Step-by-step explanation:
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
-6y - 30 = -6 • (y + 5)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true:
2.1 Solve : -6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
2.2 Solve : y+5 = 0
Subtract 5 from both sides of the equation :
y = -5
One solution was found :
y = -5
Answer: y=-5
Explanation:
3y-1-9y=29
3y-9y=-6y
-6y-1=29
+1 on both sides
-6y=30
÷-6
y=-5
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.
If you want to learn more about the half-life, you can read:
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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
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 cm³What 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]
The following shape has 1 pair of parallel sides
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!
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:
A 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]
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.
How much money would you have after 7 years if you invested$12,000 at 2% in order to have compounded annually?
Answer:
$1,680
Step-by-step explanation:
i think it is right because 12,000 at 2 percent=280 then 280×7= 1,680
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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A parabola has a vertex at (0,0). The equation for the directrix of the parabola is x = –4. In which direction does the parabola open? up down right left.
The parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.
What is a directrix?A parabola is a collection of points on a plane that are all at the same distance from a particular point and line. The point is called the focus of the parabola while the line is called the directrix. The directrix is perpendicular to a parabola's axis of symmetry and does not contact it.
As we know that the directrix is perpendicular to the axis of the parabola, now since the directrix is at x=-4, the parabola will be horizontal and will be opening either towards the left or the right.
As it is given that the vertex of the parabola is at (0,0) and we know that the parabola can not touch the directrix, therefore, the parabola's vertex will be at (0,0) and will open towards the right side. As shown below.
Hence, the parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.
Learn more about Directrix:
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Answer:
right
Step-by-step explanation:
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.
A large company produces an equal number of brand-mame lightbulbs and generic lightbulbs. The director of quality control sets guidelines that lightbulbs that are defect lightbulbs that are defective is not equal to the director wants to estimate the average of the two proportions. Production will be stopped if there is evidence that the proportion of all ve is greater than 0. 10. The director also believes that the proportion of brand-name proportion of generic lightbulbs that are defective. Therefore, the o estmate the proportion of brand-name lightbulbs that are defective, a simple random sample of 400 brand-name lightbulbs brand-name lightbulbs that are defective in a sample of 400, and let px represent the proportion of all brand-name lightbulbs that are defective. It is reasonable to assume that X is a binomial random variable.
(a) One condition for obtaining an interval estimate for px is that the distribution of px is approximately number of is taken and 44 are found to be defective. Let X represent the normal Is it reasonable to assume that the condition is met? Justify your answer.
(b) The suandard error of hr is approumately O 0156 Show how the value of the standard error is calculated
Using the Central Limit Theorem, we have that:
a) Since there are at least 10 successes and 10 failures, the condition is met.
b) Using the formula [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], with n = 400 and p = 0.11, the standard error is of 0.0156.
What does the Central Limit Theorem state?
It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
Item a:
44 are found to be defective, hence:
np = 44.n(1 - p) = 356.Which means that the conditions are met.
Item b:
We have that the parameters are:
[tex]n = 400, p = \frac{44}{400} = 0.11[/tex]
Hence, the standard error is given by:
[tex]s = \sqrt{\frac{0.11(0.89)}{400}} = 0.0156[/tex]
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
Which statement is true about the transformation?
It is isometric because not all side lengths and angle measures remained the same.
It is isometric because all side lengths and angle measures remained the same.
It is not isometric because not all side lengths and angle measures remained the same.
It is not isometric because all side lengths and angle measures remained the same.
Answer:
B. It is isometric because all side lengths and angle measures remained the same
Step-by-step explanation:
Answer:
B) It is isometric because all side lengths and angle measures remained the same.
Step-by-step explanation:
Got it right on edge <3
Elena drives for 3 hours at 44mph claire drives 144miles in 4 hours how far would elena travel if she drove for 3hours at the same speed as claire?
Answer:
108 miles
Step-by-step explanation:
144m/4h = 36m/1h or 36mph
36mph · 3 = 108m
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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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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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
help me quickly
102% of 120=
102 is what percent of 120? = 85.
Answer:
122.4
Step-by-step explanation:
this is easy, all we need to do is multiply 120 by 1.02, since it is 2%, and it is increasing not decreasing. when we do that, we get 122.4. to check, you can also do .02x120, to get 2.4. please mark as brainlest.
Find the missing value to the nearest hundredth.
Answer:
24.62°
Step-by-step explanation:
sin^-1 (5/12)
=24.62
Answer:
24.62°
Step-by-step explanation:
sin^-1(5÷12) = 24.62°
(if you are allowed to use calculator)
Help me due in 5 mins!
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
Solve for k.
Give an exact answer.
2.5(4k+2)=12k2.5(4k+2)=12k
Answer:
The answer would be k=5/2
Step-by-step explanation:
2.5 (4k+2)12k <- distribute the 2.5 into the parentheses
10k+5=12k <- take the parentheses out of the equation
10k-12k= -5 <- Move the like terms to one side and change the sign
-2k= -5 <- Collect the like terms & divide by -2 on both sides of the equation
k=5/2 <- Answer at the end
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 :)
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??
3a+2(4a-b)
please simplify this equation with processing
[tex]\bf \colorbox{black} {\bf {\textcolor{blue}{topic= }{ \bf { \textcolor{orange}{mathematics= }{ \bf{ \textcolor{cyan}{answer = }}}}}}}[/tex]
3a+2(4a-b)=
3a+8a-2b=
[tex] \bf \textcolor{green}{ \underbrace{11a - 2b}}[/tex]
xLasersx✨Solve for x if 2(5x + 2)^2 = 48
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
I WILL GIVE YOU BRAINLIEST PLEASE HELPPPPP
Answer: 3/2
Step-by-step explanation:
Let's consider the points (6,9) and (4,6).
The difference in the y coordinates is 3, and the diffeence in the x coordinates is 2.
So, the slope is 3/2.