[tex]\dfrac{3a^2-6a+3}{a^2-1}\\\\=\dfrac{3(a^2 -2a+1)}{(a+1)(a-1)}\\\\=\dfrac{3(a-1)^2}{(a+1)(a-1)}\\\\=\dfrac{3(a-1)}{a+1}\\\\=\dfrac{3a-3}{a+1} ~~~\text{for}~ a\neq 1[/tex]
A rental car company charges $36.39 per day to rent a car and $0.09 for every mile
driven. Miguel wants to rent a car, knowing that:
He plans to drive 225 miles.
• He has at most $480 to spend.
Which inequality can be used to determine x, the maximum number of days Miguel
can afford to rent for while staying within his budget?
Answer:
12 days
Explanation:
480 >/= 36.39x + 20.25
The inequality to determine x, the maximum number of days Miguel
can afford to rent while staying within his budget is
202.5 + 36.39x ≤ 480
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Charges per day = $36.39
Charges per mile = $0.90
Total miles = 225
Total charges for 225 miles.
= 225 x 0.90
= $202.5
The maximum amount to spend = $480
The inequality for the maximum number of x days.
202.5 + 36.39x ≤ 480
Thus,
The inequality to determine x, the maximum number of days is
202.5 + 36.39x ≤ 480
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The temperature in the freezer is -15°C. The temperature outside the freezer is 10°C. Find the difference between these two temperatures.
Is the answer 25? Just checking :)
Answer:
Yes it is 25
Step-by-step explanation:
10 - 25 = -15
-15 + 25 = 10
Researchers are recording how much of an experimental medication is in a person's bloodstream every hour. they discover that half-life of the medication is about 6 hours.
By using the known half-life, we can see that if the initial dose is 500mg, after 4 days the medication will be 0.0076 mg.
What is the half-life?
We define half-life as the time such that the initial amount is reduced to its half.
So, if a given substance has a half-life T, then the amount of substance as a function of time, we have:
S(t) = A*e^{-t*ln(2)/T}
Where t is the variable in time units.
We know that T = 6 hours, and A, the initial dose, is 500 mg, so the formula is:
S(t) = 500mg*e^{-t*ln(2)/6h}
Then after 4 days (or 4*24h = 96h) the amount of medication is:
S(96h) = 500mg*e^{-96h*ln(2)/6h} = 0.0076 mg.
If the initial dose was 750mg, after 4 days the person would have:
S(96h) = 750mg*e^{-96h*ln(2)/6h} = 0.0114 mg
So the person would have:
0.0114 mg - 0.0076 mg = 0.038 mg more of medication.
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A construction company transported 8 stones that weighed a total of 70.22 kilograms. How much did each stone weigh?
Answer:
8.7kilos
Step-by-step explanation:
70.22 divided by 8
hope this helps!
Help me solve this please
There are 372 children, I hope my answer will be of use to you.
Ayan has $48 andis saving $10 per week and Gemma has $300 and is spending $8 per week. When will they both have the same amount of money?
Answer:
14 weeks
Step-by-step explanation:
First, write as an equation with x the number of weeks Ayan and Gemma's money:
-> Ayan's money: 48+10x because every week he wins 10 more dollars
-> Gemma's money 300-8x
Finally just solve the equation for x where ayan's money = gemma's money so :
48+10x=300-8x
add 8x on both side: 48+18x=300
substract 48 on both side to isolate x : 18x =252
devide by 18 on both side : x=14
on thursday and friday last week miss kelly rode her snowmobile 249 miles. ON friday she rode 35 more miles than she did on thursday. Howmany milesdid she ride each day? Write a system of eqautions for this situation and solve.
Step-by-step explanation:
x = miles ridden on Thursday
y = miles ridden on Friday
x + y = 249
y = x + 35
we can use the identity of the second equation in the first equation and solve :
x + (x + 35) = 249
2x + 35 = 249
2x = 214
x = 107 miles
y = x + 35 = 107 + 35 = 142 miles
on Thursday she rode 107 miles.
on Friday 142 miles.
10 people each wants 3 slices but a box has 8 slices
Answer:
you need 30 slices
a minimum of 4 boxes of pizza
Step-by-step explanation:
Planes Q and R are parallel planes. Plane Q contains line a. Plane R contains line b.
Planes Q and R are parallel. Plane Q contains line a and plane R contains line b. Both lines are going the same direction.
If a third plane could be drawn which contains both lines a and b, then
lines a and b must be parallel.
lines a and b cannot be parallel.
lines a and b must be skew.
lines a and b must be perpendicular.
Answer:
lines a and b must be parallel
Step-by-step explanation:
if lines a and b are parallel in plane r and q, then the lines must always be parallel.
Answer:
A
Step-by-step explanation:
on e2020
Please help answer the attached question
Answer:
angle BCD = 108
Step-by-step explanation:
opposite angles in a cyclic quadrilateral add to 180
so angle BDC is 180 - 72 = 108
what are the angles 32 and 114 there for??
Solve this for 100 points
Answer:
you may check in your book this question is related with stastics
Answer:
(S)=0
Step-by-step explanation:
Pleaseeeee helpppp neeed doneee asappp
Answer: 107 meters
Step-by-step explanation:
There are 2 ways to solve this:
1. The formula for arc length is: arc length = angle (in radians) * radius.
Thus, convert 123 degrees to radians by multiplying it by (pi/180), and then multiply this number by 50 (half of the diameter is the radius) in order to get 107.
2. Find the circumference of the track using C = pi*diameter and get 314.16. Then, set up a proportion: 314.16 meters / 360 degrees = x meters / 123 degrees and solve to get 107 :)
Rachel's starting salary was $45,000 per year.
Rachel received a 3.7% raise every year after her first
year. How much is Rachel making now, & years later?
Answer:
After 1 year $46,665
Vf = Vi ( 1 + r/m) ^ tm
Step-by-step explanation:
Vf = Final Value
Vi = Initial Value ($45,000)
r = Interest Rate (3.7%, put in decimal form so .037)
m = Compound Rate (amount of times it increases every year, for this it would be 1)
t = Amount of years you are forecasting
45000 * (1 + .037)²
45000 * (1.037)²
45000 * 1.075369
$48,391.605 in 2 years
Literacy
Fill in the missing letters to make Maths related words:
Venn
Set
Diagram
Universal
S_r_i_g
Event
Probability
Not
Answer:
Sorting
Step-by-step explanation:
Tom knows that in his school 10 out of every 85 students are left-handed.
There are 391 students in Tom's school.
how many students in Tom's school are left handed?
Answer:
46 are left handed
Step-by-step explanation:
divide 10 by 85 and you get 0.11764705882352941176470588235294 then multiply that by 391 and you get 46
the following shape has 1 pair of parallel sides 2, 7, 3, 8
Answer:
I think it's 8
Step-by-step explanation:
because if you think of an octagon it has eight sides and the only parallel sides is pn the top of the octagon and the bottom of the octagon
Possible or impossible?
The difference is 3.
The difference is also
-3.
Helen is having a birthday
party. Her friends arrive at
her house at 8:15 p.m. They
leave three hours later. What
time do Helen's friends leave?
Answer: 11:15 p.m 5:15 p.m.
Step-by-step explanation:
Express 6 m as a percentage of 16 m.
Answer:
37.5%
Step-by-step explanation:
the percentage is calculated as a fraction of the quantities multiplied by 100% , that is
[tex]\frac{6}{16}[/tex] × 100% = 0.375 × 100% = 37.5%
Answer:
37.5%
Step-by-step explanation:
6/16×100
37.5%
brainiest please
A national survey is conducted to assess the association between hypertension and stroke in persons over 75 years of age with a family history of stroke. Development of stroke is monitored over a 5 year follow-up period. The data are summarized below and the numbers are in millions. Compute the RELATIVE RISK of stroke in hypertensive as compared to non-hypertensive persons.
The relative risk of stroke in hypertensive as compared to non-hypertensive persons will be 1.8367.
How to calculate relative risk?From the complete information, those with hypertension that had strike is 12. Those with no hypertension but had stroke is 4.
Also, those with hypertension but don't have stroke is 37 while those with no hypertension but had stoke is 26.
Therefore, the relative risk will be:
= (12/12 + 37) / (4/4 + 26)
= 12/49 / 4/30
= 1.8367
In conclusion, the correct option is 1.8367.
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A simple random sample is drawn from a normally distributed population, and when making a statistical inference about the population mean, the margin of error is found to be 5. 9 at a 95% level of confidence. If the mean of the sample is 18. 7, what is the 95% confidence interval for the population mean? 18. 7 ± 5. 9 18. 7 ± 9. 7 18. 7 ± 11. 6 18. 7 ± 15. 2.
The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The population mean with a 95% confidence interval is 18.7±5.9.
What is the margin of error?The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.
In order to find the population of the mean, we need to subtract the margin of error from the sample mean. Therefore, the population mean with a 95% confidence interval is 18.7±5.9.
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An electrician has an income of $41,500. The income tax the electrician has to pay is 12%. What is the amount of income tax that the electrician has to pay? A) $3,840 B) $4,164 C) $4,980 D) $5,210.
Answer:
he has to pay 4980$ in tax So its C) 4,980
The amount of income tax that the electrician has to pay is $4980. Then the correct option is C.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
An electrician has an income of $41,500.
The income tax the electrician has to pay is 12%.
Then the amount of income tax that the electrician has to pay will be
Amount of income tax = 0.12 × $41500
Amount of income tax = $ 4980
Thus, the amount of income tax that the electrician has to pay is $4980.
More about the percentage link is given below.
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1. Suppose that a theater charges a school group $4.50 per student to show a special film. Suppose that the theater's operating expenses include $130 for the staff and a film rental fee of $1.25 per student.
a. What equation relates the number of students x to the theater's income I?
b. What equation relates the theater's operating expenses E to the number of students x?
c. Copy and complete the table below.
Theater Income and Expenses
Number of Students, x 0 10 20 30 40 50 60 70
Income, I ($) box box box box box box box box
Expenses, E ($) box box box box box box box box
d. On the same set of axes, graph the theater's income and operating expenses for any number of students from 0 to 100.
e. Describe the patterns by which income and operating expenses increase as the number of students in a group increases.
f. Write and solve an equation that you can use to answer the question “How many students need to attend the movie so that the theater's income will equal its operating expenses?”
g. Write an equation that represents the theater's profit. Compare your equation to those your classmates wrote.
h. Find the number of students that make each of the following inequality statements true.
i. E < 255
ii. I > 675
The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.
The equation of the theatre's incomeThe theatre charges $4.50 per student.
Assume the number of students is x, the equation of the theatre's income would be:
I(x) = 4.5x
The equation of the theatre's expensesThe theatre expense per student is $1.25, and the operating cost on the staff is $130
The equation of the theatre's expenses would be:
E(x) = 1.25x + 130
Complete the tableUsing the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:
Students, x 0 10 20 30 40 50 60 70
Income, I 0 45 90 135 180 225 270 315
Expenses, E 130 142.5 155 167.5 180 192.5 205 217.5
The graph of the theatre's income and expensesSee attachment
The pattern by which theatre's income and expenses increaseThe functions I(x) and E(x) are linear functions.
So, the pattern with which the functions increase is a linear pattern.
The number of students when the theatre's income and expenses are equal
This means that:
I(x) = E(x)
So, we have:
4.5x = 1.25x + 130
Subtract 1.25 from both sides
3.25x = 130
Divide both sides by 3.25
x = 40
Hence, the number of students is 40
The theatre profitThis is the difference between the theatre expenses and their income.
So, we have:
P(x) = E(x) - I(x)
This gives
P(x) = 1.25x + 130 - 4.5x
Simplify
P(x) = 130 - 3.25x
Solution to the inequalitiesWe have:
E(x) < 255
This gives
1.25x + 130 < 255
Subtract 130 from both sides and divide by 1.25
x < 100 students
Also, we have:
I(x) > 675
This gives
4.5x > 657
Solve for x
x > 146 students
Hence, the number of students for the inequalities are less than 100 and greater than 146
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base radius of 7cm and height of 35cm what is the cylinder's volume
Answer:
5390 cm³Step-by-step explanation:
It is given that the base radius of a cylinder is 7cm and the height is 35cm and we are asked to find the volume of the cylinder.
We must know this formula :
⇒ Volume(Cylinder) = πr²hWe will take the value of π as 22/7Now substituting the values :
⇒ Volume(Cylinder) = 22/7 × (7)² × 35
⇒ Volume(Cylinder) = 22/7 × 49 × 35
⇒ Volume(Cylinder) = 22 × 7 × 35
⇒ Volume(Cylinder) = 22 × 245
⇒ Volume(Cylinder) = 5390
Therefore,
The volume of the cylinder is 5390 cm³A circular counter top has a radius of 5 feet.
Enter the area, in square feet, of the counter top. Round your answer to the nearest tenth.
Answer:78.6[tex]ft^{2}[/tex]
Step-by-step explanation:
Area=π[tex]r^{2}[/tex]
Area=[tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex]
=[tex]\frac{22}{7}[/tex] x 25
=78.6[tex]ft^{2}[/tex]
very easy math do you know whats the answer?
3 is less than w , 7 is greater than or equal to w
[tex]3 < w \\ 7 \geqslant w[/tex]
Answer:
3 < w = 7 ≥ w
Step-by-step explanation:
Less than= "<"
Greater than or equal to = ≥
steps for Is (–5, 5) a solution to the equation y=x?
Answer:
Step-by-step explanation:
To check , substitute x = -5 and y = 5 into the given equation:
y = x
5 = -5
which is not true so (-5, 5) is not a solution.
The following shape has 1 pair of parallel sides
What is the measure of arc XZ if the angle equals 135 and the radius is 17 km
now, let's make the assumption that the arcXZ has a central angle of 135° and a radius of 17.
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=17\\ \theta =135 \end{cases}\implies s=\cfrac{(135)\pi (17)}{180}\implies s=\cfrac{51\pi }{4}\implies s\approx 40.06[/tex]
100 BRAINLY POINTS!!!
The scatter plot below shows the association between two variables.
Which two variables are most likely to have the association displayed by the scatter plot?
A. An animal's height and the number of legs it has.
B. The day of the month on which a person was born and the person's height.
C. The number of hours a person works and the amount of tips the person earns.
D. The number of hours a person spends studying and the number of hours the person spends doing
other activities.
HURRY CUH PLS
EXPLAIN YOUR ANSWER
SHOW YOUR WORK
Answer:
C
Step-by-step explanation:
This is a very interesting question,
Let's start off by determining what kind of function this is,
by looking at the graph we can say this is an almost linear function. So the correlation between the 2 values must be that if one increases the other increases according to a certain ratio which is our slope.
We want to eliminate wrong answers.
A. Does it make sense that an animal acquires more legs the taller it is?
This doesn't make any sense so A is out.
B. This is like saying, if i'm born in august i must be a good manager. There absolutely no correlation with the month you're born in, to your height.
So B is out.
C. Thus might actually make sense, the more you work, the more tips you make.
D. So basically here i'm saying is, the more i study the more activities i can do? this would be logical if the function were to be a line with a negative slope or "a decreasing line" or a "line going down". But this is not the case.
D is out.
so C must be our answer