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3 years ago

Solve by factoring 7b^2-8b+3=2

Mathematics

2 answers:

Ahat [919]3 years ago

6 0

$7b^2-8b+3=2 \\ 7b^2-8b+1=0 \\ (7x-1)(x-1)=0 \\ x=1 \\ x= \frac{1}{7}$

mixas84 [53]3 years ago

5 0

Subtract the 2 over from the 3 which leaves you with 1 as the constant. Then you have 7b^2-8b+1. Slide the 7 over to the 1 using the slide and divide method. This leaves you with b^2-8b+7. Then just think "what multiplies to get 7, and adds to -8." The answer to that is (x-7)(x-1). Then you have to divide by 7 because you slid it earlier. So that gives you the answer of : (x-1)(7x-1).

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The table displays the number of students in each grade at Richmond High School who will or will not be attending the amusement

Pani-rosa [81]

Answer:

$P( eleventh\: \: |\: \: FT)= 0.2453 \\\\P( eleventh\: \: |\: \: FT)= 24.53\% \\\\$

Step-by-step explanation:

We are given a joint probability table.

There are four different graders in a school

1. Grade Ninth

2. Grade Tenth

3. Grade Eleventh

4. Grade Twelfth

Field trip refers to the students who will attending the amusement park field trip.

No field trip refers to the students who will not be attending the amusement park field trip.

We want to find out the probability that the selected student is an eleventh grader given that the student is going on a field trip.

$P( eleventh\: \: |\: \: FT)= \frac{P( eleventh\: \: and \: \: FT)}{P(FT)}$

Where P(eleventh and FT) is the probability of students who are in eleventh grade and will be going to field trip

$P(eleventh\: and \: FT) = \frac{13}{92} \\\\P(eleventh \: and \: FT) = 0.1413$

Where P(FT) is the probability of students who will be going to field trip

$P(FT) = \frac{12}{92} + \frac{9}{92} + \frac{13}{92} + \frac{19}{92}\\\\P(FT) = 0.1304 + 0.0978 + 0.1413 + 0.2065\\\\P(FT) = 0.576 \\\\$

So the required probability is

$P( eleventh\: \: |\: \: FT)= \frac{P( eleventh\: \: and \: \: FT)}{P(FT)} \\\\P( eleventh\: \: |\: \: FT)= \frac{0.1413}{0.576} \\\\P( eleventh\: \: |\: \: FT)= 0.2453 \\\\P( eleventh\: \: |\: \: FT)= 24.53\% \\\\$

6 0

3 years ago

The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increas

Mazyrski [523]

Answer:

The population in 40 years will be 1220.

Step-by-step explanation:

The population of a town grows at a rate proportional to the population present at time t.

This means that:

$P(t) = P(0)e^{rt}$

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.

The initial population of 500 increases by 25% in 10 years.

This means that $P(0) = 500, P(10) = 1.25*500 = 625$

We apply this to the equation and find t.

$P(t) = P(0)e^{rt}$

$625 = 500e^{10r}$

$e^{10r} = \frac{625}{500}$

$e^{10r} = 1.25$

Applying ln to both sides

$\ln{e^{10r}} = \ln{1.25}$

$10r = \ln{1.25}$

$r = \frac{\ln{1.25}}{10}$

$r = 0.0223$

$P(t) = 500e^{0.0223t}$

What will be the population in 40 years

This is P(40).

$P(t) = 500e^{0.0223t}$

$P(40) = 500e^{0.0223*40} = 1220$

The population in 40 years will be 1220.

7 0

3 years ago

Solve the equation: 5/6x - 10 = 1/3(x - 15)

Harlamova29_29 [7]

Answer:

X =10

Step-by-step explanation:

If you have a scientific calculator that can help you a lot.

I will upload a picture you can follow to solve this problem.

4 0

2 years ago

The cost of 3 notebooks and 4 pencils is $8.50. Determine the cost of one notebook and one pencil

Assoli18 [71]

Call the notebooks x, and the pencils y.
3x + 4y = $8.50 and 5x + 8y = $14.50 
Then just solve as simultaneous equations: 
3x + 4y = $8.50 
5x + 8y = $14.50 

5(3x + 4y = 8.5) 
3(5x + 8y = 14.5) 

15x + 20y = 42.5 
15x + 24y = 43.5 

Think: DASS (Different Add, Similar Subtract). 15x appears in both equations so subtract one equation from the other. Eassier to subtract (15x + 20y = 42.5) from (15x + 24y = 43.5) 

(15x + 24y = 43.5) - (15x + 20y = 42.5) = (4y = 1) which means y = 0.25. 

Then substitue into equation : 
15x + 20y = 42.5 
15x + 5 + 42.5 
15x = 42.5 - 5 = 37.5 
15x = 37.5 
x = 2.5 

15x + 24y = 43.5 
15(2.5) + 24(0.25) 
37.5 + 6 = 43.5 

So x (notebooks) are 2.5 ($2.50) each and y (pencils) are 0.25 ($0.25) each.

6 0

2 years ago

Which of the following documents were influenced by John Locke's principles?

Alborosie

Answer:U.S Declaration of Independence

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers