.069N$

Multiply both sides by $dt$ :

$dN=-0.069N dt$

Divided both sides by $N$ :

$\frac{dN}{N}=-0.069 dt$

Integrate both sides:

$\ln|N|=-0.069t+C$

The equivalent exponential form is:

$e^{-0.069t+C}=N$

Using law of exponents you can write this as:

$e^{-0.069t}e^C=N$

$e^C$ is just a positive constant that I'm going to replace with K:

$e^{-0.069t}K=N$

Applying the symmetric property of equality:

$N=e^{-0.069t}K$

Applying the commutative property of multiplication:

$N=Ke^{-0.069t}$

K actually represents the initial amount of chemical substance since when plugging in 0 for t you get K for N, like so:

$N=Ke^{-0.069 \cdot 0}$

$N=Ke^{0}$

$N=K(1)$

$N=K$

We are given at time 0 the amount of chemical substance,N, is K. They want us to represent this value with $N_0$ instead. So the exponential equation is:

$N=N_0e^{-0.069t}$

We are given $N_0=800$ at $t=0$ .

We are asked to find how much of the chemical substance, N, remains after 2 days. So we replace t with 2 in $N=800e^{-0.069t}$ :

$N=800e^{-0.069 \cdot 2}$

Put into calculator:

$N=696.9$ (this was rounded to the nearest tenths)

The last part is asking for how many days will it take a initial 800 grams to go down to half of 800 grams.

We need to see the following equation:

$\frac{1}{2}(800)=800e^{-0.069t}$

$400=800e^{-0.069t}$

Divide both sides by 800:

$\frac{400}{800}=e^{-0.069t}$

Reduce the fraction:

$\frac{1}{2}=e^{-0.069t}$

Convert to logarithmic form:

$\ln(\frac{1}{2})=-0.069t$

Divide both sides by -0.069:

$\frac{\ln(\frac{1}{2})}{-0.069}=t$

Input into calculator:

$10.0=t$

$t=10.0$

$t=10$

6 0

3 years ago

Damian traveled 18ft below sea level larry remained on the boat 6ft above sea level. How far apart are larry and damian

Marat540 [252]

Answer:

They are 24ft apart.

Step-by-step explanation:

Larry is 6 feet above sea level, so his height is 6.

Damian is 18 feet below sea level, so his height is -18.

How far apart are larry and damian

To find this, we subtract their heights.

6 - (-18) = 6 + 18 = 24

They are 24ft apart.

8 0

3 years ago

If a =1 + r + 7r and b = 1 -r ,find an expression that equals A+ 3B in standard form. Answer: ​

If a =1 + r + 7r and b = 1 -r ,find an expression that equals A+ 3B in standard form. Answer: