Answer:
Step-by-step explanation:
The formula you will need for this is:
[tex]A=A_0(\frac{1}{2})^{\frac{t}{H}[/tex] where A is the amount after some decay has happened, A₀ is the intial amount, t is the time in hours, and H is the half-life in hours. Those values for us are:
A = 2 g
A₀ = 25 g
H = 4.95 hrs and
t = ?
Filling in:
[tex]2=25(\frac{1}{2})^{\frac{t}{4.95}[/tex] Keep in mind that, because of the nature of the exponential form of this equation, you CANNOT simply multiply the 25 by the 1/2. Exponential equations don't work that way. Begin instead by dividing both sides by 25 to get
[tex].08=(\frac{1}{2})^{\frac{t}{4.95}[/tex] The goal is to get that t out from its exponential position. Do that by taking the natural log of both sides:
[tex]ln(.08)=ln(.5)^{\frac{t}{4.95}[/tex]
After you take the natural log of the right side, the property allows you to bring the exponent down out front:
[tex]ln(.08)=\frac{t}{4.95}ln(.5)[/tex]
Now divide both sides by ln(.5) to get
[tex]\frac{ln(.08)}{ln(.5)}=\frac{t}{4.95}[/tex]
Simplify the left side out on your calculator to get
[tex]\frac{-2.525728644}{-.6931471806}=\frac{t}{4.95}[/tex] and then divide:
[tex]3.643856=\frac{t}{4.95}[/tex]
Finally, multiply both sides by 4.95 to get
3.643856(4.95) = t so
t = 18.0 hours which is choice C
Clinical literature reports that the duration of a typical cold is roughly 18 days. Researchers wanted to know if people tend to underestimate the duration of a typical cold, on average. They surveyed a random sample of 352 healthy adults in Georgia and asked them how long they think that a typical cold lasts. The researchers reported a 95% confidence interval of 6.9 to 8.2 days for the mean expected duration of typical cold. The researchers reported that the answers to this question were strongly right-skewed. The 95% confidence interval (6.9, 8.2) they obtained is
Answer:
The 95% confidence interval (6.9, 8.2) they obtained means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".
Option B from the complete Question.
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution if there is no information provided for the population standard deviation and it is obtained from the z-tables if the population standard deviation is known or the sample size is large enough that the sample properties can be approximated to be the same as the population properties.
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample
n = sample size
Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
So, the confidence interval (6.9, 8.2) obtained in the question means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".
Hope this Helps!!!
Un ascensor sube desde el primer piso al quinto piso, baja al segundo, sube al octavo. Si cada piso tiene 3 metros de altura, ¿cuántos metros recorrió el ascensor?
Answer:
El ascensor recorrió unos 39 metros
Step-by-step explanation:
Segun la pregunta cada cada piso tiene 3 metros de altura, por lo tanto para calcular los metros que recorrió el ascensor tenemos que hacer el siguiente calculo:
metros desde el primer piso al quinto piso=3 metros*4=12 metros
metros desde el quinto piso al segundo piso=3 metros*3=9 metros
metros desde el segundo piso al octavo piso=3 metros*6=18 metros
Por lo tanto los metros que recorrió el ascensor=12 metros+9 metros+18 metros
metros que recorrió el ascensor=39 metros
El ascensor recorrió unos 39 metros
PLZ HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1²+3
Step-by-step explanation:
I'm not to sure I hope this helped.
A top view of two walls of a room is represented by the x and y-axis, with units in meters. A ball is rolled from the point (0,15). It hits the adjacent wall at (20,0). Find the absolute value function that models the path of the ball. Determine when the ball passes within 3 meters of the wall represented by the x-axis.
Answer:
The absolute value function that models the path of the ball is
[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]
The coordinates when the ball passes within 3 meters of the wall is [tex]\left (3, 12\tfrac{3}{4} \right )[/tex]
Step-by-step explanation:
Given that the ball rolls without other external influences, we have;
(y - 0) = (x - 15)
The slope, m is give by the relation;
m = (y₂ - y₁)/(x₂ - x₁)
m = (15 - 0)/(0-20) = -3/4
The equation of the path of the ball in slope and intercept form is presented as follows;
y = m·x + c
15 = -3/4 ×0 + c = 15
c = 15
The absolute value function that models the path of the ball is then;
[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]
The vale of the function when x = 3 is given by the relation
[tex]f(x) = \left | -\dfrac{3}{4}\times 3 + 15 \right | = \dfrac{51}{4}[/tex]
Therefore, we have the coordinates as [tex]\left (3, 12\tfrac{3}{4} \right )[/tex].
1. The perimeter of the given triangle PQR is
cm
P
7cm
3cm
R
4cm
O 16
28
26
65
Answer:
No, it is not possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm because here we see that sum of the lengths of two sides is equal to third side i.e., 4+3 = 7. As we know that, the sum of any two sides of a triangle is greater than its third side, so given statement is not correct.
Step-by-step explanation:
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answer:
42.1
Explanation step-by-step:
Working out the lenght of the blue-dashed line:
SOH
47 is the Hypotenuse.
the blue line is the adjacent.
adjacent= Cos(30) x47
adjacent= 40.7
Working out x :
40.7 is the opposite this time.
x is the adjacent.
x = 40.7/ Tan(44)
x = 42.1
If a family threw away 2.4 Kg of aluminum in a month, how many cans did they throw away?
Answer:
150 cans were thrown away
Step-by-step explanation:
If the weight of 10 aluminum cans=0.16 kilogram
Each can weighs=0.16 kilograms/10
=0.016kg per can
If the family threw away 2.4 kilogram of aluminum in a month,
How many cans did they throw away?
Total cans thrown away= Total kilogram of cans/each kilogram of cans
=2.4kg/0.016kg
=150 cans
150 cans were thrown away
Write the expression in simplest form. (-11/2x+3)-2(11/4x-5/2)
Answer:
-11x+8 or 8-11x
Step-by-step explanation:
I need help fast please
Answer:
The answer is D
What are the three main areas of a machine?
Answer:
Well on a machine there are 3 fundamental areas which are the point of operation, the power transmission device, and the operating controls.
You can find more of this information on google if youd like.
plz answer this one clip is down below will mark brainiest if get it right thank you
Answer:
Third option is correct.
Step-by-step explanation:
Take a closer look at the box plot given in the question. The range of the values represented in the box plot is starts from where the whiskers begins from our left, and where the whiskers to our right ends. The range of values of the points awarded ranges from 0 - 100, as represented on the box plox. Also,the median is indicated by the vertical line that divides the rectangular box into two. The median point = 70.
Now, examine all the dot plots given as options. The dot plot that has a range of 0 - 100, and a median of 70, is the dot plot that best represents the box plot.
Thus, the third option among the answer choices given would be out answer. The third option shows a dot plot with range of values of points from 0 - 100, and also a median of 70 points.
If the number of bacteria in a colony doubles every 10 hours and there is currently a population of 300 bacteria, what will the population be 20 hours from now?
Answer:
1200 bacteria
Step-by-step explanation:
20 hours divided by 10 hours = 2, so it will be doubled two times.
300 times 2 for the first doubling = 600
600 times 2 for the second doubling = 1200
Plz help fast Question 1(Multiple Choice Worth 5 points) (8.01 LC) Two lines, A and B, are represented by the equations given below: Line A: x + y = 6 Line B: x + y = 4 Which statement is true about the solution to the set of equations? There are infinitely many solutions. There is no solution. It is (6, 4). It is (4, 6).
Answer:
(B) There is no solution.
Step-by-step explanation:
Given the two lines A and B where:
[tex]L$ine A: x + y = 6 \implies y=6-x\\$Line B: x + y = 4 \implies y=4-x\\$Therefore:$\\6-x=4-x\\-x+x=4-6\\0=-2\\$Since, $ 0\neq -2,$ there is no solution.[/tex]
The correct option is B.
Answer:
A
Step-by-step explanation:
Just took test, can I have Brainliest.
Hiya can someone please help me on my maths ratio work?!?
Arthur is organising his collection of DVDs. He has 152 altogether
The ratio of comedy films to action to horror is 6:8:5
How many of each DVD does he have?
What is the mean of this data set? If necessary, round your answer to the
nearest tenth.
20, 23, 32, 36, 41, 43, 44, 45, 47, 54, 55, 59, 61, 63, 66
Answer:
A
Step-by-step explanation:
Answer:
A. 45.9
Step-by-step explanation:
the sum of the data values(numbers), divided by the number of data values (in your case 15)
Rectangle A,B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-8, -6), B(-3,-6), C(-3, -4), D(-8, -4). Given these coordinates, what is the length of side AB of this rectangle?
Answer:
AB= 5 units
Image of coordinates is shown in the attachment.
Twice the difference of a number and 5 is equal to three times the sum of the number and 2. Find the number.
Answer:
The number is - 16Step-by-step explanation:
Let the number be x
Twice the difference of a number and 5 is written as
2( x - 5)
three times the sum of the number and 2 is written as
3( x + 2)
Equate them
We have
2(x - 5) = 3(x + 2)
Expand
2x - 10 = 3x + 6
Group like terms
2x - 3x = 16 + 10
- x = 16
Multiply through by - 1
x = - 16
Hope this helps you
What is the answer please help! make sure to explain. thanks!! Mrs. Anderton is giving a test in her third-period class. She has decided to record the amount of time that each student takes to finish the test (in minutes) and compare that to the grade each student receives on the test (out of 100). A plot of her results is below. Which of the following does this situation represent? A. both a relation and a function B. a function only C. neither a relation nor a function D. a relation only
Answer:
A
achievements
Step-by-step explanation:
In a school auditorium, the number of chairs in a row is the same as the number of rows of chairs. There are 7033 students in the school. If we know that less than 31 chairs were empty, how many chairs were empty after all the students sat down?
Same number of rows to chairs in a row would form a square.
Use the total number of students as the area
Find the number or rows by taking the square root of student:
The square root of 7033 is 83.86
Round up to 84
Total seats would be rows x seats per row:
84 x 84 = 7,056 total seats
7056 seats - 7033 students = 23 empty seats
Which of the two functions below has the largest maximum y-value?
f(x) = -3x^4-14
g(x) = -x^3 + 2
Answer:
B. g(x)
Step-by-step explanation:
If you graph both equations in a graphing calc, you should see that the maximum y-value of f(x) is -14 (it's a parabola facing down) while the maximum y-value of g(x) is infinite.
If c+1/d=5 , what is the value of 30d/2c+2
Answer:
3
[tex]d\in R,\hspace{5}d\neq 0[/tex]
Step-by-step explanation:
You can solve for any variable. From the first equation, let's solve for c :
[tex]\frac{c+1}{d} =5\\\\c+1=5d\\\\c=5d-1[/tex]
Now, replace the value of c into the other equation:
[tex]\frac{30d}{2c+2} \\\\\frac{30d}{2(5d-1)+2} \\[/tex]
Using distributive property
[tex]\frac{30d}{10d-2+2} =\frac{30d}{10d} =3[/tex]
However, keep in mind that this is true for:
[tex]d\in R,\hspace{5}d\neq 0[/tex]
Find the length of side a
Answer:
a = 8.
Step-by-step explanation:
a^2 + b^2 = c^2
b = 6; c = 10
a^2 + 6^2 = 10^2
a^2 + 36 = 100
a^2 = 64
a = plus or minus 8
Since side lengths can't be negative, a = 8.
Hope this helps!
The shorter leg of a 30°−60°−90° triangle is 4 in. Find the hypotenuse and the other leg. Answer: The length of the hypotenuse is ________ in. The length of the other leg is __________in.
Answer:
The length of the hypotenuse is 8 inches; the length of the longer leg is 4√3 inches.
Step-by-step explanation:
Note that tan 60 degrees = (length of longer leg) / (length of shorter leg), or
tan 60 degrees = (length of longer leg) / 4 in.
Thus, (length of longer leg) = (4 in)(tan 60 degrees)
= (4 in) [√3/1] = 4√3 in
Also, cos 60 degrees = (adjacent side) / (hypotenuse. We want to find the hypotenuse and thus solve this equation for it:
(hypotenuse) = (adjacent side) / (cos 60) = (4 in)( 2/1 ) = 8 in
The length of the hypotenuse is 8 inches; the length of the longer leg is 4√3 inches.
There are only green pens and red pens in a box. there are 3 more red pens than green pens in the box. sheila is going to take at random two pens from the box the probability that sheila will take two pens of the same color is 17/35 work out two different numbers of green pens that could be in the box
Answer: 6 or 9
Step-by-step explanation:
Given the following :
Let the number of green pens = x
Number of red pens = x + 3
Probability of picking same color = 17/35
Taking two pens at random; probability of picking two pens of same color.
Probability of picking red on first pick then red on second pick ; or picking blue on first pick then blue on second pick
Probability = (Required outcome / Total possible outcomes)
Total number of pens = x + x + 3 = 2x + 3
Probability of picking red then red:
P(red first) = (x+3)/2x+3
P(red second) = x+3-1 / 2x+3-1 = (x+2)/2x+2)
Therefore, probability of red then red =
(x+3)/(2x+3) × (x+2)/2x+2)
= (x+3)(x+2) / (2x+3)(2x+2)
Probability of green then green:
P(first green) = x/(2x+3)
P(second green) = (x-1) / (2x+3-1) = (x-1) / (2x+2)
P(green then green) = x(x-1)/(2x+3)(2x+2)
Therefore,
[(x+3)(x+2) / (2x+3)(2x+2)] + [x(x-1)/(2x+3)(2x+2)] = 17/35
(x+3)(x+2)+x(x-1) / (2x+3)(2x+2) = 17/35
Cross multiply :
35(x+3)(x+2)+x(x-1) = 17(2x+3)(2x+2)
35(2x^2 + 4x + 6) = 17(4x^2 + 10x + 6)
70x^2 + 140x + 210 = 68x^2 + 170x + 102
70x^2 - 68x^2 + 140x - 170x + 210 - 102 = 0
2x^2 - 30x + 108 = 0
Now we have a quadratic equation which can be factoeized used using any known factorization method.
Factorizing this, we get
(x-6) = 0 or (x-9) = 0
x = 6 or x = 9
HELP WITH MATH PLS!!!
Answer:
Option A, y=8
Step-by-step explanation:
If you graph each of the equations, you will find that y=8 is the only line that crosses through the point (-3,8)
Also,
If you notice the given point, the y-coordinate is 8 indicating that the point lies on the line that has y as 8
Hope that helps!!
What does it mean if P(A or B) equals 1?
[tex]P_(_A_o_r_B_)[/tex] = 1
This means that the probability of event A or event B of happening is 1 or certainly would happen.
based on the function h(t), what will be the account value five years after the account is opened?
Answer:
Option B
Step-by-step explanation:
f(t) = 5000
g(t) = 250t
h(t) = f(t) + g(t) = 5000 + 250t
After 5 years, the amount of money in the account is:
h(t = 5) = 5000 + 250(5) = 5000 + 1250 = 6250$
Expand the following using the Binomial Theorem and Pascal's Triangle. Please show work.
(2x+3)^5
What is the domain of this function?
{x|x >0}
{x|x <8)
{x|0
{xlx < 0x8}
Answer:
x≥0, or x=[0,∞)
Step-by-step explanation:
Domain is values of x.
x≥0, or x=[0,∞)
What two numbers multiply to 1/4 and add to -1?
Answer:Are there any options?
Step-by-step explanation:
Two or more expressions with an Equal sign is called as Equation. Two numbers are x =-1/2 and y=-1/2 whose product is 1/4 and which add to -1.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We need to find two numbers whose product is 1/4 and add to -1.
Let the two numbers are x and y.
By given,
Two numbers multiply to 1/4
xy=1/4
Two numbers add to -1
x+y=-1
Let x=-y-1
Substitute in equation 1.
(-y-1)y=1/4
-y²-y-1/4=0
Multiply negative on both sides
y²+y+1/4=0
Use quadratic formula
b=1,c=1/4,a=1
y=-1±√1-1/2=-1/2
Now substitute y in x+y=-1
x-1/2=-1
x=-1+1/2
x=-1/2
Hence the two numbers are x =-1/2 and y=-1/2 whose product is 1/4 and which add to -1.
To learn more on Equation:
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