Answer:
(a) The probability of getting someone who was not sent to prison is 0.55.
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is 0.63.
Step-by-step explanation:
We are given that in a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
Let the probability that subjects studied were sent to prison = P(A) = 0.45
Let G = event that subject chose to plead guilty
So, the probability that the subjects chose to plead guilty given that they were sent to prison = P(G/A) = 0.40
and the probability that the subjects chose to plead guilty given that they were not sent to prison = P(G/A') = 0.55
(a) The probability of getting someone who was not sent to prison = 1 - Probability of getting someone who was sent to prison
P(A') = 1 - P(A)
= 1 - 0.45 = 0.55
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is given by = P(A'/G)
We will use Bayes' Theorem here to calculate the above probability;
P(A'/G) = [tex]\frac{P(A') \times P(G/A')}{P(A') \times P(G/A') +P(A) \times P(G/A)}[/tex]
= [tex]\frac{0.55 \times 0.55}{0.55\times 0.55 +0.45 \times 0.40}[/tex]
= [tex]\frac{0.3025}{0.4825}[/tex]
= 0.63
Ava is buying paint from Amazon. Ava needs 3⁄4 cup of blue paint for every 1 cup of white paint. Ava has 28 ounces of white paint. How much blue paint does he need?
Answer:
Blue paint=21 ounces
Step-by-step explanation:
3/4 cup=6 ounces
1 cup=8 ounces
3/4 cup of blue paint=6 ounces of blue paint
1 cup of white paint= 8 ounces of white paint
Ava has 28 ounces of white paint
Find the required blue paint
Let the required blue paint=x
Blue paint ratio white paint
6:8=x:28
6/8=x/28
Cross product
6(28)=x(8)
168=8x
x=168/8
x=21 ounces
Trigonometry Dilemma
Answer:
17.1
Step-by-step explanation:
The missing side is x
tan 25° = [tex]\frac{opposite }{adjacent }[/tex] tan 25° = [tex]\frac{8}{x}[/tex]switch tan 25° and x
x = [tex]\frac{8}{tan 25}[/tex] x= 17.15≈17.1Consider the statemen P. P.X=5 which of the following is an equivalent statement
Answer:
(D)R: x+2=7
Step-by-step explanation:
Given the statement P:x=5
An equivalent statement will be a statement whose result is exactly x=5.
From the given options:
R: x+2=7
R: x=7-2
R: x=5
Therefore, R is an equivalent statement.
The correct option is D.
Price of an item is reduced by 40% of its original price. A week later it’s reduced 20% of the reduced price. What’s the actual % of the reduction from the original price
Answer: 52%
Step-by-step explanation:
Let the original price be 100.
After 40% reduction, price will be 100 - 40% = 60
After further 20% reduction, price will be 60 - 20% = 48
%age = (cur val - orig. val ) / orig val x 100
= (48 - 100) / 100 x 100%
= -52
The actual percentage of reduction is 52%
The first reduction is given as:
[tex]r_1 = 40\%[/tex]
The second reduction is given as:
[tex]r_2 = 20\%[/tex]
Assume that the original price of the item is x.
After the first reduction of 40%, the new price would be:
[tex]New = x\times (1 -r_1)[/tex]
So, we have:
[tex]New = x\times (1 -40\%)[/tex]
[tex]New = x\times 0.6[/tex]
[tex]New = 0.6x[/tex]
After the second reduction of 20% on the reduced price, the new price would be:
[tex]New = 0.6x\times (1 -r_2)[/tex]
So, we have:
[tex]New = 0.6x\times (1 -20\%)[/tex]
[tex]New = 0.6x\times 0.8[/tex]
[tex]New = 0.48x[/tex]
Recall that the original price is x.
So, the actual reduction is:
[tex]Actual = \frac{x - 0.48x}{x}[/tex]
[tex]Actual = \frac{0.52x}{x}[/tex]
Divide
[tex]Actual = 0.52[/tex]
Express as percentage
[tex]Actual = 52\%[/tex]
Hence, the actual percentage of reduction is 52%
Read more about percentage change at:
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Just trying to finish this so I can get my stanceboy racecar back
Answer:
x ≥ 4 AND x + y ≤ 10
Step-by-step explanation:
If you need up to 10 volunteers, then you can take 10 or less. If we add y and x, we'll get the total amount of people, therefore making the inequality:
x + y ≤ 10.
Now, he needs no fewer than 4 females, so he can take 4 or greater. This means that x should be greater than or equal to 4.
x ≥ 4.
Nothing was mentioned about how many males he needed (y) so these two inequalities match the situation.
Hope this helped!
Need Assistance
Show Work
Answer:
-52, and the opposite of this is 52.
Step-by-step explanation:
If we are losing 52 pounds, then our number is -52 since we are losing 52 pounds (adding a negative number to a positive number is the same as subtracting that number).
The opposite of a number is when we negate the number, or multiply it by -1.
A negative number times a negative number is a positive number.
[tex]-52\cdot-1 = 52\cdot1 = 52[/tex]
Hope this helped!
Answer:
Hey there!
Loss of 52 pounds, -52
Opposite, 52
Hope this helps :)
Two angles are supplementary. Angle A is twice as large as angle B. What is the measure of each angle ?
Find the value of Xº if
Question: Find the value of Xº if <ADC = 71°
Answer:
15
Step-by-step explanation:
Given:
<ADC = 71°
<ADB = (x + 7)°
<BDC = (2x + 19)°
Required:
Value of x
Solution:
<ADB + <BDC = <ADC
(x + 7)° + (2x + 19)° = 71°
x + 7 + 2x + 19 = 71
x + 2x + 7 + 19 = 71
3x + 26 = 71
Subtract 26 from both sides
3x + 26 - 26 = 71 - 26
3x = 45
Divide both sides by 3 to make x the subject of formula
[tex] \frac{3x}{3} = \frac{45}{3} [/tex]
[tex] x = 15 [/tex]
The value of x is 15.
The eighth grade class at Seven Bridges Middle School has 93 students. Each student takes a current events class, a foreign language class, or both a current events class and a foreign language class. There are 70 eighth graders taking a current events class, and there are 54 eighth graders taking a foreign language class. How many eighth graders take only a current events class and not a foreign language class?
Answer:
31
Step-by-step explanation:
The computation of eighth graders take only a current events class and not a foreign language class is shown below:-
We will assume the x that shows the number of students which we will take both languages
So, the equation will be
70 + 54 - x = 93
-x = 93 - 124
x = 31 students
So the number of eighth graders only take a current event class is
= 70 - 39
= 31 students
11) $ 8,000 is invested in an account that yields 6% interest per year. After how many years will the account be worth 13709.60$ if the interest is compounded monthly?
Answer:
[tex]\large \boxed{\sf \ \ 9\text{ years} \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all, a few remarks:
>>> 1 year is 12 months, right?
>>> Monthly compounding means that each month we compute the interest and they will be included in the investment for the next month.
>>> 6% is an interest per year, it means that to compute the interest for 1 month we need to compute by 6% multiplied by [tex]\dfrac{1}{12}[/tex]
Let's do it !
At the beginning, we have:
$8,000
After 1 month, we will have:
[tex]8000 + 8000\cdot \dfrac{6\%}{12}=8000\cdot (1+ \dfrac{6}{1200})= 8000\cdot (1+ \dfrac{1}{200})[/tex]
After 2 months, we will have:
[tex]8000\cdot (1+ \dfrac{1}{200})\cdot (1+ \dfrac{1}{200})=8000\cdot \left(1+ \dfrac{1}{200}\right)^2[/tex]
After n months, we will have
[tex]8000\cdot \left(1+ \dfrac{1}{200}\right)^n=8000\cdot \left(1.005\right)^n[/tex]
We are looking for n such that
[tex]8000\cdot \left(1.005\right)^n=13709.60\\\\ln(8000)+ n\cdot ln(1.005)=ln(13709.60)\\\\\\n = \dfrac{ln(13709.60)-ln(8000)}{ln(1.005)}=108[/tex]
So, we need 108 months to reach this amount, which means 108/12=9 years.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A clinic treated 536 children over a 4month period how many children did the clinic treat in 1month
536 children = 4 months
536/4 children = 4/4 months ... divide both sides by 4
134 children = 1 month
The clinic treated 134 children in 1 month. This is assuming that every month was the same number of patients.
Answer: 134Step-by-step explanation:
Solution,
Number of children treated in 4 months = 536
Now, let's find the number of children treated in one month:
[tex] = \frac{total \: number \: of \: childrens \: }{total \: month} [/tex]
Plug the values
[tex] = \frac{536}{4} [/tex]
Calculate
[tex] = 134 \: [/tex] childrens
Therefore, A clinic treated 134 childrens in one month.
Hope this helps...
Best regards!!
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.
2, 10, 15, 4, 11, 10, 15, 10, 2, 10
Answer:
a
[tex]R =13[/tex]
b
[tex]\= x =8.9[/tex]
c
[tex]var(x) = 16.57[/tex]
d
[tex]\sigma = 4.1[/tex]
Step-by-step explanation:
From the question we are given a data set
2, 10, 15, 4, 11, 10, 15, 10, 2, 10
The sample size is n = 10
The range is
[tex]R = maxNum - MinNum[/tex]
Where maxNum is the maximum number on the data set which is 15
and MinNum is the minimum number on the data set which is 2
So
[tex]R = 15 - 2[/tex]
[tex]R =13[/tex]
The mean is mathematically represented as
[tex]\= x = \frac{\sum x_i}{N}[/tex]
substituting values
[tex]\= x = \frac{2 + 10 + 15 + 4 + 11 + 10 + 15 + 10 + 2 + 10 }{10}[/tex]
[tex]\= x =8.9[/tex]
The variance is mathematically evaluated as
[tex]var(x) = \frac{\sum (x - \= x)^2}{N}[/tex]
substituting values
[tex]var(x) = \frac{(2 - 8.9 )^2 + (10 - 8.9 )^2 + (15 - 8.9 )^2 +(4 - 8.9 )^2 +(11 - 8.9 )^2 +(10 - 8.9 )^2 +(15 - 8.9 )^2 +(10 - 8.9 )^2 +} {10}[/tex] [tex]\frac{(2 - 8.9 )^2 +(10 - 8.9 )^2 }{10}[/tex]
[tex]var(x) = 16.57[/tex]
The standard deviation is [tex]\sigma = \sqrt{var(x)}[/tex]
substituting values
[tex]\sigma = \sqrt{16.57}[/tex]
[tex]\sigma = 4.1[/tex]
The winery sold 81 cases of wine this week. If twice
as many red cases were sold than white. how many
white cases were sold this week?
Answer:
21 cases
Step-by-step explanation:
red cases=2x. white cases=x
2x+x=81
3x=81
x=21 cases
Which of the following expressions could be used to find 80% of X (the lines are there to show the different expressions)
Answer:
80/100 times x => [tex] \frac{80}{100}*x [/tex]
(0.8) times x => [tex] (0.8)*x [/tex]
4/5 times x => [tex] \frac{4}{5}*x [/tex]
8/10 times x => [tex] \frac{8}{10}*x [/tex]
Step-by-step explanation:
80% of x means 80 ÷ 100 × x
that is: [tex] \frac{80}{100}*x = \frac{8}{10}*x = \frac{4}{5}*x = (0.8)*x [/tex]
Therefore, the expressions that can be used to find 80% of x are:
80/100 times x => [tex] \frac{80}{100}*x [/tex]
(0.8) times x => [tex] (0.8)*x [/tex]
4/5 times x => [tex] \frac{4}{5}*x [/tex]
8/10 times x => [tex] \frac{8}{10}*x [/tex]
3/25 as a percentage
Answer:
12%
Step-by-step explanation:
3/25 = .12
.12 x 100 = 12%
Answer:
12%
Step-by-step explanation:
All you have to do is divide this on a calculator and multiply it by 100. 3/25 = 0.12; 0.12 x 100 = 12%.
Using this model, what would be the cost of a flight that travels 1375 miles?
Round your answer to the nearest dollar.
Answer:
C) $143.
Step-by-step explanation:
We are given an equation: y = 0.0714x + 44.8.
x is the number of miles, and y is the cost.
y = 0.0714 * 1,375 + 44.8
y = 98.175 + 44.8
y = 142.975
So, the cost is about C) $143.
Hope this helps!
find the standard deviation for the binomial distribution which has the stated values of n and p n=47 p= 0.4 round you answer to the nearest hundredth
Answer:
Option (3)
Step-by-step explanation:
Standard deviation for the binomial distribution is given by,
σ = [tex]\sqrt{n\times P(1-P)}[/tex]
where n = Number of trials
P = probability of success of an individual trail
If n = 47 and P = 0.4
σ = [tex]\sqrt{47\times 0.4(1-0.4)}[/tex]
= [tex]\sqrt{47\times 0.24}[/tex]
= [tex]\sqrt{11.28}[/tex]
= 3.3586
≈ 3.36
Therefore, standard deviation for the binomial distribution will be 3.36.
Option (3) will be the answer.
He claims that the measures of the three sides of triangle ABX are all equal to AX, making AABX equilateral. Since this makes central angle AXB
measure 60°,mAB = 60°. Dylan also claims that by repeatedly applying the same argument, he can prove that the inscribed hexagon is regular.
Which statement is true?
Statement A " Dylan's reasoning about arc AB is correct, and the hexagon is regular. option (A) is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
Three sides of the triangle ABX are all equal to AX, making ΔABX equilateral. Since this makes central angle AXB measure 60°,
m(arc)AB = 60°
AX = BX = AB
The measure of AXB = 60 degrees
m(arc)AB = 60 degrees
On applying the same argument, the inscribed hexagon is regular.
Statement A is correct.
Thus, statement A " Dylan's reasoning about arc AB is correct, and the hexagon is regular. option (A) is correct.
Learn more about the regular polygon here:
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The exact heights of different elephants Choose the correct answer below. A. The data are continuous because the data can only take on specific values. B. The data are discrete because the data can take on any value in an interval. C. The data are discrete because the data can only take on specific values. D. The data are continuous because the data can take on any value in an interval.
Answer:
Option d: The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
The data are continuous if they can take on any value within a range. In this case study, there are different elephants including small/young ones and big ones/old ones.
Thus, their heights will vary and can take on any value within a particular range.
WHY CAN'T ANYONE HELP ME PLEASE? THANKS! A student at a university makes money by buying and selling used cars. Charles bought a used car and later sold it for a 15% profit. If he sold it for $4669, how much did Charles pay for the car?
Step-by-step explanation:
Given,
a student (Charles) bought a car and sold it in 15 % profit for $4669.
we have the formula,
[tex]cp = \frac{sp \times 100}{100 + p\%} [/tex]
so,
[tex]cp = \frac{4669 \times 100}{100 + 15} [/tex]
by simplifying it we get,
CP is $4060.
Therefore, the cp was $4060.
Hope it helps...
an office supply company sells two types of printers. they charge $95 for one of the printers and $125 for the other. if the company sold 32 printers for a total of$3340 last month, how many of each type were sold
Answer:
22 of the 95$ ones and 10 of the 125
Step-by-step explanation:
22 times 95 = 2090
10 times 125 = 1250
2090+1250=3340
hope this helped
The JUST-SAY-MOW lawn mowing company consists of two people: Marsha and Bob. If Marsha cuts the lawn by herself, she can do it in 3 hours. If Bob cuts the same lawn himself, it takes him an hour longer than Marsha. How long would it take them if they worked together? Round to the nearest hundredth of an hour.
Answer:
it will take them 1.71 hours to finish cutting the lawn if they work together.
Step-by-step explanation:
If Marsha cuts the lawn by herself it will take her 3 hours, this mean that in one hour she cuts 1/3 of the lawn.
On the other hand Bob needs one more hour to finish the lawn, this means it takes him 4 hours to cut it and therefore he cuts 1/4 of the lawn per hour.
Now, to know how much they cut by working together we need to sum up the amount of lawn they cut per hour:
Working together in one hour: Marsha's one hour + Bob's one hour
Working together in one hour: [tex]\frac{1}{3}+ \frac{1}{4}=\frac{4+3}{12}=\frac{7}{12}[/tex]
Therefore, working together they will cut 7/12 in one hour.
Now, to know how long will it take it to cut the entire lawn (which is equivalent to 12/12), we can write this in terms of proportions
Time Total amount of lawn
1 hour 7/12
x hours 12/12
Solving for x (to know the amount of hours it will take them) we have:
[tex]x=\frac{12}{12}[/tex]÷[tex]\frac{7}{12}[/tex]=[tex]1[/tex]×[tex]\frac{12}{7}=\frac{12}{7}=1.714[/tex]
Rounded to the nearest hundredth, we have that working together it will take them 1.71 hours to finish cutting the lawn.
what is the quotient of (2x^4-3x^3–3x^2+7x-3)/(c^2-2x+1)
Answer:
[tex]2x^2 + x - 3[/tex]
Step-by-step explanation:
We want to divide [tex]2x^4 - 3x^3 - 3x^2 + 7x - 3[/tex] by [tex]x^2 - 2x + 1[/tex]
To do the long division, divide each term by [tex]x^2[/tex] and then subtract the product of the result and [tex]x^2 - 2x + 1[/tex] from the remaining part of the equation.
Whatever term/value you obtain from each step of the division is a part of the quotient.
When you reach 0, you have gotten to the end of the division.
Check the steps carefully and follow them below:
Step 1:
Divide [tex]2x^4[/tex] by [tex]x^2[/tex]. You get [tex]2x^2[/tex].
Step 2
Multiply [tex]2x^2[/tex] by [tex]x^2 - 2x + 1[/tex] and subtract from [tex]2x^4 - 3x^3 - 3x^2 + 7x - 3[/tex]:
[tex]2x^4 - 3x^3 - 3x^2 + 7x - 3 - (2x^4 - 4x^3 + 2x^2)[/tex] = [tex]x^3 - 5x^2 + 7x - 3[/tex]
Step 3
Divide [tex]x^3[/tex] by [tex]x^2[/tex]. You get x.
Step 4
Multiply x by [tex]x^2 - 2x + 1[/tex] and subtract from [tex]x^3 - 5x^2 + 7x - 3[/tex]:
[tex]x^3 - 5x^2 + 7x - 3 - (x^3 - 2x^2 + x) = -3x^2 +6x - 3[/tex]
Step 5
Divide [tex]-3x^2[/tex] by [tex]x^2[/tex]. You get -3
Step 6
Multiply -3 by [tex]x^2 - 2x + 1[/tex] and subtract from [tex]-3x^2 +6x - 3[/tex]:
[tex]-3x^2 +6x - 3 - (-3x^2 + 6x -3) = 0[/tex]
From the three divisions, we got [tex]2x^2[/tex], x and -3.
Therefore, the quotient is [tex]2x^2 + x - 3[/tex].
The product of 6 and a number (n) is 48 . Which equation shows this relationship? ANSWER CHOICES: 6n=48 n+6=48 48n=6 n-6=48
Answer:
6n=48
Step-by-step explanation:
product means multiplication
6×n=48
6n=48
An equation that shows this relationship is: A. 6n = 48.
How to determine the equation representing the product?In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:
Let the variable n represent the unknown number.
Based on the statement "The product of 6 and a number is 48," we can logically deduce the following algebraic equation;
6 × n = 48
6n = 48
n = 48/6
n = 8.
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What is the solution to the system that is created by the equation y = 2 x + 10 and the graph shown below? On a coordinate plane, a line goes through (negative 2, 0) and (0, 2). (–8, –6) (–4, –2) (0, 2) (2, 4)
Answer:
(–8, –6)
Step-by-step explanation:
The given points represent the x- and y- intercepts of the line, so we can write the equation in intercept form as ...
x/(x-intercept) +y/(y-intercept) = 1
x/(-2) +y/2 = 1 . . . use the given intercepts
x - y = -2 . . . . . multiply by -2
Then the system is ...
y = 2x +10x - y = -2Using the first to substitute into the second, we get ...
x - (2x +10) = -2
-8 = x . . . . . . . . . . . add x+2, simplify
y = 2(-8) +10 = -6
The solution is (x, y) = (-8, -6).
Answer:
(-8,-6)
Step-by-step explanation:
Got it right on edge soooo <3
Graph the equation y=−4x+3 by plotting points.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
y=4x+3
The circumference of C is 72cm. What is the length of AB (the minor arc)
Answer:
Step-by-step explanation:
Can you please include a image?
Thanks!!!
(25 points) PLEASE HELP! Gotta get this done before my mom comes home
1. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag?
A. Cashews: 0.10 lb.; peanuts: 0.40 1b.
B. Cashews: 0.42 lb.; peanuts: 0.08 1b.
C. Cashews: 0.40 lb.; peanuts: 0.10 1b
D. Cashews: 0.27 lb.; peanuts: 0.23 1b.
E. Cashews: 0.23 lb.; peanuts: 0.27 1b.
F. Cashews: 0.08 lb.; peanuts: 0.42 1b
2. A nursery owner has 288 rose bushes. There are 36 fewer red roses than pink roses. How many of each type of roses are there?
A. Red roses: 162; pink roses: 252.
B. Red roses: 162; pink roses: 126.
C. Red roses: 99; pink roses: 126.
D. Red roses: 126; pink roses: 162
E. Red roses: 126; pink roses: 99
F. Red roses: 252; pink roses: 162
3. The sum of the ages of Stephanie and Heather is 46. Heather is two years younger than Stephanie. Write a system of equations to determine the ages of Stephanie and Heather.
A) S + H = 46
H = S + 2
B) S - H = 46
H - 2 = S
C) S + H = 46
H = S - 2
D) S - H = 2
H = S - 46
E) S + H = 2
H = S - 46
F) 2S – H = 46
4. You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here’s the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?
A. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 12 country CDs, and 3 soundtracks.
B. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and 3 soundtracks.
C. After borrowing 3 rock CDs, your friend will have 25 rock CDs, 10 country CDs, and 4 soundtracks.
D. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 9 country CDs, and 3 soundtracks.
E. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and no soundtracks.
F. After borrowing 3 rock CDs, your friend will have 18 rock CDs, 15 country CDs, and 3 soundtracks.
5. Three times the width of a certain rectangle exceeds twice its length by two inches. Four times its length is twelve more than its perimeter. Write a system of equations that could be used to solve this problem. (hint: P = 2L + 2W)
A) 3W = 2L + 2
2L = 2W + 12
B) 3W + 2 = 2L
4L = P – 12
C) 3W = 2L + 2
4L + 12 = P
D) 2W + 2 = 2L
4L = 12 + P
E) 3W + 2 = 2L
4L = 12 + P
F) 2L – 2 = 3W
P = 4L - 12
Thank you!!!!
HELP PLEASE FOR 35 POINTS!!!! Solve the rational equation 3 divided by x equals quantity 4 times x plus 3 divided by x squared, and check for extraneous solutions.
Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
So, we are given:
[tex]\frac{3}{x}=\frac{4x+3}{x^2}[/tex]
First, we should immediately rule out 0 as an answer. This is because the if [tex]x=0[/tex], the equation would be undefined.
[tex]x\neq 0[/tex]
Now, cross multiply.
[tex]3(x^2)=x(4x+3)[/tex]
[tex]3x^2=4x^2+3x[/tex]
Divide everything by x (and we can do this safely because we already know x cannot be equal to zero).
[tex]3x=4x+3[/tex]
[tex]-x=3[/tex]
[tex]x=-3[/tex]
We didn't run into any possibilities for extraneous solutions.
The half-life of a radioactive isotope is the time it takes for a quantity of the Isotope to be reduced to half its initial mass. Starting with 210 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Round your answer to the nearest gram
Answer:
after 6 half lives: 210(1/2)^6= 3.28125
Step-by-step explanation:
isotope to be reduced to half its initial mass at first:
210(1/2)=105 half it is original weight
after second life: 210(1/2)^2=105(1/2)=52.5
after third : 210(1/2)^3=52.5/2=26.25
after fourth : 26.25/2=12.125
after fifth : 13.125/2
after 6 half lives: 210(1/2)^6= 3.28125