The half life of the radioactive substance is 10.22 years.
What is Half Life ?Half Life is the amount of time needed by the radioactive substance to reduce to its half concentration (as compared to the initial concentration).
It is given that
y = ae⁻ᵇˣ
here a is the initial amount , y is the amount remaining after x years
a = 90mg at x =0
Value of y = 12.6 mg at x = 29 years
On substitution of value
12.6 = 90 e⁻²⁹ᵇ
0.14 = e⁻²⁹ᵇ
b = 0.0678
The equation is
[tex]\rm y = 90 e^{-0.0678 * x}\\[/tex]
Half life is when the concentration is reduced to half
On 1st half life , the concentration = 90/2 = 45 mg
[tex]\rm 45 = 90 e^{-0.0678 * x}\\[/tex]
x = 10.22 years
Therefore the half life of the radioactive substance is 10.22 years.
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Which table correctly shows all the sample spaces for tossing a coin to get heads and rolling a number on a six-sided number cube?
Using it's concept, the sample space for the experiment is given as follows:
{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
What is the sample space of an experiment?The sample space is the set that contains all possible outcomes for an experiment.
In this problem:
For the coin, there are 2 outcomes, H for heads and T for tails.For the number, there are 6 outcomes, which are the 6 numbers.Hence the sample space is given as follows:
{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
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On Monday, the water was shut off 3 times for ¼ hours, 2/3 hours, and 1-3/4 hours, respectively. What was the total number of hours the water was off?
Answer:
2-2/3 hours
Step-by-step explanation:
1/4 + 2/3 + 1-3/4 = 1/4 + 2/3 + 7/4. Use common is 12, so we get 3+8+21/12 = 32/12. Simplify equal 8/3 or 2-2/3 hours!
A bag contains Red, Green or Yellow balls. A ball is taken at random from the bag. The probability that it is Red is 0.4 and the probability that it is Green is 0.375.What is the possible number of balls in the bag?
Answer:
1000 balls
(there are infinitely many solutions to this question; you can scale up 1000, use a different total, etc.)
Step-by-step explanation:
there are, of course, multiple possible numbers,
but the easiest way is to go with 1000, because we can say 375 / 1000 and 400 / 1000
(0.4 + 0.275 + 0.225 = 1)
400 out of 1000 balls are red (400/1000 = 4/10 = 0.4)
375 out of 1000 balls are green (375/1000 = 3.75/10 = 0.375)
225 out of 1000 balls are yellow (225/1000 = 2.25/10 = 0.225)
the question never gave detail as to if the answer should be the lowest number of possible balls, so this value is possible.
So, a possible number of balls in this bag is 1000.
A florist is making blue and white flower arrangements for the arrangements he places a red ribbon on every third Arrangement and a blue ribbon on every fifth Arrangement which Arrangement will be the first to have a red and blue ribbon
The Arrangement that will be the first to have a red and blue ribbon is the 15th arrangement.
What is LCM?The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.
Given the florist places a red ribbon on every third Arrangement and a blue ribbon on every fifth Arrangement. Therefore, to find the arrangement that will have both a red and a blue ribbon, you need to take the LCM of 3 and 5.
Since the LCM is 15, therefore, the Arrangement that will be the first to have a red and blue ribbon is the 15th arrangement.
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Help me and i'll help you earn more points if the question is right
To find the possible roots of the polynomial 4x3 + x4 – 7x2 – 8x - 8
divide factors of ± __ by factors of ± __ .
The complete statement is divide factors of ± 8 by factors of ± 1
How to complete the statement?The polynomial is given as:
4x^3 + x^4 - 7x^2 - 8x - 8
Rewrite properly as:
x^4 + 4x^3 - 7x^2 - 8x - 8
The first term in the above equation is 1 i.e. 1x^4, while the last term is 8
To determine the possible rational roots, we divide the factors of the last term i.e. 8 by the factors of the first term i.e. 1
Hence, the complete statement is divide factors of ± 8 by factors of ± 1
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S
Which triangle is similar to ABC if sin(A) = cos(A)=√15, and tan(A)=√1
R
5
12
13
T
D
3
12
f
3√15
O
2
K
√15
Σ.
M
O
3
L√6 N
X
6√15
N
O
24
6
Answer: Option 4
Step-by-step explanation:
Similar triangles have congruent angles, so this means that the sines, cosines, and tangents should be the same.
Thus, the side lengths of the triangle we want to find should be multiples of [tex]1, \sqrt{15}, 4[/tex].
This eliminates options (1) and (3).Between options 2 and 4, we know that the Pythagorean theorem is not satisfied by option (2), thus we should eliminate it.
This leaves us with option (4)
a) Students returning to a secondary school have to pass through a check point at the rate of 50 per though. The average time for checking is 35 seconds. The arrival rate and service rate follow a Poisson distribution. There is a delay and the principal is willing to include another check point to reduce the average time of checking to 28 seconds if the idle time is less than 10% and the average queue length is more than 10 students, check whether the introduction of an extra check point is justifiable
Answer:
175
Step-by-step explanation:
Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)
For the given problem, the average queue length is:
Average queue length = (50 * 35) / (1 - 50 * 35)
= 175
The function y = f(a) is graphed below. What is the average rate of change of the
function f(a) on the interval -8 < < 8?
Answer: -35/16
Step-by-step explanation:
[tex]f(8)=-5\\\\f(-8)=30\\\\\frac{f(8)-f(-8)}{8-(-8)}=\frac{-5-30}{16}=\boxed{-\frac{35}{16}}[/tex]
A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.77 hours. Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the rebuilding times are normally distributed, what percentage of sample means is greater than 8.8 hours? Express your answer as a percent rounded to hundredths of a percent.
Using the normal distribution, it is found that 7.64% of of sample means are greater than 8.8 hours.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters are given as follows:
[tex]\mu = 8.4, \sigma = 1.77, n = 40, s = \frac{1.77}{\sqrt{40}} = 0.2799[/tex]
The proportion of sample means greater than 8.8 hours is one subtracted by the p-value of Z when X = 8.8, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.8 - 8.4}{0.2799}[/tex]
Z = 1.43
Z = 1.43 has a p-value of 0.9236.
1 - 0.9236 = 0.0764.
7.64% of of sample means are greater than 8.8 hours.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
2(x2 + 6x + 9) = 3 + 18
2(x2 + 6x) = –3
2(x2 + 6x) = 3
x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot
2(x2 + 6x + 9) = –3 + 9
The correct answers are option 1, Option 3 and option 4 which are:-
2(x² + 6x + 9) = 3 + 18
2(x² + 6x) = 3
x+3 = ±√21/√2
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
We will check all three options one by one:-
2(x² + 6x + 9) = 3 + 18
2x² + 12x + 18 = 3 + 18
2x² + 12x -3 = 0
We are getting the original equation so it is correct.
2(x² + 6x) = 3
2x² + 12x = 3
2x² + 12x - 3 = 0
This is also right.
x+3 = ±√21/√2
Squaring on both the sides:-
( x + 3 )² = 21 / 2
x² + 6x + 9 = 21 / 2
2x² + 12x + 18 = 21
2x² + 12x = 21 - 18
2x² + 12x -3 = 0
This is also right
Therefore the correct answers are option 1, Option 3 and option 4 which are:-
2(x² + 6x + 9) = 3 + 18
2(x² + 6x) = 3
x+3 = ±√21/√2
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Answer:
A, C, D
A: 2(x2 + 6x + 9) = 3 + 18
C: 2(x2 + 6x) = 3
D: x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot
Step-by-step explanation:
Got 100% on quiz
Step 2 of 2 : Suppose a sample of 782 suspected criminals is drawn. Of these people, 548 were not captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.6625, 0.7388).
What is confidence interval?A confidence interval is the mean of your estimate plus and minus the variation in that estimate.
Given sample, n= 782
As, 548 were not captured.
x= 548
So, p= 548/ 782
p = 0.7007
q= 1- 0.7007 = 0.2993
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
Now,
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
For confidence level of 98% , z is 2.33
Now,
(0.70007 - 2.33√ (0.7007(0.2993))/782 , 0.70007 + 2.33 √(0.7007(0.2993))/782
= (0.6625, 0.7388)
Hence, 98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.6625, 0.7388).
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The means and mean absolute deviations of the individual times of members on two 4 times 400 meter relay track teams are shown in the table below.
Means and Mean Absolute Deviations of
Individual Times of Members of 4 times 400 meter Relay Track Teams
Team A
Team B
Mean
59.32 s
59.1 s
Mean Absolute Deviation
1.5 s
2.4 s
What is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B?
0.09
0.15
0.25
0.65
The correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.
What is mean?Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
The difference between the mean times is about 16 times the mean absolute deviation of the data set.
59.32 - 59.1 = 0.22
2.4 - 1.5 = 0.9
0.22 / 0.9 = 0.25
Therefore the correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.
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In the standard Normal distribution, 43% of observations lie below which z-score?
Find the z-table here.
–1.08
–0.18
0.18
1.08
Picture posted below
The answer is -0.18
when you convert 43% to decimal, it is 0.43
And the z-score of 0.43 is closest to -0.18
Hope it helps!
3(x-5)² +14(x-5)-24
Answer:
3x^{2} -16x-19
Step-by-step explanation:
If we are going to be simplying this problem, then we need to take it step by step.
Start off by using the distributive property, and then combining like terms. Keep in mind the square, and make sure that gets sorted out correctly.
Answer:
(3x - 19) • (x + 1)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
((3•((x-5)2))+14•(x-5))-24
STEP
2
:
Equation at the end of step 2
(3 • (x - 5)2 + 14 • (x - 5)) - 24
STEP
3
:
Trying to factor by splitting the middle term
Factoring 3x2-16x-19
The first term is, 3x2 its coefficient is 3 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is -19
Step-1 : Multiply the coefficient of the first term by the constant 3 • -19 = -57
Step-2 : Find two factors of -57 whose sum equals the coefficient of the middle term, which is -16 .
-57 + 1 = -56
-19 + 3 = -16 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -19 and 3
3x2 - 19x + 3x - 19
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (3x-19)
Add up the last 2 terms, pulling out common factors :
1 • (3x-19)
Step-5 : Add up the four terms of step 4 :
(x+1) • (3x-19)
Which is the desired factorization
Given the following equation of a circle in general form, find the equation in standard form by completing the square.
4x² + 8x + 4y² + 32y +52 = 0
Provide your answer below:
The standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have an equation that represents the circle:
4x² + 8x + 4y² + 32y +52 = 0
Divide by 4 on both the sides:
x² + 2x + y² + 8y + 13 = 0
x² + 2x + 1 - 1 + y² + 8y + 4² - 4² + 13 = 0
x² + 2x + 1 + y² + 8y + 4² - 1 - 16 + 13
(x + 1)² + (y + 4)² = 4
(x + 1)² + (y + 4)² = 2²
Thus, the standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²
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1/5 (10x+30)-14= - 1/3 (6x-18)
Answer:
x = 7/2
Step-by-step explanation:
1/5 (10x+30)-14= - 1/3 (6x-18)
10x + 30/5 - 14 = -6x + 18/3
(2*5)x+2*3*5/5-14 = -(2*3)x-2*3^2/3
x = 7/2
A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many committees can be formed if no person can serve on more than one committee?
Answer:
1,260
Step-by-step explanation:
[tex]\implies C(9,4)*C(5,3)*C(2,2)[/tex]
[tex]\implies 9!/4!(9-4)!*5!/3!(5-3)!*2!/2!(2-2)![/tex]
[tex]\implies 9!/4!5!*5/3!2! *2!0![/tex]
[tex]\implies (9 * 8 * 7 * 6 / 4 * 3 * 2 * 1) * (5 * 4 / 2 * 1) * 1[/tex]
[tex]\implies 1260[/tex]
Therefore, 1,260 committees can be formed.
a.- Representa el cálculo del porcentaje de cada par de artículos y marca el que es más conveniente comprar.
1 el par de zapatos cuesta $90.Por la compra de dos pares , tienes el 25% del descuento total
2 el par de zapatos cuesta $90.El segundo par de zapatos esta con el 40% de descuento
El costo en la opción uno es menor que el de la opción dos, asi que la primera es la más conveniente.
¿Cual opción es más conveniente?
En la primera opción, el par de zapatos cuesta $90, y el segundo par tiene un descuento del 25%.
Entonces el costo por 2 pares es:
C = ($90 + $90)*(1 - 25%/100%)
Donde le aplicamos un descuento del 25% al total del costo de los dos zapatos, resolviendo esto obtenemos:
C = ($180)*(0.75) = $135.
En la segunda opcion tenemos que los pares cuestan $90, pero esta vez le aplicamos un descuento del 40% al segundo par.
C = $90 + $90*(1 - 40%/100%) =
C = $90 + $90*(0.6) = $144
Así, vemos que en la primera opción el costo es menor, entonces esa es la mejor opción.
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Need help with this! Brainliest to who answers.
Answer: K
Step-by-step explanation:
The subtraction with the negatives can cancel out, resulting in a possible positive answer.
Answer:
k
Step-by-step explanation:
K you CAN get a positive number....
example :
-3 - (-5) = -3 + 5 = + 2
What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer:
all real number {x | x is a real number}
Of the three functions in the tables, which represent linear relationships?
Answer:
D. f and h
Step-by-step explanation:
The function f is a liner function because for every increase in x, there is a proportional increase in f(x). This can be seen when the x value goes from 2 to 4, so a 2 unit increase, the f(x) value increases by 3. Since this is true for every interval of 2 in f(x) -- increase x by 2 results in an increase in 3 of f(x) -- then f(x) is a linear function.
The same principle can be applied to h(x), with each 4 unit increase in x, the h(x) value increase by 36.
The function g(x) is not a linear function because for each unit increase of x, there is not a proportional increase (or decrease) in g(x). As seen in the table, g(2)-g(1)= 8-4= 4. For g(x) to be a linear function, every other one unit increase in x should result in a 4 unit increase in g(x0. But this does not occur. g(3)-g(2)= 16-8= 8 , g(4)-g(3)= 32-16= 16, 8 and 16 are not equal to four so g(x) cannot be a linear function.
From Khan Academy Pre Algebra
Please Evaluate This Question:
answer is this in decimal form if this is what ur looking for 4.21900462…
hope it helps....
Answer:
17.8
Step-by-step explanation:
Find the slope of the line passing through the points (3,-9) and (2, -3).
Answer:
The slope of the line passing through is -6.
50 people sponsor Paula and she raises a total of $180.65 for charity. 28 people sponsor Kate and she raises a total of $135.60 for charity. 45 people sponsor Sam and he raises a total of $169.25 for charity.
How much money is raised altogether by three of them?
$_____________
Answer:
485.5
Step-by-step explanation:
180.65+135.60+169.25
help me please ! due soon!
Answer:
Step-by-step explanation:
Comment
An x intercept occurs when y = 0. So the table shows three of them.
Answer
There are 3 x values when y = 0. They are
x = - 1x = 2x = 3Answer: A. [tex](-1, 0)[/tex]
Step-by-step explanation:
The x-intercept is every point where y=0. To see this, we should look at the table's f(x) section to find any zeroes.
According to the table and this knowledge, one x-intercept of this continuous function is [tex](-1, 0)[/tex].
I hope this helps! Pls mark brainliest!! :)
Mr. Harry had 4 daughters, each daughter had a brother. How many Children does Mr. Harry have?
Answer:
Mr. Harry has 5 children.... I know what you were going for...
Solve x2 − 3x = −8. (2 points)
x equals quantity of 3 plus or minus I square root of 29 all over 2
x equals quantity of 3 plus or minus I square root of 23 all over 2
x equals quantity of negative 3 plus or minus I square root of 29 all over 2
x equals quantity of negative 3 plus or minus I square root of 23 all over 2
x equals negative 2 plus or minus 4 I square root of 2
x equals negative 2 plus or minus 2 I square root of 2
x equals negative 1 plus or minus 4 I square root of 2
x equals negative 1 plus or minus 2 I square root of 2
The value of x equals quantity of (3 ± √23)/2.
What is Quadratic Equations?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Here, given equation;
x² - 3x = -8
x² - 3x + 8 = 0
x² - 2 X 3/2 x + 8 = 0
x² - 2.3/2 x + (3/2)² - (3/2)² + 8 = 0
(x - 3/2)² - 9/4 + 8 = 0
(x - 3/2)² + 23/4 = 0
(x - 1.5)² = -5.75
x - 1.5 = ±√(-5.75)
x = 1.5 ± i√(5.75)
x = (3 ± i√21)/2
Thus, x equals quantity of 3 plus or minus I square root of 23 all over 2.
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Algebra 2 point slope form help
The slope of the line is
[tex]\frac{-1-4}{-1-0}=5[/tex]
So, the equation of the line in point-slope form is [tex]\boxed{y+1=5(x+1)}[/tex]
Two buses leave a station at the same time and travel in opposite directions. One bus travels12m/hrslower than the other. If the two buses are 765 miles apart after 6 hours, what is the rate of each bus?
distance = speed * time
the first bus speed = x
second bus = x - 12
the sum of distance = 765 miles
first distance = 6x
second distance = 6 (x -12)
6x + 6(x-12) = 765
x + x -12 = 127.5
2x = 139.5
x = 69.75 mi/h which is the faster bus
the second bus speed = 57.75 mi/h
