Answer:
The upper confidence bound for population mean escape time is: 379.27
The upper prediction bound for the escape time of a single additional worker is 413.64
Step-by-step explanation:
Given that :
sample size n = 26
sample mean [tex]\bar x[/tex] = 371.08
standard deviation [tex]\sigma[/tex] = 24.45
The objective is to calculate an upper confidence bound for population mean escape time using a confidence level of 95%
We need to determine the standard error of these given data first;
So,
Standard Error S.E = [tex]\dfrac{\sigma }{\sqrt{n}}[/tex]
Standard Error S.E = [tex]\dfrac{24.45 }{\sqrt{26}}[/tex]
Standard Error S.E = [tex]\dfrac{24.45 }{4.898979486}[/tex]
Standard Error S.E = 4.7950
However;
Degree of freedom df= n - 1
Degree of freedom df= 26 - 1
Degree of freedom df= 25
At confidence level of 95% and Degree of freedom df of 25 ;
t-value = 1.7080
Similarly;
The Margin of error = t-value × S.E
The Margin of error = 1.7080 × 4.7950
The Margin of error = 8.18986
The upper confidence bound for population mean escape time is = Sample Mean + Margin of Error
The upper confidence bound for population mean escape time is = 371.08 + 8.18986
The upper confidence bound for population mean escape time is = 379.26986 [tex]\approx[/tex] 379.27
The upper confidence bound for population mean escape time is: 379.27
b. Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.
The standard error of the mean = [tex]\sigma \times \sqrt{1+ \dfrac{1}{n}}[/tex]
The standard error of the mean = [tex]24.45 \times \sqrt{1+ \dfrac{1}{26}}[/tex]
The standard error of the mean = [tex]24.45 \times \sqrt{1+0.03846153846}[/tex]
The standard error of the mean = [tex]24.45 \times \sqrt{1.03846153846}[/tex]
The standard error of the mean = [tex]24.45 \times 1.019049331[/tex]
The standard error of the mean = 24.91575614
Recall that : At confidence level of 95% and Degree of freedom df of 25 ;
t-value = 1.7080
∴
The Margin of error = t-value × S.E
The Margin of error = 1.7080 × 24.91575614
The Margin of error = 42.55611149
The upper prediction bound for the escape time of a single additional worker is calculate by the addition of
Sample Mean + Margin of Error
= 371.08 + 42.55611149
= 413.6361115
[tex]\approx[/tex] 413.64
The upper prediction bound for the escape time of a single additional worker is 413.64
HELP PLEASE! A Blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if she hides 20 acorns per tree, there will be extra space for an additional four acorns (the number of trees is always the same). How many acorns is the Blue Jay going to store for the winter, and in how many trees?
Answer:
Step-by-step explanation:
Let
T = number of trees
A = number of acorns
Given:
A = 18T + 4 ...........................(1)
A = 20T -4 .........................(2)
Equate A from (1) and (2)
20T-4 = 18T+4
simplify and solve for T
20T - 18T = 4+4
2T = 8
T = 4 trees
A = 18T + 4 = 72+4 = 76 acorns, or
A = 20T - 4 = 80 - 4 = 76 acorns.
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
Write the equation of the line in point-slope form that passes through (1, -4) and has a slope of 1/4.
Answer:
y + 4 =(1/4)(x - 1)
Step-by-step explanation:
The point slope equation is y - k = m(x - h), where (h, k) is the given point and m is the given slope.
In this particular case we have y + 4 =(1/4)(x - 1)
Why 200/3 doesn’t work
Answer:
it does work
i think u mean why is it not whole
but it is not a whole number
Step-by-step explanation:
200/3=66.6(6 is repeating)
for example if u have 200 chocolates and u give them to 3 people
everyone will have 66
and u will have 2 left
2/3 is also 0.66(6 repeating)
66+0.66(6repeating)
=66.66(6repeating0
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
-ZYLYNN JADE ARDENNE
Answer:
Step-by-step explanation:
it does not work as a whole number.
but it does work in simple division with fraction.
200 / 3 = 66 and [tex]\frac{2}{3}[/tex]
Question 3
Which of the following best describes the solution to the system of equations below?
-6x + y=-3
7x-y=3
The system of equations has exactly one solution where x = 6 and y = 3.
The system of equations has no solution.
The system of equations has infinitely many solutions.
The system of equations has exactly one solution where x = 0 and y=
-3
Answer:
The system has exactly one solution where x = 0 and y = -3.
Step-by-step explanation:
-6x + y = -3
7x - y = 3
(7x - 6x) + (y - y) = 3 - 3
x + 0 = 0
x = 0
7(0) - y = 3
0 - y = 3
-y = 3
y = -3
-6(0) + y = -3
0 + y = -3
y = -3
So, the system has exactly one solution where x = 0 and y = -3.
Hope this helps!
A Car Salesman sold $450000.00 in cars for the month of July.
He is paid a monthly salary of $6000.00 and 5% commission on
total sales. How much did he earn in July?
Answer:
$28,500
Step-by-step explanation:
$6,000 + 5% of $450,000 =
= $6,000 + 0.05 * $450,000
= $6,000 + $22,500
= $28,500
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 240240 engines and the mean pressure was 7.57.5 pounds/square inch (psi). Assume the population standard deviation is 1.01.0. The engineer designed the valve such that it would produce a mean pressure of 7.67.6 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.10.1 will be used. Find the P-value of the test statistic. Round your answer to four decimal places.
Answer:
p-value = 0.1213 (to 4-decimal places)
Step-by-step explanation:
Given:
N = 240
mean = 7.5
s = 1.0
Solution
With N=240 and using the central limit theorem, distribution can be approximated as normal.
Let
Null hypothesis H0, mu = 7.6
Alternate hypothesis, mu not equal to 7.6 (two-tail test)
for
Alpha = 0.1 (two sided)
Z = sqrt(N)(mean – mu)/s = sqrt(240)(7.5-7.6)/1.0 = -1.54919
p-value
= P(|Z|>1.54919)
= 2P(Z>1.54919)
= 2(1-P(Z<1.54919)
=2(1-0.9393) (using normal distribution table)
=0.12134
Since alpha = 0.1 < p-value (0.1213), H0 that mean = 7.6 is not rejected.
A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the 0.10 significance level, is there a relationship between job pressure and age.
(Round your answers to 3 decimal places.)
Degree of Job Pressure
Age (years) Low Medium High
Less than 25 25 27 20
25 up to 40 49 53 40
40 up to 60 59 59 52
60 and older 35 42 44
H0: Age and pressure are not related. H1: Age and pressure are related.
Reject H0 if X2 > .
X2=
(Click to select)Reject Do not reject H0. Age and pressure (Click to select)areare not related.
Answer:
Reject H0
Age and pressure are related
Step-by-step explanation:
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. In the given scenario we reject the null hypothesis because job pressure and age are related to each other.
11. A certain brand of margarine was analyzed to determine the level of polyunsaturated fatty acid (in percent). A sample of 6 packages had an average of 16.98 and sample standard deviation of 0.31. Assuming normality, a 99% confidence interval for the true mean of fatty acid level is:
Answer: (16.47, 17.49)
Step-by-step explanation:
Formula for confidence interval for the true mean if population stanmdard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean
n= sample size
s= sample standard deviation
[tex]t_{\alpha/2}[/tex] = Two tailed critical value.
We assume that the level of polyunsaturated fatty acid is normally distributed.
Given,
n= 6
degree of freedom = n-1 =5
[tex]\overline{x}[/tex] = 16.98
s= 0.31
significance level[tex](\alpha)[/tex] =1-0.99=0.01
Two tailed t- value for degree of freedom of 5 and significance level of 0.01 = [tex]t_{\alpha/2}=4.0317[/tex] [by student's t-table]
Now , the 99% confidence interval for the true mean of fatty acid level is:
[tex]16.98\pm 4.0317(\dfrac{0.31}{\sqrt{6}})\\\\=16.98\pm 4.0317(0.126557)\\\\=16.98\pm 0.51024\\\\=(16.98-0.51023,\ 16.98+0.51023)\\\\=(16.46977,\ 17.49023)\approx (16.47,\ 17.49)[/tex]
Hence, a 99% confidence interval for the true mean of fatty acid level is: (16.47, 17.49)
Does Kerri's dot plot match the data in the tally
table?
Use Kerri's dot plot to complete the statements.
_classmates spent 3 hours at the park.
_classmates spent 4 hours at the park.
_classmates spent 5 hours at the park.
_classmates spent 6 hours at the park.
Answer:
no 5,3,6,4
Step-by-step explanation:
i got it right
Answer:
first one is no second is 5 third is 3 forth one is 6 and last one is 4
Step-by-step explanation:
PLZ give me brainless.
how many terms are in the expression 6y+3+y+4y+5
Answer:
5
Step-by-step explanation:
The 5 terms in the expression are ...
6y
3
y
4y
5
__
If like terms were combined, the expression could be reduced to one with 2 terms:
11y +8
Answer:
5 terms
Step-by-step explanation:
In an expression, a term can be a number, a variable, or a number and variable multiplied together. Terms are separated by addition or subtraction.
In the expression:
6y+3+y+4y+5
There are 5 terms. The 5 terms are:
1. 6y
2. 3
3. y
4. 4y
5. 5
We can simplify this expression by combining like terms. We can add the constants (just numbers) and the terms with variables being multiplied by numbers.
6y+3+y+4y+5
(6y+y+4y)+(3+5)
11y+(3+5)
11y+8
find the maximum value of c=6x+2y
Answer:
∞
Step-by-step explanation:
c can have any value you like.
There is no maximum. We say it can approach infinity.
__
Additional comment
There may be some maximum imposed by constraints not shown here. Since we don't know what those constraints are, we cannot tell you what the maximum is.
Identify the factors of x2 − 4x − 12.
(x + 4)(x − 3)
(x − 4)(x + 3)
(x − 2)(x + 6)
(x + 2)(x − 6)
Answer:
(x + 2)(x - 6)
Step-by-step explanation:
We are given the equation: x² - 4x - 12. Let's factor this.
First, look at the integer factor pairs of -12:
-1, 12
-2, 6
-3, 4
1, -12
2, -6
3, -4
We would like to find a pair whose sum is -4. Inspecting each pair, we realise that only the pair 2, -6 works because 2 + (-6) = -4.
Thus, our factors are:
x + 2 (from the 2)
x - 6 (from the -6)
The factored form of our given quadratic is:
(x + 2)(x - 6)
~ an aesthetics lover
6th grade math , help me please :)
Answer:B
Step-by-step explanation:
A basketball team plays half of its games during the day and half at night. Ten scores from day games and ten scores from night
games were randomly selected by the team's statistician. The following statistical information was calculated from the final game
scores.
Day Night
Mean 58 72
Median 46 63
Mode 50. 70
Range 21 33
Based on these samples, what generalization can be made?
A. The basketball team scored the same number of points in day games as night games.
OB. The basketball team scored more points in night games than in day games.
OC. The basketball team scored more points in day games than in night games.
OD. Not enough information is provided to draw any of these conclusions,
Option B
Because the average points scored in the night is more than that of the day
NEED HELP AS SOON AS POSSIBLE which interval describes where the graph of the function is negative
Answer:
2 < x < ∞
Step-by-step explanation:
We want where the value of y is less than zero
The value of the graph is less than zero is from x=2 and continues until x = infinity
2 < x < ∞
Answer:
[tex]\boxed{2 < x < \infty}[/tex]
Step-by-step explanation:
The value of y should be less than 0 for the graph of the function to be negative.
In the graph, when it startes from x is 2 the value becomes less than 0 and it keeps continuing until x is equal to infinity.
[tex]2 < x < \infty[/tex]
Which of the following box plot best represents the set of data below
Answer:
C. Box plot B
Step-by-step explanation:
What is the equation of the line perpendicular to y=5x-3 that passes through the point (3, 5)?
Answer:
[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex]
Step-by-step explanation:
Hey there!
Well the slope of the perpendicular line is -1/5 because that's the reciprocal of 5.
Look at the image below ↓
By looking at the image we can conclude that the equation for the perpendicular line is,
[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex].
Hope this helps :)
Answer:
[tex]\boxed{y=-\frac{1}{5}x+\frac{28}{5}}[/tex]
Step-by-step explanation:
Part 1: Finding the new slope of the line
Perpendicular lines have reciprocal slopes of a given line - this means that the slope you are given in the first equation will be flipped and negated.
Because the slope is 5 in the first line, it gets flipped to become [tex]-\frac{1}{5}[/tex].
Part 2: Using point-slope formula and solving in slope-intercept form
Input the new slope into the slope-intercept equation: [tex]y=mx+b[/tex]. This results in [tex]y=-\frac{1}{5} x+b[/tex].
Then, use the point-slope equation to get b, or the y-intercept of the equation.
[tex](y-y_{1})=m(x-x_{1})[/tex]
[tex](y-5)=-\frac{1}{5}(x-3)\\\\y-5=-\frac{1}{5}x+\frac{3}{5} \\\\y=-\frac{1}{5}x+\frac{28}{5}[/tex]
Find the volume of each solid. Round to the nearest tenth. IMG_7097.HEIC
Answer:
You didn't put an attachment to show what solid you wanted rounded
Step-by-step explanation:
Which of the following is a correct tangent ratio for the figure?
Answer:
C) tan(39°) = 11/15
Step-by-step explanation:
SohCahToa
tangent = opposite / adjacent
The given angle is 39°. The angle directly opposite of 39° is 11 and the angle adjacent to 39° is 15.
Answer:
tan(39°) = 11∕15
Step-by-step explanation:
Help with inequality
Answer:
1. x>20 2. x≤1 3.x<4 4.x>9 5.x≥-13
According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. What is the probability the sample proportion who are satisfied with the way things are going in their life is greater than 0.85
Complete Question
According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. Suppose a random sample of 100 Americans is asked "Are you satisfied with the way things are going in your life?"
What is the probability the sample proportion who are satisfied with the way things are going in their life is greater than 0.85
Answer:
The probability is [tex]P(X > 0.85 ) = 0.21745[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.82[/tex]
The value considered is x = 0.85
The sample size is n = 100
The standard deviation for this population proportion is evaluated as
[tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]
substituting values
[tex]\sigma = \sqrt{\frac{0.82(1-0.82)}{100} }[/tex]
[tex]\sigma = 0.03842[/tex]
Generally the probability that probability the sample proportion who are satisfied with the way things are going in their life is greater than x is mathematically represented as
[tex]P(X > x ) = P( \frac{X - p }{ \sigma } > \frac{x - p }{ \sigma } )[/tex]
Where [tex]\frac{X - p }{ \sigma }[/tex] is equal to Z (the standardized value of X ) so
[tex]P(X > x ) = P( Z> \frac{x - p }{ \sigma } )[/tex]
substituting values
[tex]P(X > 0.85 ) = P( Z> \frac{ 0.85 - 0.82 }{ 0.03842 } )[/tex]
[tex]P(X > 0.85 ) = P( Z> 0.78084)[/tex]
from the standardized normal distribution table [tex]P( Z> 0.78084)[/tex] is 0.21745
So
[tex]P(X > 0.85 ) = 0.21745[/tex]
Penyelesaian
0.02 m: 3 cm: 4.6 cm = 2 cm : 3 cm: 4.6 cm
= 2 : 3 : 4.6
20 : 30 : 46
10 : 15
23
Latih Diri 4.1a
1. Wakilkan hubungan antara tiga kuantiti berikut dalam bentuk a : b:c.
(a) 2 minggu kepada 16 hari kepada 1 minggu
(b) 0.1 kg kepada 50 g kepada 0.25 kg
(c) 4 minit kepada 120 saat kepada 1.6 jam
(d 3 m kepada 480 cm kepada 6 400 mm
2. Tahir membayar RM5.60 untuk sepinggan nasi beriani, RM1.20 untuk segelas teh
dan 30 sen untuk sekeping kuih. Wakilkan hubungan harga bagi nasi beriani, teh dan
kuih dalam bentuk a:b:c.
76
BAB 4
Answer:
a:b:c
1a) 14:16:7
b) 2:1:5
c) 2:1:48
d) 15:24:32
2) 56:12:3
Step-by-step explanation:
Untuk membentuk nisbah tiga kuantiti, pertama-tama kita menukar masing-masing menjadi unit yang sama.
a) 2 minggu hingga 16 hari hingga 1 minggu
Menukar semuanya menjadi bilangan hari, kerana ia sangat setanding.
2 minggu = 14 hari
16 hari = 16 hari
1 minggu = 7 hari
2 minggu hingga 16 hari hingga 1 minggu = 14 hari hingga 16 hari hingga 7 hari
14: 16: 7
b) 0.1 kg hingga 50 g hingga 0.25 kg
Menukar semua menjadi gram
= 100 g hingga 50 g hingga 250 g
= 100: 50: 250
Bahagikan dengan 50
= 2 : 1 : 5
c) 4 minit hingga 120 saat hingga 1.6 jam
Menukar semua menjadi beberapa saat
= 240 saat hingga 120 saat hingga (1.6 × 60 × 60) saat
= 240 saat hingga 120 saat hingga 5,760 saat
= 2: 1: 48
d) 3 m hingga 480 cm hingga 6 400 mm
Menukar semua ini menjadi mm
= 3000 mm hingga 4800 mm hingga 6400 mm
Membahagi hingga 200 mm
= 15:24:32
2) RM5.60 hingga RM1.20 hingga 30 sen
Menukar semuanya kepada sen
= 560 sen hingga 120 sen hingga 30 sen
Membahagi hingga 10
= 56: 12: 3
Semoga ini Membantu !!!
English Translation
Solution
0.02 m: 3 cm: 4.6 cm = 2 cm: 3 cm: 4.6 cm = 2: 3: 4.6
20:30:46
10:15:23
Self Training 4.1a
1. Represent the relationship between the following three quantities in the form a: b: c.
(a) 2 weeks to 16 days to 1 week
(b) 0.1 kg to 50 g to 0.25 kg
(c) 4 minutes to 120 seconds to 1.6 hours
(d) 3 m to 480 cm to 6 400 mm
2. Tahir pays RM5.60 for a plate of beriani rice, RM1.20 for a glass of tea and 30 cents for a piece of cake.
Represent the price relationship for beriani rice, tea and cake in the form of a: b: c.
Solution
To form a ratio of three quantities, we first convert each of them to the same units.
a) 2 weeks to 16 days to 1 week
Converting all of it to number of days, as itnis very comparable.
2 weeks = 14 days
16 days = 16 days
1 week = 7 days
2 weeks to 16 days to 1 week
= 14 days to 16 days to 7 days
14 : 16 : 7
b) 0.1 kg to 50 g to 0.25 kg
Converting all into grams
= 100 g to 50 g to 250 g
= 100 : 50 : 250
Divide through by 50
= 2 : 1 : 5
(c) 4 minutes to 120 seconds to 1.6 hours
Converting all into seconds
= 240 seconds to 120 seconds to (1.6×60×60) seconds
= 240 seconds to 120 seconds to 5,760 seconds
= 2:1:48
(d) 3 m to 480 cm to 6 400 mm
Converting all of this to mm
= 3000 mm to 4800 mm to 6400 mm
Dividing through by 200 mm
= 15:24:32
2) RM5.60 to RM1.20 to 30 cents
Converting it all to cents
= 560 cents to 120 cents to 30 cents
Dividing through by 10
= 56:12:3
Hope this Helps!!!
find 10th term of a geometric sequence whose first two terms are 2 and -8. Please answer!!
Answer:
The 10th term is -524,288
Step-by-step explanation:
The general format of a geometric sequence is:
[tex]a_{n} = r*a_{n-1}[/tex]
In which r is the common ratio and [tex]a_{n+1}[/tex] is the previous term.
We can also use the following equation:
[tex]a_{n} = a_{1}*r^{n-1}[/tex]
In which [tex]a_{1}[/tex] is the first term.
The common ratio of a geometric sequence is the division of the term [tex]a_{n+1}[/tex] by the term [tex]a_{n}[/tex]
In this question:
[tex]a_{1} = 2, a_{2} = -8, r = \frac{-8}{2} = -4[/tex]
10th term:
[tex]a_{10} = 2*(-4)^{10-1} = -524288[/tex]
The 10th term is -524,288
What is the value of Sine theta in the diagram below?
Answer:
C) 24/25
Step-by-step explanation:
did the quiz and got it right
The value of the sine theta in the first quadrant in the diagram given is [tex]\mathbf{\dfrac{24}{25}}[/tex]
What is the trigonometric function in the first quadrant?The explanation of the trigonometric functions (i.e cosine, sine, tangent) in respect of point coordinates on the unit circle informs us of the signs and meanings of the trigonometric functions for each of the four(4) quadrants, depending on the signs of the x, as well as, y coordinates in each quadrant.
In the first quadrant;
cos(θ) > 0, sin(θ) > 0 andtan(θ) > 0Thus, we have a positive x and y-axis.
Taking the forms x and y, i.e. (x, y) = (cos θ, sin θ)
The value of sine theta in [tex]\mathbf{(\dfrac{7}{25}, \dfrac{24}{25} ) = \dfrac{24}{25} }[/tex]
Learn more about Trigonometric functions here:
https://brainly.com/question/24349828
#SPJ2
Please help. I’ll mark you as brainliest if correct!
Answer:
x +0y+0z = 400
-x +y+0z = 150
-8x +0y +z = 250
Step-by-step explanation:
The last column is the solution
The rest of the columns are the coefficients of the variables
x +0y+0z = 400
-x +y+0z = 150
-8x +0y +z = 250
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.
Answer:
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
Step-by-step explanation:
The amount of Carbon-14 after t years is given by the following equation:
[tex]A(t) = A(0)e^{-rt}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.
This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]
How many years will it take for carbon–14 to decay to 10 percent of its original amount?
This is t for which:
[tex]A(t) = 0.1A(0)[/tex]
So
[tex]A(t) = A(0)e^{-rt}[/tex]
[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]
[tex]e^{-0.000124t} = 0.1[/tex]
[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]
[tex]-0.000124t = \ln{0.1}[/tex]
[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]
[tex]t = 18569.2[/tex]
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
6.52
65.2
0.652
order it least to greatest which comes first?
Answer:
Hey! The answer will be below!! :)
Step-by-step explanation:
In least to greatest the answer will be....
0.652, 6.52, 65.2
0.652 comes first because since the decimal point is between the 0 and 6
It’s also because 0 is less than 6 and 65.
Here is a easy way to do this, when you have this kind of question.
First look where the decimal is.
Pretend it’s a whole number like, 0.652 becomes 0
And 6.52 becomes 6, also 65.2 becomes 65
You have to use the decimal to find out least to greatest, also you will have to round the number.
So remember, when ever you have this kind of question...after the decimal point like 65.2 you take away the .2 and just have 65....this will help you do least to greatest faster! :)
Hope this helps!
Answer:
0.652, 6.52, 65.2
Step-by-step explanation:
You have to round to find the answer in a easy way.
Least to greatest would be 0.652, 6.52, 65.2
Hop it will help u
When a person throws a ball into the air, it follows a parabolic path that opens downward as shown in the figure to the right. Suppose that the ball's height in feet after t seconds is given by h(t)=-16t^2+32t+2. If possible, determine the time(s) when the ball was at a height of 14 feet.
Answer:
0.5 seconds and 1.5 seconds.
Step-by-step explanation:
h(t) = -16t^2 + 32t + 2
14 = -16t^2 + 32t + 2
16t^2 - 32t - 2 + 14 = 0
16t^2 - 32t + 12 = 0
8t^2 - 16t + 6 = 0
4t^2 - 8t + 3 = 0
(2x - 3)(2x - 1) = 0
2x - 3 = 0
2x = 3
x = 3/2
x = 1.5
2x - 1 = 0
2x = 1
x = 1/2
x = 0.5
So, the ball was at 14 feet at 0.5 seconds and 1.5 seconds.
Hope this helps!
If the image is blurry the answer choices are -1,0,1,2,and 3. The question says select each correct answer
Answer:
12Step-by-step explanation:
There is no algebraic way to solve such an equation. It can be simplified to ...
[tex]-2x-6=-2^x-6\\\\2x-2^x=0\qquad\text{add $2x+6$}[/tex]
This has solutions at x=1 and x=2 as shown in the attached graph.
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The second attachment shows the functions graphed on the same graph.